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.     

Synthesis and characterisation of copolyesters from poly(ethylene terephthalate) and poly(hexamethylene terephthalate)

Copolyesters containing poly(ethylene terephthalate) and poly(hexamethylene terephthalate) (PHT) were prepared by a melt condensation reaction. The copolymers were characterised by infrared spectroscopy and intrinsic viscosity measurements. The density of the copolyesters decreased with increasing percentage of PHT segments in the backbone. Glass transition temperatures (T_g). melting points (T_m) and crystallisation temperatures (T_c) were determined by differential scanning calorimetry. An increase in the percentage of PHT resulted in decrease in T_g, T_m and T_c. The as-prepared copolyesters were crystalline in nature and no exotherm indicative of cold crystallisation was observed. The relative thermal stability of the polymers was evaluated by dynamic thermogravimetry in a nitrogen atmosphere. An increase in percentage of PHT resulted in a decrease in initial decomposition temperature. The rate of crystallisation of the copolymers was studied by small angle light scattering. An increase in percentage of PHT resulted in an increase in the rate of crystallisation.     

Effects of hydrolysis on the physical properties of short glass-fibre reinforced poly(ethylene terephthalate)

The mechanical fracture strength and toughness of short-fibre composites, injection moulded from compounds of poly(ethylene terephthalate) (PET) containing 10 and 30% (by weight) (w/o) glass, have been investigated and the dependence upon matrix hydrolytic stability determined. Mouldings have been characterised by several physical techniques to evaluate molecular weight, degradation rates, crystallinity and morphology, whilst time-dependent gravimetric data were derived to quantify sorption kinetics and allow comparisons with theoretical reaction rates to be made. During melt processing, PET is hydrolysed extremely rapidly by traces of moisture (<0.02w/o). yet the inherent strength of moulded composites declines significantly only below an apparently critical molecular weight. However, on long-term humid ageing in hot water, impact behaviour especially is rendered more complex by simultaneous crystallisation, molecular reorder and losses of interfacial bond strength.     

Some factors affecting the electrical properties of carbon-black-loaded butyl rubber during vulcanization

Butyl rubber mixtures loaded with 70 phr general purpose furnace black (GPF) and tetramethyl thiuram disulphide (TMTD)/S as vulcanizing system were prepared. The kinetics of their electrical conductivity development during the vulcanization process were followed by using an especially devised system. It was found that the increase in the electrical conductivity during vulcanization obeys an exponential growth function with time constant τ, which markedly decreases with increasing vulcanization temperature as well as with the efficiency of the vulcanizing system. After completion of the vulcanization process, about 80 min, the samples obtained possess reasonable stability and reproducibility of electrical conductivity.     

Synthesis and characterization of poly(ethylene aspartate)-metal complexes

Poly(ethylene aspartate) [PEA] was synthesized by the melt condensation of D,L-aspartic acid and ethylene glycol. PEA containing pendent amino and carbonyl groups in its repeating chain was used as the polymeric ligand for complexation with transition metal ions, viz. Co(II), Ni(II), Cu(II), Mn(II), Zn(II), Cd(II), Ca(II), Mg(II), Pb(II) and Hg(II). Complexation was found to be most effective in DMSO. The resulting polyester-metal complexes were solid coloured materials which have been characterized by IR spectroscopy, elemental analysis and magnetic susceptibility measurements. The thermal stability of the polyester-metal complexes was investigated by thermogravimetric analysis (TGA). On the basis of the physico-chemical studies, an oxygen and nitrogen coordinated structure for the polyester-metal complexes is proposed.     

Associative properties of perfluorooctyl end‐functionalized polystyrene–poly(ethylene oxide) diblock copolymers

The synthesis of 2,2,3,3‐tetrahydro‐perfluoroundecanoyl end‐functionalized polystyrene–poly(ethylene oxide) block (PS‐block‐PEO‐R_F) copolymers and their matching PS‐block‐PEO diblock copolymers was carried out by sequential anionic polymerization. Viscometry and ¹⁹F NMR studies show that the PS‐block‐PEO copolymers, in contrast to their matching PS‐block‐PEO‐R_F copolymers, exhibit a micellar rather than the associative behavior seen for the latter. However, the presence of an excess of fluorinated acid, used for end‐functionalization, produces a reduction of the associative behavior above the overlap concentration, with the fluorinated acid acting like a surfactant. A competition may also occur between PS—and R_F—mediated micellization. Copyright © 2004 Society of Chemical Industry     

Microstructure-related fracture toughness and fatigue crack growth behaviour in toughened, anhydride-cured epoxy resins

Fracture toughness and fatigue crack propagation (FCP) of plain and modified anhydride-cured epoxy resin (EP) were studied at ambient temperature. Liquid carboxyl-terminated acrylonitrile-butadiene (CTBN) and silicon (SI) rubber dispersions were used as tougheners for the EP. The morphology of the modified EP was characterized by dynamic mechanical analysis (DMA) and by scanning electron microscopy (SEM). The fracture toughness, K_c, of the compositions decreased with increasing deformation rate. K_c of the EP was slightly improved by CTBN addition and practically unaffected by incorporation of the SI dispersion when tests were performed at low cross-head speed, v. Both modifiers improved K_c at high v, and also the resistance to FCP, by shifting the curves to higher stress intensity factor ranges, ΔK, by comparison with the plain EP. It was established that both fracture and fatigue performance rely on the compliance, J_R, at the rubbery plateau, and thus on the apparent molecular mass between crosslinks, M_c. The failure mechanisms were less dependent upon the loading mode (fracture, fatigue), but differed basically for the various modifiers. Rubber-induced cavitation and shear yielding of the EP were dominant for CTBN, whereas crack bifurcation and branching controlled the cracking in SI-modified EP. The simultaneous use of both modifiers resulted in a synergistic effect for both the fracture toughness at high deformation rate and the FCP behavior.     

Thermal and thermoelastic properties of fast extrusion furnace (FEF) carbon black loaded SBR vulcanizates

The effect of FEF carbon black as filler on the thermal capacity c, diffusivity a, and thermal conductivity λ, of styrene butadiene rubber (SBR) composites in the temperature range 300–420 K was studied. The filler strongly increases the thermal diffusivity, whilst strongly decreasing the thermal capacity and the thermal conductivity (except at high FEF content ≥80 phr). The influence of the filler on the thermoelastic behaviour of the same composites was also investigated. It was found that the thermoelastic temperature change (ΔT) increased with carbon black concentration as well as the entropy change per unit extension.