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.     

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.     

Kinetics of the gas-phase thermal elimination of N-alkyl-pyrazoles

The kinetic study of the gas-phase thermal elimination reactions of N-ethyl-3,5 dimethyl-pyrazole (I), N-ethyl-pyrazole (II), N-sec-butyl-pyrazole (III), and N-tert-butyl-pyrazole (IV) using a flow system is reported. After obtaining activation parameters for I we carried out competitive reactions with II, III and IV using I as internal standard to obtain their E_a. The values of Δ(ΔH) calculated for II, III and IV agree with the little differences in E_a experimentally found.     

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.     

Critical behavior of brittle‐ductile transition of polymers

We report that the brittle‐ductile transition of polymers induced by temperature exhibits critical behavior. When t close to 0, the critical surface to surface interparticle distance (ID_c) follows the scaling law: ID_c ∝ t^?v, where t = 1 ? T/T (T and T are the test temperature and brittle‐ductile transition temperature of matrix polymer, respectively) and v = 2/D. It is clear that the scaling exponent v only depends on dimension (D). For 2, 3, and 4 dimension, v = 1, 2/3, and 1/2 respectively. The result indicates that the ID_c follows the same scaling law as that of the correlation length (ξ), when t approach to zero. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 766–769, 2008     

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.     

Analysis of branched polymers by high resolution multidetector size exclusion chromatography: Separation of the effects of branching and molecular weight distribution

This article presents the SEC analysis of branched polyisobutylene PIB and polystyrene PS with high molecular weight and broad multimodal molecular weight distribution. Both polymers were synthesized using an inimer technique, which results in long‐chain branched polymers with statistical branching and broad multimodal distributions. Using high resolution multidetector Size Exclusion Chromatography SEC the polymers were analyzed based on three branching factors: g = (R_z,br/R_z,lin)_Mw; h = (〈R_h〉_z,br/〈R_h〉_z,lin)_{Mw ;} and ρ = (R ^1/2/〈R_h〉_z). It is generally accepted that for monodisperse branched polymers g and h < 1. In the case of our polydisperse PIB and PS, it was seen that g and h > 1, and ρ increases with molar mass and the number of chain ends as predicted earlier. The multidetector SEC system allowed for the separation of branching and polydispersity, reported here for the first time experimentally. The g parameter as a function of DP_i was compared to the theory developed by Zimm and Stockmayer. The plots followed a similar trend, but were shifted by a factor related to the average chain length between branching points. The ρ parameter decreased with increasing DP_i, as predicted theoretically by Kajiwara. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Melt‐state polymer chain dimensions as a function of temperature

The unperturbed chain dimensions (〈R²〉_o/M) of cis/trans‐1,4‐polyisoprene, a near‐atactic poly(methyl methacrylate), and atactic polyolefins were measured as a function of temperature in the melt state via small‐angle neutron scattering (SANS). The polyolefinic materials were derived from polydienes or polystyrene via hydrogenation or deuteration and represent structures not encountered commercially. The parent polymers were prepared via lithium‐based anionic polymerizations in cyclohexane with, in some cases, a polymer microstructure modifier present. The polyolefins retained the near‐monodisperse molecular weight distributions exhibited by the precursor materials. The melt SANS‐based chain dimension data allowed the evaluation of the temperature coefficients [dln 〈R²〉_o/dT(κ)] for these polymers. The evaluated polymers obeyed the packing length (p)‐based expressions of the plateau modulus, G = kT/np³ (MPa), and the entanglement molecular weight, M_e = ρN_anp³ (g mol^?1), where n_t denotes the number (～21) of entanglement strands in a cube with the dimensions of the reptation tube diameter (d_t) and ρ is the chain density. The product np³ is the displaced volume (V_e) of an entanglement that is also expressible as pd or kT/G. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1768–1776, 2002     

Extremal Wiener and Kirchhoff indices of globular caterpillars

The Wiener and Kirchhoff indices of a graph G are two of the most important topological indices in mathematical chemistry. A graph G is called to be a globular caterpillar if G is obtained from a complete graph K _s with vertex set {v₁,v₂,…, v _s} by attaching n _i pendent edges to each vertex v _i of K _s for some positive integers s and n₁,n₂,…,n _s, denoted by . Let be the set of globular caterpillars with n vertices (). In this article, we characterize the globular caterpillars with the minimal and maximal Wiener and Kirchhoff indices among , respectively.     

On the Sanibel coefficients in the expansion of spin-projected slater determinants

Every Slater determinant D may be uniquely analyzed in terms of spin components D_l = O_lD which are pure spin eigenfunctions, so that S²D_l = l(l+1)D. Every component D_l = O_lD may in turn be written as a sum of symmetric combinations of Slater determinants, T_k = [α^μ?kβ^k‖α^kβ^ν?k], and the coefficients c in the expansion O_lD = ∑_k c T_k are known as the “Sanibel coefficients.” By using the relation S²D_l = l(l+1)D, a recursion formula for the coefficients c is derived, which is then explicitly solved in the special case when S_z has the pure quantum number m = 0.     

Dynamic light scattering of polystyrene single chains in a semidilute solution of poly(methyl methacrylate) and benzene

Translational diffusion and internal motion have been observed by dynamic light scattering of optically labeled single chains of polystyrene (PS) in a semidilute solution of poly(methyl methacrylate) and benzene for the case in which the dimension R_g of the PS chain is comparable to the correlation length of the matrix solution. The molecular weight M_w dependence of the hydrodynamic radius R_h is expressed as R_h ～ M, while R_h ～ M in pure benzene. The average linewidth Γ for internal motions (KR_g > 1) appears to depend on the magnitude K of the scattering vector approximately as Γ ∝ K⁴ at higher KR_g ( > 1), in contrast with the fact that Γ ∝ K³ approximately for KR_g > 1 in pure benzene. The scaling law for the K dependence of Γ does not hold in low-molecular-weight PS owing to the K dependence of Γ /K² for KR_g < 1.     

Effect of solution concentration on the gelation of aqueous polyvinyl alcohol solution

The concentration dependence of cryogenic gelation for aqueous solution of poly(vinyl alcohol) was studied by measuring the apparent gel fraction G and the swelling ratio Q of the gel formed by freezing and thawing. It was found that for the gelation process there were three distinct regions of solution concentration bounded by two concentrations C_gel and C. The gel started to form at C = C_gel, while no visible gel could be detected even upon repeated freezing and thawing of the extremely dilute solutions of C < C_gel. The entire solution was gelatinized as a whole in the high concentration region of C > C. In the intermediate concentration region, C_gel < C < C, which covers three orders of magnitude in concentration, gel and sol phases coexist. Both concentration dependencies of G and Q show two branches jointed at a concentration very close to the overlap concentration C^*. The curve of G?Q versus C shows a sharp cusp. In case the sharp cusp concentration is really the value of C^*, gelation offers a precise method to determine the overlap concentration. ©1995 John Wiley & Sons, Inc.     

Structures of three crystal modifications of poly(3,3-dimethyloxacyclobutane)

Three crystal modifications of poly(3,3-dimethyloxacyclobutane) [? CH₂C(CH₃)₂CH₂O? ]_n were found and their structures were analyzed by x-ray diffraction. Modification I is obtained only under tension and disappears on relaxing the tension. From the fiber period of 4.83 Å, the molecular structure seems to be planar zigzag. In modification II, two chains in T₃GT₃? conformation pass through a monoclinic cell with parameters a = 8.93 Å, b = 7.48 Å, c (fiber axis) = 8.35 Å, β = 97.9°, and the space group P2₁/c-C. In modification III, two (T₂G₂)₂ chains pass through an orthorhombic cell with parameters a = 15.60 Å, b = 5.74 Å, c (fiber axis) = 6.51 Å, and the space group, C222₁–D. Molecular conformations of the three crystal modifications correspond to those of polyoxacyclobutane.     

Effect of preswelling of polymers in radiation-induced graft copolymerization

The graft copolymerization of styrene onto preirradiated poly(isobutylene oxide) was studied. An alkyl radical, ? C(CH₃)₂? CH? O? , was mainly observed by the irradiation of preswelled poly(isobutylene oxide) in aerated methanol. Kinetic analysis of the graft copolymerization indicated that the preswelling influenced k_tr and k_t and did not influence of ∫ R_idt and k_p.     

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.     

Surface thermodynamics of Efavirenz and a blend of Efavirenz with cellulose acetate propionate by inverse gas chromatography

The purpose of this paper is to study the effect of an excipient on the surface energetics of Efavirenz (EFV) drug. The net retention volumes, V_N, for n‐alkanes and polar solutes on the two columns, namely, EFV drug and a blend of EFV with cellulose acetate propionate have been measured by inverse gas chromatography. The dispersive surface free energy, , Lewis acid parameter, K_a, and Lewis base parameter, K_b, have been determined using V_N values. The values are decreased linearly with increase of temperature for pure EFV as well as for the blend. Furthermore, the values of EFV are higher than in the blend, for example, values at T = 318.15 K for EFV, and for the blend are 28.09 ± 6.02 mJ/m² and 28.30 ± 2.31 mJ/m², respectively. The specific component of surface free energy has been obtained by the Schultz method as well as by the Dong et al. method. The values have been used to calculate Lewis acid‐base parameters for the EFV as well as the blend. The K_a values for the EFV and the blend are almost similar, where as the K_b values are higher in EFV than in the blend. Similar trend in K_a and K_b has been observed in both methods studied. Copyright © 2015 John Wiley & Sons, Ltd.     

Radical polymerizations of 4-pentamethyldisilylstyrenes

Radical polymerization of 4-pentamethyldisilylstyrene ( 1 ) and 4-pentamethyldisilyl-α-methylstyrene ( 2 ) have been conducted. Monomer reactivity ratious (r₁ and r₂) of 1 and 2 with styrene (M₁) were measured with Fineman-Ross plots. The resonance factor (Q) and polar factor (e) of a Q–e scheme for 1 were conculated with the r₁ and r₂ values. The inductive effect (σ_I) resonance effect (σ) of the pentamethyldisily group were monitored with the ₁H- and ₁₃C-NMR spectra of 1 . The magnitudes of σ_I and σ were found to be analogous to those of the trimethylsilyl group, indicating that the disilyl group shows a net electron-withdrawal effect     

Ionization potential of excited states of Be‐like sequence in the concept of iso‐spectrum‐level series

With the introduction of the concept of the iso‐spectrum‐level series, a linear relationship is found between the first differences of the ionization potential of excited states and nuclear charge Z along an iso‐spectrum‐level series, and the ionization potential of excited states of Be‐like sequence are studied systematically on the basis of the weakest bound electron potential model theory. The expression of nonrelativistic ionization potential is derived from the weakest bound electron potential model theory, and relativistic effects are included by using a fourth‐order polynomial in Z. As a demonstration, the ionization potentials of [He]2s2p ³P, [He]2s3s ¹S₀, [He]2s3p ¹P, [He]2s3d ¹D₂, and [He]2s4d ¹D₂ series for a range of Be‐like sequence from Z = 4–23 are calculated. The results are compared with the experimental data and the recent sophisticated ab initio results. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 344–350, 2003     

Effects of high pressure on the conductivity and dielectric constant of conductive organic polymers

Previous theory for pressure effects on conduction in amorphous macromolecular solids is extended to include pressure effects on hyperelectronic polarization. A theoretical estimate of hopping activation energies is given. Experimental studies of the frequency effects of the pressure coefficients of conduction and permittivity permits resolution of the salient factors. Carrier mobility in ekaconjugated polymers is best represented by activated hopping, for conductivity increase with frequency, and permittivity drops. Conductivity and hyperelectronic polarization increase markedly with pressure. Their activation energies, E_a0, and the pressure coefficients of their activation energies (b_E + b_H) are nearly identical. E_a0 is frequency-dependent, but the (b_E + b_H) terms are not, showing the frequency dependence of E_a0 to lie in the hopping activation enthalpy. Similar arguments on the “total” pressure coefficients b and b for conduction and polarization show the latter coefficients to have a frequency dependence lying in the hopping activation entropy.