Carothers theory

While the theory of Flory underestimates the gel point, the theory of Carothers overestimates it. For example, for the case of a trifunctional and bifunctional reaction system presented above, at equimolar reactive groups, while Flory s theory forecasts pg = 0.707, Carothers theory forecasts a value of pgei=0.833, while the experimental pgei is 0.765-0.775. Recently, however [18,19], thermodynamic reasons why the two formulas should be combined came to Kght. This led to the proposal of a very simple equation affording much higher precision than each theory alone. This simple equation also gave much better precision of all the very complex and difficult to use theories devised and presented since Flory s 1942 one ... 

Calculate the critical extents of reaction for gelation using the Statistical Theory of Flory and the Carothers Theory. 

Flory statistical theory givesPc = 0.816 whereas Carothers theory gives = 0.917. 

Stine refused to take no for an answer. That very week, he sent his second-in-command to Harvard with orders to stay until Carothers took the job. Why was Du Pont so very interested in Carothers Of course, Carothers exceptional scientific talent and outstanding recommendations were significant, but Du Pont had another reason as well. During Carothers visit to Wilmington, he had expressed interest in the theory of polymers— and polymers were Du Pont s bread and butter. 

On another occasion, Carothers left his parents in Arden to attend a chemical meeting at Cornell University. Two years before, he had panicked at the Yale meeting, but this time he felt happy and free. My head was practically on fire with theories, he said. When his parents returned to Des Moines after a year in Wilmington, Carothers celebrated with a little boulder hopping in nearby Brandywine Creek. 

Bayer, A. 1878. Phenol-formaldehyde condensates. Ber. Bunsenges. Phys. Chem., 5 280, 1094. Brunelle, D.J. and Korn, M. 2005. Advances in Polycarbonates. Oxford University Press, New York. Carothers, W.H. 1929. An introduction to the general theory of condensation polymers. J. Amer. Chem. Soc., 51 2548. 

In 1934 Paul Flory was hired to work with Carothers to help gain a mathematical understanding of the polymerization process and relationships. Thus, there was an early association between theory and practice or structure-property relationships. 

Early developments in polymers were largely empirical because of a lack of knowledge of polymer science. Advancement in polymers was rapid in the 1930s and 1940s because of the theories developed by Staudinger, Carothers, Mark, and many other scientists. 

First study of co-polymerisation by Wagner-Jauregg Early theories of rubber-elasticity (Mark, Meyer, Guth, Kuhn and others) Carothers famous work proves by means of organic synthesis that polymers are giant, stable molecules. He first proves it by the discovery of neoprene (polychloro-butadiene), then by the condensation polymerisation of amino acids and esters. As a consequence the first fully synthetic textile fibre, nylon, is developed. In Carothers group Flory elucidates the mechanisms of radical and condensation polymerisation... 

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. 

In 1928 directors at E. I. du Pont de Nemours Company (Du Pont) placed Dr. Wallace H. Carothers in charge of fundamental research into what are now classic studies on the formation of polymer chains. During his years at Du Pont, Carothers published his theory on polycondensation, and discovered both neoprene and nylon. 

The gel theory of Carothers [4] in which the critical degree of conversion at the gel point (pgei) is defined as pg = 2jf, with /being the average functionality of the monomers in the system. 

However, a second theory, older than Flory s, does indeed exist. This is the theory of Carothers. According to Carothers... 

This equation is nothing other than the average of the equations of Carothers and Flory, and for instance yields a p i = 0.770, while the most exact of the complex theories yields a Pgei = 0.800 [18,19] for the simple case just shown above. The 1/2 operator is not there (but ajr is) in the case where no bifunctional monomer is present. This is valid also for the generalized Eqs. (17) and (18) which follow and which have been developed from Eq. (16) above. For two monomers, Eq. (16) can be developed to eliminate the presence in the... 

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