Equilibrium swelling ratio

These simplified relationships offer a clearer insight into the dependence of the equilibrium swelling ratio qm on the quality of the solvent as expressed by Xh on the extent of cross-linking. Because of the nature of the approximations introduced to obtain Eqs. (40) and (40 ), their use as quantitative expressions must be limited to networks of very low degrees of cross-linking in good solvents. 

It has been shown in Chapter XI that the force of retraction in a stretched network structure depends also on the degree of cross-linking. It is possible therefore to eliminate the structure parameter ve/Vo) by combining the elasticity and the swelling equations, and thus to arrive at a relationship between the equilibrium swelling ratio and the force of retraction at an extension a (not to be confused with the swelling factor as). In this manner we obtain from Eq. (XI-44) and Eq. (39)... 

Fig. 135.—The relationship between the equilibrium retractive force T(x (in lbs./in.2) at 241 °C for various multilinked poly (e-caproamides) at the extensions (a) indicated, and their equilibrium swelling ratios in m-cresol at 30°C. O, tetralinked polymers octa-linked polymers. The lines have been calculated according to Eq. (41), with appropriate revision for the octafunctional case (broken lines), an arbitrary value being assigned to the parameter Xi for each elongation. (Schaefgen and Flory.33)...

Fig. 137.—Equilibrium swelling ratio qm of poly-(methacrylic acid) gels prepared by copolymerizing methacrylic acid with 1, 2, and 4 percent (upper, middle, and lower curves, respectively) of divinylbenzene plotted against degree of neutralization i with sodium hydroxide. (Katchalsky, Lifson, and Eisenberg. )...

Solvent Resistance. One of the distinct advantages of a crystalline thermoplastic elastomer over an amorphous one should be its superior solvent resistance, since the latter types are generally soluble. Table III shows the swelling behavior of the H2-BIB triblocks in toluene at 25°C. It can be seen that the maximum swelling obtained was in the case of the H2-BIB-34, which had the lowest end-block content. Furthermore, the equilibrium swelling ratio of 3-26 obtained for this polymer is considerably less than the value of 5 or 6 generally exhibited by a well-vulcanized natural rubber. 

The two network precursors and solvent (if present) were combined with 20 ppm catalyst and reacted under argon at 75°C to produce the desired networks. The sol fractions, ws, and equilibrium swelling ratio In benzene, V2m, of these networks were determined according to established procedures ( 1, 4. Equilibrium tensile stress-strain Isotherms were obtained at 25 C on dumbbell shaped specimens according to procedures described elsewhere (1, 4). The data were well correlated by linear regression to the empirical Mooney-Rivlin (6 ) relationship. The tensile behavior of the networks formed In solution was measured both on networks with the solvent present and on networks from which the oligomeric PEMS had been extracted. 

Assuming a homogeneous distribution of crosslinks, the equality, given by Eq. (4), becomes independent of conversion. Thus on complete conversion (x = 1), Qx(x)reduces to Q°° (initial degree of dilution of the monomers) and Qv(x) can be replaced by the experimentally determined equilibrium swelling ratio Qv. Accordingly, the condition of phase separation becomes... 

Fig. 9. Equilibrium swelling ratio as a function of pH for a samples containing PEG grafts of molecular weight 1000 with the ratio of MAA PEG being ( ) 60 40, ( ) 50 50, ( ) 40 60...

Another unique feature of ionized NIPA gel has been found recently both of the equilibrium swelling ratio a and the first-order transition temperature T0 depend strongly on the shape of samples [31]. The measurement of equilibrium a has been made on ionized NIPA gel rods of various diameters, and also on plates and cubes. The gel contained 680 mM NIPA, 20 mM acrylic acid (AA), and 8.6 mM BIS. All samples were prepared from the same pregel solution at the same time so as to guarantee that the composition and the structure of all samples were the same. 

Fig. 5. Temperature dependence of equilibrium swelling ratio of poly(APy)/PEO IPNs in water PEO repeating unit 20.6% mole fraction (A) 36.3% mole fraction (V) 49.2% mole fraction ( ) 58.7% mole fraction ( ) crosslinked polyfAPy) ( ) crosslinked PEO (O)...

Fig. 6. Effect of the poly(APy)/PEO IPNs composition on the equilibrium swelling ratio at 10 °C...

NMR spectroscopy. On the other hand it was found that T2 of the solute in the rubber cured in the presence of triallyl cyanurate (TAC) increased on curing, despite the equilibrium swelling ratio decreasing. This surprising result was explained by a change in the polymer-solvent interactions on copolymerisation with TAC. 

Figure 1. Equilibrium uptake of phenol at Figure 2. Equilibrium swelling ratio of PNIPA gel in 20 °C V phenol, O resorcinol, and water ( ), 5 ( ) and 50 (A) mM aqueous...

The equilibrium swelling ratio hf> of PNIPA gels of a specific [monomer]/[crosslinker] ratio depends on the temperature and the concentration... 

At swelling equilibrium, the elasticity is balanced by the osmotic pressure n of a semidilute solution of uncrosslinked chains at the same con-centration. Since the modulus is proportional to the elastic free energy per unit volume, any gel swells until the modulus and osmotic pressure are balanced. The equilibrium swelling ratio Q is the ratio of the volume in the fully swollen state and the volume in the dry state ... 

From the condition of swelling equilibrium [Eq. (7.72)] using Eqs (7.74) and (7.75) for -solvents, the equilibrium swelling ratio is obtained ... 

However, in practice Eq. (7.84) is not as useful as Eq. (7.77). Most good solvents are not in the athermal limit (with vseZ ) meaning that the exact value of the excluded volume (or x) must be known to calculate N from equilibrium swelling measurements in a good solvent, as discussed in the next section. As in a 0-solvent, the modulus in the dry state G(l) is universally related to the equilibrium swelling ratio Q in an athermal solvent ... 

A network with strands of number-average degree of polymerization iV=100 has equilibrium swelling ratio Q = 25 in an athermal solvent. Assuming the network was prepared in an athermal solvent, estimate the preparation concentration. 

Consider a PDMS network prepared in the dry state that swells to an equilibrium swelling ratio of 2 = 4 in the concentrated regime (0-like swelling). Estimate the dry modulus of the network at room temperature. Compare your result with Fig. 7.17 and estimate the numerical prefactor in Eq. (7.91). 

As usual, the equilibrium swelling ratio is obtained by setting pj - Pj = 0 and solving for 92. Let us now apply the above formalism to experimental rubber swelling data. 

Swelling of elastomers by liquid is known to be a diffusion controlled process and up to the equilibrium swelling ratio, the volume of liquid absorbed is proportional to the square root of the time during which the elastomer has been immersed in the liquid. For most liquids, the rate of penetration depends also upon the viscosity of the swelling liquid rather than its chemical nature. 

Prior to the start of each experiment, the plugs were equilibrated with 0.03M phosphate buffer (pH 7.4) at 4 C for at least 2 hours. This time period was found to be sufficient for the cartilage specimens to attain their equilibrium swelling ratios. The buffer contained, in addition to the dissolved salts, 1 x 10 M phenylmethylsulfonylfluoride (PMSF). This compound inhibited degradative enzyme reactions from occurring within the tissue during the experimental period (17). All experiments were carried out at room temperature. The tissue s load-deformation and load dissipation characteristics were found to be insensitive to temperature variations in this small range (23-27 C) (18). 

Finally, the total swelling ratio is obtained by using (1) combined with (2)-(8). A typical plot of the swelling behaviour for different kinds of gels in a solution bath is depicted in Fig. 4 and schematically in Fig. 5. In Fig. 4, the equilibrium swelling ratio q = VIVq - where V is the actual volume of the gel immersed in solutions of different salt concentrations and Vo represents the volume of the xerogel - of two gel cylinders of PAAm/PNa A and PAAm/PAA is plotted as a function of the outer KCl concentration. 

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