Mechanical selfsimilarity of polymers during chemical gelation

Abstract

Network polymers near their gel point exhibit selfsimilar mechanical behavior, as expressed by power law relaxations. The range of selfsimilarity is defined by two limiting length scales. The upper limit is the correlation length, defined by the linear size of the typical cluster, and a lower limit, roughly given by the size of one preformed linear chain, i. e., the mean distance between crosslinks. The correlation length increases with the approach to the gel point, and diverges at the critical extent of reaction, i. e., the gel point where the infinite cluster is formed. Above the gel point, it decreases again with further crosslinking. Dynamic mechanical measurements of the complex modulus at the gel point show a power law in the frequency dependence over the entire frequency range, monitoring selfsimilarity. Swelling effects reduce the fractal dimension of the percolation cluster form 2.5 to 2. It is shown how the power law G(ω) ∼ω 1/2, found by experiment, is connected to the structure of the polymeric cluster.