This work studies intramolecular reactions in irreversible linear and nonlinear random (co)polymerizations with computer simulations. We find a relative rate for the formation of rings of i chains proportional to i -3/2 in agreement with predictions of rate theory based on Gaussian chain statistics. This result is used to develop a general ansatz for ring formation in irreversible random polymerizations or in cyclization equilibria. Using the approximation c ext ≫ c int for the concentrations of reactive groups on the external molecules c ext and on the selected molecule c int, this ansatz reduces to a result previously found by Suematsu. In this special case we find that the ring size distribution R i is proportional i -5/2[(f − 1)(g − 1)p A p B] i -1, where f and g denote the functionality of two different types of molecules A and B, and p A and p B are the conversions of the reactive groups on the molecules, respectively. Our findings explain preceding experiments, simulations, and all results within this work as well as we can discuss the limitations of previous theoretical approaches.

The collapse transition of a single polymer chain in two and three dimensions was studied using the bond-fluctuation model. The obtained exponents ν of the scaling law 〈S2N〉∼N2ν agree with values proposed in the literature as well as above, at and below the Θ-temperature TΘ. Transition curves and scaling analysis plots are presented. The scaling function α3SτN1/2 vs τN1/2 has a pronounced maximum before leveling off in the fully collapsed regime in accordance with the theory [α2S=〈S2N〉/〈S2N〉Θ, τ=‖(T−TΘ)/TΘ‖]. An analyzing of the subchain distances leads to disagreements with the blob model. The subchains are locally swollen for T≳TΘ and shrunken for T<TΘ. The probability distribution function of internal distances for T≥TΘ can be described by scaling functions of the form fs(x)∼xκs exp(−Dsxδs) for large x, x being the scaled distance. In contrast for T<TΘ none of these functions describe the data. The dynamic properties above TΘ are in agreement with the Rouse model, but below TΘ differences occur; the center of mass diffusion becomes anomalous and the relaxation times rise with a power law in N of the form τi(N)∼N2+3/d (d being the dimension of space).

This work focuses on density, complexity, and experimentally observable effects of trapped entanglements in polymer networks. Using the bond-fluctuation method we crosslinked and end-linked systems with a random initial distribution of polymer and crosslinker. The structure of the generated networks has been analyzed by knot theory and graph theory concerning defects, ring structures, and trapped entanglements, resulting in a detailed description of network topology and connectivity. The knowledge on network structure is used to analyze computer simulations of swelling and solfraction experiments. The simulated swelling experiments show that the size of the fully swollen network depends strongly on the presence of trapped entanglements although the zero second Money-Rivlin term upon deformation indicates the absence of a tube like environment for individual network chains. Permanently trapped rings and the formation of network defects affect the weight of the measured gel component as function of the degree of crosslinking. The experimentally observed shift in size of the gel can be estimated based on the data of this study and is typically smaller than the shift due to ineffective reactions that lead to the formation of dangling rings and network defects.

A general theory is presented for computing the distributions and averages of the lengths of subchains and chain ends in cross-linked polymer networks. This theory was tested by computer simulations, and we show the results of both theory and simulations, for a better comparison. We find a significant difference between the values of chain ends and subchains depending on the extent of the reaction. As a consequence, the fraction of elastically active or effective material was clearly overestimated in previous works. We show how the different length distributions of intramolecular loops or cycles, subchains, and chain ends influence each other and how they can be combined into one general distribution. The influence of the spatial density or homogeneity of the chains, the functionality of the cross-links, the length distribution of the initial polymer chains, and other deviations from an idealized system are discussed briefly.

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