Sorption and diffusion in polymers

Sorption and diffusion in polymers are of fundamental and practical concern. However, data acquisition by conventional methods is difficult and time consuming. Again, IGC represents an attractive alternative. Shiyao and co-workers, concerned with pervaporation processes, use IGC to study adsorption phenomena of single gases and binary mixtures of organic vapors on cellulosic and polyethersulfone membrane materials (13). Their work also notes certain limitations to IGC, which currently restrict its breadth of application. Notable is the upper limit to gas inlet pressure, currently in the vicinity of 100 kPa. Raising this limit would be beneficial to the pertinent use of IGC as an indicator of membrane-vapor interactions under conditions realistic for membrane separation processes. 

Fig. 38. Permeability as a function of molar volume for a mbbery and glassy polymer, illustrating the different balance between sorption and diffusion in these polymer types. The mbbery membrane is highly permeable the permeability increases rapidly with increasing permeant size because sorption dominates. The glassy membrane is much less permeable the permeability decreases with increasing permeant size because diffusion dominates (84).

For gas and vapor systems, by combining the laws of sorption and diffusion in the sequence (l)-(3), general permeation equations are obtained. For sheet membrane samples of polymers above Tg, if the definition is made that permeation coefficient Q = Ds,... 

Dual-Mode Gas Sorption and Diffusion in Glassy Polymer Membranes. 97... 

Dual-Mode Ionic Sorption and Diffusion in Charged Polymer Membranes.. 109... 

Sefcik M. D., Raucher D. The Matrix Model of Gas Sorption and Diffusion in Glassy Polymers, to be published... 

In the following chapter we present the matrix model of gas sorption and diffusion in glassy polymers which is based on the observation that gas molecules interact with the polymer, thereby altering the solubility and diffusion coefficients of the polymer matrix. 

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. 

Fiarticle morphology porosity, relative length scale of polymer and pore phases, particle shape, distribution of phases in high-impact polypropylene Interphase heat and mass transfer phenomena Intraphase heat and mass transfer phenomena Observed kinetics, rate limiting steps Phase equilibrium, monomer sorption and desorption in polymer phase, diffusion Fbrticle agglomeration Micromixi ng... 

Free volume is an intrinsic property of the polymer matrix and is created by the gaps left between entangled polymer chains. Under the free volume model the absorption and diffusion of molecules in polymers depend greatly on the available free volume. For instance, many polymers show a sorption increase as the amount of free volume increases. One of the earliest models describing this behavior was developed by Fujita et al. [32]. Since then many researchers have worked with different models based on the free volume concept to describe sorption and diffusion in the glassy state [33-36]. 

Miguel, O., Barbari, T. A., and Iruin, J. J. (1999b). Carbon Dioxide Sorption and Diffusion in Poly(3-hydroxybutyrate) and Poly(3-hy-droxybutyrate-co-3-hydroxyvalerate). Journal of Applied Polymer Science 71,2391-2399. 

BAR Barrer, R.M. and Banie, J.A., Sorption and diffusion in ethyl cellulose. Part n. Quantitative examination of settled isotherms and permeation rates,/. Polym. Sci., 23, 331,1957. 

PARAMETERS INFLUENCING SORPTION OR DIFFUSION Molecule sorption and diffusion in a polymeric material are influenced by several factors, like the molecule structure, its concentration and its temperature, arrdthe polymer... 

Theodorou, D. N. Molecular simulations of sorption and diffusion in amorphous polymers. Plast Eng.-New York. 1996, 32, 67-142. 

This work offers a contribution to the understanding of some fundamental aspects of sorption and diffusion in glassy polymers. The research focuses on an extensive experimental study of sorption and mass transport in a specific polymeric matrix. A high free volume polymer, (poly l-trimethylsilyl-l-propyne) [PTMSP], has been used here in order to emphasise aspects of sorption and transport which are peculiar to polymer/penetrant mixtures below the glass transition temperature. The discussion of the experimental data presented in this work permits a clarification of concepts which are of general validity for the interpretation of thermodynamic and mass transport properties in glassy systems. 

Vittoria, V., Russo, R., de Candia, F. Solvent-induced crystallization of syndiotactic polystyrene in different liquids. Sorption and diffusion phenomena. Polymer, 32(18), 3371-3375 (1991). 

The main emphasis in this chapter is on the use of membranes for separations in liquid systems. As discussed by Koros and Chern(30) and Kesting and Fritzsche(31), gas mixtures may also be separated by membranes and both porous and non-porous membranes may be used. In the former case, Knudsen flow can result in separation, though the effect is relatively small. Much better separation is achieved with non-porous polymer membranes where the transport mechanism is based on sorption and diffusion. As for reverse osmosis and pervaporation, the transport equations for gas permeation through dense polymer membranes are based on Fick s Law, material transport being a function of the partial pressure difference across the membrane. 

Hietala, S., Maunu, S. L. and Sundholm, E. 2000. Sorption and diffusion of methanol and water in PVDE-y-PSSA and Nafion 117 polymer electrolyte membranes. Journal of Polymer Science Part B Polymer Physics 38 3277-3284. 

The discussion above explains why basic information on sorption and diffusion under the reaction conditions, especially at elevated pressures, is required for kinetic and mass- and heat- transfer modelling of catalytic polymerization reactors. If such information is sufficiently available, one should be able, for example, to compare the kinetics of gas-phase and slurry-processes directly by taking into account both gas solubilities in swollen polymers and the hydrocarbons used in slurry processes. 

Earlier work on the application of the concept of dual mode sorption and diffusion to glassy polymer-gas systems has been reviewed in detail 6) and important aspects of more recent work have been dealt with in more recent reviews 7 10). Eq. (5) was first applied by Michaels et al U). Sorption in the polymer matrix and in the specific sorption sites was represented by linear (Henry s law) and Langmuir isotherms respectively so that Sj in Eq. (5) is given by... 

---