Sorption, 159 defined polymer

Modeling of gas sorption in polymers is very difficult and presents a permanent challenge to theoreticians and experimenters. The gas permeation process is defined... 

This relative importance of relaxation and diffusion has been quantified with the Deborah number, De [119,130-132], De is defined as the ratio of a characteristic relaxation time A. to a characteristic diffusion time 0 (0 = L2/D, where D is the diffusion coefficient over the characteristic length L) De = X/Q. Thus rubbers will have values of De less than 1 and glasses will have values of De greater than 1. If the value of De is either much greater or much less than 1, swelling kinetics can usually be correlated by Fick s law with the appropriate initial and boundary conditions. Such transport is variously referred to as diffusion-controlled, Fickian, or case I sorption. In the case of rubbery polymers well above Tg (De < c 1), substantial swelling may occur and... 

Colloids are always present in natural waters containing the transuranium elements. (Colloids are defined as particles with sizes ranging from 1 to 450 nm. These particles form stable suspensions in natural waters.) Colloids of the transuranium elements can be formed by hydrolysis of transuranium ions, or by the sorption of transuranium elements on the naturally occurring colloids. The naturally occurring colloids include such species as metal hydroxides, silicate polymers, organics (such as humates), and the like. The mobility of the transuranium elements in an aquifer is determined largely by the mobility of its pseudocolloids, that is, those colloidal species formed by the adsorption of the transuranium ions upon the naturally occurring colloids. 

Polymer hydrophilicity can be judged in the cases (a), (c), or (d) of Fig. 14.1. It is defined as the affinity of a polymer for water, which can be quantified by the equilibrium mass gain, W, determined in standard conditions, e.g., in a saturated atmosphere from a sorption experiment. depends on the vapor pressure or activity of water and on the temperature. It varies, typically from 0 to 10% in most networks. 

When the gas or vapor feed stream contains a component that is highly soluble in the polymer membrane and causes plasticization, then the selectivity as defined by Equation 4.6 will depend on the partial pressure or the amount of the plasticizing component sorbed into the membrane. Furthermore, pure-gas permeation measurements are generally not a good indicator of the separation performance, and mixed-gas permeation measurements will be needed [21-23]. Often, the mixed-gas selectivity is less than predicted from pure-gas measurements [8] however, the opposite has been observed [24], Competitive sorption effects can also compromise the prediction of mixed-gas behavior from pure-gas measurements [25], For gas pairs where each component is less condensable than C02, like 02/N2, it is generally safe to conclude that the selectivity characteristics can be accurately judged from pure-gas permeabilities at all reasonable pressures. When the gas pair involves a component more condensable than C02, plasticization is likely to be a factor and pure-gas data may not adequately reflect mixed-gas selectivity. When C02 is a component, the situation depends on the partial pressures and the nature of the polymer. 

Hailwood-Horrobin Solution Sorption Theory. The Hailwood-Horrobin (57) model treats moisture sorption as hydration of the polymer, taken here to be dry wood, by some of the sorbed water called water of hydration, m. The hydrate forms a partial solution with the remaining sorbed water, called water of solution, m,. An equilibrium is assumed to exist between the dry wood and water and the hydrated wood with an equilibrium constant K. Equilibrium is also assumed to exist between the hydrated wood and water vapor at relative vapor pressure h, with equilibrium constant K2. A third constant is defined as the moisture content corresponding to com-... 

Thermodynamic measurements must define both the water-polymer interaction and the structural change of the polymer. This information can be given from the direct measurement of the heat of sorption of the water molecules. 

Another quantity which is often encountered in discussions of gas solubility in polymers is Henry s law coefficient of sorption (ko). For rubbery and molten polymers, kD is defined very simply as the low-pressure limit (p—>0) of the solubility where C varies almost linearly with p. 

Where v. is the partial molar volume, G is the clustering integral defined such that when G/v is greater than -1 there is a probability for clustering to occur. This sorption isotherm has been applied to high water adsorbing polymers [nylon (13), polyurethanes (13), and polyacrylonitrile (13) ] at high water activities (5). 

Upon emptying the containers, three additional specimens were cut, blotted on filter paper to remove surface solvent, weighed and dried at 60°C in an air circulating oven. The solvent loss of these specimens in (g. toluene/g. dry polymer) was defined as the dynamic toluene sorption for the tested container. Equilibrium toluene sorption was determined at RT and 50°C by immersion to constant weight of replicated cutouts from control bottles. 

The solubility coefficient indicates the sorption capacity of a polymer with respect to a particular sorbate. The simplest solubility coefficient is defined by Henry s law of solubility, which is valid at low concentration values for most substances. For other combinations, such as CO2 in PET at high pressure, Henry s and Langmuir s laws must be combined. These are also discussed in Chapter 14. 

Relative sorption of the permeants in the membrane depends on the interactions between the solutes and the membrane polymer. Solubility or miscibility of a component with the membrane polymer depends on their relative solubility parameter values. For good mutual solubility of two components, their free energy of mixing AGm should be negative. AG , is defined as... 

The two preceding effects are due to true polymer-phase sorption and transport phenomena. At veiy high pressures, an additional complexity related to nonideal gas-phase effects may arise and cause potentially incorrect conclusions about the transport phenomena involved. This confusion can be avoided by defining an alternative permeability P" in terms of the fiigacity difference rather than the partial pressure difference driving diffusion across the membrane. The benefit of using this thermodynamic permeability is illustrated for the CO2-CH4 system at elevated pressures. 

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