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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.