Free volume estimation

Fig. 37. Swelling efficiency and free volume estimation in well-cured Fi-berite 934 network epoxies, as affected by sub-Tf annealing. Percent swelling is plotted on the ordinate axis while percent of moisture uptake is plotted on the abscissa...

The value of activation volume for I is in excellent agreement with the free volume estimated in the previous section. The free volume is consequently a dominant factor deciding the ease of forming the TICT state. Both concentration and pressure effects can be thus interpreted by a single factor of free volume. 

A. Kreituss and H, L. Frisch. Free Volume Estimates in Heterogeneous Polymer Systems, 1. 

The crosses in Figure 11.9 show the free volume for PC calculated from Eq. (11-5) and the determined o-Ps hole size (u/,). The specific hole number A was used as a fitting parameter. A constant value of A = 0.67 x 10 was sufficient for the temperature range between 300 and 570 K to get agreement between the free volumes estimated from = A (w ) and Vf = hV. The volume- elated hole density A = A /y varies with T. Therefore, the hole volume ( > cannot be scaled to the hole fraction h to determine Aft [Higuchi et al., 1995 Schmidt and Maurer, 2000b Kilbum et al., 2005]. 

FIGURE 11.21 Summary and classification of the temperature variation of the mean, (Vh)> and mean dispersion, Oh, of the local tree-volume sizes for PFE as example. Vf is the specific hole free volume estimated from the S-S equation-of-state analysis of PVT data. (From Dlubek et al [2004e], Dlubek [2006].)... 

A new group contribution model has been developed which accurately describes the CO2 and CH4 permeability and selectivity of 87 polymers. Unlike previous group contribution models, it is not based on fiactional free volume estimated from density measurements but rather, in this approach, the volume fractions of the structural elements comprising the polymer serve as the basis for correlation. The volume of these groups were calculated from commercially available computer software. This new model quantifies a variety of structure-property relationships which have been reported in the literature. 

T Aa is seen to be a function of V only, and since, according to quite well established observations of Simha and Boyer this product is a constant for all polymers (10), eqn. (1) implies an iso-free volume glass transition state. In fact, using the empirical Simha-Boyer constant of 0.113 for T Aa, it is found that V = 0.025 at T, identical with the free volume estimated from tne WLF equation (11). The hole formation energy, E, in the Gibbs-DiMarzio treatment is a function of T alone and is directly proportional to the latter, as is seen in eqn. (2). 

The time-temperature superpositioning principle was applied f to the maximum in dielectric loss factors measured on poly(vinyl acetate). Data collected at different temperatures were shifted to match at Tg = 28 C. The shift factors for the frequency (in hertz) at the maximum were found to obey the WLF equation in the following form log co + 6.9 = [ 19.6(T -28)]/[42 (T - 28)]. Estimate the fractional free volume at Tg and a. for the free volume from these data. Recalling from Chap. 3 that the loss factor for the mechanical properties occurs at cor = 1, estimate the relaxation time for poly(vinyl acetate) at 40 and 28.5 C. 

These two nomographs provide a convenient means of estimating the equivalent diameter of almost any type of particle Figure 1 of regular particles from their dimensions, and Figure 2 of irregular particles from fractional free volume, specific surface, and shape. 

To evaluate the time-dependent function, X(t), a simple model of diffusion is proposed. Starting from Langmuir adsorption theory, we consider that liquid molecules having diffused into the elastomer are localized on discrete sites (which might be free volume domains). In these conditions, we can deduce the rate of occupation of these sites by TCP with time. Only the filhng of the first layer of the sites situated below the liquid/solid interface at a distance of the order of the length of intermolecular interaction, i.e., a few nanometers, needs to be considered to estimate X(t). 

Figure 10 (a) Free-volume persistence time extracted from the free-volume autocorrelation function (Eq. [9]) for an attractive colloidal fluid as a function of the strength of the interparticle attraction, (b) Comparison of colloidal self-diffusivity (closed symbols) with that estimated using the free-volume scaling relationship D — A(v )2 /tf discussed in the text (open symbols). Data taken from Ref. 75. 

After the initial volume estimate has been determined, testing of a pilot recovery system should be initiated to evaluate recovery rates. However, factors that significantly affect recovery rates include the areal distribution and geometry of the free-hydrocarbon product plume, type(s) and design of recovery system selected, and the performance and efficiency of the system with time. 

Further development of the Flory-Huggins method in direction of taking into account the effects of far interaction, swelling of polymeric ball in good solvents [4, 5], difference of free volumes of polymer and solvent [6, 7] leaded to complication of expression for virial coefficient A and to growth of number of parameters needed for its numerical estimation, but weakly reflected on the possibility of equation (1) to describe the osmotic pressure of polymeric solutions in a wide range of concentrations. 

Molecular modeling techniques are a powerful tool to obtain a very detailed insight in the three-dimensional structure of dendrimer molecules at the atomic level. They have been applied to calculate sizes of the polypropylene imine) dendrimers and radial density profiles in order to estimate the free volume inside the dendrimers, as well as to make predictions about de Gennes dense-packed generations. The molecular modeling work by Coussens and co-workers [20] was focused on the generations 1-5 of the DAB-dendr-(CN)n and DAB-dendr-(NH2)n (n = 4, 8, 16,32, 64). 

Equilibrate a 1 x 10 cm Sephadex G-25 column with 50 ml Soln. F. Apply the iodinated sample, elute with Soln. F, and collect 1-ml fractions. The iodinated protein appears in the void volume, and free iodine-125 elutes with the total volume. Estimate its radioactivity and calculate the specific radioactivity (Bequerel per milligram of protein). 

Hougham et al. reported that, on average, the decrease in dielectric constant in a polyimide series that was attributable to the change in fractional free volume that accompanied fluorine substitution was greater than 50% Recently, these authors have further refined these estimates. ... 

This is shown semiquantitatively for a series of polyimides, where hydrogen/ fluorine, and symmetric/asyirunetric analogues were synthesized and measured. The free-volume contribution is estimated by a free-volume normalization method developed for this purpose.In these materials, the contribution of changes in free volume to the observed change in dielectric constant ranged from 25 to 95% in moisture-free materials. ... 

Recently, the same series of six polyimides was studied by positron annihilation spectroscopy to determine die fractional free volume directly. In all three H/F analogue pairs, the increased free volume of the fluorinated polymer accounted for around 50% of the observed decrease in refractive index and dielectric constant. This result confims an astonishingly large free volume contribution predicted by our earlier estimates.Future work will investigate the generality of this result to other polymer systems. 

The molecular volume Vt of each species (considered impenetrable) may be estimated from empirical Van der Waals radii or other theoretical measures of molecular bulk, and all species are considered to have access to the same free volume in the numerator. However, Vexcl is often neglected entirely for gaseous reactions at low density, and approximations to trans are generally found to have little effect on overall AGrxn or KQq. 

The cavity of the A-type zeolite is approximately spherical with diameter 11.4 A. If the occluded molecule is regarded as a hard sphere, the free diameter of the cavity (the distance through which the center of the occluded molecule can move) will be reduced by a distance a corresponding to the van der Waals diameter of the molecule. The free volume of the cavity, and hence the value of K0 may be estimated on this basis. This method of calculation is equally applicable to other zeolites which consist of discrete cavities interconnected through small (eight-membered) oxygen windows. 

Studies by Nishiyama and Fujihara [149] utilizing azobenzene derivative (27) as isomerizable chromophores have demonstrated the importance of reaction cavity free volume in L-B films. The L-B films of amphiphilic derivative 4-octyl-4 -(3-carboxytrimethyleneoxy)-azobenzene (27) upon irradiation was found to be stable, no geometric isomerization of the azobennzene moiety occurred. This compound forms L-B films with water soluble polyallylamine 28 at an air-water interface. Reversible cis-trans photoisomerization occurs in the film containing 28. The reversible photoisomerization reaction in polyion complexed films is thought to occur because of the increased area per molecule provided in the film. The cross sections of molecule 27 in the pure film and in film containing 28 were estimated to be 0.28 and 0.39 nm2. Such an increased area per molecule... 

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