Download Material encapsulation and transport in core–shell micro/nanofibers

FEATURE ARTICLE
www.rsc.org/materials | Journal of Materials Chemistry
Material encapsulation and transport in core–shell micro/nanofibers,
polymer and carbon nanotubes and micro/nanochannels
A. L. Yarin,*a E. Zussman,b J. H. Wendorffc and A. Greinerc
Received 18th December 2006, Accepted 30th March 2007
First published as an Advance Article on the web 24th April 2007
DOI: 10.1039/b618508h
In this article, we review recent work on the co-electrospinning of polymer core–shell nanofibers
and the manufacture of hollow nanotubes. The encapsulation and release of bioactive compounds
from co-electrospun core–shell fibers is considered next, bearing in mind such applications as
sensors and drug release. Then, nanofluidic phenomena in nanotubes made via co-electrospinning
(as well as via the other processes) are discussed. We also consider dielectrophoresis in
microchannels as a possible tool for the separation of viruses, nanoparticles and macromolecules.
I Introduction
Electrospinning of polymer nanofibers is part of the field of
polymer solution electrohydrodynamics.1 The technique has
attracted significant attention in the last decade, since it allows
for a straightforward, relatively easy and cheap method of
manufacturing polymer nanofibers. The process involves
interesting physical phenomena and the resulting nanofibers
are expected to find numerous practical applications because
of their huge surface area, length, physical properties and
relative ease of chemical and biological functionalization.
Recently, a new branch of electrospinning, named co-electrospinning, emerged.2 Co-electrospinning allows for the manufacture of core–shell nanofibers. This process leads to
encapsulation of the core material (not necessarily polymeric)
which is potentially beneficial for the storage and drug delivery
a
Department of Mechanical and Industrial Engineering, University of
Illinois at Chicago, Chicago, IL 60607-7022, USA.
E-mail: [email protected]
b
Faculty of Mechanical Engineering-Israel Institute of Technology,
Haifa 32000, Israel
c
Department of Chemistry and Center of Material Science, PhilippsUniversity Marburg, Germany
Dr Alexander Yarin received his
PhD and Habilitation in physics
and mathematics from the
Institute for Problems in
Mechanics of the USSR
Academy of Sciences. He was a
professor at the Israel Institute of
Technology (Technion). At present he is a professor at the
University of Illinois at Chicago.
His research interests include the
hydrodynamics of flows with
free surfaces (jets, films and
droplets), rheology and hydrodynamics of non-Newtonian
Alexander Yarin
(e.g. polymeric) liquids, combustion and nanotechnology. Currently his research activities are
centered on electrospinning and co-electrospinning of polymer
This journal is ß The Royal Society of Chemistry 2007
of bioactive agents. A single-step post-processing of core–shell
fibers allows one to dispense with a core if a hollow nano- or
microtube is needed. At the same post-processing step, the
shell material can be carbonized or calcinated. The resulting
nano- and microtubes are unique in their length—which might
reach several centimeters. The length of the tubes made via
co-electrospinning allows their easy manipulation and integration in nano- and microdevices. Nano- and microfluidics in
such devices is challenging and promises the manipulation,
orientation and segregation of macromolecules, proteins,
viruses, bacteria and other microscopic objects.
In the present article we review the current state of the art of
the co-electrospinning process and post-processing of core–
shell fibers and hollow tubes (section II). The encapsulation
and release of biologically active agents in core–shell fibers and
their possible application for drug release and sensors are
discussed in section III. Liquid transport and manipulation of
particulates inside polymer and carbon nanotubes are considered in section IV. The general idea and design of a
microchannel-based device, dielectrophoretic quadrupole
lens, DQL, is outlined in sections V and VI. In the following
sections, DQL operation and efficacy are analysed. In
particular, the dielectrophoretic diffusion equation is derived
nanofibers and their applications,
suspensions and emulsions of
nanoparticles, nanofluidics and
coating of nanoparticles in lowpressure plasma.
Dr Eyal Zussman is a professor
at the Department of Mechanical Engineering at the TechnionIsrael Institute of Technology.
He received his DSc degree in
Mechanical Engineering from
the Technion. He worked as a
post-doctoral associate at the
Technical University of Berlin,
Eyal Zussman
Germany. Dr Zussman’s main
areas of research are nanotechnology and polymer processing,
electrospinning, nano-assembly and material characterization.
J. Mater. Chem., 2007, 17, 2585–2599 | 2585
in section VII. Based on it, the mass transfer of the dielectrophoretic particles (e.g., viruses) through the interface is
described in section VIII. The numerical estimates in section
IX show that under realistic conditions DQL can enhance the
interfacial mass flux by a factor of 100. Conclusions are drawn,
as well as perspectives are discussed, in section X. The main
aim of the present article is in the exposition of the whole
spectrum, beginning from the technological and scientific
aspects of manufacturing of long nano- and microchannels
with encapsulated biologically active agents inside, to fluidic
manipulation, transport and release in the existing and potential nano- and microfluidic devices. The article reviews the
existing literature, as well as contains a number of the original,
as yet unpublished results. The latter are discussed in full detail.
II Co-electrospinning of core–shell polymer micro/
nanofibers and manufacturing nanotubes
1
Advanced techniques, such as electrospinning and co-electrospinning,2 have recently been established to yield nanofibers
and core–shell fibers from natural and synthetic polymers with
diameters as small as a few nanometers. In addition, core–shell
fibers can be produced via post-treatment of monolithic
electrospun nanofibers used as templates. A polymer shell
can be deposited via chemical vapor deposition, CVD3 (tubes
by a fiber template process—TUFT), whereas metal shells can
be either deposited by electroless plating,4a,b or sputtering.4c If
needed, the third stage, heat treatment, is used to eliminate the
template core and make hollow nanotubes. On the other hand,
co-electrospinning allows single-step formation of core–shell
fibers, whereas hollow tubes can be obtained at the second
stage: heat treatment or chemical withdrawal. Co-electrospinning allows encapsulation of catalytic and magnetic nanoparticles, chromophores, enzymes, proteins and cell growth
factors directly during the process.5 In co-electrospinning, a
syringe with two compartments containing different polymer
Dr Joachim Wendorff received
his PhD in physics from the
Philipps-Universität Marburg,
Germany. He was a postdoc
at the University of
Massachusetts, Amherst, USA
and received his Habilitation
from the University of Mainz,
Germany. He is a professor at
Philipps-Universität Marburg,
Germany. His research interests include polymers and polymer hybrids in nanotechnology,
in particular: fibers, tubes and
rods, preparation techniques
Joachim Wendorff
and applications; polymers for
medical applications: tissue engineering, surface modification of
implants, drug delivery; opto-electronic properties of low molar
mass and polymer liquid crystals and functional polymers;
structure and properties of polymer blends, polymer interfaces
and ordered glasses; computer modelling.
2586 | J. Mater. Chem., 2007, 17, 2585–2599
Fig. 1 A double-compartment plastic syringe for co-electrospinning
features separate supplies of core and shell materials. E 2003 WileyVCH. Used with permission.
solutions or a polymer solution (shell) and a non-polymeric
liquid or powder (core) is used to initiate a core–shell jet
(Fig. 1). At the exit of the core–shell needle attached to the
two-compartment syringe appears a core–shell droplet. Being
subjected to a sufficiently strong electric field, it issues a
compound jet, which undergoes the electrically-driven bending
instability characteristic of the ordinary electrospinning
process.1 Strong jet stretching, resulting from the bending
instability, is accompanied by enormous jet thinning and rapid
solvent evaporation, with solidified core–shell nanofibers
depositing on a counter-electrode.
Compound nanofibers co-electrospun from PSU–PEO
[poly(sulfone)–poly(ethylene oxide)] solutions had an outer
diameter on the order of 60 nm, a core diameter of about 40 nm
and a relatively smooth core–shell interface, as apparent from
Dr Andreas Greiner received
his PhD and Habilitation in
chemistry from PhilippsU n i v e r s i t a¨ t M a r b u r g ,
Germany. He was a postdoc
at the University of California,
Santa Barbara, USA. At present he is a professor at
Philipps-Universität Marburg,
Germany. His research interests include: monomer and
polymer synthesis, functional
polymers, metal catalysis of
polymerizations, modern reaction techniques (vapor phase
Andreas Greiner
deposition polymerizations,
microreaction, microwave), structure–property relationships of
polymers, designed polymer morphologies by controlled polymerizations, liquid crystalline polymers, confinement structures
(carbon nanotubes, polymer nanotubes, and polymer nanofibers), polymers for medical, optical, and microelectronic
applications and sensors, advanced polymer processing techniques (CVD, electrospinning, TUFT, and WASTE-process).
This journal is ß The Royal Society of Chemistry 2007
Fig. 2 TEM micrograph of a core–shell nanofiber. The core and shell
solutions are PSU and PEO, respectively. E 2003 Wiley-VCH. Used
with permission.
Fig. 2. The co-electrospinning process is very versatile and is
already fostering new materials design. In ref. 2a a 2 wt%
solution of PEO in chloroform and a 1 wt% solution of PDT,
poly(dodecylthiophene), in chloroform were co-electrospun as
shell and core, respectively (Fig. 3). The total fiber diameters
were about 1000 nm, whereas the diameters of the core region
were about 200 nm.
It is important to stress that the PDT used in these
experiments did not form fibers by itself in electrospinning,
due to its low molecular weight being effectively nonspinnable. However, fibers encapsulating PDT were obtained
by co-electrospinning, since the PEO shell served as a template
for the formation of PDT fibers. Co-electrospinning can also
be applied to polymer/metal salt systems. A 3 wt% PLA,
poly(L-lactide), chloroform solution was co-electrospun as a
shell with a 5 wt% solution of Pd(OAc)2 in tetrahydrofurane as
a core. In order to generate metalization, the core–shell fibers
were annealed for 2 hours at 170 uC which caused conversion
of Pd(OAc)2 in the core into elemental Pd (Fig. 4). The outer
diameter of the coaxial fibers was about 500 nm and the
Fig. 3 TEM micrograph of co-electrospun PEO (shell) and PDT
(core) fiber. E 2003 Wiley-VCH. Used with permission.
This journal is ß The Royal Society of Chemistry 2007
Fig. 4 TEM micrograph of an annealed sample of co-electrospun
(PLA) and Pd(OAc)2. E 2003 Wiley-VCH. Used with permission.
diameter of the core phase was about 60 nm. Pd(OAc)2 is
non-spinnable and does not form fiber-like structures upon
electrospinning. However, fiber-like structures can be obtained
by co-electrospinning with PLA as a shell, which results in the
one-dimensional arrangement of Pd. It is of particular interest
that non-electrospinnable materials like PDT and Pd(OAc)2
can be forced into one-dimensional arrangements by coelectrospinning using a good fiber-forming shell polymer.
As mentioned before, co-electrospinning yields a two-stage
method of fabrication of hollow nanofibers (nanotubes)
instead of the previously-used three-stage approach.3 In such
a process, co-electrosopinning is followed by a selective
removal of the core material in the core–shell fiber via selective
solvents or heat treatment at the second stage. Calcination and
pyrolysis of the electrospun sol–gel solutions or polymers
containing metal atoms in the shell transform nanotubes into
ceramic, silica and metal ones.2c,3c,6 Preparation of organic–
inorganic materials, semiconductor systems which are functionalized by a structuring process taking place on the
submicrometer scale is a promising goal of the co-electrospinning process7. Manufacturing of structured yet compact
polymer fibers with diameters down to less than ten
nanometers is also of significant interest.
A two-stage technique for producing turbostratic carbon
nanotubes via co-electrospinning of two polymer solutions—
PMMA [poly(methylmethacrylate); core] and PAN [poly(acrylonitrile); shell] was introduced in ref. 8. The core
capillary was a stainless steel needle with inner and outer
diameters of 0.42 and 0.64 mm, respectively. The shell capillary
was a plastic needle with inner and outer diameters of 1.2 and
1.75 mm, respectively. The tip of the core capillary protruded
0.3 to 1 mm below that of the shell capillary. During coelectrospinning, the solutions were subjected to an electrostatic
field of about 0.3 kV cm21, and the as-spun core–shell
nanofibers were collected on an aluminium foil that was placed
18 cm below the tip of the core needle. The carbonization
process was carried out as follows: the as-spun core–shell
nanofibers were placed on alumina substrates in a tube furnace
and stabilized in air for 30 min at 250 uC, which resulted in
thermal decomposition of the PMMA core. The fibers were
J. Mater. Chem., 2007, 17, 2585–2599 | 2587
Fig. 6 Optical image of core–shell fibers, with an outer fiber diameter
of around 7 mm and a core diameter of about 2–3 mm. E 2006 WileyVCH. Used with permission.
Fig. 5 Flow pattern in the compound droplet attached to the core–
shell spinneret with PAN solution (shell) and PMMA solution dyed
with malachite green (core). The protruding core nozzle is visible. E
2006 Wiley-VCH. Used with permission.
then carbonized by heating in nitrogen, first at 750 uC for 1 h,
and then at 1100 uC for another hour. The ramp rate was
5 uC min21 between the 250, 750 and 1100 uC plateaus.
Fig. 5 shows the typical pattern of the co-electrospinning
process close to the core–shell spinneret. The core polymer
capillary protrudes below the shell capillary. As can be seen,
the core liquid experiences a sudden increase in diameter upon
exiting the capillary tube, which may be attributed to the die
swell effect. Below the point of maximum swelling, the outer
solution forms a thin shell that attaches to the core polymer
stream. The as-spun core–shell PMMA–PAN fibers are shown
in Fig. 6. Subsequently, the collected as-spun fibers were
stabilized in air at 250 uC and then heated in stages to 1100 uC
in an inert nitrogen atmosphere as described above. PMMA in
the core was completely thermally degraded which made the
core hollow, whereas PAN in the shell carbonized, forming a
turbostratic carbon structure.8,9 Fig. 7 shows an SEM images
of several broken carbonized PAN fibers. These images clearly
demonstrate the formation of hollow tubular structures. The
average inner diameter is 500 nm (STD = 100 nm) and the
average wall thickness is 200 nm (STD = 50 nm). The core
channel is approximately concentric with the shell, with the
occasional offset probably resulting from core buckling during
the initial formation of the as-spun fibers. Fig. 7d shows a
SEM image of a sample which was collected as a uniaxiallyaligned array using the electrostatic lens technique proposed in
ref. 10. The average fracture strength of turbostratic carbon is
0.64 GPa, which shows that the nanotubes are rather strong.
These strong carbon nanotubes can be produced with lengths
of about 1 to 10 cm, while still maintaining submicron inner
and outer diameters. The ordered arrays of turbostratic carbon
nanotubes similar to the one in Fig. 7d can be used for
membrane manufacturing. Another advantage of this process8
is that it does not involve the more elaborate sol–gel
Fig. 7 (a–c) SEM images of fractured surfaces of single carbonized hollow nanofibers, (d) Aligned array of carbonized hollow nanofibers. E 2006
Wiley-VCH. Used with permission.
2588 | J. Mater. Chem., 2007, 17, 2585–2599
This journal is ß The Royal Society of Chemistry 2007
Fig. 8 Turbostratic carbon nanotubes made via co-electrospinning.
In all the monolithic fibers with no channel seen in the cross-section
the core material has not been entrained into the jet, which is a
technological drawback. E 2006 American Institute of Physics. Used
with permission.
procedures usually required for manufacturing of ceramic
nanofibers. Because of their unique characteristics, carbon
nanotubes can be used in numerous applications in medicine
(e.g., for drug delivery), for hydrogen storage with high
uptake,11 in microelectronics (as molecular wires, diodes,
field-effect transistors and single-electron transistors)12 and for
development of fiber-reinforced materials to meet demanding
weight and strength requirements.
The analysis of the thermally treated nanotubes has shown
that in several cases the original nanofibers do not possess a
core–shell structure. For example, Fig. 8 shows the turbostratic carbon nanotubes where the PMMA core was removed
using heat treatment in the post-processing step. Many
nanotubes are hollow, but several nanotubes in Fig. 8 are
monolithic and show no hollow structure. Apparently, the core
solution (PMMA) in these cases had not been entrained into
the shell (PAN), thus producing monolithic fibers. Fig. 8
visually displays the major challenge faced by co-electrospinning, namely the ultimate quality of the fiber sample. Both
experimental and theoretical results8,13 show that formation of
core–shell jets and nanotubes via co-electrospinning is greatly
facilitated when the core nozzle protrudes outside the shell
nozzle by around 50% of radius of the latter (cf. Fig. 5).
Recently, it was found that 50/50 by weight blends of
PMMA and PAN in DMF are unstable and in about a day
transform into emulsions of 100 mm PMMA–DMF droplets in
a PAN–DMF matrix. Electrospinning of such emulsions from
a single nozzle results in PMMA–PAN core–shell fibers.14a A
PMMA droplet sucked through the tip of the PAN Taylor
cone is stretched to length of about 1 m. Therefore, the core in
such fibers has practically no defects related to the switch from
one PMMA–DMF droplet to another. Being carbonized,
core–shell fibers electrospun from a single nozzle yield carbon
nanotubes similar to those produced via co-electrospinning
from the core–shell nozzle described above. It was noted that
blends of PMMA and PAN in DMF in other proportions
should result in multi-core nanofibers.14a Indeed, the latter
have been obtained when such emulsions were electrospun
from a single nozzle.14b,c Carbonization of the resulting
fibers, yielded multi-channel carbon tubes. Significant simplification of co-electrospinning to a single nozzle process,
happened at the same time when the opposite limit was
tackled, namely co-electrospinning from a bundle of parallel
nozzles located inside an outer envelope nozzle.14d After a
post-processing calcination stage, this technique resulted in
3- to 5-channel ceramic tubes.
This journal is ß The Royal Society of Chemistry 2007
The question whether solvents in core and shell solutions in
co-electrospinning should be miscible or immiscible was
discussed in ref. 2 and 6c. While the first works on coelectrospinning used miscible (in fact, identical) solvents in
the core and shell, in some others claims were made that the
process can be stabilized only when the solvents are
immiscible. This question was recently re-examined,15 and it
was shown that both miscible and immiscible solvents allow
for an uninterrupted co-electrospinning process, while in the
as-spun fibers the core–shell boundary is sharper when
solvents are immiscible.
Experiments show that under appropriate conditions, the
solvent rapidly evaporates through the polymer network that
constitutes the nanofibers undergoing electrospinning. As a
result, hollow nanofibers emerge.15,16 Coelectrospun fibers can
be also made hollow if the polymer concentration in the core is
very low, whereas volatile solvent from the core evaporates
through nanopores and other defects in the outer shell.15 Such
hollow polymer tubes are subject to a pressure difference,
with the atmospheric pressure outside being higher that the
one inside. Then, the hollow tubes can completely collapse,
resulting in ribbons16 (which approximately correspond to the
elliptic shapes), or acquire complicated non-circular crosssectional shapes.15 The Young’s modulus of the nanotube
walls can be easily determined from the photographs of their
collapsed shapes. Indeed, the well-known expression for the
critical external pressure qcr leading to a non-circular collapse
of a pipe17
Eh3 n2 {1
(1)
qcr ~
12a3 ð1{n2 Þ
can be employed. In the present case qcr = Dpcr, which is the
pressure drop at the nanotube wall, Dpcr # l atm. Young’s
modulus is denoted by E, Poisson’s ratio n should be taken
equal to 1/2, since polymers can be roughly assumed to be
incompressible. The tube wall thickness is denoted by h, and
the cross-sectional radius of the hollow tube before collapse is
denoted by a. The azimuthal wave-number n corresponds to
collapse patterns seen on the photographs. For example, for
flattened (elliptical) cross-sections n = 2 and eqn (1) yields
E~
3q3
Dpcr
h3
(2)
Taking Dpcr = l atm = 105 Pa and a/h = 10, we obtain
E = 3 6 108 Pa = 0.3 GPa, which is comparable with the
values of Young’s modulus for polymers (known to be of the
order of 1 GPa).
III Encapsulation and release of bioactive agents
from core–shell nanofibers
A number of bioactive agents have already been encapsulated
in nanofibers (or could be potentially encapsulated). These
include drugs, proteins and enzymes, and the release rates
of different molecular compounds from electrospun and
co-electrospun fibers have been studied in a number of
experiments.18 As basic polymers for electrospinning and coelectrospinning (of the shell) for biomedical applications use is
J. Mater. Chem., 2007, 17, 2585–2599 | 2589
typically made of solutions of biocompatible, sufficiently
stable polymers with mechanical properties in the solid state
comparable with those of soft tissues, for example PCL
[poly(caprolactone)]. Several possible methods can be, in
principle, employed to make monolithic and core–shell nanofibers with embedded bioactive agents. They are the following:
(i) Host/guest electrospinning of monolithic nanofibers
An aqueous solution of a bioactive agent is mixed with a
polymer and electrospun as nanofibers. In this method, a
spinnable polymer solution plays the role of the host, whereas
a non-spinnable solution of a bioactive agent is the guest. In
many cases a non-aqueous polymer solution is a must. Then,
the resulting nanofibers will contain water inclusions with a
bioactive agent.19a The main question here is whether the
embedded bioactive agent will survive the electrospinning
process and retain its biological properties after encountering
non-aqueous solvents. Some results indicate that there are
cases where the bioactivity of proteins is not altered by contact
with various solvents during electrospinning. For example,
bacteriorhodopsin, enzymes (e.g., bovine serum albumin), and
albumin conjugated with fluorescein isothiocyanate were
successfully immobilized in the electrospun nanofibers and
retained their activity.5 Electrospun biopolymers, such as
collagen types I, II and III, fibrinogen, elastin and chitosan,19b,c,d also retained bioactivity and have gained a great deal
of attention because they can be used to fabricate biomimetic
scaffolds for tissue engineering or wound dressing. Human
b-nerve growth factor (NGF), stabilized with a carrier protein
[bovine serum albumin (BSA) dissolved in phosphate buffered
saline (PBS)], was mixed with a solution of a copolymer of
e-caprolactone and ethyl ethylene phosphate (PCLEEP) in
dichloromethane and electrospun as nanofibers.18b NGF was
released via diffusion from the electrospun nanofibers for at
least three months and retained its bioactivity. DNA has been
encapsulated for potential therapeutic applications in gene
therapy.19e It was found that plasmid DNA released directly
from the electrospun scaffold was indeed intact, capable of
transforming cells, and still encoded the alpha portion of the
enzyme b-galactosidase. Filamentous bacterial viruses suspended in polymer solution were electrospun and found to
remain viable when examined immediately and some time after
electrospinning.19f,g
(ii) Co-electrospinning of core–shell nanofibers
Co-electrospinning of core–shell nanofibers allows one to
diminish the direct contact of bioactive agents with the
potentially dangerous solvents of the spinnable polymer. In
such a process, the core contains an aqueous solution of a
bioactive agent and shell contains a polymer in a non-aqueous
solvent. Physical contact between the core aqueous solution
containing bioactive agent and the shell polymer solution
containing its solvents will be minimal, only at the core–shell
interface. Co-electrospinning of core–shell fibers with coreand shell-containing aqueous solutions is a particular example
of this method. In this case no potentially-detrimental solvents
are involved in the system. Non-spinnable aqueous solutions
of bioactive agents can be embedded in the core of the as-spun
2590 | J. Mater. Chem., 2007, 17, 2585–2599
core–shell nanofibers, whereas spinnable aqueous polymer
solutions [for example, an aqueous solution of poly(vinyl
alcohol), PVA] will create a shell. Core spinnability can be
significantly enhanced by adding a small amount of a watersoluble and biocompatible polymer such as PEO.
Following the general scheme of core–shell electrospinning,
drugs (an antioxidant resveratrol and an antibiotic gentamycin
sulfate) and proteins (BSA and lysozyme) were encapsulated in
nanofiber cores surrounded by PCL solution shells with
chloroform or DMF as solvents.18a,c Release profiles of drugs
and proteins were studied experimentally. In particular, it was
proven that lysozyme maintained its structure and was
bioactive. Release of proteins from the core–shell nanofibers
was accompanied by development of pores in the shell.18c
Tailoring the shell thickness, the initial porosity and its
variation with time should be a goal towards targeting an
appropriate release rate and profile. Polymer choice (molecular
weight and concentration in solution prior to co-electrospinning) in both the core and shell can be effectively used to
control the release rate. In certain cases, a non-biocompatible
polymer in the core might be the best choice for an appropriate
release rate, whereas biocompatibility could be achieved by
using a biocompatible polymer in the shell.
It is well known that there are a broad range of application
benefits from exploitation of biological species, e.g. enzymes,
proteins, viruses and bacteria, in technical areas such as optical
information technology, sensorics, catalysis, chemical synthesis or drug delivery.20 In the majority of cases these
applications require that the biological objects are immobilized
in specific carriers, and this has been achieved via adsorption,
chemical binding or by encapsulation. Carbon nanotubes,
zeolites, gold surfaces, polymer surfaces or hydrogels are
examples for the spectrum of carrier systems used for
immobilization. A major problem of this is that such types
of immobilization tend to affect the specific structure (in
particular the conformation) of the biological objects and,
thus, their functions.21
A promising approach is based on fluid compartments in
which the biological object will preserve its native conformation, its native functions and in which its rotational and
translational degrees of freedom are not suppressed completely. This fluid compartment, in turn, will have to be
immobilized within a solid carrier system. Such a carrier
system should be structured on the nanoscale, since a rapid
transport of matter into and out of the compartment is
required for most of the applications introduced above.
Nanostructured systems based on synthetic or natural polymers, and having the shape of core–shell fibers, have a lot to
offer in this context. Nanofibers offer large specific surface
areas and the number of natural or synthetic polymers
available is huge, providing a multitude of materials
appropriate for the preparation of the compartment. These
organic materials can furthermore be functionalized by
chemical, physical or via hybrid systems approaches within a
broad range.
Within this fluid compartment approach, the shell is not
only responsible for keeping the compartments localized in a
given place, but will also assume additional functions
depending on the application. In drug release systems it will
This journal is ß The Royal Society of Chemistry 2007
have to control the release kinetics, as mentioned above, and in
protein-based sensor applications it should allow the compound(s) to be detected (i.e., the analyte) to diffuse to the
proteins and out again into the environment. To obtain a rapid
response, nanostructured core–shell fibers should be used with
compartment diameters in the range of a few 100 nm (or even
less) and with a shell thickness in the range of 200 to 500 nm.
The particular architecture of the non-woven fiber assemblies
offers additional advantages, as is obvious from extended
Monte-Carlo simulations.22 The non-woven fiber assemblies
are highly porous, with a porosity of about 90%. They can
readily be permeated by viscous fluids, since all pores are
accessible and the small sizes of the pores (as well as the
corresponding high magnitude of the surfaces, as controlled by
the nanofiber diameter) allow a rapid exchange of matter
between the fluid reaction mixture and the compartments
within the fibers. The core–shell fibers can be prepared as
a non-woven fiber assembly or a set of parallel fibers or
crossbars which are placed onto a porous solid support.
Preparation of core–shell nanofiber systems containing
localized fluid environments for functional materials and the
approaches used are demonstrated in the following for core–
shell nanofibers carrying the green fluorescent protein (GFP)
as model system.5,23 It is composed of 238 amino acids and has
a compact shape with a diameter of about 2.4 nm and a length
of about 5 nm. These numbers are important with respect to a
permanent immobilization in the fibers. A correlation exists
for this protein between its conformation and its fluorescence.
This correlation has been the subject of various investigations.24 Fluorescence is absent in the denaturated state and the
denaturation can be caused by different environments such as,
for instance, in the presence of urea. One advantage of GFP is
that it transforms reversibly between the native and the
denatured conformation if the surroundings are switched. This
behaviour suggests that GFP can be used as model sensor
system for sensor applications. The signal to be detected is the
decay of the fluorescence as compounds such as, for instance,
urea are present in the environment of the fiber arrangement
and diffuse to the nanocontainers carrying GFP.
The co-electrospun fibers were made by method (ii) from a
10 wt% polycarbonate solution (shell; Mw = 64 kDa, solvent:
dichloromethane) and from a 150 mM GFP-solution (core). A
distance of 15 cm between the die of the spinning set-up
and the counter electrode was chosen along with a field of
1 kV cm21. In ref. 23 a DNA fragment encoding the eGFP was
amplified by the polymerase chain reaction (PCR) from the
vector pEGFP-N1 (Clontech, Heidelberg) and ligated into the
expression vector pET22b (Novagen, Schwalbach/Ts.) to give
plasmid pTK024. The synthetic oligonucleotides used for the
PCR reactions contained the appropriate endonuclease restriction sites and encoded a few extra amino acids added to the
termini of eGFP to give the following primary sequence:
MCFFKDELGT-eGFP-GSRSHHHHHH (calculated mass
29.2 kDa). For the expression of the eGFP protein, E. coli
BL21 cells were transformed with plasmid pTK024. A 6 mL
overnight culture of the resulting strain in LB-medium
containing 100 mg mL21 ampicillin was used to inoculate
600 mL of the same medium. Cells were grown at 37 uC and
250 rpm to an optical density (600 nm) of about 0.7. The
This journal is ß The Royal Society of Chemistry 2007
temperature was then shifted to 30 uC and the expression was
induced by the addition of isopropyl-b-D-thiogalactopyranoside to a final concentration of 0.4 mM. After 3–4 h, cells were
pelleted by centrifugation, resuspended in wash buffer (50 mM
Tris–HCl pH 8.0, 300 mM NaCl) with 5 mM imidazole, and
frozen at 280 uC. For protein purification, cells were thawed
on ice and disrupted in a French pressure cell. Insoluble
cell material was pelleted by centrifugation for 15 min at
15 000 rpm in a Sorval SS-34 rotor. The soluble cell extract
was loaded on a Ni2+–NTA agarose column (Qiagen),
previously equilibrated with 10 column volumes of wash
buffer with 5 mM imidazole. The subsequent washing steps
were performed with 10 column volumes of wash buffer with
5 mM imidazole, 5 column volumes of wash buffer with
20 mM imidazole, and 3 column volumes of wash buffer
with 40 mM imidazole. Proteins were eluted with elution
buffer (50 mM Tris–HCl pH 8.0, 300 mM NaCl, 250 mM
imidazole). The fractions containing the protein with .90%
purity at an adequate concentration were pooled and dialyzed
against PBS buffer (10 mM phosphate, 150 mM NaCl, pH 7.2)
containing 2 mM DTT and 10% (v/v) glycerol and stored at
280 uC until further use.
Fluorescence spectra were studied by an experimental set-up
described previously in ref. 25. The fibers were characterized
by a scanning electron microscope (Hitachi model 300), by a
digital optical microscope (VHX 100, Keyence Comp.) and a
fluorescence microscope (DMR Leica Comp.).
The obvious advantage of co-electrospinning for the
preparation of the biohybrid nanofibers mentioned above is
that the core can be made from low viscosity fluids as well. A
theory has been put forward which allows optimization of the
co-electrospinning process in terms of the experimental set-up
and the choice of the spinning parameters.13 It also allows
an estimate of the electric and mechanical stresses acting, for
instance, on biological objects subjected to entrainment in the
core by co-electrospinning. An important feature of coelectrospinning (with respect to the incorporation of biological
objects) is that the electric charges are practically only located
at the outer surface. Therefore, the inner droplet in the twoliquid Taylor cone (Fig. 5) and, thus, biological objects
dispersed in it, are not charged at all. They are only affected
mechanically by the predominantly viscous stresses in the
droplet. Predictions of these forces are already available
from the theoretical investigations.13 Typical mechanical
stresses which arise during electrospinning are of the order
of 102 N m22. Biological macromolecules and biological
structures can be destroyed by stresses of the order of
103–105 N m22 (ref. 19g and 26). The expectation, therefore,
is that biological objects such as proteins, viruses or bacteria
will not experience electrical stresses in co-electrospinning and
that the viscous stresses can be adjusted to stay moderate.
In any case, experiments show that biobased objects which
have been subjected to co-electrospinning are still functional.
Fig. 9a displays a microscope image of the core–shell fibers
obtained by co-electrospinning and Fig. 9b the corresponding
fluorescence microscope image. It is apparent that the GFP
in the core is able to display fluorescence, and that nanocompartments are arranged in a regular fashion along the
length of the core–shell fiber.
J. Mater. Chem., 2007, 17, 2585–2599 | 2591
Fig. 9 (a) Core-shell nanofibers with GFP in the core compartments.
(b) Fluorescence microscope image of the fibers. The shell is made
from a 10 wt% polycarbonate solution and the core from a 150 mM
GFP solution.
To test the sensor functions of such core–shell fibers, they
were brought into contact with a water environment containing urea. The observation was that the fluorescence signal
(Fig. 10a) decayed as a function of the immersion time
(Fig. 10b). A replacement of the urea solution by water causes
the fluorescence to build up reversibly.
The experimental results presented in this section have
shown that the concept of immobilization of sensitive
biological objects in fluid compartments within nanostructured
polymer core–shell fibers works in principle. The approach
sketched here used the model protein GFP in nanofiber
carriers and the aim was a sensor application. The concept
discussed here can be exploited in a variety of different
architectures and applications. The incorporation of the GFP
protein into porous membranes in a fluid environment where
the pores are covered with a permeation layer is one example
that is currently under study.
IV Liquid transport in carbon and polymer
nanotubes and encapsulation and orientation of
particulates in confinements
Encapsulation of liquids inside nanofibers and nanotubes
implies, in many applications, their further transport along the
confinement. The latter amounts, in fact, to micro- and
nanofluidics, and attracts attention due to the peculiar
transport phenomena and wide range of possible applications.27 Miniaturization results in lab-on-a-chip devices with
smaller amounts of reagents and analytes, as well as higher
2592 | J. Mater. Chem., 2007, 17, 2585–2599
Fig. 10 (a) Fluorescence spectrum of the GFP within the core–shell
fibers. (b) Decay of the fluorescence of the GFP within the core
compartments in contact with a urea solution.
reaction rates (if a device is used as a chemical reactor) due
to the higher concentrations attainable. Microfabrication
of microfluidic devices is typically complicated and expensive.
Nanofluidics follows the same trend of miniaturization,
however nanotube fabrication might be significantly simpler
and cheaper. In this section we consider three types of carbon
nanotubes (CNT): (a) traditional closed CNTs made of rolled
graphene sheets,28 (b) open amorphous CNTs made by CVD
inside pores, and (c) open turbostratic carbon nanotubes made
via co-electrospinning.
Traditional CNTs made of rolled graphene sheets are
usually considered to be hydrophobic. Single-wall carbon
nanotubes, SWCNTs, can be as narrow as 1 nm and are
assumed to be atomically smooth. In general, water in large
CNTs of 50–200 nm in diameter shows clearly distinguishable
continuum-like patterns, while only in small CNTs (of the
order of 2–5 nm or less) do continuum-like patterns
disappear.29 In SWCNTs and the smallest multi-wall carbon
nanotubes, MWCNTs, the combination of non-continuumlike behavior of the flowing medium and atomic smoothness
and hydrophobicity of the wall results in transport rates
several orders of magnitude higher than those which can be
expected according to the classical fluid mechanical results (the
Knudsen theory for rarefied gases and Poiseuille laminar flow
for continuum fluids), as demonstrated by theoretical works
based on molecular dynamics (MD) simulations30a,b and
several experimental works.30c,d,e The most probable physical
reasons for enhanced transport in these cases are related to
This journal is ß The Royal Society of Chemistry 2007
alignment of water molecules due to hydrogen bonding in
narrow confinements, and specular rather than diffusive
reflections of transferring molecules from the atomically
smooth walls. It is interesting that polymer nanopores with
diameters of 16.8 nm probably do not possess the required
atomic smoothness, as well as already being wide enough
for continuum-like behavior of transferring fluid.30f As a
result, gas diffusion in such nanopores follows the classical
Knudsen theory, whereas water flow agrees with the
Poiseuille law.30f
The hydrothermal method of CNT synthesis results in water
encapsulation inside the nanotube cavity.31 Water plugs
surrounded by vapor in CNTs with diameters of the order of
100 nm have clearly expressed interfaces and behave in an
almost continuum-like manner, even though they are strongly
affected by intermolecular forces. The experiments31 showed
that water plugs can be transferred along CNTs when observed
using a transmission electron microscope. The reason for this
is heating by the electron beam with the following vapor
condensation due to intermolecular forces.32 Modelling32
revealed the pattern shown in Fig. 11. The results show that
some material transport towards the cold end of CNT is
indeed possible, and a liquid plug is seen growing there. The
process is very slow and based on the model predictions—it is
very difficult to say whether the whole liquid plug from the
right-hand side end of the CNT in Fig. 11 can be transferred to
the cold end.
Open CVD-made nanotubes were brought into contact with
such polar liquids as water, glycerol, ethylene glycol, ethanol,
Fig. 11 Directional transport of liquid from the hot (right) to the cold
(left) end of CNT. (a) The almost steady-state temperature field.
Concentration fields are shown at t = (b) 0.3, (c) 0.4, (d) 0.5 (e) 0.6,
where t is dimensionless time with the time scale being 102 s. A deep
blue color in the concentration patterns corresponds to liquid, the
lower concentration areas to vapor. E 2005 American Institute of
Physics. Used with permission.
This journal is ß The Royal Society of Chemistry 2007
Fig. 12 Video frame sequence of capillary filling of co-electrospun
PCL tubes by silicon oil. E 2007 Wiley-VCH. Used with permission.
tetrahydrofuran (THF) and 2-propanol alcohol, and such
nonpolar liquids as cyclohexane, hexadecane, polydimethylsiloxane and fluoro-silicone, as well as with suspensions
of several of these liquids laden with 50 nm diameter of
fluorescent particles.33 Wettability-driven flows brought these
fluids into CVD-nanotubes. Liquid evaporation at an open
end of a CVD-nanotube can also contribute to the imbibition
through the other end. The flows brought fluorescent particles
into these CNTs which was visible through the transparent-tolight 15 nm-thick CNT walls.
Co-electrospun hollow PCL nanotubes were filled with
silicon oil which easily wets the PCL surface. Silicon oil was
sucked by capillary forces through the porous shell.15 The
meniscus propagation inside a hollow PCL tube recorded
in ref. 15 is shown in Fig. 12. It is emphasized that, in
contrast to regular capillary filling experiment where liquid is
supplied at the entrance of the tube,33 in ref. 15 a silicon oil
drop was placed on top of the micro-tube mat and the
penetration was through the shell pores. As a result, the
meniscus propagation laws recorded in ref. 15 and 33
significantly differ; namely, in ref. 33 it follows the
Washburn equation, L(t) = (sa?cos h?t/2g)1/2, whereas in
ref. 15 it does not (g, s and h are the liquid viscosity, surface
tension and contact angle, a the tube inner cross-sectional
radius, and L(t) is the meniscus position depending on time t).
Electrospinning was used to entrain and encapsulate
magnetic nanoparticles and carbon nanotubes in polymer
nanofibers.34 The electrical conductivity and strength of the
nanofibers are expected to be significantly improved when
single- and multi-wall carbon nanotubes are incorporated in
them. Attempts in this direction show that nanofibers
containing both SWCNTs and MWCNTs can be electrospun
from a polymer-based solution. Nanotubes were oriented and
embedded inside nanofibers during electrospinning.34f,g
Various colloidal particles, including titania nanoparticles,
quantum dots and clay particles, were encapsulated in
electrospun nanofibers.34j–o
Flows in converging microchannels resemble that in the
Taylor cone on top of the electrospun jet and represent
themselves as an effective tool for reorientation and ordering
of elongated micron-size particles. Theoretical predictions for
the orientation–distribution probability density function in
such converging flows and the corresponding experimental
results on parallel arrangement of such elongated particles as
J. Mater. Chem., 2007, 17, 2585–2599 | 2593
a Taylor–Couette apparatus,37a–d due to Dean vortices in
curved channels,37e,f due to natural convection,37g and due to
stationary d.c. streaming resulting from standing capillary
waves.37h,i The circulatory vortices described in ref. 37 enhance
particulate delivery to the interface, which builds a steep
concentration gradient there. As a result, the particulate mass
flux through the interface is enhanced, even though the
diffusion coefficient stays low. None of the opportunities
considered in ref. 37 are available in micro- and nanochannels.
Given the fact that the particles (e.g., viruses) we are going to
deal with could be uncharged and solvents could not contain
any electrolytes, the temptation is to employ the dielectrophoretic force instead of vorticity to build steeper concentration gradients at the interface. This could be achieved by DQL,
as is shown below.
Fig. 13 Alignment of rod-like Bacillus magaterium bacteria in a
converging sink/jet-like flow in a microchannel. E 2006 American
Institute of Physics. Used with permission.
CNTs and Bacillus magaterium bacteria (Fig. 13) can be found
in ref. 34f and 35.
V Microchannels as a dielectrophoretic quadrupole
lens-on-a-chip for separation of viruses,
nanoparticles and macromolecules
Microchannel flows of encapsulated suspensions can be used
for separation of particulates. For example, dielectrophoretic
phenomena recently attracted significant attention in relation
to the separation of uncharged cells, fine particles and
macromolecules. A number of the previously published results
were reviewed in ref. 36. In the present and following sections
a new microscopic fluidic device is discussed, namely a
dielectrophoretic quadrupole lens, DQL. This device should
allow for an enhanced purification of liquids from suspended
particles. In a biomedical context, we envision, for example,
the purification of blood from viruses. The general design idea
is supported by detailed calculations, which show that the
device is feasible and effective.
Purification of liquids from suspended submicron particulates is a tough engineering problem. Such particles being
practically inertia-less, they follow the flow streamlines.
For uncharged particles, the electrophoretic motion is out of
scope, and the only realistic means of extraction are those
related to their Brownian motion, i.e. diffusion. However, the
particle diffusion coefficient Dp is extremely low (y1027 to
1025 cm2 s21), as compared to that of molecular compounds
(y1021 cm2 s21). Therefore, the rate of diffusion processes
towards interfaces or surfaces where the particles can be
withdrawn/annihilated is extremely low, and mass transfer is
rather ineffective. Recently, several attempts were made to
intensify particulate mass transfer through interfaces between
two immiscible liquids in macroscopic systems.37 In those
cases, particles (proteins) were suspended in one of the liquids
and should be removed to the other through the interface. In
macroscopic two-liquid systems, mass transfer enhancement
at the interface was achieved by means of secondary
vortical circulatory flows emerging due to Taylor vortices in
2594 | J. Mater. Chem., 2007, 17, 2585–2599
VI DQL design
If two immiscible liquids would be in contact over their joint
interface with particles suspended in one of them (liquid 1),
then due to diffusion the particles will pass to the other liquid
(liquid 2). In a biomedical context, liquid 1 is, for example,
blood, the particles are viruses, and liquid 2 could contain
virus-specific antibody molecules which bind and kill the
viruses. The diffusion process is, however, extremely slow, as
explained in the previous section. The mass transfer process
can be enhanced hydrodynamically using an impingement flow
of liquids 1 and 2 (cf. Fig. 14), which will sustain a steep
gradient of viruses near the interface, and keep the diffusion
flux high enough even though the diffusion coefficient is low.
The interfacial mass flux can be further dramatically enhanced
employing dielectrophoresis. The micro-nanochannel walls
depicted in Fig. 14 should be shaped as hyperbolas and be
electrodes arranged in a quadrupole lens. They should be
subjected to a high voltage with the electrode corresponding to
the first quadrant in Fig. 14 (x . 0, y . 0) being, say, at the
electric potential Q = B*. Following the subsequent quadrants
in Fig. 14 clockwise, the potentials at the electrodes should be
2B*, B*, and 2B*. Moreover, the electric field should be ac
to eliminate any electrophoretic effects related to charges
on the particles and/or dissolved electrolytes if any. Therefore,
Fig. 14 Sketch of DQL.
This journal is ß The Royal Society of Chemistry 2007
B* = B0* exp(ivt), where v is a chosen (high) frequency.
Volumetric Joule heating is not important in micro-nanochannels, since they are dominated by surface heat removal.
Therefore, the system will effectively be isothermal even
though a high electric power is applied. The hyperbolic shapes
of the electrodes will facilitate a simple potential hydrodynamic flow field of the two impinging fluxes with blood
(liquid 1) entering the device at y = ye and a decontaminant
(liquid 2) at y = 2ye. The flow should be sustained by pumps.
The hyperbolic shapes of the electrodes will also provide an
electric field responsible for the dielectrophoretic force acting
on the viruses. If the dielectric permittivity of blood is higher
than that of the viruses, the latter will be pushed by the
dielectrophoretic force towards the interface, which can
dramatically enhance the virus transfer from blood to the
decontaminant. An array of such devices could constitute a
blood ‘‘dialysis’’ tool. Being attached to a patient, it can help
decontaminate his/her blood from viruses, or sustain their
concentration there under a certain level. Micro-devices similar
to the one sketched in Fig. 14 could also be used for protein
extraction and in many other processes requiring particulate
removal from liquid 1. They may be manufactured on a chip.
In the following sections we show that the dielectrophoretically-driven enhancement of the interfacial mass flux could be
very significant under realistic conditions.
The balance of forces acting on an inertia-less and
uncharged particle is given by
kB T+c
6pga vp {v zSd +E2 {
~0
c
where the first term is the Stokes drag force, the second is the
dielectrophoretic force of eqn (3), and the third term is the
pseudo-force corresponding to diffusion; g is the solvent
viscosity, vp and v the particle and solvent velocities,
respectively, kB Boltzmann’s constant, T temperature and c
the particle concentration.
Then, the particle velocity can be expressed from eqn (6) as
vp ~vzS1 +E2 {D
F = Sd+E2
(3)
1
Sd ~ a3 ee Ref f g
2
(4)
where Sd is given as
where ee is the dielectric permittivity of solvent, a the particle
radius, E = 2+Q is the electric field strength, the Clausius–
Mossotti factor f is
f~
ei {ee
ei z2ee
(5)
and Re{} denotes the real part. Eqn (4) and the equations
hereinafter are written using Gaussian (CGS) units. In eqn (5)
ee* and ei* are the complex permittivities of solvent and
particle, respectively. They are given as ee* = ee 2 i4pse/v and
ei* = ei 2 i4psi/v, where ei is the particle dielectric permittivity,
and se and si are the electric conductivities of solvent and
particle, respectively; i is the imaginary unit.
This journal is ß The Royal Society of Chemistry 2007
+c
c
(7)
where D = kBT/(6pga) is the particle diffusion coefficient and
S1 = Sd/(6pga).
The mass balance of the particles is given by the following
equation
Lc
z+:(cvp )~0
Lt
(8)
where t is time.
Substituting eqn (7) in eqn (8), we arrive at the following
dimensionless dielecrophoretic diffusion equation
VII Dielectrophoretic diffusion equation
Dielectric particles in electric fields polarize. The solvents
surrounding them, also being dielectrics, polarize as well. If the
dielectric permittivities of a particle and a solvent differ,
electric Maxwell stresses should arise at the particle surface. In
spatially non-uniform electric fields a non-zero net force (a
non-zero stress integral over the particle surface) appears,
which is called the dielectrophoretic force. Polarized particles
could also be viewed as electric dipoles. In spatially nonuniform electric fields, such dipoles should inevitably
experience a non-zero force, which is precisely the dielectrophoretic force F. It is given by the following expression38
(6)
Lc
z+:(cv)~+2 c{S+: c+E2
Lt
(9)
where
S~
a2
e2
ee Ref f g
2
L 12pgDL2
(10)
Eqn (9) is rendered dimensionless using the following scales:
L for the coordinates x and y (say, L = ye), e/L - for Q and e/L2
- for E (where e is proton charge), L2/D - for t, and D/L - for v.
Bars over dimensionless variables were dropped for brevity.
Particle concentration c can be taken as dimensionless by
definition or rendered dimensionless by a given characteristic
concentration. The most interesting case corresponds to S , 0
(Re{f} , 0), where the solvent dielectric permittivity is higher
than that of the particles.
VIII Mass transfer in DQL
The dimensionless electric potential in DQL is given by
Q = Bxy
(11)
where B = B*L3/e.
The solvent flow field is potential, i.e. given by the
hydrodynamic potential W = (c/2)(x2 2 y2) with c being the
rate of strain, which yields the following velocity components u
and v corresponding to the Cartesian axes x and y
u = cx, v = 2cy
(12a,b)
Note that the dimensionless rate of strain c is related with
the dimensional rate c* as c = c*L2/D.
J. Mater. Chem., 2007, 17, 2585–2599 | 2595
Eqn (11) and (12) allow calculation of the solvent velocity
field v and the electric field strength E to be substituted into
eqn (9). We consider a steady-state situation. In DQL,
similarly to the other cases involving impinging flows,39 we
expect that h2c/h2x ,, h2c/hy2and then, eqn (9) reduces to the
following form
ðczAÞx
Lc
Lc
L2 c
zð{czAÞy z2Ac~ 2
Lx
Ly
Ly
(13)
where A = 2B2S and the most interesting case corresponds to
A , 0.
Solutions of eqn (13) are subjected to the following
boundary conditions
y = 0 c = 0, y = 1 c = c0
(14a,b)
which means that we assume liquid 2 to be able to immediately
annihilate viruses entering it through the interface y = 0, ad
virus concentration at the entrance into DQL is given as c0.
Eqn (13) can be converted into the standard form
L2 c
Lc
Lc
zPðxÞy {RðxÞc~QðxÞ
Ly2
Ly
Lx
(15)
where
P(x) = c 2 A, Q(x) = (c + A)x, R(x) = 2A
(16)
The solution of the problem (15)–(16) is searched in the
form37h,39,40
ðx
PðjÞ
:
dj
W ðxÞ~2
QðjÞ
o
2x
3{1=2
ð W ðjÞW ðxÞ
e
Z~y4
dj5
QðjÞ
(17a c)
o
Substituting eqn (17) in (15), we obtain
2x
3
ð W ðjÞW ðxÞ
d2 F Z dF
e
~RðxÞF |4
z
dj5
dZ 2
2 dZ
QðjÞ
K29M(1/2 + b/2, 1/2, f2/2)]
(22)
where K19 and K29 are the integration constants, b = 2A/(c 2
A), and M(?,?,?) is Kummer’s function.42
Eqn (17b) and (20) yield Z = [2(c 2 A)]1/2y and thus f =
(c 2 A)1/2y, which yields
cðx,yÞ~cð yÞ~
ðc AÞy2
c
3 ðc AÞy2
, ,
K1 yM
exp cA 2
2
2
2
1
A 1 ðc AÞy
, ,
zK2 M z
2 cA 2
2
(23)
It is seen that the concentration field in DQL does not
depend on x.
The integration constants in eqn (23) are denoted as K1 and
K2. They can be easily found using the solution (23) and the
boundary conditions (14a,b). The result is
cðx,yÞ~cð yÞ~
ðc AÞ 1 y2
c
3 ðc AÞy2
, ,
c0 exp
yM
cA 2
2
2
c
3 ðc A Þ
, ,
=M
cA 2
2
(24)
Differentiating eqn (24), we find the concentration gradient
at the interface
Lc ðc AÞ
c
3 ðc A Þ
=M
,
,
(25)
~c
exp
0
Lyy~0
2
cA 2
2
Lc 2
c A 3=2c=ðcAÞ
~c0 pffiffiffi Cðc=ðc AÞÞ
Lyy~0
2
p
(18)
o
ðc AÞ j
‘n
ðczAÞ x
(19)
Therefore,
(26)
where C(?) is the gamma function. The latter expression yields
the flux of viruses towards liquid 2 as
2
c A 3=2c=ðcAÞ
j~ c0 pffiffiffi Cðc=ðc AÞÞ
2
p
Substituting eqn (16a,b) in eqn (17a), we find
ðx
F(f) = exp (2f2/2)[K19fM(1 + b/2, 3/ 2, f2/2) +
For (c 2 A)/2 .. 1 eqn (25) yields
c~F ðZÞ
W ðjÞ W ðxÞ~2
Eqn (21) belongs to the family of the equations related to
Whittaker’s equation.41 Its solution reads
(27)
where the flux j is rendered dimensionless by D/L.
IX Numerical estimates: the efficacy of DQL
eW ðjÞW ðxÞ
1
dj~
QðjÞ
2ðc{AÞ
(20)
o
and eqn (18) reduces with the help of eqn (16c) and (20) to the
following form
d2 F
dF
2A
zf
{
F ~0
df ðc{AÞ
df2
where f = Z/!2.
2596 | J. Mater. Chem., 2007, 17, 2585–2599
(21)
The following parameters are used to estimate the efficacy of
DQL: the length scale L = 1022 cm, the diffusion coefficient
D = 1025 cm2 s21, the strain rate c* = 1021 s21, the virus
radius a = 1025 cm, the blood viscosity g = 1022 g cm21 s21.
The corresponding velocity scale D/L = 1023 cm s21 (c*L =
1023 cm s21 as well). The electric potential parameter B*L2 =
10–1000 V. Therefore, B*= (103–105)/3 g1/2 s21 cm23/2. The
electric field strength which is of the order of B*L is of
the order of 1–100 kV cm21, which can indeed be realized
This journal is ß The Royal Society of Chemistry 2007
Fig. 15 Mass transfer enhancement in DQL.
practically. The dielectric permittivity of blood is taken as ee =
81, whereas Re{f} = 21.
The dimensionless groups corresponding to the abovementioned parameter values are c = 1 and A = 20.0486 to 486.
The normalized particulate flux of eqn (27) J = j/[2c02/!p] is
plotted in Fig. 15. Its value at A = 0 corresponds to the purely
diffusion-convective transport and is equal to 0.7071. On
the other hand, the values at A , 0 are higher due to the
dielectrophoretic-related enhancement. At A = 210c = 210, a
more than 100-fold increase in the virus flux through
the liquid/liquid interface is achieved. At lower values of A
(A , 210) the enhancement is even much higher. According to
ref. 43, diffusion coefficients of some viruses can be as low as
D = 1027 cm2 s21. With the other parameters being fixed, that
corresponds to c = 100 and A = 24.86 to 48600. Then, for
example at A = 210c = 2103, the relative enhancement
(compared to the case of A = 0) will be more than 104-fold.
The estimated values of the dielectrophoretic enhancement
look promising and show that the efficacy of DQL may be
quite high. Microfabrication methods make feasibility of
DQL quite probable. In particular, turbostratic carbon
nanotubes made via co-electrospinning might be used as
building elements.
X. Conclusion and perspectives
Electrospinning and co-electrospinning will certainly continue
to attract the attention of researchers in the fields of applied
chemistry and material sciences, applied physics, polymer
science and fluid mechanics, since they proved to be relatively
simple and cheap methods for production of micro- and
nanofibers and tubes. The basic physical mechanisms of these
processes have already been elucidated, explained and
described theoretically, however there are still numerous
technological challenges to be faced on the way to high quality
nanofibers and long nanotubes. These include tools for a
better process control to guarantee robust production of
uniform nanofibers and nanotubes with diameters about
100 nm, as well as functionalization of their outer and inner
surfaces for a growing number of applications. For example,
stimuli-responsive nanofibers and nanotubes could be
This journal is ß The Royal Society of Chemistry 2007
envisioned based on polymer blends including such polymers
as poly(N-isopropylacrylamide), PNIPAAm, which change
their conformation in response to the surrounding temperature
or pH level. PNIPAAm-based nanofibers and nanotubes can
become a key element of self-regulating stimuli-responsive
membranes and drug delivery devices.
Nanofibers with embedded drugs, proteins and growth
factors undoubtedly will be widely used for drug delivery,
wound healing and in tissue engineering. Release mechanisms
of many of these compounds are quite different from the
simple Fickian diffusion models adopted in traditional
controlled-release literature. This situation will almost
certainly lead to a revision of our ideas on release mechanisms
and incorporation of those of them which weren’t considered
before. This will also be accompanied by development of novel
types of nanofiber carriers with an extended release period
(several months), without any initial burst of drug release.
Major challenges to be addressed in the future concern
electrospinning from the melt rather than from solutions, the
extension of electrospinning to ceramic, metals and inorganic
glasses, and finally a significant technical upscaling of the
production rate, which is crucial for most of the potential
applications envisioned for electrospun functional fibers.
Nanotubes will definitely be used for storage of different
compounds including such biological materials as bacteria,
viruses, proteins and macromolecules (e.g., DNA). Then,
understanding of the filling mechanisms becomes of the utmost
importance. There are some experimental indications that
wettability is not the only possible mechanism for filling of
CVD and coelectrospun nanotubes. The goal is to achieve a
relatively dense filling by high molecular weight compounds
and it can probably be achieved using physical mechanisms
stronger than wettability.
New micro- and nanofluidic devices will almost certainly
benefit from parallel bundles of centimeter-long nanotubes
produced via co-electrospinning. They are relatively easy to
handle and can be integrated in different ultrafiltration
membranes, separators, ‘‘nanofluidic’’ interconnectors, labon-a-chip schemes and flow-through reactors. These devices
can on one hand, guarantee the micro- and nanoconfinement
required for a number of chemical and biological processes,
and on the other hand, guarantee a relatively high throughput.
All types of flow actuation in such nanotubes could be
important: wettability-driven, pressure-driven and electricallydriven (electroosmosis and all its diffusion-mingled variants).
A novel resistive-pulse DNA detection method44 presents
itself for use in the carbon nanotubes produced via coelectrospinning for DNA detection. Parallel nanotube bundles
of co-electrospun nanotubes can also become a key element
of devices delivering several immiscible compounds into a
cell, for example: two different types of growth factors.
Dielectrophoteric virus separation in devices similar to DQL
was reported in a recent paper45 and will definitely continue to
attract attention.
Acknowledgements
We gratefully acknowledge the financial support by
the VW Foundation (Programs-Komplexe Materialien:
J. Mater. Chem., 2007, 17, 2585–2599 | 2597
Verbundprojekte
der
Natur-,
Ingenieur-,
und
Biowissenschaften and the Project-Functional Composite
Nanofibers by Co-electrospinning: Functional Nano-objects
for Life Science). ALY gratefully acknowledges financial
support by the National Science Foundation through grant
NIRT CTS-0609062. The authors appreciate collaboration
and contributions of their students and postdocs R. Avrahami,
A. Bayer, A.V. Bazilevsky, L. Berkovici, R. Dersch, Y. Dror,
N. Füchtjohann, E. Katz, S. N. Reznik, W. Salalha, Z. Sun
and A. Theron, as well as collaboration with Doctors
Y. Gogotsi and C. M. Megaridis.
15
16
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18
References
1 (a) D. H. Reneker, A. L. Yarin, H. Fong and S. Koombhongse,
J. Appl. Phys., 2000, 87, 4531; (b) A. L. Yarin, S. Koombhongse
and D. H. Reneker, J. Appl. Phys., 2001, 89, 3018; (c)
M. M. Hohman, M. Shin, G. Rutledge and M. P. Brenner, Phys.
Fluids, 2001, 13, 2201; (d) M. M. Hohman, M. Shin, G. Rutledge
and M. P. Brenner, Phys. Fluids, 2001, 13, 2221; (e) A. Frenot and
I. S. Chronakis, Curr. Opin. Colloid Interface Sci., 2003, 8, 64; (f)
Z. M. Huang, Y. Z. Zhang, M. Kotaki and S. Ramakrishna,
Compos. Sci. Technol., 2003, 63, 2223; (g) Y. Dzenis, Science, 2004,
304, 1917; (h) S. Ramakrishna, K. Fujihara, W. E. Teo, T. C. Lim
and Z. Ma, An Introduction to Electrospinning of Nanofibers,
World Scientific, Singapore, 2005; (i) D. H. Reneker, A. L. Yarin,
E. Zussman and H. Xu, in Adv. Appl. Mech. 2007, 41, 43–195.
2 (a) Z. Sun, E. Zussman, A. L. Yarin, J. H. Wedorff and A. Greiner,
Adv. Mater., 2003, 15, 1929; (b) D. Li and Y. Xia, Nano Lett., 2004,
4, 933; (c) D. Li and Y. Xia, Adv. Mater., 2004, 16, 1151; (d)
Y. Zhang, Z. M. Huang, X. Xu, C. T. Lim and S. Ramakrishna,
Chem. Mater., 2004, 16, 3406; (e) J. H. Yu, S. V. Fridrikh and
G. C. Rutledge, Adv. Mater., 2004, 16, 1562; (f) I. G. Loscertales,
A. Barrero, M. Marquez, M. Spretz, R. Velarde-Ortiz and
G. Larsen, J. Am. Chem. Soc., 2004, 126, 5376; (g) M. Wang,
N. Jing, C. B. Su and J. Kameoka, Appl. Phys. Lett., 2006, 033106;
(h) D. Li, J. T. McCann, Y. Xia and M. Marquez, J. Am. Chem.
Soc., 2006, 89, 1861.
3 (a) M. Bognitzki, H. Hou, M. Ishaque, T. Frese, M. Hellwig,
C. Schwarte, A. Schaper, J. H. Wedorff and A. Greiner, Adv.
Mater., 2000, 12, 637; (b) M. Bognitzki, W. Czado, T. Frese,
A. Schaper, M. Hellwig, M. Steinhart, A. Greiner and
J. H. Wedorff, Adv. Mater., 2001, 13, 70; (c) W. Liu, M. Graham,
E. A. Evans and D. H. Reneker, J. Mater. Res., 2002, 17, 1.
4 (a) F. Ochanda and W. E. Jones, Langmuir, 2005, 21, 10791; (b)
F. Ochanda and W. E. Jones, Langmuir, 2007, 23, 795; (c)
Q. F. Wei, H. Ye, D. Y. Hou, H. B. Wang and W. D. Gao, J. Appl.
Polym. Sci., 2006, 99, 2384.
5 A. Greiner, J. H. Wedorff, A. L. Yarin and E. Zussman, Appl.
Microbiol. Biotechnol., 2006, 71, 387.
6 (a) D. Li, Y. Wang and Y. Xia, Adv. Mater., 2001, 16, 361; (b) D. Li
and Y. Xia, Nano Lett., 2004, 3, 555; (c) J. T. McCann, D. Li and
Y. Xia, J. Mater. Chem., 2005, 15, 735; (d) M. Wang, N. Jing,
C. B. Su, J. Cameoka, C. K. Chou, M. C. Hung and K. A. Chang,
Appl. Phys. Lett., 2006, 88, 033106.
7 D. Li, J. T. McCann and Y. Xia, Small, 1, 83.
8 E. Zussman, A. L. Yarin, A. V. Bazilevsky, R. Avrahami and
M. Feldman, Adv. Mater., 2006, 18, 348.
9 E. Zussman, X. Chen, W. Ding, L. Calabri, D. A. Dikin,
J. P. Quintana and R. S. Ruoff, Carbon, 2005, 43, 2178.
10 (a) A. Theron, E. Zussman and A. L. Yarin, Nanotechnology, 2001,
12, 384; (b) E. Zussman, A. Theron and A. L. Yarin, Appl. Phys.
Lett., 2003, 82, 973.
11 (a) A. C. Dillon, K. M. Jones, T. A. Bekkedahl, C. H. Kiang,
D. S. Bethune and M. J. Heben, Nature, 1997, 386, 377; (b) P. Chen,
X. Wu, J. Lin and K. L. Tan, Science, 1999, 285, 91.
12 A. Bachtold, P. Hadley, T. Nakanishi and C. Dekker, Science,
2001, 294, 1317.
13 S. N. Reznik, A. L. Yarin, E. Zussman and L. Bercovici, Phys.
Fluids, 2006, 18, 062101.
14 (a) A. V. Bazilevsky, A. L. Yarin and C. M. Megaridis, Langmuir,
2007, 23, 2311; (b) M. Peng, D. Li, L. Shen, Y. Chen, Q. Zheng and
2598 | J. Mater. Chem., 2007, 17, 2585–2599
19
20
21
22
23
24
25
26
27
H. Wang, Langmuir, 2006, 22, 9368; (c) C. Kim, Y. I. Jeong,
B. T. N. Ngoc, K. S. Yang, M. Kojima, Y. A. Kim, M. Endo and
J. W. Lee, Small, 2007, 3, 91; (d) Y. Zhao, X. Cao and L. Jiang,
J. Am. Chem. Soc., 2007, 129, 764.
Y. Dror, W. Salalha, R. Avrahami, E. Zussman, A. L. Yarin,
R. Dersch, A. Greiner and J. H. Wendorff, Small, 2007, 3, DOI:
10.1002/smll.200600536.
S. Koombhongse, W. Liu and D. H. Reneker, J. Polym. Sci.,
Polym. Phys. Ed., 2001, 39, 2598.
S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability,
McGraw-Hill, New York, 1961.
(a) Z. M. Huang, C. L. He, A. Yang, X. J. Han, J. Yin and Q. Wu,
J. Biomed. Mater. Res., 2006, 77A, 169; (b) S. Y. Chew, J. Wen,
E. Yim and K. Leong, Biomacromolecules, 2005, 6, 2017; (c)
H. Jiang, Y. Hu, Y. Li, P. Zhao, K. Zhu and W. Chen, J. Controlled
Release, 2005, 108, 237; (d) Y. Z. Zhang, X. Wang, Y. Feng, J. Li,
C. T. Lim and S. Ramakrishna, Biomacromolecules, 2006, 7, 1049;
(e) E. Luong-Van, L. Grondahl, K. Ngiap Chua, K. Leong,
V. Nurcombe and S. Cool, Biomaterials, 2006, 27, 2042; (f) K. Kim,
Y. Luu, C. Chang, D. Fang, B. Hsia, B. Chu and M. Hadjiargyrou,
J. Controlled Release, 2004, 98, 47; (g) J. Zeng, X. Xu, X. Chen,
Q. Leng, X. Bian, L. Yang and X. Jing, J. Controlled Release, 2003,
92, 227; (h) G. Verreck, I. Chun, J. Rosenblatt, J. Peeters, A. Dijck,
J. Mensch, M. Noppe and M. Brewster, J. Controlled Release,
2003, 92, 349; (i) G. Verreck, I. Sun, J. Peeters, J. Rosenblatt and
M. Brewster, Pharm. Res., 2003, 20, 810; (j) E. Kenawy, G. Bowlin,
K. Mansfield, J. Layman, G. Simpson, E. Sanders and G. Wnek,
J. Controlled Release, 2002, 81, 57; (k) L. Moroni, R. Licht,
J. de Boer, J. R. de Wijn and C. A. van Blitterswijk, Biomaterials,
2006, 27, 4911; (l) X. Zong, K. Kim, D. Fang, S. Ran, B. S. Hsiao
and B. Chu, Polymer, 2002, 43, 4403; (m) C. L. He, Z. M. Huang,
X. J. Han, L. Liu, H. S. Zhang and L. S. Chen, J. Macromol. Sci.
Phys., 2006, 45, 515.
(a) E. H. Sanders, R. Kloefkorn, G. L. Bowlin, D. G. Simpson and
G. E. Wnek, Macromolecules, 2003, 36, 3803; (b) E. D. Boland,
J. A. Matthews, K. J. Pawlowski, D. G. Simpson, G. E. Wnek and
G. L. Bowlin, Front. Biosci., 2004, 9, 1422; (c) L. Buttafoco,
N. G. Kolkman, P. Engbers-Buijtenhijs, A. A. Poot, P. J. Dijkstra,
I. Vermes and J. Feijen, Biomaterials, 2006, 27, 724; (d) P. Ye,
Z. K. Xu, J. Wu, C. Innocent and P. Seta, Biomaterials, 2006, 27,
4169; (e) Y. K. Luu, K. Kim, B. S. Hsiao, B. Chu and
M. Hadjiargyrou, J. Controlled Release, 2003, 89, 341; (f) S. W.
Lee and A. M. Belcher, Nano Lett., 2004, 4, 387; (g) W. Salalha,
J. Kuhn, Y. Dror and E. Zussman, Nanotechnology, 2006, 17, 4675.
(a) K. Sajkaguchi, M. Matrsui and F. Mizukami, Appl. Microbiol.
Biotechnol., 2005, 67, 306; (b) H. W. Scouten, J. H. T. Luong and
R. S. Brown, Trends Biotechnol., 1995, 13, 178; (c) B. Johnsson,
S. Lofas and G. Linquist, Anal. Biochem., 1991, 198, 268; (d)
R. J. Chen, Y. Zhang, D. Wang and H. Dai, J. Am. Chem. Soc.,
2001, 123, 3838; (e) S. Sano, K. Kato and Y. Ikada, Biomaterials,
1993, 14, 817; (f) N. Hampp and D. Oesterhelt, in
Nanobiotechnology: Concepts, Applications and Perspectives, ed.
C. Mirkin and C.Niemeyer, Wiley-VCH, 2004, p. 146; (g)
T. Fischer and N. Hampp, IEEE Trans. Nanobiosci., 2004, 2,
118; (h) H. Jia, G. Zhu, B. Vugrinovich, W. Kataphinan,
D. H. Reneker and P. Wang, Biotechnol. Prog., 2002, 18, 1027.
(a) B. Lu, M. R. Smyth and R. O. Kennedy, Analyst, 1996, 121,
29R; (b) W. Jin and J. D. Brennan, Anal. Chim. Acta, 2000, 461, 1.
(a) M. M. Tomadakis and S. V. Sitirchos, AIChE J., 1991, 37, 74;
(b) M. M. Tomadakis and S. V. Sitirchos, AIChE J., 1993, 39, 397;
(c) M. M. Tomadakis and S. V. Sitirchos, J. Chem. Phys., 1993, 98,
616.
N. Füchtjohann, PhD thesis, Marburg, 2005.
(a) R. Y. Tsien, Annu. Rev. Biochem., 1998, 67, 509; (b)
O. Shimomura, F. H. Johnsen and Y. Saiga, J. Cell Comp.
Physiol., 1962, 59, 223; (c) F. H. Johnson and J. R. Waters, J Cell.
Comp. Physiol., 1962, 60, 85.
A. Bayer, PhD thesis, Marburg, 2003.
S. Deutsch, J. M. Tarbell, K. B. Manning, G. Rosenberg and
A. A. Fontaine, Annu. Rev. Fluid Mech., 2006, 38, 65.
(a) M. Gad-el-Hak, J. Fluids Eng., 1999, 121, 5; (b) H. A. Stone and
S. Kim, AIChE J., 2001, 47, 1250; (c) H. A. Stone, A. D. Stroock
and A. Ajdari, Annu. Rev. Fluid Mech., 2004, 36, 381; (d) E. Lauga,
M. P. Brenner and H. A. Stone, in Springer Handbook of
Experimental Fluid Mechanics, Springer, Heidelberg, New York,
This journal is ß The Royal Society of Chemistry 2007
28
29
30
31
32
33
34
2007 (in press); (e) T. M. Squires and S. R. Quake, Rev. Mod.
Phys., 2005, 77, 977; (f) A. A. Darhuber and S. M. Troian, Annu.
Rev. Fluid Mech., 2005, 37, 425; (g) P. A. Thompson and
S. N. Troian, Nature, 1997, 389, 360; (h) T. Thorsen, S. J. Maerkl
and S. R. Quake, Science, 2002, 298, 580; (i) M. W. J. Prins,
W. J. J. Welters and J. W. Weekamp, Science, 2001, 91, 277; (j)
G. B. Lesinski, S. Sharma, K. A. Varker, P. Sinha, M. Ferrari and
W. E. Carson, Biomed. Microdevices, 2005, 71; (k) T. T. Huang,
D. G. Taylor, K. S. Lim, M. Sedlak, R. Bashir, N. Mosier and
M. R. Ladisch, Langmuir, 2006, 22, 6429.
E. G. Rakov, Russ. Chem. Rev., 2001, 70, 827.
H. Ye, N. Naguib and Y. Gogotsi, JEOL News, 2004, 39, 38.
(a) A. I. Skoulidas, D. M. Ackerman, J. K. Johnson and D. S. Sholl,
Phys. Rev. Lett., 2002, 89, 185901; (b) H. Chen and D. S. Sholl,
J. Am. Chem. Soc., 2004, 126, 7778; (c) M. Majumder, N. Chopra,
R. Andrews and B. J. Hinds, Nature, 2005, 438, 44; (d) J. K. Holt,
H. G. Park, Y. Wang, M. Stadermann, A. B. Artyukhin,
C. P. Grigoropoulos, A. Nay and O. Bakajin, Science, 2006, 312,
1034; (e) M. Whitby and N. Quirke, Nature Nanotechnol., 2007, 2,
87; (f) W. A. Phillip, J. Rzayev, M. A. Hillmyer and E. L. Cussler,
J. Membr. Sci., 2006, 286, 144.
(a) J. Libera and Y. Gogotsi, Carbon, 2001, 39, 1307; (b)
Y. Gogotsi, J. Libera, A. Guvenc-Yazicioglu and C. M.
Megaridis, Appl. Phys. Lett., 2001, 79, 1021; (c) C. M. Megaridis,
A. G. Yazicioglu, J. A. Libera and Y. Gogotsi, Phys. Fluids, 2002,
14, L5.
(a) A. L. Yarin, A. G. Yazicioglu and C. M. Megaridis, Appl.
Phys. Lett., 2005, 86, 013109; (b) A. L. Yarin, A. G. Yazicioglu,
C. M. Megaridis, M. P. Rossi and Y. Gogotsi, J. Appl. Phys., 2005,
97, 124309.
(a) B. M. Kim, S. Sinha and H. H. Bau, Nano Lett., 2004, 4, 2203;
(b) B. M. Kim, S. Qian and H. H. Bau, Nano Lett., 2005, 5, 873; (c)
D. Mattia, H. H. Bau and Y. Gogotsi, Langmuir, 2006, 22, 1789.
(a) D. Li, T. Herricks and Y. Xia, Appl. Phys. Lett., 2003, 83, 4586;
(b) H. Yang, L. Loh, T. Han and F. Ko, Polym. Prepr., 2003, 44,
163; (c) A. Wang, H. Singh, T. A. Hatton and G. C. Rutledge,
Polymer, 2004, 45, 5505; (d) F. Ko, Y. Gogotsi, A. Ali, N. Naguib,
H. H. Ye, G. L. Yang, C. Li and O. Willis, Adv. Mater., 2003, 15,
1161; (e) C. Seoul, Y. T. Kim and C. K. Baek, J. Polym. Sci.,
Polym. Phys. Ed., 2003, 41, 1572; (f) Y. Dror, W. Salalha,
R. Khalfin, Y. Cohen, A. L. Yarin and E. Zussman, Langmuir,
2003, 19, 7012; (g) W. Salalha, Y. Dror, R. L. Khalfin, Y. Cohen,
A. L. Yarin and E. Zussman, Langmuir, 2004, 20, 9852; (h) H. Ye,
This journal is ß The Royal Society of Chemistry 2007
35
36
37
38
39
40
41
42
43
44
45
H. Lam, N. Tichenal, Y. Gogotsi and F. Ko, Appl. Phys. Lett.,
2004, 85, 1775; (i) J. J. Ge, H. Q. Hou, Q. Li, M. J. Graham,
A. Greiner, D. H. Reneker, F. W. Harris and S. Z. D. Cheng,
J. Am. Chem. Soc., 2004, 126, 15754; (j) S. Kedem, J. Schmidt,
Y. Paz and Y. Cohen, Langmuir, 2005, 21, 5600; (k) M. Bashouti,
W. Salalha, M. Brumer, E. Zussman and E. Lifshitz,
ChemPhysChem, 2006, 7, 102; (l) J. M. Lim, J. H. Moon,
G. R. Yi, C. J. Heo and S. M. Yang, Langmuir, 2006, 22, 3445;
(m) I. S. Chronakis, A. Jakob, B. Hagstrom and L. Ye, Langmuir,
2006, 22, 8960; (n) H. Liu, J. B. Edel, L. M. Bellan and
H. G. Craighead, Small, 2006, 2, 495; (o) Y. Ji, B. Li, S. Ge,
J. C. Sokolov and M. H. Rafailovich, Langmuir, 2006, 22, 1321.
E. Katz, A. L. Yarin, W. Salalha and E. Zussman, J. Appl. Phys.,
2006, 100, 034313.
C. F. Gonzales and V. T. Remcho, J. Chromatogr., A, 2005, 1079,
59.
(a) G. Baier and M. D. Graham, Phys. Fluids, 1998, 10, 3045; (b)
G. Baier, T. M. Grateful, M. D. Graham and E. N. Lightfoot,
Chem. Eng. Sci., 1999, 54, 343; (c) A. L. Yarin, A. Yu. Gelfgat and
P. Z. Bar-Yoseph, Int. J. Heat Mass Transfer, 2002, 45, 555; (d)
A. Y. Gelfgat, A. L. Yarin, P. Z. Bar-Yoseph, M. D. Graham and
G. Bai, Phys. Fluids, 2004, 16, 4066; (e) A. Yu. Gelfgat, A. L. Yarin
and P. Bar-Yoseph, Phys. Fluids, 2001, 13, 3185; (f) A. Yu. Gelfgat,
A. L. Yarin and P. Z. Bar-Yoseph, Phys. Fluids, 2003, 15, 330; (g)
A. Yu. Gelfgat, A. L. Yarin and P. Z. Bar-Yoseph, Phys. Fluids,
2003, 15, 790; (h) A. L. Yarin, J. Fluid Mech., 2001, 444, 321; (i)
A. L. Yarin, Fluid Dyn. Res., 2002, 31, 79.
P. R. C. Gascoyne and J. Vykoukal, Electrophoresis, 2002, 23,
1973.
I. Silverman, A. L. Yarin, S. N. Reznik, A. Arenshtam, D. Kijet
and A. Nagler, Int. J. Heat Mass Transfer, 2006, 49, 2782.
A. L. Yarin, G. Brenn, O. Kastner, D. Rensink and C. Tropea,
J. Fluid Mech., 1999, 399, 151.
E. Kamke, Differentialgleichungen. Loesungsmethoden und
Losungen, Teubner, Stuttgart, 10th edn, 1983.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical
Functions., Dover Publ., New York, 1965.
V. N. Morozov, M. Evanskey, Y. K. Tan, D. Shaffer,
T. Ya. Morozova and Ch. Bailey, Langmuir, 2006, 22, 1742.
C. C. Harrell, Y. Choi, L. P. Horne, L. A. Baker, Z. S. Siwy and
C. Martin, Langmuir, 2006, 22, 10837.
A. Docoslis, L. A. Tercero Espinoza, B. Zhang, L. L. Cheng,
B. A. Israel, P. Alexandridis and N. A. Abbot, Langmuir, 23, 3840.
J. Mater. Chem., 2007, 17, 2585–2599 | 2599