Penetrant polymers

Eqs. (l)-(5) are still the basic sorption and transport equations used today for "ideal systems, penetrant-polymer systems in which both (Jo and Do are pressure and concentration independent. This "ideal" behavior is observed in sorption and transport of permanent and inert gases in polymers well above their Tg. 

Section IIA summarizes the physical assumptions and the resulting mathematical descriptions of the "concentration-dependent (5) and "dual-mode" ( 13) sorption and transport models which describe the behavior of "non-ideal" penetrant-polymer systems, systems which exhibit nonlinear, pressure-dependent sorption and transport. In Section IIB we elucidate the mechanism of the "non-ideal" diffusion in glassy polymers by correlating the phenomenological diffusion coefficient of CO2 in PVC with the cooperative main-chain motions of the polymer in the presence of the penetrant. We report carbon-13 relaxation measurements which demonstrate that CO2 alters the cooperative main-chain motions of PVC. These changes correlate with changes in the diffusion coefficient of CO2 in the polymer, thus providing experimental evidence that the diffusion coefficient is concentration dependent. 

Nonlinear, pressure-dependent solubility and permeability in polymers have been observed for over 40 years. Meyer, Gee and their co-workers (5) reported pressure-dependent solubility and diffusion coefficients in rubber-vapor systems. Crank, Park, Long, Barrer, and their co-workers (5) observed pressure-dependent sorption and transport in glassy polymer-vapor systems. Sorption and transport measurements of gases in glassy polymers show that these penetrant-polymer systems do not obey the "ideal sorption and transport eqs. (l)-(5). The observable variables,... 

A number of attempts have been made to explain the nonlinear, pressure-dependent sorption and transport in polymers. These explanations may be classified as "concentration-dependent (5) and "dual-mode (13) sorption and transport models. These models differ in their physical assumptions and in their mathematical descriptions of the sorption and transport in penetrant-polymer systems. 

Pressure-dependent sorption and transport properties in polymers can be attributed to the presence of the penetrant in the polymer. Crank (32) suggested in 1953 that the "non-ideal" behavior of penetrant-polymer systems could arise from structural and dynamic changes of the polymer in response to the penetrant. As the properties of the polymer are dependent on the nature and concentration of the penetrant, the solubility and diffusion coefficient are also concentration-dependent. The concentration-dependent sorption and transport model suggests that "non-ideal" penetrant-polymer systems still obey Henry s and Fick s laws, and differ from the "ideal" systems only by the fact that a and D are concentration dependent,... 

The basic difference between Mconcentration-dependentM and dual-mode, models is in their assumption about penetrant-polymer interactions. Concentration-dependent sorption and transport models are based on the assumption that the concentration-dependence of the solubility and diffusion coefficients arises... 

The last section gives a presentation on the present status of so-called ab initio computer simulations of the diffusion of small penetrants in polymer matrices. This is a domain currently in rapid development and there are many expectations that, computer simulations will one day become a practical and performant tool to predict diffusion phenomena in complex penetrant polymers system. 

Since about 15 years, with the advent of more and more powerfull computers and appropriate softwares, it is possible to develop also atomistic models for the diffusion of small penetrants in polymeric matrices. In principle the development of this computational approach starts from very elementary physico-chemical data - called also first-principles - on the penetrant polymer system. The dimensions of the atoms, the interatomic distances and molecular chain angles, the potential fields acting on the atoms and molecules and other local parameters are used to generate a polymer structure, to insert the penetrant molecules in its free-volumes and then to simulate the motion of these penetrant molecules in the polymer matrix. Determining the size and rate of these motions makes it possible to calculate the diffusion coefficient and characterize the diffusional mechanism. 

In approaching the problem of modelling diffusion in polymers, regardless if in a classical or computational manner, an important feature must be highlighted, namely that markedly different diffusion mechanisms operate at temperatures above and below the glass transition temperature, Tg, of the polymer. This is due in principal to the fact that polymers at temperatures T > Tg, so-called rubbery polymers, respond rapidly to changes in their physical condition. Therefore, the penetrant polymer system adjusts immediately to a new equilibrium when a penetrant species is... 

Historically most of the microscopic diffusion models were formulated for amorphous polymer structures and are based on concepts derived from diffusion in simple liquids. The amorphous polymers can often be regarded with good approximation as homogeneous and isotropic structures. The crystalline regions of the polymers are considered as impenetrable obstacles in the path of the diffusion process and sources of heterogeneous properties for the penetrant polymer system. The effect of crystallites on the mechanism of substance transport and diffusion in a semicrystalline polymer has often been analysed from the point of view of barrier property enhancement in polymer films (35,36). 

Among the popular methods for interpreting the diffusion of small penetrants in polymers are the so called free-volume models (6,11,13,51-54). The basic assumption of these models is that the mobility of both polymer segments and penetrant molecules is primarly determined by the available free-volume in the penetrant polymer system. The free-volume of the polymer is regarded as an empty volume between the chains of the polymer. Similarly the free-volume of the penetrant can be regarded as the volume not occupied between the molecules of the penetrant. 

Because of the assumed dual sorption mechanism present in glassy polymers, the explicit form of the time dependent diffusion equation in these polymers is much more complex than that for rubbery polymers (82-86). As a result exact analytical solutions for this equation can be found only in limiting cases (84,85,87). In all other cases numerical methods must be used to correlate the experimental results with theoretical estimates. Often the numerical procedures require a set of starting values for the parameters of the model. Usually these values are shroud guessed in a range where they are expected to lie for the particular penetrant polymer system. Starting from this set of arbitrary parameters, the numerical procedure adjusts the values until the best fit with the experimental data is obtained. The problem which may arise in such a procedure (88), is that the numerical procedures may lead to excellent fits with the experimental data for quite different starting sets of parameters. Of course the physical interpretation of such a result is difficult. 

Local density fluctuations occur in penetrant polymer systems both above and below Tg. It is then reasonable to expect that a free-volume diffusion model should also provide an adequate description of the diffusion of small penetrants in glassy polymers. To reach this goal the free-volume model for diffusion of small penetrants in rubbery polymers, second part of Section 5.1.1, was modified to include transport below Tg (64,65,72,91-93). 

The above sections have presented models that link the process of diffusion of small penetrants in polymers to microscopic features of the penetrant polymer system. Strictly speaking the type of diffusion models presented above are not truly microscopic because they actually describe average and not truly local - microscopic - properties of the penetrant polymer system. Sometimes even excellent correlations of experimental data offered by these models are due to the fact that the experimental methods used to determine the diffusion coefficients are in turn probing the penetrant polymer system over non-microscopic distances and comparatively long times. 

Somewhat closer to the designation of a microscopic model are those diffusion theories which model the transport processes by stochastic rate equations. In the most simple of these models an unique transition rate of penetrant molecules between smaller cells of the same energy is determined as function of gross thermodynamic properties and molecular structure characteristics of the penetrant polymer system. Unfortunately, until now the diffusion models developed on this basis also require a number of adjustable parameters without precise physical meaning. Moreover, the problem of these later models is that in order to predict the absolute value of the diffusion coefficient at least a most probable average length of the elementary diffusion jump must be known. But in the framework of this type of microscopic model, it is not possible to determine this parameter from first principles . 

First, with no exception, in all classical diffusion models one or more adjustable parameters enter in the formula of D. To calculate the magnitude of this/these param-eter/s a number of diffusion experiments must be performed with the very penetrant polymer system which one intends to simulate theoretically. In practice such experiments most often require quite sophisticated equipment to obtain the experimental data, and often non-trivial theoretical schemes to evaluate them. The attempt to save experimental work by using the adjustable parameters determined for a certain penetrant polymer system in order to estimate/predict Ds in a related system is generally not recomendable. Hence, in a first step, in order to use one or other of the classical diffusion models, one is forced to replace migration experiments with diffusion ones. 

Finally, in some of the most widely used classical models - the free-volume models of Fujita, Vrentas and Duda and their alternatives (171-175) - more than a dozen structural and physical parameters are needed to calculate the free-volume in the penetrant polymer system and subsequently the D. This might prove to be a relatively simple task for simple gases and some organic vapors, but not for the non-volatile organic substances (rest-monomers, additives, stabilizers, fillers, plasticizers) which are typical for polymers used in the packaging sector. As suggested indirectly in (17) sometimes in the future it will maybe possible to calculate all the free-volume parameters of a classical model by using MD computer simulations of the penetrant polymer system. 

How much software development and computing time will be needed to predict the D for a penetrant polymer system not yet investigated In (120) it was stated that even the rather fast TSA simulation technique will presumably not lead to a fast predictability of transport paramaters for large numbers of hypotetical polymers in the near future. This was mainly atributed to the fact, that the construction of well equili-... 

Then an important aspect is how precise the predicted D will be So far an agreement within one order of magnitude between an experiment and an atomistic simulation is considered to be a good achievement. For completely amorphous polymer structures and simple penetrants even better agreements have been reported in Tables 5-1 and 5-2. From the point of view of estimating the migration from polymeric materials used in the technical sector a prediction of D within the order of magnitude of the experimental one would be a result of certain practical use, see Chapter 15. The question is to what sophistication must be developed the computer simulation approach to meet this requirement also for the type of penetrant polymer systems which are usual in the named sector ... 

Chemical modification will be defined for this chapter as any chemical reaction between some reactive part of a wood cell wall component and a simple single chemical reagent, with or without catalyst, that forms a covalent bond between the two components. This excludes in situ polymerizations of monomers in the lumen structure of the wood and those reactions that result in cell wall-penetrating polymer systems that do not result in any cell wall attachment. It is well known that lumen-filling polymer treatment results in large improvements in mechanical properties, but these are mainly a result of the properties of the new polymer introduced [ 1 ]. 

Counterface asperities penetrate polymer, wear rate characteristic of initial roughness (microcutting, low cycle fatigue)... 

Is a versatile emulsifier for solvents, vegetable oils, and waxes. In the leather industry, it is used as an emulsifier for tanning chemicals. Textile uses include resin bath penetrants, polymer stabilizers, solvent scour emulsifiers, and enzyme bath penetrants. It is also used in cold water scours for felted fabrics. 

In the absence of specific penetrant/polymer interactions, solubility of the penetrant is determined mainly by its chemical namre and depends on condensability, which is represented by boiling temperamre (Tb), critical temperature (Ter), or Lennard-Jones constant (s/fe) [7,8]. It is known that in the hydrocarbon series the increase in condensability is accompanied by a parallel increase in the size of molecules (Table 9.1 [9-17]). It is therefore not surprising that in both glassy and rubbery polymers correlations of hydrocarbon solubility in the polymers with condensability and sizes of hydrocarbon molecules are observed (Figures 9.1 through 9.3). 

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