(588g) Configurational-Bias Monte Carlo Simulation to Predict the Supramolecular Self-Assemblies of Amphiphiles

Amphiphiles are long-chain molecules that possess a polar head and non-polar tail [1]. This unique chemical property of these molecules enables them to form a wide range of supramolecular self-assembled structure in polar solvents [2]. These structures impart unique properties to the surfactant solutions. Hence, these self-assembled structures have been explored extensively over the past decade [3]. Significant theoretical progress and fundamental understanding of these self-assemblies have been achieved in the advent of simulation methodologies like molecular dynamics (MD) [4]. MD simulations coupled with significant progress in modern supercomputing architectures have paved the path for multiple discoveries in the field of self-assembly [8]. However, MD algorithms are limited in terms of the time-scales they can simulate [7]. MD simulations can simulate only a few microseconds of self-assembly in the most advanced forms while requiring substantial computational resources [5]. This limits MD's application to explore a wide range of self-assembled structures as many self-assemblies take much longer times to form. Moreover, it becomes incredibly challenging to simulate complex self-assembles as numerical solutions tend to diverge in such instances.
Monte Carlo simulations are another class of techniques used for molecular studies at multiple length scales [6]. Specifically, Monte Carlo simulations involve the statistical sampling of energetically stable configurations of molecules in an ensemble. In recent years, many strategies such as the Gibb’s ensemble Monte Carlo [7] and grand canonical ensemble Monte Carlo with histogram reweighting methodologies [8] have been used extensively to compute the phase equilibrium of pure molecules with simple chemical structures. To further implement these strategies to complex macromolecules, specific biasing techniques are often utilized. One such biasing technique is the configurational-bias Monte Carlo (CBMC), which involves re-growing a molecule to explore its configurational space. Over the years, to improve the efficiency of CBMC sampling, multiple studies have been proposed [9-12]. However, these studies are specific to particular classes of surfactant molecules and cannot be readily extended to all the amphiphiles in general.
Motivated by the absence of such a generalized framework, we propose a CBMC simulation methodology that can be applied to predict a wide range of supramolecular self-assemblies of the surfactants. Here, we performed fragmentation to explore the bond-angle configurational space and dihedral angle space separately. In the proposed methodology, the amphiphiles are broken into fragments of sizes not greater than three. It was found that with a fragment size of three atoms, sampling of individual fragments enables us to explore the energy variations associated with only the bond-angles. This is because three points are always coplanar, and therefore, no dihedral conformations are explored when sampling individual fragments' configurations. The dihedral space is explored only when the fragments are regrown in the CBMC procedure. This proposed procedure prevents the CBMC algorithm's confinement to a local minimum and improves sampling efficiency. Furthermore, using the proposed CBMC scheme, equilibrium structures of various surfactant self-assemblies were predicted. Finally, the model predictions were validated with experimental data from small-angle X-ray scattering (SAXS).
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