Dependencies of swelling coefficients

Erman B, Flory PJ (1978) Theory of elasticity of polymer networks. II The effect of geometric constraints on junctions. J Chem Phys 68 5363—5369 Erukhimovich IYa, Irzhak VI, Rostiashvili VG (1976) On concentration dependence of swelling coefficient of weakly non-Gaussian macromolecules. Polym Sci USSR 18 1682-1689... 

The stability of interpolymer complexes of linear and crosslinked polymers was studied in water-DMSO mixtures. It is known that DMSO is the acceptor of H-bonds and interpolymer complexes stabilized by H-bonds are usually destroyed in this solvent (3,4). Figures 3 and 4 represent the dependencies of swelling coefficients Kg and intrinsic viscosities [q] of [AA-VBE]/[CPVP] and [TMVEP-VP]/[LPAA] complexes on water-DMSO mixture. 

Figure 2. Dependencies of swelling coefficients Ks(l) and binding degree 0 (2) on the logarithm of concentration of linear [AA-VBE] copolymer. [Gel]=l,8 10 mol/L.

Figure 3. Dependencies of swelling coefficients Kg and intrinsic viscosity [r ] in [AA-VBE]/[CPVP] (1) and [AA-VBE]/[LPVP] (2) systems on water-DMSO composition.

Figure 4. Dependencies of swelling coefficients Kg of CPAA (1), intrinsic viscosity h] of [TMVEP-VP]/[LPAA] (2) and Kg of [TMVEP-VP]/[CPAA] complexes (3) on water-DMSO composition.

The composition of polyacrylic acid-crosslinked poly-Nvinylcaprolactam (PAA-CPVCL) complexes determined from the dependence of swelling coefficients of CPVCL on concentration of linear poly aery lie acid is equal to 1 1. The swelling coefficients of pure gel and gel-polymer complex in water-DMSO mixtures are compared in Figure 7. Poly-N-vinylcaprolactam gel undergoes sharp volume-phase transition in dependence of the thermodynamic quality of the solvent. In the case of gel-polymer complex at first the destruction of this complex occurs in mixtures containing up to 30 vol.% of DMSO, then the behavior of the system becomes similar to that for pure crosslinked polymer in water-DMSO mixtures. 

Figure 6.1.3. Kinetic curves of plane layer swelling at different values of concentration dependence of diffusion coefficient (e=0.1,d = 2/9) a - power law mode (l-s = 0 2-s=l 3-s = 1.5 4-s = 2.5) b - exponential (5 - s = 5) and blow-up mode (6 - s = 5.5). [Adapted, by permission, from E. Ya. Denisyuk, V. V. Tereshatov, Vysokomol. soed., X42,74 (2000)].

An improved model in regard to the simple model presented in Section 9.4.2 has been cut out for more realistic conditions [42]. Not only is the swelling process explicitly tied to an ionic pressure, but there are also other improvements the transport description includes the solvent flow as weU as the dynamics of charged species, the dependence of diffusion coefficients on the gel density is accounted for, and, finally, the kinetic toy model is replaced by a reaHstic model of a spatially bistable reaction. We consider that the functional unit HA of the polyacid has a unique weak-acid function. 

Figures 3.33-3.36, left-side lines, show the dependence of permeability coefficients (a) and diffusion coefficients (b) on fractional accessible volume (FAV) in the system one polymier—different gases, after swelling with SC-CO2. Table 3.20 presents the slope of these dependences (B) before and after swelling with SC-CO2. This slope can be considered as general selectivity of a polymier to the studied gases. In Table 3.20, it can be seen that with regard to permeability coefficients, the selectivity increased for all polymers from 4 to 49%. With regard to diffusion coefficients, the selectivity increased for polymers 3 and 6, but it decreased for polymers 4 and 5. For these polymers 4 and 5, the increase of free volume is significantly lower than in case of polymers 3 and 6 (Table 3.11).

FIG. 14-2. Dependence of diffusion coefficient of n-hexadecane on the degree of cross-linking in three polymers in the rubberiike state at 25°C. (PB) 1,4-Polybutadiene, cis trans vinyl = 40 53 7 (NR) natural rubber (pips denote four different initiai molecular weights before cross-linking, from 2.3 to 7.7 X 10 ) (SBR) styrene-butadiene random copolymer, 23.5% styrene. Abscissa is moles effective network strands per cubic centimeter estimated from swelling measurements. (Chen. )... 

The advantage of using the time lag method is that the partition coefficient K can be determined simultaneously. However, the accuracy of this approach may be limited if the membrane swells. With D determined by Eq. (12) and the steady-state permeation rate measured experimentally, K can be calculated by Eq. (10). In the case of a variable D(c ), equations have been derived for the time lag [6,7], However, this requires that the functional dependence of D on Ci be known. Details of this approach have been discussed by Meares [7], The characteristics of systems in which permeation occurs only by diffusion can be summarized as follows ... 

Both the Yasuda et al. and Schnitzer theories indicate that the key variables defining permeability in a gel are the swelling degree of the gel and the average dimension of the solute. Thus the dependence of permeability on swelling degree for a responsive gel inert to solutes can be predicted using the theory of Yasuda et al. to obtain the ratio D/Dc (the ratio of the diffusion coefficient of a solute in the gel to its value in free solution) and the theory of Schnitzer for ideal size exclusion to obtain K. A dimensionless permeability can be defined as the... 

The diffusion coefficient for water is also strongly dependent on interaction with the polymer. Polymers with many H bonds forming groups increase the D value as one of the consequences of the beginning of swelling. A good approximation is ... 

In both cases, an analysis of the diffusion front as a function of time shows a t2 dependence of the front line which indicates Fickian diffusion and allows for the determination of a diffusion coefficient according to x2 = 2Dt from the slope of the curves in Fig. 24. The inter-diffusion coefficient was measured at [1.15 + 0.05] x 10 9m2/s, while the self-diffusion coefficient was measured at [8.4 + 0.5] x 10 10m2/s, which is the same order of magnitude as that recorded for non-swelling technical-grade kaolinite at similar water content.97 This indicates... 

In selective separation of hydrocarbons from their mixtures with air or from their aqueous solutions, it makes sense to use membranes based on rubbery polymers, whose permeability increases with the decrease in glass transition point. Permselectivity of rubbery polymers is dominated by the sorption component, which increases with condensability of the hydrocarbon penetrant. Higher activity of the component being separated in the feed mixture results in plasticization of the membrane and can make it swell. This can produce a non-monotonic dependance of selective properties of the membrane on activity of the component being separated. As a rule, permselectivity for mixtures of penetrants is significantly lower than their ideal values. Negative values of sorption heat of easily condensable hydrocarbons can result in existence of non-monotonic temperature dependencies of mass transfer coefficients. 

To convert the intra(self-)diffusion coefficients (Dseif) to inter(Fickian)diffusion coefficients (Dchem). Zawodzinski and co-workers [64] have corrected the selfdiffusion coefficients they measured for water activity coefficient variations along the membrane thickness dimension and for the effects of swelling of the polymer [87]. The resulting Dchem for water in the Nafion membrane was 2 x lOr cm /s at 30 °C and did not exhibit a strong dependence on water content (however, recent reevalua-... 

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