Self- and mutual-diffusion coefficients in the dodecane/polystyrene system

The self-diffusion coefficient of dodecane in cross-linked polystyrene was measured using pulsed gradient spin echo nuclear magnetic resonance (PGSE–NMR) spectroscopy. The concentration and temperature dependence of the diffusion coefficient was analyzed by the Fujita and Vrentas–Duda models. Parameters describing the Fujita model were determined from fitting of diffusion data to the PVT behavior of the system. Parameters describing the Vrentas–Duda model were determined from the analysis of the viscosity of dodecane, the viscoelastic relaxation properties, and the glass transition temperature of polystyrene as well as from the diffusion coefficient of the system, measured from independent experiments. Both the Fujita and Vrentas–Duda models described well the concentration and temperature dependence of the diffusion coefficient. Mutual diffusion coefficients were determined from these results. © 1994 John Wiley & Sons, Inc.     

Transport properties of dichloromethane in glassy polymers. I. Atactic polystyrene films

Sorption and diffusion of dichloromethane vapor were measured in atactic polystyrene films, obtained with different cooling conditions and after controlled aging times at different temperatures. The diffusional behavior is characterized by three zones, depending on temperature and penetrant activity. In Zone I, at low activity, the diffusion coefficient is independent of vapor concentration; Zone II is characterized by concentration-dependent diffusion, whereas in Zone III structural transformations are possible. The study of diffusion at three temperatures allowed building of a temperature-penetrant concentration diagram, which is very useful to visualize the different zones of behavior. The aging at room temperature has no effect on the curve of sorption as a function of vapor activity, whereas it determines two effects on the diffusion: a decrease of the zero concentration diffusion coefficient and a more and more anomalous behavior with the aging time. The aging at 70°C produces the same effects on the diffusion behavior as the aging at room temperature; in addition, a decrease sorption is observed at low penetrant activity. The possible presence of ordered domains, impermeable to the vapor, in the samples stored at 70°C, was suggested on the basis of sorption results.     

Solvent and temperature effects on diffusion in polymer–solvent systems

The temperature dependence of the mutual diffusion coefficient at zero solvent concentration for a number of polystyrene–solvent systems is satisfactorily represented by an equation derived from a new version of the free-volume theory of molecular transport. The free-volume parameter which governs the temperature dependence of the diffusion rate is linearly related to the size of the solvent as estimated by its molar volume at OK. Data taken on various polystyrene–solvent systems are used to deduce information on the mechanism of solvent transfer in polymeric systems.     

A tubular film extrusion of poly(vinylidene fluoride): structure/process/property behavior as a function of molecular weight

Five different poly(vinylidene fluoride) (PVDF) resins spanning the molecular weights from 85,000-250,000 g/mol with nearly comparable polydispersities of ca. 2.0 were investigated with respect to their strain induced crystalline morphologies as produced by a tubular uniaxial film extrusion process. By holding the process time window constant through the use of fixed melt temperature, line speed, quench height and film thickness, it was noted that as molecular weight increased, the uniaxial films produced systematically change from nearly a spherulitic structure to that of an extremely high concentration of fibril nuclei with minimal growth of folded chain lamella developing perpendicular to the fibrils. The systematic variation in the morphology was directly coupled through consideration of the melt process time window in conjunction with the characteristic relaxation time of a given resin at a given temperature. The latter was determined through use of a Carreau-Yasuda analysis of the melt rheological behavior of each resin and this relaxation time, when correlated to the process time, produced a relative Deborah number. It was distinctly shown that when the Deborah number was considerably less than unity, little crystal orientation was observed in the morphological texture whereas in the range of unity, a distinct rise in crystalline orientation occurred leading to fibril nucleation with lamella side growth in the form of the well known row structure morphology. Exceeding a Deborah number of unity led to nearly full crystalline orientation saturation and to a very high concentration of fibril nucleai with relatively few orthogonal lamella observable. The morphological textures were investigated using AFM, WAXS, SALS, SAXS and birefringence. Use of thermal analysis to determine some of the polymorphic character of the PVDF crystal form was also undertaken.     

The Dynamics of Solvent Evaporation from Hydroxypropylcellulose/Methanol Solutions with Lyotropic Liquid Crystalline Capability

Summary Thin films of hydroxypropylcellulose (HPC)/methanol (MeOH) solutions were juxtaposed against air in a diffusion couple geometry at room temperature and the solvent was allowed to diffuse away and evaporate from the solution in a controlled manner. The diffusion couple geometry produced a uniform film for optical assessment of liquid crystalline potential between crossed polarizers. After an induction period, a stable microstructure developed in which the interior of the sample remained isotropic followed by a cholesteric liquid crystalline band, with characteristic disclination defects and texture, followed by a crystalline band nearest to the external surface. The width of the total characteristic birefringent band was measured over time and provided information concerning the dynamics and trajectory of solvent transport and evaporation from the cover slip edge. The apparent solvent diffusion coefficient for the HPC/MeOH system was measured at room temperature as a function of initial concentration. Diffusion couple optical microscopy data were compared to both solution rheological characteristics as well as model diffusion data from finite difference calculations in order to validate the observed concentration dependence of diffusion. This revised version was published online at the end of November 2004. Unfortunately, the received date was incorrect due to a technical problem.     

Relaxation characteristics of poly(vinylidene fluoride) and ethylene-chlorotrifluoroethylene in the transient uptake of aromatic solvents

Poly(vinylidene fluoride) (PVDF) and ethylene-chlorotrifluoroethylene (ECTFE) exhibited non-Fickian diffusion behaviors in the transient uptake of aromatic solvents. The diffusional exponents at the final stage of uptake exhibited asymptotic values ranging from 0.9–1.0 for the sigmoidal sorption of PVDF and 1.2–2.0 for the drastic accelerating sorption of ECTFE. The asymptotic diffusional exponent decreased with rising temperature. PVDF film exhibited a linear increase in both machine and transverse directions with fractional uptake, whereas ECTFE film increased linearly in the transverse direction and exponentially in the machine direction. A rate-type viscoelastic [Camera-Roda and Sarti, 1990] model was applied to reproduce the anomalous sorption of fluoropolymer-solvent systems. The fitted Deborah numbers ranged from 0.2–0.3 for PVDF, and 2–5 for ECTFE. The diffusivity ratio, D _eq /D _o ,of PVDF-solvent system was fitted as tenth order of magnitude lower than that of ECTFE-solvent system. The fraction of initial surface concentration, S_o, was fitted in the range of 0.6–0.8 for both ECTFE and PVDF. It is plausible to assume that diffusion coupled with comparable structural relaxation has the asymptotic diffusional exponents that are strongly dependent on accelerating curvature, and total sorption is contributed by relaxation-induced viscoelastic volume change along with concentration-driven Fickian diffusion.     

Transport properties of dichloromethane in glassy polymers. II. Amorphous syndiotactic polystyrene films

Sorption and diffusion of dichloromethane vapor were measured in amorphous syndiotactic polystyrene films, obtained with different cooling conditions and after controlled aging times at different temperatures. The diffusional behavior, at the temperature of 25°C, was characterized by three stages, depending on penetrant activity. In the first stage, at low activity, the diffusion coefficient was independent of vapor concentration; the second stage was characterized by concentration-dependent diffusion, whereas in the third stage, at high activity, the strong interaction solvent–polymer increased the mobility, allowing the polymer crystallization. The different cooling conditions neither have an effect on the diffusional behavior nor on the sorption curve. The aging, both at room temperature and at 70°C, did not change the diffusion parameters, but led to the appearance of more and more anomalous sorption behavior. The sorption curve, as a function of vapor activity, did not show any difference for the fresh and the aged-at-room temperature samples, whereas the samples aged at 70°C presented a lower sorption at low activity. The presence of ordered domains, impermeable to the penetrant at low activity, was suggested on the basis of sorption results. The solvent-induced crystallization was investigated for all the samples. Crystallization was induced at an activity of 0.45 for the fresh and the aged-at-room temperature samples; at variance, the samples aged at 70°C crystallize at a slightly higher activity, reaching, nevertheless, a higher level of crystallinity. © 1993 John Wiley & Sons, Inc.     

Numerical simulation of anomalous penetrant diffusion in polymers

This work introduces a new numerical algorithm that can be used to analyze complex problems of penetrant transport. Penetrant transport in polymers often deviates from the predictions of Fick's law because of the coupling between penetrant diffusion and the polymer mechanical behavior. This phenomenon is particularly important in glassy polymers. This leads to a model consisting of two coupled differential equations for penetrant diffusion and polymer stress relaxation, respectively. If the polymer relaxation is the rate-limiting step, both the concentration and stress profiles are very steep. A new algorithm based on a finite difference method is proposed to solve the model equations. It features the development of a tridiagonal iterative method to solve the nonlinear finite difference equations obtained from the finite difference approximation of the differential equations. This method was found to be efficient and accurate. Numerical simulation of penetrant diffusion in glassy polymers was performed, showing that the integral sorption Deborah number is a major parameter affecting the transition from Fickian to anomalous diffusion behavior. © 1993 John Wiley & Sons, Inc.     

A proton magnetic relaxation study of the mechanism and solvent dependence of the molecular motion of polystyrene in dilute solution

¹H spin-lattice relaxation in polystyrene has been studied as a function of molecular weight, solvent and temperature. The relaxation times are reported for the aliphatic CH and CH₂ and the aromatic ortho and (meta + para) signals. In addition the aliphatic relaxation times under the influence of strong irradiation at the aromatic peaks have been measured. The results have been interpreted in terms of three-bond conformational jumps combined with a rotational diffusional process and show that the conformational jump correlation time is about an order of magnitude shorter than the diffusional correlation time. The solvent dependence of the relaxation times has been correlated by means of a reduced temperature scale and activation energies are reported.     

异戊二烯在聚苯乙烯高分子膜中的扩散系数测定

为了探讨在反应挤出过程中异戊二烯在聚苯乙烯中的扩散传递机理,采用石英弹簧法测定了298.15K、308.15K和318.15K下异戊二烯在聚苯乙烯膜中的吸收动力学曲线。探讨了温度、压力、分子量对扩散吸收的影响,并对实验结果进行了关联。结果表明异戊二烯在聚苯乙烯膜中的扩散吸收呈S型吸收,由吸收曲线获得了平均扩散系数和平衡溶解度。     

Diffusion,swelling, and consolidation in glassy polystyrene microspheres

The effects of prior thermal and swelling history on the kinetics and apparent equilibria of subsequent n-hexane sorption in monodisperse, submicrometer diameter, glassy polystyrene microspheres were studied. Repetitive sorption and desorption cycling was compared with continuous sorption and desorption experiments. The apparent equilibrium uptake of n-hexane in preswollen samples decreased monotonically with the cumulative time under vacuum independent of the cycle frequency or the number of sorption-desorption cycles. This consolidation was modeled as a first order relaxation process with a single characteristic relaxation time. “As-received” samples swelled in the presence of the penetrant and the apparent equilibrium n-hexane content increased monotonically with the time under n-hexane. The Berens-Hopfenberg diffusion-relaxation model accurately describes the cyclic and continuous swelling behavior of the “as-received” sample. At each temperature studied, a true equilibrium n-hexane content was approached asymptotically for the preswollen and “as-received” samples after sufficient time under vacuum or n-hexane, respectively. Whereas the apparent sorption equilibria were controlled by the cumulative time under vacuum or n-hexane for the preswollen and “as-received” samples, respectively, the absorption kinetics are subject to a systematic variation which depends only on the immediate prior vacuum history of the sample. The temperature dependence of the kinetic and equilibrium parameters describing diffusion, consolidation, and swelling suggests a unified molecular interpretation of these diverse glassy-state transport and relaxation processes.     

Diffusional behavior of multi-arm star polymers by H pulsed field gradient spin-echo NMR method

The diffusional behavior of multi-arm star-shaped p(tBMA) was investigated in a concentration range from dilute to semidilute region with ¹H pulsed field gradient spin-echo NMR (PFGSE-NMR). An 142-arm star-shaped p(tBMA) showed two diffusional mode, which reflected the coexistence of liquid ordering phase and liquid phase near the ordering transition. On the other hand, for star-shaped p(tBMA) with 55 arms showed a single diffusional relaxation in all concentration ranges during observation time. In the semidilute region, the relationship between the diffusion coefficient against the polymer concentration was affected strongly not only the arm number but also liquid ordering structure.     

Self-diffusion in concentrated polystyrene solutions measured by fluorescence recovery after photobleaching

A polystyrene polymer of narrow molecular weight distribution was carboxylated, then reduced, and finally esterified with NBD-aminohexanoic acid [6-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)-aminohexanoic acid]. The self-diffusion of the NBD-labelled polystyrene polymer in concentrated solutions of the unlabelled polystyrene polymer was measured by the method of fluorescence recovery after photobleaching over a concentration range from 0.017 g/ml to 0.41 g/ml at room temperature. In the semi-dilute region, the concentration dependence of diffusion coefficient was found to be in agreement with the predictions of scaling concepts.     

The effect of penetrant activity and temperature on the anomalous diffusion of hydrocarbons and solvent crazing in polystyrene part I: Biaxially oriented polystyrene

The effects of temperature and penetrant activity on the sorption kinetics and equilibria of a series of alkanes in glassy, biaxially oriented polystyrene were studied. Normal isomers of pentane, hexane, and heptane cause crazing of polystyrene film samples at high penetrant activities (> 0.85). Crazing kinetics are identical to the kinetics of Case II transport. Transport of these normal hydrocarbons in glassy polystyrene in the temperature range 25 to 50°C is markedly non-Fickian; limiting Case II transport is observed at activities in exces of 0.6. Sorption appears to be controlled by highly activated relaxation processes including primary bond breakage at these high penetrant activities. Fickian diffusion behavior is approached, however, as penetrant activity is reduced. Sorption of the branched isomers of these compounds does not result in polymer microfailure. The sorption kinetics of the branched isomers, although time dependent, appear to be controlled primarily by thermally activated diffusion rather than large scale polymer relaxations which control Case II transport.     

NATURAL CONVECTION FLOW OF SECOND-GRADE FLUID ALONG A VERTICAL HEATED SURFACE WITH POWER-LAW TEMPERATURE

In this study we investigated the effects of free convection flow of a viscoelastic second-grade fluid along a vertical flat surface with power-law temperature distribution. The boundary layer equations for the momentum and the energy transport have been reduced to local similarity equations using appropriate transformations. Solutions of the reduced equations are obtained employing the local non-similarity method as well as the implicit finite difference method against ξ (the local Deborah number) in the range [0, 10] for fluids having Prandtl numbers of 10, 50, and 100. The regular perturbation solutions are also been obtained for smaller values of ξ together with the Padé approximation. Results thus obtained are discussed in terms of the local skin friction and local rate of heat transfer for different values of the physical parameters, like n and Pr. Effect of the Deborah number, De, on the velocity and temperature profiles has also been shown graphically. It is observed that both the local skin friction and heat transfer coefficients decrease with increase in the value of De for given values of n and Pr.     

Diffusion of p-aminoazobenzene in SBS block copolymer

The temperature dependence of p-aminoazobenzene diffusion in a styrene–butadiene–styrene (SBS) triblock copolymer film, prepared from a toluene or ethyl acetate solution, was investigated in the temperature region from 40° to 110°C by using a sublimative desorption method. Parallel studies on the mechanical relaxations of this copolymer were carried out in the same temperature range to be compared with the diffusion data. The penetrant-diffusion characteristics were interpreted in terms of Fujita's free-volume theory with due consideration of the different SBS domain morphology. The value of B_d, defined as the diffusional volume ratio of a penetrant molecule to a segment, was then estimated as 0.45–0.55 above the T_g of the polystyrene phase or 0.7 below that temperature. Interestingly, sigmoidal desorption appeared in the range under the T_g of the polystyrene phase for film cast from ethyl acetate; the anomalous behavior was considered to reflect the slow relaxation process of the copolymer chain ascribable to the predominant exposure of the polystyrene phase on the film surface.     

Diffusion in polymers

Concentration dependent diffusion coefficients explain Case II type diffusion. Solutions to the diffusion equation yield straight lines for weight gain vs time when the exponential variation of the diffusion coefficient is included. Boundary layer resistance together with concentration dependent diffusion coefficients explain Super Case II type diffusion. The increase in the rate of weight gain after a prolonged period is predictable. The surface concentration rises slowly to its equilibrium value in this case. Boundary layer resistance appears to be quite common, particularly where the penetrant has low affinity (not a true solvent) for the polymer, such as water in most polymers or hexane in polystyrene. Boundary layer resistance is quite significant for coatings (where film thicknesses are usually measured in microns), accounting for the majority of the resistance in some cases. A method to separate diffusional resistance from the surface resistance is suggested, but studies at different film thicknesses appear mandatory.     

疲劳/蠕变复合作用下聚苯乙烯的时温等效关系

研究了疲劳／蠕变复合作用下聚苯乙烯的时温效关系。试验条件加载最大应力，最大应力保持时间和温度而变化，但是都得到一致的试验结果：即随最大应力保持时间的延长或试验温度的升高，聚苯乙烯的断裂寿命下降；最大应力保持时间t和断裂寿命Nf的关系曲线与试验温度T和断裂寿命Nf的关系曲线十分相似；疲劳／蠕变复合作用下的聚苯乙烯，时温等效关系仍然适用。     

13C nuclear spin-lattice relaxation study of anisotropic solvent rotational diffusion in the polystyrene/trans-decalin system

The rotational diffusion tensor for the solvent trans-decalin has been determined as a function of temperature (21°–55°C) and polystyrene concentration (0–13% w/w) from ¹³C spin-lattice relaxation data. The sensitivity of rotational diffusion behaviour of the trans-decalin molecule to changes in solution conditions was found to be essentially proportional to the axial ellipticities of the respective principal rotational axes. The degree of anisotropic motion was found to increase strongly upon increasing the polystyrene concentration and decreasing the temperature. Apparent activation energies for rotation about each of the principal axes of inertia have been calculated for the series of polystyrene concentrations.