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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
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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
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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
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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
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6
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Figure S3: Transmittance intensity profile for different CNC film of 45˚ and 90˚
configuration along its optical image under cross polarizer.
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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
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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.
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Section 4: 2DXRD diffractogram for CNC films
Figure S5: 2DXRD diffractogram for different CNC samples with linear polarizer.
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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.
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Section 6: Comparison of both technique and amorphous contribution:
Figure S7: Crystalline and amorphous contributions to order parameter with
different shear rates.
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