Dynamical considerations of network properties

Elasticity is discussed as an aspect of viscoelasticity, which is described by the tube model. The effects of both crosslinks and entanglements contribute to this model and a discussion of how these effects can be quantified is given. At high enough concentration, entanglements ensure the existence of elastic effects even without crosslinks, and a theory is presented on how this dynamical phase change comes about.     

Network topology and the theory of rubber elasticity

The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters.     

Peel Adhesion of Poly(Vinyl Chloride) to Nitrile Rubbers

In addition to molecular interaction and physical entanglement of the molecular chains across the interface in poly (vinyl chloride)-nitrile rubber joints, at high temperatures and long contact times interfacial chemical bonds may be formed which seem to couple the two adherends thereby resulting in cohesive failure of the rubber matrix on peeling. This is verified by performing the peel tests at high temperatures, low peel rates and under swollen conditions. Infrared spectroscopic studies of the PVC/NBR blend reveal the formation of chemical bonds at the contact temperatures studied. The peel fracture energy is found to depend on the acrylonitrile content and presence of carboxylic content in the NBR, and the presence of stabilizer and plasticizer in the PVC phase, in addition to the molding and testing conditions.     

Role of Chain Entanglements in the Electrospinning of Wheat Protein-Poly(Vinyl Alcohol) Blends

The aim of this investigation was to determine if the rapid solvent removal evaporation that occurs during electrospinning enabled the gluten protein and poly(vinyl alcohol) (PVOH) chains to remain at least partially entangled in the final product. Natural and synthetic biopolymer blends are known to phase separate in the melt. Differential scanning calorimetry (DSC) was used to test our hypothesis, which we achieved by systematically comparing the thermal profiles of the nonwoven fibrous sheets comprising: 1) 100% commercial wheat gluten, 2) 100% PVOH, and 3) the (75/25) wheat gluten/PVOH blend. The DSC scans of the two PVOH-containing, nonwoven fibrous sheets exhibited differences in the characteristics and positions of the melting peaks (T_m) of the PVOH crystalline phase, while the DSC scans of the nonwoven fibrous sheets comprising either 100% commercial wheat gluten or the wheat gluten/PVOH blend yielded neither a measurable glass transition temperature (T_g) nor a T_m. Energy dispersive spectroscopy (EDS) was used to compare the elemental compositions of the individual fibers with the compositions of the spherical domains found in the nonwoven fibrous mats. These scans revealed that the mineral matter found in commercial wheat gluten (roughly 1% by weight) had phase-separated from the bulk gluten protein as a result of electrospinning.     

Entanglement Tightening and Stress Relaxation

The contribution of entanglements to the modulus of a time independent polymer is satisfactorily accounted for by the C₂/λ term in the Mooney-Rivlin equation. On the other hand, the role of entanglements in time dependent polymers is less evident and seems to give rise to a non-linear Mooney plot. A model is introduced which considers an entanglement as a topological knot that tightens with initial deformation and subsequently inhibits chain slippage. The observed maximum in a Mooney plot at small values of λ is predicted, and the experimental data of plasticised PVC polybutadiene and styrenebutadiene copolymer are fitted reasonably well.     

Tensile strength elevation of brittle polymers by entanglements

Plots of tensile strength (T) versus reciprocal number average molecular weight (M^?1) have been made using previously reported data for linear polymers tested in the glassy state. Over a wide range of molecular weights there is conformity to Flory's empirical equation T = A - BM^?1, in which A and B are constants. Values of M obtained by extrapolation to T = 0 correlate with critical values of molecular weight which are diagnostic of incipient formation of an entangled network. The entanglement thesis is developed further by reference to a model in which brittle strength is attributed to the breaking of covalent backbone bonds. Theoretical values are calculated which exceed experimental values by a factor of only three. Such close agreement is attributed to the insensitivity of glassy linear polymers to flaws.