Influence of the Linear Chain Length Between Branch Points on Branched Polymer Structure and Rheology.
The structural and rheological properties of randomly branched polymer systems are studied as the chain length N between branch points is systematically varied. The experimental and theoretical literature are reviewed and presented in a manner that forms a coherent picture of the gelation process for any N. The observed critical exponents depend on N, and the Ginzburg criterion is applied to understand this crossover phenomena. We present experimental measurements of oscillatory shear modulus, viscosity, recoverable compliance, intrinsic viscosity, weight-average molar mass, and molar mass distribution for three series of randomly branched polymers, below their gel point, with N = 2, 50, and 900. Data from a system with N = 20, studied previously, are also included and discussed. Analysis of the molar mass distribution is shown to be the most unambiguous manner to measure the static scaling exponents and determine N. In the crossover between the critical percolation (N = 2) and vulcanization (N = 900) limits, analysis of experimental and simulated molecular structure data verify the predicted dependence of the Ginzburg crossover point as a function of N. A speculation for the form of the cutoff function in the critical percolation limit is also proposed and shown to be consistent with high quality simulation data taken from the literature. We demonstrate that dynamic scaling holds in systems with N< 50 and find that the branched polymer Rouse theory is the only model to correctly predict the rheological response for systems with N = 2, 20, and 50. In the vulcanization limit, the Rouse model does not describe the rheological properties; Its failure is attributed to the existence of entanglements between the long linear chains between branch points. The influence of the linear sections is apparent in both the static and dynamic quantities. Interestingly, dynamic scaling seems to apply in systems with N> 50, but the values of the observed exponents vary with N.
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- Physics: Condensed Matter; Chemistry: Polymer; Engineering: Chemical