The mechanical, chemical, and electronic properties of materials change depending on the scale at which we are measuring. Scales typically range from the nano to micro to macro levels. My question is, what frameworks have people found particularly useful for the mesoscopic scale of materials modeling, i.e., the level between micro and macro. A related question can be found here: What are the main computational frameworks used in materials modeling?

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    $\begingroup$ I think it's worth pointing out here that choosing a model/method at mesoscopic scales will require careful consideration of what aspects of the behavior are important. Mesoscopic is difficult because nanoscale behavior is probably still important, but impractical to model directly. $\endgroup$ May 4, 2020 at 7:06

2 Answers 2


I assume when you are asking about mesoscopic modeling you are looking for a scale higher than molecular dynamics and quantum mechanical simulations and a scale smaller than macroscopic finite element or finite volume modeling that typically mechanical engineers do for designing for example aircraft, reactors, etc. In this regime of mesoscopic modeling, typically two different approaches are famous:

  1. Dissipative Particle Dynamics (DPD): This method is nothing but just a coarse-grained molecular dynamics. It starts from coarse-graining of big molecular structures such as proteins or polymers into some beads that represent the structure of your material and then solves it by conventional molecular dynamics methods. The only difference is that in DPD the force fields represent the interaction of beads, not atoms in your structure and that's the challenging part to develop a coarse-grain model that could capture the properties of a large-scale molecular dynamics accurately and be much faster as well. So, overall, you coarse-grain your structure into beads, and then you solve it with methods similar to molecular dynamics to have a more efficient and cheaper computation in comparison to conventional molecular dynamics simulation.
  2. Lattice Boltzmann Method (LBM): I believe you know about computational fluid dynamics that mechanical engineers use for designing channels, aircraft, etc. to model the movement of fluids. Lattice Boltzmann method is similar to computational fluid dynamics method to capture the hydrodynamics of fluids but it comes from Boltzmann equation and kinetics theory as well as non-equilibrium thermodynamics instead of solving macroscopic Navier-Stokes equation. In the end, you solve Navier-Stokes equation but with a completely different approach. Here again, you coarse-grain your material into some particles or beads that contain a pre-defined number of atoms and then track their probability distribution function deterministically by using Maxwell-Boltzmann probability distribution and then calculate the hydrodynamics parameters (e.g. density, momentum, stress, energy, temperature, etc.) by taking ensemble average. The advantage in comparison to macroscopic computational fluid dynamics approaches is that you have a solid physical theory to capture complex phenomena easily such as the interaction of multi-component or multiphase fluids and materials and it is straightforward to couple this LBM approach with a coarse-grained molecular dynamics method (e.g. DPD) to for example study the hydrodynamics of polymeric solution where you capture the fluid movement of the solution with LBM and the movement of polymer chain with DPD or coarse-grained molecular dynamics.

Of course, you could consider other methods such as Monte-Carlo or Phase-Field as well in the mesoscopic regime (note that Phase-Field could be coupled with LBM usually) to capture the microstructure of materials or fluids.

Update: Definition of DPD beads, PCL is grouped into P beads, MDI is grouped into M beads, and BDO is grouped into B beads for example:

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Source: Hu et. al., Revealing the morphological architecture of a shape memory polyurethane by simulation, Scientific Reports 6:29180 ยท July 2016.

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    $\begingroup$ Could you add a definition of bids to your answer? $\endgroup$ May 4, 2020 at 7:04
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    $\begingroup$ @taciteloquence See updated answer. $\endgroup$ May 4, 2020 at 14:23

Calphad techniques should also be of interest. Calphad is based on thermodynamic models of the Gibbs energy starting from describing the pure elements in gas, liquid and different crystalline structures (also meta-stable ones) and more or less complex models describing solutions with model parameters fitted to experimental data and (for the last 20 years or so) DFT data.
Multi-component databases with such model parameters, normally fitted to binary and ternary systems over some temperature range, can be extrapolated to calculate the stable state with systems up to 5-10 elements with reasonable accuracy.
Calphad started some 50 years ago as a tool to calculate phase diagrams from thermodynamics with model parameters fitted to experimental data. But the thermodynamic description can provide chemical potentials, heat capacities, enthalpies etc also in meta-stable phases and it has become an important tool to simulate phase transformations.
There are a few commercial and free software available but the main problem is to find a good database, development of the databases is a tedious and slow process and the good databases can be quite expensive.


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