Rigid backbone polymers. XI. Solution phase-viscosity relationship

Using combined results of isothermal viscosity measurements and cross-polarized light microscopy on four polyisocyanate/solvent systems, the following were demonstrated: (a) an anisotropic phase appears, associated with a shoulder in the viscosity curve, at a concentration v lower than the peak viscosity at v; (b) the inversion from anisotropic inclusions in an isotropic matrix to isotropic inclusions in an anisotropic matrix, occurs at concentrations v > v and (c) the attainment of a single phase, microscopically anisotropic, occurs at v > v; where the viscosity is decreasing but has not yet reached its minimum. When the experiments were repeated with changes in temperature, the following were observed: (a) within each single phase the viscosity drops with increased temperature; (b) in the biphasic range, the total viscosity η⁰ remains about constant in the concentration range ≤ and increases with temperature in the range v > v; (c) in the interval v > v of the biphasic range, at constant temperature an increase in concentration decreases η⁰, and at constant concentration, a decrease in temperature lowers η⁰. Qualitative explanations of the observations are proposed.     

Ultradrawing of high-molecular-weight polyethylene cast from solution. II. Influence of initial polymer concentration

Ultradrawing of films of high-molecular-weight polyethylene (M?_w = 1.5 × 10⁶) produced by gelation crystallization from solution is discussed. The influence of the initial polymer volume fraction (?) on the maximum draw ratio (λ_max) of the dried films is examined in the temperature region from 90–130°C. The results can be described very well by the relation λ_max = λ ?^?1/2 where λ is the (temperature-dependent) maximum draw ratio of the melt-crystallized film. An attempt is made to discuss the marked influence of the initial polymer volume fraction on λ_max in terms of the deformation of a network with entanglements acting as semipermanent crosslinks.     

Dilute-solution properties of trans-1,4-polyisoprene

Trans-1,4-polyisoprene was fractionated by both fractional precipitation and preparative gel permeation chromatography to obtain possibly sharp fractions of narrow molecular weight distribution. Selected fractions were characterized by light scattering, viscosity, and gel permeation chromatography. Necessary corrections for molecular heterogeneity were applied. Some of the characteristic relations between [η] and M _w are [η] = 1.81 × 10^?4 M in benzene at 30°C, [η] = 1.38 × 10^?4 M in n-hexane at 30°C, which are found to be in good agreement with literature data when corrected for molecular heterogeneity.     

Studies of polar and nonpolar probes in the determination of infinite-dilution solubility parameters

Partial molar heats of mixing ΔH and Flory-Huggins χ parameters have been determined for a series of polar and nonpolar organic probes in the polymer systems polychloroprene, poly(butadiene-acrylonitrile) (34 wt. % acrylonitrile), poly(ethylene-vinylacetate) (40 wt. % vinylacetate) and cis-1,4-polybutadiene in the range 65–85°C. Using the Flory-Huggins χ parameters, infinite-dilution solubility parameters δ were calculated for the polymers at 75°C to be 8.8 ± 0.2 for polychloroprene 10.0 ± 0.3 for poly(butadiene-acrylonitrile), 8.3 ± 0.2 for poly(ethylene-vinylacetate) and 7.9 ± 0.1 for polybutadiene. These δ values are in good agreement with literature δ₂ values. δ values were also calculated using only polar or nonpolar probes. The change in δ as the set of probes changed was negligible, leading to the conclusion that Hanson's three-dimensional solubility parameter concept may not be applicable to the infinite-dilution case.     

Dilute solution properties of a polybenzimidazole

Light scattering and viscometric studies have been carried out on dilute solutions of a polybenzimidazole in N,N-dimethylacetamide. The data, which span the molecular weight range 2.9 ≦ 10^?4M_w ≦ 23.3, and the temperature range 290 ≦ T/K ≦343, yield the dependence of the mean-square radius of gyration 〈s²〉_LS, the second virial coefficient A₂, and the intrinsic viscosity [η] on molecular weight M_w and temperature. The unperturbed mean-square radius 〈s〉_LS was calculated using experimental values of 〈s²〉_LS and A₂. It was found that excluded volume effects on 〈s²〉_LS are very small. The unperturbed hydrodynamic chain dimension 〈s〉_η was estimated by considering draining effects. A small value of the draining parameter was obtained. Analysis of the temperature dependence of A₂ and [eta;] leads to the conclusion that this system approaches a lower theta temperature with increasing temperature. The steric factor σ = 〈s〉/〈s〉f, based on the value of 〈s〉_f calculated for the polymer chain with free rotation, is nearly unity. Most of these properties can be interpreted in terms of long rotational units within the main chain.     

Dynamic x-ray diffraction studies of high-density polyethylene

Dynamic x-ray diffraction is conducted to explore the structural origin of the α and β mechanical dispersions of a melt-crystallized high-density polyethylene. It is shown that the real component of the strain orientation coefficient for the crystal c axis C decreases with increasing frequency at a rate which decreases with decreasing temperature. Values of C for the c axis are positive, C for the a axis negative, and C for the b axis close to zero, suggesting that the predominant relaxation process is crystal rotation about the b axis. The activation energy found from Arrhenius plots of C corresponds to that of the α₁ mechanical dispersion. The dynamic birefringence in this region is dominated by the contribution from crystal orientation changes. At low temperatures, the imaginary component KC of the strain-optical coefficient of the crystal phase approaches zero, while KC of the amorphous phase exhibits a somewhat broad dispersion peak corresponding to the β birefringence dispersion. This suggests that the principal contribution to the β birefringence dispersion arises from the amorphous phase, probably owing to the amorphous orientation process. Contrary to the case of low-density polyethylene, the dynamic crystal lattice deformation and compliance functions reveal distinct frequency dispersions corresponding to the α₁ and α₂ mechanical processes. The α₁ lattice dispersion is thought to be associated with the α₁ crystal orientation dispersion, while the α₂ lattice dispersion is believed to be the inherent one arising from the onset of intracrystalline chain motions.     

Relationship of stress to uniaxial strain in crosslinked poly(dimethylsiloxane) over the full range from large compressions to high elongations

Experiments on inflated sheets of crosslinked poly(dimethylsiloxane) covering a sixfold range of compression are combined with measurements in elongation conducted on specimens from the same sample to obtain the relationship of stress to strain over a 24-fold range in the extension ratio λ₁. With increase in λ the reduced force [f] ≡ f(λ₁ – λ)^?1 rises to a maximum near λ = 1.2–1.4, then decreases very slowly with further increase in λ. The form of the relationship of [f] to λ confirms recent theory.     

Specific volume of polysulfone as a function of temperature and pressure

The pressure–volume–temperature (PVT) properties of a commercial polysulfone derived from bisphenol A and 4,4′-dichlorodiphenylsulfone are studied experimentally and theoretically in the temperature range 30–370°C and for pressures to 2000 kg/cm². PVT surfaces are determined for an annealed glass, formed under zero pressure, and for the melt. Two glass-transition lines must be distinguished: T(P) which is the intersection of the glass and melt PVT surfaces, and T_g(P), which is obtained by pressurizing the melt isothermally. The application of Ehrenfest-type equations to these transitions are discussed. The Prigogine–Defay ratio r = Δ_kΔC_p/TV(Δα)² at P = 0 is found to be equal to 0.95 (±20%), using ΔC_p data determined on identical samples. The melt data is compared with the Simha–Somcynski hole theory, using the reducing parameters V^* = 0.788 cm³/g, T^* = 12,560°K, P^* = 10,875 bar. The hole fraction appearing in the theory is found to be constant along T(P), but the glass PVT relationship cannot be reproduced by using the Simha–Somcynsky theory together with the assumption that the hole fraction remains constant in the glass. At P = 0 the hole fraction must be allowed to decrease with decreasing temperature, but at a slower rate than in the melt.     

Internal field of polymer crystals: Polarizability tensor of the methylene group from the birefringence of paraffin crystal

Using the concept of a point dipole lattice, it is shown that the internal field of induced dipoles can be calculated for crystals comprised of simple chain molecules. The only structure which must be taken into account accurately is that of the chain molecule itself. From the calculations, reliable values of the polarizability tensor of the CH₂ unit are deduced from the birefringence of the paraffin crystal. In addition, it is shown that birefringence measurements provide a method for demonstrating the consistency of polarizability data so that no detailed structural information is needed. For the CH₂ unit, it is found by both methods that α^∥ ? α^? = ? 0.63 with respect to the chain direction [the units of polarizability α are 10^?24 cm³ (cgs)]. The most probable anisotropies for the bond polarizabilities are α ? α = 0.30, α ? α = ? 0.62.     

The elastic potential function of slightly compressible rubberlike materials

In order to obtain an analytical expression for the stored energy function W of slightly compressible rubberlike materials, two recent results are used to obtain a unified expression where Γ_i are a new set of invariants, and H(Γ₁,Γ₂) is the shear part of the stored energy function which is now assumed to be a separate symmetric function of the modified stretch ratio, λ = λ_i/I, i.e., Various analytical forms of h(λ) are proposed. Also, a straightforward transformation technique is formulated such that one can easily relate the stress-strain relation in terms of modified stretch ratio λ to the new invariants Γ_i. Thus, by a combination of the above equations and the transformation technique, one may readily determine the elastic strain energy function of slightly compressible materials from careful measurements of the volume change in multiaxial deformations.     

Deformation mechanisms of constrained polymer chains. II. Deformation energetics of tie molecules

Energy-deformation characteristics for the primary T, S, and U conformational units of tie molecules were obtained from the analysis of data generated from a constrained minimization algorithm. Energy-deformation profiles (covering the range from compact equilibrium defect structures to the fully extended chain) are reported for the S₀ and S₁ members of the S_λ family and for the U₀₀ member of the U_mn family. Estimates of the energy content V⁰ and the elastic modulus E were obtained from the computed energy-deformation data in the vicinity of the equilibrium Structure—S₀ → {60°, 180°, ?60°}, V = 1.7 kcal/mole, E = 60 kcal/cm³ [250 × 10¹⁰ dyn/cm²];S₁ → {60°, 180°, 180°, 180°, ?60°}: V = 1.7 kcal/mole, E = 25 kcal/cm³ [100 × 10¹⁰ dyn/cm²]; and U₀₀ → {60°, 180°, 60°, 180°, 60°}: V = 2.7 kcal/mole, E = 80 kcal/cm³ [340 × 10¹⁰ dyn/cm²]. Although the elastic modulus of the U₀₀ unit is comparable to the elastic modulus of the fully extended chain, the highenergy content of this unit (V₀ = 2.7 Kcal/mole) prohibits a significant population and thereby mitigates an appreciable reinforcing effect from this rigid unit. A model for a surrogate force constant is introduced to generalize the results from this study to any member of the S_λ or U_mn family as well as any combination of S_λ and U_mn units. This generalization provides a basis for estimating the deformation characteristics of tie molecules comprised of various populations of these primary conformational building blocks.     

A thermodynamic approach to the stress-induced crystallization in cross-linked rubbers

The thermodynamic treatment of crystallization phenomena in a prestretched rubber was undertaken. Emphasis was put on defining conditions for the thermodynamic stability of the extendedor folded-chain crystal structure. The extended-chain structure is found to be stable thermodynamically at temperatures higher than the isotropic melting point of un-cross-linked polymer T in the stretched state, while the folded chain one is not. Below T, the stretch ratio of the network structure determines which crystal structure is more stable. The relation among the critical stretch ratio for the extended/folded crystalline structure transition, temperature, and molecular weight is also discussed. The crystallinity predicted by this work becomes zero at a temperature of T, the isotropic melting point of a cross-linked system. The value of T decreases with increasing cross-link density, and this is consistent with the experimental data reported in the literature.     

Unperturbed dimensions of random and alternating styrene/n-alkyl methacrylate copolymers

The steric factors σ of homopolymers of ethyl, n-butyl, and n-octyl methacrylate, of equimolar random and alternating copolymers of these monomers with styrene, and of polystyrene, were determined by measuring intrinsic viscosities in a good solvent (butanone, 25°C) and extrapolating the data thus obtained to zero molecular weight of the polymer. For all comonomeric pairs under investigation, the σ² of an equimolar random copolymer and, particularly, of an alternating copolymer, is higher than the arithmetic mean (σ + σ)/2 of the σ² values of the parent homopolymers. The positive deviation from the linear dependence of σ² on the copolymer composition, expressed as an increment of σ², is proportional to the mole fraction of alternating dyads in the copolymer chain with in the limits of experimental error. The effect of copolymer microstructure on the unperturbed dimensions of the chains has been compared for equimolar copolymers of styrene with methyl, ethyl, n-butyl, and n-octyl methacrylate by using a relative increment ξ defined as the ratio of σ² of the alternating copolymer to (σ + σ)/2. The dependence of ξ on the number of carbon atoms in the alcohol substituent of the methacrylate component of the copolymer seems to exhibit a maximum for ethyl methacrylate.     

Kinetics and mechanism of the cationic polymerization of tetrahydrofuran in solution. THF–CH2Cl2 and THF–CH2Cl2/CH3NO2 systems

Cationic polymerization of tetrahydrofuran (THF) in CH₂Cl₂ solvent and in mixed CH₂Cl₂/CH₃NO₂ solvent was initiated with 1,3-dioxolan-2-ylium cations with AsF and SbF anions. Dissociation constants of the polytetrahydrofuranium ion pairs into ions were measured (e.g., K_D = 1.5 × 10^?5M at 25°C and [THF]₀ = 7.0M; CH₂Cl₂ solvent) and were found to be more than 100 times lower than in CH₃NO₂ solvent at the same [THF]₀ and temperature. The rate constants k and k, measured for degrees of dissociation ranging from 0.03 to 0.35 in CH₂Cl₂, were the same within an experimental error of measurements (±15% of the value of k_p). Dependence of k( = k = k) on the dielectric constant was a monotonous function in three different solvents, namely, CCl₄, CH₂Cl₂, and CH₃NO₂, which covered a large range of dielectric constants of the medium (from D = 5 to D = 22) and degrees of dissociation of the macroion pairs, α (from 0.03 to more than 0.70). Thus a decrease in the dielectric constant increases the rate constant k in the whole range of studied polarities of the medium. This result confirms an earlier conclusion that the rate constant of propagation does not depend on the state of aggregation of ions and k = k.     

Dielectric anisotropy in oriented poly(chlorotrifluoroethylene)

Dielectric measurements between ?50 and 60°C have been made on isotropic and oriented samples of poly(chlorotrifluoroethylene) with draw ratios λ of 1 to 3.5 at frequencies ranging from 30 Hz to 1 MHz. For the oriented samples, the dielectric loss has been measured with the electric field normal (ε) and parallel (ε) to the draw direction. At low frequency (say 60 Hz) the loss data for the oriented samples reveal two peaks at 25 and ?5°C, which are associated with the amorphous (γ_a) and the crystalline (γ_c) relaxations, respectively. Analysis of these data using a two-phase model yields values for the amorphous orientation function f_a which are only about 25 to 60% of those for the crystalline orientation function f_c. Upon annealing, the anisotropy ε/ε at the γ_a peak decreases significantly while that at the γ_c peak remains largely unchanged. This implies a roughly unaltered f_c and a large decrease in f_a, which is consistent with the results of wide-angle x-ray diffraction and birefringence measurements.     

Light scattering study of an aromatic polyamide-hydrazide polymer

The aromatic Polyamide-hydrazide, Monsanto X-500, has been studied by light scattering in dimethyl sulfoxide, a thermodynamically good solvent. The unperturbed dimensions, (〈r〉_av/M)^1/2 = 1.93 × 10^?8 at 25°C., indicate a rather highly extended chain. The persistence length falls in the range 35–63 Å, which corresponds to a length of between two and four formula units. This is considerably smaller than the values which have been reported for the aromatic polyamides, poly(p-benzamide) and poly(p-phenylene terephthalamide). X-500 appears to approximate coil-like behavior at a molecular weight of 45,000. Theoretical predictions, based upon the 〈r〉_av/bL ratio, are compared with the observation that no evidence for an anisotropic phase has been found in X-500 solutions in dimethyl sulfoxide at polymer volume ranging from 0.12 to 0.19 (depending upon the concentration of added LiCl).     

Photoinduced electron transfer from polystyrene pendant tris(2,2′-bipyridyl)ruthenium (II) complex to methylviologen

The characteristics of the photoinduced electron transfer reaction from polystyrene pendant tris(2,2′-bipyridyl)ruthenium (II) complex [Ru(bpy)] to methylviologen (MV²⁺) were studied. The rate constant k₁ from the excited state of the complex, Ru(bpy), to MV²⁺ were determined for both the polymeric and monomeric complexes from the lifetime τ of Ru(bpy) and the quenching rate of Ru(bpy) by MV²⁺. The polymer pendant Ru(bpy) showed three kinds of τ components ranging from 7 to 474 ns, in contrast to the monomeric complex, which showed one component of 350 ns. The k₁ values for both complexes were almost the same, on the order of 10⁸ L/mol s. The photoinduced electron transfer from solid-phase Ru(bpy) to liquid-phase MV²⁺ was realized by utilizing the polymer complex, and the solid–liquid interphase reaction system is discussed.     

The reactions of polyacetylene with trimethyloxonium hexachloroantimonate. Covalent doping of (CH)x

Polyacetylene, (CH)_x, has been doped with trimethyloxonium hexachloroantimonate, (CH₃)₃O⁺SbCl(1), in dichloromethane and acetonitrile. The maximally doped (CH)_x films have moderate conductivities [σ_RT(CH₂Cl₂) = 10, σ_RT(CH₃CN) = 0.7 Ω^?1 cm^?1]. Reactions between 1 and (CH)_x CH₂Cl₂ or CH₃CN were followed in situ by ¹H nuclear magnetic resonance spectroscopy and x-band electron spin resonance spectroscopy. It was found that the reactions in the two solvents are different. In dichloromethane the dopant is SbCl₅, which forms from the decomposition of 1, and doping proceeds by electron removal from (CH)_x chains. Based on the ESR signal loss, an estimate can be made of the diffusion rate of SbCl₅, into the (CH)_x fibrils in CH₂Cl₂; it is found to be ca. 10^?17 cm²/s. In acetonitrile the dopant appears to be either CH₃CNCH, H⁺, CH, or a combination of one or more of these dopants. It is postulated that the CH₃CNCH, CH, and/or H⁺ dopant covalently binds to the (CH)_x chain. X-ray photoelectron spectra show that films doped with excess 1 in both solvents have approximately one SbCl per 33 CH units.     

Magnesium chloride supported high mileage catalysts for olefin polymerization. XII. Polymerization of ethylene

Polymerizations of ethylene by the MgCl₂/ethylbenzoate/p-cresol/AlEt₃ TiCl₄-AlEt₃/methyl-p-toluate (CW-catalyst) have been studied. The initially formed active site concentration, [Ti] has a maximum value of 50% of total titanium at 50°C and lower values at other temperatures. The Ti decays rapidly to Ti sites with conc. ca. 10 mol %/mol Ti. The rate constants for four chain transfer processes have been obtained at 50°C: for transfer with AlEt₃, k = 2.1 × 10^?4 s^?1 and k = 4.8 × 10^?4 s^?1; for transfer with monomer, k = 3.6 × 10^?3 (M s)^?1 and K = 8.3 × 10^?3 (M s)^?1; for β-hydride transfer, k = 7.2 × 10^?4 s^?1 and k = 4.9 × 10^?4 s^?1; and transfer with hydrogen, k = 4.0 × 10^?3 torr^1/2 s^? and k = 5.1 × 10^?3 torr^1/2 s^?1. The rate constants for the termination assisted by hydrogen is k = 1.7 (M^1/2 torr^1/2 S)^?1. If monomer is assisting termination as was observed for propylene polymerization, then k = 7.8 (M^3/2 s)^?1. Values of all the rate constants can be higher or lower at other temperatures. Detailed comparisons were made with the results of propylene polymerizations. There are more than four times as many Ti active sites for ethylene polymerization than there are for stereospecific polymerization of propylene; the difference is more than a factor of two for the Ti sites. Certain rate constants are nearly the same for both monomers while others are markedly different. Some of the differences can be explained by stereoelectronic effects.