Dual-mode sorption theory

The basic assumptions of the dual mode sorption theory as it applies to the transport model of Vieth and Sladek, have been stated by Vieth et al. in their excellent review of the subject The sorption isotherm was described by the combination of a Henry s law dissolved component, Cp, and a Langmuir hole filling term, Ch, i.e.. 

In some cases deviations from Fickian behavior in glassy epoxy polymers (19-25) have been adequately described using dual mode sorption theory (22-24). This theory is based upon the premise that the sorbed penetrant exists in two thermodynamically distinct populations. These populations consist of molecules adsorbed in "holes", and species simply dissolved in the polymer matrix. 

Figure 20 Schematic representation of the dependence of concentration on partial pressure illustrating predications of Henry s law and dual mode sorption theory.

It appears that moisture transport in conditions of less than 100% relative humidity is largely dominated by diffusion. The diffusion phenomenon is best described using dual mode sorption theory. 

The three parameters of the dual mode sorption theory, ko, Ch. and b, are determined by analyzing an isothermal plot of C versus p. For gas sorption at low pressure, where bp 1, the sorption isotherm in Equation 1 reduces to the following linear expression. 

Plots of permeability coefficients versus (1 + bpY should be linear. The intercept and slope of the line correspond to koDp and CnbDn, respectively. Once the equilibrium parameters from the dual mode sorption theory are known, the two diffusion coefficients. Do and D//, can be determined. 

The solubility of hydrocarbons in rubbery polymers can be described in more detail by several theories of solutions using various criteria of thermodynamic affinity [7,25-28], of which the Flory-Huggins theory is the most popular one. It takes into account the volume content of the penetrant dissolved in the polymer and the change in the length of the polymer s thermodynamic segment as a result of dissolution [7]. However, it should be pointed out that to describe dissolution, a rehned dual-mode sorption model can be used, e.g., the model by Pace and Datyner [7,29,30]. 

A phenomenological theory known as the "dual-mode sorption" model offers a satisfactory description of the dependence of diffusion coefficients, as well as of solubility and permeability coefficients, on penetrant concentration (or pressure) in glassy polymers (4-6,40-44). This model postulates that a gas dissolved in a glassy polymer consists of two distinct molecular populations ... 

In Section I we introduce the gas-polymer-matrix model for gas sorption and transport in polymers (10, LI), which is based on the experimental evidence that even permanent gases interact with the polymeric chains, resulting in changes in the solubility and diffusion coefficients. Just as the dynamic properties of the matrix depend on gas-polymer-matrix composition, the matrix model predicts that the solubility and diffusion coefficients depend on gas concentration in the polymer. We present a mathematical description of the sorption and transport of gases in polymers (10, 11) that is based on the thermodynamic analysis of solubility (12), on the statistical mechanical model of diffusion (13), and on the theory of corresponding states (14). In Section II we use the matrix model to analyze the sorption, permeability and time-lag data for carbon dioxide in polycarbonate, and compare this analysis with the dual-mode model analysis (15). In Section III we comment on the physical implication of the gas-polymer-matrix model. 

The basic premise of the dual-sorption theory is that a glassy polymer contains microvoids, or holes created during the process of cooling the polymer below its glass transition temperature. Therefore, gas molecules can either dissolve in the bulk polymer or go into these holes. Consequently, glassy polymers have a high gas solubility due to the availability of dual-sorption modes. It is found that gas dissolution in the matrix follows Henry s law, whereas that in the holes displays a Langmuir-type dependence. Thus, at equilibrium, the total gas concentration in the polymer can be separated into a normal sorption term c, and a hole contribution [65] ... 

---