Analysis of the Gel Point of Polymer Model Networks by Computer Simulations

Abstract

The gel point of end-linked model networks is determined from computer simulation data. It is shown that the difference between the true gel point conversion, p c , and the ideal mean field prediction for the gel point, p c,id , is a function of the average number of cross-links per pervaded volume of a network strand, P , and thus, contains an explicit dependence on junction functionality f . On the contrary, the amount of intra-molecular reactions at the gel point is independent of f in a first approximation and exhibits a different power law dependence on the overlap number of elastic strands as compared to the gel point delay p c − p c,id . Therefore, p c − p c,id cannot be predicted from intramolecular reactions and vice versa in contrast to a long standing proposal in literature.Instead, the main contribution to p c − p c,id for P > 1 arises from the extra bonds (XB) needed to bridge the gaps between giant molecules separated in space and scales roughly ∝ (P − 1) −1/2 . Further corrections to scaling are due to non-ideal reaction kinetics, composition fluctuations, and incompletely screened excluded volume, which are discussed briefly.

Theory of Flexible Polymer Networks: Elasticity and Heterogeneities

“…, in accordance with the result of numerical simulations [26]. A more rigorous description of this effect requires the inclusion of fluctuation corrections.…”

“…A similar effect was observed in numerical simulations of networks obtained near the gel point, which is an analog of the percolation transition in low-molecular-weight solids. It is shown that the elastic modulus of such networks vanishes at a finite density of the network monomers [26]. One can estimate the corresponding shift in critical conversion p cµ at which G = 0, compared with the gel point at the conversion p cγ , at which the average degree of polymerization of soluble molecules diverges.…”

“…A more rigorous description of this effect requires the inclusion of fluctuation corrections. Inside the strongly fluctuating Ginzburg region, Equation (18), the overlap parameter of elastically effective chains is small (which is why strong density fluctuations develop in this region), and they can be described by critical exponents of percolation theory, see Reference [26].…”

The hierarchical bulk molecular structure of poly(acrylamide) hydrogels: beyond the fishing net

“…A large number of studies exist, highlighting the heterogeneous character of the polymer network structure of vinylic hydrogels. [8][9][10] In this study, we build upon existing knowledge of this system by combining it with a focused analysis of the network architecture in relation to the bis-acrylamide (bis-AAm) cross-linker concentration. The distribution of the cross-linker in the polymer network is analyzed on both nanoscopic and microscopic scales by means of smallangle X-ray scattering (SAXS) and light transmittance.…”

Bond percolation on simple cubic lattices with extended neighborhoods

“…A theoretical analysis of finite-z corrections for the bond thresholds has recently been given by Frei and Perkins [32]. Some related work on polymer systems has also appeared recently [33].…”