Free volume of polymer

This apparent anomaly may be due to increased dipolar contributions as well as to possible decrease in the free volume of polymer. Free volumes of the resin... 

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 rotors allow us to study changes in free volume of polymers as a function of polymerization reaction parameters, molecular weight, stereoregularity, crosslinking, polymer chain relaxation and flexibility. Application to monitoring of polymerization reactions is illustrated in Box 8.1. 

Correlation of the permeation properties of a wide variety of polymers with their free volume is not possible [32], But, within a single class of materials, there is a correlation between the free volume of polymers and gas diffusion coefficients an example is shown in Figure 2.24 [33], The relationship between the free volume and the sorption and diffusion coefficients of gases in polymers, particularly glassy polymers, has been an area of a great deal of experimental and theoretical work. The subject has recently been reviewed in detail by Petropoulos [34] and by Paul and co-workers [35,36],... 

The free volume of the polymer solution may be written by assuming additivity of the free volume of polymer and monomer, and is given by... 

The holes from the free volume affect the mechanical, thermal and relaxation properties of polymers. Despite the importance of free volume only limited experimental data about the free volume of polymers has been reported. This is mainly due to the lack of suitable probes for open volumes of molecular dimensions of a few A and the short time scale of many of the dynamic holes (from as short as 10"l3s). 

The permeation of a simple permeant, e.g., O2, through a polymeric membrane could occur, in principle, by two different mechanisms. One is the transport through pores, and the other is the transport through the free volume of polymer solid. The size of pore and its distribution is the most crucial parameter in the former case (porous membrane), and the value of a is determined by the molecular sizes of permeants A and B. The values of Ps are in the reverse order of the size of permeant, i.e., Pn2 > -P02 > -Pco2, and P can be dealt as a kinetic parameter. 

Increased moisture can plasticize a polymer matrix. Water acts not only as a solvent for small solutes but as an agent that increases the free volume of polymer molecules and their degree of segmental motion (i.e., water is differentially solvated and mobilizes parts of the heterologous structure of protein and polysaccharide polymers). When polymers, or segments within them, are given more freedom of movement, then other diffusion-based phenomena might occur more readily. Chemical reactions should not necessarily be expected to be affected by increased free volume of the polymer, and a review of the literature yields little support for this theory for most chemical reactions. Instead, some of the increased reaction rates that have been attributed to plasticization are instead the result of increased solvation. 

PALS is a well-established technique for studying the free volume of polymers... 

For a further comparison of the free volume of polymers with different Tg values and different chemical structures, we show in Figure 11.11 the fractional hole free volume h calculated from PVT experiments employing the S-S equation of state. Polymers denoted as conventional (hydrogen polymers and others) have hole fractions ranging up to 0.15, while at 606 K Teflon AF2400 has a value of A = 0.374. 

The experimental data on the temperature dependence of Xi of polymer-solvent systems are described by the dependence Xi =on-p/T. Often in temperatmes below 1(X) C, P < 0. In a wide temperature range, this dependence decreases non-linearly. The negative contribution to AS and positive contribution to the Xi parameter are connected with the difference of free volume. On heating the difference in free volumes of polymer and solvent in-... 

Results of shock tests (Ast) in very big degree depend on plasticity of samples. On the other hand, in plasticity brings the contribution not all free volume, but only his "effective" part. Efficiency of influence of additives PhOC on shock durability depends, thus, on a parity of the sizes of a molecule of the additive with "effective" free volume of polymer and, thus, from as far as eoneentration PhOC is picked optimum up. In a case block-copolyester BSP-7D in eonditions of shock tests are salts of iron and phosphinic acids for the PC-trivalent iron phosphinate. 

In 1962 Simha and Boyer (132) proposed another relationship for calculating the free volume of polymers at T. The authors found empirically that... 

The increase of free volume of polymers containing methyl substituents leads to the decrease of dielectric constant compared with related pol5rmers which do not contain such substituents as seen in Table 3.1. 

Gas diffusivity and permeabihty are generally understood to dqiend sensitively on free volume, which corresponds to the amount of free space, in a polymer matrix(7fti7). Generally, linear correlations between log(D) or log(P) and reciprocal free volume are observed(7,3,77-27). Gas diffusion coefficients, D, are often correlated with fractional free volume of polymers, Vf, as follows. 

There are some problems of interest in the description of the free volume of polymers. As has already been mentioned, both fluctuation free volume and clusters have a thermofluctuational nature. It is obvious that the energy of thermal fluctuations can be expressed as kT (where k is Boltzmann s constant, T is temperature), while microvoid formation energy is equal to [80] ... 

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