Swelling volume fraction

Feed ratio of OC2H5 TEOS groups to OH chain ends. b Volume fraction of polymer present at swelling equilibrium in benzene at room temperature. c Elongation at initial upturn in modulus. d Ultimate strength as represented by the nominal stress at rupture. Energy required for rupture... 

FIGURE 38.3 Volume swelling (%) of composites against volume fraction of fiber. (Reprinted from Naskar, A.K., Bhowmick, A.K., and De, S.K., J. Appl. Polym. Sci., 84, 622, 2002. With permission from Wiley InterScience.)... 

For the purpose of testing the validity of what we have called the deformation factor, it is convenient to plot rl a — l/a ) vs. a if rubbers swollen permanently (not merely for purposes of equilibration) are included, the quantity roV2 /(a — l/a ) is to be preferred, where To is the tension referred to the cross section when unswollen and unstretched, and V2 is the volume fraction of polymer in the swollen mixture (see Appendix B, Eq. B-5). According to theory, both of these quantities should be independent of the deformation, and the latter should be independent of the degree of swelling as well. On the basis... 

Polymer gels and ionomers. Another class of polymer electrolytes are those in which the ion transport is conditioned by the presence of a low-molecular-weight solvent in the polymer. The most simple case is the so-called gel polymer electrolyte, in which the intrinsically insulating polymer (agar, poly(vinylchloride), poly(vinylidene fluoride), etc.) is swollen with an aqueous or aprotic liquid electrolyte solution. The polymer host acts here only as a passive support of the liquid electrolyte solution, i.e. ions are transported essentially in a liquid medium. Swelling of the polymer by the solvent is described by the volume fraction of the pure polymer in the gel (Fp). The diffusion coefficient of ions in the gel (Dp) is related to that in the pure solvent (D0) according to the equation ... 

Volume fraction of polymer at equilibrium swelling in CgHg. 

Here, u2,r is the polymer volume fraction in the relaxed state, which is defined as the state of the polymer immediately after crosslinking but before swelling. 

Fiber swelling, in paper pulping, 21 434 Fiber volume fraction, 26 775, 776 Fiber-wall morphology, 16 3-5, 11 Fiber width (FW), 18 148 Fibrates, 5 145... 

For comparison, a telechelic sulfonated polystyrene with a functionality f = 1.95 was prepared. In cyclohexane the material forms a gel independent of the concentration. At high concentrations the sample swells. When lower concentrations were prepared, separation to a gel and sol phase was observed. Thus, dilution in cyclohexane does not result in dissolution of the gel even at elevated temperatures. Given the high equilibrium constant determined for the association of the mono functional sample, the amount of polymer in the sol phase can be neglected. Hence, the volume fraction of polymer in the gel phase can be calculated from the volume ratio of the sol and gel phases and the total polymer concentration. The plot in Figure 9 shows that the polymer volume fraction in the gel is constant over a wide range of concentrations. 

Here, nt is the moles of the swelling agent, and u2 are the corresponding volume fractions of swelling agent and polymer, yA is the Flory interaction parameter, and k and T are the Boltzmann constant and absolute temperature, respectively. 

Swelling equilibrium is defined as the point at which the activity of the solvent is unity, or p, = p , and the polymer volume fraction at this point is defined as o2jS (see Fig. lb). At equilibrium, Eq. (9) becomes,... 

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