Photoelastic Birefringence Research Articles

Two-Inch Aluminum Nitride (AIN) Single Crystal Growth for Commercial Applications

Aluminum Nitride (AlN) is an Ultra-wide Bandgap (UWBG) semiconductor that attracts significant interest for its potential application for high power switches, high power density, high frequency and high operating temperature for rf. Currently, AlN substrates are being used for ultraviolet (UV) light emitters at wavelengths shorter than 300nm including UVC Light Emitting Diodes (UVC LED) as well as laser diodes. Successful commercialization of the aluminum nitride as an UWBG substrate depends on several factors such as substrate availability, size, quality, and cost. Here we report on the current status of the bulk growth of AlN single-crystals as well as their subsequent processing for making substrates.The AlN crystals are grown using a proprietary physical vapor transport (PVT) technique where a sublimation-recondensation approach is utilized. This method shows very high potential in terms of growing large (> 2-in in diameter) bulk AlN crystals. However, some challenges have yet to be resolved en route to 100 mm diameter crystals. The crystal growth is carried out in a Tungsten crucible that contains the AlN seed and the source material. The AlN source material sublimes and decomposes into Aluminum atoms and Nitrogen molecules. These species are then transported to the seed where they form AlN and incorporate into the growing crystal along the c-axis. Aluminum nitride is used as a native seed utilizing the Al-polar face. Increasing the crystal dimensions demands careful tailoring of thermal gradients to lower the thermally induced stresses and achieve high crystalline quality. Currently, AlN single crystals with diameters > 2 inch are grown using the method described above and larger diameters are possible with appropriate furnace design. Large bulk crystals could be beneficial for production of non-polar and semi-polar substrates which are used to reduce the internal electric fields due to polarization.The AlN crystals are sliced into c-face oriented wafers and subsequently polished. Several substrate parameters are tracked such as the wafer bow, thickness variation, surface roughness, and sub-surface damage. The two-inch AlN wafers have a radius of curvature ≥ 20 m, RMS ≤ 5 Å, and zero sub-surface damage. The crystalline quality is measured by X-ray diffractometry (XRD) rocking curves, etch pit density, and photo-elastic birefringence pattern (cross-polar imaging). Narrow rocking curves for both symmetric and asymmetric reflections with full width at half maximum (FWHM) of 6 - 10 arcsec are measured across the whole the wafer area. The AlN wafers are transparent in the UV region. The graph shows a 52-point map of the absorption coefficient values 8 – 10 cm-1 at 265nm wavelength for a 2-in AlN substrate. The very low UV absorption is linked to the material purity measured by Secondary Ion Mass Spectrometry (SIMS) and Glow Discharge Mass Spectrometry (GDMS). Excellent material purity ensures achievement of high thermal conductivity, a crucial parameter for an UWBG substrate. We measure the thermal conductivity using a Xenon flash method conforming to the ASTM E1461-01 or ASTM E1461-13 standards. Using this method directly on 2-inch AlN substrate we obtain room temperature thermal conductivity 293 W/m*K at room temperature (RT) and with very high slope of about -1.6 for the temperature range from RT to 300°C suggesting minimal phonon scattering.AlN substrates made using the above described methods are used to fabricate high performance, long lifetime UVC LEDs for air purification, water disinfection, surface cleaning, and environmental sensing. High quality pseudomorphic epitaxial layers are grown using Metal-Organic Chemical Vapor Deposition (MOCVD) process to form the device structure. Commercially available WD product (Klaran™) achieve germicidal power outputs that exceed 80 mW with drive currents up to 700 mA at a nominal wavelength of 265 nm. The devices feature long lifetimes exceeding 6000 hours at L50B10 as well as a wide radiation pattern with a viewing angle of 130°. Figure 1

Thermal, Mechanical, and Optical Properties of Maleimide Copolymers Containing Twisted N‐Phenyl Substituents in the Side Chain

AbstractUV absorption spectroscopic measurements and DFT calculations revealed that N‐(alkyl‐substituted phenyl)maleimides with substituents at the ortho position favored a twisted N‐phenyl conformation, due to the steric hindrance between the maleimide ring and the substituted N‐phenyl moiety. High‐molecular‐weight copolymers were synthesized by radical copolymerization of the N‐(alkyl‐substituted phenyl)maleimides with n‐butyl vinyl ether and n‐butyl acrylate. The thermal properties of the copolymers were determined by thermogravimetric analysis and differential scanning calorimetry. The mechanical tensile tests under temperature control revealed the mechanical features of the copolymers depending on their repeating structure and composition. The significant temperature dependence of the modulus and strain of the copolymers was also clarified. Then, the transparency, refractive indices, and birefringence properties of the copolymer films were evaluated. It was confirmed that the maleimide copolymers had negative orientational birefringence with small absolute values and positive photoelastic birefringence. The effect of the conformational structure of the N‐phenyl groups on the thermal, mechanical, and optical properties of the copolymers was discussed.

Birefringent properties of poly(phosphonate)s and poly(thiophosphonate)s derived from various bisphenols

The birefringent properties of poly(phosphonate)s and poly(thiophosphonate)s possessing various bisphenol structures were investigated. The CR values (orientational birefringence) of the poly(phosphonate)s and the poly(thiophosphonate)s range from −0.3 × 10−9 to + 1.3 × 10−9 Pa−1 and from −0.6 × 10−9 to + 0.8 × 10−9 Pa−1, respectively, which are lower than those of the corresponding bisphenol A-based polymers. The CD values (photoelastic birefringence), which range from + 4.0 × 10−11 to + 4.9 × 10−11 Pa−1, are also lower than those of the corresponding bisphenol A-based polymers. The birefringent properties of poly(phosphonate)s and poly(thiophosphonate)s possessing various bisphenol structures were investigated. The CR values (orientational birefringence) of the poly(phosphonate)s and the poly(thiophosphonate)s range from −0.3 × 10−9 to + 1.3 × 10−9 Pa−1 and from −0.6 × 10−9 to + 0.8 × 10−9 Pa−1, respectively, which are lower than those of the corresponding bisphenol A-based polymers. The CD values (photoelastic birefringence), which range from + 4.0 × 10−11 to + 4.9 × 10−11 Pa−1, are also lower than those of the corresponding bisphenol A-based polymers.

Photoelastic birefringence of copolymers with non-planar structure

We demonstrate the utility of nonplanar building blocks to tune the polymer photoelastic birefringence and obtain near zero and negative photoelastic coefficients. Photoelastic properties of two novel random copolymers systems: 2-vinlypyridene (2VP)-hydroxyadmantyl methacrylate (HAMA) and vinyl pyrrollidone (VP)-isobornylacrylate (iBOA) were investigated at a function of comonomer composition. Photoelastic coefficient of the copolymers could be facilely tuned by changing the copolymer composition. In particular, we show that negative stress optic coefficient could be obtained from VP - iBOA copolymers and near zero stress optic coefficient could be obtained from 2VP -HAMA copolymers. In addition, we investigate the effect of addition of triethylene glycol (TEG) as a plasticizer on the photoelastic properties for the 2VP-HAMA copolymers. We found that addition of TEG led to a reduction in both the polymer Tg and photoelastic coefficient. Our study indicates that bulky non-planar side groups in the polymer backbone tend to induce negative photoelastic birefringence and can be utilized as important building blocks for the design of optical polymers.

Low Birefringent Properties of Poly(phosphonate) Derivatives

The birefringent properties of bisphenol A-based poly(phosphonate) and poly(thiophosphonate) were investigated. The orientational birefringences (CR values) of the poly(phosphonate) derivatives are in the range from +1.2 × 10–9 to +1.5 × 10–9 Pa–1, which are less than half of those of the conventional bisphenol A-based polymers. In addition, their photoelastic birefringences (CD values) are in the range from +5.7 × 10–11 to +6.1 × 10–11 Pa–1, which are also lower than those of the conventional bisphenol A-based polymers. From the DFT calculations of the polarizability anisotropies of the model compounds, the low birefringent properties of the poly(phosphonate) derivatives are most probably due to the presence of the P═O and P═S groups and the phenyl substituents perpendicularly oriented to the main chain direction.

Effect of trifluoromethyl substituents on birefringence of polystyrene

Transparent thermoplastic polymers that exhibit no birefringence are ideal for optical components such as optical films for liquid crystal displays and various lenses. Copolymerization of a positive birefringent monomer with a negative monomer is an effective technique for obtaining low birefringent polymers, especially zero‐photoelastic birefringence polymers that exhibit no photoelastic birefringence even during elastic deformation. We prepared four types of trifluoromethyl‐substituted polystyrenes. By substituting hydrogens at the ortho or meta positions of the benzene ring of polystyrene, we demonstrated that poly(2‐(trifluoromethyl)styrene), poly(3‐(trifluoromethyl)styrene), and poly(3,5‐bis(trifluoromethyl)styrene) had negative photoelastic coefficients. However, poly(4‐(trifluoromethyl)styrene) had a positive photoelastic coefficient similar to that of polystyrene. Based on these results, we synthesized a zero‐photoelastic birefringence polymer of poly(2‐(trifluoromethyl)styrene‐co‐4‐(trifluoromethyl)styrene) (55/45 wt.) exhibiting no photoelastic birefringence in elastic deformation, in which the positive photoelastic birefringence of the poly(4‐(trifluoromethyl)styrene) unit was compensated for by the negative photoelastic birefringence of the poly(2‐(trifluoromethyl)styrene) unit. The discovery of polymers having negative photoelastic coefficients is valuable for the design and synthesis of zero‐photoelastic birefringence polymers. The four types of trifluoromethyl‐substituted polystyrenes are promising optical materials because they have high transparency (transmittance > 89–92% for 27–34‐µm thickness films) in the visible and near‐infrared regions and a high decomposition temperature of approximately 400°C. Copyright © 2016 John Wiley & Sons, Ltd.

Generalized characteristics of photo-elastic birefringence in polymer strip waveguides

This work investigates the material birefringence in a polymer strip waveguide which originates from thermal stress during the fabrication process. The stress is estimated through a comprehensive numerical study based on a realistic finite element model. The characteristics of birefringence are obtained in a generalized form and expressed by an empirical formula, which is applicable to various polymer materials. The developed formula can be employed to specify the photo-elastic birefringence of a polymer strip channel only by knowing the birefringence in its planar film. This will eliminate the necessity of extensive numerical analysis of thermal stress in such polymer waveguides, and accordingly help the management of stress-induced effects efficiently.

Mechanisms of orientational and photoelastic birefringence generation of methacrylates for the design of zero–zero‐birefringence polymers

The intrinsic birefringence Δn0 and photoelastic coefficient C of poly(methyl methacrylate), poly(2,2,2‐trifluroethyl methacrylate), poly(phenyl methacrylate), and poly(2,2,3,3,3‐pentafluorophenyl methacrylate) were determined. We categorized these methacrylate polymers into four birefringence‐types, even though their molecular structures differed only by the substituents on the side chains. Based on the results of Δn0 and C, novel polymers that exhibit neither orientational nor photoelastic birefringence, i.e., zero–zero‐birefringence polymers, were designed and synthesized by quaternary copolymerization system. Furthermore, we confirmed that the mechanisms of orientational birefringence and photoelastic birefringence generation were different in these methacrylate polymers. The conformation of the repeat unit of the polymers was nearly constant during the generation of orientational birefringence. In contrast, the conformation of the repeat unit of the polymers changed during the generation of photoelastic birefringence in the glassy state. 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. POLYM. ENG. SCI., 55:1330–1338, 2015. © 2015 Society of Plastics Engineers

High sensitive measurement of optical rotation based on photo-elastic modulation

In order to realize the continuous and stable, high speed, high precise and high sensitive measurement of optical rotation, and considering the application advantages of photo-elastic polarization modulation technology with high modulation frequency, high modulation purity, high modulation accuracy and good modulation stability, a new scheme about the measurement of optical rotation based on photo-elastic modulation is presented. Probe laser orderly passes through a polarizer, the rotation sample to be measured, a photo-elastic modulator, and a analyzer, and finally reaches the detector, this system uses less optical devices than any others previously reported, so it considerably reduces the measurement error that may be introduced by the optical devices. In the detecting of light path, the polarization axes of the polarizer and analyzer are respectively adjusted with respect to the photo-elastic modulator's fast axis directions 0° and 45°, the optical arrangements make the rotation angle to be measured appear in the alternating current signal, and the photo-elastic modulator's residual birefringence only appears in the odd harmonics. Consequently, the second harmonic signal of photo-elastic modulation is selected as the object to study, which effectively avoids the influence of residual birefringence of the photo-elastic modulator on optical rotation measurement, and efficiently improves the accuracy of optical rotation measurement. What is more, the detector output signal is separated into two parts, the direct current and alternating current signal. The alternating current signal is amplified, then outputs by a lock-in amplifier, which enhances the measurement sensitivity further. A ingenious verification test experiment is done, firstly, the probe laser is modulated into circularly polarized light, and then precisely rotates the polarizer to replace the optical rotation sample. The results show that the new scheme is feasible, this experiment gives the proportion coefficient of the measurement system, the sensitivity of optical rotation measurement increasing up to 3.15× 10-7 rad, and the measurement precision exceeding 0.3%. Therefore, in this scheme achieved is a high sensitive and precise measurement of optical rotation, and it is expected to be applied to the high sensitive and precise rotation measurement. The verification test experiment designed by us can also provide a outstanding calibration reference for high sensitive rotation measurement system.

Design and synthesis of zero–zero‐birefringence polymers using N‐methylmaleimide

ABSTRACTZero–zero‐birefringence polymers which exhibit no orientational birefringence and no photoelastic birefringence may be suitable candidates for the components of optical devices. To develop zero–zero‐birefringence polymers, a novel copolymerization system is required. We investigated two types of birefringence of poly(N‐methylmaleimide) (PMeMI) and showed that PMeMI exhibits positive orientational and photoelastic birefringence. On the basis of the results, we calculated the optimal composition for compensating both types of birefringence by solving three equations which describe the relationship between birefringence properties and weight fraction of monomers. When the copolymer compositions were MMA/BzMA/MeMI = 86/8/6 and 88/8/4 (wt %), zero–zero‐birefringence polymers were obtained. By using MeMI as a comonomer, these zero–zero‐birefringence polymers have a much higher glass transition temperature (Tg) than those of previous researches. Also, this polymer film has high transparency comparable with that of PMMA film. Therefore, we conclude that we successfully prepared zero–zero‐birefringence polymers using N‐substituted maleimide and that N‐substituted maleimide is a promising material for zero–zero‐birefringence polymers for optical devices. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40423.

Design of zero–zero‐birefringence polymers in methacrylate copolymer systems containing trichloroethyl methacrylate

AbstractPolymers that exhibit neither orientational nor photoelastic birefringence, called zero–zero‐birefringence polymers, are candidate materials for preparing optical components of liquid crystal displays (LCDs). Analyzing the birefringences for various methacrylate polymers is an issue of current importance in developing zero–zero‐birefringence polymers with appropriate characteristics for LCDs. The researchers have investigated different types of birefringence for poly(2,2,2‐trichloroethyl methacrylate) (PTCEMA) and have shown that PTCEMA exhibits negative orientational and photoelastic birefringences. By using TCEMA as a comonomer, a zero–zero‐birefringence polymer having much higher glass transition temperature (Tg) compared with previous researches has been prepared by ternary copolymerization. Moreover, the researchers have fabricated zero–zero‐birefringence polymers in a quaternary system containing TCEMA. The property analyses indicate that Tg can be controlled while maintaining the zero–zero‐birefringence property, which shows that designing a quaternary zero–zero‐birefringence polymer permits selective synthesis with the most appropriate characteristics. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013

A polarized laser backlight using a zero-zero-birefringence polymer for liquid crystal displays

We proposed a polarized laser backlight to improve light use efficiency of liquid crystal displays, and evaluated its basic polarization properties. In order not to degrade the polarization state, light guide plates were fabricated of polymer free of orientational and photoelastic birefringence, which is called zero-zero-birefringence polymer.

Copolymers of methyl methacrylate with N‐trifluorophenyl maleimides: High glass transition temperature and low birefringence polymers

AbstractCopolymers of methyl methacrylate (MMA) with 2,3,4‐ and 2,4,6‐trifluorophenyl maleimides (TFPMIs) were synthesized by a free radical initiator, azobisisobutyronitrile, in 1,4‐dioxane and also in bulk. The refractive indexes of the copolymers were in the range of 1.49–1.52 at 532 nm. The Tgs were 133–195 °C depending on copolymer compositions. In addition, the copolymers were thermally stable, Td > 350 °C. The orientational and photoelastic birefringence of the copolymers were also investigated. As both of the orientational and photoelastic birefringences of PMMA are negative, whereas those of poly(TFPMI)s are positive, we could obtain nearly zero orientational and photoelastic birefringence polymers when the ratios of 2,3,4‐TFPMI/MMA were 15/85 and 5/95 mol %, respectively. For 2,4,6‐TFPMI, zero orientational and photoelastic birefringences could be obtained when the ratios of 2,4,6‐TFPMI/MMA were 12/88 and 3/97 mol %, respectively. The Tgs of those copolymers with zero birefringences were in the range of 135–140 °C. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012

Design and synthesis of zero–zero-birefringence polymers in a quaternary copolymerization system

We designed and synthesized quaternary copolymers of methyl methacrylate (MMA), 2,2,2-trifluoroethyl methacrylate (TFEMA), benzyl methacrylate (BzMA), and 3,3,5-trimethylcyclohexyl methacrylate (TMCHMA) and we investigated their birefringence, thermal properties, and other optical properties. When the copolymer composition was MMA/TFEMA/BzMA/TMCHMA = 50:38:8:4, 40:30:7:23, or 30:21:7:42 (wt%), a zero–zero-birefringence polymer that exhibited neither orientational nor photoelastic birefringence was obtained. We demonstrated that such zero–zero-birefringence polymers with a variety of compositions could be successfully prepared in the quaternary system by using the same compensation method as applied in ternary random copolymerization. We also demonstrated that the glass-transition temperature (Tg) and refractive index (nD) of these copolymers could be controlled with high accuracy while retaining their zero–zero-birefringence property. We can therefore predict the type of birefringence, the Tg, and the nD of a particular copolymer before polymerization. Zero–zero-birefringence polymers with the most appropriate characteristics can then be synthesized selectively by quaternary copolymerization.

Improvement of the physical properties of poly(methyl methacrylate) by copolymerization with N-pentafluorophenyl maleimide; zero-orientational and photoelastic birefringence polymers with high glass transition temperatures

Copolymers of N-pentafluorophenyl maleimide (PFPMI) with methyl methacrylate (MMA) were synthesized by a free radical initiator, such as AIBN. The refractive indexes of the copolymers remained nearly constant (1.4970 at 532 nm) regardless of the polymer composition. These copolymers also showed high thermal stability. The orientational and photoelastic birefringence of the copolymers obtained were measured. Since both of the orientational and photoelastic birefringences of PMMA are negative whereas poly(PFPMI) exhibits positive, thus we have obtained nearly zero orientational and photoelastic birefringence polymers when the ratios of MMA/PFPMI were 91.8/8.2 and 97.0/3.0 mol%, respectively. Based on the experimental data, the ratios of MMA/PFPMI for zero birefringence were determined to be 88.9/11.1 and 93.8/6.2 mol% for orientational and photoelastic birefringence, respectively. The T gs of corresponding copolymers were estimated to be 128 and 122 °C.

Compensation and control of the birefringence of polymers for photonics

We demonstrated that a method based on the analysis of both orientational birefringence (intrinsic birefringence) and photoelastic birefringence (photoelastic coefficient) is effective for designing polymers that are processed in a molten state and used in a glassy state. The designed polymer exhibits no birefringence for any orientation of the polymer main chains or under elastic deformation. Birefringence is close to zero even in injection-molded plates of the polymer. We have also shown that it is possible to compensate and control birefringence of polymers using inorganic nanocrystals, and we have obtained valuable information on the optimal size of nanocrystals for compensation and control of birefringence. Nanocrystals measuring ∼200 nm in length and 20 nm in width are sufficiently small to compensate for birefringence, but sufficiently large to permit control of orientation by casting. Reverse birefringence wavelength dispersion of a polymer film containing nanocrystals was achieved by casting and heat drawing. We demonstrated that a method based on the analysis of both orientational birefringence and photoelastic birefringence is effective for designing polymers that are processed in a molten state and used in a glassy state. The designed polymer exhibits no birefringence for any orientation of the polymer main chains or under elastic deformation. Birefringence is close to zero even in injection-molded plates of the polymer. We have also shown that it is possible to compensate and control the birefringence of polymers using inorganic nanocrystals, and we have obtained valuable information on the optimal size of nanocrystals for compensation and control of birefringence.

Mechanism of generation of birefringence in poly(methyl methacrylate/styrene)

The relationship between the intrinsic birefringence and the composition ratio and between the photoelastic coefficient and the composition ratio in poly(methyl methacrylate (MMA)/styrene (St)) was investigated. A linear relationship was observed between the orientational birefringence and the composition ratio but not between the photoelastic coefficient and the composition ratio. The influence of the compositional distribution on the birefringence was investigated, and the results suggested that the compositional distribution of poly(MMA/St) minimally affects birefringence. We also analyzed the mechanism by which birefringence is generated in poly(MMA/St) by focusing on changes in St conformation. The results of this analysis suggested that the conformational changes in St units are different for orientational and photoelastic birefringence generation. We analyzed the generation mechanism of birefringence in poly(methyl methacrylate (MMA)/styrene (St)) through measurement of infrared (IR) dichroism. Through IR measurement, the conformational changes in the St unit were suggested and found to differ between orientational and photoelastic birefringence generation. We thought that, during photoelastic birefringence generation, the α-CH3 group of the MMA unit hinders the rotation of the benzene ring of St units that are adjacent to MMA units. The influence of compositional distribution on birefringence was also investigated and the results suggested that the compositional distribution of poly(MMA/St) minimally affects the birefringence.

Optical stress sensor based on electro-optic compensation for photoelastic birefringence in a single crystal

An optical stress sensor is proposed by using a single crystal with both electro-optic and photoelastic effects. Different from previous crystal-based stress sensors, the proposed sensor is based on electro-optic compensation for stress-induced birefringence and does not need an additional quarter-wave plate or modulator, because the stress-sensing element is simultaneously used as an electro-optic compensator. Candidate sensing materials include electro-optic crystals of the 3 m symmetry group and all glass with large Kerr coefficients. A primary experiment has demonstrated that the stress-induced birefringence in lithium niobate crystal can be compensated by its electro-optic birefringence. The proposed stress sensor is compact and low cost, and it is possible to achieve closed-loop stress measurement.

60.2: A Polarized Laser Backlight Using a Polymer Free of Orientational and Photoelastic Birefringence

AbstractWe proposed a polarized laser backlight to improve light use efficiency of liquid crystal displays, and evaluated the basic polarization properties of prototype of the backlight. The prototype backlight consisted of a laser, a polarizer, a diffusion sheet and two light guide plates of zero zero‐birefringence polymer, which is free of orientational and photoelastic birefringence. The front output light from the backlight was highly polarized and the backlight maintained high degree of polarization.

Design and synthesis of a zero-photoelastic birefringence polymer with a high glass-transition temperature by a random copolymerization method

We designed and synthesized a zero-photoelastic birefringence polymer that had a high glass-transition temperature (Tg) by introducing trans-stilbene units into the side chains of the copolymer by a random copolymerization method. The concentration of the trans-stilbene units required to compensate for photoelastic birefringence in the random copolymer was lower than that required in a polymer prepared by an anisotropic molecule dopant method, because the presence of an anisotropic moiety in the side chain of the polymer has a greater effect than an anisotropic molecule doped in the polymer. Furthermore, the polymer with trans-stilbene units in side chains showed a higher Tg than the polymer containing an anisotropic dopant. We conclude that the introduction of an anisotropic molecule of a similar or larger size to trans-stilbene into the side chain gives a polymer with a high Tg. We designed and synthesized a zero-photoelastic birefringence polymer that had a high glass-transition temperature (Tg) by introducing trans-stilbene units into the side chains of the copolymer by a random copolymerization method. The concentration of the trans-stilbene units required to compensate for photoelastic birefringence in the random copolymer was lower than that required in a polymer prepared by in anisotropic molecule dopant method, because the presence of an anisotropic moiety in the side chain of the polymer has a greater effect than does an anisotropic molecule doped in the polymer.