Experimental characterisation and further molecular modelling of the conformational and elastic behaviour of poly(ethylene terephthalate) network chains

The Monte-Carlo (MC) method developed to model the elastomeric stress-strain behaviour of polyethylene (PE), poly(dimethyl siloxane) (PDMS) and poly(ethylene terephthalate) (PET) networks and the stress-optical behaviour of PE networks is now developed to investigate further the stress-strain behaviour of PET networks. Accurate infrared (IR) spectrometry measurements have been used to determine the populations of gauche conformers in the glycol residues of PET chains in melts. The proportion of gauche states was found to be 76%, consistent with the rotational energy difference of −4.16 kJ mol⁻¹ between trans and gauche states used previously.The greater conformational flexibility of the PET chain compared with the PE chain leads to lower network moduli and smaller deviations from Gaussian and affine network behaviour. Previous results are briefly reviewed and new comparisons of the elastic behaviour of PET and PE chains are made using normalised plots. Subsequent publications will apply the present results to interpreting the measured stress-strain and the stress-optical properties of entangled PET melts.     

Experimental studies and molecular modelling of the stress-optical and stress-strain behaviour of poly(ethylene terephthalate). Part III: Measurement and quantitative modelling of birefringence-strain, stress-strain and stress-optical properties

Experimental measurements and Monte-Carlo (MC) modelling of the birefringence-strain, stress-strain and stress-optical behaviour of poly(ethylene terephthalate) (PET) are used, together with the analysis of orientation-strain and conformation-strain behaviour reported in Paper I, to give a detailed, quantitative interpretation and characterisation of its deformation-related properties. The difference between the stress-strain and stress-optical behaviour of PET that had been reported previously is confirmed. Except for the stress, the measured values of all the properties studied are in agreement with those calculated using the MC modelling, which suggests that not all of the junctions or the chains in the entangled PET network are elastically active.The results given by Kuhn and Grün theory are compared with those given by the MC modelling. The expected shortcomings of Kuhn and Grün theory are found. However, distinct from the behaviour reported previously for polyethene, the theory can be used to evaluate, semi-empirically, the stress-optical coefficient of PET.     

Effect of network structure on the stress-strain behaviour of endlinked PDMS elastomers

Endlinked poly(dimethylsiloxane) (PDMS) networks synthesized from telechelic precursor chains of different molar mass were prepared with varying volume fractions of non-reactive chains acting as solvent. Uniaxial extension and compression measurements were performed on these networks to investigate their stress-strain behaviour. The effect of the network structure and of solvent on the stress-strain behaviour is examined by controlling the extent of crosslinks and entanglements during the network synthesis. The master curve of the Rubinstein and Panyukov non-affine slip-tube (NAST) model provide an adequate fit to most of the extension and compression data. Furthermore, the crosslink and entanglement parameters of the NAST model (G_c and G_e) are found to be in general in reasonable agreement with the 2C₁ and 2C₂ parameters of the Mooney-Rivlin continuum model applied to the extension data. For high molar mass precursor chains, the entanglement contribution to the modulus surpasses the crosslink contribution.     

Experimental and theoretical investigations on petroleum-based elastomers with two cross-linking systems of different lengths viewed as bimodal networks

A review with 36 references discussing the chemistry and the structure-property relationship of elastomers cured with two cross-linking systems of different chain lengths such as sulfur and the polymerization products of p-benzoquinone and viewed as bimodal networks. These exceptional networks have shown remarkable improvements in the overall mechanical properties which are anticipated to be due to the non-Gaussian effects known for bimodal networks and evident by the anomalous upturn in the modulus values in Mooney-Rivlin stress-strain data representations. Proton and ¹³C NMR as well as energy minimization calculations were used to study the chemical structures and single chain contributions of polyquinones. Nuclei bending of these oligomers have shown to be greatly influenced by the restricted torsional behavior due to the presence of the hydrogen bonds between the benzenoid nuclei. Intrinsic atomic-level forces for the networks were evaluated using molecular dynamics techniques and showed that while the forces acting on the junction points of the cross-linking segments and the elastomeric chains had no apparent change as a consequence of the networks' bimodal formation, forces acting on the short chains of the bimodal networks are of much higher values as compared to those of unimodal networks. The presence of the relatively long polyquinone chains in the bimodal networks has caused the short sulfur chains to stretch to its maximum extensibility and no longer can increase its end-to-end distance separation by simple rotations about its skeletal bonds. Limited chain extensibility of the short chains resulting from the deformation of the bond angles and bond lengths has lead to higher potential energies. Studies on the swollen bimodal networks have validated the above conclusions since swelling of the networks will prevent the elastomeric chains from undergoing possible strain-induced crystallization during the stress-strain experiments and any abnormalities in the mechanical behavior of these networks must be therefore the result of the limited extensibility of the short chains of the networks.     

The Effects of Network Imperfections on the Small-Strain Moduli of Polydimethylsiloxane Elastomers Having High Functionality Cross Links

Abstract

Poly(dimethylsiloxane) networks of high cross-link functionality have been prepared by end linking vinyl-terminated chains with multifunctional poly(methylhydrosiloxane) chains. They covered a wide range in the extent of reaction, P_vi , of the vinyl end groups. At small strains, these networks had elongation moduli that significantly exceeded the values predicted by the Flory-Erman theory. Neglected in such standard analyses, however, is the fact that the segments between cross links along the junction precursor molecule can themselves act as short network chains, contributing to the modulus and giving a strongly bimodal distribution of both network chain lengths and cross-link functionalities. As would be expected, an unmistakable transition is observed in values of the shear modulus G toward the phantom limit of deformation as the crosslink density increases. Calculations based on recognition of such short chains give results in much better agreement with experiment. The results so obtained showed strong dependence of the elastomeric properties on the extents of reaction and the inherent network imperfections. Such imperfections have a pronounced effect on the equilibrium modulus, more specifically on the empirical constant 2C ₂. The dependence of 2C ₂ on the volume fraction of the elastically “effective” chains is thus established. Moreover, the results unambiguously demonstrate that the empirical constant 2C ₂ is essentially a topological contribution and contains no contributions from the chemical network.     

Deformation of doubly oriented polyethylene,nylon 66 and poly(ethylene terephthalate)

Doubly oriented specimens of high density polyethylene (HDPE), nylon 66 and poly(ethylene terephthalate) (PET) were re-stretched along a direction perpendicular to the molecular chain axis at temperatures ranging between room temperature and the respective polymer melting points. Brittle failure was observed for PE samples at all the test temperatures with no significant amount of plastic deformation; whereas, for both PET and nylon 66 samples, ductile deformation was observed at elevated temperatures with plastic strain of >400%. The ductile deformation of nylon 66 and PET occurred with an anisotropic change in the cross-sectional dimensions of the specimen, the reduction taking place predominantly in only one lateral direction. The morphological change accompanying the drawing of the doubly oriented PET and nylon 66 material was examined by using X-ray and optical methods. The implications of the difference in deformation behaviour with respect to the morphological differences among oriented PE, PET and nylon 66 materials are discussed.     

Interpenetrating bimodal networks

Sequential interpenetrating networks (IPN's) were obtained from a tetrafunctionally end-linked network [prepared from hydroxyl-terminated poly(dimethylsiloxane) (PDMS) chains having a number-average molecular weight of 21.3 × 10³ g mol^?1] by swelling it with very short vinyl-terminated PDMS chains (～450 g mol^?1), which were then themselves tetrafunctionally end linked, Simultaneous IPN's were prepared from a mixture of the same two types of PDMS chains, with different end-linking agents and catalysts for the two separate reactions. In elongation studies, both types of IPN's showed upturns in modulus which were similar to those shown by the usual bimodal networks, which are prepared from mixtures of chains having identical end groups, and are thus entirely interconnected. The sequential IPN's have values of the high deformation modulus close to those of the interconnected networks, possibly because their lack of connectivity is compensated for by the stretching of the long chains by the short-chains used to form the second network, Values of the ultimate strength are smaller for the IPN's, thus demonstrating the advantage of direct bonding between the long and short network chains. The simultaneous IPN's, however, have unusually large extensibilities, which makes their energies for rupture comparable to those of the corresponding interconnected bimodal networks.     

A modification of rubber elasticity theory

Summary Based on a reconsideration of the packing conditions in amorphous polymers, a modification of the statistical theory of rubber elasticity is derived. The main assumption is, that the mean square end-to-end distance of a free chain in the bulk state depends on the dimensions of the surrounding chains. The theory describes quite well the deformation behaviour of real elastomeric networks.     

Orientation of poly(vinyl alcohol) nanofiber and crystallites in non-woven electrospun nanofiber mats under uniaxial stretching

The development of macroscopic nanofiber orientation and microscopic crystallite and molecular chain orientation have been investigated during uniaxial stretching of electrospun poly(vinyl alcohol) (PVA) non-woven nanofiber mats. Scanning electron microscopy and stress-strain/small-angle X-ray scattering show that the macroscopic nanofiber orientation significantly increases during the initial stage of deformation, and approaches a plateau on the way of stretching. Detailed analyses of the stress-strain/wide-angle X-ray diffraction measurement and polarized Fourier transform infrared spectroscopy indicate that the microscopic crystallite and molecular chain orientation rapidly increase at the initial stage of stretching due to macroscopic nanofiber orientation. At higher deformation, the microscopic modes of orientation continuously develop as a result of the nanofiber stretching. The complicated deformation process of non-woven nanofiber mats is discussed in terms of macroscopic nanofiber orientation and the microscopic crystallite and molecular chain orientation.     

Interpenetrating polymer networks of poly(dimethylsiloxane): 1. Preparation and characterization

Model networks of ,ω-dihydroxy-poly(dimethylsiloxane) (PDMS) were prepared by tetrafunctional crosslinking agent tetraethyl orthosilicate (TEOS) and the catalyst stannous 2-ethylhexanoate. Hydroxylterminated chains of PDMS having molecular weights 15 × 10³ and 75 × 10³ g mol⁻¹ were used in the crosslinking reaction. Bimodal networks were obtained from a 50% (w/w) mixture of PDMS chains with M_n = 15 × 10³ and 75 × 10³ g mol⁻¹. A sequential interpenetrating network of these PDMS chains was also prepared. Physical properties of the elastomers were determined by stress-strain tests, swelling and extraction experiments, and differential scanning calorimetry measurements.     

Molecular models of polymer networks and constitutive equations of rubber elasticity

Equilibrium elastic behaviour of crosslinked polymers (networks) is analysed both from the macroscopic (phenomenological) and microscopic (molecular) points of view. Molecular mechanisms possibly responsible for non-linear rubber elasticity are discussed. They include: conformational entropy of network chains at small and large extensions, hindered rotation of such chains and intra-chain point interactions, dipole-dipole interactions between asymmetric chain segments, and topological constraints leading to chain entanglement.     

Monte Carlo simulation of two interpenetrating polymer networks: Structure, swelling, and mechanical properties

The swelling and mechanical properties of various interpenetrating polymer networks (IPNs) were studied. Six networks made from permutations of a moderately crosslinked polyelectrolyte network (ref), a moderately crosslinked neutral polymer network (net1), and a highly crosslinked polyelectrolyte network (net2) were first swollen in water and structural properties such as end-to-end chain lengths and radial distribution functions were compared with the component networks' equilibrium properties. The swelling of composite IPNs was discussed in terms of a balance between the osmotic pressure due to mobile counterions and the restoring force of the network chains, which act in parallel to counteract the osmotic swelling. For the ref-net2 system, the strong stretching of net2 chains increases the network restoring force and the further swelling due to the counterions is suppressed. The swollen networks were then uniaxially stretched, and equilibrium stress-strain plots were obtained up to high extension ratios. The equilibrium volume decreased upon uniaxial extension, and the elastic moduli of IPNs of the A-A type were slightly greater than that of their respective single networks.     

Deuterium magnetic resonance studies on strained selectively deuterated elastomers

The lineshape analysis of the ²H nuclear magnetic resonance of uniaxially strained poly(1,4-butadiene) networks deuterated homogeneously and selectively at network junctions shows that the orientation of chain segments attached to crosslinks is larger than the average segmental orientation. In addition, it is shown that the molecular effective extension ratio of all elastically effective chains is smaller than the macroscopic extension ratio, and short chains are stretched to a higher extent than long chains. The deviation from the affine deformation behaviour and the onset of inhomogeneous deformation of individual chains takes place at the transition from the Gaussian to the non-Gaussian network. In the Gaussian regime the segmental orientation varies with the inverse of the molecular weight of elastically effective chains in agreement with molecular theories of rubber elasticity. ²H n. m. r. spectra of a thermoplastic poly(styrene-b-butadiene-b-styrene) block copolymer carrying selectively deuterated butadiene segments at the block boundaries reveal an enhanced mobility of these segments under deformation. ²H n. m. r. experiments on amorphous segmented polyurethanes selectively deuteratured in hard and soft segments, respectively, show that the elasticity in these samples is achieved by physical crosslinks formed by very small highly mobile aggregates of hard segments dispersed in the soft phase. Within the hard domains two processes for motion due to phenyl groups in 4. 4'-methylenebis(phenylisocyanate) units and CH₂ groups in 1. 4-butanediol units can be discriminated.     

Investigations of polymer chains in oriented fluid phases with deuterium nuclear magnetic resonance

Deuterium nuclear magnetic resonance (D n.m.r.) is a potentially powerful technique for exploring molecular structural and dynamical properties of polymer chains in bulk fluids and concentrated solutions. A variety of systems can be investigated (the solid state, elastomeric networks, sheared polymer fluids, chain solutes in liquid crystal solvents, and polymeric liquid crystals), over a wide range of dimensions (local chain properties, rotational isomeric state parameters, behaviour between network junctions or entanglements, evolution of tube distributions, and domain sizes of homogeneous chain alignment). A coarse comparison of low molar mass liquid crystals with condensed phases of entangled polymer fluids and elastomeric networks illustrates the key features of the D n.m.r. technique and establishes a common framework for interpreting experiments.     

Molecular Modelling of the Conformational Flexibility and Elastic Behaviour of Short Poly(ethylene terephthalate) Chains

The Monte-Carlo (MC) rotational-isomeric-state (RIS) method developed previously to model the stress–strain behaviour of poly(ethylene terephthalate) (PET) is now applied to short PET chains of between 42 and 84 skeletal bonds. The effects on the radial and probability density distribution functions of the long, flexible virtual bond used to represent the terephthaloyl unit are investigated. The distribution functions generated, based on finite samples of chains, are found to be discontinuous with subsidiary maxima in their tails. The discontinuities lead to uncertainties in the simulated network elasticity properties and, in order to reduce the uncertainty, it is necessary to truncate the distributions at the values of r where they first become discontinuous. The stress–strain properties calculated from the truncated distributions are shown to be consistent with those presented previously for longer PET chains, for which discontinuities in the sampled functions are not apparent.     

Rheological properties of the liquid crystalline poly(γ-benzyl α, L-glutamate) gels in benzyl alcohol

We have determined the degree of stiffness of a poly(γ-benzyl α, L-glutamate) (PBLG) chain in benzyl alcohol by measuring the intrinsic viscosities of dilute Solutions with differing molecular weights. Viscoelastic properties in oscillatory shear flow have been studied and the dependence of the loss and storage moduli on temperature, composition, and frequency are reported. We have also studied the transient shear stress relaxation behavior of the PBLG gel at different temperatures and concentrations. A comparison has been made between these gels and a classical poly(dimethyl siloxane) (PDMS) network, as well as, typical glassy polymers. Shear creep and recovery measurements have been made for this system. Some extensional step strain experiments using lubricated squeezing have been investigated. Tensile experiments have been made to determine stress-strain relationship during elongation. Preliminary experiments using the impulse approach to viscoelasticity further indicate the high elastic contribution in the gel.     

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.     

Structure-mechanical property correlations of model siloxane elastomers with controlled network topology

We review our recent studies towards the molecular understanding of mechanical properties-structure relationships of elastomers using model polydimethylsiloxane (PDMS) networks with controlled topology. The model elastomers with controlled lengths of the network strands and known amounts of cross-links and dangling chains are obtained by end-linking the functionally terminated precursor PDMS with known molecular weights using multi-functional cross-linkers. Several modern entanglement theories of rubber elasticity are assessed in an unambiguous manner on the basis of the nonlinear stress-strain behavior of the model elastomers under general biaxial strains. The roles of cross-links and entanglements in the large-scale structure of the swollen state are revealed from small angle X-ray scattering spectra. A remarkably stretchable elastomer with the ultimate strain over 3000% is obtained by optimizing the network topology for high extensibility, i.e., by reducing the amounts of trapped entanglements and the end-to-end distance of the network strands. The model elastomers with unattached chains exhibit a pronounced viscoelastic relaxation originating from the relaxation by reptative motion of the guest chains. The relaxation spectra provide a definite basis to discuss the dynamics of guest linear chains trapped in fixed polymer networks. The temperature- and frequency-insensitive damping elastomers are made by introducing intentionally many dangling chains into the networks.     

Theoretical investigation of SANS from elastomeric networks with topological constraints

Summary This paper presents a theoretical investigation of SANS from labeled chains in polymer networks which are characterized by the topology of tube-like deformation dependent configurational constraints. The deformation dependence of the constraints is assumed to relax and to be determined by a microscopic deformation law. The results lead to the conclusion that the change of the radius of gyration of a network chain may be much less than the deformation of the macroscopic sample. It is pointed out that network defects favour the effect of constraint release.     

Effect of filler amount on thermoelastic properties of poly(dimethylsiloxane) networks

End-linked poly(dimethylsiloxane) (PDMS) networks were prepared in the presence of fumed silica particles with hydroxyl groups at their surfaces. The silica particles were introduced into the polymer solution prior to end-linking. Hydroxyl ended PDMS chains were end-linked via the tetra functional crosslinker, tetraethoxysilane. The filler content varied in the range 0-5 wt%. Atomic Force Microscopy was used to image and characterize the silica particles. Swelling, stress-strain and thermoelasticity experiments were performed. The temperature coefficient and the energetic part of the force in uniaxial extension are found to increase with increasing silica amount. This observation is ascribed to effects contributed possibly by the adsorption layer around the silica particles.