Interdiffusion of solvent into glassy polymer films: a molecular dynamics study

Large scale molecular dynamics and grand canonical Monte Carlo simulation techniques are used to study the behavior of the interdiffusion of a solvent into an entangled polymer matrix as the state of the polymer changes from a melt to a glass. The weight gain by the polymer increases with time t as t(1/2) in agreement with Fickian diffusion for all cases studied, although the diffusivity is found to be strongly concentration dependent especially as one approaches the glass transition temperature of the polymer. The diffusivity as a function of solvent concentration determined using the one-dimensional Fick's model of the diffusion equation is compared to the diffusivity calculated using the Darken equation from simulations of equilibrated solvent-polymer solutions. The diffusivity calculated using these two different approaches are in good agreement. The behavior of the diffusivity strongly depends on the state of the polymer and is related to the shape of the solvent concentration profile.     

Process of drying a polymeric paint by diffusion-evaporation and shrinkage. Determination of the concentration-dependent diffusivity

The process of drying a paint made of a dispersion of a polymer in a solvent is experimentally and theoretically studied at various constant temperatures. The diffusion of the solvent through the paint and evaporation from the surface is considered, as well as the subsequent shrinkage. From measurements made at the beginning and at the end of the drying operation on the kinetics of drying, the diffusivity is found to largely depend on the solvent concentration. An exponential relationship of the diffusivity versus the concentration is thus found and successfully tested for the whole process of drying, the diffusivity increasing with the solvent concentration.     

Molecular dynamics simulation of solvent-polymer interdiffusion: Fickian diffusion

The interdiffusion of a solvent into a polymer melt has been studied using large scale molecular dynamics and Monte Carlo simulation techniques. The solvent concentration profile and weight gain by the polymer have been measured as a function of time. The weight gain is found to scale as t(1/2), which is expected for Fickian diffusion. The concentration profiles are fit very well assuming Fick's second law with a constant diffusivity. The diffusivity found from fitting Fick's second law is found to be independent of time and equal to the self-diffusion constant in the dilute solvent limit. We separately calculated the diffusivity as a function of concentration using the Darken equation and found that the diffusivity is essentially constant for the concentration range relevant for interdiffusion.     

Dissolution of rubbery and glassy polymers

A mathematical model is formulated for solvent dissolution of rubbery and glassy polymers. An exact solution to the problem is derived for the constant diffusivity case, and a weighted residual solution is developed for the case of a concentration-dependent diffusion coefficient. The solution is used to calculate concentration profiles, dissolution curves, dissolution half-times, and pseudointerface positions at various times. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2607–2614, 1998     

Prediction and estimation of solvent diffusivities in polyacrylate and polymethacrylates

The relationship between polymer side‐chain length and the hole free volume that is effective for solvent diffusion was investigated for polyacrylates and polymethacrylates on the basis of free‐volume theory. Measurements of a polymer's viscoelasticity and solvent diffusivity provided experimental evidence for polymer segment mobility, and the results indicated that hole free volume in a linear polymer increases with hydrocarbon side‐chain length. Because the molecular mechanisms of polymer viscoelasticity and diffusivity are identical, the free‐volume parameters obtained for polyacrylates and polymethacrylates by measuring the polymer viscoelastic‐temperature dependence can reliably be used in predicting the solvent diffusion coefficient. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1393–1400, 2003     

A molecular thermodynamic model for the swelling of thermo-sensitive hydrogels

A new molecular thermodynamic model for describing the swelling behavior of thermo-sensitive hydrogels was developed. The model consists of two terms. One is the contribution of the mixing of hydrogel network and water, which is dependent on the local polymer concentration and the interaction between polymer segment and solvent. A closed packed lattice model for polymer solution developed by Yang et al. was adopted for this term. The other is the elastic contribution derived from the network elasticity, which is dependent on the cross-linking degree of gel network. The elastic Gibbs energy model based on the Gaussian chain model developed by Flory was adopted. The model equation has two parameters. One is an energy parameter ? reflecting the interaction between water and gel network, the other is a size parameter V^* that represents the cross-linking degree of the hydrogel. When the energy parameter ? is expressed as a quadratic of inverse temperature, this model can describe the swelling equilibrium behavior of neutral thermo-sensitive hydrogels quite well. The influences of model parameters were discussed in details. The experimental swelling curves of two kinds of polyacrylamide-based gels were correlated and good agreement was obtained.     

The viscosity anomaly of polymer mixture solution in extremely dilute concentration region

The measured reduced viscosity-concentration (η_sp/C-C) curves of compatible PPO/PS incompatible PMMA/PS mixtures with different composition in toluene all deviate linear and reveal downward turn in extremely dilute concentration region. Moreover, with the variation of composition, the η_sp/C-C curve of PS/PMMA/m-xylene solution bends downwards sometimes and bends upwards sometimes in the extremely dilute concentration region. It indicates that such viscosity anomaly should not be attributed simply to incompatibility, but be related to solvent, composition and so on. It is further suggested that, like the single polymer solution, the viscosity anomaly of polymer mixture solution be resulted mainly from the interference of wall effects on viscosity measurement, which could be eliminated quantitatively with a proposed theoretical formula.     

Disentanglement and reptation during dissolution of rubbery polymers

The dissolution mechanism of rubbery polymers was analyzed by dividing the penetrant concentration field into three regimes that delineate three distinctly different transport processes. The solvent penetration into the rubbery polymer was assumed to be Fickian. The mode of mobility of the polymer chains was shown to undergo a change at a critical penetrant concentration expressed as a change in the diffusion coefficient of the polymer. It was assumed that beyond the critical penetrant concentration, reptation was the dominant mode of diffusion. Molecular arguments were invoked to derive expressions for the radius of gyration, the plateau modulus, and the reptation time, thus leading to an expression for the reptation diffusivity. The disentanglement rate was defined as the ratio between the radius of gyration of the polymer and the reptation time. Transport in the second penetrant concentration regime was modeled to occur in a diffusion boundary layer adjacent to the polymer-solvent interface, where a Smoluchowski type diffusion equation was obtained. The model equations were numerically solved using a fully implicit finite difference technique. The results of the simulation were analyzed to ascertain the effect of the polymer molecular weight and its diffusivity on the dissolution process. The results show that the dissolution can be either disentanglement or diffusion controlled depending on the polymer molecular weight and the thickness of the diffusion boundary layer. © 1996 John Wiley & Sons, Inc.     

The study of structure formation in a polymer-containing ionic liquid in terms of the integral equation theory

The structural properties of a polymer-containing ionic liquid under the conditions of good solubility of a flexible polymer are studied theoretically. Two systems are discussed: In one, polymer solubility is due to the presence of specific interaction between polymer chains and solvent cations; in the other, polymer solubility is due to the presence of specific interactions between the polymer and solvent anions. The dependences of the structural characteristics of a solution on the polymer concentration and the energy of attraction between polymer chains and solvent ions are calculated. In a semidilute polymer solution, long-range correlations of polymer chains with a power dependence of the characteristic scale of ordering on the polymer density appear. The conditions under which, along with the intermediate ordering typical of a pure ionic liquid, the long-range ordering of the solvent cations and anions occur after addition of a polymer to the ionic liquid are studied.     

Diffusion in ethylene–propylene rubber

A study of sorption in a copolymer of ethylene and propylene is presented. Long-time sorption and desorption measurements provided the actual diffusion coefficient in the limit of zero concentration gradient. An analysis of the diffusion–sorption data reinforced the Frisch hypothesis about diffusion in a polymer matrix. The better solvent deforms the microstructure, allowing a more marked dependence of the diffusivity upon concentration.     

聚合物-溶剂相互作用参数研究

根据液体混合的通用Gibbs自由能模型,导得了一个能满意地描述高分子溶液中聚合物-溶剂相互作用参数随浓度和温度变化的方程。它由焓贡献和熵贡献两部分组成,在形式上与Koningsveld-Kleintijen关系式相同,但它的熵贡献是浓度的复杂函数,而不象Koningsveld建议的是一个随意的常数。该方程能够很好地解释高分子溶液的某些特性。     

Diffusion phenomena in ternary systems polymer-nonsolvent-solvent

Diffusion in a boundary between a polymer+solvent solution and non-solvent was treated by accounting for the presence of the four diffusion coefficients that describe the isothermal transport process in a three component system. Diffusion equations were integrated assuming a concentration dependence of diffusion coefficients that account for the thermodynamic conditions on the cross diffusion terms of Eq. (1). The presence of non-zero cross terms promotes an incongruent diffusion of polymer whose concentration increases at the boundary between the polymer+solvent solution and the non-solvent. Although our model describes diffusion in the range of homogeneous solution, this incongruent polymer diffusion is a process similar to that promoted by the solvent evaporation from the polymer+solvent film that some authors suggested as an intermediate step before the film immersion into the coagulation bath to obtain good asymmetric membranes.     

Effect of mixed solvent on solution properties and gelation behavior of poly(vinyl alcohol)

In this work, the static and dynamic light scattering measurements were used to investigate the solution properties and the aging effects on PVA/DMSO/water ternary system in dilute region at 25 °C. It was found that the phase separation and aggregate behavior occurs rapidly and obviously when DMSO mole fraction (X₁) in the solvent mixture is between 0.2 and 0.33, especially at 0.25. In this solvent composition range, a broad peak which indicates phase separation and chain aggregation can be observed from static light scattering measurement. However, when DMSO mole fraction is increased to 0.37, no such peak is present. For this ternary system, the gelation mechanism and the relationship between the phase separation behavior and the gelation of the formed physical gels were also investigated through the gelation kinetic analyses in the dilute and semi-dilute region. It is concluded that the cononsolvency effect in the dilute solution is not the sole origin that affects the phase separation, aggregation, and gelation behavior for the ternary system in a higher polymer concentration range. The hydrodynamic factors such as the higher viscosity and slower polymer chain diffusion that are resulted from higher polymer concentration should be also considered.     

Incorporation of an abnormally high amount of poly(ethylene glycol) into poly(ethylene terephthalate) during tensile drawing in liquid media

Tensile drawing of PET via the mechanism of solvent crazing in adsorption-active media containing poly(ethylene glycol) with M < 1 × 10⁶ is accompanied by their penetration into the porous structure of the matrix polymer. In this case, the amount of PEG in PET exceeds its concentration calculated on the assumption that the porous structure is filled with the polymer solution. This excess is evidently due to the adsorption of PEG on the highly developed surface of crazes.     

Polymerization of tetraoxane at low concentration catalyzed by BF3·O(C2H5)2

In the solution polymerization of tetraoxane catalyzed by BF₃·O(C₂H₅)₂, trioxane and methanol-insoluble polymer were produced. However, the amounts of these products depend on the nature of solvent used. A critical concentration of tetraoxane is observed for the formation of methanol-insoluble polymer; at less than this critical concentration of tetraoxane no methanol-insoluble polymer is obtained, but trioxane is preferentially produced. This critical concentration of tetraoxane is higher in a more polar solvent, so the amount of methanol-insoluble polymer produced decreases and the amount of trioxane produced increases with increasing the polarity of solvent used. These results may be explained in terms of a stabilization of the active center leading to formation of trioxane by a solvation with solvent.     

Solvent and concentration effects on fluorescence emission in MEH-PPV solution

We systematically studied the excitation and the fluorescence steady-state spectroscopy of poly[2-methoxy-5-(2′-ethylhexoxy)-p-phenylene vinylene] (MEH-PPV) in two solvents and several concentrations. Fluorescence spectra were recorded for solutions in several concentrations (10⁻⁵ mg/ml to 10⁻³ mg/ml), showing that tetrahydrofuran (THF) and toluene solvate the polymer chain differently. Dilute solution (10⁻⁵ mg/ml) in THF exhibit broader fluorescence spectra due to greater conformation disorder. The degree of the aggregation depends on both the solvent and the polymer concentration. Aggregation is promoted in toluene solution and hindered in THF solvent.     

Reversible thermoresponsive behavior of poly(2-chloroethyl vinyl ether-<Emphasis Type="Italic">alt</Emphasis>-maleic anhydride) in mixed solvent of tetrahydrofuran/hexane

Poly(2-chloroethyl vinyl ether-alt-maleic anhydride) can exhibit lower critical solution temperature-type phase behavior reversibly by tuning the solvent composition in mixed solvent of tetrahydrofuran (THF) and hexane. The effect of solvent composition and polymer concentration on cloud point of polymer solution was investigated. The cloud point temperature for high molecular weight polymer was lower than that for lower molecular weight polymer. High resolution ¹H NMR spectra in mixed solvent of THF-d ₈ and hexane were also measured for comprehending thermoresponsive behavior of polymer solution in molecular level; however, any discontinuous change in the NMR signals around the cloud point could not be recognized.     

Single-chain and aggregation properties of semiconducting polymer solutions investigated by coarse-grained langevin dynamics simulation

A coarse-grained (CG) model and Langevin dynamics scheme are proposed to investigate the material properties in dilute solution of a model semiconducting conjugated polymer, poly(2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylenevinylene) (MEH-PPV). While the intra- and intermolecular potentials for the CG particle (currently, a monomer unit) were determined from the molecular dynamics (MD) simulation of a united atomistic model, fluctuation-dissipation forces arising from the treatment of a solvent field were self-consistently constructed from the measured particle diffusivity in a given solvent (i.e., chloroform or toluene) through the atomistic MD simulation. It is shown that the resultant Langevin dynamics simulation, which is substantially more efficient than the counterpart MD simulation of the same CG model, is able to capture the dynamic (such as center-of-mass diffusivity) as well as the structural (such as radius of gyration) features of the investigated polymer solutions. Essential material properties that can now be directly studied include the following: Scaling exponents for estimating the exact solvent qualities were, for the first time, determined for the two solvent systems investigated; the persistence length obtained was also noted to be in excellent agreement with early experimental estimations. Preliminary observations on the supramolecular aggregation properties were in good agreement with the general observations from a wide range of recent experiments, and shed light on the essential impact of solvent quality on the supramolecular aggregation structures.     

毛细管内高分子溶液的浓度分布

采用连续自洽场理论分析了毛细管中发生凝胶化之前的聚合物溶液浓度分布的影响因素及其规律. 结果表明, 体系尺寸有限时, 改变聚合物链段、溶剂与壁面的相互作用参数之差, 聚合物溶液浓度分布会发生贫化/吸附转变; 临界作用参数与聚合物链长的倒数呈线性关系, 且拟合常数与体系尺寸、聚合物溶液平均体积分数有关; 聚合物分子量分布为多分散时, 分子量较低的组分更容易接近容器壁面, 分子量较大的组分则相反. 总之, 增加聚合物溶液浓度、链长, 选择优良溶剂, 减小体系尺寸等都会使浓度分布更加均匀.     

A novel method for determining the viscosity of polymer solution

The relative viscosity η_r and, thus, the reduced viscosity η_sp/C of polymer solution could be obtained by recording the flow times of the polymer solution and the pure solvent in a capillary viscometer. Our experimental results indicated that the measurement of the flow time of the pure solvent was unnecessary. In particular, if the recorded flow time of the pure solvent was used to determine the viscosity of polymer solution, the reduced viscosity η_sp/C exhibited either a drastic increase or a significant decrease in an extremely dilute solution, depending upon the properties of the polymer solution investigated. In this research work, a new method for determining the viscosity of polymer solutions is reported. In the proposed method, the flow time of polymer solution at zero concentration, t₀^*, instead of the measured flow time of the pure solvent, was used to determine the viscosity of polymer solution. The reduced viscosity η_sp/C determined by the new method is proportional to concentration C even in an extremely dilute solution. The relative viscosity η_r vs. C plot also indicated clearly that t₀^*, instead of the measured flow time of the pure solvent, should be used for determining the viscosity of polymer solution. At low concentrations, the flow time of the polymer solution was proportional to C. As a result, t₀^* could be determined by extrapolating the flow time of the polymer solution to C=0.