THE AUSTRALIAN NATIONAL UNI~~y ~.t.r.Df

.e 12/1972

RESEARCH SCHOOL OF PHYSICAL SCIENCES

DIFFUSION RESEARCH UNIT

Annual Report 1971

Head of Unit (Senior Fellow) Dr. R. Mills, MSc. (N.Z.), Ph.D(Wash. St. Louis), D.Sc.

Fellow Dr. L.A. Woolf, M.Sc. (W.A.), Ph.D(N.E.)

Research Fellow

Honorary Fellow

Dr. R.O. Watts, B.Sc. (Lond.), Ph.D.

Prof. R.H. Stokes, Ph.D (Cantab.) D.Sc. (N.Z.) F.A.A. (arrived April 1971)

GENERAL

Conferences, Lectures, Seminars, Visitors

Professor, R.H. Stokes visited the United States in November/

December to attend the J.H. Hildebrand 90th Birthday Symposium held at

Berkeley and gave a paper on "Dipole interactions in solution". He also

lectured at several other universities in the United States. Dr. R. Mills

attended the ANZAAS Conference at Brisbane in May and presented a paper

entitled "Water - the solvent". Dr. R.O. Watts attended an Applied Mathematics

Conference at Smiggins Hole in March giving a lecture on "Friction coefficient

formalism".

Dr. Watts lectured at the Research School of Chemistry on

"Intermolecular forces and the properties of liquids" and in the School

Seminar series on ''Machine simulation methods in physics". He also gave

a semester course in chemical physics to senior chemistry students at the

School of General Studies.

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The Unit's monthy seminar series was continued and this year has

seen the beginnings of what promises to be a very fruitful collaboration

with the Applied Mathematics Department.

normally attend each other's seminars.

Members of both groups now

Among overseas visitors to the unit during the year were

Dr. P.C. Carman, Director of the National Chemical Laboratories,

CSIR, South Africa, Dr. P. Fields, Director of the Chemistry Division,

Argonne National Laboratories and Professor Emeritus P. Emmett, of

John Hopkins University .

INTRODUCTION

This year can be regarded as somewhat of a turning-point in

the Unit's development. Much time and effort has been spent in the

last three or four years in developing several major new types of equip-

ment and their associated operating techniques. During the last eighteen

months these have progressively come into operation. As foreshadowed

in last year's report, the Unit has entered a more productive phase in

1971 and this is well reflected in our current publication list.

A second encouraging event that has emerged during the year is

the increasing integration of our experimental and theoretical programmes.

Since moving into the liquid-state physics area some three or four years

ago, this kind of integration has been one of the main long-term aims of

the Unit. For example the theoretical group have computed by the

molecular dynamics technique, self-diffusion coefficients of argon over a wide

range of densities and temperatures. Experimental values from the

cryogenic apparatus are now becoming available to compare with them and this

will be the first aaccurate comparison to be made. From our experimental

pressure-diffusion studies we have obtained coefficients for three organic

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liquids over a considerable density range. It is now proposed to

try and develop potential functions for these liquids as a prelude

to further theoretical treatment. What we wish to emphasize here

is that we prefer our hard-won experimental data to be exploited

theoretically by people in our own Unit. Conversely, the experiment-

alist working closely with his theoretical colleague should be better

able to choose the right experiments to do.

In the New Year we are setting up an NMR spin echo apparatus

to measure self-diffusion in liquids. This means that we will be

able to obtain self-diffusion coefficients using three methods+ tracer

techniques, NMR and molecular dynamics. To the best of our knowledge

no other single laboratory has more than one such technique at its

disposal. On this basis we ought to be able to make a very significant

contribution to this section of liquid-state physics for some considerable

time.

More detailed accounts of work in the various sections of

the Unit are given below.

(1) Pressure Diffusion Studies

Benzene, carbon tetrachloride and cyclohexane have been

investigated over a range of temperatures and pressures in the liquid

region. The results, which are being prepared for publication, have

emphasized the inadequacies of present simple model theories of transport

properties in liquids. Preliminary indications suggest a close relation-

ship between the self-diffusion coefficient and the internal energy of a

liquid. Equipment has been obtained to extend the range of temperatures

and pressures of the diffusion measurements. Ancillary devices for this

equipment have been designed and are awaiting completion by the School

Workshop.

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(2) Self-Diffusion in Organic Liquids

This study, as will be seen from previous reports, is a continuing

one using conventional diaphragm-cell techniques at room temperature.

This year the main area of work has been on mixtures of octamethylcyclo­

tetrasiloxane with benzene or carbon tetrachloride and here one is in-

vestigating the effect of disparate size on diffusion. There have been

some problems in radioactave labelling of the siloxane as it apparently

polymerises under strong radiation. This anomalous labelling is of some

interest in itself and is being jointly studied by a group at the University

of N.S.W. and ourselves. We now propose to use NMR spin-echo technique

to measure the self-diffusion of the siloxane and overcome the difficultly

that way.

(3) Water Silica Interactions

NMR line-width measurements of water adsorbed on two types

of silica showed significant differences according to the acidity of

the surface. It was decided therefore to investigate thoroughly the

nature of the surfaces of the two silicas. Surface areas have been

measured by the BET method, using both nitrogen and water vapour, and

the strength of adsorption by differential thermal analysis. In an-

other study the self-diffusion of water adsorbed on silica has been

measured by an NMR spin-echo method. From these experiments, a large

amount of interesting data has been accumulated which is being used

to test current adsorption theories. In this section of the work, we

have had valuable help from the School of Physics, U. of N.S.W.; the

J.C.S.M.R., the Geology Dept., S.G.S. and the Chemistry Dept., R.M.C.

Duntroon.

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(4) Cryogenic Studies

At the beginning of the year, the cryostat and its associated

electronic apparatus had been proven out operationally. A great deal

of time and effort has been spent on overcoming "teething" difficulties

such as refining temperature control and improving purity of materials

and counting characteristics. These problems were not large but in a corn-

plex machine of this type, each involved considerable effort. The first

actual diffusion run was in October and we now have obtained a self-

diffusion coefficient for liquid-argon. Small drifts in the electronic

counting apparatus need to be eliminated before we can routinely produce

data of the accuracy that we require.

(5) Statistical Mechanics of Dense Systems

This year work has continued on the problem of using data

from liquids and solids to determine the intermolecular forces between

particles. Probably the most important work was the completion of a study

on argon interactions. The equilibrium results for liquid argon reported

last year were used to make a small adjustment to the Barker-Bobetic

potential, leading to significant improvement in the results. By the

end of the year calculations for liquid state transport coefficients

had been completed. The diffusion coefficient data was in reasonable

agreement with both experimental results and with previous calculations

using a less sophisticated potential. However the first test of this

data cannot be carried out until accurate experimental data for the

liquified rare gases are available. The thermodynamic data and elastic

constants of solid argon were also calculated over the temperature range

40°K- 80°K, with excellent results. Using the final form of the argon

potential we now have one model that fits all solid, liquid and gas

thermodynamic data from 0°K up to 2000°K within experimental error. It

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also reproduces exactly high and medium energy molecular beam

scattering data and measurements of the weak Van der Waals binding

spectrum. This work, which has been carried out in co-coperation

with Dr. J.A. Barker of IBM Research Laboratories, has resulted in

the most accurate potential function yet derived for any real system.

The polymer work carried out in co-operation with Dr. W.P. Wood

of the Department of Theoretical Physics was terminated in the middle

of the year. After calculating various properties of polymer chains

as a function of chain length it was discovered that for some properties

it was not possible to obtain accurate estimates of their asymptotic

form using Monte Carlo calculations. It is believed that this result throws

doubt upon the usefulness of numerical estimates of asymptotic forms

in this field.

At the end of the year work was in progress on gas and liquid

phase studies of helium - 4. Dr. I. Snooks of the Research School of

Chemistry has obtained a fully quantum mechanical potential function for

helium- 4 pair interactions. In this Unit classical and quantum

mechanical calculations on the fluid properties are in hand. In addition

work has started on the problem of obtaining an accurate potential function

for benzene. This model would account for the non-spherical shape of

benzene and include three-body effects. As a preliminary to this work a

program for calculating the third virial coefficient for non-spherical

systems has been written. This program is being used at present to examine

the third virial coefficient of a gas composed of hard spheres with imbedded

dipoles.

Early in the year work on the properties of water came to a stand-

still owing to the lack of adequate computing facilities within the University.

Some work on the problem has still to be completed and it is possible that

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when more powerful computing facilities are available this work may be

restarted. Given the great success of the argon work it is unfortunate

that more work cannot be undertaken on the water interactions at this stage.

PUBLICATIONS

1. Barker J.A.+ Fisher, R.A. and Watts, R.O.

"Liquid Argon: Monte Carlo and Molecular Dynamics Calculations".

Molecular Physics, ~. 657 (1971)

* 2. Collings A.F., Hall, D.C., McCool, M.A. and Woolf, L.A.

"A Diaphragm Cell for Diffusion Measurements in Liquids under pressure",

Journal of Physics E. (Scientific Instruments) ~. 1976-1982 (1971)

* 3. Collings A.F., Hall, D.C., Mills, R. and Woolf, L.A.

"A Conductance -Monitored Diaphragm cell for diffusion measurements",

Journal of Physics E. (Scientific Instruments) ~. 425-428 (1971)

* 4. Collings A.F., Watts, R.O. and Woolf, L.A.

"Thermodynamic properties and self-diffusion coefficients of simple

liquids",

Molecular Physics, lQ, 1121-1133 (1971)

* 5. Collings A.F., and Woolf, L,A.

"Recalculation of the friction constant and transport coefficients

of liquid argon from the Rice - Allnatt theory",

Australia Journal of Chemistry, ~, 225-235 (1971)

6. Lewis J.E.+ and Woolf, L.A.

"Air buoyancy corrections for single-pan balances",

Journal of Chemical Education, 48, 639 (1971)

* Former member. Based on work done while a member of the Unit.

Not a member of this University.

+ Visiting research worker.

Member of the Department of Theoretical Physics.

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7. Mills, R.

"Isotopic self-diffusion in liquids".

Berichte Bunsenges PhysiKalische Chemie, 12, 195 (1971)

8. Mills, R.

"Intradiffusion of benzene in mixtures with

octamethylcyclotetrasiloxane at 25°C".

Transactions Faraday Society, ~' 1654 (1971).

9. Morariu, V.V.

"The Electrical Conduction of Aqueous Sulphuric Acid in Glass Powders".

Journal of Colloid and Interface Science. ~' 511 (1971).

10. Watts, R.O.

"Approximate Equation of State for Soft Spheres".

Australian Journal of Physics, ~' 53 (1971)

11. Watts, R.O.

"A New Perturbation Theory for Transport Coefficients",

Molecular Physics, ~' 765 (1971)

12. Watts, R.O.

"Recent Advances in the Theory of Liquids",

Reviews of Pure and Applied Chemistry, ~' 0000 1971

13. + 1! Watts, R.O. Henderson, D. and Baxter, R.J.

"Hard Spheres with Surface Adhesion: The Percus-Yevick Approximation

and the Energy Equation", in "Chemical Dynamics",

Advances in Chemical Physics, ~' 421 (1971)

* Former member. Based on work done while a member of the Unit.

+ Not a member of this University.

+ Visiting research worker.

1! Member of the Department of Theoretical Physics.

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THESES PRESENTED 1971

Fisher R.A.

"The Statistical Mechanics of Argon". (1971)

McCool, M.A.

"Diffusion of organic liquids: Pressure

Temperature Studies" (1971)

12/1972