Bifunctional vinyl-terminated poly(dimethylsiloxane) chains are end-linked 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.

中文翻译：

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末端连接聚合物网络熵粘弹性的对比实验和分子模拟研究

双官能乙烯基封端的聚（二甲基硅氧烷）链通过四官能四（二甲基甲硅烷氧基）硅烷交联剂进行末端连接，以产生具有可控化学计量失衡和反应程度的不规则聚合物网络。结果被用作创建比较性的，名义上相同的三维蒙特卡洛计算机微结构的输入。进行应力松弛实验室测量和磁珠弹簧分子动力学（MD）模拟以估计松弛剪切模量。发现MD估计值很好地再现了测得的平衡剪切模量G，尽管测量和MD松弛模量的时间尺度截然不同。但是，还可以看到，对于近化学计量网络，经典仿射网络模型（ANM）给出了对G的同样好的预测。使用幻像链和常规网络进行其他MD仿真。事实证明，ANM的成功是偶然的，因为它是基于对两个互不相关的不正确假设的偶然取消，这些假设是无缺陷的规则聚合物网络和幻像链可以自由地相互和自身通过。考虑了几种关于理想的高斯聚合物网络弹性的当代理论，并且证明了它们中没有一个特别适合于预测所研究的末端连接的聚二甲基硅氧烷（PDMS）网络的剪切模量。结果表明，考虑到陷入纠缠的影响，可以实现合理的定性预测，有时甚至可以进行半定量预测。然而，由于对被困纠缠的有效浓度进行经验拟合时存在歧义性问题，因此所得的理论预测总体上比使用自动解决网络链的不可交叉性的粗粒度MD模拟所获得的理论预测准确性和可靠性低得多。这强调了目前关于纠缠对具有不同反应程度和化学计量不平衡值的不规则末端连接的聚合物网络的弹性行为的影响的理论描述的不完备性，并且还建议使用我们经过验证的蒙特卡洛微观结构来进一步研究这些影响。所得的理论预测总体上比使用粗粒度MD模拟获得的预测准确度和可靠性显着差，这些模拟自动考虑了网络链的不可交叉性。这强调了目前关于纠缠对具有不同反应程度和化学计量不平衡值的不规则末端连接的聚合物网络的弹性行为的影响的理论描述的不完备性，并且还建议使用我们经过验证的蒙特卡洛微观结构来进一步研究这些影响。所得的理论预测总体上比通过粗粒度的MD模拟获得的预测准确度和可靠性显着差，这些模拟自动考虑了网络链的不可交叉性。这强调了目前关于纠缠对具有不同反应程度和化学计量不平衡值的不规则末端连接的聚合物网络的弹性行为的影响的理论描述的不完备性，并且还建议使用我们经过验证的蒙特卡洛微观结构来进一步研究这些影响。