Rubbery polymers molecular modeling

One of the most popular and detailed statistical molecular models for the diffusion of simple penetrants in amorphous rubbery polymers was proposed in refs. (45,46). This model is based on features taken from those presented briefly above. Because it is frequently cited in the literature, it will be presented here in some detail. 

The models most frequently used to describe the concentration dependence of diffusion and permeability coefficients of gases and vapors, including hydrocarbons, are transport model of dual-mode sorption (which is usually used to describe diffusion and permeation in polymer glasses) as well as its various modifications molecular models analyzing the relation of diffusion coefficients to the movement of penetrant molecules and the effect of intermolecular forces on these processes and free volume models describing the relation of diffusion coefficients and fractional free volume of the system. Molecular models and free volume models are commonly used to describe diffusion in rubbery polymers. However, some versions of these models that fall into both classification groups have been used for both mbbery and glassy polymers. These are the models by Pace-Datyner and Duda-Vrentas [7,29,30]. 

Several detailed analyses of the diffusion process in both rubbery polymers and in hindered glasses are offered in Chapter 2 (28). Approximate molecular interpretations have been offered for the parameters in these models (25). Nevertheless, more work is needed to verify any molecular scale connection between such parameters and the structures and motions of the polymer backbone. Spectroscopy and molecular modeling of the differences in segmental motions in a systematically varied family of polymers, e.g, the polyesters, or polyamides, can offer insight in some cases. Unfortunately, the exact segmental motions involved in the diffusive process are only partially understood, so one must be cautious about drawing conclusions based on such studies unless they are supported by actual complementary transport data. Hopefully the structure-property results presented in this book will further stimulate thinking to improve the connection between spectroscopically sensed motions, and diffusion to complement the correlations based on specific free volume in Chapters 5 S 7 (50,51). ... 

MODELS FOR DIFFUSION IN BOTH RUBBERY AND IN GLASSY POLYMERS Some models are applicable to diffusion of small molecules in glassy as well as in rubbery polymers. These too fall into the general categories of molecular models and free-volume models. Recent molecular dynamics simulations of simple polymer/penetrant systems will also be discussed. 

The model equations (Eqs. (60) and (61)) were solved numerically using an implicit finite difference technique. Typical profiles for the solvent volume fraction as a function of position and time in the rubber and the polymer volume fraction in the diffusion boundary layer are shown in Figs. 31 and 32 respectively. Other features of the simulation are the prediction of the temporal evolution of the rubbery-solvent interface and the mass fraction of the polymer dissolved as a function of time (Figs. 33 and 34). The simulations showed that the dissolution could be either disentanglement or diffusion controlled depending on the polymer molecular weight and the thickness of the diffusion boundary layer. 

The experimental data were compared to the model predictions for all three molecular weights studied. The model presented earlier was modified (since PEG is rubbery) and used to predict the temporsd evolution of the gel layer thiclmess for PEG dissolution in water at 21 C. Figures 14-16 show Ae comparison between the model predictions and the experimental data for PEG (Mn = 10,000 20,000 and 35,000) dissolution in deionized water. It is seen that there is good agreement between the predictions and the data within experimental error. This indicated that the model for rubbery polymer dissolution was able to correctly predict dissolution behavior of such polymers. 

During the last decades interest in membrane separation processes and in solutions for packaging problems has given a substantial boost to research on sorption and mass transport in polymeric materials. Several interpretative models for the solubility and diffusivity in rubbery polymers are now available which, at least in principle, allow for the prediction of the permeability of low molecular weight species in polymeric films above their glass transition temperature. 

Molecular modeling of the type described above has been conducted on a number of polymer systems. Of these systems the great majority have been based on rubbery polymers. It is only recently that molecular simulations based on glassy polymer systems are appearing in the literature (200-206). From these studies, differences in the diffusion mechanism of rubbery and glassy polymers... 

It is somewhat difficult conceptually to explain the recoverable high elasticity of these materials in terms of flexible polymer chains cross-linked into an open network structure as commonly envisaged for conventionally vulcanised rubbers. It is probably better to consider the deformation behaviour on a macro, rather than molecular, scale. One such model would envisage a three-dimensional mesh of polypropylene with elastomeric domains embedded within. On application of a stress both the open network of the hard phase and the elastomeric domains will be capable of deformation. On release of the stress, the cross-linked rubbery domains will try to recover their original shape and hence result in recovery from deformation of the blended object. 

Figures 3.9 and 3.10 show the temperature dependencies of Ti and NOE of the CH2 (rrr) of the same PMMA solution and the results (solid and broken curves) simulated by the second-order model-free treatment with p = 3 [17]. Here, the Arrhenius equation was assumed for the respective correlation times tj = tio exp(AEi/RT) and ta/ = ta,o exp(AEA,/RT). In this case the simulated results with p = 3 are also in good accord with the experimental results, indicating the validity of the model-free treatment. Similar analyses of the temperature dependencies of the Tj were successfully performed for the rubbery components of the solid polyesters with different methylene sequences [20, 21]. These results are also well analyzed by the second-order model-free treatment with p = 3. There are a large number of the publications of the temperature dependencies of Ti and NOE analyzed by different models of molecular motions for polymers in the dis-...

Crystallites may also be considered to act as reinforcing fillers. For example, the rubbery modulus of poly(vinyl chloride) was shown by lobst and Manson (1970,1972,1974) to be increased by an increase in crystallinity calculated moduli in the rubbery state agreed well with values predicted by equation (12.9). Halpin and Kardos (1972) have recently applied Tsai-Halpin composite theory to crystalline polymers with considerable success, and Kardos et al (1972) have used in situ crystallization of an organic filler to prepare and characterize a model composite system. More recently, the concept of so-called molecular composites —based on highly crystalline polymeric fibers arranged in a matrix of the same polymer—has stimulated a high level of experimental and theoretical interest (Halpin, 1975 Linden-meyer, 1975). 

It has been shown in a previous section that, in most cases of practical interest, the rate of gas permeation through nonporous polymer membranes is cOTitrolled by the diffusion of the penetrant gas in the polymer matrix. Many theoretical models have been proposed in the literature to describe the mechanisms of gas diffusion in polymers on a molecular level. Such models provide expressions for gas diffusion coefficients, and sometimes also for permeability coefficients, derived from free volume, statistical-mechanical, energetic, structural, or other considerations. The formulation of these coefficients is complicated by the fact that gas transport occurs by markedly different mechanisms in rubbery and glassy polymers. 

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