Sorption/transport model

Transient-transport measurements are a powerful tool for evaluating the validity of any sorption-transport model. The ability of a model to predict diffusion time lags is a test for its validity, as all the parameters are fixed by the equilibrium sorption and steady state transport, and because the time lag depends on the specific form of the concentration and diffusion gradients developed during the transient-state experiments. 

Axley J.W. and Lorenzetti D. (1993) Sorption Transport Models for Indoor Air Quality Analysis. Proceedings of Modeling of Indoor Air Quality and Exposure, ASTM STP 1205, N. L. Nagda (ed), 105 -127. 

These methods are interested in studying the distinction between the pure dualmode sorption/transport model curve and the actual sorption and permeation experiment curve that seems to contain the various unsolved appearances for diffusion and sorption of gases in glassy polymer. It becomes obvious that the deviations from the Fickian model in an experimental transport or sorption/desorp-tion curve for a gas in a glassy polymer are not necessarily consistent with the onset of concomitant diffusion and relaxation [11], but are just owing to the dual-mode model. That is to say, only the combinations of parameters of the dual mode model make the curve either fit with or deviation from the Fickian model curve. 

As one might expect, moisture sorption is controlled by both mass and heat transport resistance. The heat transport model discussed earlier was based on the concept that condensation of water would generate heat, which at steady state would... 

UTM-TOX. The Unified Transport Model for Toxicants (UTM-TOX, 52) was developed at Oak Ridge National Laboratory (ORNL) on the base of the ORNL Unified Transport Model (UTM), itself under development from the early 1970 s. UTM-TOX includes air, water, and terrestrial submodels. The aquatic fate submodel includes volatilization, hydrolysis, biolysis, photolysis, and sorption equilibria. Sorbed phases are assumed unreactive in the 1982 version. 

I expand treatment of sorption, ion exchange, and surface complexation, in terms of the various descriptions in use today in environmental chemistry. And I integrate all the above with the principals of mass transport, to produce reactive transport models of the geochemistry and biogeochemistry of the Earth s shallow crust. As in the first edition, I try to juxtapose derivation of modeling principles with fully worked examples that illustrate how the principles can be applied in practice. 

Of the various equilibrium and non-equilibrium sorption isotherms or sorption characteristics models, the most popular are the Langmuir and Freundlich models. The correct modeling of an adsorbate undergoing both transport and adsorption through a clay soil-solid system necessitates the selection of an adsorption isotherm or characteristic model which best suits the given system. The use of an improper or inappropriate adsorption model will greatly affect the... 

The results from this case study can be used as input to the general comprehensive RRR fate and transport model (i. e., which includes volatilization, photolysis, biodegradation, and sorption/desorption modules) in order to predict organic leachate-generated chemical loads and concentrations at highway boundary or landfill sites. 

Recently there has been interest in the sorptive behavior of natural clays toward metal ions potentially present in radioactive wastes. Initial studies of the transplutonium elements have been carried out to define their sorption behavior with such materials ( ). However, it is also important to understand the stability of the clay-actinide product with regard to radiation damage and to be able to predict what changes in behavior may occur after exposure to radiation, so that accurate transport models may be constructed. 

Implications of the Dual-Mode Sorption and Transport Models for Mixed Gas Permeation... 

Transport, A companion transport model that also acknowledges the fact that penetrant may execute diffusive jumps into and out of the two sorption environments expresses the local flux, N, at any point in the polymer in terms of a two part contribution (17-20) ... 

The discussion directly following Eq (6) provides a simple, physically reasonable explanation for the preceding observations of marked concentration dependence of Deff(C) at relatively low concentrations. Clearly, at some point, the assumption of concentration independence of Dp and in Eq (6) will fail however, for our work with "conditioned" polymers at CO2 pressures below 300 psi, such effects appear to be negligible. Due to the concave shape of the sorption isotherm, even at a CO2 pressure of 10 atm, there will still be less than one CO2 molecule per twenty PET repeat units at 35°C. Stern (26) has described a generalized form of the dual mode transport model that permits handling situations in which non-constancy of Dp and Dh manifest themselves. It is reasonable to assume that the next generation of gas separation membrane polymers will be even more resistant to plasticization than polysulfone, and cellulose acetate, so the assumption of constancy of these transport parameters will be even more firmly justified. 

One can easily show that the appropriate equation derived from the dual mode sorption and transport models for the steady state permeability of a pure component in a glassy polymer is given by Eq (7) (18) when the downstream receiving pressure is effectively zero and the upstream driving pressure is p ... 

Whereas the dual sorption and transport model described above unifies independent dilatometric, sorption and transport experiments characterizing the glassy state, an alternate model offered recently by Raucher and Sefcik provides an empirical and fundamentally contradictory fit of sorption, diffusion and single component permeation data in terms of parameters with ambiguous physical meanings (28), The detailed exposition of the dual mode model and the demonstration of the physical significance and consistency of the various equilibrium and transport parameters in the model in the present paper provide a back drop for several brief comments presented in the Appendix regarding the model of Raucher and Sefcik,... 

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. 

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,... 

In summary, the dual-mode sorption and transport model assumes (13) ... 

In the dual-mode sorption and transport model the pressure-dependence of a (= C/p), P and 0 in gas-glassy polymer systems arises from the pressure-dependent distribution of the sorbed gas molecules between Langmuir sites and Henry s law dissolution. Although k, Dg and are assumed to be constant, the average or effective solubility and diffusion coefficients of the entire ensemble of gas molecules change with pressure as the ratio of Henry s to Langmuir s population, C /C, changes continuously with pressure [eq. (14)]. 

In Section IB we presented experimental evidence that diffusion coefficients correlate with PVC main-chain polymer motions. This relationship has also been justified theoretically (12). In the previous section we demonstrated that the presence of CO2 effects the cooperative main-chain motions of the polymer. The increase in with increasing gas concentration means that the real diffusion coefficient [D in eq. (11)] must also increase with concentration. The nmr results reflect the real diffusion coefficients, since the gas concentration is uniform throughout the polymer sample under the static gas pressures and equilibrium conditions of the nmr measurements. Unfortunately, the real diffusion coefficient, the diffusion coefficient in the absence of a concentration gradient, cannot be determined from classical sorption and transport data without the aid of a transport model. Without prejustice to any particular model, we can only use the relative change in the real diffusion coefficient to indicate the relative change in the apparent diffusion coefficient. 

The experimental evidence presented here and in the literature (15) show that the real diffusion coefficient depends on concentration. These results are incompatible with the notion of concentration-independent diffusion coefficients for the dissolved and Langmuir sorbed molecules [D and Djj in equation (15)] as proposed by the dual-mode sorption and transport model ( 13). 

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... 

Experimental results presented in this work and in the literature are inconsistent with the assumptions and the physical interpretations implicit in the dual-mode sorption and transport model, and strongly suggest that the sorption and transport in gas-glassy polymer systems should be presented by a concentration-dependent model ... 

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