Trapped Entanglements in Polymer Networks

Abstract

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.

Theory of Flexible Polymer Networks: Elasticity and Heterogeneities

“…The case P (0) ≈ 1 with the loop size l ≈ 1 describes the "elementary networks" in Equation (13). In accordance with the results of numerical simulations [13], the loop length l decreases with dilution and with increasing functionality f of cross-links.…”

“…The case P (0) ≈ 1 with the loop size l ≈ 1 describes the "elementary networks" in Equation (13). In accordance with the results of numerical simulations [13], the loop length l decreases with dilution and with increasing functionality f of cross-links. Note that the minimal size loops do not directly determine the network elasticity since each elastically effective chain is simultaneously part of a large number of loops.…”

The Non‐effect of Polymer‐Network Inhomogeneities in Microgel Volume Phase Transitions: Support for the Mean‐Field Perspective

“…Our results suggest considerably strong and efficient crosslinking: in all our samples, ν eff is multiple times larger than what can be calculated from the stoichiometric ratio between crosslinker and monomer. This finding can be interpreted by assumption of additional network nodes that are formed by trapped chain entanglements in the crosslinked networks . Despite this deviation from ideality, we observe consistent correlation of the parameters ν eff and N eff with the extent of gel heterogeneity determined by static light scattering: the more inhomogeneous the gels are, the lower is ν eff and the higher is N eff .…”

Olympic Gels: Concatenation and Swelling

“…This expectation stems from the fact, that the structure of any network can be decomposed into a set of connected cycles [20,37] whereby the average cycle size is of the order of 8 chains for typical strand lengths around 50-100 Kuhn segments between 4-functional junctions. [38,39,40] Therefore, most elastomers are located in the regime f n / N where des-interspersion of non-concatenated cyclic structures upon swelling occurs. Based upon our results, therefore, we expect a clear impact of desinterspersion onto the equilibrium swelling degree of polymer gels.…”