Mesoscale modelling

The linkage of microscopic and macroscopic properties is not without challenges, both theoretical and experimental. Statistical mechanics and thermodynamics provide the connection between molecular properties and the behavior of macroscopic matter. Coupled with statistical mechanics, computer simulation of the structure, properties, and dynamics of mesoscale models is now feasible and can handle the increase in length and time scales. 

Finally, it should be mentioned that a combination of COSMO-RS with tools such as MESODYN [127] or DPD [128] (dissipative particle dynamics) may lead to further progress in the area of the mesoscale modeling of inhomogeneous systems. Such tools are used in academia and industry in order to explore the complexity of the phase behavior of surfactant systems and amphiphilic block-co-polymers. In their coarse-grained 3D description of the long-chain molecules the tools require a thermodynamic kernel... 

Lipfert, F.W. Dupuis, L.R. Schaedler, J.S. Methods for Mesoscale Modeling for Materials Damage Assessment, Brookhaven National Laboratory Report to U.S. Environmental Protection Agency, BNL 37508, April 1985. 

Sewell and co workers [145-148] have performed molecular dynamics simulations using the HMX model developed by Smith and Bharadwaj [142] to predict thermophysical and mechanical properties of HMX for use in mesoscale simulations of HMX-containing plastic-bonded explosives. Since much of the information needed for the mesoscale models cannot readily be obtained through experimental measurement, Menikoff and Sewell [145] demonstrate how information on HMX generated through molecular dynamics simulation supplement the available experimental information to provide the necessary data for the mesoscale models. The information generated from molecular dynamics simulations of HMX using the Smith and Bharadwaj model [142] includes shear viscosity, self-diffusion [146] and thermal conductivity [147] of liquid HMX. Sewell et al. have also assessed the validity of the HMX flexible model proposed by Smith and Bharadwaj in molecular dynamics studies of HMX crystalline polymorphs. 

In this chapter we focus on atomistic predictions of thermophysical and mechanical properties of HMX crystals and liquid important to the development of reliable mesoscale equations of state. The outline of the remainder of the chapter is as follows In section 2 we describe briefly the philosophy and overall approach we have taken to force field development, including the results of quantum chemistry calculations for HMX and smaller model compounds that were used in the force field parameterization. The focus of section 3 is on the properties of liquid HMX, for which experimental data are completely lacking. Structural, thermal, and mechanical properties of the three pure crystal polymorphs of HMX are presented in section 4, where the results are compared to the available experimental data. At the ends of sections 3 and 4 we discuss briefly the importance of the various properties with mesoscale models of high explosives, with an emphasis on conditions relevant to weak shock initiation. We conclude in section 5, and provide our opinions (and justifications, based on our interactions with mesoscale modelers) regarding which HMX properties and phenomena should comprise the next targets for study via atomistic simulation. 

Of course, nanocomposites are not the only area where mesoscale theories are being used to predict nanostructure and morphology. Other applications include—but are not limited to—block copolymer-based materials, surfactant and lipid liquid crystalline phases, micro-encapsulation of drugs and other actives, and phase behavior of polymer blends and solutions. In all these areas, mesoscale models are utilized to describe—qualitatively and often semi-quantitatively—how the structure of each component and the overall formulation influence the formation of the nanoscale morphology. 

Fio. 4. Types of multiscale modeling and solution strategies. Hybrid models (one model at each scale) apply well when there is separation of scales (onion or nested-type models). When there is lack of separation of scales, mesoscale models need to be developed where the same technique (e.g., MD or MC) is accelerated. Alternatively, multigrid (heterogeneous) hybrid models can be employed where the unresolved degrees of freedom are determined from a finer scale model and passed to a coarser scale model. 

Fig. 6.19 The basis of the mesoscale model of Rouby and Reynaud. The axial stress, oy in the fiber decreases linearly over the slip length, from a peak value of oy° at the edge of the matrix crack, to a value of o(Ef/Ec) at the end of the slip-zone (z = ls). It is assumed that the crack spacing / is larger than twice the load transfer length /,. It is assumed that the fiber stress decreases linearly to zero over the load transfer length l,. After Rouby and Reynaud.46...

One mesoscale model, i.e., the National Oceanic and Atmospheric Administration (NOAA) s Weather Research Forecast model with Chemistry (WRF/Chem) (Grell et al. 2005 Fast et al. 2006 Zhang et al. 2010a)... 

MM5 The Perm State University (PSU)/NCAR mesoscale model... 

The on-line coupled regional meteorology-chemistry model MCCM (Mesoscale climate chemistry model, GreU et al. 2000) has been developed at the IMK-IFU on the basis of the non hydrostatic NCAR/Penn State University mesoscale model... 

The multiscale meteorology and chemistry model system M-SYS consists of the mesoscale models MEsoscale TRAnsport and Stream (METRAS Schliinzen 1990 Schliinzen and Katzfey 2003) and MEsoscale Chemistry Transport Model (MECTM Muller et al. 2000 Schliinzen and Meyer 2007), which are used in... 

Cox R, Bauer BL, Smith T (1998) Mesoscale model intercomparison. Bull Am Meteorol Soc 79 265-283... 

Lenz C-J, Muller F, Schliinzen KH (2000) The sensitivity of mesoscale chemistry transport model results to boundary values. Environ Monit Assess 65 287-298 L6pez SD, Liipkes C, Schliinzen KH (2005) The effects of different k-e-closures on the results of a micro-scale model for the flow in the obstacle layer. Meteorol Z 14 839-848 Muller F, Schliinzen KH, Schatzmann M (2000) Test of numerical solvers for chemical reaction mechanisms in 3D air quality models. Environ Model Softw 15 639-646 Schliinzen KH (1990) Numerical studies on the inland penetration of sea breeze fronts at a coastline with tidally flooded mudflats. Beitr Phys Atmos 63 243-256 Schliinzen KH, Katzfey JJ (2003) Relevance of subgrid-scale land-use effects for mesoscale models. Tellus 55A 232-246... 

Martini A, Clappier A, Rotach MW (2002) An urban surface exchange parameterisation for mesoscale models. Bound Layer Meteorol 104 261-304... 

Modeling of the PFSA membrane has been investigated for the past two decades using phenomenological approaches " based on experimental findings, atomistic modeling "" based on classical molecular mechanics, and mesoscale modeling "" "... 

Despite these successes, molecular modelling will never be able to address phenomena, which involve length scales of hundreds of nanometers and more, such as the phase separation of block-copolymers, or very long timescales, such as mechanical properties related to sub Tg relaxations. Therefore more and more effort is devoted to the development of mesoscale models linked in a well defined way to the atomic level. 

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