Hybrid particle-field molecular dynamics under constant pressure

Abstract

Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field interactions to represent systems coupled to constant external pressure. First, we show that the commonly used particle-field energy functional can be modified to model and parameterize the isotropic contributions to the pressure tensor without interfering with the microscopic forces on the particles. Second, we employ a square gradient particlefield interaction term to model non-isotropic contributions to the pressure tensor, such as in surface tension phenomena. This formulation is implemented within the hybrid particle-field molecular dynamics approach and is tested on a series of model systems. Simulations of a homogeneous water box demonstrate that it is possible to parameterize the equation of state to reproduce any target density for a given external pressure. Moreover, the same parameterization is transferable to systems of similar coarse-grained mapping resolution. Finally, we evaluate the feasibility of the proposed approach on coarse-grained models of phospholipids, finding that the term between water and the lipid hydrocarbon tails is alone sufficient to reproduce the experimental area per lipid in constant-pressure simulations, and to produce a qualitatively correct lateral pressure profile.

Hamiltonian and alias-free hybrid particle–field molecular dynamics

“…5 A disadvantage however, is that this approach does not allow reducing the grid size in order to control the accuracy. Direct dependence of the interactions on the grid size is in particular not ideal for the newly developed constant-pressure simulations methodology, 25 where the simulation box, and thus the grid size, changes with time. In this work our goal is to establish a formulation that, being still consistent with the hPF-MD procedure of Milano and Kawakatsu, 3 additionally allows for the systematic control of the accuracy by grid refinement.…”

“…In hPF-MD, the most prominent example of reported aliasing appears when studying molecular assemblies, where instead of predicting spherical vesicles or droplets, a cubic shape oriented according to the grid is produced. 25,26 This particular artifact has two main causes. First, the grid size can be too coarse to represent a spherical shape.…”

Automated determination of hybrid particle-field parameters by machine learning

“…Second, the protocol is very general, and can thus be used to concomitantly optimise the mixing terms of the interaction energy (χ) and any other parameter of relevance present in other parts of the energy functional. This is particularly interesting in the view of recent advances for hPF model potentials, which include, for example, specific potentials for peptides, for electrostatics [22][23][24], or for surface energy terms [29,30]. Finally, being an automatic procedure, BO does not require userbased fine tuning of the parameters, ensuring a more systematic and reproducible determination of the potentials, especially for chemically complex systems.…”

“…Nonetheless, satisfactory quantitative agreement with reference data, especially in chemically complex systems, usually requires an a posteriori heuristic fine tuning of at least some of the values of theχ matrix [21]. Importantly, even though the first term of the interaction energy in (2) accounts in principle for the total energy of mixing, in recent times the addition of other terms to the W functional, for example explicitly describing electrostatics [22][23][24] or surface interactions [29,30], poses the problem of appropriately factorising such contributions out the mixingχ term to avoid non-physical double-counting. In these cases,χ loses a direct physical meaning, and for this reason it is problematic to define plausible values forχ directly from theoretical models.…”

RuSseL: A Self-Consistent Field Theory Code for Inhomogeneous Polymer Interphases

“…Mesoscopic simulations have been instrumental in unveiling the phenomena and mechanisms that govern the thermodynamics and dynamics of polymer interfaces [1,2]. Over the years, a wide class of such mesoscopic approaches have been developed for addressing such systems, including Lattice Boltzmann [3], particle (e.g., Dissipative Particle Dynamics [4]), hybrid particle-field [5][6][7][8], and purely field theoretic methods, such as density functional theory [9] and Self-Consistent Field Theory (SCFT) [10][11][12][13]. Regarding the latter, mesoscopic calculations of polymer systems based on SCFT have been established as a powerful theoretical tool for the description of their thermodynamic and structural properties [12,14,15].…”