Free volume element sizes

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>.

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.

Wilks BR, Chung WJ, Ludovice PJ, Rezac MR et al. (2003) Impact of average free-volume element size on transport in stereoisomers of polynorbomene. 1. Properties at 35°C. J Polym Sci Part B Polym Phys 41 2185-2199... 

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. 

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... 

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. 

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. 

It has been reported recently that flux and even selectivity of PMP and PTMSP can be enhanced by the addition of nanoparticles (285, 286]. Merkel et al. [285] added fumed sihca to PMP and observed a simultaneous increase of butane flux and butane/methane selectivity. This unusual behavior was explained by fumed-silica-induced disruption of polymer chain packing and an accompanying increase in the size of free volume elements through which molecular transport occurs. Gomes et al. [286] incorporated nanosized sihca particles by a sol-gel technique into PTMSP and found also for this polymer a simultaneous increase in flux and selectivity. It has to be studied, if physical aging of the polyacetylenes is reduced by the addition of nanoparticles. 

In most of the two-component systems discussed so far, such as rubber-reinforced polyblends, the density or specific volume is approximately an average of the values for each component. There may be some exceptions to this generalization for example, if the smaller component fills free volume available in the major phase (Chander, 1971 Harmer, 1962 Huang and Kanitz, 1969). A similar but more important phenomenon exists when the volume available for filling by a monomer comprises not only free volume elements, but also gross pores, which may range in size from tens of angstroms to the order of micrometers or more. Examples of matrices may include partially sintered polymers, ceramics or metals, cement, concrete, minerals and rocks, paper, and wood (American Chemical Society, 1973). Clearly such systems tend to be complex even the matrix itself is often a multiphase material. 

Further information about the sizes of free volume elements or micropores can be obtained from inverse gas chromatography and positron annihilation lifetime spectroscopy (PALS), as is discussed later. 

The size of free volume elements in a glassy polymer can be estimated from the dependence of AHra on solute size [31]. A plot of against Vc, where 14 is the critical volume of the solute, generally passes through a minimum at a value of 14 that corresponds to a mean size of free volume elements. The data for n-alkanes in Table 2.5 show increasingly negative values of AH up to decane. Unfortunately, temperature limitations meant that... 

Reaction of a positron with an electron gives a metastable positronium (Ps) particle, which may have antiparallel spins (para-positronium, p-Ps) or parallel spins (ort/jo-positronium, o-Ps). Within a polymer, the longer lifetimes of o-Ps may be related to the size, concentration and distribution of free volume elements. There have been a number of studies of PIM-1 by positron annihilation lifetime spectroscopy (PALS) [33-36]. 

In Table 3.10, the sizes of free volume elements (Vf, A ) in PTMSN and other polymers are compared. They were found via PALS and IGC. The pairs of Vf values for PTMSN based on the IGC method correspond to the two minima shown in Figure 3.6. 

The scope of this chapter is to determine the average free volume size and size distribution for Hyflon AD (Figure 4.1) by the photochromic probe method and to study the transport of organic vapours in membranes of this polymer. The final aim is to correlate the transport data in the polymer with the free volume element (FVE) size distribution and to gain a better understanding of structure-property relationships in perfluoropolymers. 

Positron annihilation lifetime spectroscopy (PALS) studies the lifetime spectrum of ortho-positrons after being injected into the sample [3,4]. This lifetime depends on the probability of the ortho-positronium (o-Ps) particle (a hydrogen-like bound state formed by a positron-electron pair) to be quenched and annihilate. This probabihty is higher in condensed matter than in vacuum. Of all the probe methods PALS is nowadays probably the most versatile one and the most widely used. The o-Ps particle is the smallest probe available and can thus detect the smallest free volume elements furthermore, the method furnishes information on the average free volume size and on the FV size distribution. 

The size of the free volume elements is in the range of about 250-560in Hyflon AD60X and ca. 280-640 in Hyflon AD80X. This means that, if we assume a spherical... 

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