## Undergraduate level

Mekaniske og dielektriske målinger på
1,2-propandiol og methyl m-toluate

1. modul, 2007/2008. [KN]

This project deals with the relationship between the mechanical and
dielectric properties for supercooled viscoelastic liquids at
temperatures above the glass transition temperature TG of liquids.
Mechanic and dielectric measurements have been made for the liquids;
1,2 propanediol and methyl m-toluate. It is shown how the measurements
differ frrom the basic models; Maxwell and Debye.

The relaxation timesT of the liquids are found and it is shown, that
the Vogel-Tammann-Fulcher equation is a good description of the
relationship between temperature and relaxation time, for both
mechanical and dielectric measurements. By using this equation, the
glass temperature of the liquids is determined. Moreover the project
shows, that the relaxation time of the mechanical measurements are
shorter than the dielectric at a given temperature.

We have examined whether the liquids obey time-temperature
superposition (TTS), for the dielectric as well as the mechanical
measurements. In view of this it is shown, that the top of the
alpha-relaxation for the mechanical measurements are wider than for the
dielectric.

The maximum dielectric loss (formel) for 1,2- propanediol is found to
be relatively high about 15-19, whereas for methyl m-toluate it is
determined to be approximately low, about 1-2. The minimum slope is
determined and its association with the maximum dielectric loss of the
liquids have been found.

Furthermore we estimatem the maximum loss of shear modulus (formel) as
a function of minimum slope. It is shown, that there is tendency for
liquids with high maximum dielectric loss, to have a numerical minimum
slope around 0.5. It has been found, that the same relation between the
maximum loss of shear modulus and minimum slope applies. Finally it is
shown, that liquids, which obey TTS, has a numerical minimum slope
around 0.5 (formel) 0.1.

**Modeller og computere i astrofysikken - erkendelsesmæssige aspekter**

1. modul, 2004. [TBS]

Vi præsenterer en analyse af brugen af modeller indenfor
astrofysikken, specielt med fokus på den rolle som computersimulationer
spiller.

Vi har gennem litteraturstudier opstillet et videnskabsteoretisk
grundlag for, hvorledes arbejdet med at opbygge modeller i fysikken generelt kan
beskrives.

Dernæst har vi rettet blikket mod noget af den forskning som
foregår i forbindelse med supernovaeksplosioner. Vi har specielt fokuseret på
hydrodynamiske instabilitetsfænomener i forbindelse med selve eksplosionen.
Udforksningen af disse fænomener har taget fart efter supernovaeksplosionen SN
1987 A. Netop i forbindelse med opbygningen af modeller for dette, viser det
sig, at computersimulationer har spillet en afgørende rolle.

Vi beskriver
hvad det er for en type koder man arbejder med, hvordan man gør det - og ikke
mindst hvorledes man forsøger at sikre sig, at man kan stole på resultaterne af
simulationerne.

Vi viser, at man godt kan beskrive udviklingen af de
modeller denne case beskæftiger sig med ud fra det generelle
videnskabsteoretiske grundlag for modelbygning på trods af de begrænsede
muligheder astrofysikeren har for aktivt at gøre noget ved de systemer han/hun
studerer.

Vi diskuterer brugen af eksperimenter i astrofysikken i
relation til brugen af computersimulationer og ser, hvordan disse to
aktiviteter, med deres ligheder og forskelle, støtter hinanden.

The dynamical properties of supercooled liquids,

4th semester. 6 students, 2002. [TEC]

Niels
Boye Olsens model, describing the coupling between thermal and
mechanical properties of viscous liquids was studied. The model is
abstractly expressed as an electric equivalent diagram, in which each
of the eletric components has a specific physical interpretation.
Energy bond graph technique and linear response theory were utilized in
accounting for the construction of the model, its predictions, and the
deduction of how the component values can be determined. An
experimental method was developed building on the piezoelectric bulk
transducer (PBG) from IMFUFA. With an NTC-semiconductor positioned in
the centre of the bulk transducer, it was intended to measure the
frequency dependency of 3 independent thermodynamic responsefunctions;
a pure mechanical, a pure thermal and a joined thermo-mechanical
response. The experiment was performed on polypropylene glucol (PPG400)
in the temperature range of 202-220K at frequencies in the range of
10mHz-1MHz. A transfer matrix was computed to determine the exact
measured respone, thereby defining the connection between thermodynamic
coordinates in the centre and at the surface of the bulktransducer.
With these instruments, the adiabatic bulkmodulus was calculated from
experimental data, but neither the thermal nor the joined response
function could be identified as pure thermodynamic coefficients. It was
not possible to conclude the validity of the model from the outcome of
the experiment.

Measuring Entropy - Construction of a differential scanning
calorimeter

4th semester. 4 students, 2001. [NBO]

The aim of this project is to create a differential scanning
calorimeter that enables us to measure entropy and specific heat as a
function of temperature. The concept of the calorimeter is to keep a
sample thermally insulated from anything but one side of a peltier
element. The other side of the peltier element is kept in thermal
contact with a heat reservoir. By leading a well-known electrical
current through the peltier element, we can move a well-known entropy
current between the sample and the heat reservoir. The temperature of
the sample and the heat reservoir are measured with two temperature
detectors. We can now let the heat reservoir go through the temperature
interval in which we want to know the entropy development of the
sample. By means of PI-regulation of the current in the peltier
element, the temperature difference between the heat reservoir and the
sample is continuously equalised. From the development of the
electrical current needed to sustain the temperature equilibrium, we
can calculate the entropy development of the sample. The modelling of
the entropy flow to the sample is based on the so-called energy bond
graph technique. The first part of the project deals with this
modelling process. The second part deals with the calibration and
testing of the calorimeter and the problems we had in this connection.
We have not succeded in measuring the development of the entropy in a
large temperature interval correctly. The problem is that calibration
of the temperature detectors is not sufficiently accurate. However by
recalibrating the temperature detectors at room temperature, we managed
to measure the specific heat of water with an accuracy of about 1%

**Refleksion over fysikforskning med Molecular Dynamics simuleringer - en
undersøgelse med udgangspunkt i underafkølede væsker**

1. modul, 2000. [NBO]

Formålet med dette projekt har været, dels at undersøge hvilke
fællestræk Molecular Dynamics simuleringer har med henholdsvis eksperimentel og
teoretisk fysik, og dels at undersøge om det med disse simuleringer er muligt at
frembringe resultater, som fysiske eksperimenter ikke kunne have
belyst.

Dette har vi gjort gennem et casestudie indenfor underafkølede
væsker, hvor vores arbejde har taget udgangspunkt i Ph.D-afhandlingen >>
Hopping in Disordered Media: A Model Glass Former and A Hopping Model<<
skrevet af Thomas Schrøder.

Gennem vores arbejde har vi fundet, at Molecular
Dynamics simuleringer på trods af sin grundlæggende teoretiske natur har visse
fællestræk med eksperimentel fysik. Disse fællestræk omhandler hovedsageligt den
måde modellen tjekkes på, og den måde som simuleringerne indgår i fysikforskinen
på.

Med hensyn til frembringelse af nye reslultater finder vi, at man med
Molecuar Dynamics simuleringer kan finde i hvert fald kandidater til reslutater,
der ikke er observeret eksperimentelt.

**Hvad matematikken og fysikken gjorde for vektorregningen**

META-projekt kombineret med matematik, 1. modul, 1999. [CLP, JD]

Dette projekt handler om hvorvidt den moderne vektorregning stammer
fra matematikken eller fysikken. Der ses mere præcist på hvilke koncepter,
motivationer, faglige behov, krav og forventninger der fra hhv. matematikkens og
fysikkens side gav anledning til udviklingen af den moderne vektorregning. Dette
er undersøgt på baggrund af en vurdering af de centrale led i den moderne
vektorregnings udvikling, samt ved en speciel grundig analyse af Oliver
Heavisides arbejde med udviklingen af den moderne vektorregning. Der konkluderes
at vektorregningen stammer fra både matematikken og fysikken. Specielt
konkluderes det at quaternionregningen stammer fra matematikken, samt at
udviklingen fra quaternionregningen til den moderne vektorregning var styret af
fysikken.

Rheological investigations of solutions of Maizena and water

4th semester. 4 students, 1999. [NBO]

When a force is applied to a solution of Maizena in water, it can
thicken to such a degree, that it gets the consistency of soft clay.
When the force is removed, the solution becomes liquid again. This
project investigates which external forces gives rise to this behavior.
This is done by determining the rheological properties of a 50/50
mixture (by weight) of Maizena and water, at 21ºC. First we determine
if the thickening is caused by pressure. To that purpose a
pressure-viscosimeter was constructed, by which varying pressure can be
applied to the sample, at the same time as the sample is deformed by a
certain force. Secondly, the linearity between stress and deformation
is investigated, as well as the temopral relations between these
properties. In other words, it is investigated, if the solution is
viscous, visco-eleastic, or exhibits non-liniear behavior. The results
are evaluated, and we conclude that the thickening of the solution does
not depend on pressure, that it is linear frequency dependent for
stresses smaller than 1 Pa in the frequency range 6.81*10^-2 Hz to 6.81
Hz, and is non-linear for stresses larger than 1 Pa. Shear thickening
is found in the non-linear regime.

**Analogier i fysik**

Metaprojekt, 1. modul, 1997. [JD]

Projektet giver et bud på, hvad der karakterierer en anvendelse
indenfor forskning og formidling. I forskning benyttes analogier til
fremsættelse af hypoteser og udvikling af teorier indenfor nye områder, og
indenfor formidling som pædagogisk redskab i forbindelse med undervisning, men
også i forbindelse med udveksling af teorier forskere
imellem.

Indledningsvis gives der en beskrivelse af de mange betydninger
og anvendelser af begrebet analogi, samt en redegørelse for en blandt
videnskabsteoretikere udbredt opdeling af analogier i to grundlæggende
kategorier, materiel analogi og formel analogi.

Der tages i besvarelsen
af problemformuleringen udgangspunkt i en analyse af fire eksempler, som anses
for værende repræsentative for fysiske analogier, der har vist sig at være
anvendelige: Analogien mellem lys og lyd, Maxwells analogi mellem elektriske
feltlinier og væskers strømningslinier, analogien mellem Bohrs atommodel og
solsystemet, samt analogier baseret på energibåndsformalismen.

Det
konkluderes på baggrund af eksemplerne, at der udover identiske matematiske
beskrivelser kræves, at mindst en af de fysiske størrelser i det ene system
korresponderer til en identisk fysisk størrelse i det andet system. Endvidere
skal disse identiske størrelser være enten tid eller rumkoordinater, hvilket
indebærer, at systemerne har identiske dynamik (forstået som tidslig udvikling)
eller har identisk geometrisk konfiguration.

**Nærvirkning kontra fjernvirkning**

Metaprojekt, 1. modul, 1997. [JD]

I projektet "Nærvirkning kontra fjernvirkning" undersøges det, om
der er sket et Kunsk paradigmeskrift i England, ved overgangen fra den
Newtonianske fjernvirkningsteori til Faraday´s nærvirkningsteori. Dette er
undersøgt via en litteraturanalyse, hvor Faraday´s nærvirkningsteori
sammenholdes med samtidens videnskabsmænds holdninger. Disse holdninger er
repræsenteret i form af en række udvalgte artikler forfattet af ovennævnte
videnskabsmænd.

Projektet konkluderer, at der ikke er sket et
paradigmeskift i England ved indførelsen af Faraday´s
nærvirknngsteori.

**Det afgørende eksperiment**

Metaprojekt, 1. modul, 1996. [NBO]

Dette projekt omhandler en undersøgelse af begrebet "det afgørende
eksperiment". Via en teoretisk udredning af eksperimentets rolle i
almindelighed, udleder vi teoretisk tre forskellige definitioner af bagrebet.
Denne definition, som vi betragter som et teoretisk postulat, søges sammenlignet
med to historiske cases: Michelson-Morley eksperimentet og Compton
effekten.

Sammenlagt finder vi, at vores tre "nye" definitioner giver en
bedre og mere nuanceret måde at omtale "afgørende" eksperimenter
på.

Help! - its viscoelastic!

2nd semester. 5 students, 1994. [TEC]

The first part of this report shortly introduces some material
properties of liquids, like elasticity and viscosity. The ability of
liquids to deform, depends among other things on these properties. The
next two sections deals with the fundemental wave theories, which are
necessary to understand the the last part of this report, and the wave
equation is discussed. This is the base for a couple of other theories
on waves, and at the end of this section, we descripe various wave
phenonoma. The last part of the report contains our two experiments.
The first and primary experiment deals with determining bulk moduli
(the resistance against compression) of different liquids. In this
experimant laser light and standing waves in the liquid are utilized.
In the second experiment, we investigate bulk moduli of mixtures. This
experiment is only decribed
briefly.

Et udviklingstrin i Elasticitetsteoriens historie i et metafysisk
perspektiv

Metaprojekt, 1. modul, 1993. [TEC]

Vi vil forsøge at redegøre for nogle af de metafysiske strukturer,
der ligger til grund for den tidlige udvikling af elasticitets-teorien. Vi vil i
særdeleshed afdække den særlige dualisme, der udgøres af henholdsvis kontinuitet
og diskontinuitet som fundamental-begreber i emergensen af den tidlige
elasticitets-teori.

## Projects at the master’s level, before master’s thesis

**Merging af dielektrisk alpha- og beta-relaksation**

Internt-fagligt, 2. modul, 2007/08. [NBO, KN]

Formålet med dette projekt er at undersøge en ny mode for
dielektrisk alpha- og beta-relaksation ved merging-området og sammenligne denne
med en additiv model, som er en af de to traditionelle modeller til beskrivelse
af alpha/beta-merging.

Den nye model, som er foreslået af Niels Boye
Olsen (Roskilde Universitetscenter), er udtrykt som en analogi til et elektrisk
kredsløb, hvor den rene alpha-relaksation beskrives ved en viskoelastisk model
og den rene beta-relaksation beskrives ved en Cole-Cole model. De to
relaksationsprocesser er parallelforbundne i det elektriske kredsløb, og de er
begge serieforbundne med det rotationelle bidrag til dipolmomentet. I den
additive model er det samlede spektrum en sum af de rene alpha- og
beta-relaksationer. Modellerne adskiller sig fra hinanden ved måden hvorpå de to
relaksationsprocesser er relaterede.

Modellerne testes ved at fitte dem
på egne data fra DBP målt over et temperaturinterval fra Tg til Tb. Resultaterne
fra fittene viser igen betydelige forskelle på parametrene i de to modeller.
Parametrenes temperaturafhængighed ses tydeligst ved de lavere
temperaturer.

Der konkluderes at modellerne er overparametriserede ved
høje temperaturer i nærheden af Tb, og der foreslås en ny fitteprocedure med
færre frie fitteparametre.

**Sammenhæng mellem bulk- og shearmodulet i væsker - En undersøgelse af
mono-, di- og tripropylenglykol
**

Internt-fagligt projekt, 2. modul, 2007/08.

**[TEC]**

**The aim of this project is to investigate if there in the high frequency limit exists a relation between the bulk modulus, (formel), and the shear modulus, (formel), in the liquids propyleneglycol, dipropyleneglycol and tripropyleneglycol. Furthermore we wish to determine if this relation is consistent under various temperature conditions.**

The frequency dependent bulk and skear moduli are measured from which (formel) and (formel) are determined. This is done through a mechanical system xonsisting of a piezoelectric transducer. The transducer is placed in a cryostat, through which temperature conditions can be controlled. Throughout this project the primary focus is on the method for determining the bulk modulus.

As a result of the chosen temperature conditions, we have not been able to achieve usable results. Therefore it has not been possible to establish a relation between (formel) and (formel).

**2 + 3. modul, 2007/2008. [TEC]**

Er det muligt at anvende en planar heater og 3omega-metoden til at undersøge proteiners foldningsenthalpi?

Er det muligt at anvende en planar heater og 3omega-metoden til at undersøge proteiners foldningsenthalpi?

**In this project we research, whether or not a planar carbon film and the 3omega-method can be used to measure the denaturational enthalpy of lysozyme.**

During the course of this work we encountered unforseen problems related to the usage of carbon films in the 3omega-method. It is shown that the gold-carbon junction of certain films to some estenc behaves like a Schottky Diode. Furthermore an annealing-like process is observed, in which the resistance of the carbon films declines at 330K.

The effusivity of glycerol is found within a 14% accuracy. This is in all probability is not accurate enough to observe the denaturational enthalpy of lysozyme.

The following conclusions are drawn: 1) Carbon films and the 3omega-method cannot at the present time be used to measure the denaturational enthalpy of lysozyme, 2) If however the problems encounted in this project are worked through the 3omega detection technique might eventually be applicable to proteins.

**Decoupling mellem translation og rotation i viskøse væsker**

Internt-fagligt, 2. modul, 2006. [NBO]

Problemet er at afgøre om der reelt findes en decoupling mellem translation og rotation i den viskøse væske Dibutyl-Phthalat. Metoden der benyttes er en kombineret multimeter-LCR-meter opstilling der skal måle det dieektriske tab ved temperaturer omkring glasovergangen. Resultaterne viser at translationen klart ikke følger rotationen, emn dette ses også i områder hvor de burde følges ad. Ved at tage lidt løst på usikkerhedsområdet, observeres at to af måleserierne viser svage tendenser til at opføre sig som grafer der motiverede problemstillingen. På ingen af de i alt fem måleserier ses dog antydningen af et pludseligt "knæk" ved overgang til decouplingsområdet.

**Internt-fagligt projekt, 2. modul, 2006. [TBS]**

Bestemmelse af Magnetokalorisk Effekt ved 3w-Metoden

Bestemmelse af Magnetokalorisk Effekt ved 3w-Metoden

**This work investigates the magnetocaloric effect in the lanthanium manganite La0,67Ca0,22Sr0,11MnO3 (formel) by means of the so-called 3w detection technique. The aim is to determine whether the 3w detection technique is suitable for measuring the magnetocaloric effect of certain magnetic materials. An experiment is conducted by subjecting the material to an oscillating magnetic field. The oscillating magnetic field is gererated by applying a voltage to a solenoid. By means of Fourier transformation, the third harmonic is extracted from the output voltage. It is concluded that the magnetocaloric effect cannot be detected in the conducted, due to fact that the resulting third harmonic is too small to be measurable. However, an improved experimental design might make it possible to enhance the signal to a measurable level. In this case, the 3w detection technique has some advantages compared to the usual techniques used for measuring magnetocaloric effect**

**.**

**Måling af temperaturændringer i ferromagnetiske materialer**

Internt-fagligt projekt, 2. modul, 2006. [TBS]

The report is inspired by a former RUC-project that tried to measure the magnetocaloric effect in (formel) with the 3omega-method. It did not succeed. This report shows through an expansions of the method, the experiment and the hypothesis, that there is measurable non-linear signals on both 2nd and 3rd harmonic voltage signal, measured over a coil with a ferromagnetic core.

By measuring the harmonic signals in experiments with (formels), with and without a bias on the harmonic voltage signal, a real signal and an imaginary signal is found. The report concludes that everything points at the magnetocaloric effect and hysteresis loss as explanations.

The RMC model - a simple model for viscous liquids

2 students, 2004. [TBS]

The RMC-model is a lattice model of a viscous liquid, where each particle is assigned a unique energy landscape. The equilibrium dynamics of the model is investigated through Monte Carlo simulations, where only nearest-neighbour jumps and no overlapping of particles is allowed. Simulations were made for three different densities for a number of temperatures. At high densities and low temperatures the model exhibits non-exponential relaxation in the energy correlationfunction and fragility plots of the temperature dependent diffusion constant and the relaxation times show non-Arrhenius behaviour. A monitoring of time-development of distribution of particle-displacement shows, that a Gaussian approximation is reasonable at high temperatures in all densities, while gradual shift towards a ``broader'' distribution, where some particles remain trapped for long times, while others are very mobile, is seen with decreasing temperature. These results lead to the conclusion, that the model captures some of the important charactaristics of a viscous liquid.

The connection between thermal admittance and frequency dependent heat capacity in viscous liquids

The connection between thermal admittance and frequency dependent heat capacity in viscous liquids

1 student, 2003. [TEC]

This project deals with the theoretical connection between the measured thermal admittance of a planar geometry experiment, and the sought after liquid property: the frequency dependent heat capacity. The problem is formulated as a set of coupled differential equation, which are solved numerically.

Empirical test of the shoving model, via measurements of shear-mechanical properties of glycerol/water solutions

Empirical test of the shoving model, via measurements of shear-mechanical properties of glycerol/water solutions

2 students, 2002. [TEC]

Viscosity and the instantaneous shear modulus was measured using the piezoelectric shear modulus transducer. The results were found to be in agreement with the shoving model.

Reflections on the use of Molecular Dynamics simulations i physics research

Reflections on the use of Molecular Dynamics simulations i physics research

2 students, 2000. [NBO]

The aim of this project was to investigate how Molecular Dynamics relates to respectively experimental and theoretical physics, and whether or not if simulations can generate results not attainable by experiment. The PhD-thesis “Hopping in Disordered Media: A Model Glass Former and A Hopping Model” was used as a case-study, and it was concluded that despite its theoretical nature, Molecular Dynamics simulations has certain similarities to experimental work.

An investigation of the Einstein-Debye equation and Time-Temperature scaling in supercooled liquids: squalane og dipropylen glycol

An investigation of the Einstein-Debye equation and Time-Temperature scaling in supercooled liquids: squalane og dipropylen glycol

2 students, 1999. [TEC]

The project concerns the limit of the Einstein-Debye equation, and the validity of Time-Temperature scaling (TTS) for supercooled liquids, by investigation of squalane and dipropylene glycol. Our measurements indicate that the Einstein-Debye equation is fulfilled, and that TTS is fulfilled for the alpha relaxation, but not the beta relaxation.

Models and measurements of shear moduli of supercooled liquids near the glass phase

Models and measurements of shear moduli of supercooled liquids near the glass phase

5 students, 1999 [TEC]

Two different models for the shear moduli of supercooled liquids are discussed. We design a prototype for a new rheometer to measure the shear moduli of supercooled liquids. One goal for this PSSA (Piezo Soft Shear module Analyser), is that it should be able to measure shear moduli between 10^3 Pa and 10^8 Pa. We conclude that the principle of PSSA works, but that further development of the method is needed.

**Er der en forskel på grundforsknig og anvendt forskning?**

Metaprojekt, 3. modul, 1998 [TEC]

Jeg har i projektet beskæftiget med med de to forskellige slags forskning; grundforskning og anvendt forskning. Derudover har jeg set på vekselvirkningen imellem dem, idet der i dag er en tendens til at den ene slags forskning ikke forekommer uden at den anden også er der. Hvor der grundforskning er der oftest også anvendt forskning., fordi det i dag kræver så meget ny teknologi at opstille nye eksperimenter. På samme måde er det med anvendt forskning. Når der skal udtænkes et nyt produkt eller en ny metode, kræver det oftest grundforskning. I projektet har jeg udd ovr at se på teori om forskning, også set på to cases fra fysikken. Den ene case er konstruktionen af atombomben, hvor forskningen var meget målrettet mod at danne et produkt - nemlig atombomben. Den anden case er partikelfysikforskningscenteret CERN, hvor der søges efter viden om elementarpartiklerne og deres indre kræfter. Dette er ikke forskning der kan bruges til noget i øjeblikket, og må derfor karakteriseres som grundforskning.

The Kauzmann paradox

The Kauzmann paradox

2 students, 1998. [TEC]

A theoretical description of the Kauxmann paradox and the suggested solutions is given. In particular we investigate the Adam-Gibbs theory for the relation between the relaxation time and the configurational entropy. It is argued, that according to this theory it will not be possible to measure the Kauzmann temperature, defined as the temperature where the excess entropy goes to zero. We put forward a hypothesis in disagreement with this view, and we test this in the experimental part of the project. We perform measurement of the frequency dependent heat capacity on DiMetylphtalate, and our measurements indicate that it indeed is possible to measure the Kauzmann temperature directly.

Measurements of the dipole moment of Chlorobenzene

Measurements of the dipole moment of Chlorobenzene

Interdisciplenary project: Physics and Chemistry. 3 students, 1998. [NBO]

Equipment available at IMFUFA is used to measure the complex dielectric coefficient as a function of temperature and concentration of dipoles. The results are compared to 3 models.

An asymmetric hopping model for ac conduction in disordered solids

An asymmetric hopping model for ac conduction in disordered solids

1 student, 1997. [JD]

We develop an asymmetric hopping model for ac conduction in disordered solids, with the symmetric model as the starting point. A numerical method for symmetric models is modified to be able to solve asymmetric models. Numerical results indicate the existence of an universal curve, but further large scale simulations are needed.

Shear mechanical and dielectric relaxation in o-terphenyl - Anthron and Squalan – DMSO solutions

Shear mechanical and dielectric relaxation in o-terphenyl - Anthron and Squalan – DMSO solutions

1 student, 1996. [NBO]

This is an experimental project, where shear mechanical end dielectric relaxation was measured on two supercooled liquids: Anthron in an o-terphenyl solutions and DMSO in a Squalan solution. A model for the polarization of a thin solution of dipoles in a non-polar solvent is developed from the Debye model. The model does not fit the experimental data on our liquids.

A method for measuring the frequency dependent heat capacity for a liquid near the glass transition

A method for measuring the frequency dependent heat capacity for a liquid near the glass transition

3 students, 1995. [TEC]

The purpose of this project was to develop a measuring cell, suitable for measuring the frequency dependent heat capacity at constant pressure using the 3-omega method. Two cells were designed; The first cell consists of a Pt-wire in a cylinder, but preliminary results indicated that it was impossible to maintain constant pressure in this cell. The second cell consists of two thin layers of plastic with metal-electrodes (applied by evaporation). This second design was not tested.

Modelling the dispersion of piezo-electric ceramics

Modelling the dispersion of piezo-electric ceramics

4 students, 1995. [TEC]

This project deals with the modelling of frequency dependent behavoir of piezo-electrical ceramics. This is done by modelling the constitutive parameters as frequency dependent power-laws, where the second law of thermodynamics put a limit on the exponents. This limit is investigated experimentally, and applied to the model of PZ29. The new model clearly improves the agreement between measurements and calculations.

The adjustable piezo-ceramic transducer

The adjustable piezo-ceramic transducer

5 students, 1995. [NBO]

We have constructed a transducer consisting of three piezo-ceramic shells. This is used to measure the frequency dependent stiffness of a silicone oil (MS704). There is a possible defect in the transducer, since we find the frequency dependence of the stiffness to be a factor two too small.

Development of a method for measuring the frequency dependent thermal expansion coefficient

Development of a method for measuring the frequency dependent thermal expansion coefficient

3 students, 1994. [NBO]

A new method for measuring the frequency dependent thermal expansion coefficient was designed from scratch. Only a part of this design was implemented; the precise measurement of the height of a liquid column in a tube. This was achieved by a resonance method in which standing waves in the column were excited by a piezo-ceramic at the bottom. With this method we were able to measure changes in the height of the liquid column with a precision of 2*10^-3 mm.

Measuring the frequency dependent temperature/pressure coefficient for supercooled liquids

Measuring the frequency dependent temperature/pressure coefficient for supercooled liquids

4 students, 1994. [NBO]

The purpose of this project is to design a new method for measuring the frequency dependent temperature/pressure coefficient for supercooled liquids.

Dibutylphthalate – an experimental project on the shear mechanical and dielectric properties of a liquid

Dibutylphthalate – an experimental project on the shear mechanical and dielectric properties of a liquid

2 students, 1994. [NBO]

We investigate the shear mechanical and dielectric properties of Dibutylphthalate, and our results are compared to results in the literature. A universal scaling principle is discussed.

## Master’s thesis’

**Master thesis, 2007. [NBO]**

Pyroelectricity - A new Application for the Piezoelectric Bulk Transducer

Pyroelectricity - A new Application for the Piezoelectric Bulk Transducer

**This report presents a new experimental technique based on an alternative use of the piezoelectric bulk transducer used at IMFUFA/NSM, RUC. The measurements rely on the pyroelectric effect of the piezoceramic material that compose the spherical hollow tranducer shell. In order to explain and analyze the experimental test results, an analytic model is proposed as a solution to the thermo-electro-mechanical differential equations describing the phenomena in the transducer and what fills the cavity inside.**

Measurements involving the highly viscous 5-PPE / Santovac 5 liquid are conducted in the temperature range from 248 K to 260 K near the supposed glass transition of the liquid, during which a drastic change in the physical thermodynamic variables is documented for the liquid.

The practical test measurements and the theoretical thermo-electro-mechnical equations are compared for a discussion of the potential of the experimental technique and possible improvements before its application in experimental glass physics are proposed; it is concluded that the technique may be an excellent method for measuring the isobaric thermal expansivity, (formel), but at present it needs complementing experiments to decrease the number of independent variables.

**Master thesis, 2006/07. [JD, JL]**

Mechanical Spectrum of a Viscous Liquid

Mechanical Spectrum of a Viscous Liquid

The goal of this thesis is to extend the newly developed narrowband picosecond laser ultrasonic technique to measure the acoustic properties of liquids in addition to solids and polymer films. The method covers a frequency window of roughly 1-400GHz and thus bridges a gap in the existing experimental methods.

A sample holder to fabricate thin liquid films was constructed, where the liquid is confined between two metal coated substrates. The construction allows for both a Brillouin backscattering measurement as well as the picosecond laser ultrasonic measurement. This provides a cross-check of the results obtained as the two different measurements ususlly overlap in frequency. To validate the method, measurements are first carried out in the prototypical glass-former glycerol and compared to data in the literature. A series of measurements is then performed on the silicon oil (tetramethyl-tetraphenyl-trisiloxane) at temperatures ranging from 210-295K. The acoustic damping dtermined in the ultrasonic measurement on the silicon oil follows a parabola that seems to agree fairly well with the reference point determined by Brillouin scattering. However, the reproducibility of the results remains to be demonstrated.

The prevalent method of data analysis of this type of measurement reveals the frequency dependence of the acoustic damping, but assumes a constant sound velocity. In order to analyze the data obtained with acoustically dispersive media (such as viscous liquids), the experiment is modeled mathematically.

The sample construction consists of five layers (substrate-metal-liquid-metal-substrate) that are mechnically and thermally coupled. Each layer is modeled by two coupled partial differential equations for the temperature and displacement fields - the so called thermo-(visco)-elastic equations. Boundary conditions are matched at each interface of the inner layers, while the outer layers (two substrates) are assumed semi-infinite. The direct problem, i.e. assuming that the input and all parameters of the model are known, is formulated as a system of ordinary differential equations and solved algebraically.

A comparison of model solutions to data is carried out in the frequency domain and shows that the model agrees qualitatively well with the data. Peak positions, widths of the peaks and the relative manitudes of subsequent peaks all agree excellently with the data. It is thus concluded that the model provides a good description of the experiment and can be a platform for a fitting routine to determine the liquid parameters from data.

Test of the Shoving Model by Flow Event Investigations

Test of the Shoving Model by Flow Event Investigations

Interdisciplinary master’s thesis: Physics and Mathematics. 1 student, 2004. [JCD]

The purpose of the work reported in this thesis is to test the central assumption of the Shoving Model for the temperature dependence of the viscosity of supercooled liquids, developed at the Institute for Mathematics and Physics at Roskilde University, by performing numerical calculation on a model liquid. The central assumption of the Shoving Model is that the activation energy necessary to make a flow event in supercooled liquids is due to a compression of the surroundings of the rearranging molecules. Therefore the activation energy is only associated with the molecules in the surroundings defined as those which moves less than a certain threshold value during a flow event.

The major part of the work done has been the development of an algorithm capable of finding the molecular configurations responsible for the activation energy. These configurations are equivalent to first order saddle points of the energy function of the entire system. Similar a flow event can be described as a transition from one minimum of this function to another. The system used in this work is a bulk binary Lennard-Jones model liquid consisting of 500 molecules in which the energy is given purely by pair interactions. The basic idea behind the algorithm, called Meta Line Drag (Meta LiD), is that a saddle point between the minima in a flow event can be found by making consecutive plane minimisations along the vector connecting the minima on hyperplanes which are perpendicular to this vector.

The Meta LiD algorithm is able to find saddle points in 50% of the investigated flow events. The failure of the remaining is mainly due to a disability to handle directions of negative curvature within the minimisation hyperplanes or areas where the eigenvector of the smallest eigenvalue and the vector connecting the two minima in the flow event diverges. By performing energy calculations on the molecular configurations of the saddle points it is found that the majority (75%) of the activation energy is in the surroundings. This supports the central assumption of the Shoving Model, although only partly because the Shoving Model assumes that all of the activation energy is in the surroundings.

Dielectric and Shear Mechanical Relaxation in Glass Forming Liquids

Dielectric and Shear Mechanical Relaxation in Glass Forming Liquids

2 students, 2003. [NBO]

The goal of this thesis is to elucidate whether a relation can be established between shear mechanical and dielectric relaxation in glass forming liquids. The starting point is a genralized Debye model, which has been proposed by DiMarzio & Bishop (1974). The DiMarzio-Bishop model is thoroughly analyzed and reformulated in such a way that different unphysical simplifications that have been used earlier are avoided. New testable qualitative predictions of the DiMarzio-Bishop model are formulated and the model is put in a form where quantitative tests can be made by using only one macroscopic parameter. The DiMarzio-Bishop model is tested by extensive dielectric and shear mechanical measurements on various molecular liquids. The shear mechanical measurements are performed using a transducer that has been developed at IMFUFA by Christensen & Olsen (1995). This transducer allows measurements to be made in an exceptionally large frequency range (1mHz-50kHz). The systematic errors and uncertainties of the two measuring methods are analyzed in detail. Furthermore these errors and uncertainties are taken into account in the reformulation and tests of the DiMarzio-Bishop model. It is found that the DiMarzio-Bishop model to a large extend has qualitative agreement with our data and data form the literature, whereas the quantitative agreement is moderate or poor depending on the liquid tested. This suggests that the model is too coarse grained to capture details of the relaxation processes, but that it does in fact capture the fundamentals of the physics involved, and consequently that there is a direct relation between shear mechanical relaxation and dielectric relaxation.

The one-dimensional hopping model

The one-dimensional hopping model

1 student, 2003. [JD]

This master´s thesis is a contribution to the ongoing research into the field of disordered or non-crystalline solids. The hopping model accounts for the characteristic frequency dependent conductivity of disordered solids through the Effective Medium Approximation (EMA) and the Percolation Path Approximation (PPA). The approximation method PPA uses results from EMA and also from the one dimensional hopping model. In a series of articles published 1978-1981, a number of results regarding the one dimensional hopping model were derived. Particularly an integral equation was derived, the solution of which provides characteristic physical quantities. This integral equation is analyzed and solved numerically. Results from these separate theories are combined and analyzed. The results show that both theories supplement the understanding of the properties of disordered solids described by the hopping model.

The coupling between thermal and mechanical response functions at the glass transition

The coupling between thermal and mechanical response functions at the glass transition

1 student, 2001. [TEC]

Supercooled liquids have the property that through continued cooling they will reach a temperature where their behaviour will change from liquid like to solid like behaviour - This phenomenon is called the glass transition. The temperature range around the glass transition is characterised by the fact that the physical properties of the material become frequency dependent, because the characteristic times of the relaxation processes in the material become comparable to the times of the experiments. Through an experimental investigation of the heat capacity and mechanical modulus of 1,2,4-butanetriol an attempt is made to describe the connection between the frequency dependent response functions in the thermal and mechanical domain. The experimental data are compared with two existing models of coupling between the response functions. The first model can not give a full description of the experimental results, but the possibility of making a final conclusion about the model is decreased by the ability of the liquid to absorb water from the surrounding air. This absorption leads to a big change in the glass transition temperature. The second model has a fundamental problem in explaining the experimental data, which can not be explained by the absorption of water. This means that this model can not explain the connection between the thermal and mechanical response functions near the glass transition.

Low-temperature ac conductivity of disordered non-metals

Low-temperature ac conductivity of disordered non-metals

1 student, 2001. [JD]

The random site no barrier (RSNB) hopping model consists of random site energies and Miller-Abrahams transition rates. Particle interactions are disregarded and jumps are only nearest neighbour. At low temperatures the model can equally well describe ion- and electron transport. The RSNB model is investigated in the one-dimensional case. The model is only solvable through approximate methods. First the analytic effective medium approximation (EMA) is tested. Various asymmetric EMA methods are analyzed, among them the only one at the present time that incorporates the RSNB model as its main target. I extend this method to the low-temperature limit, where the result equals that of low-temperature limit random barrier EMA. This is the expected result, since the effective charge transport of the RSNB model at low-temperatures is expected to consist of transport between few low-energy sites, and movement between these sites resembles over-barrier jumps with spatial disorder. According to computer simulations on a N = 1024 lattice, the RSNB model with box distributed site energies converges towards a single curve in the low-temperature limit. The curve is compared to the EMA low-temperature prediction, which resembles that of low-temperature random barrier EMA. The result is not nearly as close to EMA as seen for random barrier simulations.

Accelerated dynamics in viscous model liquids

Accelerated dynamics in viscous model liquids

2 students, 2001. [JD]

In this master thesis we have investigated two methods for accelerating molecular dynamics simulations of viscous liquids. We have described the methods bias potential dynamics (hyper dynamics) and temperature accelerated dynamics. We have estimated the gain in calculation time. These estimates show that the methods may not be useful in large disordered systems. We have written a program that can be used to simulate a viscous model liquid. We have added a bias potential in order to accelerate the dynamics of the liquid. Unfortunately we found that our bias potential accelerates the dynamics too irregularly to be useful.

Heat capacity and compressibility of supercooled liquids

Heat capacity and compressibility of supercooled liquids

1 student, 2001. [TEC]

This master thesis is an experimental investigation of ability of two models to predict the relation between changes in heat capacity, expansion coefficient, and compressibility. Three different methods developed at IMFUFA are used; The 3-omega method in a spherical geometry for measuring the frequency dependent heat capacity, and the bulk and shear tranducers to measure the frequency dependent bulk and shear moduli respectively. The experimental results indicate limitations of the two models, but further work is needed to support this.

The dielectric relaxation spectra of poly(propylene glucole) of 9 different chain lengths

The dielectric relaxation spectra of poly(propylene glucole) of 9 different chain lengths

Interdisciplinary master’s thesis: Physics and Chemistry. 1 student, 2001. [NBO]

The dielectric spectra of PPG of 9 different molecular weights have been measured. The dielectric spectra showed both alpha, beta and “alpha-prime” relaxation peaks. In addition a small beta` peak was discovered. The spectra were well described by a visco-elastic model, developed on grounds of the generalized BEL model. The temperature dependence of the alpha relaxation peak intensity was well described by the Debye model. The alpha relaxation time were well described by the shoving model. The beta relaxation was successfully modeled by a two level potential well model. The alpha` peak appeared for molecular weights above a certain molecular weight (Mw*) attributed to the polymer limit. For weights below Mw* the behavior were small molecule-like, with the alpha relaxation involving the relaxation of the entire molecule. For higher molecular weights the alpha' peak was attributed to the longest normal mode, described by the Rouse model. No entanglement behavior was seen for the molecular weights studied, ranging from 58 g/mol to 4000 g/mol.

Shear-mechanical and dieletric properties of hydrogels

Shear-mechanical and dieletric properties of hydrogels

Interdisciplenary master’s thesis: Physics and Chemistry. 1 student, 2000. [TEC]

Hydrogels were produced by radiation of polyacrylmid, polyacrylacid, and poly(acrylacid-co-acrylmid). Their shear-mechanical properties were measured in the frequency range from 10mHz to 20 Hz, and the dieletric properties were measured in the frequency range from 5Hz to 13MHz. The shear mechanical measurements indicate that the number of cross-links increases with the strength of the applied radiation. The dielectric measurements indicate that Na+ ions are the only charge carriers in the hydrogels under investigation.

The Fermi model for AC conduction in disordered solids

The Fermi model for AC conduction in disordered solids

1 student, 2000. [JD]

This master thesis concerns the universality of ac-conductivity in disordered solids and the Fermi-model, which is created to explain this phenomenon. The Fermi-model is a lattice-gas model, where the charge carriers hop on a regular lattice with site energies which are randomly chosen from a distribution. The question is: Does the Fermi-model exhibit ac-universality as the temperature goes to zero? This question has been answers by a “no” by Porto et. al. (2000) based on computer simulations, but they stated that the answer might be another at lower temperatures. The goal of this thesis was therefore to examine the model at low temperatures, using computer simulations. At such temperatures the charge carriers very seldom hop and the standard Metropolis algorithm becomes very time consuming. The thesis describes four algorithms to increase the speed of simulation: An algorithm with an external field present, another which uses a connection between conductivity and the noise spectrum of the speed of the charge carriers, an algorithm developed by Roling (2000) which changes the energy landscape, and a Bortz-Kalos-Lebowitz-type waiting time algorithm. The first two are rejected because they, respectively, give the wrong results and are too slow. Roling's algorithm seems promising, but further study is needed. In the form in this thesis, the waiting time algorithm is too slow, but it seems probable that it can be improved.

**Salt i saaret?**

Speciale, 3. modul, 1998. [JD]

Vi tager udgangspunkt i at undersøge "de Statistisk mekanisk redegørelser for den Anden Lov i Termodynamikken" (forkortet SALT), hvor vi ser på Boltzmanns H-teorem og coarsegraining i emsembleteorien. Vi fremhæver nogle aspekter i SALT, som vi mener kræver yderligere afklaring i form af en filosofisk tolkning.

Herefter præsenterer vi nogle filosofiske positioner, som vi benytter til at give tolkninger af SALT. Omdrejningspunktet er her en realisme - antirealismediskussion. Målet er at komme frem til den tolkning af SALT, som vi finder mest tilfredsstillende.

De filosofiske positioner, som vi forholder os til, er videnskabelig realisme (repræsenteret af blandt andre Michael Devitt, Richard N. Boyd og Ian Hacking), konstruktiv empirisme (Bas C. van Fraassen) og empirisk realisme (Immanuel Kant). Vi ser, hvorledes henholdsvis en videnskabelig realist, en konstruktiv empirist og en empirisk realist vil tolke SALT.

På denne baggrund og på baggrund af den filosofiske diskussion argumenterer vi for en empirisk realistisk tolkning af SALT.

The symmetric hopping model for AC conduction in disordered solids

The symmetric hopping model for AC conduction in disordered solids

Interdisciplenary master’s thesis: Physics and Computer Science. 1 student, 1996. [JD]

The thesis deals with the numerical solution of the symmetric hopping model, using an electric network analog of the model. It is shown that the low frequency AC conduction exhibits Time-Temperature scaling and universality (shape of conduction curve independent of distribution of barrier heights). In three dimensions good agreement is found with a new analytical approximation (The Percolation Path Approximation), suggesting that the low frequency AC conduction at low temperatures is dominated by nearly one-dimensional percolation-paths.

Investigations of dieletric and shear mechanical relaxation in thin solutions

Investigations of dieletric and shear mechanical relaxation in thin solutions

1 student, 1996. [NBO]

This master thesis deals with the connection between dielectric and shear mechanical relaxation. In the theoretical part of the thesis models for dielectric relaxations are discussed. A new model for thin solutions of dipoles in a non-polar solvent is developed. In the experimental part of the thesis, measurements are performed on DMSO in squalane and anthron in o-terphenyl, and the results are compared to the developed model.

**Undersøgelse af den dielektriske og shearmekaniske relaxation i tynde opløsninger**

Speciale, internt-fagligt, 3. modul, 1996. [NBO]

Denne specialerapport omhandler sammenhængen mellem den dielektriske og den shearmekaniske relaxation. I den teoretiske del af rapporten diskuteres modeller opstillet ud fra Debyes model for dielektrisk relaxation. Debyemodellen bygger på den antagelse, at den dielektriske relaxation skyldes dipolernes gnidning med de omkringliggende molekyler. Der opstilles en model, som gælder for tynde opløsninger af dipoler i en upolær solvent.

Den eksperimentelle del af rapporten beskriver målinger foretaget på tynde opløsninger. Der er dels målt på en opløsning af DMSO i squalan, og på en opløsning af anthron i o-terphenyl. Disse målinger sammenlignes med den opstillede model.

Master equation models for the glass transition: Thermal and mechanical relaxation

Master equation models for the glass transition: Thermal and mechanical relaxation

Interdisciplenary master’s thesis: Physics and Mathematics. 2 students, 1995. [JD]

An existing model (EME) for supercooled liquids based on the assumption of the existence of regions, is reformulated from a phenomenological starting point. An expression for the frequency dependent heat capacity is derived, and the model is shown to give a good fit to experimental data for the mean relaxation frequency, but not to the shape of the relaxation curve. A more general model (EVME), coupling the thermal and mechanical relaxation is developed and analyzed.

Order in disorder? - Universality of the frequency dependent conductivity in disordered solids at low temperatures

Order in disorder? - Universality of the frequency dependent conductivity in disordered solids at low temperatures

1 student, 1994. [JD]

In this thesis a new numerical method for solving the so-called macroscopic model for ac conduction in disordered solids is developed. This new method makes it possible to investigate the model in three dimensions in the low temperature limit. In agreement with experimental data from the literature, the model is found to exhibit Time-Temperature scaling and universality (independence of probability distribution generating the disorder). Furthermore the results are found to be in reasonable quantitative agreement with experimental data.