Relative free volume

The three most important factors in the equation are the viscosity and the thermodynamic parameters G and Gm- The viscosity can be approximated between the liquidus temperature, Tuq, and the liquid-+glass transition temperature, Tg, by a Doolittle expression involving the relative free volume (Ramachandrarao et al. 1977) while G can be calculated using the relationship... 

It is now generally accepted that the viscous flow of polymeric liquids is connected with chain segment rotation, i.e. with configurational entropy. From this point of view Miller concluded that the Simha-Boyer equation was not correct since the relative free-volume in SB theory equals zero at 0 K, not at T = T0. If the latter... 

On the other hand, as in the analysis of the previous systems the temperature dependence of the a relaxation follow the Vogel-Fulcher-Tamman-Hesse (VFTH) [88-90], The 7% values obtained are 337 5 and 274 5 for PBCHM and PBCHMM respectively. By this way and using equation (2.31) the m parameter obtained are 1579 and 1804 and the relative free volumes at Tg are 3.2 and 2.6% for PCBuM and PCHBMM, respectively, in good agreement with the free volume theory. 

The higher n-alkanes and polyethylene (PE) have been studied by Patterson and Latham (9). There is a general relation between V(d and relative free volume for all the homologs ... 

Figure 5. Relative free volume as measured by PALS as a function of relative draw ratio for (a) PVOH and (b) HDPE. Curve drawn to indicate trend.

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.

The net relative free volume accessible to oPs (X33l3+X4 l4) is 80% larger in TFE/PDD87 than in TFE/PDD65. 

At high density, hard spheres with D > 1 have a solid phase which terminates in the close-packed crystal. The equation of state for this phase has a first-order pole at the crystal packing fraction rjo (For hard disks and spheres, the close-packed crystals are those of hexagonal closest packing and cubic closest packing the packing fractions Tjo are respectively 0.90690 and 0.74048.) The equation of state is usually ej ressed as a series in the relative free volume... 

Since it is very difficult to measure experimentally the viscosity of supercooled liquid, there have been few measurements of it. In this case, the viscosity can be generally described as being between the liquidus temperature Tm and the glass transition Tg using a Doohttle-type expression involving the relative free volume/r (Ramachandrarao, et al., 1977) as... 

The openness of solvents is measured by their relative free volumes, (V V )/V. The fluidity, = 1/r/, of a liquid was shown by Hildebrand and Lamoreaux [33] to be a linear function of (V - V )/V for various kinds of liquids as the temperature changes, but when this notion is applied to a comparison of solvents at a given temperature. 

Structuredness The openness of a solvent is defined as the difference between its molar volume and its intrinsic volume. The relative free volume, (V-V )IV, (Section 3.3.1) of the binary aqueous mixtures with cosolvents may be practically prorated according to the mole fractions of the components, because the excess molar volumes are only small fractions of the molar volumes of the mixtures. 

As it is well-known [60], in deformation process up to yielding point in polymers the dilatation effect is observed, characterized by relative free volume increase by the value A. As the estimations shown [7], the increment usually makes up the value -0.06 0.08. This effect induces a corresponding structural changes, which can be described with the aid of the... 

The phenomenon observed here, which is common to most polymerization reactions, demonstrates that polymers can interfere sterically with processes involving movement of parts of the guest molecules (fluorescent probes). As the polymer glassy state is approached, the relative free volume diminishes sharply, and the medium viscosity increases rapidly mobility becomes restricted and the deactivation rate of the probe becomes controlled by the microscopic free volume provided by the polymer. This accounts for the abrupt increase in fluorescence until the limiting conversion is reached, at which point fluorescence levels off. 

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