Effect of propionyl group on birefringence and wavelength dispersion of propionylated cellulose acetate optical compensation films

Propionylated cellulose acetate (PCA) with different propionyl substitution degrees (DSPr) was synthesized, and the corresponding optical films were prepared by solution casting. The birefringence and its wavelength dispersion of PCA films stretched at 10 °C above and below the glass transition temperature (Tg) with different draw ratios (DR) were studied. The introduction of propionyl group at different substitution sites present different contribution to birefringence and its wavelength dispersion. The propionyl group at C-2 and C-3 sites have a larger positive orientation birefringence with stronger normal wavelength dispersion, while that at the C-6 site shows a smaller negative orientation birefringence with weaker normal wavelength dispersion compared with the acetyl group. Compared with CA film, the introduction of the propionyl group weakens the orientation birefringence of PCA film. With the increase of DSPr from 0.023 to 0.303, the occurrence of propionyl substitution only at the C-6 site turns to C-2, C-3 and C-6 sites and the wavelength dispersion of in-plane birefringence (Δnin) decreases. When DSPr is further increased to 0.537, the Δnin and out-of-plane birefringence (Δnth) of PCA films at different DR show a very weak wavelength dispersion with the relative horizontal curves. Current results indicate that when the substitution degree of the propionyl group and acetyl group is suitable, the wavelength dispersion of PCA film can be eliminated.


Introduction
Liquid crystal display (LCD) devices have developed rapidly in recent decades, which has greatly enhanced the information interaction experience of people (Kim and Song 2009;Allen et al. 2021;Wang et al. 2022). According to the panel type, LCD can be divided into traditional twisted nematic LCD (TN-LCD), in-plane switching LCD (IPS-LCD) and vertically aligned LCD (VA-LCD), while IPS-LCD and VA-LCD occupy most of the current LCDs (Kim et al. 2011). Due to the vertical arrangement of liquid crystal molecules, the VA-LCD has a higher contrast ratio than IPS-LCD and TN-LCD and has been widely applied in the field of large size televisions (Kim et al. 2015;Ochi et al. 2017).
The optical compensation film is the core component for VA-LCD to achieve a high contrast ratio. Optical birefringence and wavelength dispersion are two important parameter indicators of optical compensation film. For VA-LCD, the optical compensation film is required to have a very weak wavelength dispersion of birefringence and specific in-plane (50 ~ 70 nm) and out-of-plane retardation values (100 ~ 130 nm) (Sang Park et al. 2017), which can avoid light leakage, contrast reduction, and serious chromatic aberration in LCD. The compensation film for traditional VA-LCD is made by a combination of multiple layers of negative C-plates and positive A-plates or multiple layers of biaxial plates and negative C-plates, which causes a very large thickness, complex processes and high costs for compensation film (Nobukawa et al. 2013;Kim et al. 2015). Therefore, people want to develop a compensation film that is equivalent to the superposition effect of multilayer compensation film in traditional VA-LCD. A VA-TAC compensation film with certain optical retardation values in-plane and out-of-plane was developed by Japan's Konica Minolta by blending other cellulose acetate derivatives and additives with cellulose triacetate (TAC) (Okubo et al. 2005). It has been widely used in new VA-LCD, greatly reducing the thickness of the display panel. However, the method of blending with low-mass molecules (Tagaya et al. 2001a(Tagaya et al. , b, 2003Koike et al. 2006;Yamaguchi et al. 2009b;Abd Manaf et al. 2011) or other polymers (Uchiyama and Yatabe 2003a, b;Kuboyama et al. 2007) has some problems of compatibility and dispersion uniformity, which will lead to the difficult control of the structural stability for compensation film, and ultimately affect its application performance. In addition, copolymerization (Iwata et al. 1997;Uchiyama and Yatabe 2003c;Diani and Gall 2006;Shafiee et al. 2011;Iwasaki et al. 2013) has also been attempted, but it was difficult to take into account the optical, mechanical and thermal properties of compensation film at the same time (Tamura et al. 2022). Chemical modification is a method to improve one aspect of the properties of the original material without affecting other properties, which may be a good method to prepare VA-LCD compensation film. In the previous work (Min et al. 2022), we have successfully prepared IPS-LCD compensation film by using the method of chemical modification. Although there were many research studies on the preparation of VA-LCD compensation film, most of them focused on the methods of blending and copolymerization. Little attention was paid to the chemical modification method for the preparation of the VA-LCD compensation film.
In this work, cellulose diacetate (CA) was selected for chemical modification to prepare VA-LCD compensation film. Compared with TAC, CA has more residual substitution sites, which is more suitable for chemical modification with different substitution degrees. The propionyl group will be the chosen modifying group because propionyl can provide positive birefringence and weak wavelength-dependent normal wavelength dispersion (Yamaguchi et al. 2009a(Yamaguchi et al. , 2012Nobukawa et al. 2015Nobukawa et al. , 2017, both of which are opposite to the acetyl group. Theoretically, the combination of the above two groups can prepare the compensation film meeting the requirements of VA-LCD. The propionylated cellulose acetate (PCA) with different substitution degrees of propionyl (DS Pr ) were successfully synthesized and the corresponding optical films were prepared. When DS pr is 0.537, the PCA film shows a large in-plane birefringence (Δn in ) and out-of-plane birefringence (Δn th ) and the corresponding wavelength dispersion remains relatively flat with the change of DR compared with TAC film (Yamaguchi et al. 2009b;Abd Manaf et al. 2011).

Materials
The raw material CA with acetyl substitution degree of 2.45 used in this study was purchased from Sinopharm Chemical Reagent Company. The reagents used in this study were commercially available products of analytical purity like pyridine and propionyl chloride. Prior to the reaction, CA was dried in the vacuum oven at 80 °C for 24 h. N, N-Dimethylformamide (DMF) was purchased from Shanghai Reagent Company. All reagents were not further purified before use.
Synthesis and characterization of PCA Figure 1a illustrates the chemical structure of PCA. The synthesis mechanism of PCA with different degrees of propionyl substitution is similar to our previous work (Min et al. 2022). Firstly, the raw material CA was completely dissolved in DMF. Then the above solution was moved to an ice-water bath, and pyridine and propionyl chloride were added slowly dropwise successively. After two hours reaction at 60 ℃, the reacted solution was gradually added to a large amount of deionized water with rapid stirring to precipitate the product. Finally, the product was purified by multiple dissolutions and precipitation, and a pure white fiber solid was obtained after vacuum drying as shown in Fig. 1b. Figure 1c shows the 1 H NMR spectra of CA and PCA. CA and PCA have the same proton peaks of the chain backbone with chemical shifts in the range of 3.2-5.5 ppm (Kono et al. 2015;Wei et al. 2020). The chemical shift between 1.8 ppm and 2.2 ppm is assigned to the acetyl group and the substitution degree of the acetyl group for CA film is 2.45, including those at C-2, C-3 and C-6 sites as shown in Fig. 1d. In addition, the degrees of substitution of the acetyl group calculated from the integral area at C-2, C-3 and C-6 sites are 0.98, 0.58 and 0.89, respectively (Nilsson et al. 2022). Compared with CA, PCA has a new chemical shift at 1.06 ppm, which is attributed to the proton peak of the propionyl group (Enomoto-Rogers et al. 2014). No other impurities were found from the NMR hydrogen spectrum results, indicating the successful synthesis of PCA. The substitution degree for propionyl (DS Pr ) was also calculated by 1 H NMR according to the following equation (Huang et al. 2011): where I Pr is the integral of the propionyl proton peak and I Backbone is the integral of the proton peak of the chain backbone.

Preparation of films
Both CA and PCA films were prepared by the solution casting method. Using DMF as the solvent, CA and PCA solutions with a mass concentration of 10% were prepared by stirring at room temperature for 2 h, respectively. The above solutions were slowly poured onto the flat glass plate after standing for 40 min. The uniform rate of solvent evaporation was ensured by controlling the programmed temperature. The thickness of the films was about 120 μm. The PCA films with DS Pr of 0.023, 0.303 and 0.537 were named as PCA 0.023 , PCA 0.303 and PCA 0.537 , respectively.
The uniaxially stretched films were obtained with a homemade stretching device (Meng et al. 2013 Figure S1 presents a schematic diagram of tensile deformation. All film samples were equilibrated at a stretching temperature (T s ) for 10 min before stretching and then stretched at a rate of 0.1 mm/s. The initial distance between the clamps before stretching was 20 mm. All samples were quenched rapidly by blowing liquid nitrogen after stretching to reduce the relaxation of the molecular chain. Representative photos of PCA films with different draw ratios are shown in Figure S1.

Measurements
Nuclear magnetic resonance ( 1 H-NMR, Bruker AVANCE III 600) was used to characterize the structure of CA and PCA and determine the substitution degree of the propionyl group. CA and PCA samples were dissolved in a precise amount of deuterated DMSO-d6, and then 1 H-NMR spectra were collected.
Dynamic mechanical analysis (DMA, DMA Q850) of CA and PCA films were performed at 10 Hz from 30 to 180 ℃ to obtain the glass transition temperature (T g ), which was extracted from the loss factor (tanδ) curve. The length and width of samples for the DMA test were 20 mm and 5 mm, respectively.
The average refractive indexes (n av ) of CA and PCA films were measured by an Abbe refractometer (ATAGO, NAR-2 T) at 25 ℃ with α-bromonaphthalene being used as the contact liquid. The test results are presented in Table S1.
The optical retardation values of CA and PCA films were measured by the retardation measurement system (Otsuka Electronics Co, Ltd. RETS-100L) equipped with a halogen lamp over a wavelength range of 400-800 nm. The in-plane birefringence (∆n in ) and out-of-plane birefringence (∆n th ) are determined from in-plane retardation (R in ) and the out-of-plane retardation (R th ) as follows (Songsurang et al. 2014): where d is the film thickness, n x , n y , and n z are the refractive indices along the x, y, and z-axis, respectively. (2) Wide-angle X-ray scattering measurements (WAXS) of CA and PCA films were carried out in the beamline BL16B1 of Shanghai Synchrotron Radiation Facility (SSRF). The X-ray wavelength was 0.124 nm. The two-dimensional (2D) X-ray scattering pattern was collected using a detector (Pilatus 300 k) with a pixel size of 172 um. The sample-to-detector distance was 175.17 mm and calibrated by CeO 2 . The 2D WAXD pattern was integrated by using the Fit2D software to obtain the 1D WAXD profile .
The ratio of oriented and unoriented amorphous can be evaluated by diffracting the intensity of a small fixed area at the same q-value in the equatorial and meridional directions, which is illustrated in Fig. 2. The two red circles possess the same area and their intensities are defined as I a (equator) and I a (meridian), respectively. Therefore, the ratio of oriented amorphous (O a ) can be calculated as follows (Murakami et al. 2002;Chen et al. 2019): The degree of crystal orientation of the film sample was estimated from 1D WAXD azimuthal integration curves by using Herman's method (Hermans and Platzek 1939;An et al. 2019). The average orientation of a set of (hkl) plane can be calculated by Eq. (5). where and I( ) are the azimuthal angle and scattering intensity corresponding to the azimuthal angle, respectively. Herman's orientation parameter is defined as the following equation, where f hkl represents the orientation value of the normal direction of the (hkl) plane at an angle of to the reference direction (stretching direction) ). The differential scanning calorimetry (DSC) test of all samples were performed on a differential scanning calorimeter (DSC 250, TA Instruments) under nitrogen protection. The test temperature range was 30 ~ 300 ℃ and the heating rate was 10 ℃/min.
The infrared dichroism measurement of all samples were performed on the BL01B beamline (Hefei Synchrotron Radiation Facility) (Hu et al. 2020). The spectrum wavenumber range and resolution were 500-4000 cm −1 and 4 cm −1 , respectively. The orientation states of the main chain and side groups were evaluated by the infrared dichroism ratio D, which can be calculated by the following equation (Yamaguchi et al. 2009b, a) where A ∥ and A ⟂ are the absorbance of linearly polarized light with polarization directions parallel and perpendicular to the stretching direction, respectively (Yamaguchi et al. 2009a). For uniaxially stretched samples, the polymer chains are preferentially oriented along the stretching direction (Shafiee et al. 2001). Figure 3 shows the temperature dependence of storage modulus (G′), loss modulus (G″), and loss factor (tanδ) of CA and PCA films. Compared with CA film

DMA analysis
(G′ > 7500 MPa), the introduction of the propionyl group can significantly reduce the G′ (G′ < 2500 MPa) of PCA films at 30 ℃, which may be caused by the reduction of hydrogen bond due to the propionyl substitution. Furthermore, the G′ of PCA film decreases gradually with the increase of DS Pr . As shown in Fig. 3, the tanδ curves of CA and PCA films present a peak at a temperature from 180 to 240 ℃, which corresponds to the T g of films. When DS Pr is 0.023, the T g of PCA film is slightly higher than CA film. However, when DS Pr increases to 0.303 and even to 0.537, the T g of PCA film presents a dropping trend. In this work, the temperatures at 10 ℃ below and above T g (T g -10 and T g +10) were selected as the stretching temperatures (T s ) of films.
Optical properties Figure 4 presents the wavelength dependence of Δn in and Δn th for CA and PCA films stretched at T g -10 with different DR and Figures  Considering the significant effect of stretching temperature on the orientation of molecular chains, the optical properties of CA and PCA films stretched at T g +10 are characterized. Figure 5 shows the wavelength dependence of Δn in and Δn th for CA and PCA films stretched at T g +10 with different DR, while of Δn in and Δn th at the wavelength of 550 nm with DR. Similar to those stretched at T g -10, Δn in of both CA and PCA films increases with increasing DR. But the increasing extent of Δn in for PCA films with the increase of DR is weaker than that of CA film. In addition, Δn in of PCA films at large DR (DR ≥ 1.5) shows a slight increase with rising DS Pr . Different from CA film whose Δn th increases with increasing DR, Δn th of PCA 0.023 and PCA 0.303 films decrease and even show a transition from positive to negative values, while that of PCA 0.537 film is little affected by DR. With the increase of DS Pr , the variation degree of Δn th for PCA films with increasing DR gradually weaken, which is similar to that of PCA films stretched at T g -10 (Figs. 4(f-h)). As presented in Fig. 5(a), the Δn in wavelength dependence of CA film has a slight increase with increasing DR. However, it is noteworthy that the Δn in wavelength dependence of PCA 0.023 , PCA 0.303 and PCA 0.537 films are very small, and they still keep approximately flat curves even when DR increases. With increasing DR, the Δn th wavelength dependence of CA first increases and then decreases, and those of PCA 0.023 and PCA 0.303 films obviously strengthen, while that of PCA 0.537 film is unaffected and the corresponding curves still remain flat. Moreover, the Δn th wavelength dependence for PCA film at DR of 2.0 shows a dropping trend with the increase of DS Pr .
In order to analyze the evolution of refractive index in three directions for CA and PCA films during the stretching process, the three-dimensional refractive index (n i ) is obtained from the birefringent characterization and shown in Fig. 6, where n x , n y , and n z are defined as the refractive indices in the stretching direction, the direction perpendicular to the stretching direction in the film plane and the film thickness direction, respectively. At T g -10 (Figs. 6(ad)), n x of both CA and PCA films increases with the increasing DR, while their n y gradually drops and n z slightly decreases. Moreover, with increasing DS Pr , the increasing extent of n x with DR weakens and the decreasing trend of n y becomes weaker. At T g +10 (Figs. 6(e-h)), the n x of CA film still rises with the increase of DR, accompanied with the drop of n y and n z . However, with increasing DR, the n y of PCA films decreases and the corresponding n z present an increasing trend. In addition, the n x of PCA 0.023 and PCA 0.303 films have a dropping trend with the increase of DR, while that of PCA 0.537 shows a slight upward trend. Note that both the decrease of n y and the increase of n z with DR weaken when the DS Pr increases to 0.537.
For further analysis, the normalized wavelength dependence of in-plane birefringence (Δn in (λ)/ Δn in (550)) and out-of-plane birefringence (Δn th (λ)/ Δn th (550)) for CA and PCA films stretched at T g -10 with different DR are obtained and plotted in Fig. 7. The Δn in (λ)/Δn in (550) of both CA and PCA 0.023 films have strong wavelength dependence before stretching, but they all gradually weaken with  (550) for PCA films with different DR becomes very weak, especially those of PCA 0.537 film. As opposed to Δn in (λ)/Δn in (550), the wavelength dependence of Δn th (λ)/Δn th (550) for CA and PCA films strengthens with increasing DR. Interestingly, with rising DS Pr , the change of Δn th (λ)/Δn th (550) wavelength dependence for PCA films with increasing DR gradually decrease. Especially, when DS Pr is increased to 0.537, the Δn th (λ)/Δn th (550) wavelength dependence of PCA film has almost no change with DR. Figure 8 presents the normalized wavelength dependence of Δn in (λ)/Δn in (550) and Δn th (λ)/ Δn th (550) for CA and PCA films stretched at T g +10 with different DR. As presented in Figs. 8(a-d), the wavelength dependence of Δn in (λ)/Δn in (550) for CA and PCA films stretched at T g +10 have the same change trend. For PCA 0.537 film, the wavelength dependence of Δn in (λ)/Δn in (550) at different DR is still very weak. With the increase of DR, the  (550)) and out-of-plane birefringence (Δn th (λ)/ Δn th (550)) for CA, PCA 0.023 , PCA 0.303 and PCA 0.537 films stretched at T g -10 with different DR Δn th (λ)/Δn th (550) wavelength dependence of CA, PCA 0.023 and PCA 0.303 films stretched at T g +10 have more large change compared with those at T g -10. However, the Δn th (λ)/Δn th (550) of PCA 0.537 films with different DR still retain a very weak wavelength dependence though the stretching temperature is raised above T g .

Polarized infrared analysis
The Δn in and Δn th of CA and PCA films are seriously influenced by the orientation of the main chain and side groups. Therefore, it is very necessary to obtain the orientation differences between the main chain and side groups. The polarized infrared tests of CA and PCA films were performed. Figure 9 shows the infrared dichroism results for CA and PCA films stretched at different T s and DR. The infrared dichroism ratio (D = A || /A ⊥ ) can be used to evaluate the orientation difference of the main chain and side groups after stretching, where A || and A ⊥ represent the absorbances parallel and vertical to the stretching direction, respectively. The detailed spectra of the polarized Fourier infrared tests are presented in the supporting information ( Figure S3). The absorption bands at 2981 and 2890 cm −1 are respectively the results of the asymmetric stretching and symmetric stretching of -CH 2 , which originate from those at the C-6 site of the main chain (Fig. 1a) and propionyl group. The band at 1768 cm −1 in Figures S3(a-d) is assigned to C = O stretching, which is present in both acetyl and propionyl groups and cannot be specifically distinguished. Moreover, the characteristic absorption band at 1276 cm −1 is associated with the C-O stretching at three substitution sites on the main chain, while the absorption band at 1097 cm −1 is attributed to the C-O-C symmetric bending in the ring of the chain backbone (Ilharco and Brito De Barros 2000;Hu et al. 2010;Rynkowska et al. 2017;Wei et al. 2020). As shown in Fig. 9a, D of C-O for CA film has a slight distinction with the main chain (C-O-C) and other groups at different T s and DR, which may be caused by the hydrogen bond due to low substitution degree. However, D of -CH 2 , C-O, C = O and C-O-C for PCA 0.023 film is almost equal to each other and all slightly higher than 1 at different T s and DR, while those of PCA 0.023 and PCA 0.537 films have the same situation. The above results indicate that the acetyl and propionyl groups of PCA 0.023 , PCA 0.303 and PCA 0.537 films have the same orientation direction with the chain backbone during stretching, and the orientation difference between acetyl and propionyl groups is very small during stretching.

WAXS analysis
To obtain more information about the chain orientation, the WAXS analysis of CA and PCA films stretched at different T s and DR are carried out.  (550)) and out-of-plane birefringence (Δn th (λ)/ Δn th (550)) for CA, PCA 0.023 , PCA 0.303 and PCA 0.537 films stretched with different DR at T g +10 films stretched at different T s and DR. The vertical direction is the stretch direction (SD). The 2D WAXS patterns of CA film before stretching (DR = 1.0) show several clear crystal diffraction rings, which are weakened with the introduction of a small amount of the propionyl group (DS Pr = 0.023). However, the crystal diffraction signals of PCA film before stretching gradually strengthen with the increase of DS Pr . With increasing DR, the crystal diffraction signals for CA and PCA films stretched at T g -10 and even at T g + 10 gradually weaken and orient along the equator or meridian. Obviously, CA and PCA films stretched at different T s and DR have different structural orientations. Therefore, more information needs to be obtained for researching the chain orientation of CA and PCA films at different T s and DR, which will be presented in the following sections. Fig. 9 Infrared dichroism results for a CA, b PCA 0.023 , c PCA 0.303 and d PCA 0.537 films stretched at different T s and DR, where L and H denote that T s is 10 ℃ lower and higher than T g , respectively  (Watanabe et al. 1968;Roche et al. 1978;Kono et al. 1999;Sikorski et al. 2004;Wada and Hori 2009). As shown in Fig. 11a, the strong crystal diffraction peaks are presented on 1D WAXS curves of CA film before stretching (DR = 1.0). With the introduction of the propionyl group with 0.023 degrees of substitution (DS Pr = 0.023), the strong crystal diffraction peaks weaken, but they gradually strengthen again with increasing DS Pr . With the increase of DR, the strong diffraction peaks of CA and PCA films stretched at T g -10 and T g + 10 all gradually become weak, indicating that their degree of crystallinity has a dropping trend, which is verified by the DSC results shown in Figures S4 and S5.
Figures 11e-h present the 1D WAXS curves through the azimuthal integration of the (110) plane  for CA and PCA films stretched at different T s and DR. With increasing DR, the peaks at the azimuth angle between 90º and 270º for CA and PCA films stretched at T g -10 and T g +10 present a trend of narrowing, which suggests the rise of crystal orientation. Furthermore, with the increase of DS Pr , the peak at 90º ~ 270º for PCA film stretched at T g +10 with DR of 2.0 gradually narrows down.
For quantitative analysis, the degree of crystal orientation of the (110) plane for CA and PCA films stretched at different T s and DR are calculated from the 1D WAXS curves shown in Fig. 11e-h. Figure 12a-b plot the evolution of f 110 for CA and PCA films stretched at different T s with the increase of DR. At T g -10 (Fig. 12a), f 110 of CA and PCA films at the same DR are very close to each other though those of CA and PCA 0.023 films show a slightly higher value at DR ≥ 1.3 than those of PCA 0.303 and PCA 0.537 films. With increasing DR, f 110 of CA and PCA films first rise rapidly and then keep almost constant. At T g +10 (Fig. 12b), the f 110 of CA and PCA films first increases rapidly and then rises slowly. At the rapidly increasing stage, f 110 of CA and PCA films almost have the same values at the same DR. At the slowly rising stage, the f 110 of CA and PCA 0.023 films increase more slowly with DR than those of PCA 0.303 and PCA 0.537 films, which may be caused by the hydrogen bond due to low propionyl substitution. Moreover, f 110 of CA and PCA films at DR of 1.5 at T g +10 is slightly lower than that at T g -10 due to the easy relaxation of the chain at high T s . 1D WAXS azimuth integral curves of (110) plane for e CA, f PCA 0.023 , g PCA 0.303 , and h PCA 0.537 films stretched at different T s and DR. The stretching temperatures are labeled as H and L, where H stands for T g -10 and L stands for T g +10 (Fig. 12c), O a of CA and PCA films present a gradual increasing trend with increasing DR, while those of CA and PCA 0.023 films have slightly larger values than those of PCA 0.303 and PCA 0.537 films, especially when DR equals to 1.5. These results indicate the amorphous regions of CA and PCA 0.023 films orient more easily than those of PCA 0.303 and PCA 0.537 films. At T g + 10 (Fig. 12d), O a of CA film first increases rapidly and then drops with rising DR and that of PCA 0.023 film first rises and keeps almost constant, while those of PCA 0.303 and PCA 0.537 films present a straight upward trend, indicating the increase of DS Pr is more beneficial to the amorphous orientation of PCA film at high T s and large DR.

Discussion
The above experimental results revealed the effects of the propionyl group on birefringence and wavelength dispersion of birefringence for PCA films with different DS Pr . Compared with CA film, the introduction of the propionyl group weakens the orientation birefringence (Δn in ) of PCA films at large DR. As DS Pr increases to 0.537, the birefringence of PCA film shows a very weak normal wavelength dispersion with different DR. In the discussion, the effect mechanisms of the propionyl group on birefringence and wavelength dispersion of birefringence for PCA films will be addressed in combination with the influence of chain orientation and DS Pr .
PCA is composed of four parts including the main chain and three different side groups of acetyl group, propionyl group and hydroxyl group. Since the contribution of the main chain on orientation birefringence is relatively small and can be neglected (Yamaguchi et al. 2012;Nobukawa et al. 2017), the orientation birefringence of PCA films can be expressed by the following equation (Yamaguchi et al. 2012): where Δn Ac ( ) , Δn p r ( ) and Δn OH ( ) are the orientation birefringence of acetyl, propionyl and hydroxyl groups, respectively. According to the Kuhn and Grun model (Yamaguchi et al. 2009b), the orientation birefringence of the stretched PCA film can be written as the following equation: (8) Δn in ( ) = Δn Ac ( ) + Δn p r ( ) + Δn OH ( ) Δn in ( ) = Δn 0 Ac ( )F Ac + Δn 0 Pr ( )F Pr + Δn 0 OH ( )F OH Fig. 12 The degree of crystal orientation of (110) plane (f 110 ) for CA and PCA films stretched at different T s (a T g -10, b T g +10) and DR. The ratio of oriented amorphous (O a ) for CA and PCA films stretched at different T s (c T g -10, d T g +10) and DR Vol.: (0123456789) where Δn 0 Ac , Δn 0 Pr and Δn 0 OH are the intrinsic birefringence of the acetyl group, propionyl group and hydroxyl group, respectively. F Ac , F Pr and F OH are the orientation function of the acetyl group, propionyl group and hydroxyl group, respectively.
For the convenience of discussion, we present a schematic diagram of the substituent group orientation at different substitution sites and the corresponding wavelength dependence of orientation birefringence for stretched PCA films in Fig. 13. Nobukawa et al. (Nobukawa et al. 2015) found that the acetyl group at the C-2 and C-3 sites of TAC contributes the positive orientation birefringence with weak normal wavelength dispersion, while that at the C-6 site provides the negative orientation birefringence with strong normal wavelength dispersion. PCA films have two substitution groups including acetyl and propionyl groups. The orientation of the acetyl group in C-2, C-3 and C-6 sites for stretched PCA film are similar to those of TAC film as shown in Fig. 13a, which is consistent with the infrared dichroism results that both the C = O stretching and C-O stretching have the same direction as the main chain (Fig. 9). Similarly, the propionyl group of PCA films should also present the different orientation birefringence at different substitution sites. According to infrared dichroism results (Fig. 9b-d), the directions of C = O stretching, -CH 2 asymmetric and symmetric stretching stretched PCA films at different DR are the same as that of the main chain, which is assigned to acetyl and propionyl groups. Therefore, the orientation of the propionyl group at C-2, C-3 and C-6 sites can be plotted as presented in Fig. 13a. Compared with the acetyl group, the propionyl group at the C-2 and C-3 sites should have a larger positive orientation birefringence with stronger normal wavelength dispersion, while that at the C-6 site shows a smaller negative orientation birefringence with weaker normal wavelength dispersion (Fig. 13b). The hydroxyl group has a great contribution to orientation birefringence though the wavelength dispersion is weak (Yamaguchi et al. 2009b;Songsurang et al. 2013), which is also plotted in Fig. 13b with the red dotted line.

Birefringence of PCA films
The substitution degrees of the acetyl group at C-2, C-3 and C-6 for CA are 0.98, 0.58 and 0.89, respectively (Fig. 1c). Since the activity of C-6 is the highest among the three sites (Wu et al. 2004), the propionyl substitution first occurs at C-6 and then at C-2 and C-3. Therefore, the propionyl substitution of PCA 0.023 takes place at C-6, while those of PCA 0.303 and PCA 0.537 films occur at C-6, C-2 and C-3.
At T g -10, CA and PCA films have little difference in molecular chain orientation including crystalline and amorphous regions between each other ( Fig. 12a and c), which indicates that the change in orientation birefringence is mainly caused by the substitution degree of propionyl group. The increase of Δn in with DR for CA and PCA films is because of the orientation increase of side groups along the chain  Fig. 13b, the hydroxyl group contributes a larger orientation birefringence than the propionyl group even at C-2 and C-3. Compared with CA film, the obvious drop of Δn in of PCA 0.023 film at DR ≥ 1.3 is due to the propionyl substitution at C-6 with negative orientation birefringence. The gradual decrease of Δn in with increasing DS Pr at DR ≥ 1.3 is mainly attributed to the propionyl substitution at C-2 and C-3 sites with lower orientation birefringence than that of the hydroxyl group. Furthermore, Δn th of CA and PCA films with increasing DR have no large change, especially that of PCA 0.537 film, which may be due to the difficult orientation of side groups along the thickness direction of film at T g -10. As presented in Figs. 6a-d, with the rising DR, n z of CA and PCA films show a slight change.
Compared with those at T g -10, Δn in of CA and PCA films at T g + 10 show a lower value at the same DR (DR = 1.5) which is caused by the lower orientation of the molecular chain as shown in Fig. 12. With the increase of DS Pr , the higher chain orientation especially in the amorphous region is in charge of the slight rising of Δn in for PCA films at DR ≥ 1.5 (Figs. 12b and d). With the increase of T s , Δn th at T g + 10 presents a clearer change trend than that at T g -10. For CA film, the increase of Δn th with DR is attributed to the contribution of the hydroxyl group with large orientation birefringence and weak normal wavelength dispersion. With the introduction of the propionyl group at the C-6 site, Δn th of PCA 0.023 film decreases with DR and shows a negative orientation birefringence with strong normal wavelength dispersion at DR of 2.0 (Fig. 5f). Moreover, the n z of PCA 0.023 film has a large change with DR (Fig. 6f). These results support the inference of the orientation birefringence of the propionyl group at the C-6 site as shown in Fig. 13. With increasing DS Pr , the drop of n x gradually turns to an upward trend and the rising of n z weakens, which is in line with the increase of chain orientation along the stretching direction. Since the introduction of the propionyl group at C-2 and C-3 sites instead of the hydroxyl group will decrease the orientation birefringence, the increase of Δn th with DS Pr at DR ≥ 1.5 should be attributed to the rising of chain orientation especially in the amorphous region ( Fig. 12a and d). Additionally, Δn th wavelength dispersion at DR of 2.0 weakens with increasing DS Pr accompanying the increase of propionyl substitution at C-2 and C-3 sites, indicating the propionyl group at C-2 and C-3 sites have a strong normal wavelength dispersion as shown in Fig. 13b. Interestingly, the inference in Fig. 13 can perfectly explain the effect of the propionyl group on the birefringent properties of PCA films and is in accord with the infrared dichroism results, which suggests the inference of the propionyl group is correct. More discussion on wavelength dispersion of orientational birefringence will be provided in the following section.
Wavelength dispersion of birefringence for PCA films As presented in Fig. 13b, the propionyl group at different substitution sites has a different contribution to orientation birefringence and its wavelength dispersion. With the DS Pr increased from 0 to 0.303, the wavelength dispersion of Δn in weakens and that of Δn th strengthens. However, when the DS Pr increased to 0.537, both Δn in and Δn th present a very weak wavelength dispersion at different DR, which means the wavelength dispersion of Δn in and Δn th are almost unaffected by the orientation of molecular chain and wavelength. For further analysis, we should discuss from the theory of wavelength dispersion. The wavelength dispersion can be derived as For PCA films, the wavelength dispersion can be written as where 0 is the reference wavelength, and generally 0 is selected as 550 nm.
The relationship between birefringence and wavelength can be acquired from the Cauchy equation (Yamaguchi et al. 2012;Uchiyama et al. 2012;Tojo et al. 2013;Mialdun and Shevtsova 2017) as Equation (9) can be further rewritten as Δn in ( ) The wavelength dispersion of PCA film can be expressed as the following equation For PCA 0.537 film, the degree substitution of the hydroxyl group in PCA 0.537 is quite small and can be neglected. Thus, the wavelength dispersion can be simplified as The results of the dichroism calculations in the polarized infrared suggest that the orientation variation of acetyl and propionyl groups with increasing DR are almost the same during stretching. Therefore, F Ac is almost equal to F Pr . The above equation is finally simplified as where A Ac , A Pr , B Ac , and B Pr are all constant terms in the Cauchy equation, which are related to the site and content of the substitution group. Considering the contributions of acetyl and propionyl groups at C-2, C-3 and C-6 sites are different, the equation can be written as (13 According to Fig. 13a, B 2,3 Ac and B 2,3 Pr are less than zero, while B 6 Ac and B 6 Pr are greater than zero. Moreover, the acetyl group has a strong normal wavelength dispersion at the C-6 site and the propionyl group presents a strong normal wavelength dispersion at C-2 and C-3 sites though both the acetyl group at C-2 and C-3 sites and propionyl group at C-6 site show a weak wavelength dispersion. Therefore, when acetyl and propionyl groups have a suitable proportion of substitution, B can be achieved to zero and then the wavelength dispersion at all wavelength is constant 1 with a flat wavelength dispersion curve, i.e., the birefringence does not change with wavelength. The PCA film with DS Pr of 0.537 seems to just fit the above situation. Both the wavelength dispersion of Δn in and Δn th at all wavelength are very close to 1.

Conclusion
PCA with different degrees of propionyl substitution was synthesized by a simple chemical modification method and the PCA optical films were prepared through the solution casting method. The effects of the propionyl group on the birefringence and wavelength dispersion of PCA films at different T s and DR were investigated. Compared with acetyl group, propionyl groups at C-2 and C-3 sites contribute a larger positive orientation birefringence with stronger normal wavelength dispersion, while that at C-6 site provides a smaller negative orientation birefringence with weaker normal wavelength dispersion. When DS Pr is 0.023, the substitution of the propionyl group is located at the C-6 site and Δn in of PCA film shows a decrease compared with CA films. With DS Pr increasing to 0.303, the propionyl substitution begins to occur at C-2 and C-3 sites except for C-6, meanwhile, the Δn in wavelength dispersion of PCA film at the same DR becomes weaker than that of PCA 0.023 film. With the further increase of DS Pr to 0.537, the total wavelength dispersion of the propionyl group of PCA film nearly cancels with that of the acetyl group. Therefore, the wavelength dispersion of Δn in and Δn th of PCA film at different DR become very weak and present nearly horizontal curves, which can satisfy the requirements of the present VA-LCD for (19) B = B 2,3 Ac + B 6 Ac + B 2,3 Pr + B 6 Pr optical compensation films. Furthermore, the increase of propionyl substitution weakens the Δn in and its wavelength dispersion of PCA film when the chain orientation is almost the same. The Δn th of PCA films stretched at T g -10 have an unclear change trend with increasing DR, while those stretched at T g + 10 decrease due to the rising of T s . Our work shows that the synthesis and preparation of VA-LCD optical compensation films can be achieved through the combination of chemical modification and stretching process, which provides a new idea for the design and preparation of optical compensation films for VA-LCD.