Free volume, definition

R.E. Robertson Can I ask you a question about that as well Free volume has no totally agreed upon significance and since I ve been working with Simha, I m persuaded that his free volume is a better parameter for some things than the Williams-Landel-Ferry free volume. When you say it s iso free volume, is this iso free volume in the same system, the same free volume definition as Simha uses ... 

The free volume is considered to represent the difference between the actual volume of the liquid (or the amorphous polymer) and the minimum volume which it would occupy if its molecules were packed firmly in contact with each other. Incompressible molecules with rigid dimensions are implied in this definition of a free volume. The unrealistic nature of this implication undermines precise determination, or even an exact definition, of the free volume. The concept has proved useful nevertheless. 

Although, the true density of solid phase p=m/Vp (e.g., g/cm3) is defined by an atomic-molecular structure (/ ), it has become fundamental to the definition of many texture parameters. In the case of porous solids, the volume of solid phase Vp is equal to the volume of all nonporous components (particles, fibers, etc.) of a PS. That is, Vp excludes all pores that may be present in the particles and the interparticular space. The PS shown in Figure 9.17a is formed from nonporous particles that form porous aggregates, which, in turn, form a macroscopic granule of a catalyst. In this case, the volume Vp is equal to the total volume of all nonporous primary particles, and the free volume between and inside the aggregates (secondary particles) is not included. 

It was shown, that the conception of reactive medium heterogeneity is connected with free volume representations, that it was to be expected for diffusion-controlled sohd phase reactions. If free volume microvoids were not connected with one another, then medium is heterogeneous, and in case of formation of percolation network of such microvoids - homogeneous. To obtain such definition is possible only within the framework of the fractal free volume conception. 

It was also noted by Farrington and co-workers that the chemical nature of the end-groups may have a substantial effect on the viscosity of bulk dendrimers, even under iso-free volume conditions [49]. This seems consistent with the establishment of interdendrimer interactions and supramolecular organization at rest in the bulk state. However, as in most other areas of dendrimer rheology, more data are desirable before definite conclusions can be drawn. 

In an effort to optimize the solvent-containing passive sampler design, Zabik (1988) and Huckins (1988) evaluated the organic contaminant permeability and solvent compatibility of several candidate nonporous polymeric membranes (Huckins et al., 2002a). The membranes included LDPE, polypropylene (PP), polyvinyl chloride, polyacetate, and silicone, specifically medical grade silicone (silastic). Solvents used were hexane, ethyl acetate, dichloromethane, isooctane, etc. With the exception of silastic, membranes were <120- um thick. Because silicone has the greatest free volume of all the nonporous polymers, thicker membranes were used. Although there are a number of definitions of polymer free volume based on various mathematical treatments of the diffusion process, free volume can be viewed as the free space within the polymer matrix available for solute diffusion. 

The lower cycle represents the chemical changes occurring during polymerization and relates them to the free volume of the system. In general, free volume of a polymer system is the total volume minus the volume occupied by the atoms and molecules. The occupied volume might be a calculated van der Waals excluded volume [139] or the fluctuation volume swept by the center of gravity of the molecules as a result of thermal motion [140,141]. Despite the obscurity in an exact definition for the occupied volume, many of the molecular motions in polymer systems, such as diffusion and volume relaxation, can be related to the free volume in the polymer, and therefore many free volume based models are used in predicting polymerization behavior [117,126,138]. 

Now the definition of 0 is generalized to include the free volume per plasticizer molecule. Equation 14a is equivalent to the one proposed by Fujita and Kishimoto (6) for the effect of plasticizer on T0 as shown in Table II. Originally was defined... 

The average free volume per particle is (fifree) = Vfree/N = k/0. Therefore, comparison of the average free volume to its definition from a probability distribution,... 

The definitions of the free-volume fraction discussed above are dependent on taking the volume as an initial marking-off state, i.e. on the manner of calculation. It is already apparent here that there is some uncertainty regarding the physical meaning of free-volume. 

Covacs6 proposed another definition of the fractional free-volume. As the extrapolated volume of supercooled liquids reaches the crystalline state, vc, at temperature rc > 0 K, it is possible to compare this critical temperature with rg , the limit glass temperature at infinitely slow cooling. Free-volume in the crystalline state is assumed to be zero. In this case the value /g according to Doolittle may be compared with /g, c, which characterizes the excess free-volume of glass as compared with the crystalline state ... 

This condition may be regarded as an additional criterion of the glass-liquid transition. According to this definition, the greater the free-volume for segmental motion the smaller the cooperative unit necessary for such motion and for the maintenance of isomobility at Tg. 

Some very interesting ideas concerning the relationship between free-volume formation and the energy of one mole of hole formation were developed in detail by Kanig42. Kanig introduced some improvements to the definition of free-volume, On the basis of Frenkel s ideas43 he divided the free-volume into two parts, one of which is determined only by the thermal vibrations of atoms in the lattice of a real crystal while the other is connected with inherent free-volume, i.e. voids and holes. It is the latter that makes possible the exchange of particles, i.e. the very existence of the liquid state. He introduced some new definitions of fractions of free-volume ... 

Equation (54) represents the ratio of real volume of holes and expansion volume to the total free-volume, as distinct from its usual definition as the ratio of free-volume to total volume, the latter being determined by... 

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