Free volume elements

The difference between the solution-diffusion and pore-flow mechanisms lies in the relative size and permanence of the pores. For membranes in which transport is best described by the solution-diffusion model and Fick s law, the free-volume elements (pores) in the membrane are tiny spaces between polymer chains caused by thermal motion of the polymer molecules. These volume elements appear and disappear on about the same timescale as the motions of the permeants traversing the membrane. On the other hand, for a membrane in which transport is best described by a pore-flow model and Darcy s law, the free-volume elements (pores) are relatively large and fixed, do not fluctuate in position or volume on the timescale of permeant motion, and are connected to one another. The larger the individual free volume elements (pores), the more likely they are to be present long enough to produce pore-flow characteristics in the membrane. As a rough rule of thumb, the transition between transient (solution-diffusion) and permanent (pore-flow) pores is in the range 5-10 A diameter. 

Reverse osmosis, pervaporation and polymeric gas separation membranes have a dense polymer layer with no visible pores, in which the separation occurs. These membranes show different transport rates for molecules as small as 2-5 A in diameter. The fluxes of permeants through these membranes are also much lower than through the microporous membranes. Transport is best described by the solution-diffusion model. The spaces between the polymer chains in these membranes are less than 5 A in diameter and so are within the normal range of thermal motion of the polymer chains that make up the membrane matrix. Molecules permeate the membrane through free volume elements between the polymer chains that are transient on the timescale of the diffusion processes occurring. 

Although the literature of gas separation with microporous membranes is dominated by inorganic materials, polymer membranes have also been tried with some success. The polymers used are substituted polyacetylenes, which can have an extraordinarily high free volume, on the order of 25 vol %. The free volume is so high that the free volume elements in these polymers are probably interconnected. Membranes made from these polymers appear to function as finely microporous materials with pores in the 5 to 15 A diameter range [71,72], The two most... 

Drusch S, Ratzke K, Shaikh MQ et al. (2009) Differences in free volume elements of the carrier matrix affect the stability of microencapsulated lipophilic food ingredients. Food Biophysics 4 42—48. 

Figure 1. Free volume distribution from the Cohen-Tumbull model, po is the probability of finding an infinitely small free volume element, y/. The relative free volume element size is 7v/cvf>.

Positron Annihilation Lifetime Spectroscopy of HIQ-40 Films Positron annihilation lifetime spectroscopy has emerged as a sensitive technique to probe free volume in polymers (33, 34), PALS uses orthoPositronium [oPs] as a probe of free volume in the polymer matrix. oPs resides in regions of reduced electron density, such as free volume elements between and along chains and at chain ends (33), The lifetime of oPs in a polymer matrix, T3, reflects the mean size of free volume elements accessible to the oPs. The intensity of oPs annihilations in a polymer sample, la, reflects the concentration of free volume elements accessible to oPs. The oPs lifetime in a polymer sample is finite (on the order of several nanoseconds), so PALS probes the accessibility of free volume elements on nanosecond timescales (33),... 

Table II presents PALS results and other physical property data for an as-cast HIQ-40 sample and for a sample that was annealed for one hour at 200 C. The annealing protocol results in a 2,5% increase in density, which corresponds to a 17% decrease in fractional free volume. The acetone diffusion coefficient decreases almost five-fold and acetone solubility decreases by approximately 90% as a result of the ordering induced by the annealing protocol. The oPs lifetime decreases by 14%, suggesting that the average free volume cavity size decreases due to annealing. Based on the oPs lifetime, the mean free volume cavity diameter may be estimated (36) these values are reported in parentheses in Table n. The PALS I3 parameter, which reflects the relative concentration of free volume elements in the polymer matrix, is approximately 22% lower in the annealed, liquid crystalline sample.

PALS results allow a comparison of the effect of polymer substituent and backbone chemistry on the relative size and concentration of free volume elements. The methane solubility is not strongly correlated with the PALS free volume parameters (similar to the result shown for fractional free volume in Figure 6a). The methane diffusivity and permeability of these polyisophthalamides are strongly... 

Figure 7. Relationship of methane diffusivity and permeability and PALS relative free volume element size. The transport data were determined at 3S C and an upstream pressure of 3 atmospheres, and the PALS data were collected at ambient conditions.

X3 l3+X4 l4), in PTFE, only 0.4% in TFE/PDD 65 and TFE/PDD87 and only 0.2% in PTMSP. Thus, the vast majority of the free volume accessible to oPs is in the larger free volume elements. 

The relative concentration of the free volume elements, I3 and I4, is 20% and 10% lower, respectively, in TFE/PDD87 than in TFE/PDD65. Thus, while the size of these elements is higher in the copolymer with more PDD, the concentration is lower. 

These composite results suggest that the distribution and availability of free volume in PTMSP and the TFE DD copolymers are very different. Both PTMSP and the TFE/PDD copolymers are high Tg, stiff chain materials, so it is unlikely that the vast differences in accessible free volume and permeability coefficients is solely related to great differences in segmental dynamics between these materials which would render the free volume in PTMSP much more accessible on the time scales appropriate for PALS and permeation. Rather, it seems more likely that free volume elements in PTMSP are interconnected and span the sample, providing extremely efficient pathways for penetrant diffusion. In fret, the notion of interconnected free volume elements in ITMSP has been invoked to explain the unusual transport... 

However, the fast physical aging limits the practical application of PTMSP membranes. One solution is the cross-linking of PTMSP, which stabilizes the large excess free volume elements and hence improves physical stability [86-88]. Cross-linking generally reduces gas permeability due to free volume reduction, while the polymer network becomes more size selective and gas selectivity increases. 

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