Estimation of diffusion coefficients for trace amounts of solvents in glassy and molten polymers

Two methods based on the free-volume theory of transport are developed for the estimation of diffusion coefficients for trace amounts of solvents in amorphous polymers. The first method uses diffusivity data for a polymer–solvent system above the glass transition temperature to estimate the temperature dependence of the mutual diffusion coefficient below this temperature. In the second method, mutual diffusion coefficients are estimated for a particular polymer–solvent system both above and below the glass transition temperature using no diffusivity data for the system. The predictions of the proposed theory are compared with diffusivity data for the n-pentane–polystyrene and ethylbenzene–polystyrene systems.     

Prediction of solvent‐diffusion coefficient in polymer by a modified free‐volume theory

Several versions of free‐volume theory have been proposed to correlate or predict the solvent diffusion coefficient of a polymer/solvent system. The quantity of free volume is usually determined by the Williams–Landel–Ferry (WLF) equation from viscosity data of the pure component in these theories. Free volume has been extensively discussed in different equation‐of‐state models for a polymer. Among these models, the Simha–Somcynsky (SS) hole model is the best one to describe the crystalline polymer, because it describes it very approximately close to the real structure of a crystalline polymer. In this article, we calculated the fractions of the hole free volume for several different polymers at the glass transition temperature and found that they are very close to a constant 0.025 by the SS equation of state. It is quite consistent with the value that is determined from the WLF equation. Therefore, the free volume of a crystalline polymer below the glass transition temperature (T_g) is available from the SS equation. When above the T_g, it is assumed that the volume added in thermal expansion is the only contribution of the hole free volume. Thus, a new predictive free‐volume theory was proposed. The free volume of a polymer in the new predictive equation can be estimated by the SS equation of state and the thermal expansion coefficient of a polymer instead of by the viscosity of a polymer. The new predictive theory is applied to calculate the solvent self‐diffusion coefficient and the solvent mutual‐diffusion coefficient at different temperatures and over most of the concentration range. The results show that the predicted values are in good agreement with the experimental data in most cases. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 428–436, 2000     

The diffusion of nonionic penetrants in polyamide

The diffusion behavior of nonionic penetrants in aqueous solution into nylon 6 was examined in the temperature range 5°–95°C. The Arrhenius plot of the diffusion coefficients is linear and its slope changes at 30–40°C higher than the glass transition temperature in water, as determined by dilatometry and viscoelastic measurements. The results are discussed in relation to the molecular size of the penetrant and the segmental motion of polymer chains.     

Diffusion controlled kinetics of crosslinking

Reactions of polymer formation and crosslinking become diffusion controlled when, during the reaction, the increasing glass transition temperature T_g comes close to the reaction temperature, the reaction still goes on below T_g but the reaction rate decreases steeply. A theory is presented relating the apparent rate constant to the difference between the reaction temperature and T_g based on the free volume or the Adam-Gibbs theory of glass transition. The theory is correlated with experiments on curing of diglycidyl ether of bisphenol A with 1,3-propanediamine. The implications for formation of protective films chemically crosslinked are discussed. The presence of a solvent and its evaporation affects the reaction rate through a change in concentrations of reactants as well as in T_g.     

Gas sorption and transport in poly(phenylene oxide) and comparisons with other glassy polymers

The sorption and transport of several gases in poly(phenylene oxide) were measured at 35°C, and the results have been analyzed in terms of the dual sorption/mobility models which have been successfully employed for this purpose for other glassy polymers. Both the extent of sorption and rate of permeation of gases are quite large for poly(phenylene oxide) compared to other glassy polymers with rigid chain backbones. It is shown that the high extent of sorption is owing to the high glass transition temperature of this polymer, but this is not a significant factor in its high permeability to gases. The latter stems from large diffusion coefficients. It is shown that the capacity of the Langmuir mode of sorption inherent to glassy polymers is related to the value of the glass transition temperature in a general way for a wide variety of polymers. Observations about the diffusion coefficients for numerous gas–polymer pairs are discussed.     

ESR study on the effect of temperature on the diffusion of oxygen into PMMA and PVAC polymers

The free radicals produced by γ irradiation in the polymer network are formed with ionizing radiation. The decay rates of radicals in the temperature range were used to estimate the diffusion coefficient of oxygen into polymeric spheres by an electron spin resonance (ESR) technique. The ESR results showed that the activation energy of the diffusion of oxygen into poly(methyl methacrylate) (PMMA) in the temperature range 10–40°C is 29.6 kJ/mol. There are two activation energies of the diffusion of oxygen into poly(vinyl acetate) (PVAc) in the temperature range 25–50°C. The activation energies below and above 35°C, which is the glass transition temperature of PVAc, were found to be 16.8 and 82.5 kJ/mol, respectively. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 1203–1207, 1999     

A lattice‐fluid,group‐contribution treatment of the glass transition of homopolymers,copolymers, and polymer solutions

The glass transition temperature of polymers and polymer solutions was approached through a combination of the group‐contribution, lattice‐fluid equation of state and the Gibbs–DiMarzio criterion. The model assumes zero entropy at the glass transition temperature and treats molecules as semiflexible chains. This stiffness is associated with a flex energy obtained from the glass transition temperature at atmospheric pressure. Whereas the application of the model is straightforward for homopolymers and polymer solutions, a new formalism using the dyad concept was developed for copolymers. It takes into account the copolymer composition as well as the sequencing of the monomers. The results obtained are consistent with experimental data. For polymer solutions, the model predictions are semiquantitative depending on the system. The interaction parameter required for binary systems was found to have little effect on the glass transition temperature predictions. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 697–705, 2003     

Plasticizer diffusion as the rate-determining step in dry blending of poly(vinyl chloride)

Differential thermal analysis has been used to examine the process of dry blending of plasticizer and PVC. The rate of transformation of the glass transition from that of the polymer initially in the cold mix to the glass transition of the blend (blend T_g) has been examined at various temperatures from room temperature to above the polymer T_g. The dependence on temperature of this rate of transformation of the observed T_g is similar to the temperature dependence of the diffusion of plasticizer into PVC. It is concluded that diffusion of plasticizer into polymer particles is the rate-determining step in the dry blending of PVC. It also appears that a single mechanism of diffusion is involved both below and above the glass transition of the polymer.     

Study by gas-liquid chromatography of the interactions between linear or branched polystyrenes and solvents in the temperature range 60°–200°C

Thermodynamic interactions between linear or branched polystyrene and various solvents have been studied by gas chromatography below and above the glass transition temperature. In the lower temperature range (<80°C) interactions between non-solvent probes (alkanes) and the polymer are restricted to adsorption phenomena; analysis of these effects leads to an estimation of the specific surface area of the inert support which is actually accessible to the polymer. In the higher temperature range (140°–200°C) the activity coefficients at infinite dilution and the Flory χ interaction parameters have been calculated taking into account both diffusion and adsorption of the probe into the polymer.     

Effect of glass transition on the concentration dependence of self‐diffusion coefficients

The free‐volume theory of diffusion is used to predict the effect of the glass transition on the concentration dependence of the solvent self‐diffusion coefficient at constant temperature. The theoretical prediction is in agreement with experimental data. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 1682–1684, 2003     

粉末涂料的玻璃化温度

重点讨论了粉末涂料玻璃化温度、玻璃化转变理论,并对玻璃化温度与粉末涂料稳定性、熔融黏度、热应力、分子量、化学结构和聚合物的关系做了全面的阐述。     

Study of motional processes in polymer blends composed of isotactic polypropylene and ethylene–propylene–diene monomer rubber by broad‐line 1H‐NMR

The broad‐line ¹H‐NMR study of the polymer blend composed of isotactic polypropylene and ethylene–propylene–diene monomer rubber was carried out. The NMR measurements were performed on the samples of the polymer blend and on the components of the blend in the temperature range covering the glass‐transition regions of all studied polymers. Conclusions were drawn from the temperature dependencies of the second moment M₂ and of the data obtained by the decomposition of the spectra into the components related to the motionally distinct regions of the partially crystalline polymer. The mass fractions of the amorphous, intermediate, and crystalline domains and the widths of the spectra related to the particular phases were computed from the spectra. A double glass transition was revealed for the polymer blend. Different mechanisms of the motional processes related to the glass transition were deduced from the data. The gradual increase of the number of the chains and the enhancement of the chain mobility within noncrystalline regions of the polymer blend are responsible for the motion related to the lower glass transition and only transformation of the hindered motion into free motion was found in the temperature region of the upper glass transition. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 91: 247–252, 2004     

Predicting ability of free-volume theory for solvent self-diffusion coefficients in rubbers

The effect of solvent size on the diffusion process is studied for various solvents with natural rubber and polybutadiene in terms of the free-volume theory. The importance of energy effects on the diffusion of penetrants in rubbers is examined. The critical molar volume of the polymer jumping unit is correlated with its glass transition temperature over the range 172 K to 305 K. The correlation shows a linear relationship between these two properties and can be used to predict one of the most sensitive free-volume parameters. Using this parameter in conjunction with the Vrentas-Duda free-volume theory, solvent self-diffusion coefficients in rubbers are then predicted over wide ranges of concentration and temperature. For all the systems, the predictions are comparable with experimental data. © 1996 John Wiley & Sons, Inc.     

聚合物-溶剂体系中能量对溶剂扩散的影响

The Vrentas-Duda free-volume theory has been extensively used to correlate or predict the solvent diffusion coefficient of a polymer/solvent system.The energy term in the free volume diffusion equation is difficult to estimate,so the energy term was usually neglected in previous predictive versions of the free volume diffusion coefficient equation.Recent studies show that the energy effect is very important even above the glass transition temperature of the system. In this paper, a new evaluation method of the energy term is proposed,that is the diffusion energy at different solvent concentrations is assumed to be a linear function of the solvent diffusion energy in pure solvents and that in polymers under the condition that the solvent in infinite dilution.By taking consideration of the influence of energy on the solvent diffustion,the prediction of solvent diffusion coefficient was preformed for three polymer/solvent systems over a wide range of concentrations and temperatures.The results show an improvement on the predictive capability of the free volume diffusion theory.     

On the chain cross-sectional area and motion of macromolecular chains

This paper attempts to relate the chain cross-sectional area to the glass transition temperature of a polymer and to discuss the effect of the chain cross-sectional area in view of the motion of molecular chains. It has been found that the definite relationship between glass transition temperature and cross-sectionalarea can be obtained only when taking account of intermolecular interaction of polymer chains. It is considered that the chain cross-sectional area will characterize the chain flexibility of a polymer since the glass transition temperature is related both to intermolecular interaction and chain flexibility of a polymer. The concept of the structural parameter cross-sectional area per chain, first introduced by Vincent¹ and used by Boyer and Miller,^2–5 is useful in empirically correlating properties and structures of polymers. The glass transition temperature is a basic parameter of bulk polymers and is characteristic of their intermolecular interactions and chain flexibility. This paper attempts to relate chain cross-sectional areas to glass transition temperatures of polymers and to discuss the effect of the chain cross-sectional area in view of the motion of molecular chains.     

Application of the Vrentas–Duda free-volume theory of diffusion below the glass-transition temperature: Application to hypromellose acetate succinate–solvent systems

The Vrentas–Duda free-volume theory for diffusion characterizes the diffusivity of a solvent in a polymer in terms of the concentration and size of the solvent, the temperature, and the glass transition temperature (T_g) of the individual components. The effective T_g of the polymer, however, is a function of the concentration of the solvent. This article introduces a modification that corrects for this change in the glass-transition temperature, thus providing more accurate diffusivities. The model has been verified by comparison with experimental diffusivities of water, acetone, methanol, and tetrahydrofuran in hypromellose acetate succinate (HPMCAS). HPMCAS is widely used in the production of pharmaceutical formulations. One common application is the formation of amorphous solid dispersions with poorly soluble active pharmaceutical ingredients (APIs) for dissolution and solubility enhancement. Frequently, the APIs and HPMCAS are put into solution and spray dried at an outlet temperature below the normal glass-transition temperature. The modified free-volume theory is able to directly predict or correlate with only one adjustable parameter the diffusivities as a function of the concentration and temperature. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47351.     

Influence of Internal Stresses on the Glass Transition Temperature of Filled Polymers

Abstract

It is assumed that, in a system of filler in polymer, an internal stress distribution is associated with a shift in the glass transition temperature of the polymer. Experimental results supporting this theory are presented.     

Study on the gas permeabilities in styrene-butadiene rubber by molecular dynamics simulation

In this research, molecular dynamics (MD)simulations were used to study the transport properties of small gas molecules in the butadiene-styrene copolymer(SBR). The condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field was applied. The diffusion coefficients were obtained from MD (NVT ensemble) and the relationship between gas permeability; the chemical structure and free volume of butadiene-styrene copolymer were investigated. The results indicated that the diffusion coefficient of oxygen declined with increasing styrene content. The fraction of free volume (FFV) in butadiene-styrene copolymer was calculated. It was concluded that diffusion coefficient increased as the FFV increases, which is in accordance with the analysis of the small molecular hop through the free volume in polymer matrix. Subsequently, the glass transition temperatures of these copolymers were calculated by MD. The result showed that the glass transition temperature increased with increasing styrene content in polymer.     

微孔塑料成型过程中影响聚合物／气体均相体系形成的工艺因素

综述了微孔塑料成型过程中聚合物/气体均相体系形成的影响因素。表征均相体系的重要参数是气体在聚合物中的溶解度，因此通过SEM、玻璃化转变温度法、粘度法等间接方法来衡量溶解度，可以间接表征均相体系。对影响均相体系形成的压力、温度、时间和剪切作用等工艺条件进行了分析。适当增加压力、升高温度有利于均相体系的形成.剪切作用可提高气体的扩散性和溶解性，同时还可大大缩短均相体系形成所需要的时间。