# Calculation of process paramters for phase transitions

This White Paper demonstrates the capabilities of modern molecular dynamics simulations illustrated by the description of phase transitions. In particular, the identification of technically relevant parameters is shown by the example of the transition of methane from the liquid to the solid phase. These parameters have technical relevance for a variety of industrial processes, such as air conditioning and refrigeration technology or crystal growth.

# Introduction

In thermodynamics a phase transition is the conversion of one or more phases in other phases. In particular, the classification of the transitions between the gaseous, liquid and solid phases is shown in figure 1.)

There are a number of further complex phase transitions such as the metal-insulator transition.

In thermodynamics, the Ehrenfest classification is often used. In this case, thermodynamic parameters (enthalpy, volume) are considered as a function of a variable (such as temperature). If the (n-1) th derivative of this function is continuous, then it is a phase transition of n-th order.

Thus, for example melting, evaporation or solidification are first order phase transitions. Using the Ehrenfest representation, important parameters of the phase transition can be extracted. For example the critical temperature and the heat of evaporation will be obtained for the evaporation, using enthalpy-temperature diagram.

Phase transitions play an important role in nature and technology. Thus, for example refrigerants which have a particularly high heat of vaporization are used in compression refrigeration machines (refrigerators, air conditioners). Another example is the heat-transfer fluids which are used in solar systems. Their melting temperature is very low (<-20 ° C) and the boiling point is relatively high (> 100 ° C). Fig 1: Possible phase transitions between solid, liquid and gaseous phase.

# Phase transition of methane

As prototypicall example, the transition from the liquid to the gaseous phase in methane was evaluated.

## Simulation details

For the simulation the reactive force field ReaxFF [Duin01, Duin03, Forg10] with a specially developed set of parameters was used. The required length and time scales, which are necessary for the determination of the phase transition, can be achieved by the use of a force-field. The simulation included a total of 5000 methane molecules and a total simulation time of 5 ns.

## Simulation results:

The enthalpy as a function of the temperature allowed the determination of the enthalpy of vaporization and heat of the boiling point. As can be seen, both the enthalpy as well as the density as a function of temperature exhibits a jump. Thus, there is a phase transition of first order. Due to the fact that the system is heated up in a finite time it is not a "sharp" jump. Therefore the choice of the total simulation time depends on the desired accuracy. Fig. 2: Simulation cell with 5000 molecules.Left liquid phase. Right gaseous phase. Fig 2: Enthalpy (left) and density (right) depending on the temperature.

# Summary

The performed simulation has shown that the reactive force field ReaxFF is ideally suited to simulate phase transitions. Particularly for chemicals for which the experimental study is difficult (eg, fire, pollution, etc.), it is of advantage to determine the parameters using molecular dynamics simulations in advance.

One potential application of the methodology outlined here can be the development of new cooling and solar agents or the description of deposition processes and crystal growth.