Sorption data, matrix model

In one of their comparisons between the matrix model and the dual mode model, a somewhat misleading presentation of data is unintentionally offered in Figure 4 of the Raucher and Sefcik paper "Matrix Model of Gas Sorption and Diffusion in Glassy... 

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. 

II. ANALYSIS OF SORPTION AND TRANSPORT DATA BY THE MATRIX MODEL... 

Both the matrix-model and the dual-model represent the experimental data satisfactory (Fig. 1). After modeling sorption measurements in several gas-polymer systems we have observed no systematic differences between the mathematical descriptions of the two models. 

Figure 1. Sorption isotherm at 35 °C for CO2 in polycarbonate conditioned by exposure to 20 atm CO2. The experimental data are from Ref. 15. The curves, based on the matrix model (solid line) and the dual-mode model (broken line), are calculated using the parameters given in the text.

Using the dual-mode parameter values determined from sorption and permeation experiments, calculated time lags agree with the experimental data only at gas pressures above 5 atm. At lower pressures, dual-mode time lags are appreciably shorter than the observed ones, whereas time lags calculated from the matrix model by eq. (15) agree with the experimental data over the entire pressure range. 

The fit of these expressions to experimental results is very good. At low pressure regimes, the fit was shown to be even better than that of dual sorption expressions. Except for these regimes, the two models seem to do equally well in describing sorption and permeability data. Concentration dependent diffusivity and permeability have been considered before mainly for vapors. The new aspect of the matrix model is that it broadens these effects to fixed gases. The important difference between the matrix and dual sorption models is in the physical picture they convey of gas transport and interaction with the polymer. Additional experimental evidence will be needed to determine the preference of these different physical representations. 

Modeling of transient data. The model takes mass transport into account at two different levels Knudsen flow in the interstitial voids of the bed and in the macropores of the matrix, lumped into one diffusion coefficient and an activated diffusion process inside the micropores of the zeolite. The reversible sorption between the gas phase and zeolite sorbate... 

Wolfe (1989) suggested a model to describe abiotic reduction in sediments, where a nonreactive sorptive site and an independent reactive sorptive site are considered. The nonreactive sorptive sink is consistent with partitioning of the contaminant to the organic carbon matrix of the solids. The model is described by Fig. 13.5 where P S is the compound at the reactive sorbed site P is the compound in the aqueous phase S and S are the sediments, P S is the compound in the nonreactive sink k, k , k , and k are the sorption-desorption rate constants, and k, k, and k are the respective reaction rate constants. If the reaction constants k and k are neglected, two rate-limiting situations are observed transport to the reactive site and reduction at the reactive site. The available kinetic data, however, do not allow one to distinguish between the two mechanisms. 

Silica-based SBA-15 materials, synthetised using triblock copolymers as templates, have a 2-dimensional hexagonal symmetry. PEO chains are deeply occluded within silica walls of SBA-15 and therefore the density of these walls, after calcination and elimination of PEO chains, may not be uniform. Hydrothermal treatment of SBA-15 can be used to increase their main mesopore diameter and decrease their wall thickness. Unique informations provided by modelling of XRD data complemented by TEM and N2 sorption show that calcined SBA-15 solids cannot be considered as ideal arrays of mesopores imbedded in a uniform silica matrix. The silica walls structure is complex as mesopores appear to be surrounded by a microporous corona of silica. We will also describe how this corona is affected by hydrothermal treatment. 

The models and material property data for predicting fission metal release from fuel particles and fuel elements are described in Ref. 4. The transport of fission metals through the kernel, coatings, fuel rod matrix, and fuel element graphite is modeled as a transient diffusion process in the TRAFIC code (Section 4.2.5,2.2.1.2). The sorption isotherms which are used in the calculation of the rate of evaporation of volatile metals from graphite surfaces account for an increase in graphite sorptivity with increasing neutron fluence. 

The FFV in the unpenetrated polymer phase of the MMM calculated from the sorption isotherm of the test penetrant (n-C4) throngh the NELF model can also be used to correlate the diffusivity data collected during sorption tests. The infinite dilution diffusion coefficient in the polymeric phase, T>p(0) determined from the experimental diffusivity data can be related to the FFV initially present in the polymer matrix (FFVm). As shown in Figure 7.7 for diffusion of n-bntane in AF 2400, there is a correlation between the infinite dilution diffusion coefficient and l/FFVS, that agrees with Eqnation (7.16). Similar behaviour is observed for n-Cs, with different valnes of the parameters A and B, as it can be seen from the results reported in Table 12. This is not surprising, because the values of these empirical parameters are expected to be a function of the penetrant nature and size. 

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