Swelling equations

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)... 

This result is the analog of the swelling equation (XIII-39) for a network. It rests principally on the assumption that the intramolecular interactions of the segments with one another are the same as would obtain for a cloud of particles, not connected to each other, but having the same radial distribution as the average radial density distribution occurring for the molecule made up of a linear sequence of particles. 

F Horkay, AM Hecht, E Geissler. Effect of cross-links on the swelling equation of state Polyacrylamide hydrogels. Macromolecules 22 2007-2009, 1989. 

The expressions derived above may be inserted for Ai, N2 and Nz. They indicate the effect of temperature and concentration and also the absolute order of magnitude of the individual components contributing to Ng, If, as has happened repeatedly,the train of thought of the van der Waals theory is applied to solutions of this kind, we should insert the expression N/Vo in the volume correction. The term (v — b) generally used can be regarded as a first, but too strictly ideal, approximation. A better appi-oximation is the swelling equation by G. V. Schulz, who replaced the co-volume b by an expression dependent upon the concentration. 

Apart from the filler, the stiffening effect can also arise from the rubber network itself such as the crosslink concentration, as shown in Figure 3.9. The results shown here are based on compound formulations given in Table 3.4. The tensile modulus MlOO increased linearly with increasing crosslink concentration of the rubber network. The crosslink concentration was calculated by the Flory-Rehner equilibrium swelling equation ... 

Elastic Free Energy of Ddbnnation and Swelling Equations.232... 

Elastic Free Energy of Deformation and Swelling Equations... 

Equations (10), (38), (39) and (78) then lead to the isotropic swelling equation... 

For many years, the Flory-Rehner equilibrium swelling equation has served to relate the volume fraction of polymer in the swollen mass, Vu to the number of moles of network chains per cm, i i ... 

J. L. Thiele and R. E. Cohen, Synthesis and Characterization of Single-Phase Interpenetrating Polymer Networks, Polym. Prepr. 19(1), 137 (1978). Swelling and modulus behavior Polystyrene/polystyrene IPNs. Swelling equation. 

Swelling curves for neutral NIPAAm gel, 77 Swelling equation, 86 Swelling equilibrium, 71, 73-5, 79, 81 Swelling relaxation time, 86 Sylpinski gasket, 137 Syndiotactic polystyrene, 177 Syndiotactic polystyrene/o-dichlorobenzene solutions, 360 Synthetic gels, 7 Synthetic polymers, 110-12... 

VARIATIONS OF THE BASIC SWELLING EQUATION Highly Crosslinked Networks... 

The previous swelling equations are valid for molecularly homogeneous systems. However, some polymer gels contain pores or voids which contribute to the volume of the system. Such is the case with many porous ion-exchange resins or porous superabsorbent particles. Therefore, the measured polymer volume fraction in the swollen gel, )2,app> s larger than the actual polymer volume fraction in the swollen polymer, U2 s. The apparent polymer volume fraction in a porous system may be... 

Comparison of Temperatures Used for U02 Swelling Equation From FRAPCON/MATPRO... 

Swelling equations for phantom networks are recovered through ic=0 and K(A )=0. Equations... 

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