Ph.D.:

Long-time simulations of viscous liquids - from strong correlations to crystallization

Ulf R. Pedersen

Supervisor: Thomas B. Schroder

Committee: Prof. Jeppe C. Dyre, Prof. Gregor Diezemann and Prof. Francesco Sciortino

The thesis was submitted to Roskilde University ("Glass and Time") the 30th of January 2009 and defended 3rd of April 2009.

Thesis (no papers). thesis_URPedersen_30jan09-NoPapers.pdf (3.3Mb).

Thesis (all). thesis_URPedersen_30jan09.pdf (15Mb).

Lecture given at defense. urp_phdDefence.pdf (3.9Mb)

Lecture: Strong pressure-energy correlations in liquids - Origin and consequences. urp_strongCorr.pdf (4.3Mb).

Abstract

This philosophi� doctor thesis has thirteen companion papers. The major part is a theoretical and simulation study of a class of liquids referred to as strongly correlating liquids. However, one chapter is dedicated to a study of thermodynamic fluctuations of simulated phospholipid membranes, and another to a simulation study of crystallization of a binary mixture. The thesis also includes a short introduction to supercooled viscous liquids and molecular dynamics simulations. The final chapter is an outlook. The conclusions are as follows:

A class of model liquids exhibit strong correlation in the thermal fluctuations of the virial and potential energy at constant volume. The origin of the correlation is explained for the Lennard-Jones liquid. The pair energy can to a good approximation be replaced by an inverse power-law plus a linear term. At constant volume only the inverse power-law gives a contribution to fluctuations, thereby explaining the correlation. Two quantities characterize a strongly correlating liquid: i) A correlation coefficient, R, that determine the degree of correlation and ii) a slope, gamma, that determine the proportionality between virial and potential energy. If the correlation coefficient is close to unity the liquid is strongly correlating and 3*gamma equals the exponent of the inverse power-law.

For viscous liquids, the correlation coefficient equals the inverse square-root of a Prigogine-Defay ratio defined from three response functions. Also the slope can be determined from response functions. Literature values of the classical Prigogine-Defay suggests that van der Waals bonded liquids in general are strongly correlating.

Strongly correlating viscous liquids are more simple than viscous liquids in general: i) Slow dynamics are determined by a single relaxing parameter. Thus, time- and frequency-dependent response functions of a given ensemble are proportional. ii) Scale invariance is inherited from soft-sphere liquids though the effective inverse-power law. Thus, state points with the same value of rho**gamma/T have the same scaled structure and dynamics. These conclusions are verified in simulations.

Slow thermal fluctuations of volume and energy of simulated phospholipid membranes are strongly correlated. The origin of the strong correlation can be traced to the van der Waals bonded core of the membranes and, thus, have the same origin as simple strongly correlating liquids.

The last part of the thesis reports crystallization into the MgZn2 Laves phase of the binary Lennard-Jones mixture suggested by Wahnstrom [1991].

Abstract in danish:

Denne philosophi� doctor afhandling er ledsaget af tretten artikler. Hoveddelen er et teoretisk og simulerings studie af en klasse af v�sker refereret til som st�rkt ko- rrelerede v�sker. Dog er et kapitel dedikeret til et studie af termiske Fuktuationer af simulerede phospholipidmembraner, og et kapitel til et simuleringstudie af krystallis- ering af en bin�r blanding. Afhandlingen inkluderer ogs� en kort introduktion til underafk�lede visk�se v�sker samt molekyledynamik simuleringer. Det sidste kapitel omhandler fremtidige unders�gelser. F�lgende er konkluderet:

En klasse af modelv�sker udviser ved konstant volumen en st�rk korrelation i de termiske Fluktuationer af virial og potentiel energi. Korrelationens ophav er forklaret for Lennard-Jones v�sken. Parenergien kan med god tiln�rmelse erstattes med en in- vers potensfunktion plus et line�rt led. Ved konstant volumen er det kun den inverse potensfunktion som giver bidrag til Fluktuationer, og derved forklarer korrelationen. To st�rrelser karakteriserer en st�rkt korreleret v�ske: i) En korrelationskoeficient, R, som bestemmer graden af korrelation og ii) en h�ldning, gamma, som bestemmer pro- portionaliteten mellem virial og potentiel energi. Hvis korrelationskoeficienten er t�t p� 1, er v�sken st�rkt korrelerende og 3gamma er lig med eksponenten af den inverse potensfunktion.

For visk�se v�sker er korrelationskoeficienten lig med den inverse kvadratrod af en Prigogine-Defay kvotient defneret ud fra tre responsfunktioner. H�dningen kan ogs� bestemmes ud fra responsfunktioner. V�rdier af den klassiske Prigogine-Defay kvotient fra litteraturen indikerer, at van der Waals v�sker i almindelighed er st�rkt korrelerede.

St�rkt korrelerede visk�se v�sker er simplere end visk�se v�sker i almindelighed: i) Langsom dynamik er styret af en enkelt relakserende parameter. Derved er de tids- og frekvensafh�ngige responsfunktioner for et givet ensemble proportionale. ii) Ska- leringsinvarians af soft sphere-v�sker nedarves gennem den inverse potensfunktion. Derfor har tilstande med samme v�rdi af rho**gamma/T den samme skallerede struktur og dynamik. Simuleringer bekr�fter disse konklusioner.

Simulerede phospholipidmembraners langsomme termiske Fluktuationer af volu- men og energi er st�rkt korrelerede. Forklaringen p� den st�rke korrelation skal Findes i den indre van der Waalske del af membranen. Derved er oprindelsen den samme som for de st�rkt korrelerede simple v�sker.

Den sidste del af afhandlingen beretter om krystallisering ind i MgZn2 Laves-fasen af den bin�re Lennard-Jones blanding foresl�et af Wahnstr�m [1991]. Mekanismen for krystallisering af den underafk�lede smelte er unders�gt i detaljer.