### Resumé

a part of its density-temperature phase diagram spanning six decades of

temperatures: from 10−6 to 1 and three decades of densities: from 10−5 to 0.

01. The EXP potential is purely repulsive and cannot uphold a liquid-

gas interface, but a narrow fluid-solid coexistence region is found. The

main focus of the research has been the fluid phase. In this phase strong

correlations between the fluctuations in the potential energy and in the virial

is found. The strong correlations are found to persist far into the dilute fluid.

The properties of the EXP-potential is investigated with respect to structure,

dynamics, thermodynamics and with respect to the isomorph theory.

The investigation of the fluid phase revealed the existence of two distinct

regions: A gas phase and a liquid phase. The transition between the phases

is smooth. A structural signature to distinguish gas from liquid was defined

as the existence of a first minimum in radial distribution function. The

signature is ambiguous as it is dependant on the numerical protocols used.

It nevertheless serves the purpose of separating the two identified phases.

The gas phase has different domains in relation to the isomorph theory, since

there is a cold dilute and strongly correlating gas, and hot gas that does not

have strong correlations.

The strongly correlating gas was found to be of great interest as it is

characterized by being very dilute and controlled by single pair interaction.

This simplicity allows for prediction based on kinetic theory of: the state

point dependence of the reduced diffusion coefficient, the change in reduced

excess isochoric specific heat capacity along isomorphs, the temperature

dependent correlation coefficient (R), and the density scaling exponent (γ).

The predictions agrees with simulation results. The EXP system is found to conform well with hidden scale invariance throughout most of the explored phase diagram. The correlation is found to depend almost entirely on temperature and stays well above 0.9 for temperatures lower than 0.2. Density dependence of the correlation is only at the highest densities. Due to the strong correlations EXP system is found to have isomorphs in the low temperatures. Five isomorphs, each traced by three different techniques were investigaated. The different techniques are: The small step method tracing the “true” isomorphs, the direct isomorph check (DIC) allowing for larger density and temperature jumps, and the hp(ρ) method yielding a functional form of the isomorph. The different methods are compared and its found that the DIC method works well even for very long density jumps if the system is in the condensed region. The analytical hp(ρ) method is tested for different choices of

p(p∈ {0,1,2}) In the condensed phase p= 2 is found to give more accurate results, and that as the system becomes increasingly dilute system, p tends to zero in the gas phase. By a combination of kinetic theory and isomorph theory an ii expression to predict the optimal p for that state point, from single simula-

tion at the state point is derived and seen to agree well with the isomorph

observation.

The thesis conclude with a chapter describing how the EXP-potential

might provide a definition and explanation of quasi-universality and a demon-

stration hereof by mapping four Lennard-Jones state points to the EXP-

potential, using foremost the reduced diffusion constant and “fine tuning”

by the density scaling exponent. The quasi-universality predicts systems

with matching dynamics also have matching structure. Structure is com-

pared by the radial distribution function and a very good collapse is found.

The EXP-potential was simulated using Roskilde University Molecular

Dynamic (RUMD) open-source software on NVIDIA graphic-cards in the

Roskilde University HPC center.

Originalsprog | Engelsk |
---|

Udgivelses sted | Roskilde |
---|---|

Forlag | Roskilde Universitet |

Antal sider | 120 |

Status | Udgivet - 2018 |

### Citer dette

*EXP-potential and quasi-universality: A study*. Roskilde: Roskilde Universitet.

}

*EXP-potential and quasi-universality: A study*. Roskilde Universitet, Roskilde.

**EXP-potential and quasi-universality : A study.** / Bacher, Andreas Kvist.

Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning

TY - BOOK

T1 - EXP-potential and quasi-universality

T2 - A study

AU - Bacher, Andreas Kvist

PY - 2018

Y1 - 2018

N2 - This work investigates the exponential pair potential (EXP-potential) ina part of its density-temperature phase diagram spanning six decades oftemperatures: from 10−6 to 1 and three decades of densities: from 10−5 to 0.01. The EXP potential is purely repulsive and cannot uphold a liquid-gas interface, but a narrow fluid-solid coexistence region is found. Themain focus of the research has been the fluid phase. In this phase strongcorrelations between the fluctuations in the potential energy and in the virialis found. The strong correlations are found to persist far into the dilute fluid.The properties of the EXP-potential is investigated with respect to structure,dynamics, thermodynamics and with respect to the isomorph theory.The investigation of the fluid phase revealed the existence of two distinctregions: A gas phase and a liquid phase. The transition between the phasesis smooth. A structural signature to distinguish gas from liquid was definedas the existence of a first minimum in radial distribution function. Thesignature is ambiguous as it is dependant on the numerical protocols used.It nevertheless serves the purpose of separating the two identified phases.The gas phase has different domains in relation to the isomorph theory, sincethere is a cold dilute and strongly correlating gas, and hot gas that does nothave strong correlations.The strongly correlating gas was found to be of great interest as it ischaracterized by being very dilute and controlled by single pair interaction.This simplicity allows for prediction based on kinetic theory of: the statepoint dependence of the reduced diffusion coefficient, the change in reducedexcess isochoric specific heat capacity along isomorphs, the temperaturedependent correlation coefficient (R), and the density scaling exponent (γ).The predictions agrees with simulation results. The EXP system is found to conform well with hidden scale invariance throughout most of the explored phase diagram. The correlation is found to depend almost entirely on temperature and stays well above 0.9 for temperatures lower than 0.2. Density dependence of the correlation is only at the highest densities. Due to the strong correlations EXP system is found to have isomorphs in the low temperatures. Five isomorphs, each traced by three different techniques were investigaated. The different techniques are: The small step method tracing the “true” isomorphs, the direct isomorph check (DIC) allowing for larger density and temperature jumps, and the hp(ρ) method yielding a functional form of the isomorph. The different methods are compared and its found that the DIC method works well even for very long density jumps if the system is in the condensed region. The analytical hp(ρ) method is tested for different choices ofp(p∈ {0,1,2}) In the condensed phase p= 2 is found to give more accurate results, and that as the system becomes increasingly dilute system, p tends to zero in the gas phase. By a combination of kinetic theory and isomorph theory an ii expression to predict the optimal p for that state point, from single simula-tion at the state point is derived and seen to agree well with the isomorphobservation.The thesis conclude with a chapter describing how the EXP-potentialmight provide a definition and explanation of quasi-universality and a demon-stration hereof by mapping four Lennard-Jones state points to the EXP-potential, using foremost the reduced diffusion constant and “fine tuning”by the density scaling exponent. The quasi-universality predicts systemswith matching dynamics also have matching structure. Structure is com-pared by the radial distribution function and a very good collapse is found.The EXP-potential was simulated using Roskilde University MolecularDynamic (RUMD) open-source software on NVIDIA graphic-cards in theRoskilde University HPC center.

AB - This work investigates the exponential pair potential (EXP-potential) ina part of its density-temperature phase diagram spanning six decades oftemperatures: from 10−6 to 1 and three decades of densities: from 10−5 to 0.01. The EXP potential is purely repulsive and cannot uphold a liquid-gas interface, but a narrow fluid-solid coexistence region is found. Themain focus of the research has been the fluid phase. In this phase strongcorrelations between the fluctuations in the potential energy and in the virialis found. The strong correlations are found to persist far into the dilute fluid.The properties of the EXP-potential is investigated with respect to structure,dynamics, thermodynamics and with respect to the isomorph theory.The investigation of the fluid phase revealed the existence of two distinctregions: A gas phase and a liquid phase. The transition between the phasesis smooth. A structural signature to distinguish gas from liquid was definedas the existence of a first minimum in radial distribution function. Thesignature is ambiguous as it is dependant on the numerical protocols used.It nevertheless serves the purpose of separating the two identified phases.The gas phase has different domains in relation to the isomorph theory, sincethere is a cold dilute and strongly correlating gas, and hot gas that does nothave strong correlations.The strongly correlating gas was found to be of great interest as it ischaracterized by being very dilute and controlled by single pair interaction.This simplicity allows for prediction based on kinetic theory of: the statepoint dependence of the reduced diffusion coefficient, the change in reducedexcess isochoric specific heat capacity along isomorphs, the temperaturedependent correlation coefficient (R), and the density scaling exponent (γ).The predictions agrees with simulation results. The EXP system is found to conform well with hidden scale invariance throughout most of the explored phase diagram. The correlation is found to depend almost entirely on temperature and stays well above 0.9 for temperatures lower than 0.2. Density dependence of the correlation is only at the highest densities. Due to the strong correlations EXP system is found to have isomorphs in the low temperatures. Five isomorphs, each traced by three different techniques were investigaated. The different techniques are: The small step method tracing the “true” isomorphs, the direct isomorph check (DIC) allowing for larger density and temperature jumps, and the hp(ρ) method yielding a functional form of the isomorph. The different methods are compared and its found that the DIC method works well even for very long density jumps if the system is in the condensed region. The analytical hp(ρ) method is tested for different choices ofp(p∈ {0,1,2}) In the condensed phase p= 2 is found to give more accurate results, and that as the system becomes increasingly dilute system, p tends to zero in the gas phase. By a combination of kinetic theory and isomorph theory an ii expression to predict the optimal p for that state point, from single simula-tion at the state point is derived and seen to agree well with the isomorphobservation.The thesis conclude with a chapter describing how the EXP-potentialmight provide a definition and explanation of quasi-universality and a demon-stration hereof by mapping four Lennard-Jones state points to the EXP-potential, using foremost the reduced diffusion constant and “fine tuning”by the density scaling exponent. The quasi-universality predicts systemswith matching dynamics also have matching structure. Structure is com-pared by the radial distribution function and a very good collapse is found.The EXP-potential was simulated using Roskilde University MolecularDynamic (RUMD) open-source software on NVIDIA graphic-cards in theRoskilde University HPC center.

M3 - Ph.D. thesis

BT - EXP-potential and quasi-universality

PB - Roskilde Universitet

CY - Roskilde

ER -