Theory of Gelation

Theories of Gelation. The classical or mean field theory of polymeri2ation (4) is useful for visuali2ing the conditions for gelation. This model yields a degree of reaction, of one-third at the time of gelation for chemical species having functionaUty equal to four. Two-thirds of the possible... 

Molecular Weight Distributions in Nonlinear Polymers and the Theory of Gelation... 

The theory of gelation (Flory, 1953,1974) has been summarized in Section 2.2.3. This theory regards gelation as the consequence of the random crosslinking of linear polymer chains to form an infinite three-dimensional network. The phenomenon is, of course, well illustrated by examples drawn from the gelation of polycarboxylic acids by metal ions. 

Cations can be seen as acting as ionic crosslinks between polyanion chains. Although this may appear a naive concept, crosslinking can be seen as equivalent to attractions between polyions resulting from the fluctuation of the counterion distribution (Section 4.2.13). Moreover, it relates to the classical theory of gelation associated with Flory (1953). Divalent cations (Zn and Ca +) have the potential to link two polyanion chains. Of course, unlike covalent crosslinks, ionic links are easily broken and re-formed under stress there could therefore be chain slipping and this may explain the plastic nature of zinc polycarboxylate cement. 

The paper first considers the factors affecting intramolecular reaction, the importance of intramolecular reaction in non-linear random polymerisations, and the effects of intramolecular reaction on the gel point. The correlation of gel points through approximate theories of gelation is discussed, and reference is made to the determination of effective functionalities from gel-point data. Results are then presented showing that a close correlation exists between the amount of pre-gel intramolecular reaction that has occurred and the shear modulus of the network formed at complete reaction. Similarly, the Tg of a network is shown to be related to amount of pre-gel intramolecular reaction. In addition, materials formed from bulk reaction systems are compared to illustrate the inherent influences of molar masses, functionalities and chain structures of reactants on network properties. Finally, the non-Gaussian behaviour of networks in compression is discussed. 

As expected, addition of IV tended to increase the sol fraction in the cured specimens. The statistical theory of gelation (9) can be used to calculate the expected gel fraction as a function of crosslink functionality, extent of reaction, and proportion of difunctional units in the mixture. For these mixtures, an adequate fit to the extraction data was obtained by assuming that the primary reaction is isoindoline formation (Figure 5). Triazine or phthalocyanine formation alone cannot account for the data. 

F 4. — Molecular weight distributions in nonlinear polymers and the theory of gelation. Principles of Polymer Chemistry, 347 ff. New York Cornell University Press 1953. 

The gel point t is one of the most important kinetic characteristics of curing, since it describes the attainment of a certain critical conversion responsible for the transition from the first to the second stage of the process. In the classical statistical theory of gelation developed by Flory [8], the 1 point is characterized by the appearance in a reactive system of a macromolecule with an infinitely large molecular weight, -+ oo. Viscosity becomes infinite which corresponds to the above condition. 

In order to obtain a clearer understanding of prepolymer technology, the theory of gelation is first discussed. A classification of prepolymers is then introduced and finally the available quantitative data on stmcture-property relationships are reviewed. References cited are usually to the most complete and general source and not necessarily to the original publication. 

Table 2.3. Scaling exponents for classical and percolation theories of gelation ...

This is identical with Eq. (P5.24.7) derived from the Flory theory of gelation. 

According to the Flory-Stockmayer (29a) theory of gelation, the gel point, corresponding to the formation of an infinite network, is reached when one cross-link per initial polymer molecule present has formed. 

P ectin, a long-chain poljrmeric galacturonide partly esterified with methanol, has been used in the preparation of jellies and similar food products for over a hundred years. The mechanism by which it forms gels is not clearly understood and more information on the factors influencing pectin gel formation is required to develop a more exact theory of gelation. 

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