.jpg)
Image Credits: Supphachai Salaeman/shutterstock.com
Computational methods that can simulate reactions, how a molecule behaves in a certain environment and what properties a material will exhibit (amongst other areas) have been gaining interest in recent years to save money and time by negating the need for multiple experiments. Molecular dynamics is one of the most widely used computational methods, and in this article, we look at one variation known as non-equilibrium molecular dynamics (NEMD).
It’s no secret that running a series of experiments to find the optimal synthesis conditions, to determine the effects of doping a material or to understand how a material behaves under certain conditions, can take a lot of time and money (and both are often sparse in many research laboratories). Molecular dynamics (MD) has established itself as a useful method for studying the physical environment of atoms and molecules to define how reactions occur at the molecular level and how different constituents can interact within an ideal system.
Non-Equilibrium Molecular Dynamics (NEMD)
One variant of molecular dynamics is non-equilibrium molecular dynamics. Non-equilibrium molecular dynamics are required when the system being modelled doesn’t satisfy equilibrium conditions. Equilibrium conditions can be defined as when the atomic vibrations of the system follow the phonon modes in the system. So, if the time required to reach the equipartition of energy (i.e. an equal amount of energy in each energy state at thermal equilibrium) is quicker than the lifetime of the phonon mode, then the system is deemed to be in a non-equilibrium state.
Much like the equilibrium counterpart, non-equilibrium molecular dynamics is based on time-reversible equations of motion, however, it differs from conventional mechanics principles by using a microscopic environment for the macroscopic Second Law of Thermodynamics.
The deviation from the equilibrium state occurs through a perturbation (a deviation arising from an external environment) and there is no full theory to define how non-equilibrium states will behave. However, these perturbations can be limited and separated into linear and non-linear classes. By limiting the perturbations to certain conditions, it has enabled molecular dynamics to be adapted to treat non-equilibrium systems. The main way in which this has been achieved is by replacing the external thermodynamic environment with a series of controls that can tune the many variables of the system, such as pressure, temperature, induced stress and the energy inputted into the system. This provides the link between the dynamics at the microscopic level and the non-equilibrium properties that occur at the macroscopic level.
Equilibrium molecular dynamics provides a constant distribution of properties, be it density, temperature or pressure, across a given part of the system so that the whole system acts in unison, i.e. if the temperature is too low, then it can be adjusted by multiplying all the temperature velocities in the system by the same multiplier. This is where the tunable properties in non-equilibrium molecular dynamics can provide a high degree of control to the system. When a system is not acting in an equilibrium manner, individual variables and localized areas can be changed by a defined value, and another area can be changed by a different amount if the system requires it.
However, one downside to non-equilibrium molecular dynamics is that it requires a large perturbation strength at the macroscale to produce a detectable microscale response. This is because a large perturbation strength is required to produce a response that is greater than the surrounding statistical noise of the system. There has, however, been some new mathematical inputs created that can minimize the level of noise within the system, enabling smaller perturbations to be employed. This is known as the subtraction method.
Overall, non-equilibrium molecular dynamics offers a way to simulate systems which do not adhere to the conventional equilibrium model in many computational approaches; and to help understand what is going on at the molecular level, understand the constraints of the system and to evaluate the properties of a molecular system. Even though non-equilibrium molecular dynamics has been around for a while now, new formulae are always being developed to provide more accurate insights into non-equilibrium systems and to help reduce the statistical noise within these systems.
Sources:
- “Nonequilibrium molecular dynamics”- Hoover G. Wm. And Hoover C. G., Condensed Matter Physics, 2005
- “Chapter 2.17- NON-EQUILIBRIUM MOLECULAR DYNAMICS”- Ciccotti G. et al, Handbook of Materials Modeling. Volume I: Methods and Models, Springer Publishing, 2005
Disclaimer: The views expressed here are those of the author expressed in their private capacity and do not necessarily represent the views of AZoM.com Limited T/A AZoNetwork the owner and operator of this website. This disclaimer forms part of the Terms and conditions of use of this website.