Gelation theory

Menjivar, J.A. "On the Use of Gelation Theory to Characterize Metal Crosslinked Polymer Gels," Chapter 13, Advances in Chemistry Series 213, American Chemical Society, Washington, DC 1986. 

Ziegler and Foegeding, 1990. See above. Extensively reviews the rheological properties of various protein gels. Also includes an introduction to gelation theories. 

On the other hand, Simpson et al. [29] investigated the structure of DAP prepolymer in detail, demonstrating that cyclization is an important phenomenon in DAP polymerization and should have a major bearing on gelation theory. It was suggested that the existence of extensive formation of cyclic structures may be partially responsible for the poor correlation between the Stockmayer equation and actual degree of conversion at gelation. 

An abundance of instances of the large deviation prompted us to check the validity of Flory and Stockmayer s gelation theory (F-S theory) as a next step. 

As is evident fium the above mechanistic discussion, the problems involved in the network formation of fi-ee-radical multivinyl polymerization are quite complicated and many factors are relevant to the network formation processes and their contributions depend on the polymerization conditions. Thus, finding an appropriate model for a comprehensive gelation theory and, moreover, controlling the network structure are very important but they are quite difficult subjects. In the polymerization of multivinyl compounds having different es of vinyl... 

Theoretical and experimental treatments of gels go hand-in-hand. The former are covered first because they will help us understand gel point and other concepts. Two main theories have been used to interpret results of experimental studies on gels the classical theory based on branching models developed developed by Floiy and Stockmayer, and the percolation model credited to de Gennes. Gelation theories predict a critical point at which an infinite cluster first appears. As with other critical points, the sol-gel transition can be in general characterized in terms of a set of generally applicable (universal) critical exponents. 

Gelation Theories 237 where and are the number of moles of A and B in the reactive mixture. Despite... 

One major use of polyesters, the alkyd coating resins, is based on random prepolymers reacted with unsaturated fatty acids. Gelation phenomena have been studied extensively and the gelation theories of Carothers, Flory, and Stock-mayer were developed with polyester random prepolymers. Only recently, Gordon (iJ, 12) has extended the gelation theory to the structopendant polyester system cross-linked by vinyl monomers. 

Statistical network models were first developed by Flory (Flory and Rehner, 1943, Flory, 1953) and Stockmayer (1943, 1944), who developed a gelation theory (sometimes referred to as mean-field theory of network formation) that is used to determine the gel-point conversions in systems with relatively low crosslink densities, by the use of probability to determine network parameters. They developed their classical theory of network development by considering the build-up of thermoset networks following this random, percolation theory. 

In the traditional gelation theory formulated by Flory (1) and Stockmayer (2), it is assumed that like functional groups are equally reactive and all reactions occur intenaolecularly before the gel point. Subsequently, beyond gelation, finite species formed in the sol portion are limited to acyclic trees. This is not correct because intramolecular reaction leading to the formation of ring structures in a random polycondensation must occur. The effect of cyclization has been treated by various approaches, e.g. JacObson-Stockmayer ring-chain factors (3), cascade theory (4), and rate theory... 

J. A. Menjivar, On the Use of Gelation Theory to Characterize Metal Crossllnked Polymer Gels, Polym. Mater. Sci. Eng., 51 88 (1984). 

We generalize the treatments of the postgel regime by Pearson-Graessley [11-13] in classical gelation theory to multiple junctions [ 14]. Let (/c = 2,3,4,...) be the junction... 

Strictly, the power 3/2 in (10.21) should be replaced by v+y — 1 for swollen polymers in a good solvent, where = 3 is the space dimension, v = 3/5 Flory s exponent (Section 1.6), and y =7/6 the critical exponent for the total number of self-avoiding random walks [31]. However, we neglect the excluded-volume effect since both our solution theory and gelation theory are based on the mean-fleld treatment. 

Within the bounds of this chapter it is not possible to review the developments in gelation theories, both classical and modern , involving scaling-theory corrections to mean-field exponents, the... 

Figure 5.10 Gelation theories (Schematic), (a) Flory s model (molecular functionality / = 3). (b) Percolation on a square lattice. In each case, a spanning gel molecule is embedded in the sol. (From Ref. 23.)...

---