Swelling equilibrium concentration

Figure 4. Variation o/F/2K as a function of for a typical polyacrylamide gel sample at the swelling equilibrium concentration 2,5 X 10 g cmr. The temperature was 22 °C. Static concentration fluctuations did not heterodyne completely the dynamic intensity at large values of the scattering vector. As a result F/2K varied with K. ...

The scaling behavior of D with the equilibrium polymer concentration was observed for several gels. The experimental values of the exponent ranged from 0.66 to 0.77 12, 16, 17, 28). The nonuniversal value of the exponent can be explained, as in the case of semidilute solutions, by crossover effects (28). Figure 6 shows the log-log plot of the cooperative diffusion versus the swelling equilibrium concentration for polyacrylamide gels at the swelling equilibrium. The value obtained for the exponent is very close to the theoretical prediction. 

Figure 15.11 Slopes P=A/(X2-X 1) as a function of the polymer volume fraction at swelling equilibrium in cyclohexane < >e in a series of end-linked PDMS networks with various lengths between junctions (A, A Mn = 25000 g.mol 1 B, B Mn = 10500 g.mol1 C Mn = 3100 g.mol"1) and polymer concentration during crosslinking in toluene (A, B, C vc = 0.7 A , B vc =1)...

To determine the equilibrium uptake of the polymers, the dry discs were placed in contact with the appropriate aqueous solutions for 48 hrs, a period determined from preliminary kinetic measurements. Aqueous solutions of high purity phenols (Merck) were used. Swelling was determined by weighing, while the uptake of the small aromatic molecules was calculated from the initial and equilibrium concentrations, Co and ce, of the phenols in the free liquid.13... 

If the monomer is a good solvent for the polymer, the latex particles might be assumed to expand indefinitely beeause of inhibition of monomer. An equilibrium monomer concentration and swelling equilibrium is reached, however, because the free energy decrease due to mixing of polymer and monomer is eventually balanced by the increase in surface free energy which accompanies expansion of the particle volume. 

Equations (3.46) and (3.47) can be used in two different ways. First, if the polymer-solvent interaction parameter, Xi27 is known and the value of V2 at swelling equilibrium is measured, then the molecular weight between cross-links, can be calculated using Eq. (3.46). Second, if the value of Mf. is known and V2 is measured at equilibrium, the polymer-solvent interaction parameter xi2 at polymer concentration V2 can be determined. 

The last relation is valid for any preparation concentration, and was obtained using Eq. (7.76). Such universal relations that are independent of the details of the preparation state are useful for predicting the equilibrium swelling in a -solvent from a measurement of the modulus of the network in the dry state (and vice versa). Equation (7.78) has not been tested in a -solvent, but it does describe swelling in concentrated solution, where ideal chain statistics apply (see the small swelling part of Fig. 7.17). 

From Figure 5.42 for the adsorption on sodinm-montmorillonite, the molec-nlar weight effect is not obvious. The adsorption reaches its plateau after about 600 mg/L equilibrium concentration. Comparing the two figures, we can see that the adsorption on sodinm-montmorillonite is much higher than calcinm-montmorillonite. Probably, it is cansed by the clay swelling in... 

Studied. A cross-linked polymeric network was prepared in the presence of a given amount of diluent. When the gelation reaction was complete, the gel sample was transferred to a cell containing an excess of solvent. The cell was placed onto the stage of a profile projector. As the gel swelled to its equilibrium concentration, its size was recorded photographically. This method allowed an accurate measurement of the time evolution of the gel size during the swelling process. 

Figure 6. Variation of the diffusion coefficient of polyacrylamide gels on a double logarithmic scale as a function of their concentration at swelling equilibrium. The temperature was 22 C. The slope was 0.74 and agreed with the exponent predicted by equation 21.

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