J.I. Cail

Further computer simulation studies of the orientational behaviour of poly(ethylene terephthalate) chains

The energy parameter governing the glycol gauche conformation of the Williams–Flory rotational-isometric-state (RIS) model of poly(ethylene terephthalate) (PET) is varied to give values of (〈r2〉/M)∞ and % gauche-glycol conformers that agree with experiment for bulk PET. Such agreement is not given by the original Williams–Flory model. The RIS Metropolis Monte-Carlo (RMMC) model developed by Molecular Simulations Incorporated (MSI) can also be modified, through values of the effective relative permittivity, to match the same experimental quantities. The orientational behaviours of the glycol segments, terephthaloyl segments and the repeat units with respect to the chain end-to-end vector are investigated by calculating the Legendre polynomials 〈P2(ξgly)〉, 〈P2(ξter)〉 and 〈P2(ξrep)〉, respectively, as functions of end-to-end chain extension, r/rmax, for selected RIS and RMMC parameters. The calculations show that the more flexible glycol segments orientate more readily than the terephthaloyl segments and the repeat units show orientations between these two extremes. The various models of segmental orientation presented in this paper will enable more realistic interpretation of the experimental stress-optical behaviour of PET in bulk. In this context, the Langevin model based on freely-jointed chains is seen to be completely inadequate for describing changes in segmental orientation with chain extension.

Formation, structure and properties of polymer networks: gel‐point prediction in endlinking polymerisations

Gel points, predicted using Ahmed-Rolfes-Stepto (ARS) theory and a Monte-Carlo (MC) simulation method accounting for intramolecular reaction, are compared with experimental data for polyester (PES)-, polyurethane (PU)-and poly(dimethyhl siloxane) (PDMS)-forming polymerisations. The PES and PU polymerisations were from stoichiometric reactions at different initial dilutions and the PDMS ones were from critical-ratio experiments at different dilutions of one reactant. The predictions use realistic chain statistics to define intramolecular reaction probabilities and employ no arbitrary parameters. Universal plots of excess reaction at gelation versus ring-forming parameter are devised to enable the experimental data and theoretical predictions to be compared critically. It is shown that various gel points can be predicted by MC simulations, depending on the criterion for gelation used. Due to the lengthy computations needed and the uncertainties in the predictions, MC simulation is not a viable approach. Although inconsistencies are noted in the measured gel points, so that a unified interpretation of the data cannot be achieved, ARS theory is shown to be the preferred basis for gel-point prediction. It is also concluded that, before one can be certain of agreement between experiment and predictions, more experimental systems at different initial dilutions and ratios of reactants need to be studied and the various methods used for detecting gel points need to be compared.

Quantitative modeling of the stress-optical properties of polyethene networks

The Monte‐Carlo (MC) modeling of the deformation‐related properties of polymer networks due to Stepto and Taylor (1995a; 1995b) is applied to the stress‐optical behavior of polyethene (PE) networks published by Saunders (1954). Quantitative modeling is achieved on the bases of the realistic rotational‐isomeric‐state model of the PE chain, due to Abe, Jernigan, and Flory (1966), and the C–C and C–H bond polarizabilities of Denbigh (1940). Use of the C–H bond polarizablities of Bunn and Daubeny (1954) lead to calculated values of birefringence that greatly underestimate the experimental ones. Modeling of stress‐strain and birefringence‐strain behavior is also discussed. Finally, it is demonstrated, using PE and poly(ethylene terephthalate) as examples, that the prediction of stress‐optical behavior on the basis of Gaussian networks leads to results of variable accuracy. Dedicated to Professor John L. Stanford on the occasion of his 60th birthday.

Understanding the elastomeric properties of polymer networks

It is shown that Monte-Carlo (MC) simulations of the elastic behaviour of chains in networks using realistic rotational-isomeric-state (RIS) chain models are able to reproduce experimentally observed deviations from Gaussian network behaviour in uniaxial extension and also to interpret, quantitatively, stress-optical properties. In stress-strain behaviour, an increase in the proportion of fully extended chains with increasing macroscopic strain gives rise to a steady decrease in the rate of change of the Helmholtz energy of a network, causing a reduction in network modulus at moderate macroscopic strains. There is no need to invoke a transition from affine to phantom chain behaviour as deformation increases. To evaluate stress-optical properties, the average orientation of segments with respect to the deformation axis is calculated, taking into account the interdependence of segment orientation and chain orientation as chains become more extended and aligned under uniaxial stress. The MC method gives, in agreement with experiment, values of stress-optical coefficient that are dependent upon both deformation ratio and network-chain length. The method highlights serious shortcomings in the classical Gaussian model of stress-optical behaviour. Applications of the simulation methods to the quantitative modelling of the stress-strain behaviour of poly(dimethyl siloxane) networks and the stress-optical behaviour of polyethylene networks are described.