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.     

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.     

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.     

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.     

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.     

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.     

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 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.     

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).     

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.     

Solid-state polymerization of a diacetylene crystal: Thermal,ultraviolet, and γ-ray polymerization of 2,4-hexadiyne-1,6-diol bis-(p-toluene sulfonate)

Results are presented for the thermal, ultraviolet, and γ-ray polymerization of 2,4-hexadiyne-1,6-diol bis-(p-toluene sulfonate) (PTS). Monomer extraction is used to obtain polymer conversion-vs.-time curves at 30, 50, and 80°C. In agreement with previous work over a narrower temperature range, the curves all display a dramatic autocatalytic effect with an onset at about 10% conversion to polymer. Although the polymerization rate undergoes a 200-fold change over this temperature range, the shape of the conversion curves does not change. These data yield an activation energy (E) of 22.2 ± 0.4 kcal/mole when interpreted in terms of the time required to reach 50% polymer. An annealing technique is used to provide a closer look at the autocatalytic region. In that case, E = 22.5 ± 0.8 kcal/mole is determined from measurements of the time required to go from 10 to 50% polymer at temperatures ranging from 23 to 80°C (a 500-fold change in rate). Thermal polymerization rates measured in the low-conversion limit using a spectroscopic method based on diffuse reflectance yield E = 22.8 ± 0.6 kcal/mole. Thus E is independent of polymer conversion and the autocatalytic effect can be best understood as arising from a large increase in the propagation length of the polymer chains. The autocatalytic effect is shown to be present in both UV and γ-ray polymerization. In the case of γ-ray polymerization, conversion-vs.-time and spectroscopic measurements are consistent with inhomogeneities in the polymer concentration caused by particle tracks. Activation energies for UV and γ-ray polymerization are quite low (2-3 kcal/mole) and confirm that the chain initiation event makes the major energetic contribution to E. The polymerization mechanism is discussed in detail. The photopolymerization experiments can be consistently interpreted with a model based on the triplet excited state of the diacetylene monomer as the chain initiation species.     

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.     

Small-angle x-ray scattering from solution of rodlike particles with length distribution

The scattering function of rods with a constant radius, 8 Å, and a length distribution of the Schulz–Zimm type was calculated on a computer as a model of helical synthetic polypeptide. The influence of length and length distribution on the scattered intensity of small-angle x-ray scattering was clarified. As length grows and length distribution broadens it is difficult to obtain reliable values of molecular weight and radius of gyration from a Zimm plot. The influence of length distribution on the mass per unit length, M_q, and the radius of gyration of the cross section, 〈S〉^1/2, from the Guinier plot of the cross-sectional factor decreases as the length increases, and reliable values of M_q and 〈S〉^1/2 can be obtained even for rods with wide distribution for rods more than 600 Å long. In particular, it is pointed out that the value of 〈S〉^1/2 is little influenced by length and length distribution.     

Kinetics and mechanism of the cationic polymerization of tetrahydrofuran in solution: THF-CH3NO2 system

Polymerization of tetrahydrofuran (THF) in CH₃NO₂ solvent was initiated with 1,3-dioxolan-2-ylium cations with AsF and SbF anions, as well as with esters of FSO₃H and CF₃SO₃H acids. Polymerization shows in this solvent a living feature: values of k_p (determined directly from the semilogarithmic kinetic plots) were the same for all of the listed above initiators; thus k_p is the same for AsF, CF₃SO, FSO, and SbF anions. The identity of the k_p values for complex and noncomplex (ester-forming) anions comes from the fact that in CH₃NO₂ solvent equilibrium between macroesters and macroion pairs is shifted almost completely (K_e = 33.0 at 25°C and |THF|₀ = 7.0M) to the macroions side. Dissociation constants of the polytetrahydrofuranium ion pairs (CF₃SO and SbF anions) were measured (e.g., K_D = 2 × 10^?3 M at 25°C and |THF|₀ = 7.0M; i.e., at D = 22.8, ΔH_D = ?3.8 ± 6 kcal mole; ΔS_D = ?25 ± 2 eu). On the basis of the known values of K_D, and therefore dissociation degrees α, rate constants of propagation on the free and paired THF cations (k and k) were determined for a large range of degrees of dissociation (α from 0.15 to 0.52). The rate constants k and k were found to be the same within an experimental error of measurements (± 15% of the value of k_p). Apparently, the polytetrahydrofuranium cations are highly solvated or even separated from their anions by molecules of THF itself. At these conditions the reactivities of the solvated “free” and solvated (or separated) paired cations became undistinguishable.     

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.     

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.     

Determination of the Flory–Huggins χ parameter,the heat of dilution,and the excess heat capacity of some alkanes in polydimethylsiloxane by gas chromatography

The change in standard chemical potential of a number of alkanes on PDMS going from dilute solution to the perfect vapor Δ? was measured by gas chromatography over a large range of temperatures. The change in standard chemical potential of the alkane going from the pure liquid to the perfect vapor Δ? was calculated from fugacity data. These data were fitted separately to three Taylor's series expansions wherein the (partial) heat capacity of vaporization is zero, constant, and linearly dependent on temperature, respectively. On the basis of statistical and physical arguments it was concluded that the partial excess functions determined by gas chromatography should be described with a temperature-independent partial excess heat capacity.     

Photoinitiated cationic polymerization with triarylsulfonium salts

Triarylsulfonium salts Ar₃S⁺MX with complex metal halide anions such as BF, AsF, PF, and SbF are a new class of highly efficient photoinitiators for cationic polymerization. In this article we describe several synthetic routes to the preparation of these compounds along with their physical and spectroscopic properties. Mechanistic studies have shown that when these compounds are irradiated at wavelengths of 190–365 nm carbon–sulfur bond cleavage occurs to form radical fragments. At the same time the strong Br??nsted acid HMX_n, which is the active initiator of cationic polymerization that takes place in subsequent “dark” steps, is also produced. A study of the parameters that affect the photolysis of triarylsulfonium salts is reported with a measurement of the absolute quantum yields. The cationic polymerizations of four typical monomers—styrene oxide, cyclohexene oxide, tetrahydrofuran, and 2-chloroethyl vinyl ether—with triarylsulfonium salt photoinitiators are described.