Polymer sorption isotherm

For glassy polymers, sorption isotherms are more complex and hysteresis oetween the pressurization and depressurization steps may... 

The two examples above show that the model allows us to predict accurately the solubility of the blends when the pure polymer sorption isotherm for the solvent under investigation is known and the binary parameter associated with the polymer-polymer pair is set to its default value, as in the present cases. The results are more than satisfactory, with average errors that seldom exceed the value of 10% in the case of PS-TMPC blends and are generally even lower for the other blends considered. 

The form of polymer sorption isotherms has received mnch attention and many adsorption equations have been proposed and employed. In the present case, conformance was found with an equation of the Freundlich type ... 

Fig. 3. Water sorption isotherms of poIy(trans-3,4-dihydroxytetrahydiopyran-6,2-diyloxy-methylene) 24 and its related polymers at 20 °C.

To begin, it is essential to rationalize the equilibration of water within the membrane at AP = 0, APs = 0, j = 0, and = 0. The suggested scenario of membrane swelling is based on the interplay of capillary forces and polymer elasticity. In order to justify a scenario based on capillary condensation, isopiestic vapor sorption isotherms for Nafioni in Figure 6.9(a) are compared with data on pore size distributions in Figure 6.9(b) obtained by standard porosimetry.i In Figure 6.9(a), a simple fit function. 

Still, this theory is over-simplified, and holds only for a limited part of the sorption isotherm, which is usually the case for relative pressures between 0.05-0.30, and the presence of point B (Fig. 1.14). Thus, isotherms of Types II (macroporous polymer supports) and IV (mesoporous polymer supports), but not Type I and III, are those amenable to BET analysis [21, 80]. Attention should also be paid to the constant C, which is exponentially related to the enthalpy of adsorption of the first layer. A negative or high value of C exceeding 200-300, is likely to indicate the presence of micropores and the calculated surface area should be questioned since the BFT theory would not be applicable [79, 80]. 

The sorption of a weak electrolyte by a charged polymer membrane is another case where Nernst + Langmuir-like dual mode sorption, involving the undissociated and dissociated species respectively, may be expected. The concentration of each species in solution follows, of course, from the dissociation constant of the electrolyte. The sorption isotherms of acetic acid and its fluoroderivatives have been analysed in this manner, and the concentration dependence of the diffusion coefficient of acetic acid interpreted resonably successfully, using Nylon 6 as the polymer substrate 87). In this case the major contribution to the overall diffusion coefficient is that of the Nernst species consequently DT2 could not be determined with any precision. By contrast, in the case of HC1, which was also investigated 87 no Nernst sorption or diffusion component could be discerned down to pH = 2 and the overall diffusion coefficient obeyed the relation D = DT2/( 1 — >1D), which is the limiting form of Eq. (25) when p — 00. 

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. 

The solid line in Fig. 1 represents the sorption isotherm of carbon dioxide in polycarbonate calculated by fitting the solubility expression, eq. (11), to experimental data of Wonders and Paul (15). The best fit to the experimental data was achieved with the parameters ao=7.33cm3(STP)/cm3(polymer)-atm and a = 0.161 cm3(polymer)/cm3(STP). As can be seen in Fig. 1, eq. (11) describes the experimental data over the entire pressure range. The algorithm used to fit eq. (11) to the experimental data is described elsewhere (FI). 

The sorption isotherm for many substances in polymers in the glassy state, as well as water in cellulose, can be described by two processes that are independent of one another (dual sorption model) ... 

A. Kyritsis, P. Pissis, J. L. Gomez Ribelles, and M. Monleon Pradas, Polymer-water interactions in poly(hydroxyethyl acrylate) hydrogels studied by dielectric, calorimetric and sorption isotherm measurements, Polym. Gels Networks 3, 445-469 (1995). 

The permeation of a gas through a porous polymer is generally described by equations based on the kinetic theory of gases. The sorption isotherm described by Eq. 1 is concave to the pressure axis and is commonly observed for a penetrant gas in a glassy polymer. It is composed of Henry s law and Langmuir-terms [20] ... 

In this chapter we will mostly focus on the application of molecular dynamics simulation technique to understand solvation process in polymers. The organization of this chapter is as follow. In the first few sections the thermodynamics and statistical mechanics of solvation are introduced. In this regards, Flory s theory of polymer solutions has been compared with the classical solution methods for interpretation of experimental data. Very dilute solution of gases in polymers and the methods of calculation of chemical potentials, and hence calculation of Henry s law constants and sorption isotherms of gases in polymers are discussed in Section 11.6.1. The solution of polymers in solvents, solvent effect on equilibrium and dynamics of polymer-size change in solutions, and the solvation structures are described, with the main emphasis on molecular dynamics simulation method to obtain understanding of solvation of nonpolar polymers in nonpolar solvents and that of polar polymers in polar solvents, in Section 11.6.2. Finally, the dynamics of solvation with a short review of the experimental, theoretical, and simulation methods are explained in Section 11.7. 

Type III is the sorption isotherm of Flory-Huggins. Here the solubility coefficient increases continuously with pressure. It represents a preference for formation of penetrant pairs and clusters it is observed when the penetrant acts as a swelling agent for the polymer without being a real solvent. An example is water in relatively hydrophobic polymers containing also some polar groups. 

Precise studies of sorption of non-permanent gases in glassy polymers showed that the sorption isotherms do not follow Henry s law (see Fig. 18.9a). A very good approximation of the isotherm is ... 

A selection of hydrocarbon vapour isotherms obtained with dimethyldioctadecyl-ammonium bentonite is displayed in Figure 11.10. The toluene and ethyl benzene isotherms are almost linear over a wide range of p/p° and are more like the sorption isotherms given by organic polymers than by inorganic porous adsorbents. On the other hand, the Type lib character of the iso-octane and cyclohexane isotherms is apparent (Barter, 1978, p. 455). 

The phenomenon of polymer swelling, owing to sorption of small molecules, was known even before Staudinger reported [1] in 1935 that crosslinked poly(styrene) swells enormously in certain liquids to form two-component polymer gels. The physical state of such systems varies with the concentration (C) and molecular structure of the sorbed molecules thus, the system undergoes transition at constant temperature from a rigid state (glassy or partially crystalline) at C < Cg to a rubbery state at Cg (the transition state composition). When C > Cg and the second component is a liquid, its subsequent sorption proceeds quickly to gel-saturation and of course a solution is produced if the polymer lacks covalently bonded crosslinks or equivalent restraints. Each successive physical state exhibits its own characteristic sorption isotherm and sorption kinetics. 

A final advantage of rubbery, amorphous polymers is that their sorption isotherms are often linear over relatively large ranges in penetrant concentration. Appendix C lists some common polymers that have been used as sensor coatings along with their Tg, Tfn, and monomer repeat unit structure. 

---