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.     

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.     

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.     

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.     

The effects of morphology on 1H NMR spectra and relaxation in semicrystalline polyolefins

A brief résumé is given of the role of structural heterogeneity, magnetic dipolar couplings, molecular structure, and molecular motion in determining the ¹H NMR spectra and relaxation properties of heterogeneous solids such as semicrystalline polymers. Measurements of ¹H spin-lattice relaxation in laboratory (T₁) and rotating frames (T) are reported for a number of solid polyolefin samples. These include solution-crystallized and melt-crystallized polyethylene, annealed and quenched isotactic polypropene, and isotactic polybut-1-ene. In addition, broad-line ¹H spectra, both normal and partially (T) relaxed, are reported for these materials as well as a number of pulsed NMR experiments having the philosophy of the so-called Goldman–Shen experiment. Spin-lattice relaxation (T₁) for all samples is a single exponential process, whereas rotating-frame relaxation comprises three exponential processes both on-resonance (θ = 90°) and off-resonance at the magic angle (θ = 54.7°), with the latter generally being much slower. The spectra show clearly the existence of components having differing degrees of mobility and, with the exception of the solution-crystallized polyethylene, the partially (T) relaxed spectra indicate a correlation between breadth of resonance line and magnitude of T_1ρ. The Goldman–Shen-type experiments indicate a spin-diffusional transport of magnetization between the different spectral and (T) components. A computer program has been used to simulate the NMR behavior of a three-region system comprising repeating units of infinite lamellae of different widths, each region having different intrinsic relaxation times and spin diffusion coefficients. The results demonstrate that the observed ¹H NMR behavior of these samples can be interpreted in terms of this model and that, inter alia, the long-time T behavior reflects, qualitatively, the time taken for magnetization to diffuse a distance of the order of the dimensions of the region to which it corresponds.     

Kinetics of the reaction of poly(α-methylstyryl sodium,potassium, and cesium) with t-butyl chloride in tetrahydrofuran

The kinetics of the reaction of “living” poly(α-methylstyrl sodium, potassium, and cesium) with t-butyl chloride have been studied spectrophotometrically in tetrahydrofuran (THF) in the temperature range 283–303 K. The reactions, when the free ions present in solution are suppressed by tetraphenylboron salt, are first order with respect to both living ends and halide concentrations. Additions of tetraphenylboron salts produce a slight retardation effect on the rate of reaction in the case of sodium, indicating only a small contribution of free ions to the overall rate; in the case of potassium, there is no apparent effect. Analysis of the data indicates that the free ion is approximately 30 times more reactive than the sodium ion pair. The Arrhenius plots for contact ion-pair termination are linear and the activation energies and preexponential factors determined are E = 38.6 kJ mole^?1, log A = 4.44 liter mole^?1 sec^?1 and E = 46.0 kJ mole^?1, log A = 5.10 liter mole^?1 sec^?1. The reaction mechanism is interpreted in terms of elimination plus some side reaction to produce two unexpected reaction products—isobutane and a 315–320-nm absorbing grouping in the polymer.     

Ellipsometric study of the adsorption of comb-branched polystyrene onto a metal surface

The adsorption of well-characterized comb-branched polystyrene onto a chrome plate from cyclohexane solution at the θ temperature has been studied by ellipsometry. Both the adsorbance of the polymer and the extension of the adsorbed layer are compared with values for the linear polystyrene of the same molecular mass. The adsorbance is higher than that of the linear polystyrene, whereas the extension of the adsorbed layer is smaller, reflecting the higher segment density of the branched polymer. The extension t_b of the branched polymer is given approximately t_b = t_lg, where t_l is the extension of linear polystyrene of the same molecular mass and g is the ratio of the radii of gyration of the branched and linear polymers. The ratio of the adsorbances A_b/A_l of branched and linear polymer is approximately equal to g. These results indicate that the comb-branched polymer is adsorbed as a slightly distorted randam coil with extension and adsorbance governed primarily by the experimental g_s factor.     

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.     

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.     

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.     

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.     

Crystallization of poly(α-methyl-α-N-propyl-β-propiolactones) prepared from homogeneous and heterogeneous initiators

Half-crystallization times t_½, enthalpies of fusion ΔH, melting temperatures T_f glass transition temperatures T_g x-ray patterns, and morphologies were obtained for nine samples of poly(α-methyl-α-n-propyl-β-propiolactones) prepared from different homogeneous or heterogeneous initiators. The bulk of the results indicates that all samples can be classified into two categories: Polymers A having t_½?, 100 min, ΔH ? 26 J/g, T ? 376 K, T_g ? 275 K, and Polymers B having t_½ ? 10 min, ΔH ? 14.5 J/g T ? 425 K and T_g ? 271 K. Polymers A were prepared with homogeneous initiators while polymers B were polymerized with heterogeneous intiators. The difference in crystallization behavior between polymers A and polymers B is certainly due to a difference in microstructure, brought about by the initiators, which has been qualitatively observed by NMR.     

Small-angle X-ray and neutron scattering studies of the morphology of ionomers

Preliminary small-angle neutron scattering (SANS) studies have been made of different ionomers in the dry state and after saturation with water. Scattering from the dry samples arises from differences in the neutron scattering cross sections of the ionic and nonionic units in the polymer. The SANS technique is complementary to previous small-angle x-ray scattering (SAXS) studies since the SANS contrast differences are generally quite different than those for SAXS. A quantitative comparison is made of SANS and SAXS intensities for a dry cesium salt of an ethylene-methacrylic acid (E-MAA) copolymer. For water-saturated samples the technique of isotopic replacement can be used in conjunction with SANS since saturation can be effected with either H₂O or D₂O. In this case information about the chemical composition of the phases is obtained from an analysis of the intensity ratio I/I. Results are consistent with the presence of a separate phase containing water molecules and ions in a matrix of the nonionic units. A Guinier analysis gives a radius of gyration of 17 Å for a water-saturated cesium salt of an E-MAA copolymer.     

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.     

Properties of amorphous and crystallizable hydrocarbon polymers. I. Melt rheology of fractions of linear polyethylene

The dynamic moduli G′(ω) and G″(ω) for two groups of linear polyethylene fractions (reported M _w/M _n < 1.2) were measured in the melt state using the eccentric rotating disk method. Values of zero shear viscosity η₀ were obtained and compared with published results on similar fractions. Molecular weight data were converted to a common basis through intrinsic viscosities in trichlorobenzene (TCB) at 135°C. With recent data on M _w (light scattering) vs. [η]_TCB, for linear polyethylene, the relationship at 190°C, η₀ = 3.40 × 10^?14(M _w)^3.60, was obtained. The flow activation energy E_a was 6.4 kcal (T = 140–195°C). The plateau modulus G at 190°C was determined from the area under the loss modulus peak in one high-molecular-weight sample. The value obtained, G = 1.5₈ × 10⁷ dyn/cm², corresponds to an apparent molecular weight between entanglements of 1850. The storage compliance J′(ω) becomes anomalously large at low frequencies. The recoverable compliance J could not be determined for any of the fractions.     

Dependence of cooperative relaxation of amorphous polymers on diluent concentration

The Adam–Gibbs molecular theory, which describes the temperature dependence of relaxation phenomena in the main transition region in terms of the configurational entropy of a system, has been extended to include the effect of concentration of a low-molecular-weight compound on the viscoelastic behavior of concentrated polymer solutions. The concentration dependence of relaxation times in the polymer–diluent mixture leads to an expression of the concentration dependence both of the shift factor in the Williams–Landel–Ferry (WLF) equation and of the glass transition temperature T_g of the mixture. The constants of the WLF equation and the concentration dependence of T_g are given in terms of a difference between the specific heats of the liquid and glass ΔC_p of the equilibrium temperature T₂ of the second-order transition, and of the parameter Δμs/k, which includes the chemical potential Δμ and the configurational entropy s of the smallest cooperatively rearranging region. The resulting relationships also predict the temperature dependence of the constants of the concentration WLF equation. Good agreement was found between theory and the viscoelastic and T_g data on the systems poly(vinyl acetate) + diethyl phthalate, poly(methyl methacrylate) + diethyl phthalate and polystyrene + dibutyl phthalate. This finding indicates that the configurational entropy, at least in the first approximation, is responsible for the concentration dependence of relaxation phenomena in concentrated polymer solutions.     

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.     

Solid-state relaxations in poly(ethylene oxide). I. Study using the differential scanning calorimetry method

Differential scanning calorimetry (DSC) studies show that poly(ethylene oxide) (PEO) exhibits three transition regions below its melting point. The effects of annealing on the intensity and temperature of these transitions enable us to locate T < T_g (T_γ) T_g, and T_α at about 130–140. 190–240, and 263–313°K, respectively. Our results argue for a small transition T_g (L) at 190–200°K with a second T_g (U) above 233°K, the temperature of which increases on annealing. The shape of DSC derivative curves reveals that T < T_g and T_α are complex and suggests the possibility of two steps in these processes. In addition, a splitting of T_α is observed every time a multiple melting endotherm appears as a result of annealing. Up to three separate melting endotherms can be observed. One of them is related to the normal primary crystallization process. Its peak temperature increases linearly with the annealing temperature, yielding an extrapolated value for the equilibrium melting temperature T of 347°K as found before.     

The mechanism of O(3P) atom reaction with ethylene and other simple olefins

Reactions of oxygen atoms with ethylene, propene, and 2-butene were studied at room temperature under discharge flow conditions by resonance fluorescence spectroscopy of O and H atoms at pressures of 0.08 to 12 torr. The measured total rate constants of these reactions are K = (7.8 ± 0.6)·10^?13cm³s^?1,K = (4.3 ± 0.4) ± 10^?12 cm³ s^?1, K = (1.4 ± 0.4) · 10^?11 cm³ s^?1. The branching ratios of H atom elimination channels were measured for reactions of O atoms with ethylene and propene. No H-atom elimination was found for the reaction of O-atoms with 2-butene. A redistribution of reaction O + C₂ channels with pressure was found. A mechanism of the O + C₂ reaction was proposed and the possibility of its application to other olefins is discussed. On the basis of mechanism the pressure dependence of the total rate constant for reaction O + C₂ was predicted and experimentally confirmed in the pressure range 0.08–1.46 torr.