《纺织复合材料》课程参考文献（Computational Materials Science，From Basic Principles to Material Properties）11 Integration of Modelling at Various Length and Time Scales

11 Integration of Modelling at Various Length and Time Scales S.McGrother1,G.Goldbeck-Wood2,and Y.M.Lam3 1 Accelrys,9685 Scranton Rd,San Diego,CA,92121,USA 2 334 Cambridge Science Park,Cambridge CB4 OWN,UK 3 Nanyang Technological University,School of Materials Engineering,Nanyang Avenue,Singapore 639798 Abstract.Materials modelling tools have become increasingly integrated in the R&D portfolio.The unique insights available through simulation of materials at a range of scales,from the quantum and molecular,via the mesoscale to the finite element level,can provide discontinuous scientific advances.These tools are well validated and produce reliable,quantitative information.A key demand of academic and industrial research is that these tools become ever more integrated:integrated at each length and time scale with experimental methods and knowledge as well as integrated across the spectrum of scales in order to capture the multiscale nature of organisation in many materials. This paper will address recent efforts in this direction.The principal focus will be on the derivation of accurate input parameters for mesoscale simulation,and the subsequent use of finite element modeling to provide quantitative information regarding the properties of the simulated mesoscale morphologies. In mesoscale modeling the familiar atomistic description of the molecules is coarse-grained,leading to beads of fluid (representing the collective degrees of free- dom of many atoms).These beads interact through pair-potentials which,crucially if meaningful data are to be obtained,capture the underlying interactions of the constituent atoms.The use of atomistic modeling to derive such parameters will be discussed.The primary output of mesoscale modeling is phase morphologies with sizes up to the micron level.These morphologies are of interest,but little predic- tion of the material properties is available with the mesoscale tools.Finite element modeling can be used to predict physical and mechanical properties of arbitrary structures.Details of the link that has been established between Accelrys'Meso- Dyn [11.1]and MatSim's Palmyra-GridMorph [11.2]are given and highlighted with some recent validation work on polymer blends.These results suggest that the com- bination of simulations at multiple scales can unleash the power of modeling and yield important insights. 11.1 Introduction There are many levels at which modeling can be useful,ranging from the highly detailed ab initio quantum mechanics,through classical molecular modeling to process engineering modeling.These computations significantly reduce wasted experiment,allow products and processes to be optimized and S.McGrother,G.Goldbeck-Wood,and Y.M.Lam,Integration of Modelling at Various Length and Time Scales,Lect.Notes Phys.642,223-233(2004) http://www.springerlink.com/ C Springer-Verlag Berlin Heidelberg 2004

11 Integration of Modelling at Various Length and Time Scales S. McGrother1, G. Goldbeck-Wood2, and Y.M. Lam3 1 Accelrys, 9685 Scranton Rd, San Diego, CA, 92121, USA 2 334 Cambridge Science Park, Cambridge CB4 0WN, UK 3 Nanyang Technological University, School of Materials Engineering, Nanyang Avenue, Singapore 639798 Abstract. Materials modelling tools have become increasingly integrated in the R&D portfolio. The unique insights available through simulation of materials at a range of scales, from the quantum and molecular, via the mesoscale to the finite element level, can provide discontinuous scientific advances. These tools are well validated and produce reliable, quantitative information. A key demand of academic and industrial research is that these tools become ever more integrated: integrated at each length and time scale with experimental methods and knowledge as well as integrated across the spectrum of scales in order to capture the multiscale nature of organisation in many materials. This paper will address recent efforts in this direction. The principal focus will be on the derivation of accurate input parameters for mesoscale simulation, and the subsequent use of finite element modeling to provide quantitative information regarding the properties of the simulated mesoscale morphologies. In mesoscale modeling the familiar atomistic description of the molecules is coarse-grained, leading to beads of fluid (representing the collective degrees of free￾dom of many atoms). These beads interact through pair-potentials which, crucially if meaningful data are to be obtained, capture the underlying interactions of the constituent atoms. The use of atomistic modeling to derive such parameters will be discussed. The primary output of mesoscale modeling is phase morphologies with sizes up to the micron level. These morphologies are of interest, but little predic￾tion of the material properties is available with the mesoscale tools. Finite element modeling can be used to predict physical and mechanical properties of arbitrary structures. Details of the link that has been established between Accelrys’ Meso￾Dyn [11.1] and MatSim’s Palmyra-GridMorph [11.2] are given and highlighted with some recent validation work on polymer blends. These results suggest that the com￾bination of simulations at multiple scales can unleash the power of modeling and yield important insights. 11.1 Introduction There are many levels at which modeling can be useful, ranging from the highly detailed ab initio quantum mechanics, through classical molecular modeling to process engineering modeling. These computations significantly reduce wasted experiment, allow products and processes to be optimized and S. McGrother, G. Goldbeck-Wood, and Y.M. Lam, Integration of Modelling at Various Length and Time Scales, Lect. Notes Phys. 642, 223–233 (2004) http://www.springerlink.com/
c Springer-Verlag Berlin Heidelberg 2004

224 S.McGrother.G.Goldbeck-Wood,and Y.M.Lam permit large numbers of candidate materials to be screened prior to produc- tion. Accelrys offers quantum mechanics,molecular mechanics and mesoscale technologies.These methods cover many decades of both length and time scale(see Table 11.1),and can be applied to arbitrary materials:solids,liq- uids,interfaces,self-assembling fuids,gas phase molecules and liquid crystals, to name but a few.There are a number of factors,which need to be taken care of to ensure that these methods can be applied routinely and successfully First and foremost of course are the validity and useability of each method on its own,followed by their interoperability in a common and efficient user environment.These points are taken care of in state-of-the-art packages like the Materials Studio1 software [11.3]distributed by Accelrys. Table 11.1.Comparison of scales of modeling:quantum,classical atomistic simu- lation and mesoscale modeling Quantum AtomisticMesoscale Length Angstroms nm 100s of nm Fundamental Unit Electrons/nucleiatoms Beads representing many atoms T'ime scale 因 ns ms Dynamics Too expensive F=ma Hydrodynamics Of equal importance of course is the integration of the simulation methods with experiment.In modern materials research and development,one needs to be able to move almost seamlessly from experimental knowledge to simulation and back again,requiring multiple input-output relationships at a range of materials length and time scales.These can take the form of -Materials QSAR:quantitative structure -activity (property)relationships for materials aim to correlate molecular simulation results with experimen- tal measurements of(macroscale)properties. Parameterisation of simulations:accurate materials simulations based on input parameters gained from detailed simulation as well as experimental data. Multiscale simulations,based on establishing the appropriate communica- tion between the methods. In the following,we shall give further detail and examples for each of these cases. 1 Materials Studio is a registered trademark of Accelrys Inc

224 S. McGrother, G. Goldbeck-Wood, and Y.M. Lam permit large numbers of candidate materials to be screened prior to produc￾tion. Accelrys offers quantum mechanics, molecular mechanics and mesoscale technologies. These methods cover many decades of both length and time scale (see Table 11.1), and can be applied to arbitrary materials: solids, liq￾uids, interfaces, self-assembling fluids, gas phase molecules and liquid crystals, to name but a few. There are a number of factors, which need to be taken care of to ensure that these methods can be applied routinely and successfully. First and foremost of course are the validity and useability of each method on its own, followed by their interoperability in a common and efficient user environment. These points are taken care of in state-of-the-art packages like the Materials Studio
1 software [11.3] distributed by Accelrys. Table 11.1. Comparison of scales of modeling: quantum, classical atomistic simu￾lation and mesoscale modeling Quantum Atomistic Mesoscale Length Angstroms nm 100s of nm Fundamental Unit Electrons/nuclei atoms Beads representing many atoms Time scale fs ns ms Dynamics Too expensive F=ma Hydrodynamics Of equal importance of course is the integration of the simulation methods with experiment. In modern materials research and development, one needs to be able to move almost seamlessly from experimental knowledge to simulation and back again, requiring multiple input-output relationships at a range of materials length and time scales. These can take the form of – Materials QSAR: quantitative structure -activity (property) relationships for materials aim to correlate molecular simulation results with experimen￾tal measurements of (macroscale) properties. – Parameterisation of simulations: accurate materials simulations based on input parameters gained from detailed simulation as well as experimental data. – Multiscale simulations, based on establishing the appropriate communica￾tion between the methods. In the following, we shall give further detail and examples for each of these cases. 1 Materials Studio is a registered trademark of Accelrys Inc

11 Integration of Modelling at Various Length and Time Scales 225 11.2 Structure-Activity and Structure-Property Approaches Quantitative structure activity and property relationships (QSAR/QSPR) have long been used with great success in the life sciences.Based on exper- imental 'training set'data,correlations can be established between a range of molecular descriptors and biological activity.These correlations may take the form of equations derived by methods such as the Genetic Function Ap- proximation [11.4,or neural networks.QSAR methods have proved to be powerful tools for the design of molecular libraries,investigating similarity and diversity as well as predicting properties. Not surprisingly,such tools have also been applied successfully in a va- riety of materials cases as well [11.5,11.6.These statistical methods allow experimental information to be mined for important correlations,which can lead to deeper understanding of a material and optimised products.The cor- relations can be used to help design better materials.These new materials can be screened using the simulation methods and so an effective feedback loop is created which efficiently leads to new materials. However,the complexity and multiscale nature of many materials and their properties pose particular challenges in the application of QSAR meth- ods,which need to be address in future Materials QSAR tools.Firstly,there are many different materials classes with potentially very different sets of descriptors relevant to them.There is little knowledge so far about which are the most important ones relating for example to the prediction of per- meability properties of polymer materials.Secondly,the calculation of the descriptors may involve simulations using methods at various scales,some of which may be computationally expensive. 11.3 Atomistic and Mesoscale Simulations and Their Parameterisation Quantum,atomistic and mesoscale simulations provide valuable insights into the detailed physico-chemical behaviour of molecules and materials,and there are many properties,which can be determined directly from each,includ- ing structure,energies,stability,activity,diversity,solubility,adhesion,ad- sorption,diffusion,mechanical constants,spectra,and morphology.Ab initio quantum methods have the advantage that they can in principle be used for any element in the periodic table without specific parameterisation.They have been extensively developed so that one is now able to handle systems of a few hundred atoms routinely.For larger systems,however,methods re- quiring parameterisation are inevitable.In the following,we focus on force field developments for atomistic simulations and parameter determination for mesoscale simulations

11 Integration of Modelling at Various Length and Time Scales 225 11.2 Structure-Activity and Structure-Property Approaches Quantitative structure activity and property relationships (QSAR/QSPR) have long been used with great success in the life sciences. Based on exper￾imental ‘training set’ data, correlations can be established between a range of molecular descriptors and biological activity. These correlations may take the form of equations derived by methods such as the Genetic Function Ap￾proximation [11.4], or neural networks. QSAR methods have proved to be powerful tools for the design of molecular libraries, investigating similarity and diversity as well as predicting properties. Not surprisingly, such tools have also been applied successfully in a va￾riety of materials cases as well [11.5, 11.6]. These statistical methods allow experimental information to be mined for important correlations, which can lead to deeper understanding of a material and optimised products. The cor￾relations can be used to help design better materials. These new materials can be screened using the simulation methods and so an effective feedback loop is created which efficiently leads to new materials. However, the complexity and multiscale nature of many materials and their properties pose particular challenges in the application of QSAR meth￾ods, which need to be address in future Materials QSAR tools. Firstly, there are many different materials classes with potentially very different sets of descriptors relevant to them. There is little knowledge so far about which are the most important ones relating for example to the prediction of per￾meability properties of polymer materials. Secondly, the calculation of the descriptors may involve simulations using methods at various scales, some of which may be computationally expensive. 11.3 Atomistic and Mesoscale Simulations and Their Parameterisation Quantum, atomistic and mesoscale simulations provide valuable insights into the detailed physico-chemical behaviour of molecules and materials, and there are many properties, which can be determined directly from each, includ￾ing structure, energies, stability, activity, diversity, solubility, adhesion, ad￾sorption, diffusion, mechanical constants, spectra, and morphology. Ab initio quantum methods have the advantage that they can in principle be used for any element in the periodic table without specific parameterisation. They have been extensively developed so that one is now able to handle systems of a few hundred atoms routinely. For larger systems, however, methods re￾quiring parameterisation are inevitable. In the following, we focus on force field developments for atomistic simulations and parameter determination for mesoscale simulations

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 cohesive

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. 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

11 Integration of Modelling at Various Length and Time Scales 227 properties of a wide range of organic and some inorganic materials.The COM- PASS force field is therefore a prime example of how accurate simulation at one scale (in this case electronic)and experimental data can be combined to great advantage in parameterisation of models at the next coarser scale (in this case atomistic). As an example of the typical<1%accuracy in density prediction which can be achieved with this method,Fig.11.1 shows the comparison between experimental and predicted densities for perfluorobutane over a range of tem- peratures 11.9. 2.2 2.1 Expt 2.0 Calc 19 1.8 1.6 15 ■ 14 13 1.2 150 200 250 300 350 Temperature/K Fig.11.1.Density versus temperature of perfluorobutane,comparing a fit to ex- perimental data with values calculated from Molecular Dynamics simulations[11.9]. In Fig.11.2 we show how COMPASS performs for the solubility parame- ter,which is the square root of the cohesive energy density [11.10.It is crucial to be accurate in this parameter,in particular if mixture or diffusivity data is to be well reproduced.The toluene example shown in Fig.11.2 [11.9]is just one of many validations,which show that Molecular Dynamics simula- tions with the COMPASS force field meet this demand.We can conclude that COMPASS gives highly accurate data for key properties of bulk materials. 11.3.2 Mesoscale Methods In classical atomistic modelling,traditional Molecular Dynamics is used to obtain thermodynamic information about a pure or mixed system.Properties obtained using these microscopic simulations assume that the system is ho- mogeneous in composition,structure and density,which is a limitation.When a system is complex,comprising several components,only sparingly miscible

11 Integration of Modelling at Various Length and Time Scales 227 properties of a wide range of organic and some inorganic materials. The COM￾PASS force field is therefore a prime example of how accurate simulation at one scale (in this case electronic) and experimental data can be combined to great advantage in parameterisation of models at the next coarser scale (in this case atomistic). As an example of the typical < 1% accuracy in density prediction which can be achieved with this method, Fig. 11.1 shows the comparison between experimental and predicted densities for perfluorobutane over a range of tem￾peratures [11.9]. Fig. 11.1. Density versus temperature of perfluorobutane, comparing a fit to ex￾perimental data with values calculated from Molecular Dynamics simulations [11.9]. In Fig. 11.2 we show how COMPASS performs for the solubility parame￾ter, which is the square root of the cohesive energy density [11.10]. It is crucial to be accurate in this parameter, in particular if mixture or diffusivity data is to be well reproduced. The toluene example shown in Fig. 11.2 [11.9] is just one of many validations, which show that Molecular Dynamics simula￾tions with the COMPASS force field meet this demand. We can conclude that COMPASS gives highly accurate data for key properties of bulk materials. 11.3.2 Mesoscale Methods In classical atomistic modelling, traditional Molecular Dynamics is used to obtain thermodynamic information about a pure or mixed system. Properties obtained using these microscopic simulations assume that the system is ho￾mogeneous in composition, structure and density, which is a limitation. When a system is complex, comprising several components, only sparingly miscible