Elasticity of Polymer Networks

Abstract

We develop and solve a new molecular model for nonlinear elasticity of entangled polymer networks. This model combines and generalizes several succeseful ideas introduced over the years in the field of the rubber elasticity. The topological constraints imposed by the neighboring network chains on a given network are represented by the confining potential that changes upon network deformation. This topological potential restricts fluctuations of the network chain to the nonaffinely deformed confining tube. Network chains are allowed to fluctuate and redistribute their length along the contour of their confining tubes. The dependence of the stress σ on the elongation coefficient λ for the uniaxially deformed network is usially represented in the form of the Mooney stress, f*(1/λ) = σ/(λ − 1/λ2). We find a simple expression for the Mooney stress, f*(1/λ) = G c + G e/(0.74λ + 0.61λ-1/2 − 0.35), where G c and G e are phantom and entangled network moduli. This allows one to analyze the experimental data in the form of the universal plot and to obtain the two moduli G c and G e related to the densities of cross-links and entanglements of the individual networks. The predictions of our new model are in good agreement with experimental data for uniaxially deformed polybutadiene, poly(dimethylsiloxane), and natural rubber networks, as well as with recent computer simulations.

Characterizing Large Strain Elasticity of Brittle Elastomeric Networks by Embedding Them in a Soft Extensible Matrix

“…MA 2N_noX shows nearly the same properties as those of MA 2N . Using the Rubinstein and Panyukov equation [25] (Equation S1), we estimated the contribution to the modulus from entanglements and from crosslinks for the two samples (Table S1). (Table S1).…”

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

“…The real chain is represented by the corresponding PP, which is a series of strands of average molar mass M e connecting the links. The tube model provides a basis for working out analytically the linear and nonlinear viscoelasticty of polymer melts 9,[16][17][18][19][20] and networks 10,15,[21][22][23][24] at a molecular level. Slip link models 19,20,24 also allow for analytical 8,[11][12][13]15,25,26 or stochastic simulation 14,[27][28][29][30][31][32][33][34][35][36][37] treatments with a molecular representation, at the single or many-chain level.…”

Mechanics of Soft PSAs (Pressure Sensitive Adhesives)

“…The cavitation phenomenon is completely dominated by bulk relaxation modulus of the adhesive and arises due to the plain strain conditions that hold during the peeling just behind the peeling front. In many instances these phenomena dominate also in structural adhesives even if they lay in their glassy state [29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Indeed, the intensity of the three-dimensional stress state during peeling is strongly dependent on the flexural stiffness of the tape, once the surface properties of the backing and the tape (namely, the roughness and the surface tension) and the adhesive thickness are established.…”

“…The PSAs under study can be considered as rubbers with entanglements [41][42][43][44] where a sort of polymer network with entanglements coupling is realized. Therefore the elasticity of polymer networks, i.e.…”