A. Introduction VI-571B. Molar Refraction VI-571C. Refractive Indices of Heterogeneous Polymers VI-572D. Optical Anisotropy VI-572E. Applications VI-573

Table 1. Intrinsic Optical Properties ofSelected Polymers VI-573

Table 2. Average Refractive Indices ofPolymers (in Order of Increasing n) VI-574

Table 3. Average Refractive Indices ofPolymers (in Alphabetical Order) VI-578

F. References VI-582

A. INTRODUCTION

The refractive indices of polymers provide fundamentalphysical property information that can be used incharacterization, processing, and usage analyses. In-depthdescription of refractive indices based on classic electro-magnetic theory can be found in basic texts (1,2). Thepurpose of this monograph is to provide a convenientreference of values and some general remarks in approx-imating and utilizing refractive indices of polymers.

The refractive index, reported as the velocity of light in avacuum relative to the velocity in the polymer, depends onthe wavelength of light. All values reported in this chapterrefer to the sodium spectral line A = 5893A, referred to asHD in this literature. However, for simplicity, the subscriptD is omitted here in the subsequent discussion and tables. Ingeneral, it should be kept in mind that for any polymer, therefractive index represents an average property of itsaggregate state (3,4). Orientation, conformation, as wellas phase changes may all contribute to variations in theindex of refraction of a polymer with a given chemicalstructure. Thus, the refractive index may not be expected tobe equal along all axes of the molecule (5). Consequently,the measured refractive index is an average value, withcontributions from the refractions of the molecule'sdifferent chemical bonds. It can be shown from classicelectromagnetic theory that the square of the refractiveindex (n2) is the appropriate form to use in moleculardescriptions of refractive indices since it is related to thedielectric tensor, having a magnitude as well as a

directional description (1,4). However, since 1.3<n<1.7for most polymers, correlations proposed for n2 almostalways find a simplified version with n (3,4).

B. MOLAR REFRACTION

The molar refraction of a substance, a product of itsrefractive index, molecular weight, and density, may beassumed to be a fundamental physical property of materials(1). Furthermore, the molar refraction may be treated (asestablished by Denbigh) as the sum of the bond refractionsthat make up the molecule (6). These two postulates makepossible, the calculation of the refractive indices ofpolymers almost from first principles (7,8). Two usefulrelations for the molar refraction, /?, are provided here (1):The Lorentz-Lorentz equation

(Bl)

(B2)

where p is the density of the polymer and M its molecularweight. The molar refraction may be assumed to be the sumof the refractions of all the bonds or groups that make upthe polymer system, i.e., R — Yli &i (6/7). Chemical grouprefractivities that can be used in the calculation of refractiveindex of polymers have been recently summarized by VanKrevelen (8). For example, for a homopolymer whoserepeat monomer unit refractivity, #M> is known, withR — DPRU (where DP is the degree of polymerization) andM = D P M M (MM = molecular weight of the monomerunit), then the refractive index of the polymer by theGladstone-Dale expression (Eq. B2) becomes

(B3)

This may be calculated only from a knowledge of themonomer unit molar refraction and molecular weight. The

R e f r a c t i v e I n d i c e s o f P o l y m e r s

James C. SeferisPolymeric Composites Laboratory, Department of Chemical Engineering, University of Washington, Seattle, VVA, USA

The Gladstone-Dale equation

use of bond or group refractions in the calculation ofrefractive indices of polymers has been demonstrated to bein good agreement with the measured values for homo-geneous, unoriented polymers (8).

C. REFRACTIVE INDICES OF HETEROGENEOUSPOLYMERS

For polymeric systems whose phase dimensions are belowthe wavelength of the incident light, the application of theMaxwell relations is valid and the refractive index of thepolymer may be expressed in terms of the dielectricconstants of the constituent phases (1). The dielectricconstant, k, is equivalent to the square of the refractiveindex (k = n2), and it can be demonstrated that an upperbound of the refractive index of the polymer may beobtained as the sum of dielectric constants of theconstituent phases (4,5):

(Cl)

where m and T;/Q£ v/ = 1) are the refractive indices andvolume fractions of the constituent phases of the compo-nents that make up the polymer. Similarly, the lower boundof a polymer's refractive index may be computed as thesum of the inverse of the dielectric constants of theconstituent phases (4):

(C2)

For most heterogeneous polymers, however, whoseconstituent refractive indices differ by less than 0.2, i.e.,(rii — rij < 0.2), the refractive index of the polymer may becomputed by the Gladstone-Dale relation, assumingadditivity of the refractive indices of the constituent phases(3,4):

(C3)

The calculation methods described above may be usedfor multiphase polymers such as blends, block or graftcopolymers, composites, and semicrystalline polymers.

D. OPTICAL ANISOTROPY*

Small as well as long polymer molecules exhibit differentrefractive indices parallel and perpendicular to the mole-cular chain axis. Thus, all polymers should be viewed asintrinsically anisotropic. The degree of anisotropy exhibitedin bulk property behavior will depend on the molecularorientation imposed by deformation during processing ortesting. Only in its unoriented state can a polymer be

*See also corresponding table in this Handbook.

characterized by a single refractive index, since its opticalproperties will be identical in all directions. Consequently,optical anisotropy is one of the simplest and often usedmethods of studying orientation in polymers (5). Bypolarizing light in a specific direction, the refractive indexof a polymer can be measured in that direction. Conse-quently, all three principal refractive indices of a polymer,nx, ny, n-r, corresponding to an x, y, and z direction, can bemeasured. For example, a refractometer fitted with apolarized eye piece has been successfully used to measurerefractive indices along the major axes of polymer films (9).The average refractive indices of a polymer may becomputed from the refractive indices along the axes ofthe polymer:

(Dl)

For the unoriented (isotropic) condition (nx — ny = nz), asingle value of the refractive index provides a uniqueoptical description (n = nx = ny = nz). For oriented poly-mers, the difference in refractive indices along twoorthogonal directions can be used as the measure of opticalanisotropy and, consequently, orientation of the polymer.The difference in refractive indices is defined as thebirefringence or double refraction. According to Stein (5),there are three birefringences, A ,/s that may be defined fora cartesian coordinate system, with two of them beingindependent. They are

For a polymer exhibiting transverse isotropic symmetry,as in the case of uniaxial orientation (i.e., deformationalong one axis), a single birefringence is enough tocharacterize orientation and anisotropy. For example, fora polymer oriented uniaxially along the x direction,An^ — Anxi and Ann = O. For a fully oriented polymer,where the molecular chain axis is aligned with thedeformation axis (perfect orientation) a limiting value ofbirefringence is reached, which is defined as the intrinsicbirefringence of the polymer (10,11) and denoted as

where / is the Hermans orientation function

defined on the average angle 9 that the molecular chain axismakes with the deformation axis. The Hermans orientationfunction (D6), - 1 / 2 < / < 1 assumes the value of - 1/2when the molecular chain axis is perpendicular to thedeformation axis; 0 for random orientation (isotropy); and- 1 for perfect alignment of the chains with the deforma-

(D2)

(D3)

(D4)

(D5)

(D6)

tion axis. The use of the refractive index in the calculationof birefringence, rather than the difference of some functionof the dielectric constant (n2 or 1/rc2), is an approximationto optical anisotropy. Thus, if the birefringence is used as ameasure of orientation, as was proposed by Stein, formeffects should be considered (5,7,11)

(D7)

The importance of form may be estimated from bondpolarizabilities for a given polymer (4,7). Thus, tocharacterize completely the optical properties of a givenpolymer, its average refractive index as well as the intrinsicand form birefringences must be specified. To date, veryfew polymers have been optically characterized in suchdetail. However, as more refined and specific performanceis demanded from polymers, this information is forth-coming. In order to demonstrate the usefulness of completecharacterization and to summarize the data available tilldate, an example for semicrystalline polymers is provided,along with a table showing reported values (for a fewpolymers) of average refractive indices and intrinsicbirefringences.

E. APPLICATIONS

Using Eq. (B2), the unoriented refractive index of asemicrystalline polymer may be calculated from a knowl-edge of its intrinsic crystalline and noncrystalline densitiesand refractive indices. First, the volume fraction crystal-linity, vcr, is calculated from the densities:

(El)

where p is the bulk measured density, and pcr and pnc arethe crystalline and noncrystalline densities. Then theaverage refractive index is

From Stein's equation of birefringence additivity (neglect-ing form birefringence) (5,11)

(E3)

where An^cr and A n ^ are the crystalline and noncrystal-line intrinsic birefringences, and /c r and /nc are thecorresponding crystalline and noncrystalline Hermansorientation functions.

If the intrinsic properties of a semicrystalline polymerare known, Eq. (E2) can be used to calculate the volumefraction crystallinity by simply measuring the polymer'srefractive index, while Eq. (E3) can be used to obtain thevalue of the noncrystalline orientation function by measur-ing birefringence and crystalline orientation by an inde-pendent technique [e.g., wide angle X-ray (5)]. For a single-phase polymer like polystyrene, the orientation function canbe directly calculated from the measured birefringencevalue and the known intrinsic birefringence:

Once these quantities are known, it becomes possible tocompletely characterize and predict the optical anisotropyof a given polymer from its unoriented to its oriented state(3,4).

Table 1 is provided to demonstrate that such basic opticalparameters may be obtained from the literature (3,4,9,12-16). The recognition of polymers as anisotropic hetero-geneous systems continues to expand and their refractiveindices provide useful insight into their process-structure-property interrelations (18-20). It is hoped that continuousinvestigations in existing as well as new polymers willexpand this compilation.

Finally, Table 2 provides average refractive indices ofpolymers arranged in order of increasing values, whileTable 3 provides the same list in alphabetical order. Someadditional values from the recent literature (21-23) havebeen added to the earlier compilation (17) to form thematerial for the present edition.(E2)

TABLE 1. INTRINSIC OPTICAL PROPERTIES OF SELECTED POLYMERS

Phase average Intrinsic birefringenceCrystalline Noncrystalline refractive indices (xlO3)

density densityPolymer (pcr) (pnc) ncr nnc An°cr AHJJ 0

Poly(propylene) 0.936 0.850 1.519-1.524 1.471 23-30 60-86Poly(ethylene) 1.000 0.855 1.560-1.565 1.476-1.483 58-66

Low orientation 120High orientation 194

Poly(oxyethylene-oxyterephthaloyl) 1.455 1.335 1.639-1.643 1.570-1.577 220-230 220-275Poly(styrene) Amorphous 1.06 Amorphous 1.590-1.592 Amorphous 195

References page VI - 582

TABLE 2. AVERAGE REFRACTIVE INDICES OF POLYMERS (IN ORDER OF INCREASING n)a

Polymer n T (0C)

Poly (tetrafluoroethylene-co-hexafluoropropy lene) 1.338Poly(pentadecafluorooctyl acrylate) 1.339 25Poly(tetrafluoro-3-(heptafluoropropoxy)propyl acrylate) 1.346 25Poly(tetrafluoro-3-(pentafluoroethoxy)propyl acrylate) 1.348 25Poly (tetrafluoroethy lene) 1.35-1.38Poly(undecafluorohexyl acrylate) 1.356Poly(nonafluoropentyl acrylate) 1.360 25Poly(tetrafluoro-3-(trifluoromethoxy)propyl acrylate) 1.360 25Poly(pentafluorovinyl propionate) 1.364 25Poly(heptafluorobutyl acrylate) 1.367 25Poly(trifluorovinyl acetate) 1.375 25Poly(octafluoropentyl acrylate) 1.380 25PolyCpentafluoropropyl acrylate) 1.385 25Poly(2-heptafluorobutoxy)ethyl acrylate) 1.390 25Poly(2,2,3,4,4,4-hexafluorobutyl acrylate) 1.392 25Poly(trifluoroethyl acrylate) 1.407 25Poly(2~( 1,1,2,2-tetrafluoroethoxy)ethyl acrylate) 1.412 25Poly(trifluoroisopropyl methacrylate) 1.4177 20Poly(2,2,2-trifluoro-1 -methylethyl methacrylate) 1.4185Poly(2~trifluoroethoxy)ethyl acrylate 1.419 25Poly (trifluorochloroethy lene) 1.42 -1.43Poly(vinylidene fluoride) 1.42 25Poly(oxydimethylsilylene) (poly(dimethyl siloxane)) 1.43Poly(trifluoroethyl methacrylate) 1.437Poly(oxypropylene) 1.4495Poly(vinyl isobutyl ether) 1.4507 30Poly (vinyl ethyl ether) 1.4540 30Poly(oxyethylene) 1.4563 30Poly(vinyl butyl ether) 1.4563 30Poly(vinyl pentyl ether) 1.4581 30Poly(vinyl hexyl ether) 1.4591 30Poly(4-methyl-l-pentene) 1.459-1.465Cellulose acetate butyrate 1.46-1.49Poly(4-fluoro-2-trifluoromethylstyrene) 1.46Poly(vinyl octyl ether) 1.4613 30Poly(vinyl-2-ethylhexyl ether) 1.4626 30Poly(vinyl decyl ether) 1.4628 30Poly(2-methoxyethyl acrylate) 1.463 25Poly(butyl acrylate) 1.4631 30

1.466 20PoIy(Jer/-butyl methacrylate) 1.4638 20Poly(vinyl dodecyl ether) 1.4640 30Poly(3-ethoxypropyl acrylate) 1.465 25Poly(oxy-1 -oxopentamethylene) 1.465 50Poly(vinyl propionate) 1.4665 20Poly (vinyl acetate) 1.4665 20Poly(vinyl methyl ether) 1.467 20Poly(ethyl acrylate) 1.4685 20Poly(ethylene-co-vinyl acetate) (80%-20% vinyl acetate) 1.47-1.50Cellulose propionate 1.47 -1.49Cellulose acetate propionate 1.47Benzyl cellulose 1.47-1.58Phenol-formaldehyde resins 1.47-1.70Cellulose triacetate 1.47 -1.48Poly(vinyl methyl ether) (isotactic) 1.4700 30Poly(3-methoxypropyl acrylate) 1.471 25Poly(2-ethoxyethyl acrylate) 1.471 25Poly(methyl acrylate) 1.472-1.480Poly(isopropyl methacrylate) 1.4728 20PoIy(I-decene) 1.4730Poly(propylene) (atactic, density 0.8575 g/cm3) 1.4735 20Poly(vinyl sec-butyl ether) (isotactic) 1.4740 30Poly(dodecyl methacrylate) 1.4740 20Poly(oxyethyleneoxysuccinoyl) (poly(ethylene succinate)) 1.4744 25Poly(tetradecyl methacrylate) 1.4746 30

TABLE 2. cont'd

Polymer n T (0C)

Poly(ethylene-co-propylene) (EPR-rubber) 1.4748-1.48Poly(hexadecyl methacrylate) 1.4750 30Poly(vinyl formate) 1.4757 20Poly(2-fluoroethyl methacrylate) 1.4768 20Poly(isobutyl methacrylate) 1.477 20Ethyl cellulose 1.479 21Poly(vinyl acetal) 1.48-1.50Cellulose acetate 1.48-1.50Cellulose acetate (39.8% acetyl content) 1.4700 25Cellulose tripropionate 1.48— 1.49Poly(oxymethylene) 1.48 20Poly(vinyl butyral) 1.48-1.49Poly(w-hexyl methacrylate) 1.4813 20Poly(n-butyl methacrylate) 1.483 20-25Poly(ethylidene dimethacrylate) 1.4831 20Poly(2-ethoxyethyl methacrylate) 1.4833 20Poly(oxyethyleneoxymaleoyl) (poly(ethylene maleate)) 1.4840 25Poly(rt-propyl methacrylate) 1.484 25Poly(3,3,5-trimethylcyclohexyl methacrylate) 1.485 20Poly(ethyl methacrylate) 1.485 20-25Poly(2-nitro-2-methylpropyl methacrylate) 1.4868 20Poly(triethylcarbinyl methacrylate) 1.4889 20Poly(l,l-diethylpropyl methacrylate) 1.4889 20Poly(methyl methacrylate) 1.4893 23

1.490 20Poly(2-decyl-1,3-butadiene) 1.4899 20.5Poly(vinyl alcohol) 1.49-1.53

1.5214 20Poly(ethyl glycolate methacrylate) 1.4903 20Poly(3-methylcyclohexyl methacrylate) 1.4947 20Poly(cyclohexyl a-ethoxyacrylate) 1.4969 20Methyl cellulose (low viscosity) 1.497 25Poly(4-methylcyclohexyl methacrylate) 1.4975 20Poly(decamethylene glycol dimethacrylate) 1.4990Poly(urethanes) 1.5-1.6Poly( 1,2-butadiene) 1.5000 20Poly(vinyl formal) 1.50Poly(2-bromo-4-trifluoromethylstyrene) 1.5 25Cellulose nitrate 1.5-1.514Polype-butyl a-chloroacrylate) 1.500 25Poly (2-heptyl-1,3-butadiene) 1.5000Poly(ethyl a-chloroacrylate) 1.502 25Poly(2-isopropyl-1,3-butadiene) 1.5028 30Poly(2-methylcyclohexyl methacrylate) 1.5028 20Poly(propylene) (density 0.9075 g/cm3) 1.5030 20Poly(isobutene) 1.505-1.51Poly(bornyl methacrylate) 1.5059 20Poly(2-tert-buty\-1,3-butadiene) 1.5060 24.6Poly(ethylene glycol dimethacrylate) 1.5063 20Poly(cyclohexyl methacrylate) 1.5066 20Poly(cyclohexanediol-l,4-dimethacrylate) 1.5067 20Butyl rubber(unvulcanized) 1508Poly(tetrahydrofurfuryl methacrylate) 1.5096 20Gutta percha (P) 1-509Poly(ethylene) ionomer 1-51Poly(oxyethylene) (high molecular weight) 1.51-1.54Poly(ethylene) (density 0.914 g/cm3) 151 20(density 0.94-0.945g/cm3) 1.52-1.53 20(density 0.965g/cm3) 1-545 20Poly( 1 -methylcyclohexyl methacrylate) 1.5111 20Poly(2-hydroxyethyl methacrylate) 1.5119 20Poly(vinyl chloroacetate) 1-512 25Poly(butene) (isotactic) 1.5125Poly(vinyl methacrylate) 1.5129 20Poly(/V-butyl methacrylamide) 1.5135 20

References page VI - 582

TABLE 2. cont'd

Polymer n T (0C)

Gutta percha (a) 1.514 50Terpene resin 1.515 25PoIy(1,3-butadiene) 1.5154 25Shellac 1.51 1.53Poly(methyl a-chloroacrylate) 1.517 20Poly(2-chloroethyl methacrylate) 1.517 20Poly(2-diethylaminoethyl methacrylate) 1.5174 20Poly(2-chlorocyclohexyl methacrylate) 1.5179 20PoIy(1,3-butadiene) (35% cis; 56% trans; 7% 1,2-content) 1.5180Natural rubber 1.519-1.52Poly (ally 1 methacrylate) 1.5196 20Poly(vinyl chloride) +40% dioctyl phthalate 1.52Poly(acrylonitrile) 1.52

1.5187 25Poly(methacrylonitrile) 1.52PoIy(1,3-butadiene) (high ds-type) 1.52Poly(butadiene-co-acrylonitrile) 1.52Poly(methyl isopropenyl ketone) 1.5200 20Poly(isoprene) 1.521 20Poly(ester) resin, rigid (ca. 50% styrene) 1.523-1.54Poly((A^2-methoxyethyl)methacrylamide) 1.5246 20Poly(2,3-dimethylbutadiene) (methyl rubber) 1.525Poly(vinyl chloride-covinyl acetate) (95/5-90/10) 1.525-1.535Poly(acrylic acid) 1.527 25PoIy(1,3-dichloropropyl methacrylate) 1.5270 20Poly(2-chloro-1 -(chloromethyl)ethyl methacrylate) 1.5270 20Poly(acrolein) 1.529PoIy(I-vinyl-2-pyrrolidone) 1.53Poly(N-methylmaleimide-<2/f-isobutene) 1.53Hydrochlorinated rubber 1.53-1.55Poly(imino(l-oxohexamethylene)) (nylon 6) 1.53Poly(iminoadipoyliminohexamethylene) (nylon 6,6) 1.53Poly(iminoadipoylimino tetramethylene) (nylon moulding 6,10) 1.53

oriented fibres 1.515 -1.565Poly(butadiene-co-styrene) (-30% styrene) block copolymer 1.53Poly(cyclohexyl a-chloroacrylate) 1.532 25Poly(2-chloroethyl a-chloroacrylate) 1.533 25Poly(butadiene-co-styrene) (~ 75/25) 1.535Poly(2-aminoethyl methacrylate) 1.537 20Poly(furfuryl methacrylate) 1.5381Proteins 1.539-1.541Poly(butylmercaptyl methacrylate) 1.5390 20PoIy(I -phenyl-/?-amyl methacrylate) 1.5396 20PoIy(N-methyl-methacrylamide) 1.5398 20Cellulose 1.54Poly(vinyl chloride) 1.54-1.55Urea-formaldehyde resin 1.54-1.56PolyCsec-butyl a-bromoacrylate) 1.542 25Poly(cyclohexyl a-bromoacrylate) 1.542 25Poly(2-bromoethyl methacrylate) 1.5426 20Poly(dihydroabietic acid) 1.544Poly(abietic acid) 1.546 25Poly(ethylmercaptyl methacrylate) 1.547 20Poly(iV-allyl methacrylamide) 1.5476 20PoIy(I-phenylethyl methacrylate) 1.5487 20Poly(vinylfuran) 1.55 20Poly(2-vinyltetrahydrofuran) 1.55 20Poly(vinyl chloride) -f 40% tricresyl phosphate 1.55Epoxy resins 1.55-1.60Poly(p>-methoxybenzyl methacrylate) 1.552 20Poly(isopropyl methacrylate) 1.552Poly(/?-isopropylstyrene) 1.554 20Poly(chloroprene) 1.554-1.558Poly(oxyethylene)-a-benzoate-co-methacrylate) 1.555 20Poly(p,/7-xylylenyl dimethacrylate) 1.5559 20

TABLE 2. cont'd

Polymer n T (0C)

PoIy(I-phenylallyl methacrylate) 1.5573 20Poly(p-cyclohexylphenyl methacrylate) 1.5575 20Poly(2-phenylethyl methacrylate) 1.5592 20Poly(oxycarbonyloxy-1,4-phenylene-1 propylbutylidene-1,4-phenylene) 1.5602PoIy(I -(o-chlorophenyl)ethyl methacrylate) 1.5624 20Poly(styrene-co-maleic anhydride) 1.564 21PoIy(I-phenylcyclohexyl methacrylate) 1.5645 20Poly(oxycarbonyloxy-1,4-phenylene-1,3~dimethylbutylidene-1,4-phenylene) 1.5671Poly(methyl a-bromoacrylate) 1.5672 20Poly(benzyl methacrylate) 1.5680 20Poly(2-(phenylsulfonyl)ethyl methacrylate) 1.5682Poly(m-cresyl methacrylate) 1.5683 20Poly(styrene-co-acrylonitrile) ( - 75/25) 1.57Poly(oxycarbonyloxy-1,4-phenyleneisobutylidene-1,4-phenylene) 1.5702Poly(o-methoxyphenyl methacrylate) 1.5705 20Poly(phenyl methacrylate) 1.5706 20Poly(ocresyl methacrylate) 1.5707 20Poly(diallyl phthalate) 1.572 20Poly(2,3-dibromopropyl methacrylate) 1.5739 20Poly(oxycarbonyloxy-1,4-phenylene-1 -methy 1-butylidene-1,4- 1.5745

phenylene)Poly(oxy-2,6-dimethylphenylene) 1.575Poly(oxyethyleneoxyterephthaloyl) (amorphous) (poly(ethylene 1.5750 20

terephthalate))Poly(vinyl benzoate) 1.5775 20Poly(oxycarbonyloxy-1,4-phenylenebutylidene-1,4-phenylene) 1.5792PoIy(1,2-diphenylethyl methacrylate) 1.5816 20Poly(o-chlorobenzyl methacrylate) 1.5823 20Poly(oxycarbonyloxy-1,4-phenylene-sec-butylidene-1,4-phenylene) 1.5827Poly(oxypentaerythritoloxyphthaloyl) 1.584 20Poly(w-nitrobenzyl methacrylate) 1.5845 20Poly(oxycarbonyloxy-1,4-phenyleneisopropylidene-1,4-phenylene) 1.5850Poly(N-(2-phenylethyl)methacrylamide) 1.5857 20Poly(4-methoxy-2-methylstyrene) 1.5868 20Poly(o-methylstyrene) 1.5874 20Poly(styrene) 1.59-1.592 20Poly(oxycarbonyloxy-1,4-phenylenecyclohexylidene-1,4-phenylene) 1.5900 20Poly(0-methoxystyrene) 1.5932 20Poly(diphenylmethyl methacrylate) 1.5933 20Poly(oxycarbonyloxy-1,4-phenyleneethylidene-1,4-phenylene) 1.5937Poly(p-bromophenyl methacrylate) 1.5964 20Poly(Af-benzyl methacrylamide) 1 5965 20Poly(p-methoxystyrene) 1.5967 20Hard rubber (32% S) 1.6Poly(vinylidene chloride) 1 -60-1.63Poly(sulfides) (Thiokol) 1.6-1.7Poly(0-chlorodiphenylmethyl methacrylate) 1.6040Poly(oxycarbonyloxy-1,4-(2,6-dichloro)phenylene-isopropylidene-1,4-(2,6-dichloro)phenylene) 1.6056Poly(oxycarbonyloxybis(l ,4-(3,5-dichlorophenylene))) 1.6056Poly(pentachlorophenyl methacrylate) 1-608 20Poly(o-chlorostyrene) 1.6098 20Poly(phenyl a-bromoacrylate) 1-612 25Poly(p-divinylbenzene) 1-6150 20PoIy(N-vinylphthalimide) 1-6200 20Poly(2,6-dichlorostyrene) 1-6248 20Poly(P-naphthyl methacrylate) 1.6298 20Poly(a-naphthyl carbinyl methacrylate) 1.63Poly(sulfone) 1-633Poly(2-vinylthiophene) 1.6376 20Poly(a-naphthyl methacrylate) 1.6410 20Poly(oxycarbonyloxy-1,4-phenylenediphenyl-methylene-1,4-phenylene) 1.6539Poly(vinyl phenyl sulfide) 1.6568 20Butylphenol formaldehyde resin 1-66Urea-thiourea-formaldehyde resin 1.660 25Poly(vinylnaphthalene) 1.6818 20

References page VI - 582

TABLE 2. confd

Polymer n T (0C)

Poly(vinylcarbazole) 1.683 20Naphthalene-formaldehyde resin 1.696Phenol-formaldehyde resin 1.70Poly(pentabromophenyl methacrylate) 1.71

Temperature in 0C are listed when available. In general, n may be assumed to decrease with increasing temperature. Approximate change may be calculated asAnIAT — - 1 x 1O~4 to 2 x 10~4/°C for glassy polymers and dn/dT— - 3 x 10~4 to 5 x 10~4/°C for amorphous unoriented polymers above the glass transition.

TABLE 3. AVERAGE REFRACTIVE INDICES OF POLYMERS (IN ALPHABETICAL ORDER)

Polymer n T (0C)

Benzyl cellulose 1.47-1.58Butylphenol formaldehyde resin 1.66Butyl rubber(unvulcanized) 1.508Cellulose 1.54Cellulose acetate 1.48-1.50Cellulose acetate (39.8% acetyl content) 1.4700 25Cellulose acetate butyrate 1.46-1.49Cellulose acetate propionate 1.47-1.48Cellulose nitrate 1.5-1.514Cellulose propionate 1.47-1.49Cellulose triacetate 1.47 -1.48Cellulose tripropionate 1.48 -1.49Epoxy resins 1.55-1.60Ethyl cellulose 1.479 21Gutta percha (a) 1.514 50Guttapercha ((3) 1.509Hard rubber (32% S) 1.6Hydrochlorinated rubber 1.53-1.55Methyl cellulose (low viscosity) 1.497 25Naphthalene-formaldehyde resin 1.696Natural rubber 1.519-1.52Phenol-formaldehyde resin 1.70Phenol-formaldehyde resins 1.47 -1.70Poly(abietic acid) 1.546 25Poly(acrolein) 1.529Poly(acrylic acid) 1.527 25Poly(acrylonitrile) 1.52

1.5187 25Poly(allyl methacrylate) 1.5196 20Poly(2-aminoethyl methacrylate) 1.537 20Poly(N-allyl methacrylamide) 1.5476 20Poly(JV-benzyl methacrylamide) 1.5965 20Poly(«-butyl methacrylate) 1.483 20-25Poly(benzyl methacrylate) 1.5680 20Poly(bornyl methacrylate) 1.5059 20Poly(2-bromoethyl methacrylate) 1.5426 20Poly(p-bromophenyl methacrylate) 1.5964 20Poly(2-bromo-4-trifluoromethylstyrene) 1.5 25PoIy(1,2-butadiene) 1.5000 20Poly(l,3-butadiene) 1.5154 25PoIy(1,3-butadiene) (high ds-type) 1.52PoIy(1,3-butadiene) (35% cis\ 56% trans; 1% 1,2-content) 1.5180Poly(butadiene-co-acrylonitrile) 1.52Poly(butadiene-co-styrene) (~ 75/25) 1.535Poly(butadiene-co-styrene) ( - 30% styrene) block copolymer 1.53Poly(butene) (isotactic) 1.5125Poly(butyl acrylate) 1.4631 30

1.466 20Polype-butyl a-bromoacrylate) 1.542 25Poly(sec-butyl ot-chloroacrylate) 1.500 25Poly(2-terf-butyl-1,3-butadiene) 1.5060 24.6

TABLE 3, cont'd

Polymer n T (0C)

Poly(terf-butyl methacrylate) 1.4638 20Poly(butylmercaptyl methacrylate) 1.5390 20Poly(N-butyl methacrylamide) 1.5135 20Poly(ochlorobenzyl methacrylate) 1.5823 20Poly(2-chloro-1 -(chloromethyl)ethyl methacrylate) 1.5270 20Poly(2-chlorocyclohexyl methacrylate) 1.5179 20Poly(0-chlorodiphenylmethyl methacrylate) l .6040Poly(2-chloroethyl a-chloroacrylate) 1.533 25Poly(2-chloroethyl methacrylate) 1.517 20PoIy(I-(o-chlorophenyl)ethyl methacrylate) 1.5624 20Poly(chloroprene) 1.554 -1.558Poly(o-chlorostyrene) 1.6098 20Poly(m-cresyl methacrylate) 1.5683 20Poly(0-cresyl methacrylate) 1.5707 20Poly(cyclohexanediol-1,4-dimethacrylate) 1.5067 20Poly(cyclohexyl a-bromoacrylate) 1,542 25Poly(cyclohexyl a-chloroacrylate) 1.532 25Poly(cyclohexyl a-ethoxyacrylate) 1.4969 20Poly(cyclohexyl methacrylate) 1.5066 20Poly(^-cyclohexylphenyl methacrylate) 1.5575 20Poly(decamethylene glycol dimethacrylate) 1.4990PoIy(I-decene) 1.4730Poly(2-decyl-1,3-butadiene) 1.4899 20.5Poly(diallyl phthalate) 1.572 20Poly(2,3-dibromopropyl methacrylate) 1.5739 20Poly(l,3-dichloropropyl methacrylate) 1.5270 20Poly(2,6-dichlorostyrene) 1.6248 20Poly(2-diethylaminoethyl methacrylate) 1.5174 20PoIy(1,1-diethylpropyl methacrylate) 1.4889 20Poly(dihydroabietic acid) 1.544Poly(2,3-dimethylbutadiene) (methyl rubber) 1.525Poly( 1,2-diphenylethyl methacrylate) 1.5816 20Poly(diphenylmethyl methacrylate) 1.5933 20Poly(/?-divinylbenzene) 1.6150 20Poly(dodecyl methacrylate) 1.4740 20Poly(ester) resin, rigid (ca. 50% styrene) 1.523-1.54Poly(2-ethoxyethyl aery late) 1.471 25Poly(2-ethoxyethyl methacrylate) 1.4833 20Poly(3-ethoxypropyl acrylate) 1.465 25Poly(ethyl acrylate) 1.4685 20Poly(ethyl a-chloroacrylate) 1.502 25Poly(ethyl glycolate methacrylate) 1.4903 20Poly(ethyl methacrylate) 1.485 20-25Poly(ethylene) (density 0.914g/cm3) 1.51 20(density 0.94-0.945 g/cm3) 1.52-1.53 20(density 0.965 g/cm3) 1.545 20Poly(ethylene) ionomer 1.51Poly(ethylene-a?-propylene) (EPR-rubber) 1.4748-1.48Poly(ethylene-a?-vinyl acetate) (80%-20% vinyl acetate) 1.47-1.50Poly(ethylene glycol dimethacrylate) 1.5063 20Poly(ethylidene dimethacrylate) 1.4831 20Poly(ethylmercaptyl methacrylate) 1.547 20Poly(2~fluoroethyl methacrylate) 1.4768 20Poly(4-fluoro-2-trifluorornethylstyrene) 1.46Poly(furfuryl methacrylate) 1.5381Poly(2-heptafluorobutoxy)ethyl acrylate) 1.390 25Poly(heptafluorobutyl acrylate) 1.367 25Poly (2-hepty 1-1,3-butadiene) 1.5000Poly(hexadecyl methacrylate) 1.4750 30Poly(2,2,3,4,4,4-hexafluorobutyl acrylate) 1.392 25Poly(w-hexyl methacrylate) 1.4813 20Poly(2-hydroxyethyl methacrylate) 1.5119 20Poly(iminoadipoyliminohexamethylene) (nylon 6,6) 1.53Poly(iminoadipoylimino tetramethylene) (nylon moulding 6,10) 153

oriented fibers 1.515-1.565

References page VI-5 82

TABLE 3. coni'd

Polymer n T (° c)

Poly(imino(l-oxohexamethylene)) (nylon 6) 1.53Poly(isobutene) 1.505-1.51Poly(isobutyl methacrylate) 1-477 20Poly(isoprene) 1-521 20Poly(2~isopropyl-1,3-butadiene) 15028 30Poly(isopropyl methacrylate) 1.4728 20

1.552Poly(/?-isopropylstyrene) 1554 20Poly(methacrylonitrile) 1-52Poly(p-methoxybenzyl methacrylate) 1552 20Poly(2-methoxyethyl acrylate) 1463 25Poly((A^2-methoxyethyl)methacrylamide) 1.5246 20Poly(4-methoxy-2-methylstyrene) 1.5868 20Poly(o-methoxyphenyl methacrylate) 1.5705 20Poly(3-methoxypropyl acrylate) 1.471 25Poly(o-methoxystyrene) 1.5932 20Poly(p-methoxystyrene) 1.5967 20Poly(methyl acrylate) 1.472-1.480Poly(rnethyl a-bromoacrylate) 1.5672 20Poly (methyl a-chloroacrylate) 1.517 20Poly(methyl isopropenyl ketone) 1.5200 20Poly(methyl methacrylate) 1.4893 23

1.490 20Poly(N-methyl-methacrylamide) 1.5398 20Pory(4-methyl-l-pentene) 1.459-1.465Poly( 1 -methylcyclohexyl methacrylate) 1.5111 20Poly(2-methylcyclohexyl methacrylate) 1.5028 20Poly(3-methylcyclohexyl methacrylate) 1.4947 20Poly(4-methylcyclohexyl methacrylate) 1.4975 20Poly(iV-methylmaleimide-alt-isobutene) 1.53Poly(o-methylstyrene) 1.5874 20Poly(a-naphthyl carbinyl methacrylate) 1.63Poly(a-naphthyl methacrylate) 1.6410 20Poly(p-naphthyl methacrylate) 1.6298 20Poly(m-nitrobenzyl methacrylate) 1.5845 20Pory(2-nitro-2-methylpropyl methacrylate) 1.4868 20Poly(nonafluoropentyl acrylate) 1.360 25Poly(octafluoropentyl acrylate) 1.380 25Poly(oxycarbonyloxybis( 1,4-(3,5-dichlorophenylene)) 1.6056Poly (oxycarbonyloxy-1,4-(2,6-dichloro)phenylene-isopropylidene-1,4-(2,6-dichloro)phenylene)) 1.6056Poly(oxycarbonyloxy-1,4-phenylene-1,3-dimethylbutylidene-1,4-phenylene) 1.5671Poly(oxycarbonyloxy-1,4-phenylene-1 -methyl-butylidene-1,4-phenylene) 1.5745Poly(oxycarbonyloxy-1,4-phenylene-1 -propylbutylidene-1,4-phenylene) 1.5602Poly (oxycarbonyloxy-1,4-phenylene-seobuty lidene-1,4-phenylene) 1.5 827Poly(oxycarbonyloxy-1,4-phenylenebuty lidene-1,4-phenylene) 1.5792Poly(oxycarbonyloxy-1,4-phenylenecyclohexylidene-1,4-phenylene) 1.5900 20Poly(oxycarbonyloxy-1,4-phenylenediphenyl-methylene-1,4-phenylene) 1.6539Poly(oxycarbonyloxy-1,4-phenyleneethylidene-1,4-phenylene) 1.5937Poly (oxycarbonyloxy-1,4-phenyleneisobutylidene-1,4-phenylene) 1.5702Poly (oxycarbonyloxy-1,4-phenyleneisopropy lidene-1,4-phenylene) 1.5850Poly(oxy-2,6-dimethylphenylene) 1.575Poly(oxydimethylsilylene) (poly(dimethyl siloxane)) 1.43Poly(oxyethylene) (high molecular weight) 1.4563 30

1.51-1.54Poly(oxyethylene)-a-benzoate-co-methacrylate) 1.555 20Poly(oxyethyleneoxymaleoyl) (poly(ethylene maleate)) 1.4840 25Poly(oxyethyleneoxysuccinoyl) (poly(ethylene succinate)) 1.4744 25Poly(oxyethyleneoxyterephthaloyl) (amorphous) (polyethylene terephthalate)) 1.5750 20Poly(oxymethylene) 1.48 20Poly(oxy-l-oxopentamethylene) 1.465 50Poly(oxypentaerythritoloxyphthaloyl) 1.584 20Poly(oxypropylene) 1.4495Poly(pentabromophenyl methacrylate) 1.71Poly(pentachlorophenyl methacrylate) 1.608 20Poly(pentadecafluorooctyl acrylate) 1.339 25

TABLE 3. cont'd

Polymer n j (0C)

Poly(pentafluoropropyl acrylate) 1.385 25Poly(pentafluorovinyl propionate) 1.364 25PoIy(I -phenyl-«-amyl methacrylate) 1.5396 20Poly(phenyl ot-bromoacrylate) 1.612 25Poly(phenyl methacrylate) 1.5706 20PoIy(I-phenylallyl methacrylate) 1.5573 20PoIy(I-phenylcyclohexyl methacrylate) 1.5645 20Poly(l-phenylethyl methacrylate) 1.5487 20Poly(2-phenyiethyl methacrylate) 1.5592 20Poly(Ar-(2-phenyIethyi)methacrylamide) 1.5857 20Poly(2-(phenylsulfonyl)ethyl methacrylate) 1.5682Poly(n-propyl methacrylate) 1.484 25Poly(propylene) (density 0.9075 g/cm3) 1.5030 20Poly(propylene) (atactic, density 0.8575g/cm3) 1.4735 20Poly(styrene) 1.59-1.592 20Poly(styrene-co-acrylonitriie) ( - 75/25) 1.57Poly(styrene-co-maleic anhydride) 1.564 21Poly(sulfides) (Thiokol) 1.6-1.7Poly(sulfone) 1.633Poly(tetradecyl methacrylate) 1.4746 30Poly(tetrafluoro-3-(heptafluoropropoxy)propyl acrylate) 1.346 25Poly(tetrafluoro-3-(pentafluoroethoxy)propyl acrylate) 1.348 25Poly(tetrafluoro-3-(trifluoromethoxy)propyl acrylate) 1.360 25Poly (2-( 1,1,2,2-tetrafluoroethoxy )ethy 1 acrylate) 1.412 25Poly(tetrafluoroethylene) 1.35(- 138)Poly(tetrafluoroethylene-co-hexafluoropropylene) 1.338Poly(tetrahydrofurfuryl methacrylate) 1.5096 20Poly(triethylcarbinyl methacrylate) 1.4889 20Poly(2,2,2-trifluoro-1 -methylethyl methacrylate) 1.4185Poly(trifluorochloroethylene) 1.42-1.43Poly(2-trifluoroethoxy)ethyl acrylate) 1.419 25Poly(trifluoroethyl acrylate) 1.407 25Poly(trifluoroethyl methacrylate) 1.437Poly(trifluoroisopropyl methacrylate) 1.4177 20Poly(trifluorovinyl acetate) 1.375 25Poly(3,3,5-trimethylcyclohexyl methacrylate) 1.485 20Poly(undecafluorohexyl acrylate) 1.356Poly(urethanes) 1.5-1.6Poly(vinyl acetal) 1.48-1.50Poly(vinyl acetate) 1.4665 20Poly(vinyl alcohol) 1.49-1.53

1.5214 20Poly(vinyl benzoate) 1.5775 20Poly(vinyl butyl ether) 1.4563 30Poly(vinyl sec-butyl ether) (isotactic) 1.4740 30Poly (vinyl butyral) 1.48-1.49Poly(vinyl chloride) 1 -54-1.55Poly(vinyl chloride) 4-40% dioctyl phthalate 1.52Poly(vinyl chloride) +40% tricresyl phosphate 155Poly(vinyl chloride-co-vinyl acetate) (95/5-90/10) 1.525-1.535Poly (vinyl chloroacetate) 1.512 25Poly(vinyl decyl ether) 1.4628 30Poly(vinyl dodecyl ether) 1.4640 30Poly(vinyl ethyl ether) 1.4540 30Poly(vinyl-2-ethylhexyl ether) 1.4626 30Poly(vinyl formal) 1.50Poly(vinyl formate) 14757 20Poly(vinyl hexyl ether) 14591 30Poly(vinyl isobutyl ether) 1.4507 30Poly(vinyl methacrylate) 1.5129 20Poly(vinyl methyl ether) 1.467 20Poly(vinyl methyl ether) (isotactic) 1.4700 30

Poly(vinyl octyl ether) 1.4613 30Poly(vinyl pentyl ether) 1-4581 30Poly(vinyl phenyl sulfide) 1-6568 20

References page VI-582

F. REFERENCES

1. J. R. Partington, "An Advanced Treatise of Physical Chem-istry: Physico-Chemical Optics", vol. IV, Longmans, Greenand Co., London, 1960.

2. J. F. Nye, "Physical Properties of Crystals", Oxford Uni-versity Press, London, 1960.

3. J. C. Seferis, R. J. Samuels, Polym. Eng. ScL, 19, 975(1979).

4. A. R. Wedgewood, J. C. Seferis, Polym. Eng. ScL, 24, 328(1984).

5. R. S. Stein, G. L. Wilkes, in: I. M. Ward, (Ed.) "Structureand Properties of Oriented Polymers", Wiley, New York,1975.

6. K. G. Denbigh, Trans. Faraday Soc, 36, 936 (1940).7. R. L. Rowell, R. S. Stein, J. Chem. Phys., 47, 2985 (1967).8. D. W. Krevelen, "Properties of Polymers - Part III: Proper-

ties of Polymers in Fields of Force", 3rd ed., Elsevier, NewYork, 1990.

9. R. J. Samuels, J. Appl. Polym. ScL, 26, 1383 (1981).10. P. H. Hermans, "Contribution to the Physics of Cellulose

Fibers", Elsevier, New York, 1946.11. R. S. Stein, J. Polym. Sci. A-2, 7, 1021 (1969).

12. A. J. deVries, C. Bonnebat, J. Polym. Sci., Polym. Symp.,58, 109 (1977).

13. A. J. deVries, Pure Appl. Chem., 53, 1011 (1981).14. R. S. Stein, J. Appl. Phys., 32, 1280 (1961).15. G. W. Shael, J. Appl. Polym. Sci., 8, 2717 (1964).16. G. W. Shael, J. Appl. Polym. Sci., 12, 903 (1968).17. J. C. Seferis, in: J. Brandrup, E. H. Immergut (Eds.),

"Polymer Handbook", 3rd ed., Wiley, New York, 1989,p. VI/451.

18. C. Y. Cha, R. J. Samuels, J. Polym. Sci. B: Polym. Phys, 33,259(1995).

19. S. S. Hardaker, R. J. Samuels, J. Polym. Sci. B: Polym.Phys., 35, 777 (1997).

20. C. Cha, R. Samuels, S. Hardaker, R. Gregory, Syntheticmetals, 84, 743 (1997).

21. S. Hayashi, K. Asada, S. Hovike, H. Furahata, T. Hirai, J.Colloid Interface Sci., 176, 370 (1995).

22. D. F. Stamatialis, M. Wessling, M. Sanopoulou, H. Strath-mann, J. H. Petropoulos, J. Membrane Sci, 130, 75 (1997).

23. T. Doi, S. Yukioka, H. Inoue, A. Akimoto, J. Appl. Pol. Sci,63, 925 (1997).

TABLE 3. cont'd

Polymer n T (0C)

Poly(vinyl propionate) 1.4665 20Poly(vinylcarbazole) 1.683 20Poly(vinylfuran) 1.55 20Poly(vinylidene chloride) 1.60-1.63Poly(vinylidene fluoride) 1.42 25Poly(vinylnaphthalene) 1.6818 20PoIy(I -vinyl-2-pyrrolidone) 1.53PoIy(N- vinylphthalimide) 1.6200 20Poly(2- vinyltetrahydrofuran) 1.55 20Poly(2-vinylthiophene) 1.6376 20Proteins 1.539-1.541Shellac 1.51-1.53Terpene resin 1.515 25Urea-formaldehyde resin 1.54-1.56Urea-thiourea-formaldehyde resin 1.660 25Poly(p,p-xylylenyl dimethacrylate) 1.5559 20