Paul E. Spencer

Effect of electron-phonon interaction range on lattice polaron dynamics: A continuous-time quantum Monte Carlo study

•We present the numerically exact ground-state energy, effective mass, and isotope exponents of a onedimensional lattice polaron, valid for any range of electron-phonon interaction, applying a continuous-time quantum Monte Carlo sQMCd technique in a wide range of coupling strength and adiabatic ratio. The QMC method is free from any systematic finite-size and finite-time-step errors. We compare our numerically exact results with analytical weak-coupling theory and with the strong-coupling 1 / l expansion. We show that the exact results agree well with the canonical Frohlich and Holstein-Lang-Firsov theories in the weak and strong coupling limits, respectively, for any range of interaction. We find a strong dependence of the polaron dynamics on the range of interaction. An increased range of interaction has a similar effect to an increased sless adiabaticd phonon frequency: specifically, a reduction in the effective mass.

Performance enhancement of polymer nanocomposites via multiscale modelling of processing and properties

Abstract This paper provides an overview of research on modelling of the structure–property interactions of polymer nanocomposites in manufacturing processes (stretch blow moulding and thermoforming) involving large-strain biaxial stretching of relatively thin sheets, aimed at developing computer modelling tools to help producers of materials, product designers and manufacturers exploit these materials to the full, much more quickly than could be done by experimental methods alone. The exemplar systems studied are polypropylene and polyester terephalate, with nanoclays. These were compounded and extruded into 2mm thick sheet which was then biaxially stretched at 155°C for the PP and 90 to 100°C for the PET. Mechanical properties were determined for the unstretched and stretched materials, together with TEM and XRD studies of structure. Multi-scale modelling, using representative volume elements is used to model the properties of these products.

Modelling of polymer clay nanocomposites for a multiscale approach.

Polymer nanocomposites have been in existence for over 20 years. Recently, Okada & Usuku [1] have presented a historical review and Hussain et al. [2] have reviewed the current science and technology. Filler particles, with at least one dimension at the nanometre level, are embedded within a polymer matrix, and can effect significant improvements in mechanical properties – modulus, yield stress, fracture toughness – when present at quite low levels of a few percent by weight (wt. %). This is associated with particle geometries of very high aspect ratio and resultant high surface areas per unit volume. Significant improvements are obtained at filler concentrations so low that the optical properties of the polymer matrix are largely unaffected, so that a transparent matrix results in a transparent composite. After the pioneering success with the Nylon 6/clay system [1], further advances were reported using other polymer matrices, examples being polyolefins [3], epoxy, [4], polyesters [5], and polyamides [6].

The Use of a New Viscous Process in Constitutive Models of Polymers

In constitutive models of polymers, there has been a long history of the use of strain-rate dependent viscous processes, such as the Eyring and Argon models. These are combined with elastic elements to generate viscoplastic models that exhibit typical phenomena such as rate dependent yield, creep and stress relaxation. The Eyring process is one of the most frequently used such mechanisms. It has two significant drawbacks: it implies a temperature dependence of mechanical behaviour that is in an opposite sense to that observed; and it predicts a strain rate dependence of yield stress that is less complex than that observed, leading to the requirement for two or more Eyring processes. In recent years, new ideas for amorphous polymers have been developed that lead to an alternative plastic mechanism that addresses these concerns. In this paper a constitutive model that incorporates this mechanism is developed, and its effectiveness in modelling macroscopic mechanical behaviour of polymers is explored with respect to published data.

Development of a Constitutive Model of Polypropylene for Thermoforming

In this paper the authors outline a constitutive model, implemented within finite element analyses, which was developed for large deformation, high temperature multi‐axial stretching of polypropylenes. The model has been generalised to a fully 3‐dimensional thermally coupled form. The paper describes how model parameters were characterised using constant width, biaxial and sequential stretching of polypropylenes at elevated temperature using a custom built flexible biaxial stretching machine developed at Queen’s University Belfast. The paper presents results of finite element model predictions of material stretching behaviour compared to range of physical experiments. The results presented in the paper confirm that this model is very effective in predicting the complex thermo‐mechanical behaviours of polypropylenes at elevated temperatures.

Application of activated barrier hopping theory to viscoplastic modeling of glassy polymers

An established statistical mechanical theory of amorphous polymer deformation has been incorporated as a plastic mechanism into a constitutive model and applied to a range of polymer mechanical deformations. The temperature and rate dependence of the tensile yield of PVC, as reported in early studies, has been modeled to high levels of accuracy. Tensile experiments on PET reported here are analyzed similarly and good accuracy is also achieved. The frequently observed increase in the gradient of the plot of yield stress against logarithm of strain rate is an inherent feature of the constitutive model. The form of temperature dependence of the yield that is predicted by the model is found to give an accurate representation. The constitutive model is developed in two-dimensional form and implemented as a user-defined subroutine in the finite element package ABAQUS. This analysis is applied to the tensile experiments on PET, in some of which strain is localized in the form of shear bands and necks. These deformations are modeled with partial success, though adiabatic heating of the instability causes inaccuracies for this isothermal implementation of the model. The plastic mechanism has advantages over the Eyring process, is equally tractable, and presents no particular difficulties in implementation with finite elements.

Concurrent Multiscale Kinetic Monte Carlo-Continuum Models for the Evolution of Solids via Diffusion

A kinetic Monte Carlo (KMC) model for surface diffusion on a 2D lattice is proposed. An equivalent continuum cellular automaton (CA) model is derived from this. These models are shown to produce similar results at high temperatures. A hybrid KMC-CA model is derived which consistently allows material to transfer between a deterministic CA model and a stochastic KMC model concurrently embedded within it. The quality of the model is demonstrated by simulating the flattening of a sinusoidal surface profile and the evolution of an elliptical body into a circular one.