Theoretical Model of Polymer Network Chain Formation under Strain

Abstract

In this article, the polymer network chain formation through cross-linking and scission under n strain stages is studied based on the thermal fluctuation principle. The aim is to clarify the effects of chemical reactions, especially the network chain cross-linking, dangling chain cross-linking, cross-link scission, and network chain scission, on the free energy of network chain to generalize the classical two-network model. In our model, the free energy change for a chain formation is associated with the reaction sequences, except network chain cross-linking or cross-link scission reactions under the same strain stage. A new constitutive expression for network chain formed under two strain stages is derived according to affine deformation theory in which independent network hypothesis and stress-transfer function are not required. Comparison between our model and previous experimental data about recovered stretch ratio of γ-irradiated silicone elastomer validates that our model can give more precise result than previous two-network model.

Constitutive Model of Radiation Aging Effects in Filled Silicone Elastomers under Strain

“…Such analysis was first carried out by Flory for a Gaussian-chain network and by Fricker for a phantom network of Gaussian chains. Assuming a phantom network model, in the following analysis, we use Fricker’s formula to model such behavior, although alternative approaches have recently been suggested in the literature …”

“…Assuming a phantom network model, in the following analysis, we use Fricker's formula to model such behavior, although alternative approaches have recently been suggested in the literature. 52 ■ RADIATION-INDUCED SCISSION AND CROSS-LINKING RATES High-energy electromagnetic or electron-beam radiation is well known to produce permanent chemical changes in silicone polymers. 15,53−59 Two of the chemical changes particularly relevant to change in network topology and mechanical moduli are scission and cross-linking processes.…”

Modeling Approach to Capture Hyperelasticity and Temporary Bonds in Soft Polymer Networks

“…26−29 In 2000, Wineman added two dimensions to the original one-dimensional equations for soft materials cross-linking and experiencing scission. 30−32 The most recent contributions to this field are those from Zhao, 33 Yu, 34 and Katashima. 35 Davidson and Goulbourne have developed a nonaffine model capable of describing strain softening and strain hardening, although this model considered entanglements and permanent bonds.…”

“…This new network allows for a balancing of force in the material. Publications that followed were used to modify and refine the original models, allowing for more detailed modeling of the materials specifically by Berry, Scanlan, and Watson. − The theory presented was generalized later to include multiple-stage networks, before another large contribution to the field was made by Smith, Greene, Ciferri, and Hermans, acknowledging that chains can have non-Gaussian behavior in double networks. − In 2000, Wineman added two dimensions to the original one-dimensional equations for soft materials cross-linking and experiencing scission. − The most recent contributions to this field are those from Zhao, Yu, and Katashima …”