Transport of heavy organic vapors through silicone rubber

Permeability, solubility, and diffusion coefficients have been determined for halothane (CF₃CHClBr) and methoxyflurane (CHCl₂CF₂OCH₃) in silicone rubber at temperatures from 17 to 60°C and at relative pressures from 0.05 to 0.96. The solubility of both penetrants in silicone rubber is a strong function of penetrant concentration (or relative pressure), and can be represented satisfactorily by the Flory-Huggins relation with single values of the interaction parameter χ. The solubility coefficients decrease with increasing temperature at constant pressure. Mutual diffusion coefficients exhibit maxima when plotted against penetrant concentration; these maxima are attributed to the mass flow of polymer together with dissolved penetrant. Intrinsic diffusion coefficients increase linearly with increasing concentration. The energies of activation for diffusion are low, probably because of the ease of segmental motion about the Si? O linkage. The diffusivity data are examined in terms of Fujita's “free volume” model and of transition-state theory. Permeability coefficients for the two penetrants are large, of the order of 10^?6–10^?5 cm³(STP)-cm/(sec-cm²-cm Hg), and increase markedly with increasing concentration or decreasing temperature. This behavior is regarded as a consequence of the low energies of activation for diffusion.     

Sorption and transport of hydrocarbon and perfluorocarbon gases in poly(1‐trimethylsilyl‐1‐propyne)

Pure gas solubility and permeability of H₂, O₂, N₂, CO₂, CH₄, C₂H₆, C₃H₈, CF₄, C₂F₆, and C₃F₈ in poly(1‐trimethylsilyl‐1‐propyne) (PTMSP) were determined as a function of pressure at 35°C. Permeability coefficients of the perfluorinated penetrants are approximately an order of magnitude lower than those of their hydrocarbon analogs, and lower even than those of the permanent gases. In striking contrast to hydrocarbon penetrants, PTMSP permeability to fluorocarbon penetrants decreases with increasing penetrant size. This unusual size‐sieving behavior in PTMSP is attributed to low perfluorocarbon solubilities in PTMSP coupled with low diffusion coefficients relative to those of their hydrocarbon analogs. In general, perfluorocarbon penetrants are less soluble than their hydrocarbon analogs in PTMSP. The difference in hydrocarbon and perfluorocarbon solubilities in high free volume, hydrocarbon‐rich PTMSP is much smaller than in hydrocarbon liquids and liquidlike polydimethylsiloxane. The low solubility of perfluorocarbon penetrants is ascribed to the large size of the fluorocarbons, which inhibits their dissolution into the densified regions of the polymer matrix and reduces the number of penetrant molecules that can be accommodated in Langmuir sites. From the permeability and sorption data, diffusion coefficients were calculated as a function of penetrant concentration. With the exception of H₂ and the C₃ analogs, all of the penetrants exhibit a maximum in their concentration‐dependent diffusion coefficients. Resolution of diffusion coefficients into a mobility factor and a thermodynamic factor reveals that it is the interplay between these two terms that causes the maxima. The mobility of the smaller penetrants (H₂, O₂, N₂, CH₄, and CO₂) decreases monotonically with increasing penetrant concentration, suggesting that the net free volume of the polymer–penetrant mixture decreases as additional penetrant is added to PTMSP. For larger penetrants mobility either: (1) remains constant at low concentrations and then decreases at higher penetrant concentrations (C₂H₆, CF₄, and C₂F₆); (2) remains constant for all concentrations examined (C₃H₈); or (3) increases monotonically with increasing penetrant concentration (C₃F₈). Presumably these results reflect the varying effects of these penetrants on the net free volume of the polymer–penetrant system. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 273–296, 2000     

Solubility,diffusivity, and mobility of n-pentane and ethanol in poly(1-trimethylsilyl-1-propyne)

The diffusion coefficient of ethanol and of n-pentane in PTMSP, at 27°C, was measured as a function of concentration up to a penetrant content of about 12% by weight, for polymer samples obtained through different processes; differential sorptions and desorptions with vapor phases were considered. In the case of ethanol a nonmonotonous behavior was observed for the diffusivity, while in the case of n-pentane the same property was found to monotonously decrease with increasing the penetrant content. The sorption isotherms were also reported, indicating that n-pentane exhibits a typical dual mode behavior, while ethanol follows an unusual s-shape curve. The chemical potential of the dissolved penetrants, calculated directly from the isotherms, shows the very different importance of the energetic interactions of the two penetrants with the polymer units. In spite of the remarkably different concentration dependencies observed for both solubility and diffusivity of the two penetrants, the mobility factors are in both cases monotonously decreasing with the penetrant concentration, and follow very similar trends. The significant differences observed for the concentration dependence of the diffusion coefficients are, thus, associated to the thermodynamic contributions, which are very different for n-pentane and ethanol. Different polymeric films, obtained through different solvent evaporation processes, show quite different solubility, diffusivity and mobility for both ethanol and n-pentane. On the other hand, the ratio between the mobility of the two penetrants as well as the slope of mobility as function of the concentration remains the same for all the different samples inspected. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2245–2258, 1997     

Small-Molecule Diffusion in Semicrystalline Polymers as Revealed by Experimental and Simulation Studies

Summary: Diffusion of n-hexane in poly(ethylene-co-1-hexene)s with 15–75 wt.% crystallinity was studied by desorption experiments analyzing data using the Fickian equations with a concentration dependent diffusivity. The effect of the impenetrable crystalline phase on the penetrant diffusivity (D) is described by D = D_a/(τβ), where D_a is the diffusivity of the amorphous polymer, τ is the geometrical impedance factor and β is a factor describing the constraining effect of the crystals on the non-crystalline phase. For a polymer with 75 wt.% crystallinity, τβ varied markedly with penetrant concentration (v_1a) in the penetrable phase: 1000 (v_1a = 0) and 10 (v_1a = 0.15). This penetrant-uptake had no effect on the gross crystal morphology, i.e. β must be strongly dependent on v_1a. Samples saturated in n-hexane exhibited a penetrant-induced loosening of the interfacial structure, as revealed by an increase in crystal density that require an increased mobility in the interfacial component and by a decrease in the intensity of the asymmetric X-ray scattering associated with the interfacial component. The geometrical impedance factor has been modelled by mimicking spherulite growth and τ was obtained as the ratio of the diffusivities of the fully amorphous and semicrystalline systems. The maximum τ obtained from these simulations is ca. ten, which suggests that β in the systems with v_1a = 0.15 takes values close to unity. The simulations showed that the geometrical impedance factor is insensitive to the ratio of the crystal width and the crystal thickness. A free path length scaling parameter characteristic of the amorphous phase correlated with τ.     

Statistical mechanical model of diffusion of complex penetrants in polymers. I. Theory

A previously developed model of simple penetrant diffusion is extended to encompass complex penetrants of idealized molecular shape, characterized by dimensions of length, width, and thickness. Expressions are obtained for D(0,T), the diffusion coefficient at zero penetrant concentration (c), and the fractional increase in D(0,T) as a function of c and temperature (T). The model predicts that D(0,T) will exhibit Arrhenius behavior at temperatures well above T_g and gives the limiting activation energy as a function of penetrant thickness and the polymer energy/distance constants used previously. For T_g < T ? T_g + 150 K the model requires two new disposable parameters, in addition to the jump-length parameter of the simple penetrant theory. These parameters, however, have precise physical meanings (all are lengths) and together with the penetrant dimensions and polymer constants determine the absolute magnitude of the diffusion coefficient as well as its relative dependence on c and T. For T ? T_g + 40 the relative concentration dependence may be calculated in terms of the penetrant dimensions and polymer constants only.     

Twinkling fractal theory of the glass transition

In this paper we propose a solution to an unsolved problem in solid state physics, namely, the nature and structure of the glass transition in amorphous materials. The development of dynamic percolating fractal structures near T_g is the main element of the Twinkling Fractal Theory (TFT) presented herein and the percolating fractal twinkles with a frequency spectrum F(ω) ∼ ω^df–1 exp −|ΔE|/kT as solid and liquid clusters interchange with frequency ω. The Orbach vibrational density of states for a fractal is g(ω) ∼ ω^df–1, where d_f = 4/3 and the temperature dependent activation energy behaves as ΔE ∼ (T² − T). The key concept of the TFT derives from the Boltzmann population of excited states in the anharmonic intermolecular potential between atoms, coupled with percolating solid fractal structures near T_g. The twinkling fractal spectrum F(ω) at T_g predicts the correct dynamic heterogeneity behavior via the spatio-temporal thermal fluctuation autocorrelation relaxation function C(t). This function behaves as C(t) ∼ t^−1/3 (short times), C(t) ∼ t^−4/3 (long times) and C(t) ∼ t⁻² (ω < ω_c), which were found to be in excellent agreement with published nanoscale AFM dielectric force fluctuation experiments on a glassy polymer near T_g. Using the Morse potential, the TFT predicts that T_g = 2D_o/9k, where D_o is the interatomic bonding energy ∼ 2–5 kcal/mol and is comparable to the heat of fusion ΔH_f. Because anharmonicity controls both the thermal expansion coefficient α_L and T_g, the TFT uniquely predicts that α_L×T_g ≈ 0.03, which is found to be universal for a broad range of glassy materials from Pyrex to polymers to glycerol. Below T_g, the glassy structure attains a frustrated nonequilibrium state by getting constrained on the fractal structure and the thermal expansion in the glass is reduced by the percolation threshold p_c as α_g ≈ p_cα_L. The change in heat capacity ΔC_p = C_pL–C_pg at T_g was found to be related to the change in dimensionality from D_f to 3 in the Debye approximation as the ratio C_pL/C_pg = 3/D_f, where D_f is the fractal dimension of the glass. For polymers, the TFT describes the molecular weight dependence of T_g, the role of crosslinks on T_g, the Flory-Fox rule of mixtures and the WLF relation for the time-temperature shift factor a_T, which are traditionally viewed in terms of Free-Volume theory. The TFT offers new insight into the behavior of nano-confined glassy materials and the dynamics of physical aging. It also predicts the relation between the melting point T_m and T_g as T_m/T_g = 1/[1−p_c] ≈ 2. The TFT is universal to all glass forming liquids. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2765–2778, 2008     

Effect of pressure on gas permeability coefficients. A new application of “free volume” theory

The present work is a continuation of a general study of the effect of pressure on gas and vapor permeation through nonporous polymeric membranes. Permeability coefficients have been measured for 1,1-difluoroethylene (C₂H₂F₂) and fluoroform (CHF₃) in polyethylene at penetrant pressures up to 35 atm and at temperatures between -18 and 70°C. The permeability coefficient P? for the 1,1-difluoroethylene—polyethylene system was found to increase with increasing pressure differential Δp across the membrane. Isothermal plots of log ΔP versus Δp are generally linear and can be represented by empirical relations of the form ΔP = P(0)exp{m Δp}, where P(0) and m are constants. The slope m of these isotherms decreases with increasing temperature. Plots of log P? versus Δp for the fluoroform—polyethylene system are also linear, but exhibit negative slopes, i.e., P? decreases with increasing Δp. An extension of Fujita's “free volume” theory of diffusion in polymers shows that the dependence of P? on pressure reflects how the free volume of the polymer is affected by this pressure. An increase in the penetrant pressure may result in two opposing effects: (a) the concentration of the penetrant dissolved in the membrane is increased, thereby increasing the free volume, and (b) the hydrostatic pressure on the membrane is also increased, which causes a decrease in the free volume. If the overall effect is an increase in the free volume of the polymer, then P? will also increase, and vice versa.     

On the conjoint gradient correction to the Hartree—Fock kinetic and exchange energy density functionals

The kinetic and the exchange energy functionals are expressed in the form T[ρ] = C_TF∫ drρ^5/3(r)f_t(s) and K[ρ] = C_D∫ drρ^4/3(r)f_K(s), where C_TF = (3/10)(3π²)^2/3 and C_D = −(3/4)(3/π)^4/3 are the Thomas-Fermi and the Dirac coefficients, respectively, and s = |∇ρ(r)|/C_sρ^4/3(r), with C_s = 2(3π²)^1/3. These expressions are used to perform a comparison of f_T(s) and f_K(s) in terms of their generalized gradient expansion approximations. It is shown that f_κ(s) and is congruent to f_T(s) in the range characteristic of the interior regions of atoms and many solids and that the second-order gradient expansion of the kinetic energy provides a rather reasonable approximation to the generalized gradient expansion approximation of both the kinetic and the exchange energy functionals. © 1996 John Wiley & Sons, Inc.     

Extraction of certain actinide and lanthanide elements from different acidic media by polyurethane foams loaded with di-(2-ethylhexyl)phosphoric acid (HDEHP)

The extraction of cerium(III) from weakly acidic chloride solutions by HDEHP-nitrobenzene-loaded polyurethane foams could be analyzed quantitatively in terms of the equation: log(9.056 D_c)=log K_c+2.14 log (C_d?6C_c)+3 pH+log f_c where D_c is the distribution ratio of cerium(III) between the foam and aqueous phases, C_d and C_c are the total HDEHP and Ce(III) concentrations on the foam, respectively, log f_c=[Ce³⁺]_(sq)/[ΣCe(III)]_(aq), and K_c is the equilibrium constant of the equation: Ce _(aq) ³⁺ +2.14(HX)_2.8(o) ? ? CeX₆·H_3(o)+3H _(aq) ⁺ . Values of K_c under the different extraction conditions tested are given.     

Solid-state 13C nuclear magnetic resonance characterization of MDI-based polyurethanes

¹³C solid-state nuclear magnetic resonance (NMR) experiments on linear polyurethanes and poly(ether-urethane) block copolymers demonstrate that ¹³C spin-lattice relaxation experiments in the laboratory [T₁(C)] and rotating [T_1p(C)] frames provide the most information about domain morphology in these microphase-separated polymer systems. T₁(H) TCH, and T_1p(H) data are less useful in a 4,4′-methylene bis(p-phenyl isocyanate)-1,4-butanediol (MDI/BD) hard-segment material, the MDI bridging methylene and the MDI urethane carbonyl T₁(C and T_1p(C) times fall in characteristic ranges for crystalline, amorphous, interfacial, and dissolved species. BD methylene carbons have short T_1p(C) for crystalline and long T_1p(C) for amorphous hard-segment aggregates. The distinct T_1p(C) and T₁(C) fractins observed are attributed to the presence of several crystalline polymorphs. Both T₁(C) results and DSC endotherms indicate that the crystalline polymorphs present in the poly(ether-urethane) are less ordered than the types seen in the pure hard-segment material. © 1993 John Wiley & Sons, Inc.     

Characterization of Titania/Silica Gel by Means of Low-Pressure Nitrogen Adsorption

Adsorbents synthesized by grafting of titania onto mesoporous silica gel surfaces at different temperatures were studied by means of nitrogen adsorption–desorption and water desorption. The pore size distribution f(R_p) of titania/silica gel depends on the titania concentration (C_TiO2) and the temperature of titania synthesis. Nonuniformity of TiO₂ phase is maximal at a low C_TiO2 value (3.2 wt.% anatase deposited at 473 K), and two peaks of the fractal dimension distribution f(D) are observed at such a concentration of titania, but at larger C_TiO2 values, only one f(D) peak is seen. More ordered filling of pores and adsorption sites by nitrogen, reflecting in the shape of adsorption energy distributions f(E) at different pressures of adsorbate, is observed for adsorbent with titania (rutile+anatase) grafted on silica gel at a higher temperature (673 K).     

Fractal Dimensions of Coals and Cokes

Using adsorption data, we get formulas for the calculation of fractal dimensions: log[A_CO2(DP)/A_N2(BET)] = −5.3984(2 −D₁)/2 and log[A_CO2(BET)/A_N2(BET)] = −4.9569(2 −D₂)/2. The fractal dimensions (D) of 27 coals and 2 cokes have been obtained. TheDof coals decreased with the increase of f_aand reached a maximum at H/C equal to 0.66 (orC_dafabout 86%). The fractal dimension is relative to ash and volatiles of coal:D= 2.2237 + 0.6249V_daf+ 0.8863A_d. The relationship betweenDof coal coke and its conversions (X) obeys the following equation:D = aexp(−bX) +c.     

Diffusion coefficients of the monomer and oligomers in hydroxyethyl methacrylate

The diffusion coefficients are reported of rubbery ternary systems consisting of the polymer, its monomer analogue (i.e., the saturated equivalent of the monomer), and trace quantities of oligomers (dimer, trimer, tetramer and hexamer) for 2‐hydroxyethyl methacrylate (HEMA). These have been obtained with pulsed‐field‐gradient NMR spectroscopy with a polymer weight fraction (f_p) of 0 ≤ f_p ≤ 0.4. The oligomers are macromonomers synthesized with a cobalt catalytic chain‐transfer agent. The diffusion coefficients are about an order of magnitude smaller than those for monomers such as methyl methacrylate; this effect is ascribed to hydrogen bonding in HEMA. The diffusion coefficient D_i of an i‐meric oligomer has been fitted with moderate accuracy by an empirical universal scaling relation, D_i(f_p)/D₁(f_p) ≈ i, previously found to provide an adequate fit to corresponding data for styrene and for methyl and butyl methacrylates. The approximate empirical scaling relation seems to hold for a remarkably wide range of types of monomer/polymer systems. These results are of use in modeling rates and molecular weight distributions in free‐radical polymerization, particularly for termination (which is chain‐length‐dependent and is controlled by the diffusion coefficient of chains of the low degrees of polymerization studied here). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2491–2501, 2003     

Sorption and diffusion of organic vapors in amorphous Teflon AF2400

Vapor sorption in amorphous Teflon AF2400 of various organic solutes was studied in a wide range of activity at 25 °C by means of the gravimetric technique. The sorption isotherms of hexane, toluene, and chloroform were shown to be concave to the pressure axis and are consistent with the dual mode sorption model (DMS). The parameters of the DMS model k_D and b reveal a linear correlation with squared critical temperature of solutes T. The third model parameter, the Langmuir sorption capacity C′_H decreases when the size of solutes (critical volume) increases. Sorption isotherms of methanol and ethanol were shown to be convex to the pressure axis and are consistent with cluster formation in this strongly hydrophobic polymer. Concentration‐dependent diffusion coefficients D were determined using a linear implicit difference scheme in analysis of sorption kinetics. It was shown that D values increase exponentially with concentration for all the solutes, except alcohols for which exponential reduction of D(C) was observed. The partitioning of the thermodynamic and mobility contributions in D indicated that the reduction of D values of alcohols is consistent with clustering phenomena in AF2400. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 832–844, 2006     

The effect of plasticization on the transport of gases in and through glassy polymers

The effects of plasticization on the transport of gases and vapors in and through glassy polymers are examined from the viewpoint of the “dual-mode” sorption model with partial immobilization. The analysis assumes the existence of two penetrant populations with different mobilities in the Henry's law and Langmuir domains of the glassy polymers. These mobilities are characterized by their mutual diffusion coefficients D_D and D_H. The plasticization of the polymer by penetrant gases is reflected in the concentration dependence of D_D and D_H. Expressions for the effective (apparent) diffusion and permeability coefficients are derived assuming that D_D and D_H are exponential functions of the penetrant concentration in the polymers. The results of this study are compared with a similar analysis which assumed the existence of a single mobile penetrant population. The present analysis provides information on the effects of plasticization on the penetrant transport in the Henry's law and Langmuir domains separately. The effects of antiplasticization or clustering of penetrant molecules on the effective diffusion and permeability coefficients are also examined.     

Penicillamine and captopril: mechanistic exploration of defensive actions of thiol drugs against a metal bound-superoxo complex

In acid-media ([H⁺] = 0.01–0.06 M), each of the thiol compounds, D-penicillamine (PEN, L_PH₂) and captopril (CAP, L_CH₂) exist in several proton-dependent forms which can reduce the superoxo complex [(en)(dien)Co^III(O₂)Co^III(en)(dien)]⁵⁺ (1) to the corresponding peroxo [(en)(dien)Co^III(O₂)Co^III(en)(dien)]⁴⁺ (2) or the hydroperoxo complex [(en)(dien)Co^III(OOH)Co^III(en)(dien)]⁵⁺ (3). The observed first-order rate constants, k_o,P and k_o,C for PEN and CAP increase with the increase in [T_PEN] and [T_CAP] (which are the analytical concentrations of the respective thiols) but decrease with the increase in the media-acidity ([H⁺]) and the media ionic strength (I). The protolytic equilibria in aqueous solution allow several potentially reducing forms to coexist for both PEN (L_PH₃⁺, L_PH₂, L_PH^?, and L_P^2?) and CAP (L_CH₂, L_CH^?, L_C^2?) but the kinetic analyses reveal that the order of reactivity for the species are L_PH₃⁺ ~ L_PH₂ <<< L_PH^? and L_CH₂ < L_CH^? <<< L_C^2?, respectively. The predominance and higher reactivities of the anionic species, L_PH^? and L_C^2? are supported by the negative slopes of the plots of k_o,P or k_o,C versus I. Moreover, a large value of k_H/k_D for PEN suggests an inner-sphere electroprotic reaction pathway while the absence of such effect for CAP strongly supports an outer-sphere electron transfer reaction. These propositions are supported by the structural features of L_PH^? and L_C^2?.     

Diffusion Coefficients for Binary, Ternary, and Polydisperse Solutions from Peak-Width Analysis of Taylor Dispersion Profiles

Binary mutual diffusion coefficients D can be estimated from the width at half height W _1/2 of Taylor dispersion profiles using D=(ln 2)r ² t _R/(3W ² h) and values of the retention time t _R and dispersion tube radius r. The generalized expression D _h=−(ln h)r ² t _R/(3W ² _h ) is derived to evaluate diffusion coefficients from peak widths W _h measured at other fractional heights (e.g., (h = 0.1, 0.2,…,0.9). Tests show that averaging the D _h values from binary profiles gives mutual diffusion coefficients that are as accurate and precise as those obtained by more elaborate nonlinear least-squares analysis. Dispersion profiles for ternary solutions usually consist of two superimposed pseudo-binary profiles. Consequently, D _h values for ternary profiles generally vary with the fractional peak height h. Ternary profiles with constant D _h values can however be constructed by taking appropriate linear combinations of profiles generated using different initial concentration differences. The invariant D _h values and corresponding initial concentration differences give the eigenvalues and eigenvectors for the evaluation of the ternary diffusion coefficient matrix. Dispersion profiles for polymer samples of N i-mers consist of N superimposed pseudo-binary profiles. The edges of these profiles are enriched in the heavier polymers owing to the decrease in polymer diffusion coefficients with increasing polymer molecular weight. The resulting drop in D _h with decreasing fractional peak height provides a signature of the polymer molecular weight distribution. These features are illustrated by measuring the dispersion of mixed polyethylene glycols.     

Very-low-pressure pyrolysis of nitroso- and pentafluoronitrosobenzene C?NO bond dissociation energies

The high-pressure absolute rate constants for the decomposition of nitrosobenzene and pentafluoronitrosobenzene were determined using the very-low-pressure pyrolysis (VLPP) technique. Bond dissociation energies of DH⁰(C₆H₅? NO) = 51.5 ± 1 kcal/mole and DH⁰ (C₆F₅? NO) = 50.5 ± 1 kcal/mole could be deduced if the radical combination rate constant is set at log k_r(M^?1·sec^?1) = 10.0 ± 0.5 for both systems and the activation energy for combination is taken as 0 kcal/mole at 298°K. δH_f⁰(C₆H₅NO), δH_f⁰(C₆F₅NO), and δH_f⁰(C₆F₅) could be estimated from our kinetic data and group additivity. The values are 48.1 ± 1, –160 ± 2, and – 130.9 ± 2 kcal/mole, respectively. C–X bond dissociation energies of several perfluorinated phenyl compounds, DH⁰(C₆F₅–X), were obtained from the reported values of δH_f⁰(C₆F₅X) and our estimated δH_f⁰(C₆F₅) [X = H, CH₃, NO, Cl, F, CF₃, I, and OH].     

The evolution of steep fronts in non-fickian polymer-penetrant systems

We adapt a recently proposed model for non-Fickian diffusion of penetrants into polymers and use it to study a drug-delivery problem. The model modified Fick's diffusion equation by the addition of stress-induced flux. A stress evolution equation incorporating aspects of the Maxwell and Kelvin-Voigt viscoelastic stress models completes the model. The relaxation time in the polymer is taken as a function of the penetrant concentration. The system is studied under the assumption that the diffusivity is large. Singular perturbation techniques are used to show that the concentration and stress evolve diffusively for small time, but exhibit steep fronts in a narrow region within the domain for larger time. These predictions are verified numerically for specified parameter values. Finally, the equations are studied in the steady state and are found to predict the evolution of shocks.     

Neutral polymer slow mode and its rheological correlate

Quasi‐elastic light scattering spectroscopy intensity–intensity autocorrelation functions [S(k,t)] and static light scattering intensities of 1 MDa hydroxypropylcellulose in aqueous solutions were measured. With increasing polymer concentration, over a narrow concentration range, S(k,t) gained a slow relaxation. The transition concentration for the appearance of the slow mode (c^t) was also the transition concentration for the solution‐like/melt‐like rheological transition (c⁺) at which the solution shear viscosity [η_p(c)] passed over from a stretched exponential to a power‐law concentration dependence. To a good approximation, we found c^t[η] ≈ c⁺[η] ≈ 4, [η] being the intrinsic viscosity. The appearance of the slow mode did not change the light scattering intensity (I): from a concentration lower than c^t to a concentration greater than c^t, I/c fell uniformly with increasing concentration. The slow mode thus did not arise from the formation of compact aggregates of polymer chains. If the polymer slow mode arose from long‐lived structures that were not concentration fluctuations, the structures involved much of the dissolved polymer. At 25 °C, the mean relaxation rate of the slow mode approximately matched the relaxation rate for the diffusion of 0.2‐μm‐diameter optical probes observed with the same scattering vector. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 323–333, 2005