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Supporting Information for Improved order parameter (alignment) determination in Cellulose Nanocrystal (CNC) films by a simple optical birefringence method Authors: Reaz A Chowdhury, Shane X Peng, Jeffrey Youngblood* Authors address: School of Materials Engineering, Purdue University, West Lafayette, Indiana 47907, United States * Corresponding author Email: [email protected], Phone: +1 765-496-2294, Fax: +1 765 494-1204 Section 1: Shear rate control process for anisotropic film fabrication The overall film thickness of an anisotropic CNC film is directly related with the shear rate control process, likely due to the shear-thinning behavior of the CNC dispersion. Moreover, we have observed that wet films thicker than 400 µm experienced a non-homogeneous shear rate; hence, uneven crystal arrangement is detected. Thus, we have chosen a 250 µm wet film thickness to prevent this nonuniformity. As shear rate is dependent upon shear gap and PET strip thickness controls the wet film thickness, for a simple shear casting CNC films, following equation was used to calculate shear rate. shear rate= length(l) time * height(h) from bottom surface Here, length (l) is the total length of the PET strip, height (h) is the PET strip thickness and time (t) is the time duration of the doctor blade to cover length (l) over the PET strip. Figure S1 represents the schematic representation of shear rate 1 control process. The different shear rate is controlled by the time duration of the doctor blade, where a regular stopwatch is used to measure the time scale. Figure S1: Anisotropic CNC film fabrication process with control shear rate. Section 2: Theoretical approach for CNC films 2.1 Transmittance light intensity for different CNC crystal arrangement: Transmittance light intensity profile for CNC films depend on the overall crystal arrangement, which is expressed by equation E1. This general expression reflects the global crystal arrangement for any configuration. But, the global arrangement is the combination of local individual crystal domain at any direction, so the general expression can be written as equation E2, which is basically the combination of individual local domain arrangement. Here, subscript I0, I1, I2, I3, ………, I360 represent the transmittance intensity for the corresponding crystal domain direction with respect to any reference axis (generally, reference axis is parallel or perpendicular to the film surface). I I 0 sin 2 2 sin 2 ( nd ) ( E1) Or I ( I 0 I1 I 2 I 3 ............ I 360 ) I I o sin 2 ( nd )((sin 2 2*0 sin 2 2*1 sin 2 2*2 .................... sin 2 2*360)) ( E 2) 2 We know that the crystal arrangement of CNC films can be isotropic, anisotropic or the intermediate stage. The crystalline domains in the isotropic configuration are arranged in all directions; hence this global expression should be based on the individual crystal domain that has been accurately expressed by equation E2. This expression also confirms that the intensity value is completely angle independent. But, the crystalline alignment of an individual crystalline domain, as well as the global arrangement within an anisotropic CNC film, should have the same direction with respect to any reference axis. So, the global expression and the local expression must be identical. 2.2 Correlation between intensity profile and linear dichroic ratio: The dichroic ratio for a complete isotropic system must be 1, and a perfect anisotropic system should be infinity. So, if a system moves toward an anisotropic configuration, the dichroic ratio should increase gradually to infinity. Based on the literature survey, generally a one polarizer system is used for the dichroic ratio calculation and 0º and 90º sample configuration with respect to the incident polarized light is used for the dichroic ratio determination. The 0º configuration provides a maximum transmittance light intensity, where a 90º configuration is used for minimum intensity for a specific wavelength. Thus, the dichroic ratio is defined as(Ward 2012) D I0 ( E 3) I 90 However, here a crossed polarizer system has been used in the experiment, and no references were found that dealt with dichroic ratio for this configuration. So, a mathematical analogy is used to modify equation E3. A crossed polarizer system shows maximum light intensity for 45º anisotropic sample alignment with respect to the crossed polarizers, and the 90 º or 0 º configuration providing minimum transmittance light intensity. Hence, equation E4 can be written in the following manner for the crossed polarized system. D I 45 ( E 4) I 90 3 2.3 Correlation between linear dichroic ratio and order parameter: Orientation distribution of a polymer chain has been defined in the following coordinate system (figure S2), and we restricted this system for uniaxial polymer chain. Here, an angle θ is the corresponding angle between the shear direction and polymer chain axis, and an angle α is a selective angle between the polymer chain axis and a side chain with central polymer backbone. Figure S2: Orientation of a polymer chain with respect of shear direction. The angle θ defines the distribution of polymer chain with respect of shear direction, where angle α is dihedral angle of a side chain with respect of polymer chain axis. A theoretical distribution function for this polymer system can establish a relationship among dichroic ration and orientation parameter. In 1953, Fraser(Fraser 1953) proposed a theoretical model for polymer orientation distribution, then Beer(Beer 1956) and Elliot (Elliott 1969) further modified it for fiber-type or rod shaped polymer orientation. The assumption is that a certain fraction of polymer fiber, S is oriented to shear/ stretching direction with angle θ and rest of (1-S) fraction is unoriented. If polymer fibers contain side chain with α dihedral angle, then the dichroic ratio is given by 2sin 2 1/ 3(1 S ) 2 2 3sin D ........................................( E 5) 2sin 2 2 1/ 2S sin 1/ 3(1 S ) 2 3sin 2 S cos 2 If the polymer fiber is rod shaped materials without side chain and the rodshaped polymer is along the shear direction, then both angle α and θ should be zero. So, equation E5 converted to the equation E6. D (2S 1) .........................................( E 6) (1 S ) However, true dichroic ratio, D* depends on the correction factor g that is explained by Kiselev. He used Vuks-Chandracekhar-Madchusudana model for this derivation(Kiselev et al. 2001). Based on this model, D* =g.D. So, equation E6 can be written as 4 D* gD (2S 1) .........................................( E 7) (1 S ) Now, the dichroic ratio is defining as (I45/I90) where transmitted light intensity is expressed as I I 0 sin 2 2 sin 2 ( nd ) So nd I 0 sin 2 (2* 45) sin 2 ( ) I 45 I 90 I sin 2 (2*90) sin 2 ( nd ) 0 Hence, nd ) (2S 1) I 45 D* D.g .........................( E8) (1 S ) I 90 I sin 2 (2*90) sin 2 ( nd ) 0 I 0 sin 2 (2* 45) sin 2 ( Based on equation E8, if we have a perfect anisotropic arrangement, then I90 value should be zero, thus D= infinity, therefore, materials should have S=1. Similarly, I45 and I90 should have same value for chiral nematic configuration, thus D=1, therefore, materials should have S=0. Section 3: Transmittance light intensity profile for CNC films and corresponding dichotic ratio 5 6 7 Figure S3: Transmittance intensity profile for different CNC film of 45˚ and 90˚ configuration along its optical image under cross polarizer. 8 Table T1: Dichroic ration from maximum transmittance intensity for different specimen and resulted Herman order parameter(S). SAMPLE ID TMAX AT 45 DEGREES TMAX AT 90 DEGREES DICHROIC RATIO ORDER PARAMETER, S SO1 21.86 21.09 1.04 0.01 SI1 64.57 28.71 2.15 0.29 SI2 74.23 17.74 4.18 0.50 SI3 30.23 5.17 5.84 0.61 SI4 85.74 3.71 23.08 0.88 SI5 89.00 2.63 33.85 0.91 SI6 83.09 2.06 40.39 0.92 SI7 82.74 1.89 43.87 0.93 SI8 85.34 1.80 47.41 0.93 SI9 95.71 1.86 51.54 0.94 SI10 96.29 1.43 67.4 0.95 LINEAR POLARIZER A 39.89 0.11 349 0.99 A Commercial cellulose triacetate linear polarizer with polarizability 99.94% Section 3.1: Peak intensity position with different samples Infrared and visible spectroscopy are wavelength selective, which is based on the selective functional groups or electronic transition of the molecules, but we used intensity of light transmission based on the optical birefringence that is related to the overall crystal arrangement. For a constant film thickness with a specific crystal alignment, peak position should be same for both maximum and minimum intensity profile. We observed this phenomenon for a constant film thickness (supporting document figure S1 to SI 10). However, the maximum peak wavelength varies from specimen to specimen due to their different film thicknesses based on the well-known transmittance intensity equation that is derived by Max Born (the Noble Prize in Physics-1954). A mathematical model based on this equation validates our observation. Here, mathematical modeling is performed for a perfect anisotropic configuration (S=1) with different film thickness and the following 9 figure shows the effect of film thickness that changes the peak intensity position with the wavelength. In short, for a specific sample, 1 wavelength is observed for maximum, but between samples, the maximum varies according to well-known theory and our method reflects that. Figure S4: Effect of film thickness for the peak intensity position with different wavelength. 10 Section 4: 2DXRD diffractogram for CNC films Figure S5: 2DXRD diffractogram for different CNC samples with linear polarizer. 11 Section 5: Crystallinity index of CNC Crystalline nanocellulose composed of cellulose I crystalline form (two polymorphs Iα and Iβ)(Belton et al. 1989) and cellulose II. Cellulose I contain peaks at (110) (11̅0), (012), (200), and (004) lattice plane that is located at 2θ of 15.6, 17.5, 21, 23, and 35.3˚, respectively. Higher intensity at 21˚ represents cellulose II that is from (110) plane(Kim et al. 2013). PROFIT software was used for data deconvolution with precise peak position. Experimental data with fitted profiles of CNC are shown in figure S3. Figure S6: Deconvoluted CNC XRD pattern for cellulose I [(1-10), (110), (200), and (004)] and cellulose II [(110), (020), and (004)] polymorphs. The crystallinity index (CI%) was calculated from the following equation(Park et al. 2010): CI (%) ( Ac ) X 100 Ac Aa Ac is the total crystalline area of deconvoluted patterns, where Aa is for the entire amorphous area that is from 5˚ to 30˚ at 2θ for hump like peak and 8˚ to 13˚ at 2θ for full width at half maxima. 12 Section 6: Comparison of both technique and amorphous contribution: Figure S7: Crystalline and amorphous contributions to order parameter with different shear rates. Reference Beer M Quantitative interpretation of infra-red dichroism in partly oriented polymers. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 1956. vol 1204. The Royal Society, pp 136-140 Belton P, Tanner S, Cartier N, Chanzy H (1989) High-resolution solid-state carbon-13 nuclear magnetic resonance spectroscopy of tunicin, an animal cellulose Macromolecules 22:1615-1617 Elliott A (1969) Infra-red spectra and structure of organic long-chain polymers Fraser R (1953) The interpretation of infrared dichroism in fibrous protein structures The Journal of Chemical Physics 21:1511-1515 Kim SH, Lee CM, Kafle K (2013) Characterization of crystalline cellulose in biomass: basic principles, applications, and limitations of XRD, NMR, IR, Raman, and SFG Korean Journal of Chemical Engineering 30:2127-2141 Kiselev DF, Glushkova TM, Ivanov S, Firsova MM, Shtyrkova AP Spectrophotometrical method of ordering estimation for liquid crystal in an electro-optical cell. In: Optics of Crystals, 2001. International Society for Optics and Photonics, pp 236-240 Park S, Baker JO, Himmel ME, Parilla PA, Johnson DK (2010) Cellulose crystallinity index: measurement techniques and their impact on interpreting cellulase performance Biotechnology for biofuels 3:1 Ward IM (2012) Structure and properties of oriented polymers. Springer Science & Business Media, 13