226 S.McGrother,G.Goldbeck-Wood,and Y.M.Lam 11.3.1 Atomistic Simulation Fully atomistic simulation (where each atom is uniquely identified)is the core technology of polymer modelling.The methods use molecular mechanics,dy- namics and Monte Carlo algorithms to probe the conformational and config- urational behaviour of arbitrary materials.Most material properties can be inferred from these techniques,although properties that are fundamentally electronic (polarizability,dielectric constant,rates of chemical reaction,etc) are not the domain of classical simulation.The accuracy of property pre- diction relies on the force field,that is the mathematical expression used to create the potential function of the interacting components.These force fields comprise terms for:bond stretching,bond bending,torsional twisting,out of plane bending and pair-combinations of these.A typical force-field expression is given in 11.1. por=∑D,-ea6-]+∑o(g-oP +∑H,1+scos(no)+Hxx +∑∑6-o0-6)+∑Faw(0-og-6) ∑∑Fo6-bo)0-o)+∑∑FoXX +∑F9ecos(0-o)(g-%) Σ[()-2()门+∑aa (11.1) Most force-fields are comparable in their accuracy for the minimum en- ergy structure of simple molecules since they are parameterised to reproduce known behaviour.The true test of a force field is prediction of density and cohesive properties (heat of vaporization,solubility parameter,etc).For these properties the determining factor is the accuracy of non-bonded dispersion and electrostatic interactions(the last two terms in 11.1). Accelrys has developed its own force field called COMPASS [11.7,11.8], which stands for'Condensed-phase Optimized Molecular Potentials for Atom- istic Simulation Studies'.It is an ab initio force field because most parameters are initially derived based on data determined by ab initio quantum mechan- ics calculations.Following this step,parameters are optimized on the basis of experimental data for condensed phase properties.In particular,thermophys- ical data for molecular liquids and crystals are used to refine the nonbond parameters via molecular dynamics simulations.The result is a highly accu- rate force field,which gives unsurpassed prediction for density and cohesive226 S. McGrother, G. Goldbeck-Wood, and Y.M. Lam 11.3.1 Atomistic Simulation Fully atomistic simulation (where each atom is uniquely identified) is the core technology of polymer modelling. The methods use molecular mechanics, dy￾namics and Monte Carlo algorithms to probe the conformational and config￾urational behaviour of arbitrary materials. Most material properties can be inferred from these techniques, although properties that are fundamentally electronic (polarizability, dielectric constant, rates of chemical reaction, etc) are not the domain of classical simulation. The accuracy of property pre￾diction relies on the force field, that is the mathematical expression used to create the potential function of the interacting components. These force fields comprise terms for: bond stretching, bond bending, torsional twisting, out of plane bending and pair-combinations of these. A typical force-field expression is given in 11.1. EPOT =  b Db  1 − e−α(b−b0)  + θ Hθ(θ − θ0) 2 +  φ Hφ [1 + s cos(nφ)] + χ Hχ χ2 +  b  b
(b − b0)(b − b 0) + θ  θ
Fθθ
(θ − θ0)(θ − θ 0)  b  θ Fbθ(b − b0)(θ − θ0) + χ  χ
Fχχ
χχ +  φ Fφθθ
cos φ(θ − θ0)(θ − θ 0) + ε r∗ r 12 − 2 r∗ r 6 +qiqj/εrij (11.1) Most force-fields are comparable in their accuracy for the minimum en￾ergy structure of simple molecules since they are parameterised to reproduce known behaviour. The true test of a force field is prediction of density and cohesive properties (heat of vaporization, solubility parameter, etc). For these properties the determining factor is the accuracy of non-bonded dispersion and electrostatic interactions (the last two terms in 11.1). Accelrys has developed its own force field called COMPASS [11.7, 11.8], which stands for ‘Condensed-phase Optimized Molecular Potentials for Atom￾istic Simulation Studies’. It is an ab initio force field because most parameters are initially derived based on data determined by ab initio quantum mechan￾ics calculations. Following this step, parameters are optimized on the basis of experimental data for condensed phase properties. In particular, thermophys￾ical data for molecular liquids and crystals are used to refine the nonbond parameters via molecular dynamics simulations. The result is a highly accu￾rate force field, which gives unsurpassed prediction for density and cohesive