Comparative Experimental and Molecular Simulation Study of the Entropic Viscoelasticity of End-Linked Polymer Networks

Abstract

Bifunctional vinyl-terminated poly(dimethylsiloxane) chains are endlinked by tetrafunctional tetrakis(dimethylsiloxy)silane cross-linkers to produce irregular polymer networks with controlled stoichiometric imbalance and extent of reaction. The results are used as input to create comparative, nominally the same, three-dimensional Monte Carlo computer microstructures. Stress relaxation laboratory measurements and bead-spring molecular dynamics (MD) simulations are performed to estimate the relaxation shear modulus. It is found that the MD estimates reproduce quite well the measured equilibrium shear modulus G, despite the strikingly different time scales of measured and MD relaxation moduli. However, it is also seen that for near-stoichiometric networks the classical affine network model (ANM) gives equally good predictions of G. Additional MD simulations with phantom strands and regular networks are carried out. It is demonstrated that the ANM success is accidental since it is based on the fortuitous cancellation of two unrelated inaccurate assumptions of regular defect-free polymer networks and phantom strands that can freely pass through each other and themselves. Several contemporary theories of the elasticity of ideal Gaussian polymer networks are considered, and it is demonstrated that none of them is particularly suitable for predicting the shear modulus of the studied end-linked polydimethylsiloxane (PDMS) networks. It is shown that by taking into account the effects of trapped entanglements, reasonable qualitative and, at times, even semiquantitative predictions can be achieved. However, because of the ambiguity problems in the empirical fitting of the effective concentration of trapped entanglements, the resulting theoretical predictions are overall notably less accurate and less reliable than those obtained with the coarse-grained MD simulations that automatically account for the uncrossability of network strands. This emphasizes the incompleteness of the current theoretical descriptions of the effects of entanglements on the elastic behavior of irregular end-linked polymer networks with various values of the extent of reaction and stoichiometric imbalance and also suggests using our validated Monte Carlo microstructures to further study these effects.

Simulation of Elastomers by Slip-Spring Dissipative Particle Dynamics

“…In simulations, structural defects and slow relaxation often necessitate large time and length scales, something that is extremely challenging in molecular dynamics simulations . Coarse-grained and mesoscopic simulation techniques are capable of accessing these scales but usually have the disadvantage of employing soft-core potentials .…”

“…In simulations, structural defects and slow relaxation often necessitate large time and length scales, something that is extremely challenging in molecular dynamics simulations. 27 Coarse-grained and mesoscopic simulation techniques are capable of accessing these scales but usually have the disadvantage of employing soft-core potentials. 28 As a result, polymer chains and network strands may cross each other, which prevents these methods from correctly sampling related physical phenomena such as reptation 29 and in-tube relaxation.…”

Nonlinear Elasticity of Ultrasoft Near-Critical Gels with Extremely Sparse Network Structures Revealed by Biaxial Stretching

“…The Miller–Macosko model for nonlinear polymerization with w sol data enables us to evaluate the structural parameters of infinite networks, as was often done in previous studies. ,, The model relates the extent of reaction ( p ) for a functional group in the cross-linker with w sol . A recent study showed that the p values estimated using this approach agreed with those obtained directly in Monte Carlo simulations for the end-linked tetrafunctional PDMS gels prepared at 0.7 < r < 1.3. We apply this approach to the gels with various values of r ranging from the stoichiometric ratio ( r = 1) to the near-critical compositions, although the strict validation of the applicability to the vicinity of gel point remains to be accomplished.…”

Monte Carlo Evidence on Simple Conventional Means to Characterize the Final Extent of Reaction of Cured End-Linked Polymer Networks through the Miller–Macosko Nonlinear Polymerization Theory

“…Elastomers (cross-linked polymer networks) have gained much attention over the years owing to their vast variety of applications from drug delivery devices to vibration damping and noise cutting applications to automobile tires. , End-linked networks, elastomers in which polymer chains are connected to the network only by their ends, are highly examined by researchers due to their simplicity as well as their well-defined properties, which render them suitable candidates to be described theoretically and replicated computationally. Arguably, one of the most well-studied end-linked networks is polydimethylsiloxane (PDMS).…”

“…Although polymer networks commonly also include trapped entanglements, it is outside of the focus of this work. Loops, on the other hand, which comprise another important network imperfection, are more probable to form in gels rather than in polymer networks prepared in the molten state. , Dangling structures arise naturally during the end-linking process especially when more active precursors’ ends are present, r <1 . Further to this, as the end-linking process proceeds, it slows down at the end of curing, most likely due to the low concentration of the reactants and steric hindrance as well as topological restrictions that constrain the polymer motions .…”