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Mechanisms of orientational and photoelastic birefringence generation of methacrylates for the design of zero-zero-birefringence polymers.

INTRODUCTION

Optical polymers have been used as key materials in various devices such as optical disks, lenses, and functional films for liquid crystal displays (LCDs) because of their light weight, facile processing, high transparency, and low manufacturing cost. However, they tend to exhibit birefringence during manufacturing or upon use in various environments. Birefringence degrades the performance of optical devices that require focusing by lenses or maintaining the polarized state of light. The principal types of birefringence of amorphous thermoplastic polymers for optical applications include orientational birefringence and photoelastic birefringence [1-3]. The orientational birefringence discussed in this article is assumed to be residual birefringence

after a polymer is heated to its glass transition temperature [T.sub.g] or higher, melted, oriented by stretching, and cooled to room temperature. Orientational birefringence can be defined by Eq. I,

[DELTA][n.sub.or] = [DELTA][n.sup.0] x [f.sub.m] (1)

where [DELTA][n.sub.or] is the orientational birefringence, [DELTA][n.sup.0] is the intrinsic birefringence, and [f.sub.m] is the orientation function of the polymer main chain [4, 5]. When the polymer main chain is perfectly oriented ([f.sub.m] = 1.0), the orientational birefringence is called intrinsic birefringence. Photoelastic birefringence is defined as the birefringence generated when a polymer is elastically deformed at a temperature that is sufficiently lower than [T.sub.g] (normally, about 1% strain or less). Photoelastic birefringence, [DELTA][n.sup.ph], is defined by Eq. 2,

[DELTA][n.sup.ph] = C x [sigma] (2)

where C is the photoelastic coefficient and a is the stress.

A polymer that exhibits no birefringence in any orientation or upon elastic deformation, i.e., zero-zero-birefringence polymer, is ideal for polymer films for LCDs such as polarizer protective films [1, 3], A method for designing the zero-zerobirefringence polymer has been proposed by Tagaya et al. [2] in systems consisting of more than three components, where at least one of the components exhibits orientational birefringence and photoelastic birefringence effects opposite to those of the other components. The optimal composition ratios of monomers can be obtained by simultaneously solving Eqs. 3-5, with the condition [DELTA][n.sup.0] = C=O,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

[w.sub.1] + [w.sub.2] + [w.sub.3] + ... + [w.sub.i] = 100 (5)

where [DELTA][n.sup.o], [C.sub.i], [w.sub.i] are the intrinsic birefringence, photoelastic coefficient, and weight fraction of the /th polymer (i = 1, 2, 3, ...), respectively. Some zero-zero-birefringence polymers have been designed and synthesized by ternary and quaternary copolymerization systems [2, 6-8]. Therefore, the effectiveness of the method for designing the zero-zero-birefringence polymer has been demonstrated.

As described above, in the method for designing the zero--zero-birefringence polymer, the composition ratios of monomers used for synthesizing the zero-zero-birefringence polymers are obtained by simultaneously solving Eqs. 3-5, once the orientational birefringence (the intrinsic birefringence) and the photoelastic birefringence (the photoelastic coefficient) have been evaluated separately. However, the reasonability of evaluating orientational birefringence and photoelastic birefringence separately is still a matter of debate, because the orientation behavior of molecules during generation of these types of birefringence has not been fully elucidated. A few studies have discussed these mechanisms partially [3, 9, 10]. However, the mechanisms remain to be investigated in detail experimentally.

The purpose of this article is to demonstrate the reasonability of the method for designing the zero-zero-birefringence polymer on the basis of an analysis of the mechanisms of orientational birefringence and photoelastic birefringence. We focus on four types of methacrylates, first determining their intrinsic birefringence [DELTA][n.sup.0] and photoelastic coefficient C values. Then, we categorize these methacrylate polymers into four birefringence-type; type 1: positive orientational birefringence, positive photoelastic birefringence, type 2: negative orientational birefringence, positive photoelastic birefringence, type 3: negative orientational birefringence, negative photoelastic birefringence, and type 4: positive orientational birefringence, negative photoelastic birefringence. Next, novel zero-zero-birefringence polymers are designed and synthesized using the four methacrylates through quaternary copolymerization. The orientation behaviors of the polymer molecules of each methacrylate homopolymers during the generation of orientational and photoelastic birefringence are analyzed using infrared spectroscopy (IR). Finally, we discuss the adequacy of the classification of polymers into the four birefringence-types mentioned above. Further, we demonstrate the reasonability of the method for designing the zero-zero-birefringence polymers.

EXPERIMENTAL

Preparation of the Polymer Samples

Methyl methacrylate (MMA) (99.8%, Mitsubishi Gas Chemical), 2,2,2-trifluroethyl methacrylate (TFEMA) (Tosoh F-Tech), phenyl methacrylate (PhMA) (95.0%, Alfa Aesar), 2,2,3,3,3pentafluorophenyl methacrylate (PFPhMA) (97.0%, SynQuest Laboratories), and styrene (St) (99.9%, Sigma-Aldrich) were selected as monomers. MMA, TFEMA, PFPhMA, and St were distilled under reduced pressure before use. PhMA was used without distillation. PMMA, the copolymer of MMA and TFEMA (MMA-TFEMA: 100/0, 90/10, 80/20, 70/30, 60/40 (wt%)), the copolymer of MMA and PhMA (MMA-PhMA: 100/ 0, 90/10, 80/20, 60/40, 50/50 (wt%)) and the copolymer of MMA and PFPhMA (MMA-PFPhMA: 100/0, 90/10, 80/20, 60/ 40 (wt%)) were synthesized to measure their birefringence properties and to observe their infrared dichroism, because the homopolymer of TFEMA, PhMA, and PFPhMA are mechanically brittle. n-Butyl mercaptan (95%, Wako Pure Chemical Industries), used as a chain transfer agent and tert-butyl peroxy2-ethylhexanoate (98%, NOF), used as an initiator, were added to each monomer at a ratio to monomer concentration of 0.1 and 0.4 wt%, respectively. Polymerization was carried out at 70[degrees]C for 24 h and then the obtained bulk polymer samples were heat-treated at 90[degrees]C for 24 h. However, all of the polymers were purified after polymerization by dissolution in dichloromethanc and precipitation into methanol to remove any remaining monomers and impurities. The pure polymers were dried at 90[degrees]C for 24 h under reduced pressure. To analyze the IR absorption of the difficult-to-observe ester group and phenyl group, we prepared poly(St-MMA: 95/5 (wt%)), poly(St-TFEMA: 95/5 (wt%)), poly(St-PhMA: 95/5 (wt%)), and poly(St-PFPhMA: 95/5 (wt%)). tm-Butyl peroxy-2-ethylhexanoate as an initiator was added to each monomer at a ratio to monomer concentration of 0.2 wt%. Polymerization was terminated at ~10% conversion by rapid cooling and then the samples were poured into methanol. The compositions of the resulting binary polymers and quaternary polymers were determined by means of [sup.1]H NMR and [sup.13]C NMR spectroscopy, respectively. Some typical spectra of the binary and quaternary polymers are shown in supporting information. To prepare polymer films, the polymers were dissolved in dichloromethane and then the polymer solutions were spread onto a glass plate with a knife coater. Films were dried at room temperature for 3 h and then at 90[degrees]C for 24 h under reduced pressure to eliminate the solvent. The thickness of the cast films was adjusted to 10 to 40 [micro]m. We prepared films 10 to 20 [micro]m in thickness for observing the IR spectra of the non-heat-drawn films during the generation of photoelastic birefringence. To observe the IR spectra of the heat-drawn films exhibiting orientational birefringence, we prepared films 10 to 30 [micro]m in thickness by adjusting the drawing conditions. To check the unsaturated region during the IR measurements, we employed films of different thicknesses. Using these, we could confirm that the relation between film thickness and absorbance was in keeping with the Lambert-Beer law. The absorbance of every target IR peak was in the unsaturated region.

Birefringence Measurements

To measure the orientational birefringence Anor, polymer films with a thickness of about 40 [micro]m were uniaxially drawn at their [T.sub.g] + 10[degrees]C and 25%/min using a universal tensile testing machine (Tensilon RTC-1210A, A&D). The orientational birefringence was measured at least 24 h after heat drawing at a wavelength of 632.8 nm at room temperature by optical heterodyne interferometry using a birefringence measurement system (ABR-10, UNIOPT). The photoelastic birefringence [DELTA][n.sub.ph] of the polymer films was measured at various levels of uniaxial tensile stress at room temperature using the birefringence measurement system. Stress was measured at the same time.

Infrared Spectroscopic Measurements

The IR dichroism of a heat-drawn polymer film was measured within the spectral range of 400 to 4000 [cm.sup.-1] using a polarized IR spectrometer (7000e FT-IR, Agilent Technologies) to analyze the orientation behavior of the polymer molecules during the generation of orientational birefringence. The absorbance of polarized light was measured parallel and perpendicular to the draw direction, and the draw direction was assumed to correspond to the direction of the polymer chain axis. The IR dichroism of a polymer film in an elastically deformed state was measured to determine the orientation behavior of polymer molecules during the generation of photoelastic birefringence. A sample film was fixed and then uniaxially drawn at room temperature using a tensile stress machine. IR dichroism was measured in about 20 s in a given stress after the stress was loaded and the cumulated number of measurements was reduced to prevent the stress relaxation. Stress and strain were measured at the same time. The dichroic ratio D is defined by [A.sub.//]/[A.sub.[perpendicular]] where [A.sub.//] and [A.sub.[perpendicular]] are the absorbances of polarized IR radiation in the directions parallel and perpendicular, respectively, to the draw direction [3]. The dichroic ratio is related to the orientation function /by:

f = (D - 1/D + 2) x ([D.sub.0] + 2/[D.sub.0] - 1) (6)

[D.sub.0] = 2 [cot.sup.2] [gamma], (7)

where [gamma] is the angle between the transition dipole moment vector of the absorbing group and the chain axis of the molecule [11,12]. The orientation function of the main chain was calculated using Eqs. 6 and 7 for orientational birefringence using the [alpha]-C[H.sub.3] bending band, which possesses a dipole moment vector perpendicular to the chain axis ([gamma] = 90[degrees]) [13], Furthermore, the orientation function f of the transition dipole moment vector itself with respect to the direction of stress is related to the dichroic ratio by f = (D - 1/D + 2]) [14]. Table 1 shows the assignment of the relevant IR absorption bands for each methacrylate polymer [15-19],

Other Measurements

The [T.sub.g] of the purified polymers were measured by differential scanning calorimetry (DSC-60, Shimadzu). The polymers were heated from room temperature to around 170[degrees]C in air, and then cooled to -20[degrees]C and reheated to 160[degrees]C at a scan rate of 10[degrees]C/min. The [T.sub.g] was measured during the second heating scan as the midpoint of the heat capacity transition between the upper and lower points of deviation from the extrapolated liquid and glass lines. The thermal decomposition temperature, [T.sub.d], of the purified polymers was measured as the 5% weight loss temperature of the polymers using a thermal analysis instrument (TG/ DTA-6200, SII Nano Technology) at a scan rate of 10[degrees]C/min in an air stream. The copolymers composition ratios of binary copolymers and quaternary copolymers were analyzed by means of [sup.1]H NMR spectroscopy and [sup.13]C NMR spectroscopy (AVANCEIII 600, Bruker), respectively, in CD[Cl.sub.3] as a reference. The weight average molecular weight, [M.sub.w], of the polymers was determined by gel permeation chromatography (GPC-LC20AD, Shimadzu) using tetrahydrofuran as the eluent at a flow rate of 0.6 mL/min. The molecular weight calibration curve was obtained using polystyrene standards.

RESULTS AND DISCUSSION

Birefringence Properties of Methacrylates

Figure 1 shows the orientational birefringence as a function of the orientation of the main chain of PMMA. The slope of the straight-line approximation shows the intrinsic birefringence of PMMA. The intrinsic birefringence of the other methacrylate polymers was determined in the same manner. Figure 2a and b show the intrinsic birefringence and the photoelastic coefficient of poly(MMA-TFEMA), poly(MMA-PhMA), and poly(MMAPFPhMA) as a function of the compositional ratio of the copolymers. The intercept of the approximated straight line where the proportion of MMA is 0 wt% represents the intrinsic birefringence and photoelastic coefficient of each homopolymer. Table 2 shows the intrinsic birefringence [DELTA][n.sup.0] and the photoelastic coefficient C of PMMA, PTFEMA, PPhMA, and PPFPhMA. Figure 3 is a birefringence map showing the relationship between the intrinsic birefringence [DELTA][n.sup.0] and the photoelastic coefficient C of PMMA, PTFEMA, PPhMA, and PPFPhMA. These methacrylates are located in different quadrants of the birefringence map. The signs of An0 and C in each quadrant are as follows: positive-positive for the first quadrant [type 1], negative-positive for the second quadrant [type 2], negativenegative for the third quadrant [type 3], and positive-negative for the fourth quadrant [type 4], The reasonability of the classification is discussed in the Correlation between Molecular Structure and Types of Birefringence section.

PMMA, PTFEMA, PPhMA, and PPFPhMA showed four types of birefringence properties, even though they were all methacrylates and their molecular structures only differed in terms of the substituent R in the side chains, as shown in Fig. 4. The difference between the molecular structures of PMMA and PTFEMA is the ester substituent, C--C[F.sub.3], and the difference between the molecular structures of PPhMA and PPFPhMA is the fluorine-substituted phenyl ring, indicating that a small change in the ester substituent changes the birefringence-type. The mechanisms of birefringence generation are described in the Investigation into the Mechanisms of Birefringence Generation section.

Design and Synthesis of Zero-Zero-Birefringence Polymers

A series of novel zero-zero-birefringence polymers can be designed using a quaternary system of MMA, TFEMA, PhMA, and PFPhMA, because the plots of these polymers in the birefringence map surround the origin of the map ([DELTA][n.sup.0] = C = 0), which represents the zero-zero-birefringence. The compositions of the monomers were determined to adjust both types of birefringence to zero using Eqs. 3-5. Theoretically, there is an indefinite number of solutions, because the number of variables is four while the number of functions is three. Figure 5 shows the compositions of TFEMA, PhMA, and PFPhMA against the composition of MMA required to achieve zero-zerobirefringence. This indicates that a zero-zero-birefringence polymer cannot be designed with less than 30 wt% MMA or more than 70 wt% MMA, because Eqs. 3-5 do not yield positive solutions in these ranges. Quaternary copolymers with six different compositions of MMA/TFEMA/PhMA/PFPhMA were synthesized, and their birefringence properties, [T.sub.g], [T.sub.d], and [M.sub.w] are shown in Table 3. The results indicated that all copolymers, regardless of their composition, were free of both types of birefringence and the thermal properties ([T.sub.g] and [T.sub.d]) of these polymers were controllable. Zero-zero-birefringence polymers were reported by Tagaya et al. [2] and Iwasaki et al. [7, 8], were synthesized by type 1, type 3, and type 4 monomers. This is the first report detailing the synthesis of zero-zero-birefringence polymers by four birefringence-type monomers.

Investigation Into the Mechanisms of Birefringence Generation

Orientational Birefringence: Conformation of the Repeat Unit of the Polymers During the Generation of Orientational Birefringence. The intrinsic birefringence, [DELTA][n.sup.0] that is a specific characteristic of a polymer is generally defined as [DELTA][n.sub.or] = [DELTA][n.sup.0] x fm (Eq. 1). The linear relationship between the orientation function of the main chain [f.sub.m] and [DELTA][n.sup.or] in Eq. I has been confirmed experimentally with polymers such as PMMA [13], PSt [20], polyethylene terephthalate) [21], polyethylene 2,6-naphthalenedicarboxylate) [21], poly(bisphenol-A carbonate) [22], and poly(vinyl chloride) [23]. Furthermore, the intrinsic birefringence [DELTA][n.sup.0] and polarizability anisotropy [DELTA][alpha] can be related by the following equation, demonstrating the proportional relationship between An0 and Aa:

[DELTA][n.sup.0] = 2[pi]/9 x N[rho]/M x [([n.sup.2] + 2).sup.2]/n x [DELTA][alpha] (8)

where n is the refractive index, N is Avogadro's number, p is the density, and M is the molecular weight of the repeat unit of the polymer [24],

Two assumptions can be made regarding the conformational change of the repeat unit of the polymer during the generation of orientational birefringence. The first assumption is that the conformation of the repeat unit of the polymer changes during the generation of orientational birefringence depending on the orientation of the polymer main chain [f.sub.m]; polymer side chains are oriented with the polymer main chains, and angle [gamma] between the transition dipole moment vector of an absorbing group in the side chain and the chain axis changes by the orientation of the main chain during the generation of orientational birefringence. The second assumption is that the repeat units of polymer chains have a specific conformation during the generation of orientational birefringence; the polymer main chains bend while the repeat unit of the polymer maintains a constant conformation. In other words, the angle y between the transition dipole moment vector of an absorbing group in the side chains and the chain axis is nearly constant.

Previously, the conformation of a repeat unit of uniaxially oriented atactic PSt was assumed; angle y between the transition dipole moment vector of the out-of-plane vibration of the phenyl ring and the chain axis was determined [25] by plotting the orientation function of the main chain [f.sub.m] as a function of the dichroic ratio of the experimentally obtained out-of-plane vibration as

[f.sub.m] = (D - 1/[D.sub.s] + 2) + ([D.sub.0s] + 2/[D.sub.0s] - 1) (9)

where [D.sub.s] is the measured dichroic ratio of the absorbing group, and [D.sub.0s] = 2[cot.sup.2][gamma]. In the same manner, the angles between the transition dipole moment vectors of an absorbing group and the chain axis were determined in polymers such as PMMA [13], atactic PSt [25], poly(styrene-acrylonitrile) [26], poly(vinyl phenol) [27], and poly(2,6-dimethyl 1,4-phenylene oxide) [28].

Here, we assumed that the [gamma] of an absorbing group in the side chain was constant, and we analyzed the conformation of PMMA, PTFEMA, PPhMA, and PPFPhMA during the generation of orientational birefringence. Figures 6 and 7 show the relationship between [f.sub.m] and ([D.sub.s] - 1/[D.sub.s] + 2) of C=O, C--O--C, in-plane and out-of-plane of the phenyl ring in the side chains of the methacrylates. A linear relationship was observed between [f.sub.m] and ([D.sub.s] - 1/[D.sub.s] + 2) in each Polymer. The angle between the transition dipole moment vector of the C=O stretching and the chain axis ([[gamma].sub.c=o]), the angle between the transition dipole moment vector of the C--O--C asymmetric stretching and the chain axis ([[gamma].sub.c=o]), he angle between the transition dipole moment vector of the [[gamma].sub.in-plane] bending of the phenyl ring and the chain axis ([[gamma].sub.in-plane]), and the angle between the transition dipole moment vector of the out-of-plane bending of the phenyl ring and the chain axis ([[gamma].sub.out-of-plane]) of the methacrylates were determined using Eq. 9. Table 4 shows each [gamma]. The [[gamma].sub.out-of-plane] of PPFPhMA could not be determined because the absorbance of the out-of-plane bending of the perfluorophenyl ring was not previously assigned.

The results indicated that the determined [[gamma].sub.s] of the methacrylate polymers was nearly constant during the generation of orientational birefringence. Based on the determined [[gamma].sub.s] and Refs. [13] and [25]--28, we can conclude that the latter assumption is more reasonable than the former.

Correlation Between Molecular Structure and Orientational Birefringence of Methacrylates. Molecular structure B of a methacrylate polymer (Fig. 4) is the same as the molecular structure of poly(propylene). The positive intrinsic birefringence of poly (propylene) was reported in Ref. [29], The contribution of molecular structure B to the orientational birefringence is positive. However, the intrinsic birefringence of PMMA is negative, indicating that the contribution of the ester is negative, and the negative contribution of the ester exceeds the positive contribution of the molecular structure (except that of the ester), leading to a negative intrinsic birefringence for PMMA. In other words, molecular structure A shown in Fig. 4 had a negative contribution to the orientational birefringence when R=C[H.sub.3]. We can conclude that molecular structure A, except for R, had a negative contribution to the orientational birefringence in PTFEMA, PPhMA, and PPFPhMA as well, because their [[gamma].sub.C=O] and [[gamma].sub.C--O--C] are close to those of PMMA, and the polarizability anisotropy of C[H.sub.3] is negligibly small. The polarizability anisotropy of C[H.sub.3] was reported in Ref. [30]: ([[alpha].sub.xx], [[alpha].sub.yy], [[alpha].sub.zz])=(2.27, 2.27, 2.34), [DELTA][alpha] = 0.0. The level of theory for the calculation of polarizability is B3LYP/6-311 + G(3df,2p) and the unit of the polarizability is [[Angstrom].sup.3].

Considering the positive intrinsic birefringence of PTFEMA, we estimated that the contribution of the ester substituent, C-C[F.sub.3], was positive. However, we could not assign the orientation behavior of C-C[F.sub.3] by IR because the vibrational mode of C-C[F.sub.3] has not been designated thus far.

The intrinsic birefringence of PPhMA, [DELTA][n.sup.0.sub.PPhMA], was negative and the absolute value was twice as large than as the absolute value of [DELTA][n.sup.0.sub.PMMA]. The contribution of the phenyl ring was probably negative, and caused the difference between the values of [DELTA][n.sup.0.sub.PMMA] and [DELTA][n.sup.0.sub.PPhMA]. On the other hand, considering the positive intrinsic birefringence of PPFPhMA, the contribution of the perfluorophenyl ring was estimated to be positive.

Photoelastic Birefringence: Conformation of the Repeat Unit of the Polymers During the Generation of Photoelastic Birefringence. The orientation functions of the transition dipole moment vectors of each group shown in Table 1 were analyzed. Figures 8 and 9 show the relationship between the strain and the orientation functions of the transition dipole moment of the polymer main chains and ester groups in the side chains of PMMA, PTFEMA, PPhMA, and PPFPhMA. Figure 10 shows the relationship between the strain and the orientation functions of the transition dipole moment of the polymer main chain and phenyl groups in the side chains of PPhMA and PFPhMA. A linear relationship between the strain and the orientation functions was confirmed during the generation of photoelastic birefringence. The results demonstrated that the C=O, C--O--C, and phenyl groups on the side chains of these polymers were mainly oriented and the main chains were hardly oriented during the generation of photoelastic birefringence. Therefore, the conformation of the repeat unit of polymer changes during the generation of photoelastic birefringence in all the methacrylates. In addition, in all of the methacrylates, C=O was oriented perpendicular to the drawing direction contributing negative to the photoelastic birefringence, and the C--O--C was oriented parallel to the drawing direction contributing positive to the photoelastic birefringence.

The negative contribution of C=O was higher than the positive contribution of C--O--C in PMMA. The negative contribution of C=O was thought to be responsible for the negative photoelastic birefringence of PMMA. Regarding PTFEMA, the positive contribution of C--O--C was higher than the negative contribution of C=O, leading to a small photoelastic coefficient for PTFEMA. Quantitative estimation of the orientation behaviors of the C-C[F.sub.3] vector via experimentation was difficult.

The positive contribution of C--O--C was higher than the negative contribution of C=O, and [f.sub.in-plane] increased and [f.sub.out-of-plane] decreased as the strain increased in PPhMA. The contribution of C--O--C was positive to the photoelastic birefringence; however, the positive contribution of the phenyl ring was higher than that of C--O--C, leading to a high positive photoelastic birefringence for PPhMA, because the polarizability anisotropy of the phenyl ring (reported in Ref. [30]) is nearly 2.4 times higher that of C--O--C; dimethyl ether (C[H.sub.3]OC[H.sub.3]): ([[alpha].sub.xx], [[alpha].sub.yy], [[alpha].sub.zz])=(5.68, 4.50, 4.58), [DELTA][alpha]= 1.1 [[Angstrom].sup.3], and benzene ([C.sub.6][H.sub.6]): ([[alpha].sub.xx], [[alpha].sub.yy], [[alpha].sub.zz]) = (11.96, 11.96, 6.58), [DELTA][alpha]= 2.7 [[Angstrom].sup.3]. The level of theory for the calculation of polarizability is B3LYP/6-311 + G(3df,2p).

Regarding PPFPhMA, the contributions of C=O and C--O--C were almost the same. We estimated that the orientation behavior of the phenyl ring of PPFPhMA during the generation of photoelastic birefringence was similar to that of PPhMA; the phenyl ring had a positive contribution to the photoelastic birefringence, because [f.sub.in-Plane] increased as the strain increased, and the measured photoelastic birefringence of PPFPhMA was positive.

Correlation Between Molecular Structure and Types of Birefringence. It can be concluded that PMMA and PPhMA have almost a specific conformation during the generation of orientational birefringence; the polymer main chains were oriented while the repeat unit of the polymer maintained a constant conformation, because the determined [gamma]s of C=O, C--O--C and phenyl ring were nearly constant. Regarding PTFEMA and PPFPhMA, the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the [[gamma].sub.out-of-plane] could not be determined. We estimated that the conformation of a repeat unit of PTFEMA and PPFPhMA during the generation of orientational birefringence are almost constant based on the determined [[gamma].sub.C=O], [[gamma].sub.C--O--C], and [[gamma].sub.in-plane]. On the other hand, we confirmed that during the generation of photoelastic birefringence in the glassy state, the C=O, C--O--C and phenyl ring in the side chains were mainly oriented and the main chains were hardly oriented with an increase in the applied stress, and the conformation of the repeat unit of the polymers changed. These findings demonstrated the reasonability of evaluating orientational and photoelastic birefringence separately and also the adequacy of the classification of polymers into four birefringence-types. Given these results and the fact that zero-zero-birefringence polymers could be prepared successfully by four-birefringence type monomers mentioned above, we demonstrated the reasonability of the method for designing the zero-zero-birefringence polymers.

The birefringence properties of the molecular structure of methacrylate polymers, with the exception of the ester substituent, are expected to be located near PMMA in the birefringence map because the [[gamma].sub.C=O] and [[gamma].sub.C--O--C] of the methacrylates have similar values and the polarizability anisotropy of C[H.sub.3] is negligibly small. In other words, differences in the birefringence properties of PPFPhMA, PPhMA, and PTFEMA as compared to PMMA are caused by the contributions of the substituents on each polymer.

The orientation behavior of C-[CF.sub.3] in PTFEMA was thought to exert a positive contribution to the orientational birefringence. The orientation behavior of the phenyl ring in PPhMA had a negative contribution to the orientational birefringence, and a positive contribution to the photoelastic birefringence, causing the birefringence properties of PPhMA to be plotted as type 2. Furthermore, the orientation behavior of the phenyl ring in PPFPhMA was estimated to exert a positive contribution to the orientational birefringence and photoelastic birefringence, causing the birefringence properties of PPFPhMA to be plotted as type 1. In particular, we confirmed that the phenyl ring led to a high photoelastic coefficient for PPhMA and PPFPhMA.

CONCLUSIONS

The intrinsic birefringence [DELTA][n.sup.0] and photoelastic coefficient C of PMMA, PTFEMA, PPhMA, and PPFPhMA were determined. These polymers were categorized into four birefringence-types, even though their molecular structures differ only by the substituents on the side chains. Novel zero--zero-birefringence polymers were then designed and synthesized using the four birefringence-type methacrylates with six different compositions using quaternary random copolymerization. This is the first report detailing the synthesis of zero--zero-birefringence polymers by four birefringence-type monomers. Furthermore, we confirmed that the mechanisms of orientational birefringence and photoelastic birefringence generation were different in these four birefringence-type methacrylates. The conformation of the repeat unit of the polymers was nearly constant during the generation of orientational birefringence. In contrast, during the generation of photoelastic birefringence in the glassy state, the conformation of the repeat unit of the polymers changed. These findings demonstrated the reasonability of evaluating orientational and photoelastic birefringence separately, as well as the adequacy of the classification of polymers into four birefringence-types. Given these results and the fact that zero--zero-birefringence polymers could be prepared successfully by four-birefringence type monomers, we demonstrated the reasonability of the method for designing the zero--zero-birefringence polymers. The findings of this paper are extremely valuable for further understanding of the birefringence of polymers.

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Houran Shafiee, Shotaro Beppu, Shuhei Iwasaki, Akihiro Tagaya, Yasuhiro Koike

Keio Photonics Research Institute, Graduate School of Science and Technology, Keio University, Kawasaki 212-0032, Japan

Correspondence to: Houran Shafiee; e-mail: shafiee@kpri.keio.ac.jp

Contract grant sponsor; Japan Society for the Promotion of Science (JSPS) through its "Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program)."

Additional Supporting Information may be found in the online version of this article.

DOI 10.1002/pen.24072

Published online in Wiley Online Library (wileyonlinelibrary.com).

TABLE 1. Assignment of the relevant IR absorption bands for each
polymer.

            Main chain [15-17]            Side chain [17-19]

           [alpha]-
          C[H.sub.3]                                     C--O--C
          symmetrical   C[H.sub.2]                     asymmetrical
Polymer     bending     stretching    C=O stretching    stretching

PMMA      1388-1390     2842-2851       1730-1776       1110-1170
          [cm.sup.-1]   [cm.sup.-1]    [cm.sup.-1],    [cm.sup.-1]
PTFEMA                                (3440 cm-1 for
PPhMA                                   over tone)
PPFPhMA

          Side chain [17-19]

              In-plane        Out-of-plane
              bending           bending
             of phenyl          of phenyl
Polymer         ring              ring

PMMA             --                --

PTFEMA           --                --
PPhMA     1025 [cm.sup.-1]   690 [cm.sup.-1]
PPFPhMA   1048 [cm.sup.-1]       Unknown

TABLE 2. Intrinsic birefringence [DELTA][n.sup.0],
photoelastic coefficient C, and [T.sub.g] of
PMMA, PTFEMA, PPhMA, and PPFPhMA. (a)

Polymer                      PMMA    PTFEMA     PPhMA    PPFPhMA

Intrinsic birefringence      -5.6       3.5     -10.9      24.2
[DELTA][n.sup.0]
  (x [10.sup.-3])
Photoelastic coefficient     -5.5      -2.2      42.6      29.8
  C (T[Pa.sup.-1])
[T.sub.g] ([degrees]C)        115        75       130       139

(a) The intrinsic birefringence [DELTA][n.sup.0] and photoelastic
birefringence C of PMMA, PTFEMA, and PPFPhMA were
analyzed in previous work [2,8],

TABLE 3. Intrinsic birefringence [DELTA][n.sup.0], photoelastic
coefficient C, [T.sub.g], [T.sub.d], and [M.sub.w] of the
zero-zero-birefringence polymers in the quaternary
copolymerization system MMA/TFEMA/PhMA/PFPhMA.

                         [DELTA]
MMA/TFEMA/PhMA/         [n.sup.0]            C           [T.sub.g]
PFPhMA (wt%)         (X [10.sup.-3])   ([TPa.sup.-1])   ([degrees]C)

29.4/63.1/6.5/0.9         0.02              0.0             101
39.6/51.0/5.0/4.4         0.07              0.0             106
50.2/38.7/3.5/7.5         0.06              0.0             112
60.5/27.1/1.7/10.7        0.02              0.0             116
65.0/20.9/1.0/13.1        0.12              0.0             120
69.9/15.7/0.3/14.1        0.05              0.0             121

MMA/TFEMA/PhMA/       [T.sub.d]        [M.sub.w]
PFPhMA (wt%)         ([degrees]C)   (X [10.sup.-4])

29.4/63.1/6.5/0.9        317             28.2
39.6/51.0/5.0/4.4        311             29.2
50.2/38.7/3.5/7.5        316             27.8
60.5/27.1/1.7/10.7       309             29.6
65.0/20.9/1.0/13.1       320             27.2
69.9/15.7/0.3/14.1       321             28.8

The copolymer compositions were obtained by 13C NMR analysis.

TABLE 4. Angle between the transition dipole moment of some side chain
absorbing groups and the chain axis.

           [[gamma].     [[gamma]     [[gamma].sub.   [[gamma].sub.
Polymer    sub.C=O]      .sub.C=O]    out-of-plane]     in-plane]
          ([degrees])   ([degrees])    ([degrees])     ([degrees])

PMMA          68            68             --              --
PTFEMA        72            66             --              --
PPhMA         69            66             59              71
PPFPhMA       69            70             --              68
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Author:Shafiee, Houran; Beppu, Shotaro; Iwasaki, Shuhei; Tagaya, Akihiro; Koike, Yasuhiro
Publication:Polymer Engineering and Science
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Date:Jun 1, 2015
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