Sol → gel transition with rings in a finite polycondensing system in solution
✍ Scribed by Biman Bagchi
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 430 KB
- Volume
- 113
- Category
- Article
- ISSN
- 0009-2614
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✦ Synopsis
We report a thccrciial formulation for the mean cluster size distribution in a ftite polycondensing system. Expressions for the mean number of n-mcrs wlthj bonds (fin,) are developed. Numenal calculations show that while the non-cychs molecules make the dominant contribution to the small clnsters, the large clusters ace dominated by cyclic si~uctures. The number of particles in ringless chains. N"nfl_-l, dcays monotomcally with n at all extents of reaction. but niii, becomes bimodal near the gel point. We also fiid that the solvent plays an important role in the cluster size distribution. 1 Introduction In this Letter we present a theoretlcal calculation of the mean cluster size distribution in a finite polycondensing system in solution with a good solvent. The main motivation of this work is to study quantitatively the effects of the intramolecular reactions on the cluster size distribution. Since the probability of an intramolecular reaction in a chain depends on the solvent and on the excluded volume interactions, these factors also influence the cluster size distribution, especially near the sol + gel transition_ Since the pioneering work of Flory [I.23 and Stockmayer [3] on polymer size distribution, several authors [4-101 have tried to include intramolecular reactions within the Flory-Stoclunayer framework, But these theories are fomally, and also practically, unsatisfactory for several reasons. Firstly, none of them describes the coexisting sol and gel phases. Secondly, they left out the important influence of the solvent and the excluded volume interactions. During the last decade, several important advances have taken place in the field of sol -+ gel tmnsition. The most important is the success of the ideas of critical phenomena [l-l] in describing the qualitative fea-* Contrii;rtion No. 253 from the Solid State and Structural Chemishy Unit.
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