Diffuse movements, polymer penetrant molecules

The models most frequently used to describe the concentration dependence of diffusion and permeability coefficients of gases and vapors, including hydrocarbons, are transport model of dual-mode sorption (which is usually used to describe diffusion and permeation in polymer glasses) as well as its various modifications molecular models analyzing the relation of diffusion coefficients to the movement of penetrant molecules and the effect of intermolecular forces on these processes and free volume models describing the relation of diffusion coefficients and fractional free volume of the system. Molecular models and free volume models are commonly used to describe diffusion in rubbery polymers. However, some versions of these models that fall into both classification groups have been used for both mbbery and glassy polymers. These are the models by Pace-Datyner and Duda-Vrentas [7,29,30]. 

Diffusion of small molecular penetrants in polymers often assumes Fickian characteristics at temperatures above Tg of the system. As such, classical diffusion theory is sufficient for describing the mass transport, and a mutual diffusion coefficient can be determined unambiguously by sorption and permeation methods. For a penetrant molecule of a size comparable to that of the monomeric unit of a polymer, diffusion requires cooperative movement of several monomeric units. The mobility of the polymer chains thus controls the rate of diffusion, and factors affecting the chain mobility will also influence the diffusion coefficient. The key factors here are temperature and concentration. Increasing temperature enhances the Brownian motion of the polymer segments the effect is to weaken the interaction between chains and thus increase the interchain distance. A similar effect can be expected upon the addition of a small molecular penetrant. 

Although not necessary in terms of phenomenological applications, it is interesting to consider possible molecular meanings of the coefficients, Dq and D If two penetrants exist in a polymer in the two respective modes designated by "D" and "H" to indicate the "dissolved (Henry s law) and the "hole" (Langmuir) environments, then the molecules can execute diffusive movements within their respective modes or they may execute intermode jumps ... 

There is no fundamental qualitative difference in mechanisms of low molecular weight (MW) penetrant diffusion in polymers above and below glass transition temperature, Tg, of the polymers [5,6]. The difference lies only in the fact that the movement of structural units of the macromolecule that are responsible for the transfer of penetrant molecules takes place at different supermolecular levels of the polymer matrix. At T > Tg the process of diffusion takes place in a medium with equilibrium or near-equUibrium packing of chains, and the fractional free volume, P(, in the polymer is equal to the fractional free volume in the polymer determined by thermal mobUity of strucmral units of macromolecules V((T), i e., V(= vut). At r< Tg the process of diffusion comes about under nonequihbrium packing conditions, although there exists a quasi-equilibrium structural organization of the matrix, where Vf> It is assumed that in this case Vf= where is the fractional free volume... 

The kinetic diameter of penetrant molecules used in the gas permeation study are of the order CO2 (3.3 A) < CO (3.76 A) < CH4 (3.8 A). The selectivities of pure PDMS 2vol% Au/PDMS 3 vol% Au/PDMS are reported in Table. 1. As expected the pure polymer shows permeation to gas molecules in the order of their kinetic diameter, i.e., selectivity is based on the size exclusion of gas molecules or diffusion selective. Thus CO2 is more permeable in pure polymer and the selectivity of CH4 and CO is close to unity, which shows they are equally permeable. But when the filler loading of 2 3 vol% of Au NPs in PDMS, there is a reverse selective phenomenon of CO2, i.e., now CO2 is less permeable compared to higher kinetic diameter counterparts CO CH4. This could be CO2 has a quadrupole moment and the inter-connectivity of free volume elements enabled by Au NPS must have restricted CO2 movement. Also CO2 is expected to be more soluble in polymer with polar group, but the interaction of PDMS and Au NPs could have reduced the polarity of hybrid membrane. 

The penetration of a solvent, usually water, into a polymeric implant initiates dmg release via a diffusion process. Diffusion of dmg molecules through non-porous polymer membranes depends on the size of the dmg molecules and the spaces available between the polymeric chains. Even through the space between the polymer chains may be smaller than the size of the dmg molecules, dmg can still diffuse through the polymer chains due to the continuous movement of polymer chains by Brownian motion. 

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