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Research Collection Doctoral Thesis Development of fiber optic based dynamic ligth scattering for a characterization of turbid suspension Author(s): Urban, Claus Publication Date: 1999 Permanent Link: https://doi.org/10.3929/ethz-a-003810850 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library Diss. ETH No. 13067 Development of Fiber Optic Based Dynamic Light Scattering for a Characterization of Turbid Suspensions A dissertation submitted to the Swiss Federal Institute for the Doctor of of Technology Zurich degree of Natural Science presented by Claus Urban Dipl. Phys., University born on Prof. Dr. P. 1965 Germany the recommendation of Schurtenberger, Prof. Dr. L. Dr. H. J. Karlsruhe, Germany May 14, citizen of accepted of Gauckler, Watzke, examiner co-examiner co-examiner Zürich 1999 i CONTENTS Contents iii 1 Summary 2 Zusammenfassung 3 Introduction 1 4 Light Scattering Theory 4 Light Scattering 9 5 4.1 Static 4.2 Dynamic Light Scattering 15 4.3 Cross-Correlation 18 4.4 3d Cross-Correlation Scheme 20 7 of the Cross-Correlation Function 4.4.1 Intercept 4.4.2 Overlap Volume 4.4.3 Goniometer 4.4.4 Correction for Static Experimental 5.1 6 v Detailed Angle 22 and Scattering Angle Light Scattering Experiments 22 24 28 Realization Description 20 of the Opto-Mechanical Components 30 30 5.1.1 Producing Parallel 5.1.2 Lenses 31 5.1.3 Detection Unit 32 5.1.4 Alignment Beams of the Instrument Characterization of Turbid Model Suspensions 32 35 6.1 Materials and methods 35 6.2 Results and discussion 35 Static Structure Factor 45 7.1 Introduction 45 7.2 Materials and Methods 50 7.3 7.2.1 Experimental Set-Up 50 7.2.2 Methods 50 7.2.3 Materials 51 Results and Discussion 52 CONTENTS ii 8 Influence of Dilution the Particle Sizes in Milk 57 8.1 Introduction 57 8.2 Materials and Methods 58 8.3 9 on 8.2.1 Experimental Set-Up 58 8.2.2 Methods 58 8.2.3 Multi 8.2.4 Methods 60 8.2.5 Materials 60 Angle Laplace Transformation Inverse 58 61 Results and Discussion 8.3.1 Full-Cream Cow Milk 61 8.3.2 Skimmed Cow Milk 63 8.3.3 Emulsion Based on Vegetable Protein Stabilized Emulsions Oil 66 69 9.1 Introduction 69 9.2 Materials and Methods 69 9.3 9.2.1 Experimental Set-Up 69 9.2.2 Materials 70 9.2.3 Methods 70 Results and Discussion 72 9.3.1 Size Distribution 72 9.3.2 Interactions 74 10 Outlook 79 Danksagung 85 Lebenslauf 87 iii Summary 1 Dynamic light scattering (DLS) is one popular experimental techniques of the most application its However, in the characterization of colloidal systems. tems of industrial relevance has often been considered to be too of DLS a contributions from investigations of many high dilution, with emulsions and the industrially ments with a can so-called be cross to other to be dispersions ing volume and identical signals obtained multiple scattering are respect experiments optical and scattering an matching, a the only, this instrument two the alignment of such use We and the were highly high an particle sizing emulsions to the determination of the that can not be Experiments optically in we light scattering used state of the art able to construct turbid challenging a a suspensions. stability it laser can be used in fundamental research a of concentrated model light Due to its as well wide field of industrially relevant systems dynamics such as suspensions matched. with well defined model turbid colloidal systems scatter¬ instrument for inves¬ of the two inherent dynamic light scattering experiments from same and all contributions from Therefore high stability. instrument for measurements with applications ranging where the so-called 3d cross-correlation in industrial laboratories for routine measurements. This opens up new turbid important improve¬ industrial environment represents opto-mechanical components. easy an contrast required precise matching and the necessary for static and as in or technique highly samples. With events suppressed. However, to both the compact design, the problem Then the cross-correlation of the two vectors. single scattering tigations of complex systems task with solution to this performed simultaneously having scattering contains working With this have constructed we instrument for the characterization of turbid are require or dynamic light scattering experi¬ in dilution as possible not for artefacts when elegant A very light are changed. these considerations light scattering experiments very low concentrations. Therefore technique. such high scattering sizes with in their natural state, which is methods, sample composition need on larger particle high probability scattered correlation investigated compared Based non-negligible self-associating systems. suppressing multiply ment difficult for systems with relevant a due interpretation technique to which results in consists of systems For multiple scattering. immediately limits contrast this very exceedingly becomes experiment complicated The strong multiple scattering in undiluted solutions. to the very to many sys¬ can successfully systems demonstrate clearly that highly be characterized using the 3d instrument, 1 IV and that the factors can correlation relevance. particle correctly be technique can possible particle to an tor and which ment access on determined. In applicable unstable represents a possibilities in the dynamic step complex a against dilution. can samples. investigation protein be These particle stability for a of state, or stabilized emulsions obtained, when experiments size at least a we particle a it is dilution then show form fac¬ investigating systems show that the 3d instru¬ quantitative characterization technique opens up new distributions, equilibrium properties, complex particle suspensions. variety changes Using the 3d instrument, however, We thus believe that this of cross- 'realistic' systems of industrial dilution could lead to dramatic major improvement and allows for importance show that the 3d we interactions via measurements of the behaviour and of considerable next form factors and static structure in their 'natural' with the static structure factor are to size distribution. experiments particle a of milk show that particle of undisturbed 'native' the the investigate systems be low. On further how distribution, is also Investigations in the measured often size SUMMARY of industrial applications. This could be V Zusammenfassung 2 Die dynamische Lichtstreuung (DLS) niken Charakterisierung zur kolloidalen von einer komplexen Flüssigkeit Streuvektors q"1. hauptsächlich Lichtstreuung Im Falle kolloidaler Teilchen werden die Intensitätsfluktuationen durch die diffusive der Korrelation von der Teilchen verursacht. Basierend auf Bewegung Diffusionskoeffizient und als eine sehr grössenbestimmung praktische eine breite und zerstörungsfreie Anwendung. einigen zu vielfach zur stark wechselwirkenden kolloidalen laubt wird die dynamischen Verhaltens des Untersuchung Methode Die Technik ist geeignet. Weiterhin Mikrometern findet die Teilchengrösse kolloidalen Teilchen in einem weiten Grössenbereich von Suspensionen zur von von pliziert betrachtet. Die mit nicht schwierig. vernachlässigbaren Beiträgen niedrige Industrie relevante hohen was z. zu ses Problems besteht in der von nik. Mit dieser Technik können Zustand untersucht Methoden, z. werden, was Verdünnung B. und sie er¬ Systeme aufgrund Systemen als wird für zu der kom¬ Systeme grössere Teilchen mit einem gros¬ Konzentrationen. Deshalb können viele für die werden oder sie bedürfen einer sehr Artefakten führt. Eine sehr Unterdrückung dynamischen Lichtsreuexperiment und/oder verfolgen. Jedoch wur¬ B. bei Emulsionen und selbstassoziierenden einer hohen Wahrscheinlichkeit Nanometern mehrfach gestreuten Lichts ausserordentlich Dispersionen nicht untersucht Verdünnung, wenigen DLS-Experimentes Dies limitiert die Technik besonders für Streukontrast auf sehr sen eines Charakterisierung verwendet, und Gläsern des Lichts in unverdünnten Interpretation Teilchen- zur konzentrierten de die Anwendbarkeit der DLS auf viele industriell relevante Mehrfachstreuung dynamische dynamische Lichtstreuung beispielsweise Aggregations- und Gelierungsprozesse sehr starken zur des inversen Längenskala und untersucht diese Fluktuationen auf der Verfügung Tech¬ DLS stellt ein Mass für die Systemen. Brechungsindex Zeitskala der Fluktuationen im bis populärsten experimentellen ist eine der des mehrfach Systemen elegante Lösung gestreuten zu die¬ Lichts in einem mittels einer sogenannten Kreuzkorrelationstech¬ optisch sehr trübe eine bedeutende oder Systeme in ihrem natürlichen Verbesserung gegenüber Kontastvariation, bietet, anderen bei denen die Zusam¬ mensetzung der Probe verändert wird. Auf diesen Überlegungen tionsinstrument sem das zur basierend haben wir ein Charakterisierung Instrument werden zwei gleiche Streuvolumen lation der beiden Signale von optisch sogenanntes 3d Kreuzkorrela¬ trüben Proben gebaut. Mit die¬ Lichtstreuexperimente gleichzeitig durchgeführt, die und identische Streuvektoren besitzen. Eine Kreuzkorre¬ enthält dann nur Beiträge von Einfachstreuprozessen, alle ZUSAMMENFASSUNG 2 VI Beiträge Mehrfachstreuereignissen von chen Instruments Untersuchung zur Umfeld stellt eine herausfordernde Überlagerung bei der der beiden werden unterdrückt. Die komplexen Systemen von Aufgabe Stabilität dar. Deshalb verwendeten wir modernste Damit Komponenten. Messungen baus, an wir in der waren sehr trüben in der dynamische Lichtstreuexperimente strielaboratorien für Routinemessungen Anwendungen ausgehend neuer strierelevanten konzentrierter zu und die optische Systemen grosse optomechanische ein Laser-Lichtstreuinstrument für bauen. Wegen seines Auf¬ kompakten es für statische und Grundlagenforschung als auch in Indu¬ benutzt werden. Dies eröffnet ein weites von Teilchengrössenbestimmungen wie Emulsionen bis hin Modellsuspensionen, Präzision nötige notwendige und Justage und der hohen Stabilität kann der einfachen Gebiet Lage, Suspensionen in einem industriellen im Hinblick auf die Lichtstreuexperimente eines sol¬ Nutzung zu bei denen der der der Dynamik Kontrast nicht angepasst Bestimmung optische in indu¬ werden kann. mit Experimente Verwendung lich der gut definierten Modellsuspensionen zeigen deutlich, dass des 3d-Instrumentes sehr trübe kolloidale Teilchengrössenverteilung unter Systeme erfolgreich hinsicht¬ charakterisiert werden können; ebenfalls können Formfaktoren und statische Strukturfaktoren bestimmt werden. In einem nächsten Schritt le zeigen wir, Systeme von zeigen, dass dass die 3d Kreuzkorrelationstechnik auch auf industrieller eine Bedeutung Verdünnung oft die Möglichkeit, Systeme dest kann eine an dramatischen zu Teilchengrössenverteilung führen anwendbar ist. kann. Dagegen durch Proteine stabilisierten Emulsionen stemen durch turfaktors Messungen Wechselwirkungen gen, werden. Mittels weiterer zeigen wir dann, Verbesserung in der Lichtsreuung Sy¬ des dynamischen Verhaltens komplexer Suspensionen möglich. darstellt und unveränderter natürlicher Proben erlaubt. Da¬ Gleichgewichtseigenschaften, grosser Experimente Experimente zeigen, Untersuchung von zumin¬ wie in unstabilen zur wendungen in der gemessenen untersuchen, zu Möglichkeiten neue Milch bietet sich mit dem 3d-Instrument untersucht werden können. Diese quantitative Charakterisierung durch werden Veränderungen von rea¬ des Formfaktors der Teilchen und des statischen Struk¬ dass das 3d-Instrument eine grosse eine Untersuchungen in ihrem natürlichen Zustand Verdünnung gering gehalten komplexe von Teilchengrössenverteilunund der Stabilität Dies ist auch für eine Vielzahl industrieller An¬ Bedeutung. 1 Introduction 3 Dynamic light scattering (DLS) is popular experimental techniques of the most one suspensions. DLS provides in the characterization of colloidal scale for fluctuations in the index of refraction of these fluctuations In the the on particles intensity fluctuations of colloidal case particles. Based the diffusive motion of the by sion coefficient and DLS is particle size, non-destructive method for particles to several micrometers. Moreover, dynamic sions and over a However, its application solutions. The used to many complicated interpretation a as frequently caused very convenient and a is suitable for the char¬ few nanometers a used for and/or strongly interacting colloidal suspen¬ aggregation as DLS and multiple scattering gelation. con¬ in undiluted exceedingly becomes experiment of investigations systems of industrial relevance has often be due to the very strong of probes predominantly wide range of sizes from and it allows to follow processes such glasses, and it scattering vector, q"1. are technique The of the time the correlation between diffu¬ on widely DLS is also behaviour of concentrated sidered to be too now particle sizing. acterization of colloidal the complex fluid, a scale of the inverse of the length a measure difficult for systems with non-negligible contributions from multiple scattering. Particularly for larger particles with concentrations, and gations very already called are been of systems implemented propagation 'diffusing features such at large variety a large wave as range of imental generally particles spatial length scales. A very contributions from to this a ume problem [2, 3, 4]. scattered scattering light will can be used in order to due to the inherent this multiple scattering so- important averaging interesting opposite approach The details vectors but produce problem, works in the limit of not allow to determine over aims from the measured using idea is to isolate general see [2]). scattering experiments simultaneously with identical singly products, to this number of different theoretical and exper¬ dynamic light scattering experiment (for performing approach and suppress undesired contributions from two to very low sample [1]. Unfortunately, the of the approaches light across does There exist recent diffusion model polydispersity correlation data. scattered light spectroscopy' sufficiently suppressing photon of the a technique therefore excluded from investi¬ in commercial strong multiple scattering, where describe the a contrast this limits the dynamic light scattering. One quite with which has high scattering multiple scattering This on the different correlated fluctuations singly can same be achieved scattering geometries. on in Then both detectors. In a by vol¬ only con¬ trast, multiply scattered light will result in uncorrelated fluctuations that contribute INTRODUCTION 3 2 to the due to the fact that it has been scattered in background only a succession of different q-vectors. Several different in the past. In his presented for proposals pioneering pressing multiple scattering by a turbid a sample acterization of colloidal scattering angle a single scattering angle article Phillies outlined the of cross-correlation means [3]. However, used were discussed subsequently and requires very initial plane (kn, A^) about the 1-1 and (&/i, kf2) scattering have different for the 3d ßi2,ideal = or 0.25 experiment [2]. one of such an successfully new [6, 7], field of and experiment characterize suspension placed pairs at The outline of this thesis is of laser on are rotated terized with respect to size above some scattering angle processes processes 1-2 and 2-1 detected in this These additional clearly extremely which scattering means processes that the maximum the two-colour as have very shown that turbid characterization recently auto¬ method, i. e. demonstrated dynamic light scatter¬ suspensions. This it can opens up a using dynamic light scattering numerous areas of technology. as and static model systems. It is shown that by suspensions of small particles, but that light scattering dynamic in which quarter of the value obtained for follows: the after an experimental correlation instrument is described in detail. demonstrated A par¬ angle 6/2 an combined with novel cross-correlation schemes in soft condensed matter research and technically it is experiment, ç2 for the two = [8, 9, 10] Several research groups need not be restricted to dilute background are other cross-correlation schemes such ing experiments vectors. only feasibility completely qi = background only, the be used to vector scattering is While this method [5]. groups group in scattering experiment (see figure 1). The wave scattering will therefore contribute to the correlation by Schätzel [2], whose by several light paths vector q two other 2-2, whereas the intercept not restricted to sophisticated alignment procedures. of symmetry of the and final common experiment of this method for the char¬ scheme is the so-called 3d cross-correlation the two incident and the two detected and below the laser counterpropagating the two-colour method has been demonstrated to work very well ticularly interesting use sup¬ and described techniques only. Several other experimental lay-outs particular successfully implemented extremely demanding the possibility of is limited due to the fact that it is restricted to suspensions of 90° a was realization of this task have been in which cross-correlation of relatively simple experiment beams in experimental an The overview of the theoretical realization of the 3d feasibility of the instrument is light scattering experiments optically distribution, turbid as well with well defined particle suspensions as cross- can be charac¬ the determination of the particle 3 Figure (left) 1: Schematic description of and 3d cross-correlation form factor and static structure interactions. In a next the wave distribution, can arrangement in auto-correlation (right) experiments. factor, where the latter provides an access step then the applicability of the 3d instrument systems of substantial industrial importance the 3d instrument vector help interaction were investigated, to particle to realistic and it is shown how in the characterization of such systems in terms of size potential and stability. Light Scattering Theory 4 Scattering experiments continue to be used condensed matter research of ure well as impinges 2). With a on a information about the tered beam with sample properties polarization, to respect experiments vector q through = are of the the relation E particles microscopic its For commonly as wavelength local structural or as light x-ray properties determined by with matter obtained with quantum field namic laser theory, depends differ theory which is used for the light scattering field in the form of a in the plane response is on system. The deformation of the tensor. In a through the the reciprocal of the scattering is related to scattering small in can on on and k the or and neutron polymers, = the higher with scattering such while laser as are micelles light A 27r/A. investigated be particles wavelength a Wirkungsquantum A of the radiation or scatter¬ systems [14, 15]. the electronic structure of the mate¬ only most cases little from the classical description a = of the theoretical an incident the results electrodyof background electromagnetic E0et(k'r-a,'i) polarization charge (1) of the distribution polarizability a(u>) of the microscopic picture the mechanisms Dependent and on, wave impinges is described so scattering following chapters. When El(r,t) matter, the and scat¬ be resolved with quantum mechanical properties. In its function by analysing the is often the method of choice in the characterization of colloidal Interaction of a as (see fig¬ can particle a investigate crystal structures, used to microemulsions, magnitude example l beam. Additional wavelength, spin the smaller the structures that particles, principle the nature of the interaction between the where % is Planck's that the smaller the E of the on energy, (soft) radiation, or structures is measured be obtained can The energy E of hk, = scattering experiment. 1 by the structures that order of same 47r/Asin(0/2). means Energy depends sample. Basically beam and the rial incident beam of an tool both in powerful resulting scattering intensity the information obtained also This is very a characterization. The basic sample in and is scattered sample detector the as scattering angle 0 between the incident and the scattered of the ing as scattering experiment [11, 12, 13] a which a LIGHT SCATTERING THEORY 4 4 of by charge the distribution of the electromagnetic field system, which in general is polarization the kind of beam these structures could be atoms, of a non a conducting nuclei, electrons, particles, 5 beam stop Figure Sketch 2: emitted particles measured material field; as are with of by a alignment ot(uj) the by a The sample. scattering angle 0. increasing frequency complex part is the the of permanent higher frequencies, even is scattered source function of a An incident beam scattering experiment. a into come electromagnetic to follow the dielectric constant e(u>) [16]. resonance = 2, where the real square of the index of refraction imaginary part polarization due to the celerated mechanism describes the can (2) electromagnetic field. charges 3. subregions which are Then each of the atoms in field. In the far field geneous (and 2According an ideal gas infinite in to through 3These subregions a = small a are eoV/N(n2 a force a for each [17] — the on the charges these can then be divided wavelength essentially the a of the light incident same superposition Due to the fact that the medium is homo¬ subregion polarizability a another subregion can be found is related to the refractive index 1) homogeneous on ac¬ perfectly homogenous region to the cube of the sees acting The sample. electrodynamics, we now assume subregion the total scattered electric field is then space), still by the illuminated subregion. Clausius-Mosotti If compared picture the of the scattered fields of each light through As known from classical by light, small caused as light [18]. then radiate of absorption be viewed medium which is illuminated into at polarizability With the e' + ie" is determined and, n and the is text. see this process relaxes and oscillations of ions electrons or scattering intensity For details dipoles, which try radiation of the length scale of the wavelength of the light n of LIGHT SCATTERING THEORY 4 6 visible in a homogeneous medium, in the medium homogeneous or on medium dielectric constant fluctuations take constantly surfaces. e is, according or place, scattering that reason the index of refraction n because in in motion. Therefore scattering intensity light in the medium will fluctuate in e or n the detector by seen at inhomogeneities nevertheless is scattered liquid, for example, the a beam is primary by a result of local fluctuations of the a to only occurs light Einstein, cancellation of the scattered finite The and the Only that cancels radiation due to destructive interference. a atoms Such local [19]. or molecules given subregion no longer takes are and total and place a exists. If e(r,i) = e0I + (3) <fe(r,t) is the local dielectric constant of the medium where 5e(r, t) describes the fluctuations of the dielectric constant and I is the second rank unit tensor, the resulting scattered electric field is Es(R,t) The subscript = -r^T-e**'* / vector, ki and kf or small, or so are the incident and final the k% ~ the over simplified Es(R,t) = (k, (<fe(r, t) ni)]] x scattering volume, the q cross light electromagnetic of the wavelength products (4) R is the ki—kf is the scattering = vectors of the of the change x detector, wave out the kf. Working the scattered electric field is is polarization quasielastic scattering that integral volume and the scattering describing unit vectors For elastic d3re<^-^[nf [kf V describes that the distance between the are Jv 47rrieo in and rij and wave of the (4) the nf (see fig 3). light is zero equation for to -^e>kfR-^8etf(q,t) (5) where £e,/(q, t) is the component of the dielectric incident and final Equation (5) polarization describes the = generally, a however, two or more Se(q, t) (6) m constant fluctuation tensor in direction of the of the light. through local the refractive index of the medium. Col¬ scattering fluctuations of the dielectric constant loidal systems, nf or often consist of phase system with sizes in the range of nanometers or of electromagnetic particles dispersed where the different micrometers. waves in a phases Examples solvent, or more form structures are suspensions of 7 Figure 3: described by vector k; and the direction of polarization rn An incident scattered solid wave can plane wave then described field is scattered in Ef, kf and polarization via particles, emulsions, aerosols the electric gels. or vector (x,y,z) these structures. incoming is scattered wave A" Assuming electric field is described only particles Because the different in the wave 0. The = phases normally light is scattered volume and that the scattering before it reaches the once the rif. have different refractive indices it is clear that in colloidal systems by Ei, detector, the scattered by N Es(q) (7) EUqyqri = 1=1 where q is the at the particle scattering position n. For 1. is the at The scattering amplitude larger particles experiment Is{q) = volume the scatter light or where all the particle particles are is given by a. qa, ji(x) strongly spherical is the proportional more intensity Is(q) \Es(q)\2- Is{q) is is to the Bessel function of index particle than smaller volume and therefore ones. In a light scattering is measured rather than the electric field consequently proportional diameter to the power of six. identical of the i-th ^3j1(qal/2) ~ diameter and particle scattering amplitude is the spherical particles bt(q) Hq) where bt(q) vector and (bt(q) = Is(q) b(q)), = it is Na6a(q) Es(q) to the square of the For the with particle monodisperse case, given through (9) Here N denotes the number of the scattering section. cross differential scattering da(q)/dQ section dcr(q)/diï cross of the scattered 0. For a is scattering intensity The wavelength polarizability particle In proportional is scattered a, on to more the other the more on the scattering vector q, . 9 strongly is _ (io) section and therefore also the cross than light with directly related a with light that means a longer wavelength4. to the molar of the mass M. often the so-called excess Rayleigh ratio AR(q) [20]. and the pure between the = W^M Vsdü AIs(q) R2 Io Vs denotes the difference between the Als(q) solvent, Io scattering is not known is the the measured intensity Iref{q) Then AR(q) For suspension is a Normally the scattering to exclude unwanted effects of reference R is the distance to obtain absolute values of the is misalignment ratio volume scattering inten¬ of the instrument finally normalized with sample where the Rayleigh the scattered ARref(q) is known. given by of monodisperse particles AR(q) AR(q) 4This is the intensity scattered by the suspension volume V^s and the detector. scattering intensity, Als(q) of :iu intensity of the incident beam and exactly. Nevertheless, sity and furthermore a even important parameter, which A-4 and to a2. This AÄ(9) Here or ^r« hand, light scattering experiments is used o~(q) scatterer and in the far field detection point to note that the differential important shorter is the intensity 167T2 = It is section cross is the total a(q) and a expressed through be can with diameter scattering respectively the scattering angle limit particles The total dependence determines the on LIGHT SCATTERING THEORY 4 8 reason = can KcMP{q)S{q) for the blue colour of the sky. be written as (13) 9 Light Scattering Static 4.1 with K 47T --= 2 n 2{dn/dcy —Ar .— . NAX4n c Static particle == dn/dc 4.1 refractive index of the solvent = - ( mass/volume) concentration refractive index increment = - particle of the M == molar m -= particle S(q) -= static structure factor mass form factor Particle Form Factor and Static Light Scattering: Structure Factor In static a light scattering (SLS) experiment function of the measured as through variation of the cross a a section which <r(ç) static structure factor principle usually This is effects a S(q), done with condition S(q) = on highly the dent size 1 for all q, between the the radius of of the particle shape of the P(q) we form factor particles, diluted samples particles. S(q) is known. us can P(q), and the particles. (14) obtain the size and form of the S(q) provides gyration Rg scattering Na6P(q)S(q) = Is(q) directly yields scattering intensity if P(q) or product to the particles. to avoid influence of interaction angular dependent scattering intensity. tion the static structure factor potential V(r) a proportional which reflects interactions between the determination of through S(q) is is is available experimentally vector q, which is information about size and Is(q) Therefore from intensity of the scattered light scattering angle 0. Is{q) which in essentially yields scattering the the particle Under these form factor. In addi¬ with information of the interaction be obtained from the It is also and interaction possible to angular depen¬ get both, particle potential V(r) from the angular dependent scattering intensity. The the scattering intensity Is(q) particle form factor P{q), the local structure based illustration of the 4. Like the on therefore is product of a single particle property, and the static structure factor S(q) which describes the interactions between the individual physical background scattering by a of the particles form local fluctuations in a can be particles. A given with figure homogeneous medium, a particle LIGHT SCATTERING THEORY 4 10 q Figure Scattering of 4: For details can the a particle large compared be divided into volume elements with dimensions that A of the wavelength light scattered by forward direction 0 and shows compared a = the 0), i. form factor For a the particle of the the are same is the small compared superposition of the particle. e. P(q) = Is[q)/Is{q = 0), the scattering effects in decreases from unity with dimensions particles A don't show these extrema in the seen by all subregions particle of the form particle and therefore also interference effects. particle sizes it is wavelength A, particle P(q). form factor light and/or can for a be calculated 22, 23, 24, 25]. particle at which is characteristic for the size and also It should be mentioned that wavelength to the given by which is If the now necessary to find a relation between radius r, refractive index ratio particles small are small contrast between the compared particles m = to the np/ns The is divided and the solvent (15) using the Rayleigh-Gans-Debye (RGD) approximation [21, theory into, and wavelength qr(m-l)<l P(q) to incident electric field. scattering intensity without interference angular dependence, evaluation of the variables see P(q), factor because the difference in the electric field negligible, light. from the volume elements to the detector have to be taken into Is(q for the form of the are the of A all volume elements where interference effects due to the different intensity Is(q) divided by small consequently and resulting particle The account. light intensity Is(q) from the particle then optical path lengths = wavelength text. see The scattered q to the (l/jim) sees assumes the that each of the small volume same incident light wave. This elements, implies the that the of phase particle can a 11 Light Scattering Static 4.1 transversing wave the as it would be if the be calculated from P(q) where V is the in same Rayleigh-Gans-Debye approximation generally P(q) not there. In the were is almost the particle particle equation (16) be can qRg , calculated, and this leads to g equation (16) < 1 integral the monodisperse spheres of case 77\?fsin(^r) = (16) e'qr dV v J volume. For the P^) In the limit of = ~ ir cos(?r)]2 given through is the (17) 'Guinier-approximation' [26] P(q) and with the expansion of the exponential P(q) With the low equations (18) and (19) AR(q) from the to q — gradient 0 the molar of the 1-^S = from mass an + P(q) M of the <C 1 this qRg yields (19) ..- be calculated in the limit of can extrapolation the radius of curve (18) function for the value of scattering angles. Therefore, ratio ^ = Rayleigh of the measured particles (limg_>0 AR(q) gyration Rg of the ~ particles M) and can be obtained 5. For large larger particles, values of m the but still in the range of the RGD-approximation breaks cident electric field in the of the particle particles are particle, by caused and that of the solvent. A spheres, exists with the Mie satisfy specific boundary though Mie scattering Debye solution, and it is also is much it describes the highly particle spherical latex is taken into account. particle dependence sensitive to the particles having a of P{q) particle shape. theory 5(0) = 1 if the The inci¬ and the scattered electric field on A with the particle. However, Rayleigh-Gans- particle size very well comparison of the experimental data size in the range of Mie Dand in the limit of low concentrations where problem, where the difference difficult to calculate than the form factors calculated with RGD and Mie with to this conditions at the surface of the more light, and/or the difference in the index of refraction scattering theory [27], dent electric field outside and that inside the the down due to distortions of the in¬ complete solution in the electric field inside and outside the must wavelength of scattering particle measured is shown in Comparison of the particle form factor P(q) Figure 5: theory with m LIGHT SCATTERING THEORY 4 12 = experimental 1.2. For details 5. The Mie figure see theory data (suspension of third if the condition describes the qr{rn — the 1) regime of very large particles, rather than scattering [28]. In wave with the cross experimental depth <C 1 is qr ^> and the section or data very position the process can shifted to lower increasing particle size, While factor P(q) S(q) is a nm and with calculating particle describes the while the RGD of the minima in wave approximated by be to a sizes in small intraparticle shape grating so of the a occurs hardly can interaction particle no in¬ can be the diffraction pattern is that Fraunhofer diffraction is angle light scattering interference result of interference effects of the P(q). also very well. In aperture of the particle. Consequently regime. Similar used for 274 = well, electromagnetic obtained in the Fraunhofer mainly r 1, Fraunhofer diffraction of the light formation about the internal structure and the overall angles with satisfied, RGD works large particles penetrate and therefore the scattering of the spheres latex text. approximation fails by calculating However, calculated with RGD and Mie effects, light instruments. the static structure scattered by different par- 13 Light Scattering Static 4.1 light tides. Each particle if there is regular arrangement there exist fixed particles, a particles, taking S(q) given is of the i. an e. means system form they structure is the a particles by S(q), particles. a lattice in less strong than in neighbours. nearest correlation function pair (20) particles, Correlation between particles 1 for all q. = a crystal. However, crystal a and expression for An the consequently the local which is related to the static structure g(r) of figure particles 6 finding examples a distance as in an almost and g{r) are not to oscillations of the perfectly regular structure factor shows interaction is shown in crystals potential (B). a particle sions, however, long-range narrow potentials compared relatively that show between the shows at particles An is pronounced crystal static structure The reason, while the peaks in do not form particles particles and the rela¬ crystals formed by atoms, the static Nevertheless, colloidal suspensions Bragg peaks depending distances goes a more interaction to peaks. particles. a is the finite temperature, which leads on example for only mainly the peak for the larger show broad shown. In pair correlation function and the particles. the i. perfect lattice (A). The Because in colloidal systems The order of the consequently S(q) finding are lattices due to the Brownian motion of the weak interaction also form infinitesimally particles. potentials Bragg peaks reflects the fixed distances between the particle from the r for different interaction arranged are at (21) particles. g(r) directly describes of the density particle j a pJ<Pre"*\g{r)-l] l + = factor then shows the characteristic can scattered through probability tively light ensemble average. For uncorrelated are some where p denotes the number S(q) the correlations between spatial local structure similar to S{q) the superposition of the or an particles, S(q) ideal gas of the order is in the range of In by different scattered light jj £ (e^-1^) = bracket denotes interactions between the factor due to interactions between the between the A But with angular that particles into account interference reveals the static structure factor %) where the angular dependence given by P(q)- an path lengths. of the order in the measure with phase differences due to the different particles all a scatters a the concentration and hard sphere suspension in the range of nearest nearest neighbours, quickly to unity. Charge the neighbours, probability stabilized suspen¬ order at similar concentrations due to the potential (C). Dependent on the strength of the interaction LIGHT SCATTERING THEORY 4 14 S(q) A 9 O—Ç^^^^D o O-O^y-O-O il il 9—T^TT^^YY M TTT^YtYY 0—0—6—O—C^<^<) 9—9—9—9—9~ B o C Q Figure 6: Structure, pair correlation function g(r) and static structure factor S(q) for different systems. potential and g(r) the particles show more can order similar to a pronounced peaks than The static structure factor S(q) can lattice, in a with the consequence that hard core S(q) suspension. be calculated from 21. For monodisperse 15 Dynamic Light Scattering 4.2 scattering angles and in the limit of low particles compressibility (dli/dc^1 suspension by of the S(0) In virial a expansion S(0) of 0 it is related to the osmotic —y q ^kBT (dlL/dc)-1 (22) 2A2Mc + (23) = as 5(0) - • • • is related to the interaction A2 the second virial coefficient 1 = pair potential V(r) through A2 Combining equation ^^/[l_e-^lr2^ = 13 with the in terms of the second virial coefficient and the concentration is c can given through a in the limit of q particles As described before in + equation in the dielectric constant fact, that from the in a solvent, light liquid light particles is not a scattered in the is As to an potential ratio AR(q) (25) 2A2c can mainly scattered by by different is the general intensity at two times cause particles. the particles are particles change randomly of the an fluctuations, analysis of the But if constantly in suspended a so-called r, the r or of and also the number of a fluctuation of diffusion of the particles information about the diffusion in terms of intensity fluctuations to looks like statistical noise. separated by Particles Both effects lead to [14, 20]. Referring have different values. Due to the different refractive index a Because the Brownian motion time correlation function intensity is due to local fluctuations light scattering experiment the phase relations a volume fluctuates. be obtained from the scattered of the index of refraction of the medium. result in a scattering suspension process or scattering 5 static system, rather the scattering intensity. in the a and the interaction suspension the particles usually have Brownian motion. the yields Dynamic Light Scattering 4.2 the 0 measurement. AR(q) a —> obtained, if the Rayleigh be J\c in particle form factor (equation of the (equation 23) from which the size and form of the expression (24) J L approximations and the static structure factor 19) J Ml figure 7 the time Nevertheless, if dependence one looks at the intensity values I(t) and I(t is very small compared of + r) do in to the characteristic LIGHT SCATTERING THEORY 4 16 <I2> + <I> <I>' Time Figure 7: function. Fluctuations in the scattered For details text. see fluctuations, I(t) time of the intensity and the intensity auto-correlation and Ht + r) correlated, while with increasing separation A measure to ergodic systems so that it can relation to the starts with a a + r)> as to = maximum value of decay [29]. 0 temporal fluctuations in (I2) are tric fields the described a DLS experimentally by = a of the starting point intensity correlation function decays experiment shown in in the figure course and its 7. The correlation of time to a the fluctuations in the intensities are available property is the (I)2 with (27) measured rather than elec¬ intensity correlation function (28) = l + through the Siegert relation |5r1(ç,r)|2 Gaussian distribution of the monodisperse spherical particles amplitude <M«,0P> is related to the field correlation function assumption on {Es(q,t)E*s{q,t + T)) (\Mq,m 52(ç,r) of The independent (26) normalized field correlation function *(*'t) under the the correlation will decrease. time ra. gi(q,r) Due to the fact that in somehow /T /(*)/(* + r) dt intensity is and are rT dynamic light scattering experiment (DLS) of the electric field g2{q, t) 11 lim = r close, they intensity auto-correlation function. the infinite time average is be chosen the characteristic In in time of the correlation is the so-called (I(t0)I(t0 For will be very (29) intensity profile. the field auto-correlation function can In the case be written 17 Dynamic Light Scattering 4.2 as 9i(q,T) = S(q,T)^ (30) where N JV i %>^) iŒ&A^M0)-r'(T)]} = ly\° I H(q) denotes the dynamic structure factor, in the suspension and S(q) is the static 6 interactions in the system the function with respect to the lag describes the hydrodynamic interactions structure factor. dynamic time (31) 1,3 = 1 In the limit of structure factor is a negligible single exponential r. gi(q,T)~e-D^ (32) where Dc is the collective diffusion coefficient of the q is the scattering For the case of particles polydisperse suspensions in the inverse tion G(T) Laplace of the transformation is present in a more high suspension and a sum on In of exponentials for each particle principle gi(q,r) is not anymore it can an ill-conditioned function, Therefore it is statistical accuracy when evaluation of particle and 30 by problem, using integral over sin¬ species be done by performing in order to obtain the size distribu¬ e. any statistical will lead to different important size distributions. an i. a size from the correla¬ particle suspension [30, 31, 32]. Unfortunately measured correlation equation particles g\ (q, r) it is rather complicated. transformation the size distribution. with of The evaluation of the suspension. tion function then is an in the vector. gle exponential function of the time, of particles to the inverse Replacing measure Laplace Laplace noise, which possible is ever results for correlation functions transformation for the the discrete the size distribution the inverse sum gi(q,r) in can equation be 31 expressed through 91 This equation can {q>T) be written _ fN{ryP{qr)e-D^rdr ~ f0°° N(ryP(qr) dr ^ as 9l(q,r)= / Jo G(T)e-TrdT (34) with N{ryP{gr) Io°° N(r)reP(qr) eThen H(q) = 1 and also %) = 1. dr { } and T = expanded Doq2 is the decay From a around the average so-called cumulant the coefficient of variation For rate. decay = be can a i + analysis [33] of -(r)V gi(q,r) (36) + decay the average rate (F) and be obtained. a can Cross-Correlation 4.3 The evaluation of data from described above, is based on static a interpretation scattered suppress light general contributions from see [2]). simultaneously vectors the same kn and fc;2, and seen (Gii (r)) tered have the photons, same can GffCr) GSM where I\ and I2 are = = vector q. light by performing volume (with two multiply However, while exist a if multi¬ technique to scattering experiments two laser at final wave beams, initial vectors and wave kf\ kf2) two detectors. + scattering (37) r)) vector q, but multiple scattering, S(q, r) the use different scatter¬ corresponding relations and the measured auto-correlation where (1) indicates singly scat¬ as li1)2{l+ß\S{q,r)\2) /^/^(l+^l^r)!2) -Sq2R2 = an occurs, and suppress undesired seen (38) by detectors of the cross-correlation function ßu scat¬ dynamic light scattering experiment (for the average scattered intensities respectively, and the intercept light extremely difficult is scattered (Gi2 (r)) function, then be written only singly as so-called cross-correlation exper¬ a (h(t)I2(t structure factor and cross-correlation a by the = and in the absence of dynamic S(q, r) positioned two detectors experiments then between the in scattering G12(r) ing geometries, singly be achieved cross-correlating the signals If both scattering contributions with multiple scattering can of the scattering intensity, there idea is to isolate This on structure factor contributes to the multiple scattering iment. The details dynamic is due to the fact that impossible has lost its close relation to the the calculation of the light the laser multiple scattering If of the data is difficult if not light scattered dynamic light scattering experiment, or assumption that the tered before it reaches the detector. and gi(q,r) (T) rate e - size distributions narrow P-{T)r 9i(q,r) ply LIGHT SCATTERING THEORY 4 18 -Sx2 ße-^-e— . G12 (r) is 1 and 2, given by (39) 19 Cross-Correlation 4.3 intercept ß detected in the auto-correlation experiment primarily depends The due to intercept the additional terms describe the reduction of the optics, and the detection on vectors gi and q2) volumes). single scattering, same For In the auto-correlation Gtii(t) very difficult if not above scattered multiply denotes the This leads to the Gu(t) where I3 scattered is the average photons) only. Such structure factor visible in the S(q, r) even experiments angle tors, as outlined experiment on will result in uncorrelated light due to the fact that it has been factor of order a wave (RSk^)-1,where vector combinations following expression for kt2 experiment l)j ' contains the should thus kti G\2{t) all contributions over 5k 3 — ß^I^lSiq^y summed experiments can be realized In the Phillies provide of 0 light = 90° (figure from the wrong 8 A). For (40) (singly singly us and multiply scattered with the light dynamic will be multiple scattering be decorrelated using (figure a 8 B). experiment [3] must be signals geometries scattered light light with a prevented two variable (figure 8 single scattering experiments use different from the wrong from the wrong C). a to enter the detec¬ experiments experiments geometry where they produce different scattering This is realized in the 3d set-up for the from both Therefore it is limited to set-up [5]. Here the The different experiments and interference filters block the front of the detectors using set-up is measured with both detectors. it is done in the two colour wavelengths S(q,r) deduction of decreasing intercept only. scattering angle either scattered changes. contribute to photons a the yield intensity fluctuations correlated for turbid suspensions, and scattering experiments. two scattering the situation in the cross-correlation measured at detector j, and Cross-correlation [2]. intensity cross-correlation a match of the scattering q-vectors, and the contributions from multiple hh + « scattered of the data and of the smallest of the two magnitude kfi [2]. multiply suppressed by are spatial multiple scattering, background only succession of different signal is the produce will light In contrast, to the scattering and k%i + a [<£x[ interpretation fluctuations that contribute to the scattered in the impossible. However, only singly both detectors. an of case experiment well and make as = describes the match of the both auto- and cross-correlation therefore in the However, \Sq\ = misalignment [Sx and information. (Sq mismatch phase can in also vectors LIGHT SCATTERING THEORY 4 20 counterpropagating beams 90° fixed scattering angle 6 = qi = -02 wavelengths A,1 * X2 variable scattering angle, but difference angle 8q depends on 0 two different scattering angle 6 3-dimensional scattering geometry variable \ 11 fl Figure 8: An outline schemes. A: 4.4.1 colour, C: B: Two Phillies, vector arrangement for different cross-correlation coding 3D Intercept of the Cross-Correlation Function intercept ß of the correlation function of the can dynamic light scattering experiment, function in the limit of for wave 3d Cross-Correlation Scheme 4.4 The of the auto-correlation, i = r 0 and —> 1, j The theoretical maximum of = ß is r —> be viewed i. oo, e. = 1 for an the signal-to-noise ratio the difference in the correlation <7jj(0) — 2 for cross-correlation ßu as gij(oo) = ß (i = j = 1 experiments, respectively). auto-correlation experiment, while 3d Cross-Correlation Scheme 4,4 in cross-correlation a [2, 14]0. The experiment ß depends for this reason 21 two detectors 'sees' the light that in is, the geometry of the beam on cross-correlation a G12(r) = each of the from both incident beams and therefore also from the experiment. Thus the cross-correlation function wrong experiment paths {I{(0)P2(t)) <iï(0)i?(r)> + be written can (iî'(O)iî(r)) + as (41) <iï'(0)i?(r)> + where Arabic numbers denote the detector and Roman numbers denote the incident beam. experiment the undesired contributions from the In the 3d cross-correlation 'wrong' incident beams duce different only are scattering the second term intercept (r)) rates, the latter match of the lower is ß\2 intercept can experiment obtainable of the instrument, non-linearities volumes scattering 41 . \ßM\g?2\2 to be considered. points need pro¬ In eq. Gi2(t) ± + theoretically they or in the Sx 5q2R2 0.257. = take place due to detec¬ and due to restrictions in high count Any misalignment, either in the mainly take effect at scattering vectors will lead to a intercept described by give 0.9/?0) an for scattering not differ 7In the 488 therefore decorrelated. = ß To are but photomultipliers, 3(/x)(l2) + (iï(0)ff(r)) {ii + r?M + i?) [34], misalignment two the = overlap volume. While detector spatial q2 and for the 3d cross-correlation tor non-linearities by correlated contributions to gives A reduction of the the ^ vectors q-y Q 9l2{ The still detected nm example a of the frequently = precision (44) ßoe-Re'^~ in alignment required used value for the beam radius of R volumes should be closer than 5 pm and the two more than two colour and A2 = 514 5q = 0.005 from an Ar+-laser) therefore for the cross-correlation function M „ g"{) we - ~ = intercept of ß = intercept = 100 pm the two scattering are two laser beams different in used. ß = vectors should 1. get (see eq. = 'wrong' incident laser beam and 41) (Ji(°)W) IwfT l + wavelength (Ai Narrow bandwidth interference niters in front of the detectors block the undesired contributions from the with the maximum of an //m-1. experiment described above nm for /?Mbf2|2 ( } LIGHT SCATTERING THEORY 4 22 4.4.2 Volume Overlap Because in cross-correlation a volume seen will decrease ßxi one incident beam 9 shows the consequently. Figure by be can angle 5zi of the two beams it is distance to the center. The of the projection If the diameters of the detection beams dent the beams, there overlap volume of the of the projection approximation a regions detected exist a volume at l/sin0 larger of the cross-correlation function are the volume Because of intensities scattering two incident beams and /; equation the are (including ~Wm ~ those is a decreases for regions 0 = are = 90°. = are outside 10°. It is to first volume at 0 = incident beam. The 90°, but intercept (45) w> from the intensities are originating illuminated ß\2 e. by overlap scattering angle, i. overlap as from the total one beam only). volume and the above, the Therefore ßn discussed ß\2(Q). = volume of the scattering angles and has its maximum value at 90°, and this effect is stronger for larger values of the difference angle 5^. Goniometer can of the be determined Angle In the 3d cross-correlation plane ~ which the of 0 9 as scattering angle, and for small Experimentally /?i2(0) 4.4.3 on figure indicates the region of 6 45 and the fact that the ratio of the function of the large one originating scattering scattering volume Vov/Vsv depends intercept shaded scattering only by volume of in photomultipliers that scattering angle than the increasing than the diameters of the inci¬ brighter be written can ßl2 scattering a of the volume is illuminated larger part where I?v The region scattering angle a larger from the two beams. scattering factor are of the is marked. Due common The dark shaded volume at scattering detectors, the by smaller with is the scattering volume, however, the incident beams and the detector beams. reflects the seen overlap getting scat¬ both incident beams. geometrical arrangement two incident laser beams. The volume where the two beams to the difference from incident intensity originating must be illuminated by the detectors regions where only If there exist the intensity originating from incident beam 2, the beam 1 is correlated with the tering experiment goniometer, and QGom are a highly diluted sample. Scattering Angle experiment the plane and the two not identical. Therefore the denoted with by measuring of symmetry, which is defined by the scattering planes scattering angle of the individual 0 and the not identical. The difference angle depends on of the experiments goniometer, the difference angle 23 3d Cross-Correlation Scheme 4.4 Figure 9: tering angles of 0 (dark grey) 90° = and scattering volume (fat lines) volume Overlap and 0 (slightly grey). 10° = (shaded areas) for scat¬ For details see text. 53d of the experiment and is also a sketch of the scattering- and vector wave difference a function of the angle given through the trigonometric are . CD 0 = — OC 2 OA 5 cos2 expression for the • = m projection of the triangle OCD symmetry, the distances AB and CD results in the (46) OA sin OAB is the functions AB ®Gon triangle 10 shows arrangement of one scattering experiment. Goniometer-, sm Because the goniometer angle. Figure are identical. Combining on the the plane of equations in 47 scattering angle & 0 ®Gon /,7x sin—= cos-sin 2 In the limit of low at &Gon = from ©Gon — Aq/q < scattering angle is shown in 5° to scattering angle, vector of goniometer angle ©oon 180° the goniometer angle 2 ©Gon = ~* = 0, ©Gon ©Gon 11. In the actual — 5. and 0 are ©Gon = angular 125° results in a identical, while The relation of 0 to the range of the instrument 125° the maximum difference between located at 2%. figure is 0 K 47 J 2 goniometer- deviation of the and scattering 24 LIGHT SCATTERING THEORY 4 Figure 10: Sketch of the explain the relation of difference angle 5. the vector wave arrangement of scattering angle 0 The shaded plane is the to the scattering experiment one to goniometer angle ©Gon and the plane of symmetry or the goniometer plane of the experiment. 180 160 -, 1 1 1 1 j 1 ^— -_ —,^— 140 —><^— 120 100 ~7*^^ -_ S^ —?<£- CD 80 —^^— 60 40 —,^— -_ 20 0 1 1 ~/> — ^—i—i 0 1—i—i 20 1—i—i——i—i—i 40 60 1—i—i 1—i—i 100 80 1—i—i 1—i—i 120 140 1—i—i— 160 180 Gon Figure for a 4.4.4 11: Relation between the scattering difference angle of 5 = angle © and the goniometer angle ©Gon 14°. Correction for Static Light Scattering Experiments With the 3d cross-correlation instrument also static in turbid samples can light scattering be done. The undesired contributions from measurements multiply scattered 4.4 3d Cross-Correlation Scheme light to the measured scattered Is is determined intensity Is cross-correlation dynamic bined static and 25 dynamic by performing a com¬ In the static measurement experiment. function of q, while the as a be excluded can gives measurement the part of Is which is only singly scattered via the intercept ß\2 of the cross-correlation func¬ tion In the measurement the reduced (see equation 40). ß\2 where is the intercept measured contributions. This ing volume and of the can automatically a ß\2(ß\2 is multiple scatter¬ as a an used, by the overlap corrects for the effects caused single scattering intensity The without sample diluted of the instrument, which lead to misalignment intercept. with intercept angular dependence function of the scattering vector then be calculated from i{1)(q) yji[%)ii%)W(„\ = %h{q)h{q) - (48) \ß(i) 12 If rectangular cells together used in the experiment sample cell, the measured with the 0 in order to measure sample, angle. As a decrease at because the result, surface of the to 90°, 53d, the i. e. — = given by T (90° I/Io, The surfaces indexes for water — ©Gon)/2. Neglecting of the incoming light for this case inside the effects, namely for turbidity cell and for the vary with the and the total is the effect caused parallel water-glass nw and and glass ng angles equations to the scattering scattering intensity goniometer angle ©Gon by the sample the transmission T with their difference angle cells surface. From through light intensity for glass-water an the sample incident corresponding cell is intensity refractive result in transmission coefficients of (2 sin 9q 6w nQ cos 9g nw cos 9w \ sm($w + @g) cos Ow nGcos9G these light where i" is the transmitted nw ing scattering light paths s(©) scattered _ A scheme of the the cell under half of the difference of the equations [28] = single light paths s(©) are 20 set-up of the instrument the incident laser beams hit the sample polarization the Fresnel Io- 9 both the of the on chapter 5, different from 90°. angles Due to the 0 length with short to be corrected for two intensity has Fresnel refraction for non-incident beams of the 20 set-up, described in — cos (2s'm9w \sin(0G cos + I (49) / 9g\ 9w) J used for this calculation is shown in with the Snellius law sin 9q/ sin 9w = figure nw/na 12. Combin¬ the transmission Sketch 12: Figure refractive index mission through through a of sample glass plate Indicated nw the a sample where na = 1-54 for = sample, s~l used angles 256 the sin8(0G can for index by îîg in water with the the calculation a of the trans¬ non-incident beam Fresnel refraction is sin4 9q cos4 9w sin4 9w cos4 9g nw = + (50) 9W) 1-33 for water. inside the optical path length which hx(Io/I), the refractive cell with Fresnel equations for quartz and If s{9) denotes the of the are with the cell filled with water caused T t LIGHT SCATTERING THEORY 4 26 be calculated from angular dependent a sample cell and r is the turbidity transmission measurement correction for the sample turbidity is using given by TT(9) = e~TS^ (51) The transmission corrections for non-incident beams correction) the and for the turbidity r = sample turbidity 1 mm-1 and a are path length shown in of so = 1 on the figure mm. sample 13 for a cell (Fresnel sample with 4.4 3d Cross-Correlation Scheme 1 27 - ~~~ - Fresnel 0.8 - turbidity - e _o Ü g 0.6 - o o Ö o 0.4 - § ^^~^-~^~~ - 0.2 0 — - - i i . | 20 i i i | i i 40 i | i . 60 i 80 Goniometer angle 6 Figure 13: Correction for the transmitted intensity placed in © a — 2©-goniometer. Shown for sample turbidity. are 100 120 140 Gon through a rectangular sample cell the Fresnel correction and the correction Realization Experimental 5 A schematic layout experimental set-up of the with turbid colloidal model argon-ion the light values then 7, EXPERIMENTAL REALIZATION 5 28 laser 8 and 9. A in order to 300-8) operating (Spectra Physics, the as light bring the illuminating convex, focal which are length at a is much sThis described m a = higher, is 127) operating 632.8 nm8 for details chapter (Dantec mode fiber then focused onto the even A0 at a sufficiently large In & Spindler 5 [2]). higher our current by is used The experiments described scattering in set-up chapters chapters 7, angle R = 50 we = 14: An outline of the 14°, factor of and 63,1 an index match For the — experiments 18° which results 10-3 photomultiplier have order contributions 8 and 9 ran This efficient scattering volume and 5 cell is immersed in were an split the lens Hoyer). a nm chapters in required for an nm as 633 = 60x30) cell scattering 90 mm, diameter 63 mm, 6 beam waist and difference suppression factor of 4 Figure to DAN (The efficiency for suppressing higher see 488 = suppression of double scattering by approximately valid for the m wavelength of Ao experiments described chosen values of R < 50 pm. for the beam waist at the 7 TO-3 for A0 were experiments obtained with sample turbidity suppression of contributions from multiple scattering. a 6 14. The beam to the instrument. The laser beam is lens has been chosen in order to allow for which results in figure chapter model for the source polarization preserving single parallel beams, (planar L\ HeNe laser a implemented was Innova described in To extend the measurable lange of source. (eq. 10) into two (Coherent suspensions is shown in optical fibers experimental set-up for 3d cross-correlation. 29 vat (ALV 88/ALV, Water is used heat without flat entrance and exit the index as exchanger coil, guided by is collected and (Fi, F2, OZ side, and a Optics) [35, 36]. fiber connectors to a the scattered combination of light with GRIN lens and a home-built housing the for a scale than 1 mm important. across (photon transport principle In order to avoid free mean signal, the general length and that are of we half the rotation the outlined in a by using figure displacement For so-called 0 angle (90° — 0) is s be less cell becomes should be of the order of L. flat cells. However, displacement. 15. We use experiments — at in recover a a combination of motorized rotational stage above the a x — of the cell to is rotated can by situation in which This 0 y translation sample position, which path different from sample of the incident and scattered beam almost cancel. geometry is implemented by using mm scattering angles, scattering angles symmetrical this will implemented a corner 20 geometry, where the in order to angles, square cells with 10 at low In since these cells We therefore superior optical quality for experiments turn the cell in where easily may with beams at non-normal incidence optical path lengths. (ALV characteristic a scattering position them such that the scattering volume is located have short 90° approach exp(—s/L), path length), which light path lead to considerable beam deflection and different ~ correlator attenuation of the strong and L is light H5783P- strong reduction of the singly scattered light and a this could be achieved best will then be used in a due to the scattered singly digital a for dense colloidal suspensions, the size of the in fc/2 amplifier/discriminators two and fed into suspensions, the cell for subsequent reduction is mode fiber (PM; tube photomultiplier intensity which essentially decays like 1^ optical path length the For turbid colloidal scattered single a (L2) and kf\ vectors wave a The end of each fiber is connected via standard SMA (C3866 photon counting unit, Hamamatsu) singly An identical lens thermostat. a 01, Hamamatsu), and the PM signal is processed by 5000/E, ALV). mm). fluid. The vat temperature is controlled via matching which is connected to used for the detection outer diameter 85 windows, — 20 stage and a be controlled from within the ALV correlator software and allows for automated measurements of the angular dependence of the static and dynamic structure factor. EXPERIMENTAL REALIZATION 5 30 • K 1 / „ 90°/ 90°-e Figure 15: Description of the 0 — 20 geometry used in order to work with rectangular scattering cells and minimized optical path length. 5.1 Description Detailed of the Opto-Mechanical Compo¬ nents Producing 5.1.1 Using a compared more mode single to a Parallel Beams optical fiber for 'direct' laser beam. The precisely, the Gaussian as only filter. Out of the fiber intensity profile. Furthermore the laser beam must be whole light scattering lasers working a single coupled instrument. As at different a to the always only guides instrument, comes exchange significant advantages a as can single light it also works of the laser is easy to mode be used. the or, as beam with the desired into the fiber without long wavelengths collimator is included which allows an has mode fiber not TEMoo-mode from the laser high quality spatial a light the incident laser perform re-alignment operation is of the fulfilled, even In the used DANTEC fiber variation of the focal point from negative Detailed 5.1 of the Description values to approximately the beam propagation 200 w(z) radius is The through ©div and \ divergence 0^ \/(nw0). = divergence angle resulting parallel is small from the of ©jw a distance 5.1.2 Lenses beams Wo difference in that the beam radii are mounted nearly scattering the optical volume. Therefore axis. This system infinity. a focal planoconvex singlets length of / 90 = optical error optical axis, a the two distances of generation rotation and tilt. prism tables, which allow are an used to generate the difference are But, even because the spherical located in They used. optical axis, distance of 1.5 vat, filled with cm from the water with calculated to 53d = 14°. position on a is set-up optical a are infinity planoconvex a focal common to image optical on also In the 3d lens. mounted with to the an points clear aperture of 60 x-y-z translation a parallel mm two axis lens a stage. The main axis is spherical of the two beams is fixed with respect to the abberation is not a with arranged object of the lens system for beams For the 3d instrument chosen, axis. issue in the 3d an where the two Taking refractive index of From Gaussian beam n set-up. parallel beams have into account the index = 1.33 the difference propagation the place a matching angle can be of the beam given trough z' = (53) 7-TT2 z2 + TT-Wf where zf is the distance of the beam waist from the focal image equal identical at made of BK7 with mm are which allows to tilt the abberation. they projects holder, waist is nm divergence 3 cm, the and the mirror for the The lens of best form for this task is instrument two and 632.8 = splitting due to the beam are given This results in is used. path length of splitter on mm A is wavelength between the incident and the detection beams and to focus the beams at the in from the beam waist where the HeNe-laser with A 1 = The transmission and detection lenses L\ and L2 angle 5^ z a Although volume. The beam scattering parallel a adjusted, (52) of the laser beam with the 10-4. • beams have enough the two 2 laser beam is w0 In the actual set-up = oo) —) ( 1 + beam waist at the exit of the fiber a angle Wq = —> by then is described denotes the beam radius at wQ. (/ A collimated mm. w(z) where 31 Opto-Mechanical Components side and z accordingly for the object side, / point is the focal of the lens at the length and w0 the beam waist before with a short focal focussing. length, calculated For in the 3d set-up, z' as i. 0, = / = 90 mm, then is calculated to be Wf Wf < 100 pm using a w0 36 pm. = pinhole, With the detection unit the beam paths formed lenses. The lens and The radius at the beam waist Wf = 1 and mm z 26 = Experimentally different be estimate if rough a through. a symmetric arrangement of the detection by optical single optics has mode scattering angle incoming the laser beams and to be fulfilled. fibers optical It consists of with equipped grin fibers mount allow tilt and translation in x-y-z direction To allow measurements at the whole detection unit is mounted on the arm of the goniometer. main Alignment 5.1.4 of the Instrument Due to the fundamental light scattering principle for the two individual placed with an identical alignment leads strongly depends immediately to investigated a on the of the and of the statistics of the statistical accuracy In this particular experiment, compared to a impor¬ scattering vectors scattering volume i. e. on each other at the symmetrically scattering a any mis¬ to the volume instrument. For the detection of the scattered points at the plane of the placed light an on sample partially prolonged realization of the 3d instrument described and to direct the two beams ratio of the alignment (nearly) perfect aligned used to focus the two laser beams with the focal cross an limitation of the maximum turbidity of the instrument the duration of the measurement has to be same is signal-to-noise quality alignment the implemented is It should guarantee identical scattering experiments cross-correlation function aligned technique the rotational axis of the instrument. As the on technique of the cross-correlation instrument where this tant and often also difficult issue. they can The beam diameter cm. obtain we for the lens and in y-z direction for the fiber mounts. the the waist of the focussed e. where both beams have to pass lens L2 identical to L\ and two to be lens Detection Unit 5.1.3 a a using In the present set-up of by well collimated laser beam focussed a point of the lens. beam is at the focal a EXPERIMENTAL REALIZATION 5 32 mis¬ to obtain one. above, a lens is scattering volume, goniometer so that the rotational axis of the identical lens is used together Detailed 5.1 with two a common laser beams. This scattering plane of the goniometer, that the bisector of the must The at alignment procedure justment part, a flow chart goal order to part are ensure to that they generate the instrument two the can vectors and of paths of zero of the two goniometer plane perpendicular the degree a laser beams. mechanical and respect parallel laser beams which an optical is shown in of the housing, to the main and placing figure beams, respectively, are ad¬ 16. the index goniometer in optical the rotational axias of the two lenses in such in the middle of the two the axis without the lenses. cross of the plane the detection beam illuminating alignment with in the lays alignment procedure are course the rotational axis of the instrument be divided into the a the is thus to focus have identical rotation axis. The main steps of the two incident and detection lays paths symmetrically to between the two beams describing perpendicular, rotational axis which on 33 alignment procedure scattering angle a and the second the beam beams, which define point The main steps of the mechanical part matching vat, of the laser on one angle completely overlay pick up guarantees identical scattering incoming goniometer. Furthermore, paths that volume. The with the first lens the two such, Opto-Mechanical Components single mode optical fibers illuminating to the of the Description crossing a in that points where way that the point the beam on paths the hit 5 34 Centering of Centering Mounting Hlliill goniometer of the second the Dantec fiber and passing housing of the index match vat 111 Centering the EXPERIMENTAL REALIZATION adjustment a (separately) collimated laser beam goniometer parallel beams of the detection fibers and Mounting maximum transmitted Mounting of the rotational axis of the the laser beam into two Splitting unit and centering Mounting and adjusting intensity of the second adjusting goniometer unit the lenses ^^^11 Fine highly tuning with diluted Figure 16: sample a to Survey of measurement with achieve maximum the a intercept alignment procedure. 35 Characterization of Turbid Colloidal Suspen¬ 6 Com¬ Using Light Scattering Techniques sions bined with Cross-Correlation Methods Materials and methods 6.1 Measurements (ACF) were (CCF) correlation functions weighted individually analysed using were inverse Laplace transform size distributions CCF determination intercept ß\2 of the was suspensions The (i.e., for each also were investigate were made for scattering angles measurements for 10 seconds were cylindrical quartz were 15° cells with 8 latex at a 150° at < averaged performed polystyrene 0 < for each mm correlator). and the value by means of Measurements increment of an The angle. inner diameter temperature of T = 1°, and suspensions (Hellma, were 10 were 540.110- 25.0 ± 0.01°C. used in these measurements particles Polybead polystyrene microspheres) We have performed measurements with in order to demonstrate the multiple scattering suspensions R2 of the obtained from (specifi¬ Polyscience. Results and discussion 6.2 from each), course For goniometer system (ALV/DLS/SLS-5000F single mode compact goniometer system with ALV-5000 fast cations: s in the at very low concentrations fiber Materials: The resulting intensity obtained from the cumulant fit. commercial Measurements and scattering angle [20]. 10 measurements of 120 using inserted into The intensity measured the SLS a analysis [33] second order cumulant averaged then were used was a algorithm (CONTIN) [31, 32]. light scattering (SLS) experiments static QS). intensity auto- Measurement durations taken. were 10 60 seconds for ACF and 120 seconds for CCF determination. The correlation functions an cross- or scattering angles 0, and different performed at were = 274 nm, static and of the of bimodal of the in turbid colloidal highly monodisperse which respectively, we latex both suspensions were ratio dispersion technique particles carefully obtained with these of We have with radii of R± = 8.77) that the two prepared ~ 23 nm two and characterized by and individually The corresponding q-dependence dispersions is shown in 17. The two then mixed and the relative concentrations Ci/c2 polystyrene spheres to suppress contributions suspensions. dynamic light scattering experiments. scattering intensity (weight capability a were particle components equally adjusted such contribute to CHARACTERIZATION OF TURBID MODEL SUSPENSIONS 6 36 10000 1000 §, 100 )—i 10 - 1 - 50 0 Figure 17: Results with radii of R± from sample = 23 nm 0 of two different polystyrene spheres characterization and R2 150 100 angle = 274 Results nm. from light scattering static experiments with the individual and almost monodisperse particle suspensions (E: R = 23 nm; G: R function of solutions weight the were ratio the total as = nm). 274 magnitude of the Shown scattering used in the with pronounced particle principle to the I(q) varies intensity weighted size distribution. dynamic can 0.1 measurements the mmol/1. The sample considerably were For this particles and with the highest resulting Debye length as a The stock the same on of /c_1 in the accessible scattering angle, scattering angles have different contributions particular can concentration ratio be calculated from the Direct and structure factor hydrodynamic depend the salt content of the concentration had = 28 48°. Due particle sizing experiment particles. dynamic with done at four structure factor also influence the size and concentration of the larger spheres suspension known concentrations and form factors of the interactions which to scattering angle of a classical a Measurements of the adjusted were I(q) mixtures. form factor of the particle components of the mixture the theoretical our {Attu/Xq) sin(0/2). = of the mixture at should be measurable in dynamic light scattering. where the two vector q experiments with q-range, their relative contribution to which in the time average intensities diluted and the relative concentrations scattering intensity I(q) to the very are nm together a on sample. the In salt content of with the chosen 37 Results and discussion 6.2 particle radii and volume fractions interactions on S(q, r) neglected, be can S{q'T)= A2(q,r) where r6P(q,r) ~ and diffusion coefficient of a S(q, r) and can hydrodynamic by thus be described ( r*(r)A»(,,r)*- D0(r) and that effects of direct and ensure kT/6irnr represent = particle with radius r, scattering intensity the respectively, ' and n is the viscosity of the solvent. At 0 34° almost = only large spheres the intensity corresponds size distribution and their contribution to the total proximately 90%, at 0 = approximately 30%, weighted when 0.95) = transformation titatively = 86° the small auto-correlation measurements using Contin [31, 32] required the in order to appropriate relative amplitudes shown in as figure total latex concentration of 0.21% a tion is still has a is the mixture is pronounced very considerably, decay caused by scattering angle the inverse perform are Laplace in fact able to quan¬ intensity weighted in the for higher particle size an concentrations. undiluted mixture by weight. Although the colloid we influenced only slightly ments. As shown in istic populations concentra¬ relatively low and the collective diffusion coefficient measured by dynamic light scattering actions, intensity suspensions (transmis¬ This is demonstrated with auto-correlation measurements for at ones 18. completely changes situation distinct for each dilute on to obtain the size distribution. We distribution from Contin However, the two dynamic light scattering experiment a and recover corresponding The while and the small dominate the particles to ap¬ contribution, same approximately 70% contribute and at 0 visible in performing sion T components have the 48° both size distribution with 85%. clearly are = large spheres the 61°, at 0 intensity weighted visible in the are completely now effect on much smaller in the now. sample 9, auto-correlation 9This has been verified using concentrated length sample transmission of T = inter¬ 0.05. This measure¬ 20, the intercept of the auto-correlation function has decreased are photon path length of the coherence a interparticle the results obtained from auto-correlation the fact that the coherence an turbid with observe strong distortions at short times measured in contributions from by an from 2-3 is then the length same as intercept is mainly of the laser is shorter than the average the shift of the characteristic correlation times Ar+ laser with to times r, and the character¬ While the decrease in experiment cm lag is an a genuine étalon approximately for the diluted 10 effect of installed, m. sample The multiple scattering which leads to intercept shown in figure an increase measured for the 20. 38 6 CHARACTERIZATION OF TURBID MODEL SUSPENSIONS 10 1000 100 radius 10 tion 18: of of the (dashed line, radii Contin to the auto-correlation = (dotted line) 34°; (B): © [7, 8]. This for = = on functions large particles also evident from or such figure 18 A-D, = scattering, a decay times is and any attempt to measurement would utterly from of the individ¬ an droplets (solid line) to recover recover a and radii in the correct distribution particle sizing experiments to low concentrations only. which show the result from Contin when completely application 86°. the auto-correlation function measured with the turbid distribution of distribu¬ for different scattering angles ©.(A): 61°; (D): Q emulsion the measurement measured with dilute particle hydrodynamic as 1000 (nm) intensity-weighted with the results obtained example severely limits the ability of diffusion coefficients with based bimodal mixtures 48°; (C): 0 calculated theoretically monodisperse suspensions) concentrated 0 radius A comparison 1000 (nm) 100 1000 (nm) of hydrodynamic ual dilute radius 100 radius Figure 100 (nm) suspension. applied The distorted due to the effects of correct particle This is to resulting multiple size distribution from such fail. In contrast to the results obtained from auto-correlation experiments, the use 39 Results and discussion 6.2 19: tion of hydrodynamic tion of Contin of radii the theoretically (dashed line) to the cross-correlation and concentrated bimodal mixtures 0 = of a 34°; (B): 0 = 48°; (C): 0 multiple scattering. Contin have been intrinsically of the and the actual œ plotted. 0.17 for our a us intercept mismatch and instrument, actual distribution of from 61°; (D): © lower value for the phase decay from an = distribu¬ applica¬ measured with the 3d instrument functions corresponding The intensity-weighted with the results obtained This is shown in correlation function and the ßu = calculated (nm) (solid line) for different scattering angles 3d cross-correlation set-up allows from 1000 radius (nm) A comparison (nm) 100 1000 100 Figure radius (nm) radius 1000 100 1000 100 radius 0. (A): 86° to very figures efficiently 20 and 19 distribution of suppress any effects where the A-D, hydrodynamic cross- radii from is much lower due to the combined effect ideally aligned misalignment, and the effect of times remains instrument which results in multiple scattering unchanged comparison of the auto-correlation function cross-correlation function obtained from the turbid as is ßi2,ideai an 40. = intercept of However, already clearly from the dilute 0.25 sample the visible and the sample (see figure 20). Figures 6 40 CHARACTERIZATION OF TURBID MODEL SUSPENSIONS 1.07 01 O.OOOl 10000 100 0.01 lag tine T (ms) Figure from Results 20: auto- and cross-correlation experiments with dilute and different polystyrene spheres with radii of Ri concentrated mixtures of and R2 comparison of the measured auto-correlation function with dilute nm. (dashed line) A and concentrated A-D demonstrate that the use of determine the correct distribution of highly (dotted line) obtained with the 3d instrument function 19 274 = two turbid from 3d cross-correlation scheme allows a decay times (or hydrodynamic radii) light also we allows to isolate the us single scattering dynamic can go one the differential scattering cross single scattering particle suspensions. function section can on da(q)/dCl, form factor or the ratio between the intensity I(q) (eqn. 40). to even for multiply structure factor highly turbid suspen¬ The singly which with the can mean intercept scattered intensity scattering experiment ent orders of scattered light. us q-dependence of be used to determine the static structure factor of colloidal contains contributions from multiply for even provide The basis for this is the fact that the depends scattered us step further: combined static and dynamic light scattering experiments using the 3d spectrometer the a suspensions. and therefore to determine correct size distributions sions, nm (solid line). While the measurements above show clearly that the suppression of scattered 23 mixture and the cross-correlation concentrated mixture a = singly To extract the of the cross-correlation light I^(ç) measured in and the total a static light scattered and from differ¬ single scattering contribution Results and discussion 6.2 I^(q), I(q) has to be corrected with the reduced ß\2 correlation function where scattering only, experiment total which with diluted highly a intensity observed system for R of the q-dependence 274 — dilute a particle form factor typical for has = I(q)/I(0) = with the experimental data. a contribution from where the scattering already leads average particle suspensions becomes 21 A that to more singly to multiply contribution from a looking effects. The in experiments. figure This light, whereby decrease in the in P(q), multiple polydispersity function for at the reduced and the polydisperse a 21 intercept B, which we value of 1 means intercept corresponds I(q). ßi2/ß[2 the ratio that there is to a an no increasing ßu/ßu > 12 % transmission is due to an The fact that by as obtained from quantity directly yields artefact intercept multiple scattering important role of multiple scattering points of the sample with influence the 12% and = suspensions, the minima and (Mie) scattering The multiply scattered light caused particle concentrations, where wrong numbers for the a where light scattering the presence of small amounts of 1 for the first two data mainly 2.9% results in = lower than in forward direction. magnitude suspensions shown multiple scattering, and cr becomes dominant close the minima in data. obvious when scattered of are Mie- using higher concentrations, For these turbid even completely simultaneous cross-correlation A calculation illustrated with static smeared out due to experimental function of q for both of A). size in any attempt to fit to the even 21 is several orders of figure with radius leads to low transmission values of T multiple scattering intensity It is obvious from are particles However, the scattering data the 3d instrument for two different maxima of the form factor latex given polydispersity very different appearance when measured at 1.5%, respectively (see fig. goniometer shows distinct minima and maxima that good agreement significant multiple scattering classical a on A. In the accessible q-range the normalized 21 multiple scattering becomes important. This is T measured with on to the Pu12 relatively monodisperse spherical particles. data obtained single dynamic light scattering a \ particles a in the limit of = highly monodisperse of figure cross- thus be obtained from for these latex theory very P(q) can \Zli%)li%) suspension in °f tne sample. The single scattering contribution scattering intensity is shown in nm independently at detectors 1 and 2 = ßi2/ß\2 intercept intercept measured denotes the be measured can I{l\q) The 41 dust effects at very low we obtain scattering angles, which can of the cross-correlation function. This is also evident when CHARACTERIZATION OF TURBID MODEL SUSPENSIONS 6 42 looking which at the standard deviations for the different values also are at very low largest and which are general larger in contributions from dust latex scattering angles are not for the Figure in factor, concentration, where with the lower dominated the contribution from the by particles. A combination of the total scattered ßi2/'ß\2 together scattered with I^(q), intensity which is allows for directly 48 equation intensity I(q) and the reduced intercept a calculation of the single figure 21 C. for both concentrations in plotted P(q) The thus obtained corrected intensities agree very well with the calculated singly These results light. scattered particle form factor even under clear that such course the correction of sizing, but allows for is less than strong q-dependence and the scattered intensity The singly ability to suppress scattered light measurements. In scattered colloids, By this has one generally tries to as important some particular intensity such one multiple scattering large particles that from and However, if one can successfully we can particles completely correct for choose as 0 = and a q-dependence of light scattering of the strongly interacting does not cover the regions with to contributions from cuvettes and vat, dust exceedingly multiple scattering, dominates any background perform 5°, which would be impossible for scattering cells a etc.), difficult. these aspects lose experimental conditions where the scattering in fact been able to benefit from this and low shows system is only weakly scattering. measurements at low values of q become importance, and from the of highly susceptible background (solvent, reflexes, stray light consequently their measurements S(q) suppressed significantly [37]. suspensions or particle in pronounced q-dependence multiple scattering intensity. This makes these low where consequences for static aims for conditions where the ensure be It contributions to the static and determine the for systems with very for applications suspensions, can P(q) to the minimum in is not restricted to colloidal single evaluate the can for 10% of the total intensity. multiple scattering strongly interacting structure factor in we circumstances, where close procedure a that demonstrate, single scattering the contribution from is of B, 21 and in the minima of the form sample completely given a contamination. We have SLS measurements at conventional angles as approach using normal goniometer system. Our measurements show that the dynamic light scattering experiments multiple light scattering. use of the 3d cross-correlation allows to The current value of correlation function achieved with our effectively ß12 ~ intercept high enough correlation functions of sufficient accuracy in order to in suppress contributions of 0.2 for the instrument is technique in the that we successfully apply cross- obtain inverse 43 Results and discussion 6.2 B 1.4 'I- 1.2 I 1 a 0.8 <4 0.6 °£ 0.4 Ï I 0.2 0 0 10 5 15 q 30 25 20 .+. 4_ -0.2 0.0001 10 35 20 15 (1/pm) q 25 30 35 (1/pm) 1 T~ 0.1 B - 0.01 0.001 0.0001 Figure Results 21: from trated turbid monomodal (A): lute = light scattering experiments with dilute and particle suspensions (R Normalized scattering intensity suspension concentrated T static 12%; measured on a concentration on 0.05%, T = for polydisperse spheres following 274 and ßu/ßu polydispersity obtained from a = T = 12%; ; 1.6%). as a a a cross-correlation function 0.05%, intensity P(q) = I(q)/I(0) as a 2.9%). function of (E: T = q 0.95,)., concentration a for di¬ and 0.01%, theoretical cal¬ Schulz distribution with average radius suspensions concentration (•: The reduced intercept measurements as T (B): a = using the 3d function of q. (•: 1.5%,) The standard deviations obtained from 10 individual measurements. normalized = Also shown is 2.9% using Mie theory. ment with dilute and concentrated 0.01%, I(q)/I(Q) — the 3d instrument culation nm 274 nm, commercial goniometer system suspensions measured : P(q) = concen¬ function of q, error concentration bars (C): Single where instru¬ given are scattered multiple scatter¬ ing contributions have been corrected for by using figure 21 B and equation 48, for concentrated T = 12%; suspensions measured : concentration on 0.05%, T the 3d instrument = culation for polydisperse spheres following 274 and nm polydispersity o = 1.5%,). a (•: concentration Also shown is a 0.01%, theoretical cal¬ Schulz distribution with average radius 2.9% using Mie theory. 6 44 Laplace CHARACTERIZATION OF TURBID MODEL SUSPENSIONS transformation programs such 60-300 seconds. This opens up sizing in industrially a as Contin after measurements of wide field of relevant systems such new as applications ranging we can directly use intercept of the cross-correlation function and the multiple scattering. Therefore, but also for systematic SLS can the relation between the correct the measured values of the scattered our not be optically experimentally amount of particle matched. determined multiple scattering and intensity I(q) for contributions from 3d spectrometer studies of turbid from emulsions to the determination of the dynamics of concentrated model suspensions that Moreover, typically can not suspensions. only be used for DLS, 45 Colloidal Suspensions Introduction 7.1 properties of Structural colloidal systems are interactions, which the Understanding ence. a Strongly Interacting Static Structure Factor of 7 of considerable interest in colloid sci¬ cause relationship between microscopic characteristics these structures, and loidal systems which is also of industrial relevance light scattering experiments of the structural standing analogy an The colloidal enters such as as to simple liquids, particles then i. play the e. dielectric constant, index of the by treating by the tools used to has been achieved suspension molecules, corresponding refraction, theory and state experimental suspensions role of the fluid continuum characterized a [38, 39]. Liquid considerable progress in the under¬ of colloidal properties to find help macroscopic properties of col¬ often the theoretical and suspensions of interacting particles. A describe making are can or ionic as a 'macrofluid'. and the solvent continuum strength (or by only parameters Deb ye length) [40, 41]. The structure of colloidal particles can which is the is be suspensions arising probability finding S(q) which can sity Is{q) q is be measured in measured as given by equation size, shape tor S(q) a a = 1 + n J \g{r) function of the S(q) 14. The can particle also be written of the correlations between the for uncorrelated exhibit particles S(q) a It (57) P(q) 0 or The the scattering scattering inten¬ vector contains information about particles, and the static structure fac¬ based on the interactions between the ^X>*s(r,"r')> (58) an ensemble average. particles = r. as = brackets denote the distance 1] e~tqr d3r form factor suspension %) angular - g(r), function via scattering angle and the internal structure of the particles. S(q) particles particles separated by light scattering experiment. static reflects the order in the where the pair a of related to the static structure factor directly pair correlation described with the quantitatively of from the interactions between the i and 1 for all q. j Equation located at Suspensions 58 is positions of rt a measure and r3, and charged monodisperse characteristic form for the static structure factor, which closely STATIC STRUCTURE FACTOR 7 46 S(q) resembles S(0), small value In the limit of q simple liquids. found for related to the isothermal directly which is 0 it starts from —> a of the compressibility x suspension through S(q S(q) then increases with lations Since the d. of the suspension of the main position peak minima and maxima in which reciprocal in separated by correspond space a position experimentally the i. e. the to to e. peak a in g(r). potential, analogies particle suspension to the is treated as The the a ^/Vp/<&, higher of finding a order one S(q) in particles two relation between correlation function pair theory of simple liquids a the value of peak positions In order to find factor, = approach and probability increased an d values of q the particle gas10. ideal an determined static structure and the interaction made, r, i. pronounced become less to the value of corresponds distance interparticle mean 4n/3a3 through = higher scales with $s At S(q) of the corre¬ be calculated from the volume fraction <& can volume Vp particle and the (59) nkBTX reciprocal at the distance interparticle = the q and has its main maximum where increasing strongest, which is are 0) = 'macrofluid'. In are often the simple liquids Ornstein-Zernike equation h(r) is used to g(r) — provide 1, which this link split is particles trough c(r), particles. an Since c{r) = [42]. into f h(\r n - s\)c(s) d3s It consists of the total correlation function sum 60 contains of indirect correlations mediated no A simple approximation (MSA) [41] the interaction closure relation is for ß = potential U{r) l/(kßT) the Perçus-Yevick is the is (PY) and the leads to qmax ~ 2n/d. neighbour a two mean pair spherical weakly c{r) in¬ and given through reciprocal 10For particles that interact with related to the nearest the example which has often be used to describe relative c(r) where to the potential — potential The relation between the direct correlation function teracting particles. h{r) the other by information about the interaction additional closure relation is needed to link the interaction correlation function. (60) part describing the direct correlations between a and the equation + = thermal energy. On hypernatted chain short range hard shell of (61) -ßU{r) particles a more (HNC) [41] sophisticated level, closure relations sphere potential, the main peak around a primary particle, i. e. at d = of are S(q) is 2a, which 47 Introduction 7.1 applied often to describe the structural it is known that the PY closure relation leads to sphere potentials the Rogers-Young h(r) aims at of properties good and the HNC closure relation for results for short long ranged Because ranged Yukawa hard potentials, [43] closure = particle suspensions. e- -1 + x (l + ^{f(r)[h(r)-c(r)]}-l\ fin V from both closures taking advantage J PY and HNC with by combining a mixing function f(r) where is the a can be obtained a the isothermal fluctuation and the virial route. (63) e~ar a —> While the fluctuation xP the virial compressibility where the pressure P is can 1 3 Because these closure relations generally are irßn /•«> / compressibility a v^a the directly is 0 (64) equation of state z_,_^dU dr approximations the compressibilities calculated not identical. In the guarantees thermodynamic consistency, vides very accurate results for the (66) g(r)—— dr r jo is chosen in such way, that Xt a —> Xt anc^ Xt n 2_a_ 1 n parameter mixing parameter given through = are The closure -5(0) be calculated from the ßP via both routes = Rogers-Young compressibilities the static structure factor in the limit of q given by 0 the the HNC closure. —> oo to by calculating - In the limit mixing parameter. reduces to the PY and for 1 = = Rogers-Young Xt at least for the in closure the mixing this way the RY closure compressibility, and it pro¬ pair correlation function g(r) when compared to 'exact' Monte Carlo simulations. Light scattering experiments with polydispersity tation of the account [44]. generally is in with 'real' size, charge light scattering data or particle suspensions refractive index of the consequently often have to deal particles. An interpre¬ has to take this polydipersity In the theoretical calculation the continuous distribution of replaced by a histogram which then results in a mixture of into particles particles of p consisting components. Sizes aß and number densities raM of the components histogram chosen such that the first two moments of the are distribution have the a STATIC STRUCTURE FACTOR 7 48 set of coupled same values. The Ornstein-Zernike cßV{r) = + n^2 ( which have to be solved with the polydisperse sample a and particle components, form — ) / Kx(r)c\„(\r is now given by scattering intensity the equation 14 can na* = be written in n|) d3r1 - generalized Rogers-Young Is(q) where a6 and equation integral equations /V(r) With and the continuous closure relations. weighted is the a (67) of the sum modified form as (68) P(q) S{q) represents intensity-weighted average particle volume and particle P(q) factor, respectively, EU Nß(a)a* S(q) and no the the effective structure factor longer simply interparticle factors into taking single particle quantities P(q) S(q) only. correlations s(q) into account the size distribution. = wt and a Is{q) part describing The effective static structure factor S BMBÀq)SM () p{q) ß,u=i where denotes the Bß factors, depends factors now defined are scattering amplitudes also on and SßU single particle properties. the The partial partial static structure static structure as ^(«) Because of the different = iEE^q(Rj Ri) n size, charge (7i) j=i k=i or refractive index of the particles static structure factors have their maximum at different values of q. quence the peak in S(q) is shifted and reduced and washed out. Furthermore the value of [45], thus In this 5(0) higher increases with the As a partial conse¬ order oscillations are increasing polydispersity 5(0) ^ nkBTx. chapter we demonstrate that with the 3d cross-correlation instrument the static structure factor S(q) can be measured in particle suspensions that exhibit a 49 Introduction 7.1 high turbidity. which This provides previously were direct a excluded from these Is(q)- contributions to the measured which polystyrene spheres, matched, which neglected be when the While existing for their that values of q. is an are typical example A finding. and experimental increased forward known precisely. aggregates. To first uncorrelated gas of contribution to the values of q, where contribution to S(q) can to as Another S(q) intensity S(q) too we Particular origin of the a could then lead to values, fractions, high values for have performed care was careful a preparation charged particles measurably S(q) to exist for this at low discrepancy is known to result we believe that this performed where the size distribution to particles as a small number of something an ones. Their increase in Is(q) at low would be small and their for deionized interacting (i. could contribute like of small liquid significant non suspensions e. multiple highly screened) significantly and thus lead 5(c). a systematic study of the static our multiple scattering to the recently the presence of small amounts of volume fraction with given too low at would be the are results have been correlated is possible correspond would and polydispersity generally could be the presence of highly if data several Nevertheless published reveals peak position all, polydispersity particle suspensions in safely experimental between would contribute for the small 'monomeric' particle are There 22. Is{q) considerably suppressed. Finally, function of a figure in data. First of reason big particles to determine the amount of and given approximation they at these low volume apparently a is some can suspensions the S(q) quite accurately which would not be measurable for Therefore as reproducing scattering intensity [44]. be very low at low q scattering, particles of However, several other possible explanations theory optically particle size, the on and predictions particularly exciting possibility with very well characterized model was capable although relatively weak, unlikely explanation, an between theoretical attractive interactions of electrostatic proposed in lower, depending structure factors in deionized on integral equations low values of q. A between data or effects multiple scattering taken into account, the theoretical values for properly [47, 48], model systems, cannot be as charged of suspensions aqueous instruments. of the minima and maxima in height reasons light scattering discrepancy characteristic [46, 37]. used IO-3 to volume fractions of A survey of the a widely are example limits the concentration where standard using For multiple scattering due to investigations for systems potential to the interaction access precise in which all 3d-instrument, and structure factor which allows subsequently determination of the possible precautions us correct for it. sample polydispersity have been made to prevent 7 50 STATIC STR UCTURE FACTOR o u a u -i—» o GO 0 0 2 1 Scattering Figure sult Measured static structure 22: from deviation Rogers-Young a from theory and aggregation 7.2.1 in factor 5(c) compared (from [37]). at low q. For details remove all see experimental predicted re¬ data show a text. existing large particles. Experimental Set-Up experiments chapter 7.2.2 were performed using the 3d cross-correlation instrument described 5. Methods Measurements were done with suspensions of latex spheres (diameter: (110±10) nm) with volume fractions in the range from 0.05% to 1% the The with the Materials and Methods 7.2 The calculation Vector by volume. suspensions cristallize when fully deionized due interactions of the highly charged particles, a to the As it was long-range found that electrostatic mixture of ethanol and water was used as 51 Materials and Methods 7.2 the solvent. A volume ratio of 70% ethanol and 30% water prevents cristallization in the investigated particle decreases and the is thus lower. The cells with cylindrical and deionization the fully an Combined static and tion were kept exchanger resin s analysis fit. The ten and 120 s, by means tem an then were diluted aqueous of dynamic 10° to 0 = on were = with 2160 7.2.3 125° at analysed using a each and second a intercept ßi2 of the cross-correlation scattering intensity for multiple scattering of the latex suspensions and static size distribution transmission electron were scattering angle light scattering particles with a were also characterized commercial goniometer (ALV/DLS/SLS-5000F single mode fiber compact goniometer system). particle sec¬ cross scattering angle, the in averaged. was a 5 mM/1 NaCl was particle Laplace size distribution microscopy. The micrographs were sys¬ To avoid added to the solvent. calculated with the inverse tion routine Contin. Furthermore the The performed were the diffusion coefficient is calculated from the cumulant influence of electrostatic interactions The equal measurement. a done at each depending 10 mm, x correlation functions range from 0 were mm single scattering corresponding in order to obtain the Additionally runs to 10 in contact with days (Dowex) prior angular function needed for the correction of the contributions. particles In order to achieve Hellma). least 10 concentration. The correlation functions order cumulant Highly (rectangular cells, per (Versapor 0.8 pm filter membrane and to obtain the measurements duration between 20 sample at intensities and the temperature of 25°C. Ten the cells a dynamic light scattering experiments measured at intervals of 1° in the a using sample multiple scattering o~(q). Scattering having filtered inner diameter of 8 mm, samples volumes of mixed bed ion order to suppress were into the quartz charges groups, the number of of electrostatic interactions between the strength suspensions acrodisc, Gelman) charge of the surface equilibrium dissociation the association- changes concentration range, because the alcohol was calibrated transforma¬ measured with using a Pt-grid lines/mm. Materials suspension experiments was surface which of 8.3 % by of sulfate latex particles with the diameter of 110±10 nm used for the obtained from UDC. It is stabilized with 2500 sulfate groups are fully protonated volume. at pH 7. The stock solution has a on the concentration STATIC STRUCTURE FACTOR 7 52 1.2-r 1- 0.8- © 0.6- 0.4- 0.2- 0 1—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i— (1/nm) q Figure 23: Measured the Mie-calculation a (circles) radius (line) particle form factor P(q). and calculated of r 59 = nm 0.025 0.02 0.015 0.01 0.005 0 was From obtained. Results and Discussion 7.3 The latex particles were transmission electron highly dilute 70/30) with Mie-theory. was as the solvent are A fit to the static and figure compared 23 in an particle This behaviour could be due to a and to a = (87.2 ± radius of 59 nm, 7.3) nm combination of the effect of the shrinking of the (volume transmission electron experiments. However, from r mixture a form factor calculated particle a and data measured with ethanol/water data reveals too small values with sample preparation dynamic light scattering experimental with the experimental also found from DLS microscopy considerably in the In microscopy. by suspension (0.001 % by volume) ratio which characterized particles were obtained. drying process in the presence of the electron beam and is also described in the literature. Static structure factors 0.04 was % to 1 were measured for % by volume. As solvent used and the suspensions with suspension water low volume fractions of as was a fully particle mixture of 70 deionized concentrations parts ethanol using an ion the solvent show the formation of approximately 0.1 ranging to 30 parts exchanger. a colloidal from water Deionized crystal at % for these particles. These cristallized superimposed on the structure ethanol/water mixture measured as light scattering experiments scattering. A normalization of factor then provides performed solving Results up to polydispersity figure were good agreement from intensities were Scattering turbidity11 corrected for the measured by 5(c). dynamic and multiple form particle Theoretical calculations were equation with the Rogers-Young closure of the latex particles (r = 59 nm, a — %). 8.6 24 for different volume fractions. The results demonstrate S(q) not accessible. previously Using suspensions with combined static and and division particle suspensions be measured in can a This allows high turbidity. interaction effects in colloidal important information about to obtain than 1%. volume concentrations that exhibit high which higher Is(q) that the static structure factor clearly the alcohol prevents the the Ornstein-Zernike shown in are re-cristallization the static structure factor into account the taking Bragg peaks disappear, subsequently and are be shear melted scattering angle function of the a which too short time for the measurement. a cristallization up to volume fractions I(q) can crystal While the peak. solvent, the as in the high intensity a and the suspensions after about 10 s, which is place takes liquid the by simply shaking with Bragg-peaks show samples, however, an 53 Results and Discussion 7.3 data experimental The with theoretical results obtained from solving are now suspensions quantitatively in the Ornstein-Zernike equation with the Rogers-Young closure relation. For larger higher concentrations the values in q. The values of the effective lation vary between 160-250 data at higher knowledge of the our data per particle. However, are not we in the accessible q range in order to determines the effective investigate (SANS), the where we is highest i. e. is an have both overlap and 1%) when are shown in higher values, using rectangular figure cells 25. The as we lack a normalize the the 5(c) particle data for these symbols the very precise peak experimen¬ peak We therefore plan neutron scattering data at low q and has reached its can asymptotic form factor become high in of the main height small-angle light scattering where calcu¬ ability to analyse adjustable parameter. with light scattering Rogers-Young in the normalization of the unambiguously limit of one, and where the oscillations in the Nevertheless the our is shifted towards would need at least the second concentrations also with extend the q range to much visible. problems particularly important charge, S(q) in absolute scale and on particle concentration, tally determined 5(c). This to charges peak used in the charge concentrations is limited due to scattering data. Since S(q) of the main position concentrations represent the measured clearly (0.5% scattering particle intensities while the line represents the experimental The culations peak the using occurs Rogers-Young and test for the experimental calculations and improved However, tering it is can out that the main provide ical results for us 5(c) with a first peak colloidal theories to even has moved to theory, Nevertheless, study to dispersions, improve our of improved too the theory and sample preparation well as as software dust filter. under these conditions measurably by fluctuations of the in¬ multiple scat¬ of use high intensity a classical at low q. At values of q in sufficiently high we we still observe need additional a our data shown in structural and and to understanding figure 24 and test the of colloid = experiments and clearly dynamic properties investigate c 0.11% is in characteristic deviation for effort in order to reach any conclusions about the improved capability acting a limited are comparison between experimental data and theoret¬ 0.23%. However, it is clear that for this deviation. we in the limit of small q values. While the data at reasonable agreement with the experimental of main between theoretical at low values of q, and the completely neglected higher concentration, order to enormous use with the cal¬ determine the asymp¬ systematic comparison a scale)12. concentrations, the unambiguously cause with the would result in able which arbitrary a good agreement Under these conditions data. point to (on previously existing discrepancies protocol measurement not be in are additional effort both in an important form factor closure relation. At low light scattering set-up = 24 at values of 0 < 16°. It is clear that experiment will require an figure particles, influence of dust enormous tensity data shown in at too low values of q in order to 5(0) totic value c STATIC STRUCTURE FACTOR 7 54 stability, a consider¬ possible reasons demonstrate of strongly applicability our inter¬ of modern interactions and structure evaluation. 12We also plan to change absolute scale and therefore the present set-up for the 3d instrument to allow measurements a normalization of scattering data. on 7.3 Results and Discussion 55 0.025 0.025 0.025 0.01 0.015 q Figure at 24: different Static structure factors concentrations. The calculations. 0.025 0.02 (1/nm) measured with latex experimental data are suspensions compared with (r = 59 nm) Rogers-Young 56 7 STATIC STRUCTURE FACTOR 200 c 150-1 = 0.5% 100 50-1 (®Bmnnmni 0- 0.005 o 0.01 0.015 0.02 0.025 0.03 0.025 0.03 250 0.015 q Figure latex 25: Scattering intensity suspensions (r = 59 nm) and (1/nm) particle form factor (on a with 0.5% and 1% concentrations. arbitrary scale for 57 Influence of Dilution 8 on the Particle Sizes in Milk Introduction 8.1 Dynamic light scattering is It is a a powerful tool size distribution in colloidal of interaction However, many as suspensions, and characterization of colloidal systems. systems, often of industrial relevance, could experiment, suppressed, in the and the measurable range of samples performance tested was non-negligible turbidity, investigated with dynamic multiple scattered light be extended to can concentration. The construction of the instrument and its stability. and so-called 3d cross-correlation a contributions from disturbing was are high turbidity described before in detail measurements with well defined model using particle used for investi¬ dynamics with not be past. We therefore developed where the frequently colloidal samples of the investigations it is also potentials (see chapter 7), the method is known to fail for light scattering or a convenient and fast method for non-destructive, gations for systems (see chapter 6). Here nique to we make now methods tering effects due of sample. can to the practical of in many other of the concentration use for the or light scattering techniques undesired multiple avoided with are systems such of the significant change a as for a to much overcome larger this range of a light scat¬ dilution suspensions or self sample properties as¬ upon It is clear that the composition of the sample. help to their is in the colloidal range, Frequently problem respect systems, like for example emulsions 3d cross-correlation instrument could to particles mostly high sample turbidity a relevance. In industrial technological to be characterized with be used. principle react with sociating systems, and If the size of the While this often is not inorganic particles, changes step and demonstrate the applicability of the tech¬ systems often need size distribution. scattering of the next complex suspensions processes, 'real world' particle a problem samples and enable us than previously great interest in considered. As a the food milk is 'real world' system industry given in table 1. Milk the components choose because many trimodal distribution of particle we are also milk, products can which is are based be characterized whey proteins, polydisperse a on as a subject of it. The composition colloidal suspension casein micelles and milk fat in in size [49]. of cow with a water, where In this article the behaviour of the size distribution of milk under dilution is described. A characterization of INFLUENCE OF DILUTION ON THE PARTICLE SIZES IN MILK 8 58 cont. a whey proteins casein micelles milk fat 0.5 5 100 1000 radius nm mass % 92 0.75 2.5 4 volume % 83 1 11 5 Table 1: such phase Composition of cow milk, complex system also Laplace ments Therefore this also as content in the measured reduced due to contributions from multi¬ considerable task with respect to the data a in order to even developed signal fractions (from [49]). a recover size distributions from DLS under ideal conditions of new experi¬ high signal-to-noise analysis procedure data analysis. ratio. which is described in well. Experimental Set-Up experiments chapter were performed using the 3d cross-correlation instrument described 5. 8.2.2 Methods 8.2.3 Multi A and volume Materials and Methods 8.2.1 in we chapter 8.2 The require difficult to handle are significantly represents inversions of particles under conditions where the correlation function will be ple scattering size Angle Laplace Inverse Transformation dynamic light scattering experiment probes scattered light which are the calculation of the is performed is an leads to a mainly caused by the diffusive particle size distribution an intensity of the motion of the inverse Laplace function, typically problem, which is this ever infinite set of means that any noise present in a e(r, T) particles. For transformation the measured correlation function. The inversion of ill-conditioned correlation G{T) on the fluctuations in the on g(r), however, the measured dynamic light scattering experiment, possible results for the calculated size distribution that fit /i\ 9W{t)= f max e-rTG(r)dr + e(T,r) (72) 59 Materials and Methods 8.2 within the noise level. In general because any variation in g(r) of a polydisperse sample G(T). the two even function a peaks depends the on performed with noise height of the level, and in a experiment duration of a from each size factors, in as are distribution, taking form factors of each contribution of particle species a amplitude in the appropriate particle but there are it is are usually different be obtained in practical experiment limits for the simultaneous fit of angles improves particle species a an a an inverse to the fact that the varies with the species can at different the Laplace particle (see figure 18). Consequently the scattering be recovered best = P(q, r) a Mie calculation [27, 50] ^P^f^ additional m — (73) particles, np/ns which of the input parameter by taking advantage angles. to obtain and no longer depends particles (rip) to the for the Mie calculation. A set of correlation functions measured at different the result form poly disperse sample calculated with intensity by performing form factors as corresponding particle Ig. The angular dependence of the size distribution then is the number distribution of is needed scattering intensities calculated scattering size distribution for this Therefore the refractive index ratio (ns) often the fact that in on to the scattered GN^ solvent can measurement decreases the noise level scattering angle due be taken into account GN(r) as particle species at its maximum contribution to can that auto-correlation into account the This is based varies with the transformation, GI(q1 r) G(T) an means experiment ß\2 decreases set of correlation functions measured at different a reproduced. and the intercept accuracy of the calculated size distribution consists intensity weighted size distribution, q. good factor of a the correlation on smaller a cross-correlation 0 with the additional constraint that the angles on Because the noise prolonged resolution, improves the simultaneous fit of where not be obtained better than experiment. an A method which the as decreasing resolution, with even in inversion quite precisely using intercept ß, where a (main) peaks the sample having negligible turbidity and with comparable duration and therefore increases the angle, [30, 32] the resolution in is not of the measurement. Of course, a normally can increasing sample turbidity, cross-correlation in Contin or under close to ideal conditions. relatively higher with a of these amplitude position of While the often be recovered can exponential sampling methods like G(V), noise level restricts the resolution of smaller than the noise contribution cannot taken into account for the calculation of G(T) higher a scattering of the different contributions of the The constraint of the same angular dependence of 60 INFL UENCE OF DIL UTION ON THE PARTICLE SIZES IN MILK 8 the of the size to the results of this method be can comparable with dimensions expected or diluted prior or in a a cell rectangular rectangular the on correlation were particles given elsewhere [51].) covering the whole x 10 mm) of the for the done within a more range and P(q,r). a to 1:1000) particles were was were in 0 recover averaged s s > 400 pm, and 300 s, Ten were ratio cross- were measurements, used for the multi the size distribution of for each dilution step. used for the calculation of the performed For samples. high signal-to-noise a duration between 60 equally spaced All measurements sample time of 5 hours after dilution. Three transformation in order to 1.5 of the = turbid adjusted was were inserted either were dilutions 1:100 and other, to obtain sample, The individual results then refractive index nv form factors mm path length inside the cell angular Laplace particles. (for mm then range 30° < 0 < 120° at intervals of 5°. angular inverse inner diameter of 8 each measured for functions, an 8.2.5 will be of best light. (Details A of the wavelength samples turbidity taken in the experiments with suspensions for 1:100 and 1:1000. The a (10 cells the Measurements angle approximately A/2, radius of measurement with deionized water to volume ratios milk to (or undiluted), 1:10, depending ß\2. to round quartz cell with a pronounced a types of milk used for the experiments For the dilution series the different in a form factor possesses Methods 8.2.4 of 1:1 than than the larger performance and its algorithm particle particles larger for at their maximum contribution single particle species Because the scattering intensity. angular dependence of the to about the maximum distribution, and particularly the peak heights, resolution obtainable for every the size distribution increases the resolution intensity calculated from each individual at a A particle temperature of 25°C. Materials Measurements were performed using Customary, homogenized full-cream volume and skimmed milk with In addition a The emulsion cow protein-stabilized was a three kinds of milk different in cow milk with a milk fat content of 3.8% milk fat content of emulsion based obtained from Dr. M. on composition. 0.3% by volume vegetable oil was Leser, Nestec, Switzerland. were by used. characterized. Results and Discussion 8.3 scattering effects the hardly auto-correlation completely be can in the seen experiment performed with particle wrong size multiply measurement of the size distributions to have interactions coefficients of the particles a size distributions of full-cream particle visible for both a cases. would fail badly and an yield experiment This results in light. M/l [49], long a correct range electrostatic known to influence the diffusion are cow figure The undiluted milk shows milk measured with (see 30). eq. are dilution. From a in table 1, it measured, comparison i. e. we peak a the casein micelles and the second possible, classification is not to volume fractions small to the large particle in table 1 (1:1000) The on a using given the ratio is method, fit when compared concentrated in Mie theory, peak positions fraction are the samples a and 200 radius of 80 nm for the milk nm particle components given in the size distribution represents droplets. are both have a resulting in reasonable a clear we know However, too close and broad size distribution intensity weighted size distribution volume ratios of 1.6:1 for the agreement with the predictions globules. In the diluted sample 1.1:1. milk, cannot nm is very small be recovered because their contribution to the to the nm the milk fat conversion of the whose radius of 5 whey proteins angle peak populations dilution of shift to smaller values in size upon for casein micelles and fat only particle components peak because the from the literature that these two based a located at with the sizes of the different reasonable that the first seems [49]. Nevertheless, observe a 26. A bimodal size distribution is shoulder up to radii of 1000 nm, while radii of 65 diluted 1:1000 given While size distribution is calculated 1:1000 and with undiluted milk is shown in with light. in undiluted milk. Because milk is known which otherwise from which of the incident laser the 3d cross-correlation scattered multiple of signs Full-Cream Cow Milk 8.3.1 The neglected, be can even 1000 for the kinds scattered samples salt content of about 0.1 relatively high a these distribution, to suppress the successfully allows multiply of background paths the samples : show clear samples concentrated higher dilution of 1 highest at the with the undiluted Especially scattering. beams only negligible are investigated, of milk stages of dilution. Multiple measurements of milk at different performed We have a 61 R,esults and Discussion 8.3 large even compared with the to the other improved scattering intensity casein micelles and emulsion droplets. multi is too small While the cannot be measured with conventional DLS due to the more multiple INFLUENCE OF DILUTION ON THE PARTICLE SIZES IN MILK 8 62 radius Figure Particle size distribution 26: dilution. For details of the scattering a conventional measured the sample with size distribution is instrument, cow different steps of milk at dilution 1:1000 a dynamic light scattering particle correlation of full-cream text. see light, (nm) instrument exactly which supports the the was also measured with (ALV/DLS/SLS-5000F). same as measured with the 3d performance The cross- of the 3d cross-correlation instrument. Undiluted milk with presence of large fat at the limit of the it is still a total droplets capability measurable, the particle volume fraction of about 16 % and the with radii up to 1 pm represent of our sample a which is design13. 3d instrument in its present intercept of the cross-correlation function of about clearly limits the obtainable resolution of the size distribution due to the low to-noise ratio when sample. 13This limit regime. can be compared pushed While to even with a dilute higher turbidity using a Nevertheless laser wavelength we 0.02 signal- believe it is in the near infrared 63 Results and Discussion 8.3 quite remarkable than 15 % and that such containing a diluted An as can be more correctly resulting quality of the obtained with highly usually samples. of the behaviour of the full-cream milk upon dilution explanation found with results of are that the comparable quality obtained size distribution is of volume fraction of a large particles amount of significant dynamic light scattering, and characterized with with polydisperse sample a known to consist of sub-micelles with radii between 5 for the compact micelle is between 50 reported example due is removed for nm and 140 nm to dilution with pure water or nm and 20 nm. The size in radius. If calcium dialysis, [52, 53, 54, 55, 56]. and form small submicelles disintegrate Casein micelles measurements with casein micelles. previous be can the casein micelles For this reason the size distribution measured with the dilution 1:1000 is shifted to smaller values. Because the submicelles large fat small in are droplets. size, it is difficult to them in the presence of the see Therefore the volume concentration of the casein peak in the size distribution appears to be reduced upon dilution. A better characterization of the behaviour of casein micelles upon dilution with skimmed cow can in fact be obtained from milk. Skimmed Cow Milk 8.3.2 In the skimmed milk almost all of the milkfat is removed and of 0.3 % by figure shown in 500 peak nm. volume remains. Skim milk is in water. Measurements of suspended main at a In the undiluted 27. radius of 140 While the latter one nm in skimmed milk. an by volume the contribution of the seen in a interesting the main peak appears at a on we case a radius of 22 nm. the particle smaller one which peak obtain a whey proteins cow milk are size distribution shows located at nm are and area a a radius of about to the particle can be particle component assuming casein micelle a volume content of the milkfat of 0.5 %. scattering intensity considerably explained with a is too small milk, however, size distribution. radius decreases This the main Dilution of the skimmed the measured located at 140 and casein micelles mainly whey proteins micelles, scattering experiment. effect small amount a dilution series with skimmed a Calculated from the concentration of 11 % Again, and only represents the residual fat, the main peak describes the size distribution of the casein to be experiments The and a shows amplitude second disintegration of peak of the casein micelles into small submicelles upon dilution. Since the size distribution is normalized to a total area of 1, the peak areas 64 INFL UENCE OF DIL UTION ON THE PARTICLE SIZES IN MILK 8 i dilution: undiluted I I m_ i m -E32L 10000 1000 100 10 BE gg 1:10 ?? ^ I 3 si ^ a ^ o -1^3? 10 f t r n 1 1—r- 1000 100 10000 I "o > 10000 100 radius Figure 27: Particle size distribution micelles with details see a text. residual milkfat 1000 of skimmed content of 10000 (nm) cow 0.3 % at milk consisting mainly of different steps of casein dilution. For r-t- CD c-f. CD ta 05 m =—i to Ci re to 3 o o s s o Ci . CS- S o- co. ~3 Co to CD S- CD to CD =—i Ci as CO. c*. cd to ri CD -1 OO cm' ^^ o o o o. o o o oo ^1 S M ^ o- o o o o oo X- ^^^^^^^^SSSS^^^ | | volume distribution (a. u.) OS Ol Ü O t~*. to to O C to* Ö b cl EU c Co 0) to to 00 INFLUENCE OF DILUTION ON THE PARTICLE SIZES IN MILK 8 66 particle to the volume concentrations of the different directly correspond disintegration More than half of the volume fraction of the casein micelles shows The volume ratios into the smaller submicelles upon dilution. dilutions of 1:10 and 1:100 and 1.3:1 for the Furthermore the form of the of the peak to smaller values in continuously shifted found in the has been found upon for these systems a where [57, 58], a a Although good stability of undiluted milk Emulsion Based 8.3.3 results is not on Particle size distributions of given figure in radius of 190 a looks like the done with diluted small a sample of casein micelles use dialysis the reasonable guaranteed Vegetable light scattering time and the long high at of dilution temperature [56]. Oil case are emulsions based on vegetable the distribution shows a oil are maximum at and down to about 20 nm nm in angle light scattering show a bimodal distribution of and 6 pm. nm instrument In figure intensity weighted, particles. From a this comparison means Previous measurements (Mastersizer, Malvern) particle a However, the peaks that sample. they are a diluted sample and cross- The size distributions in figure the larger strongly weighted by of the cross-correlation measurement and the auto¬ these measurements particle a 30 the measurement with the Mastersizer dilution of the emulsion reduces the size of the made in order to avoid with sizes with its main correlation measurement with the data obtained from the Mastersizer it is visible that but it clearly understood, dissolved upon dilution. correlation measurements with the undiluted change or dialysed ultracentrifugate with auto-correlation measurements with compared ples with size distribution of the casein obtained with protein stabilized larger particles at radii of 150 are successfully to The mechanism of this is not yet to smaller values. 30 good agreement disintegration particle with shoulders up to 1000 nm disintegration If the emulsion is diluted the maximum of the size distribution is shifted radius. is were For the undiluted 29. This is in radius is considerable effort has been made in the past to find dialysed whey, skimmed milk and a prerequisite suitable diluent which does not affect the micelles. the nm removal of calcium from the solvent either due to As dilution has been [56]. dilution a at 140 size, which again supports literature, 1.2:1 for the are with the dilution of 1:1000. remaining particle class (see figure 28). of the casein micelles upon dilution previous reports sample classes. clearly demonstrate multiple scattering size distribution drastically. in a again clearly particles. that a dilution of sam¬ light scattering experiment can 8.3 67 Results and Discussion 10000 10000 (nm) radius Figure 29: Particle size distribution etable oil. For details see of a protein stabilized emulsion based particle librium a represents a major im¬ quantitative characterization of the undisturbed 'native' size distribution in natural milk believe that this veg¬ text. It is obvious that the 3d cross-correlation instrument provement and allows for on technique opens properties, dynamic up new as as in artificial emulsions. We thus possibilities behaviour and that could be of considerable well importance stability for a in the of investigation of the equi¬ complex particle suspensions variety of industrial applications. 68 8 INFLUENCE OF DILUTION ON THE PARTICLE SIZES IN MILK 0.2- 0.15- — master sizer auto-correlation 3 0.1- 0.05- / -f^ 10 y v 7J \ '"I l 100 10000 1000 100000 1000000 0.2master sizer 0.15- cross-correlation 3 0.1 0.05- 10 100 1000 radius Figure 30: sion based Intensity weighted particle on vegetable oil. For details size distribution see 100000 10000 1000000 (nm) text. of a protein stabilized emul¬ 69 Protein Stabilized Emulsions 9 i i Introduction 9.1 In chapters 6 and 7 high turbidity by a we have shown that of means particle 3d cross-correlation instrument. is also applicable been shown that due to We dilution, in the Chapter emulsions, which 8 then demonstrates that this composition with respect to size are potential of such technique It has undiluted milk. as complex systems, particle with example for size distribution. step further and investigate the possibilities in characterizing of distribution, stability As model systems light scattering. of means size distribution and interaction leads to artificial results in the measured complex systems by able to characterize model systems of real world systems such complex changes even one go now to we are great importance in and interaction whey protein stabilized choose we industry as potential well as in general research [59, 60]. Emulsions various industrial name are of gels are a only a widely occur for fields, in nature, and particular importance as one phase surfaces, emulsions are are requires be studied. a During From liquid dispersions liquids in the continuous phase. unstable. The two the emulsification process as for phases separate example detergents proteins or the stability layer of with proteins is adsorbed on the To proteins droplet droplets. surface which increases of the emulsion due to steric and electrostatic stabilization. Materials and Methods 9.2 9.2.1 The a new lower the surface tension and therefore reduce the amount of energy needed for the formation of the Furthermore to immiscible Basically two lot of energy for the formation of the such in industry, to by van der Waals interaction between the droplets. phase separation, stabilizing agents added. [61]. and in food products stabilized emulsions which droplets dispersed therrnodynamically time due to coalescence driven avoid can builds small Since the emulsification process whey protein on food model systems wide range of microstfuctures mixed where the basis of many are example paints, pharmaceuticals chapter we focus few. In this they Experimental Sef-Up light scattering experiments strument described in 5. were performed using the 3d cross-correlation in¬ PROTEIN STABILIZED EMULSIONS 9 70 9.2.2 Materials For the preparation Isolates, Sueur, MN, USA) Le content of the emulsions 89 was the as stabilizing protein. The total % consisting of the three components /?-lactoglobulin (15 %) lactalbumin used was whey protein BIPRO (Le Sueur commercial a and (5 %). albumin serum (79 %), Less than 10 % of the (Morgia) denaturated. As the oil weiused soya oil with density of a protein 915 a- protein is kg/m3 at 20°C. Methods 9.2.3 Preparation of the Protein Solution without further modification large particles, which aqueous solution of the an probably BIPRO purified prior was solution of 10% BIPRO shifted with 0.1 N HCl Because the individual urated proteins, only at 5000 g in order to which salt removed with of the was now purified protein magnetic agitation adjusted using Emulsion weight) a the the mixture clear, with the the three an protein excess Then the to pH was points of the but most of the denat¬ centrifuged adjusted the protein components. in an ultracentrifuge pH of the remaining 7 with 0.1 N NaOH. The of deionized water and the preparation of the protein solution 3 % so¬ by weight dissolved in deionized water under moderate was Small deviations from Emulsions protein solution. homogenization with weie pH 7 of the solution piepared by mixing The mixture then immediately homogenizer (Modell H5000) were afterwards was (20 % by prehomogenized homogenized using head pressure of 80 bar. a soya oil a with laboratory Two passages were process. Light Scattering Experiments of was an 0.1 N HCl. commercial mixer and means was emulsion, of the solution pH match the isoelectric larger aggiegates. for 1-2 hours. Preparation done for the exactly dialysis against lyophylized. For was points of The solution then almost a not and the prepared, small amount of the native a contains of the emulsion. An aqueous preparation the isoelectric remove solution, lution was pH of the solution did protein aggregates. was to the by1 weight near Bipro protein also the measured size distribution of the particles on studies had shown that aggregates of denaturated protein. To avoid are influence from these protein Light scattering dynamic light scattering Particle size distributions at a were determined by temperature of 25°C. Multiple scattering 71 Materials and Methods 9.2 effects due to the high turbidity technique. correlation of the emulsions Measurements were were suppressed using duration each were used. Three was taken, s > inside the were Investigations a scattered multiply (Hellma) angle [51]. 8.2.3 and chapter reasonable a adjusted were to values of the whole range of measured inverse The dynamic light scattering transformation. Laplace size distributions resulting a product of the P(q) S(q). ~ While the differential particle scribes the interactions between the section cross form factor droplets, da(q)jdVl depends cross- general the on is obtained factor, i. e. size, shape the static structure factor de¬ particles. Basically P(q) which in particle interactions, the intercept of part of Is which is singly scattered. the and the internal structure of the emulsion the absence of The measured measurements. form factor and the static structure particle performed were contains contributions of different orders j directly gives single scattering After correction the potential is corrected with the reduced light, which function, correlation do~(q)/dQ, cell multi scattering intensity Is, which which is s highly concentrated samples of the emulsions in terms of interaction with combined static and of to 300 averaged. then average with the functions, covering analysed using The routine is described in were even rectangular sample 200 pm. Each set of correlation scattering angles, In order to obtain scattering angles 0. of the cross-correlation function light paths the s where the duration of the measurements increases with the concentration, at different intercept of As solvent for the by weight. correlation functions of 120 cross- cross- protein stabilized emulsions done with different concentrations from 0.01 % to 10 % oil content dilution deionized water the 3d can be measured in is fulfilled with highly diluted i samples. But, tions concentrations hereby, strength lasting total known to are at least as s were a electrostatic, done in the and the Another with the DLS results are of direct and reduced range from 0 intercept possibility = by 20° to 0 = 120° every 2°. The to obtain the differential a calculation of In this step we profit interaction effects due to interactions. the ionic of the cross-correlation function consists in according polydispersity. hydrodynamic change Three measurements, each P(q) dynamic light scattering experiment much less affected a Particle interac¬ subsequently by increasing by adding NaCl. scattering angle distribution measured with,the theory are angular function of the section. react upon dilution with the measurement of the structure factor. scattering intensity as possibly form factors need to be determined also at the of the emulsion to 50 mM 30 analysed cross emulsions distribution, p'article of their size same as were scattering from the size and using Mie from the fact that the a partial cancellation PROTEIN STABILIZED EMULSIONS 9 72 Results and Discussion 9.3 Size Distribution 9.3.1 Size distributions of the emulsion tions diluted from The results weight. and 1.5 % by mass were from 90 droplets nm up to 700 highest two a nm radius of r peak is now sizes remains. sions are to 180 significant changes, auto-correlation experiments completely expected, as even highest the dilution measured, |a radii, a where the position of the large particle shoulder to at high be orders of diluted sample for such required magnitude higher Although the dilution measure As for 'normal' dilutions. with 0.01 % oil is still experiments would lead to However, with cross-correlation if the 'natural' concentration cannot be even small % and 5 % (10 to their size distribution. respect wrong results for the size distribution. experiments, %, A broad distribution nm. the undiluted emulsion with 20 % oil content is too turbid to too turbid to be only 1 experiments show clearly that whey protein stabilized emul¬ not stable upon dilution with series shows by in radius is visible. Further dilution of the located at radii lower than 100 nm, and These %, oil content of 5 an concentrations = emulsion then shifts the size distribution to smaller main content measured. The dilution series first shows maximum located at peak protein A maximum concentration of 10 % oil 31. distribution for the in the size with the of oil figure shown in are with 20 % oil and 3 % present set-up. Further diluted samples 0.1 % and 0.01 % changes prepared emulsion measured for different concentra¬ were content could be measured with the 3d cross-correlation instru¬ protein ment in the oil) an droplets the measured, concen¬ than for auto-correlation measurements, tration can and therefore expect the measured size distribution to be close to the 'real' size we distribution of the undiluted indicate that the series, which dilution first before it starts to Without aiming sample. This assumption change higher at to describe the distribution which needs further which in an principle can important value sions. In droplet with size previous for distributions, the studies the surface diluted a samples. as of this effect of the dilution investigations, example in on quantities area was cumulant fit of such as the obtained from a coverage and typically findings, area is needed as stability of emul¬ calculated from it is worth droplets surface area, droplet dynamic light scattering our the size on the modification of the oil study of protein In view of the dilution. be calculated from DLS results. The surface size obtained from highly clearly supported by size distribution remains constant droplet reason upon dilution has serious consequences is average an data measured pointing light scattering measurement, are out that intensity 9.3 73 Results and Discussion 3 a> S _3 "o !» 100 10000 1000 radius (nm) Figure 31: Particle size distributions stabilized with 3 % see text. whey protein of in water an emulsion consisting of for different steps of 20 % soya oil dilution. For details weighted. as PROTEIN STABILIZED EMULSIONS 9 74 This means particlel function of the a dominate the size size distribution reflects the scattered [the scattering fit, is therefore distribution, weighted by investigated, a which due to the ume theory. angle while such analysis an tional auto-correlation measurements important point the emulsion. to consider is the From a on can particles. samples diluted face allow the Such area. It is thus where one can experiments only hope from a The effect of dilution a average particle highly diluted at the same on This the vol¬ yields goniometer system, that the can be the second specific surface area surface to volume ratio of larger slightly or reasonable estimate of the total sur¬ with cross-correlation schemes that the size distribution of the form sample, facto^ changes it is as measurements of concentration a's suppressed. are sample by adding care particle dilution, P(q) done. Because S(q) Is(q) and interactions. ~ emulsion has Because the can't be measured with P(q) a then has to be measured P(q)S(q), particle Two routes for the measurement of the concentrations although with protein stabilized normally interactions have particle form factor at investigated. First electrostatic interactions of the be scattering angles. serious consequences for the determination of higher can Interactions 9.3.2 to be strongly P(q,r) where measurement with undiluted to obtain size distribution at different as by calculating be obtained effectively suppressing multiple scattering and performing droplet such polydisperse samples of we see only possible are cumulant in the size distribution upon dilution of change increases with dilution. This is caused due to the the smaller on be used in combination with tradi¬ classical a distribution histogram area also Laplace transformation used inverse distribution, from which also the surface However, can clearly improved approach. a depends would therefore area l/(r6P(q,r))Gi(q,r) = The multi form factor polydisperse samples, For Better results area. experiments represents obtained. particle example obtained from the for as intensity Is r6P(q), larger particles strongly ~ calculation of the surface density distribution Gn(r) calculated with Mie in these size, large particles. the underestimate the total surface the number Is(q) size. Because vector. An average the the emulsion that can be screened with salt. The emulsion is then has to be taken as higher (0.01%, increased ionic expected the size distribution may weaker electrostatic stabilization at at three different concentrations an to be change hard-sphere like, in response to the salt content. Emulsions 0.1% and 1% oil) strength were measured with deionized water and 9.3 Results and Discussion with a mM/1 50 solution the ratio of the as both intensities figure no corrected for were structure in the of the Ornstein Zernike 0.4 from = fitting a was charge factor, S(q) periment. Due to P(q) partial1 a Assuming a coefficient of the For the calculation of the tribution can form factor In can P(q) 33 of the particles and, for particle than a conditions for the transformation DLS a much less affected are ex¬ by in¬ the measured collective where D0 is the diffusion distribution, histogram. Using Mie-theory is1 quite or the continuous the average particle clearly required In general factor of itwo from signal-to-noise provides improved also a on are in is very sensitive to the size the relative volume fractions of attempt to quantitatively scattering amplitudes Laplace ratio. Is(q) to precise method for the determination in any relative compared Calculated and measured data remarkable since size classes. Therefore from DLS data. not better concentrations hydrodynamic interactions, 1-4$), Schultz a polydisperse systems, of the size distribution is Is(q) higher unity. form factor either the measured size dis¬ scattering intensity. agreement. This the individual agreement with calculated from the size distribution is shown the measured normalized excellent a + values then be calculated. can figure particle example by replaced by be form factor at D0(l = 60 nm, = interactions and $ is the volume fraction of the particles without be described for (r small deviations from hard-sphere like behaviour particles. distribution only DLS experiment diffusion coefficient Do behaves like Dq closure Rogers-Young experimental data), typical shows particle for the S(q) theoretically the using cancellation of direct and a that there is from the size distribution measured in measured size distributions j with teraction effects. means area, and 0.5 mM salt content. In The second route to determine the calculation of 1, that = measured size distribution Schultz distribution to the the measured static structure a calculated equation from the of 250 nm2 for the surface consists in S(q) find have also tried to estimate S(q) with 1 % oil content. is shown in multiple scattering and turbidity, we where due to electrostatic interactions. In addition to sample experimental approach, 'we sample salt, intensities measured without and with scattering calculated S(q), The static structure factor solvent. as In the accessible q-range 32. regular this cr 75 inversion However, results for the methods, the multi particle can even angle calculate be obtained under ideal inverse Laplace size distribution which are the basis for these calculations. This size now allows distributions, colloidal us for the first time to obtain interaction effects and suspensions such as stability emulsions and thus a of consistent highly perform picture of concentrated for example particle complex an in-situ 76 PROTEIN STABILIZED EMULSIONS 9 J.. J- A 1- A A A AA A "Aa A (',A -, , „A.» , ,aa.A(.A /W ^-I.uujaav'^—ft^tfWfti^tr' . A 0.5- 0- 1 ' ' 1 ' ' ' ' ' 1 ' ' ' 1 ' , . , 1.5 0.005 0.015 0.01 q Figure 32: Static structure actions. A: 0.01 investigation wide of %, o; factor determination 0.1\%, stability and D; 1 0.02 0.025 (1/nm) via screening of electrostatic inter¬ % oil aggregation under realistic conditions relevant for variety of commercially important systems. a Results and Discussion] 9.3 77 1 0.1-d 0 01 0.001 0 0001 0 0.005 0 01 0 005 0 01 q Figure 33: Normalized tribution, symbols: measured) for different : %. 0 02 0 025 0 015 0.02 0 025 (1/nm) scattering intensity (solid i 1 0 015 line: calculated from oil concentrations: A: 0.01 the size dis- %, o: 0.1 %, 78 9 PROTEIN STABILIZED EMULSIONS 79 Outlook 10 high turbidity tems of mation a DLS of the quantitatively be recovered with such can multiple can using cross-correlation techniques colloidal that clearly This work demonstrates experiment total scattered also SLS measurements can intensity. It is compared when Therefore it Another tance of commercially to be used also in can amounts of multiply example scattering angles factor have scattering scattered minimum, a and multiple scattering can also where the using the direct high stability in dependence scattered to single and is relatively easy to instruments. light scattering is the clear demonstration of the with can be particle influence strongly instrument, be avoided is industrial environment. light With the 3d data. a working when implemented technique the ratio of available normal important result of this thesis multiple scattering at an on strong suppression of shown that the 3d cross-correlation in¬ particularly strument constructed in this work possesses align be done of the cross-correlation function intercept due to the experiments the cross-correlation light. Although scattered A maximum of infor¬ investigated. be sys¬ on quite present under these form factor the other Significant conditions, for the static structure or quantitative analysis a of the light such influences of hand, it is clear that the instrument is easily. Finally, not restricted to 3d cross-correlation dilute systems. impor¬ experiments but can also be used in normal auto-correlation mode. Based on the experience instruments has design. As infrared regime a now new emerged, will be used samples spectrometers will which will have as to the even open light generation an dynamic properties systems that be studied with source, thus and of 3d cross-correlation even more higher turbidity new of the static and can a new feature modern diode lasers with the range of measurable that these with this work compact and robust wavelength considerably extending or near the concentration. 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Sein seine exzellenten Ideen und die stete Diskussionsbereitschaft persönlicher Einsatz, haben Peter bedanken, beigetragen. der Arbeit entscheidend Gelingen Bedanken möchte ich Anregungen und sein Engagement für dieses Übernahme des Korrefereates. Ebenso danke ich mich auch bei Heribert Watzke für seine Projekt bei der Nestlé sowie für die Ludwig Gauckler für seine spontane Bereitschaft, das Korreferat zu übernehmen. Bei meinen Mitstreitern während der Dissertation mochte ich mich besonders bedanken. Götz Jerke hat mir den Einstieg in die Welt der Kolloide und der Licht¬ streuung erleichtert. Luigi Cannavaciuolo konnte oft puter wieder einmal nicht das taten was genug weiterhelfen, wenn Com¬ sie sollten. Auch Cornelia Sommer und Sara Romer dürfen auf keinen Fall unerwähnt bleiben. Durch ihrer aller stete Hilfs- und Diskussionsbereitschaft wurde vieles einfacher. Mein Dank te auch geht Zusammenarbeit, ebenso terstützung konnte ich abwechslungsreiche an Thomas Gisler für seine wertvollen an Tips und die gu¬ Jerome Crassous und Martin Leser. Auf ihre Un¬ stets zählen. Mit Sabine Hilger und interessante Feldwoche im verbindet mich eine besonders bei der die Tessin, Lichtstreuung auch einmal die freie Natur erleben durfte. Rolf Weber und Horst Seinecke bin ich der Konstruktion und dem Bau der Probleme ner nicht waren der Suche nach dem für dagegen wenn Leitfähigkeitsmessgerät, Gefriertrockner gedankt. Technologie aufgehoben; Elektronische einmal ein Rech¬ konnten Harald Lehmann und Karel Zeemann helfen. Bei mehr konnte ich mich auf die Hilfe ler Geduld sei Lichtstreuapparatur verpflichtet. bei Max Wohlwend gut funktionierte, besonderem Dank für die Hilfe bei zu von Eveline Blöchliger und dergleichen Dinge immer verlassen. Ihrer al¬ Diese Arbeit wurde durch die Nestec SA und die Kommision und Innovation (KTI) finanziell gefördert. Zum Abschluss möchte ich mich bei meinen Eltern bedanken. Ohne ihre Un¬ terstützung hätte ich nicht studieren können. Lebenslauf Name: Claus Urban Geburtstag: 14. Mai 1965 Geburtsort: Karlsruhe, Deutschland Schulbildung: 1971 1976 - - Hauptschule in Karlsruhe 1976 Grund- und 1982 Realschule in Karlsruhe mit dem Abschluss der Mittleren Reife 1985 - Technische Oberschule in Karlsruhe 1987 Abschluss: Beruflicher 1982 - Fachgebundene Hochschulreife Werdegang: 1985 Ausbildung zum Physiklaboranten Bundesforschungsanstalt an Ernährung für der in Karlsruhe 1988 - 1995 Studium der - 09/1994 der Universität Karls¬ (TH) ruhe 03/1993 Physik an Diplomarbeit: Optimierung genschaften des der Materialei¬ Hochtemperatursupraleiters YBa2Cu307-x hinsichtlich der Verwendung in 1991 - 1995 magnetischen Lagern Technische Dokumentation im Reinisch - Ingenieurbüro Technische Dokumentation in Bretten 11/1995 - 03/1999 Studium mere der schule zum Doktorat am Eidgenössischen (ETH) for Optic a Poly¬ Technischen Hoch¬ Zürich Thema der Dissertation: ber Institut für Based Development of Fi¬ Dynamic Light Scattering Characterization of Turbid Suspensions