Polymer Physics (From Suspensions to Nanocomposites and Beyond) || Appendix A: Abbreviations and Notations

APPENDIX A

ABBREVIATIONS AND NOTATIONS

A.1 GENERAL AND CHEMICAL ABBREVIATIONS

5CP pentylcyanobiphenyl5OCB pentyloxycyanobiphenyl6FDA-ODA hexafluoroisopropylidene bis(phthalic anhydride-oxydianiline)8CB octylcyanobiphenyl8OCB octyloxycyanobiphenyl9DDA-9 dimer model compound of DDA-9:1,10-bis[[[4-[(4-methoxy-2-

methylphenyl)azoxy]-5-methylphenyl]oxy]carbonyl]decanea.u. arbitrary unitsac alternating currentACAR angular correlation of annihilation radiationAFM atomic force microscope or atomic force microscopyAl2O3 aluminum oxide (alumina)AN acrylonitrileARES advanced Rheometric expansion systemASTM American Society for Testing and MaterialsBaTiO3 barium titanate (BT)BLS Brillouin light scatteringBMAO behenyl dihydroxyethylamine oxideBST barium strontium titanateBT bentonite

Polymer Physics: From Suspensions to Nanocomposites and Beyond, Edited by Leszek A. Utracki andAlexander M. JamiesonCopyright © 2010 John Wiley & Sons, Inc.

709

710 ABBREVIATIONS AND NOTATIONS

BWR Benedict-Webb-Rubin equationca. circa (Latin, about as much)CaCO3 calcium carbonateCB carbon blackCD coefficient of determinationCEC cation-exchange capacityCED reduced cohesive energy densityC-F Cowie-Ferguson modelCMCII critical micelle concentration (second)CNT carbon nanotubeCONTIN continuous distribution (in PALS)CPG controlled pore glassCPNC clay-containing polymeric nanocompositesCPU central processing unitCRNI counter-rotating non-intermeshing TSECRR cooperatively rearranging regionsCSP corresponding-states principleCTAC 3MHDA cetyltrimethylammonium chlorideCTAT cetyltrimethylammonium tosylate, or

3MHDA-p-toluenesulfonateCVD chemical vapor depositionDBAR Doppler broadening of annihilation radiationdc direct currentDDS dynamic dielectric spectroscopyDHC district heating or coolingDLC diamond-like carbonDMA dynamic mechanical analysisDMT Derjaguin-Muller-ToporovDNA deoxyribonucleic acidDNS direct numerical simulationDOP di(2-ethylhexyl)phthalateDPD dissipative particle dynamicsDR drag reducingDRA drag-reducing additiveDRS dielectric relaxation spectroscopyDSC differential scanning calorimetryDTA differential thermal analysisD-W Dee and WalshDWNT double-walled nanotubesEFM extensional flow mixerEG ethylene glycolEM electron microscopyeos equation of stateEq., Eqs. equation, equations

ABBREVIATIONS AND NOTATIONS 711

ER electrorheologicalESR electron spin resonance spectroscopyFEGSEM field emission gun scanning electron microscopyFENE finitely extendable nonlinear elastic modelFF frozen free-volume fractionFH fluorohectoriteFM fluoromica (synthetic clay, e.g., Somasif ME-100)FOV Flory, Orwoll, and VrijFTIR Fourier transform infrared spectroscopyFTR Fourier transform rheologyFV force-volumeG glassy (vitreous) regionG-D Gibbs-DiMarzioGF glass fiberGPC gel permeation chromatograph [now: size-exclusion

chromatography (SEC)]HA hyaluronic acid = glycosaminoglycan (CAS #9004-61-9)HAp (nano) hydroxyapatiteHCP hairy clay platelets modelHDA hexadecanoic (palmitic) acidHES 2-hydroxyethyl styreneHFC 134a 1,1,1,2-tetrafluoroethaneHFHS hexafluoro-2-hydroxyisopropyl styreneH-H Hartmann and HaqueHMDA hexamethylene di-amineHOMO highest occupied molecular orbitalHPG high-pressure glassHRTEM high-resolution transmission electron microscopyHS 4-hydroxystyreneHT hectoriteHTR heat transfer reductionHW helical wormlike coil modelICA isotropic conductive adhesiveISM Ihm, Song, and MasonISO International Organization for StandardizationIUPAC International Union of Pure and Applied ChemistryJKR Johnson, Kendall, and RobertsKAHR Kovacs, Aklonis, Hutchinson, and Ramos (model of kinetics of

the glass transition) [Kovacs et al., 1979]K-BKZ model for non-linear viscoelastic body proposed by Kaye

(1962) and by Bernstein, Kearsley, and Zapas (1963)KP Kratky-Porod model [Kratky and Porod (1949)]KWW Kohlrausch, Williams, and WattsLAOS large-amplitude oscillatory shearLCP liquid-crystal polymer


LCST lower critical solution temperatureLDH layered double hydroxideLHS left-hand sideL-J Lennard-JonesLPG low pressure glassLT LifeTime programLT9.0 routine LifeTime program, version 9.0LUMO lowest occupied molecular orbitalM melt regionMA maleic anhydride (monomer)MAF mobile amorphous fractionMBBA 4′-methoxybenzylidene-4-n-butylanilineMBBE-x main chain dimer with POE-type spacers: α,ω-bis[4′′-(4′-(4-n-

methyl-phenyl-oxycarbonyl)-phenyloxycarbonyl)-phenyl]-oligo(ethylene glycols)

MC Monte Carlo computational methodMCLCP main-chain LCPMCM modified cell model (by Dee and Walsh)MCT mode-coupling theoryMD molecular dynamics (simulation)MDRA maximum drag reduction asymptoteME-100 Somasif = a semi-synthetic fluoromicaMEK methyl ethyl ketoneMELT maximum entropy for life time analysisMG Maxwell and GarnetMMA methyl methacrylate monomerMMT montmorilloniteMNSJ Midha, Nanda, Simha, and Jain theory of polymers in

crystalline stateMPM material-point-method simulationMPS multiphase polymeric systemMSS modified S-S equation of stateMW molecular weightMWD molecular weight distributionMWNT multi-walled nanotubeMWS Maxwell, Wagner, SillarsNa-MMT sodium montmorilloniteNC nanocompositenCB 4-n-alkyl-4′-cyanobyphenylNIRT notched Izod impact strength at room temperatureNMR nuclear magnetic resonancenOCB 4-n-alkoxy-4′-cyanobiphenylnOCCB 4′-n-alkoxycarbonyloxy-4-cyanobiphenylNW nanowireOHAO oleyl dihydroxyethylamine oxide


OM optical microscopyo-Ps ortho-positroniumo-TP ortho-terphenylp-Ps para-positroniumPAK physical aging kinetics (at Tβ ≤ T ≤ Tg)PALS positron annihilation lifetime spectroscopyPCLT nano-sized lead titanate doped with calcium and lanthanumPEA 2-phenylethyl aminePG propylene glycolphr concentration in parts per hundred of resin (also pph)PIV particle image velocimetryPLSN polymer layered silicate nanocompositeP-M Petrie-Marshall modelPMN-PT lead magnesium niobate-lead titanate:

(1 − x)Pb(Mg1/3Nb2/3) O3–xPbTiO3PMT photomultiplier tubePNC polymeric nanocompositesPOSS polyhedral oligomeric silsesquioxanepph parts per hundredPs positroniumPTM Prigogine, Trappeniers, and MathotPVT pressure-volume-temperature measurementsPZT lead zirconate titanateQAS quaternary ammonium saltsQTP quasi-two-parameter theoryRAF rigid amorphous fractionRER Rheometrics extensional rheometerRME Rheometrics elongational rheometer for meltsRT room temperatureSANS small-angle neutron scatteringSAOS small-amplitude oscillatory shear flowSAXS small-angle x-ray scatteringSCLCP side-chain LCPSDBS sodium dodecylbenzenesulfonateSDS sodium dodecyl sulfateSEC size-exclusion chromatographySEM scanning electron microscopySER Sentmanat extensional rheometerSFA surface force analyzerS-G Spencer and Gilmore equation of state (1949)SH strain hardeningSiC silicium carbideSIS shear induced structureS-L Sanchez and LacombeSN nucleophilic substitution


S-S Simha and Somcynsky cell-hole theory or equation of stateSS strain softening in elongationSSE single-screw extruderSSH slope of strain hardening (SH) vs. Hencky strain (ε); a

characteristic parameter of the materialSSI specific secondary interactionsSP saponiteSt styrene (monomer)STEM scanning transmission electron microscopySTM scanning tunneling microscopySTS scanning tunneling spectroscopySWNT single-walled nanotubeSWP square-well potential approximationT transition zoneTAC time-to-amplitude converterTDO tetradecyl oxyraneTeflon AF1600 random copolymer of tetrafluoroethylene (35 mol%) and

2,2-bis(trifluoromethyl)-4,5-difluoro-1,3-dioxole (65 mol%)Teflon AF2400 random copolymer of tetra-fluoro ethylene (13 mol%) and

2,2-bis(tri-fluoro methyl)-4,5-difluoro-1,3-dioxole (87 mol%)TEM transmission electron microscopyTFHS 1,1,1-trifluoro-2-hydroxyethyl styreneTGA thermogravimetric analysisTGAP triglycidyl p-aminophenolTGDDM tetraglycidyldiaminidiphenylmethaneTLM thread like micelleTMA thermomechanical analysisTMV tobacco mosaic virusTNM Tool-Narayanaswamy-Moynihan (model of kinetics of the

glass transition) [Tool, 1946a,b; Narayanaswamy, 1971;Moynihan et al., 1976]

TP two-parameter theoryTPBn MCLCP based on1-(4-hydroxy-4-o-bisphenyl)-2-(4-hydroxyl-

phenyl)-butane and an n-methylene spacer groupTPE-V thermoplastic elastomer vulcanizateTSC thermo-stimulated currentTSE twin-screw extrudert-T time-temperature superposition principleUCST upper critical solution temperatureUV ultravioletUVP ultimate velocity profileVAc vinyl acetate (monomer)VDW van der WaalsVFTH Vogel-Fulcher-Tammann-Hesse equation or temperatureVOH vinyl alcohol


VRH variable range hoppingWAXS wide-angle x-ray scatteringWLF Williams-Landel-Ferry equationXPS x-ray photoelectron spectroscopyXRD x-ray diffraction

A.2 ABBREVIATIONS FOR POLYMERS AND OLIGOMERS

a- PαMS atactic poly(α–methyl styrene)ABS thermoplastic terpolymer, an acrylonitrile-butadiene-styrene

copolymerADS statistical, partially aromatic copolymer of PA-6 (see PA-mXD6)a-PMMA atactic poly(methyl methacrylate)a-PS, aPS atactic polystyreneATPS amine-terminated polystyreneBR butadiene rubberBuBE-x main-chain dimer with POE-type spacers: α,ω-bis[4′-(4-n-

butoxy phenyloxycarbonyl)-phenyl]-oligo(ethylene glycols)CAc cellulose acetateCBA-n, BCBOn α,ω-bis(4-cyanobiphenyl-4′-yloxy)alkanesCBA-Tn, TCBOn 4,4′-bis[ω-(4-cyanobiphenyl-4′-yloxy)alkoxy]biphenylsCBC-n α,ω-bis[(4,4′-cyanobiphenyl)oxycarbonyloxy]alkaneCB-n α,ω-bis[(4,4′-cyanobiphenyl)carbonyloxy]alkaneCEBC ethylene(ethylene-co-butylene)ethylene block copolymerCOP cycloolefin copolymerCPI cis-polyisopreneCTC cellulose tris(phenyl carbomate)CYTOP cyclic transparent optical polymer, a copolymer consisting of

alternating tetrafluoroethylene and hexafluoro-2,3-dihydrofuran units

DDA-9 poly(4,4′-dioxy-2,2′-dimethylazoxybenzene dodecanedioyl)DGEBA diglycidyl ether of bisphenol A: ER1, monomer; ER6,

oligomer with six mersEBCA 4′-ethoxybenzilidene-4-cyanoanilineEP epoxy polymerEPDM ethylene-propylene-diene copolymerEPR elastomeric copolymer of ethylene and propyleneEPR-MA maleated EPREVA, EVAc ethylene vinyl acetate copolymerEVAl, EVOH copolymer of ethylene and vinyl alcohol (also, EVOH)HDPE high-density polyethylene (ca. 960 kg/m3)HIPS high-impact polystyreneHVBD high-vinyl polybutadieneIIR isobutylene-co-isoprene rubber


i-PMMA isotactic PMMAiPP isotactic polypropyleneIR polyisopreneLCP liquid crystal polymerLDPE low-density polyethylene (ca. 918 kg/m3)LDPE-MA maleated LDPELLDPE linear low-density polyethyleneLPE linear polyethyleneNBR elastomeric copolymer from butadiene and acrylonitrile; nitrile

rubberNR natural rubberP2VP poly(2-vinylpyridine)P4CS poly(4-chlorostyrene)P4HS poly(p-hydroxy styrene)P4MS poly(4-methyl styrene)PA polyamidesPA-11 polyamide-11PA-11T10 poly(aminoundecanoic acid-co-decane-1,10-diamine-co-

terephthalic acid)PA-6 polyamide-6, poly-ε-caprolactamPA-66 poly(hexamethylene diamine adipic acid),

poly(hexamethylene-adipamide)PAA poly(acrylic acid)PAM polyacrylamidePAM-n poly(azomethine ether) with PM-type spacersPA-mXD6 poly(m-xylylene diamine and adipic acid-co-caprolactam)PAN polyacrylonitrilePB poly(1-butene)PBA-copolymer poly(α,α′-dimethylbenzaladine ester) with PM-type spacers

(1:1 randomcopolymer of O(CH2)7O and O(CH2)10O )PBD polybutadienePBI polybenzimidazolePBMA poly(butyl methacrylate)PBO poly(p-phenylene benzobisoxazole)PBT poly(butylene terephthalate)PC bisphenol-A polycarbonatePCL poly(ε-caprolactone)PCT poly(cyclohexylene terephthalate)PDMS poly(dimethylsiloxane)PE polyethylenePEEK poly(etheretherketone)PEG = PEO poly(ethylene glycol), poly(ethylene oxide), or

poly(oxyethylene)PEMA poly(ethyl methacrylate)PE-MA maleated polyethylene


PEN poly(ethylene 2,6-naphthalene di-carboxylate)PEO = PEG poly(ethylene oxide), poly(oxyethylene), or poly(ethylene

glycol)PEST thermoplastic polyester (e.g., PBT, PET); also, TPESPET poly(ethylene terephthalate)PETG poly(ethylene terephthalate glycol); a copolymer with 66 mol

% ethylene glycol and 34 mol % cyclohexylene di-methanolPFE perfluoro elastomerPHBHV poly(3-hydroxybutyrate-co-3-hydroxyvalerate)PI polyimidePIB poly(isobutylene)PLA poly(lactic acid)PM poly(methylene)PMMA poly(methyl methacrylate)PMP poly(4-methyl-2-pentyne)PMPhS poly(methylphenylsiloxane)PnHIC poly(n-hexylisocyanate)PO polyolefinPOE poly(oxyethylene)POM polyoxymethylene, polyformaldehyde, polyacetal or “acetal”PP polypropylene; the common isotactic; syndiotactic must be

marked as sPPPPE poly(2,6-dimethyl-1,4-phenylene ether); ancient abbreviation:

PPOPPG poly(propylene glycol), also poly(propylene oxide) = PPOPPMA poly(propyl methacrylate)PP-MA maleated polypropylenePPO poly(2,6-dimethyl 1,4-phenyleneoxide); now PPEPS polystyrene (PS) (atactic; iso- or syndio-tactic are: iPS or sPs,

respectively)PSMA poly(styrene-co-maleic anhydride) copolymerPTFE poly(tetrafluoroethylene)PTMSP poly(1-trimethylsilyl-1-propyne)PU polyurethane elastomerPVAc poly(vinyl acetate)PVAl poly(vinyl alcohol); also PVOH is sometimes usedPVC poly(vinyl chloride)PVDF polyvinylidene fluoridePVDF-TrFE poly(vinylidene fluoride–co–3-fluoroethylene)PVME poly(vinyl methyl ether)PVP poly(vinylpyrrolidone)Pα MS poly(α -methylstyrene)SAN poly(styrene-stat-acrylonitrile), random copolymerSBR styrene butadiene elastomerSBS symmetric (styrene-butadiene-styrene) block copolymer


SEBS styrene-ethylene/butylene-styrene triblock polymerSHES poly(styrene-co-2-hydroxyethyl styrene)SHFHS poly(styrene-co-hexafluoro-2-hydroxyisoprpyl styrene)SHS poly(styrene-co-4-hydroxystyrene)SMA poly(styrene-co-maleic anhydride)sPS syndiotactic polystyreneSTFHS poly(styrene-co-1,1,1-trifluoro-2-hydroxyethyl styrene)TMPC tetramethyl bisphenol A polycarbonateTPO thermoplastic olefinic elastomerTPS styrenic thermoplastic elastomerTPU thermoplastic urethaneUHMWPE ultrahigh molecular weight polyethyleneVDF/HFP22 copolymer of vinylidene fluoride (78 mol%) with

hexafluoropropyleneXSBR carboxylated styrene butadiene rubber

A.3 INTERCALANTS AND ORGANOCLAYS

Intercalants

2M2DD dimethyl didodecyl ammonium chloride2M2HT dimethyl dihydrogenated tallow ammonium chloride (Arquad 2HT)2M2OD N,N-dimethyl-N,N-dioctadecyl ammonium bromide or chloride2M2TA dimethyl ditallow ammonium chloride2MBHT dimethyl benzyl hydrogenated tallow ammonium chloride2MBOD dimethyl benzyl octadecyl ammonium chloride2MHTL8 dimethyl hydrogenated tallow 2-ethylhexyl ammonium methyl

sulfate (Arquad HTL8)2MODA dimethyl octadecyl ammonium chloride3BHDP tributyl hexadecyl phosphonium3MHDA trimethyl hexadecyl ammonium chloride3MHTA trimethyl hydrogenated tallow ammonium chloride3MODA trimethyl octadecyl (or stearyl) ammonium chloride3MVBA trimethyl vinyl-benzyl ammonium chloride3OA trioctyl ammonium chlorideADA ω-aminododecyl (or lauric) acid, or 12-aminododecyl acidCPC cetyl pyridinium chlorideDDA dodecyl ammonium chlorideHDA hexadecyl ammonium chlorideM2EPPOH methyl diethyl polypropylene glycol ammonium chlorideM3OA methyl trioctyl ammonium chlorideMC2EtOH methyl coco-alkyl di-2-hydroxyethyl ammonium chlorideMOD2EtOH methyl octadecyl di-2-hydroxy ethyl ammonium chlorideMR2EtOH methyl-rapeseed- di-2-hydroxyethyl) ammonium chloride


MT2EtOH methyl tallow di-2-hydroxyethyl ammonium chloride (EthoquadT12)

ODA octadecyl ammonium chloride (C18; also stearyl ammoniumchloride)

SPN oligo(oxypropylene) diethyl methyl-ammonium chlorideSTN methyl tri-octyl ammonium chloride

Organoclays

1015C2 CPNC based on PA-6 (Mn=15 kg/mol) with 2wt% organoclay1022C5 CPNC based on PA-6 (Mn = 22 kg/mol) with 5wt% organoclayC10A Cloisite 10A, MMT pre-intercalated with 2MBHTC15A Cloisite 15A, MMT pre-intercalated with 2M2HTC20A Cloisite 20A, MMT pre-intercalated with 2M2HTC25A Cloisite 25A, MMT pre-intercalated with 2MHTL8C30B Cloisite 30B, MMT pre-intercalated with MT2EtOHC6A Cloisite 6A, MMT pre-intercalated with 2M2HT (discontinued)Cloisite organoclays from Southern Clay ProductsI.24TL MMT pre-intercalated with ADA from Nanocor, Inc.I.28E MMT pre-intercalated with 3MODA from Nanocor, Inc.I.30E MMT pre-intercalated with ODA from Nanocor, Inc.MAE Somasif ME-100 pre-intercalated with 2M2TAME-100 semi-synthetic fluorohectorite from CO-OP Chem. Co.; now CBC

Co., Ltd.MEE Somasif ME-100 pre-intercalated with MC2EtOHMPE Somasif ME-100 pre-intercalated with M2EPPOHMTE Somasif ME-100 pre-intercalated with M3OASCPX2231 Laponite synthetic clay now from Southern Clay Co. with 2M2HT

A.4 NOTATION

Roman letters

A Maier-Saupe anisotropic interaction parameter(Ch. 7)

Atotal total surface area of the dispersed matterAkj transition rate: Akj = lim

tδ→0[dPkj(tδ)/dtδ]

A, A0, Asp area, surface area of platelet, and the specificsurface area

AH Hamaker constant for attraction between twoinfinitely thick slabs

A2 second virial coefficientA, Am, B fitting coefficients


A, B, C, F rheological coefficients dependent on aspect ratiop, Eq. (16.43)

a effective bond length (Ch. 1), contact radius(Ch. 3)

a conformation tensor, Eq. (16.46)a = a(T) van der Waals measure of interactions (Ch. 6)a(x) rate function, β(λ+−λ−), for free volume xan ISM parameter (VDW analogue)ate, ata time-aging shift factor (ate = τte/τte,ref )aT , aT,P time-temperature and time-temperature-pressure

shift factorsa2, a4 second- and fourth-order orientation tensora∗o, a* domain sizes in region I and during LCP flow,

Eq. (16.11)ao, a1, a2 equation parameters in Eqs. (16.35) and (16.36)B excluded volume strength (QTP theory) (Ch. 1)B parameter in fuzzy cylinder theory (Eq. (1.133))B constant in the Vogel-Fulcher-Tammann-Hesse

equation (Chs. 6, 11, 14, 16)B = Nb/L stretching parameter in polyelectrolyte solution,

Eq. (1.151)B(T), Bo, Bglass(P) bulk modulus, its isothermal value at Po and that

of glassBLT background per channel in positron lifetime

measurementsBn number-average quantity of branch points per

chainB1/2 peak width at half height (Imax/2), B1/2 ∼= θ1 − θ2b monomer size (Ch. 1), a coefficient (Ch. 4)b = b(T, V) Clausius covolume, or van der Waals “excluded

volume”bn ISM parameter (VDW analogue)C constant in Tait equation C ≈ 0.0894 (Ch. 6), or

Cohen-Turnbull the pre-exponential factor(Ch. 11)

C crystalline phase content (Ch. 7)C, C*, C**, Cc, Ce, Cs, and Cf concentrations: polymer (molar in Ch. 1); overlap;

delineating semi-dilute and concentratedsolution regimes; critical for drag reduction; ofentanglements; molar of salt and ions

Cd coefficient of determinationCp, ∆Cp, Cp,I and CPN heat capacity at constant pressure; its change at

Tg; of component I and normalized valueCt , CT adjustable time, temperature coefficients


CI phenomenological interaction diffusioncoefficient

Cabs absorption cross section coefficientc∞ characteristic ratio of polymer in the Gaussian

limitc conformation tensor, Eq. (16.45)c, 3c, 3c/s external degree of freedom, their

volume-dependent value and the flexibility ratiocmax polyion concentrationc1, c2 coefficients in the William-Landel-Ferry (WLF)

equationD nematic coupling strength between polymer and

solvent mesogens (Ch. 1), crystallite averagedimension (Ch. 15), diameter of clay platelet orof a spherical particle (Ch. 14)

D(x), DM , diffusion function, 12β2(λ+ + λ−), for free

volume x; mutual-diffusion coefficientDD degree of dispersionDE droplet deformability in extensional flowDM

HD proton dipolar splitting due to mesogenic coreDo equilibrium separation between surfacesDo, D1 and D

†2 scaling coefficients in the Simha viscosity theory

(Ch. 1)Dr diffusive termDr, Dt , Do

r rotational and translational diffusion coefficients;that at zero concentration

D||, D||0 longitudinal diffusion coefficient of rod, that atzero concentration

d, de particle or capillary diameter (Ch. 16); “fuzzycylinder” diameter

(dp/dt)CN, (dp/dt)NI slope of the CN, NI phase boundary curvesdo and d1 scaling coefficients in the Doolittle viscosity

equationd001 clay interlayer spacingd33 longitudinal piezoelectric strain coefficientE, E∗, ER, E′

r Young’s (tensile) modulus, its reduced value;relative tensile and dynamic storage modulus

E+, E− energies of free positrons and electrons,measured against the vacuum level

E′, E′′ dynamic tensile storage and loss modulus,respectively

Ea, Ec activation energy; cohesive energy of an S-S merEf = dVf /dT specific thermal expansivity of the hole free

volume


Eo Lennard-Jones potential (Ch. 6)E0 lattice energy defined in the cell theory (Ch. 7)e, e+ , e− electronic charge, that of positron and electronei internal energy per unit volume(e2qQ/h) quadrupolar coupling constant of aliphatic CD

bondE(X/Xc) entanglement function (Ch. 1)

F, F Helmholtz free energy, in reduced variablesF, Fi force (Ch. 3), non-hydrodynamic force acting on

a particleFFT isothermal frozen free volume fractionf fraction of charged monomers in an electrostatic

blob (Ch. 1), volume filling factor, frequency(Ch. 13)

f, fs measured and solvent Fanning friction factor(Ch. 2)

f = (c2/s2)/(c1/s1) relative flexibility parameter (Ch. 6)f or fh = Vf /V, f ∗ free volume fraction and its characteristic valuefb, f0 frictional coefficient of a bead or a polymer; that

without excluded volumeft, fh,s, fi, fk free volume fraction: total (van der Waals);

hydrodynamically-accessible of the solvent; ofstate i, and state k

fθ frictional coefficient of a polymer in a theta solvent〈δf 2〉 mean-square free volume fluctuationsF function related to Helmholtz free energy (Ch. 4)G strain-energy release rate (Ch. 3)G, Gm Gibbs free energy (G = E − TS + pV = H − TS)

and its mixing valueG(t), (t, γ), Go shear stress relaxation modulus, at finite strain

and at zero timeG, G′(ω)G′′(ω), G∗(ω) shear (Ch. 1), dynamic shear storage, loss and

complex modulusG′

y, G′′y yield values for G′ and G′′

G(ξ), G∞ elastic modulus of structured material and“destroyed” structure

G(lnτ) distribution of relaxation timesg, gH , gη combinatorial factor (Ch. 6) or branching ratio

(Ch. 1) and its values from frictional coefficientor intrinsic viscosity

g′, g′′ initial slopes of the storage, loss shear modulusgb, gs, gz free energy of bulk, surface or a clusterge number of monomers in an electrostatic blobg(kβ), g(x) rate function (discrete, continuum)


gn(vh) = g(vh)/vh the number-weighted hole-volume probabilitydensity function

H rate front factor, H = Rτ−1g exp2.303c1 (Ch. 4)

H, Hh,H(∞) enthalpy, its value at hole formation and itsequilibrium value

δH departure from enthalpy equilibrium∆H, ∆HNI enthalpy change or activation enthalpy (Ch. 13);

that for nematic-isotropic phase transitionH(c) hydrodynamic screening function (Berry

viscosity theory)Hp, Hs hydrodynamic shielding parameter in Simha’s

solution viscosityH(λ) rheological relaxation spectrumh heat transfer coefficient (Ch. 2); film thickness

(Ch. 5); Planck’s constant, h = 6.6256×10−34 Jsh = 1 − y, hg hole fraction parameter in Simha-Somcynsky

eos; h = h(V, T) = h(T , P); its value at theglass transition temperature, Tg

heq hole fraction in equilibrium describe by theSchottky equation

hextrapol, hglass hole fraction at T ′ < Tg; hextrapol = h(T ′, P ′), andits value in glass

hs hydrodynamic shielding parameter for the puresolvent

∆h activation enthalpyI ionic strength (Ch. 1); isotropic phase (Ch. 7)Ii, I3 relative intensity of lifetime component i or that

of oPsI(Q), I(0) scattered intensity, extrapolated to Q = 0IPs binding energy of the Ps in matter in its ground

statei, j, k, m summing indices (Ch. 4)J axial ratio of ellipseJ ′(ω), J′′ (ω,) J*(ω) shear storage, loss, and complex compliancej number of backbone bonds per monomer (Ch. 1)K elastic coefficient (Chs. 3, 16) or reduced

compressibility; P∗V ∗/RT ∗ = 3/8 to0.272

[K] intrinsic value of the bulk modulusKM coefficient in the Martin equationk cantilever spring constant (Ch. 3), thermal

conductivity (Ch. 2); mass distributioncoefficient (Ch. 8)

k′ Huggins coefficient in solution viscosity equation


kB Boltzmann’s universal constant;kB = 1.381 × 10−23 J/K

k1, k2 kinetic constants, Eq. (16.40)L polymer contour length (Ch. 1); surface region

thickness (Ch. 8)Lc, Le capillary length and “fuzzy cylinder” lengthL/D axial ratio of an extruder barrel (length/width)l, , lc, B, D, p length: of a segment, a bond, maximum effective

length that chains can assume, Bjerrum length,Debye length and persistence length

l0 is the latent heat per unit massM number of vacancies of the Simha-Somcynsky

lattice (Ch. 11)M, Mw and Mn polymer molecular weight and its weight and

number averagesMm or Mo monomer molecular weight or massMs = Mn/s segmental molecular weightMe, Ma molecular weight between entanglements and of

star-polymer armML mass per unit contour lengthMT torqueM ′, M′′ real and imaginary parts of the dielectric modulusm number of clay platelets per stack (Ch. 14)mg, mg(τ) glass former “fragility index” and that of the

glass-forming liquid at the glass transitiontemperature, Tg

mi permanent dipole moment for two components(i = 1, 2)

N polymer degree of polymerization (Ch.1) or numberof polymer chains per unit volume (Ch. 4)

NA Avogadro’s numberNe entanglement degree of polymerizationNh = N ′

h/V ; NhSS specific hole number per unit volume; number oflattice vacancies per gram

NP , Ns number of chain segments of FENE-type modelmacromolecule and of backbone units involvedin local molecular rearrangements

N(t) experimental positron lifetime spectrumNu = hD/k Nusselt numberNξ monomer-monomer correlation length degree of

polymerizationN1 , N2 first and second normal stress difference,

respectivelyn number of molecules in volume V (Ch. 6);

number of skeletal atoms (Ch. 7)


n exponent in the power law equation betweenviscosity and the deformation rate (Ch. 16)

〈n〉 mean number of vacancies of the Simha-Somcynsky lattice within an agglomerate

n + 1 number of free volume states in discrete modelnb, nbe number of blobs per chain, per entanglementn(rh) hole radius probability density function

(considered as volume weighted function)O

(t2δ

)terms of t2

δ and higher powers of tδo-Ps ortho positroniumP , P pressure and its reduced value: P /P*P*, V*, T* scaling parameters of the Simha-Somcynsky eosPc, Vc and Tc critical point coordinates of pressure, volume and

temperatureP∗

R = ξP∗ characteristic pressure reducing parameter in flowP(x|x′, t) probability of free volume change from x′ to x in

time t

Pij(t − t0) probability of a transition to state jβ at t fromstate iβ at t0

Ps, PPs positronium and its formation probabilityPo the glass formation pressure∆P/L pressure gradient in pipe flowp number of arms in star-polymer (Ch. 1); packing

parameter (Ch. 2)p =D/t clay platelet aspect ratio (D is diameter, t its

thickness) (Ch. 14)p′ = a1 /a2 ellipsoid aspect ratio of the major to minor axesp-Ps para positroniumpe pyroelectric coefficientpr probability unit in Eqs. (4.6) and (4.7)pi, pi internal pressure and its reduced valueQ, Q scattering vector (Ch. 9); throughput (Ch. 14)q cooling rate (Ch. 9); rate of vitrification by

cooling or compressing (Ch. 14); single particleconfiguration function (Ch. 8)

qXX, qYY , qZZ XX, YY, ZZ component of quadrupolar tensor q

R universal gas constant; 8.31432 J/mol KR, Rc, R, RB radius: of a curvature (Ch. 3); of a spherical

particle or an atom (Ch. 15); of a capillary;mid-point radius in Couette geometry; Bjerrumradius

R parameter that adjusts the global kinetics to localand compensates for other terms in the frontfactor (Ch. 4)

Re = DVρ/η Reynolds number – a dimensionless flowparameter


Rg=⟨s2g

⟩1/2,⟨s2θ

⟩1/2, Rg ,MRgb,M radius of gyration, unperturbed radius of

gyration; that of linear and branched polymerhaving molar mass M

RH , RH,f , RH,η hydrodynamic radius of polymer, from frictionalcoefficient, from intrinsic viscosity

Ri, Ro inner and outer radius of Couette geometryR(t) resolution function in positron lifetime

measurementsRn(ω) FTR harmonic intensity ratio: Rn(ω) =

In(ω)/I1 (ω), with n = 3, 5, 7Rll, R⊥, Rgll, Rg⊥ rms end-to-end distances, radii of gyration of

polymer chains projected parallel andperpendicular to the nematic director

r cavity radius (Ch. 9), position coordinate (Ch. 16)r, r2 correlation coefficient and its squared valuerHD distance between the deuterium (ortho) and

proton (meta) atomsrh, rh + δr radius of the hole, radius of the hole potentialS, Sc, ∆SV entropy and configurational entropy (Chs. 14 and

16); transition entropy due to volume changeS orientational order parameter (Ch. 7)S, So number of external contacts for segment (-mer)

and hole (Ch. 6)Sconf

CN , SconfNI conformational entropy change for the CN, NI

transformation(∆Str)P , (∆Str)V transition entropy (tr = CN or NI) at constant

pressure or volumeSij hydrodynamic forces acting on a dispersed phase

particleSXX, SYY, SZZ XX, YY, ZZ component of orientational order

parameter tensorSM

ZZ orientational order parameter of mesogenic coreaxis

s number of statistical segments permacromolecule; s = Mn/Ms

s(t) theoretical positron lifetime spectrumT , ∆T , T , Tf temperature, T -difference, reduced (T /T*) and

fictive temperatureTa, Td annealing or aging, degradation temperatureTα, Tβ, Tγ temperature of α- and sub-glass relaxations β-

and γ-TB or Tc crossover transition temperature; TB/Tg ≈

Tc/Tg = 1.25 ± 0.10TCN, TNI CN, NI transition temperature


Tg, ∆Tg, T∞g glass transition temperature, change in Tg, Tg at

very high MWT g,i, T g,m Tg of component i in a blend and a miscible blendTK Kauzmann zero-entropy temperature,

TK ≈ Tg − 50 KTk or Tkv, or T kσ “knee“ temperature of the o-Ps lifetime

τ3: Tk/Tg = 1.19–1.68TLL liquid-liquid transition temperature,

TLL/Tg = 1.20 ± 0.05T Lρ Boyer high melt transition temperature,

TLρ ≈ TLL + 50 ≈ (1.35 ± 0.1) × Tg

Tm, T0 melting and reference temperatureTmax temperature at which the physical aging rate is

the highestTo Vogel-Tammann-Fulcher temperature (Ch. 14)T o glass formation temperatureT ′

0 temperature where the extrapolated hole freevolume goes to zero

T ∗R characteristic temperature reducing parameter

value for flow (K)Tr reduced temperature (T /TNI)TT upper transition temperature, Tg < TT ≈ Tc

T2 spin-spin relaxation timet time; also thickness of a clay platelet (Ch. 14)ta or te, tc physical aging, annealing or elapsed time;

characteristic timetan δ dynamic loss tangenttδ, trest infinitesimal time; rest time” during stress

overshoot teststp period of rotation for anisometric particlesU potential (Ch. 1) or internal (Chs. 6, 7) energyU depth of the potential well probe by Ps (Ch. 11)U local mean axial velocity (Ch. 2)UA van der Waals interactions (cal)Uc activation energy for viscous flowUh energy to form hairpin turn in the spacer group of

a liquid crystal polymerU(y,t) modified differential state population,

W(x, t)W−1/2∞ D1/4

u exponent accounting for aggregate sizepolydispersity (Ch. 16)

u momentum field of the fluid per unit volume,Eq. (16.45)

u* = (τW /ρ)0.5 friction velocity


u′ root mean square axial turbulent velocityfluctuations

u+ = u/u* non-dimensional local mean axial velocityUs surface energyV , V , Vo specific volume; its reduced value, V/V* at P and

P = 0Vc specific crystalline volume∆VCN, ∆VNI volume change at the CN or NI phaseVf , Vfi, Vft , Vfm specific (hole) free volume, its interstitial value,

total free volume, Vft = Vfi + Vf and partialspecific free volume of hole agglomerates

Vf /V = h free volume fraction〈vh〉 mean hole volume, first moment of the function

gn(vh)Vhc, VH, V∞ volume: of hard-core cell or hydrodynamic and at

equilibriumV mean axial fluid velocity in pipe (Ch. 2)VI or VN volume of the isotropic or nematic phase at the

NI transition pointVm, Vs molar volume of a monomer and of a segmentV0, Vocc = yV specific occupied volume from S-S eos (mL/g)〈VSV 〉 volume of the smallest representative freely

fluctuating subsystem for structural relaxationVVDW van der Waals volumev specific volumev∗, v∗

ij Lennard-Jones repulsion volume per statisticalsegment

v′ rms radial turbulent velocity fluctuationsve effective volume of hydrocarbon chainvf = v − vo excluded or free volumevi local velocityvip volume fraction of interphase layervo = 2πσ3/3 hard core of a moleculev2, v∞ specific volume: partial and at equilibriumW(x, t), W∞(x) differential free volume state population,

w(x, t) − W∞, and at the equilibriumw adhesive energy or work of adhesion (Ch. 3)W, wi mass fraction (Ch. 8) and that of component i

w, wmax clay content in wt% and its value fordisappearance of free macromolecules (Ch. 14)

wi(t), w(x, t) population of free volume state i (discrete) or x

(continuum) at time t

X, Xc dimensionless Fox parameter and its value atonset of chain entanglements (Ch. 1)


Xc or Xcryst crystalline fractionXi site fractionXp, Xs temperature scaled by polymer or by solvent Tg

x number of repeating unit (Chs. 2, 7); structuralparameter (Ch. 9)

x* reduced domain size within the LCP regions Iand II; Eq. (16.11)

x, x′ measures of free volume (continuum relaxationmodel) (Ch. 4)

xi, xss mole fraction (Ch. 6) and that of clusters in thebulk fluid phase

xi local coordinates in Eq. (16.1)xw weight average degree of polymerizationYs linearized free volume functional in Eq. (16.36)y distance from the pipe wall (Ch. 2)y = y(V , T ) or y(P , T ) occupied lattice-site fraction in S-S eos; h = 1−y

y+ = yu*ρ/η non-dimensional distance from the pipe wally(x) modified free volume,

∫ x

0 D(x′)−1/2dx′ymax range maximum for y(x)Z number of beads in chain (Ch. 1) or atoms in a

cluster (Ch. 15)Z, Zext configurational partition function (S-S eos)

(Ch. 6) and its combinatorial partZC, ZN,ZI conformational partition function for the C, N, I

phasesZeff effective charge on a polyionz strength of the excluded volume interactions (TP

theory) (Ch. 1), displacement of the piezoelectricscanner (Ch. 3), coordination number (usuallyz = 12) (Ch. 6), distance in orthogonaldirection to the clay surface (Chs. 6, 14)

z scaled excluded volume parameter (QTP theory)(Ch. 1)

zb, zs number of atoms in the bulk and at surface

Greek letters

α = (1/V)(dV/dT )P , αi, αglass(P) (volume) thermal expansion coefficient and thatof the free and occupied volumes: fori = occ, f ; of the glass as a function of P

αi (λ) annihilation rate distribution of the i-theannihilation channel

α or a′ primary dielectric or mechanical relaxationmodes Tg (Chs. 11, 13)


α mobility factor (Ch. 16)α(c) concentration-dependent chain expansion

parameterαR, αH, αη expansion parameters for Rg, for RH from

frictional coefficient, and for RH from intrinsicviscosity

αm, αg, αN, αI thermal expansion coefficient in melt, glass, andof the N, I phase

αp scaling parameter (Phillies viscosity model)α2, α3 Leslie viscosity coefficients∆α anisotropic part of the optical polarizability

tensorβ flexibility parameter of polymer (Ch. 2); free

volume unit for discrete distribution (Ch. 4),exponent of KWW stretched exponentialfunction (Chs. 9, 14)

ß, ßS mole fraction of monomers in bulk and at thesurface of random copolymers

β secondary dielectric or mechanical relaxationmodes (Chs. 11, 12, 13) or finite-sizebroadening of diffraction peak (Ch. 15)

β friction coefficient (Ch. 16)β area shape factor dependent on the nucleus shape

(Ch. 15)βT = (1/V )(dV/dP)T isothermal compressibility; (the common

compressibility symbol is κ)χh hydrodynamic parameter (“fuzzy cylinder”

theory)χm fraction of monomers bearing an effective charge

on polyion∆ cantilever deflectionδ sample deformation (Ch. 2)δ tube diameter (reptation theory) (Ch. 1); volume

departure from equilibrium: δ = (ν − ν∞) /ν∞(Ch. 5); temperature-volume coefficient(Ch. 7); phase angle (Ch. 13)

δ = δ(T, P) solubility parameter,

δ ≡ √CED =

(P∗ × CED

)1/2(Ch. 6)

δε, δv adjustable parameters in Eqs. (6.54) and (6.55)δs weight ratio of bound solvent

df 2 = 〈d2Vf 〉

/〈VSV〉2

mean square fluctuation of the fractional freevolume complex relative permittivity of metalrelative to that of the surrounding medium


ε, ε∗ Lennard-Jones maximum attractive energy andits scaling form

ε∗ complex dielectric permittivity (Ch. 13)ε∗ij, v

∗ij Lennard-Jones binary interaction parameters

(Ch. 6)ε∗

11 = ε∗11 (X1) concentration-dependent energetic matrix

interaction parameterεo, ε∞ dielectric permittivity, vacuum and high

frequency limiting valuesεo Lennard-Jones potential (Ch. 8)εs solvent dielectric constantε∗

11, ε∗22 polymer-polymer and clay-clay interaction

coefficients∆ε relaxation strengthΦFF, ΦFFo, ΦFF, ΦFF∞ Flory-Fox viscosity constant, at zero excluded

volume in a good solvent, under thetaconditions, of HW chain in the limitλL → ∞

Φi specific volume fraction of component i

φ, φ, φ* volume fraction, its scaled and scaling value(Simha theory)

φ fraction of atoms on the surface (Ch. 15)φ, φi angle between: the first bond of the spacer and

the mesogenic core axis (Ch. 7); the i-th CDbond and the molecular axis

φ(t) relaxation functionφm, φmax maximum packing volume fraction, and that for

freely rotating clay platelet: φmax ≈ 0.99/pφo potential energy when the point s-mer is in the

cell centerφp percolation threshold volume fraction combinatorial factorγ shear strain (%) (Chs. 1, 16)γ surface free energy (Ch. 3), surface tension

(Ch. 8), interfacial tension, interfacial energyper unit surface area (Ch. 15)

γ , γC, γN , γI thermal pressure coefficient (Ch. 7), and of theC, N, and I phases

γ shear rateγ2 square of the optical anisotropyγG Gruneisen parameterγH , γD gyro-magnetic ratio of proton and deuteriumγss concentration scaling parameter (Simha viscosity

theory)


γV ∗f , and γv∗

h minimum specific free volume and minimumlocal free (hole) volume in the Cohen-Turnbullequation

γI hydrodynamic parameter (“fuzzy cylinder” theory)γ1 twist viscosity of nematic liquidη, ηs, ηm, η(σ12 = const) shear viscosity of polymer solution and solvent

(Ch. 1), of matrix (Ch. 16); at constant-stress[η], [η]o, [η]θ intrinsic viscosity of polymer solution in the

absence of excluded volume, and in thetasolvent

η† specific polymer-solvent interaction contributionto [η]

η scaled viscosity (Simha viscosity theory)ηa, ηb, ηc Miesowicz viscositiesηintra, ηinter intramolecular and intermolecular contributions

of electrostatic interactions to polyion solutionviscosity

η0, ηr, ηsp zero-shear viscosity, its relative, ηr = η/ηs, andspecific, ηsp = ηr − 1 magnitude

ηon, ηoff field-on and field-off electrorheological viscosityηRouse solution viscosity in the Rouse regimeηPs positronium contact density or relaxation

parameterκ = (∂lnV/∂P)T isothermal compressibility; κ = κ(P, T)κi κ of the free and occupied volumes, i = occ, f

κR(T ) relative compressibility coefficient (Ch. 14)κ Debye screening coefficient (Ch. 1)κl isothermal liquid compressibilityκN, κI isothermal compressibility of the N, I phaseκPs positronium formation rate∆ difference between values for the liquid (l) and

glassy state (g)λ chain stiffness parameter (Ch. 1)λ wavelength (Chs. 9, 14, 15)λ ISM parameter (Ch. 6), ratio of surface areas

(Ch. 9), positron annihilation rate (Ch. 11),relaxation time (Ch. 16)

λll, λ⊥ frictional coefficients of polymer parallel andperpendicular to the director in nematicsolvents

λ±k , λ±(x) up and down transition rates from state k

(discrete) or free volume x (continuum)µ, µb chemical potential of metal atoms in solution and

in the bulk of cluster (Ch. 15), ageing rate(Chs. 5, 9), Tabor parameter (Ch. 3)


µ* and l* reducing variables for molecular dipole momentand length

µ(T , σ) physical aging shift rate:µ ≡ (

∂log ata/∂log ta)T,σ

µ11; µ12 polymer-polymer and polymer-gas mixturechemical potentials

ν, ∆ν Einstein-Simha coefficient (Ch. 1), Poisson’sratio (Ch. 3), deuterium quadrupolar splitting(Ch. 7), frequency of a structural relaxationprocess (Ch. 11)

v* Lennard-Jones volumetric scaling parameterνc, νp valence of counterion and of charged group on

polyionΠ parachorΘ angle between the Z axis and the director of the

nematic domainθ disorientation angle between the two successive

mesogenic core axes (Ch. 7)θ parameter in S-S theory of surface tension (Ch. 8)θ backbone bond angle (Ch. 1), half conical angle

(Ch. 3) and scattering angle (Chs. 9, 14)θ0 (ν0) ≡ hν0/kT ∗ characteristic crystal vibration frequency2θ Bragg angle of a diffraction peakρ, ρ* mass density or electron density, characteristic

mass densityρ* separation distance between neighboring

segments (Ch. 6)ρl, ρs, ρp, ρM density of the liquid, of the solid, of the polymer,

of the metalρ∗, s∗, η∗, c∗ FOV reducing parameters: the “hard-sphere”

radius, number of contacts per segment,respectively

σ standard deviation (Chs.6, 14), surface entropy(Ch. 9), or shear stress (Chs. 1, 16)

σC direct current (dc) conductivityσh, σi standard deviation of the hole volume

distribution gn(vh) and of the i-th lifetimedistribution

σL−J Lennard-Jones segmental repulsion radiusσl, σs specific surface energies of the liquid and of the

solidσy yield stress in shearσ3; σh o-Ps lifetime dispersion; hole volumeτ shear stress (Ch. 2) or relaxation time (Ch. 9) and

primary relaxation time (Chs. 11, 14)


τ mean positron lifetime (Ch. 11)τ∗, τaggr, τR, τσ coupled, domain, molecular and average

relaxation timeτDR proposed additional local shear stress for drag

reducing solutionsτe+ or τe+ positron mean lifetime in matterτo helix torsional parameter (HW theory)τ0pPs, τ

0oPs, and τpPs, τoPs p-Ps, o-Ps mean lifetimes in vacuum, and in

matterτRe = −ρu′v′ local Reynolds stress; time-averaged product of

u′, v′ and ρ

τrep reptation timeτte and τte,ref creep retardation time or relaxation time and its

reference valueτTotal and τviscous total local shear stress and local viscous shear

stressτW =∆PD/4L wall shear stressτy characteristic time of the yield clusterτ1 longest Rouse-Zimm relaxation timeτ3 p-Ps lifetime cone angleΩ circular frequency of a primary relaxation

process (Ch. 11)Ω angular rotation speed (Ch. 1)ω angular frequency in dynamic testing (rad/s)

(Chs. 1, 14, 16)ω or ωSS S-S cell volume: ω = yV/(Ns)ω, ωm and ψ, ψm “eigenvalues” and “eigenfunctions” from Eq.

(4.35)ωα acentric factor in Eq. (6.13)ωc critical frequencyω0 pre-exponential factor in the

Vogel-Fulcher-Tammann-Hesse equationΞ hydrodynamic interaction strength (Eq. 1.38)ξ monomer-monomer correlation length (Ch. 1),

molar ratio of counterion to surfactant (Ch. 2),characteristic length of dynamic heterogeneity(Ch. 11)

ξ ≡ PR∗/P∗ ratio of the pressure reducing parameter in flow

to P∗ (Ch. 6)ξs electrostatic blob sizeξk equilibrium occupancy of free volume state k

(discrete)ψ disorientation angle between the mesogenic core

and the molecular axis


Ψ1 and Ψ2 first and second normal stress coefficientsΨ ′′(s) total partition functionζ segmental frictional coefficient (Ch. 1), number

of relaxation neighbors (Ch. 9) ζ ≈ 12ζ, ζN, ζI strength of the interaction field, its values in the

N, I phase (Ch. 7)

Mathematical symbols

Π product∝ proportionality≈ is approximately equal to≡ congruent (identical)∴ thereforeπ 3.1415926536∑

sum⊗ symbol for mathematical convolution operation〈〉 statistical average quantity

Subscripts

a amorphous phasec crystalline phase; critical; compositeE uniaxial extensione+ positronf filler or fiber in compositesf, fh hole free volumefi interstitial free volumeft total free volumeg glass; glass transitionh holei number of the annihilation channel, inversion or dispersed phase,

interparticle frictional interaction between tactoidsi, j counting subscriptsm mixing, melt, matrixMAF mobile amorphous fractionn number averageo initial (or reference) valueocc occupied (volume)oPs ortho positroniump polymer matrixpo pick-off processpPs para positroniumR reference variable


R, r relative functionRAF rigid amorphous fractions suspension or segmentth theoreticalw weight averagey yieldz z-average

Superscripts

E excess valueL lattice gas model+ stress growth function− decay function∼ (tilde) reduced variable* complex or reducing variable

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Polymer Physics (From Suspensions to Nanocomposites and Beyond) || Appendix A: Abbreviations and Notations