Computer simulation of end-linked elastomers. I. Trifunctional networks cured in the bulk

Abstract

The end linking of difunctional poly(dimethylsiloxane) with trifunctional cross linkers in the bulk has been simulated with a computer. A random array of primary chains with a Gaussian end-toend distribution is generated in an image container on the computer. By joining chain ends at nearby junctions, inter-and intramolecular reactions occur in all species, allowing formation of cyclic structures of any size. At high extents of reaction, the sol components extracted from the spanning forest thus constructed consist of a substantial amount of cycles such as cyclic dimers. The effect of intramolecular reaction increases the extent of reaction by several percent for molecular weights in the range of thousands. Structural statistics of various types of network imperfections and the cycle ranks of the networks are reported. The gels obtained at complete conversions contain loop defects, their populations increasing with lower molecular weights of the prepolymers. The elastic activities of nonstoichiometric systems are compared and discussed.

The effect of bimodality on tensile properties of filled silicone networks

“…These inactive points may act as stress centers and hence responsible for the inferior tensile properties. The enhancement in the tear, tensile and tensileoptic behaviour due to bimodality in the unfilled state of polydimethylsiloxanes has been dealt in detail in literature [7,[25][26][27][28][29][30]. A number of studies including experimental, numerical and analytical ones have been carried out to predict the said enhancement and ascertain its relationship with the various parameters of the structure of the bimodal polymer network.…”

Random Networks, Graphs, and Matrices

“…Computer modeling of network formation [17,18] with evaluation of the eigenvalue spectrum of the KL matrix [19] has thus far offered the best insights into this problem. The particularly delicate problem of evaluating k 1 for large networks is critical, since on the face of it there is a problem with the modulus in Equation (22).…”

“…Finally, the dr term is just the volume element on the space of rigid rotations [consult your favorite differential geometry book [9] for details on the Lie group SOðmÞ]. Since the rigid body rotation does not appear in the potential of mean force [see Equation (17)], this integrates to an uninteresting constant. Thus, we are left with the significant terms for the volume element in polar coordinates, where dU signifies the volume element on the Stiefel manifold.…”

Forced Gelation in an Off‐Stoichiometric Copolymerization of A2 and B3 Monomers

“…Much preferred became the off-lattice models. [19][20][21][22][23][24] The most theoretically studied gelling system was the model of step-growth homopolymeri-zation of an A f monomer ( f ¼ 3, 4,..). [17,[25][26][27] Another widely studied system was the one comprising A f and B g (or RA f and R'B g ) monomers (f > 1, g > 2), which is more relevant to real systems (A and B denote the kinds of functional groups that are capable to react with each other, e.g.…”