A study of the dielectric properties of water emulsions obtained after a crystallization/melting cycle

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A study of the dielectric properties of water emulsions obtained after a crystallization/melting cycle

B. Lagourette, C. Boned, L. Babin

To cite this version:

B. Lagourette, C. Boned, L. Babin. A study of the dielectric properties of water emulsions obtained after a crystallization/melting cycle. Journal de Physique, 1977, 38 (7), pp.825-832.

�10.1051/jphys:01977003807082500�. �jpa-00208644�

A STUDY OF THE DIELECTRIC PROPERTIES OF WATER EMULSIONS OBTAINED AFTER A CRYSTALLIZATION/MELTING ^CYCLE

B.

LAGOURETTE,

C. BONED and L. BABIN

Laboratoire de

Thermodynamique,

Institut Universitaire de Recherche

Scientifique,

Université de Pau et des

Pays

^de

l’Adour,

^{BP 523 «} Pau-Université » 64010

Pau,

^France

(Reçu

^{le 9}

février ^1977, accepté

^{le 31 mars}

1977)

Résumé. ²⁰¹⁴ Les

propriétés

diélectriques des émulsions d’eau (dont ^le support ^{continu est un}

mélange

^{de lanoline,} agent tensio-actif et d’huile de

paraffine),

^obtenues après

congélation-fusion,

sont comparées ^avec celles des emulsions d’eau avant tout

changement

d’état. La droite

d’absorption

dont la pente ^avant congélation ^vaut 0,22 ^eV

(énergie

d’activation de conductivité de l’eau dispersée

dans l’émulsion) ^se

déplace

après ^un cycle ^{vers des}

fréquences plus

^basses (à ⁰ °C) pour occuper ^une

position

^à

laquelle

^{est associée une} énergie d’activation

plus

élevée. Le maintien à

temperature posi-

tive ramène la droite

d’absorption

^{vers sa}

position

^{initiale. On} discute le

phénomène

^{en termes de}

fusion et de structure de l’eau liquide ^aussitôt après ^{la fusion.}

Abstract. ²⁰¹⁴ The dielectric properties ^{of water emulsions} (the continuous medium of which is

a mixture of lanoline, tensio-active agent ^and

paraffin

oil) obtained after a

congelation/fusion cycle

are

compared

with those of water emulsions

prior

^to any

change

^{in state. The}

absorption

line, ^whose

slope

prior ^to

freezing

corresponds ^to 0.22 eV - activation energy of

conductivity

^{of the water}

dispersed

within the emulsion ²⁰¹⁴ shifts after a

cycle

towards lower

frequencies

(at ⁰ °C) ^{to settle}

at a

position

with which a

higher

activation energy is associated. Maintenance ^{at a}

positive

tempe-

rature

brings

^the

absorption

^{line back to its initial}

position.

^The

phenomenon

is discussed in terms

of fusion and of the structure of liquid ^water immediately after fusion.

,

Classification

Physics ^Abstracts

7.482 ^- 8.740 ^- 9.162

1. Introduction. ^- In

previous

^works

[ 1, 2],

^{we have}

discussed the dielectric

properties

^of

dispersions

^of

micro-crystals

of ice obtained from

supercooling

breakdown of

supercooled

^water

droplets.

^The

study

of

complex

^relative

permittivity

^{E* = s’}

- jE"

^showed

that at temperatures ^near

melting temperature Tf

^the

Cole-Cole

plot 8"(8J presented by

^those

systems

gene-

rally

consists of two arcs of circles characteristic of two distinct areas of dielectric

absorption.

^The

coupling

between both areas

depends

^on temperature and is such that at

Tf they

^{melt into one}

single

^arc

of a circle.

We defined a model

[3]

^whose

analysis permits

^a

satisfactory

^{account of}

experimental

results. The area

corresponding

^to

higher frequencies

is connected with the

Debye dipolar absorption

of the normal ice lattice. That related to lower

frequencies

^{- which}

exists between 0 °C and about - 20 OC - is charac- teristic of a

phenomenon

^of

prefusion

^{at those}

tempe-

ratures which results from the appearance of _per- turbed zones within the

crystal

^{lattice -} the dielectric

properties

^{of such zones}

corresponding

^{to a} process of conduction. Their

conductivity substantially

increases ^near

melting

temperature ^to

reach,

^at

0 °C,

an

approximate

^{value of}

^10-’

^0-1

m-l,

^{which can}

compare with the values of

conductivity

^of

slightly

ionized water as found in the literature. This result

suggests

^a

near-liquid

^{nature of such zones, but the}

value of their

permittivity

that the model

necessarily

leads to is low and has led us to consider them ^as

being

of near-solid structure.

Such considerations

pose

^the

problem

^{of the} pro-

perties

^{of the}

liquid immediately

after the

melting

of the

crystal

and of the

correspondance

that may exist between the structure of the

liquid

and that of the

crystal.

^{In the}

present discussion,

^{we will}

present

the dielectric

properties

^of

liquid

^{water emulsions}

obtained

through

fusion of

micro-crystals.

^{We will}

see that near

melting temperature

^the

droplets

^of

liquid

^water obtained from

micro-crystals

present

noteworthy properties, undoubtedly

^{related to the}

process of fusion.

2. Recall of the dielectric

properties

^{of water}

emulsions m kilometric waves. ^- 2.1 EXPERIMENTAL

BEHAVIOUR

[4, 5].

^{- The}

complex

^relative

permittivity

9* = s’

- j8"

^{of a}

liquid

^{water emulsion} presents ^a

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01977003807082500

826

dispersion

ⁱⁿ kilometric waves. The

plot 8"(8’)

^{is a}

semi-circular one and the

amplitude

^of

absorption

^is

greater ^{when the water} volume fraction 0 is

higher.

The relaxation

frequency Vc corresponding

^{to a}

maximum of E’ is a

decreasing

function of 0. Parame- terisation in

frequency

^{of the}

plot B"(s’) corresponds

to a

Debye-type

distribution with relaxation times distributed

according

^{to a} selective Cole-Cole law.

For a

given

volume fraction

T,

^the

limiting permit- tivities Es (lower frequencies) and 8§ (higher frequencies)

are

practically independent

^of

temperature,

^whereas the relaxation

frequency Vc

^{is an}

increasing

^function

of T in the

form : v,,

^{= A}

exp[- U/kT]

^{- with k}

being

the Boltzmann constant ^- in which

U,

^relaxa- tion activation _energy of the water

emulsion,

^{has a}

value of

(0.22

±

0.01) eV,

whatever 0 _may be.

Conversely,

^the

frequency

^{factor A varies}

along

^{with 0}

so that _Vc increases as 0 decreases.

Finally,

the behaviour of unfrozen emulsions of aqueous saline solutions is similar to that of _pure water emulsions with

only

^a shift of the relaxation band towards the

higher frequencies

^{when salt concen-}

tration increases. But the relaxation activation _energy remains

equal

^{to 0.22 eV as}

long

^as salt concentration is not too

high.

2.2 THEORETICAL INTERPRETATION

[6, 7].

^{- As}

the

droplets

may be

compared

^to

spheres,

the dielec- tric

properties

^{of the}

liquid

^{water emulsion are inter-}

preted by

^{means of the}

spherical dispersion

pattern

(distribution

^of

spheres

^{within a} continuous

medium).

A

comparison

^of

experimental

results with theoreti- cal

expectations

shows that the relaxation observed in kilometric waves results from a

Maxwell-Wagner

effect connected with the

conductivity

^{of water.}

In

particular,

^{it can} be shown that the activation energy of the relaxation

presented by

^{the emulsion}

is

actually

^the activation _energy of

conductivity

^of

water, that

is, precisely

^{0.22 eV.}

(Besides,

^{this same}

value also

corresponds

^{to the} activation _energy of

conductivity

^of aqueous saline

solutions.)

^{The varia-}

tions with 0 of the characteristics of the relaxation

- maximum of

e", s’, 8§, parametering

ⁱⁿ

frequency, dependency

^of Vc on 0 - can also be accounted for

adequately by

^the

pattern

^of

spherical dispersion.

Finally,

^{it is} shown that the shift of the relaxation band towards the

higher frequencies

^{as salt concen-}

tration increases

merely

results from the increase of

conductivity presented by

the aqueous saline solution.

3.

Experimental

process. ^- The water utilized is

permuted,

^{distilled water} with initial

conductivity equivalent to 10 - ’ Q - ’ m - ’.

The emulsion is obtained

by dispersing liquid

^{water within an}

emulsifying

medium

by

^{means of a}

homogenizer capable

^of

spin- ning

^{at 45 000} rpm. The

emulsifying

^{medium is as a}

rule a mixture of

paraffin

^{oil and}

lanolin,

^{the latter}

acting

^as surfactant agent

(the

mixture is

quite

^similar

to the one utilized to conduct the

experiments

^des-

cribed in

paragraph 2).

^{For the sake of}

comparison,

we have also

experimented

^{with an}

emulsifying

medium of a

quite

^{different nature - a mixture of}

vaseline and

Span 85,

the latter then

acting

^{as tensio-}

active agent. The dielectric

absorption

of these media is

negligible.

The

composition

of the neutral medium is charac- terized

by

parameter p ⁼

mL

_{with mL}

_referring

ML + MH

to the mass of tensio-active agent ^and mH the mass of

paraffin

^oil.

The emulsion is then

poured

^{into a} measurement cell Ferisol CS

601,

^a

fully-active condenser,

^which

is a few

cm’

in usable volume. Then the measurement cell is

placed

^{within a} thermostated container.

Owing

to the

great

thermal inertia of the

cell,

^the tempera- ture, measured with a

thermistance,

^{does not} vary

by

^more than 0.1 OC.

The

apparatus enabling

the evaluation of

complex

relative

permittivity

^{6* = s’}

- jt"

consists of two

systems ^of measurement of

admittance,

^{of the}

Schering-bridge type, capable

^of

covering

^the range from 20 Hz to 3 MHz. The real

(8)

^{and the}

imagi-

nary

(s")

parts ^are determined

by

^a method of substi- tution with an absolute

uncertainty

^{valued at Ag’= 0.01}

and As" ⁼ 0.02.

The experiment

^{is effected as follows : a}

prior study

of the water

emulsion,

^followed

by freezing

^{in order}

to obtain the

dispersion

^{of ice}

micro-crystals (this

^is

then

posterior

^to

supercooling breakdown);

^a

study

of the

prefusion phenomenon

^on

dispersed ice,

^then

melting

^and

eventually

^a

study

^{of the water emulsion}

obtained after the

crystallization/melting cycle.

^As

regards

^the

crystallization

of the emulsion and the

prefusion phenomenon,

the reader should refer to

[2, 3, 8]. However,

^we will recall that the

granulometric

distribution of

droplets

^{in the emulsion}

depends

^on

the

quantity

^of

disperse

^{water as well as on the} pro-

portion

of surfactant. The curves of

distribution,

^such

as those

presented

ⁱⁿ

figure 1,

have been determined

by

^{means of a LEITZ}

granulometric particle

^counter

from

photographs

taken with a ZEISS

photomicro-

scope.

These curves reveal in

particular

^a

fairly good

^selec-

tivity

for diameters of about a few

microns,

^{the sizes} of

droplets being

^{as a} rule all the smaller as the volume fraction of the

disperse phase

is lower and their envi- ronment richer in tensio-active agent.

Supposing

the emulsion is

perfectly homogeneous

^as

regards

^the

disposition

^of

droplets,

^the distance between the centres of two

neighbouring particles

^can be evaluated

simply.

It is about

2.5 g

^{in the case of}

particles

^which

are

2 p

ⁱⁿ average

diameter,

^the

weight

^fraction

being

0.30.

Thus,

^these considerations show that the dis- tances between

neighbouring particles

^{can be com-}

pared

^to the sizes of

droplets,

the distances

being

^even

smaller when the

proportion

^{in the}

disperse phase

increases. The ratio

surface/volume

characteristic of the

droplets

^{is itself}

important

^{- about a few}

J.1-1.

FIG. 1. ^- Granulometric distribution of emulsions 0.30 in weight ^fraction (d ⁼ diameter of the droplets).

4.

Experimental

^{results. - 4. I At}

equal tempe-

rature, the relaxation

frequencies

v, of the

dispersion

of ice

micro-crystals

and of the initial water emulsion

- in the _case,

supercooled

^{- are} different. In the

plot [log

VC,

1/71

^the

absorption

line of the

liquid

water emulsion ^-

supercooled

^below

Tf

^{- deter-}

mined

prior

^to any

freezing

^is located above the

curves

[log

VCt’

1/71

^and

[log

v, ,,,

1/T],

associated with each of the

absorption

^areas of the ice

dispersion.

Figure

²

brings

^out this result

(the

^water

weight

^frac-

tion

being 0.28).

The continuous medium contains two

portions

^of

tensio-active agent ^{for one}

portion

^of

paraffin

^oil.

At temperature ^{T =}

Tf

^{= 0}

°C,

^the difference bet-

ween the value

log

Vc of the water emulsion and that of the ice

dispersion

lies between 0.30 and 0.60

depending

^{on the}

samples

considered.

Therefore,

^at

FIG. 2. ^- Water weight fraction : 0.28. Composition of the emul-

sifying ^{medium : 2} portions of lanolin for 1 portion ^of paraffin ^oil.

T= 0

°C,

^the

frequency

^at maximum dielectric

absorp-

tion

presented by

^{the water emulsion}

prior

^to any

crystallization

^{is two to} four times

higher

^{than that}

of the ice

dispersion resulting

^{from it.}

Besides,

^the

relaxation activation _energy of the water emulsion amounts to 0.22 eV.

4.2 After

studying

^the

dispersion

of ice micro-

crystals,

^the fusion of the system ^is

provoked. By measuring

^{at 1 MHz the}

high-frequency permittivity

limit

s’,

^{it is}

possible

^{to trace} the fusion because of the difference in value at this

frequency

^{between the}

permittivity

^of

liquid

water,

88,

and that of

ice,

^{3.08 -}

in the same way that

freezing

^{can be traced.}

The measurement at T ⁼

Tf

^of

complex

^relative

permittivity

^{E* = e’}

- js"

shows that the values of

frequency

Vp ^at maximum

absorption

^are identical for the water emulsion and for the

single

^{arc of a circle}

relating

^{to ice at this same} temperature.

By repeating

the measurement at various temperatures, it is then

possible

^to

plot

^the

corresponding absorption

^line

[log

Ve,

11T].

^{On this new}

plot,

the difference at 0 OC between the water emulsion and the

dispersion

^{of ice}

micro-crystals

^no

longer

exists. The curves associated with the solid and the line

representing

^the

liquid

^are

then concurrent at

0 °C,

^{as is shown}

by

^the

two

examples

^on

figure

^3.

(Besides,

^the

plot (b)

^can

compare with that on

figure 2,

^as both reveal the same

behaviour of the same

sample

^{at different}

times.)

On

figure ^4,

^{we present} the Cole-Cole

plots

^obtained

at T ⁼

Tf

^{for the}

dispersions

^of

micro-crystals

^and

the

corresponding

^water emulsions of two distinct

samples.

^{The curves}

log vlw

⁼

f (log v),

^characte-

ristic of

Smyth’s

^method

[9],

from which the relaxa- tion

frequencies

^{have been}

evaluated,

^also appear ^on the same

figure.

4. 3 The value of the activation _energy of dielectric relaxation of the water emulsion obtained after fusion is

higher

than the initial value 0.22 eV. We have read values between 0.30 eV and 0.38 eV. We will here recall that this value is in effect

equal

^to the activation energy of

conductivity

^of

dispersed liquid

^{water. The}

828

FIG. 3. ^- Water weight fraction : (a) 0.30, (b) ^0.28. Composition

of the emulsifying ^{medium :} (a) ¹ portion of lanolin for 1 portion

of paraffin ^oil. (b) ² portions of lanolin for 1 portion of paraffin ^oil.

positions respectively occupied by

the lines of

absorp-

tion of water emulsions

prior

^to

freezing (line (1))

and after the

freezing/melting cycle

^{are as shown in}

figure

^5.

Table I indicates the

corresponding

^values.

4.4 After

determining

^the

position

of the line

(2),

if the

sample

is maintained at a

positive

temperature of about a few °C

(6 OC),

^an evolution of its dielectric

properties

^can be noticed in course of time. This is

expressed by

^a

slippage

^{of the}

points

ⁱⁿ

frequency

on the Cole-Cole arc of a circle

s"(e’)

^{towards an}

increase of the relaxation

frequency

vc. The duration

TABLE I

FIG. 5. - Lines of absorption : (1) prior ^to crystallization; (2)

after the crystallization/melting cycle. ^Water weight fraction : 0.22.

Composition ^{of the} emulsifying ^{medium : 1} portion of lanolin for 3 portions ^of paraffin ^oil.

of the evolution is about ten

days,

after which time the new line of

absorption

of the emulsion

(defined by

measurements at different

temperatures

^between

+ 10 °C and about -

10 °C) practically

shifts back to the

position occupied initially,

whose activation energy is 0.22 eV -

assuming

^the accuracy of mea- surements.

4.5 THE RESULTS OBSERVED CAN BE SUMMED UP AS FOLLOWS. ^- 4.5.1 The line

of absorption,

^whose

slope corresponds

^{to 0.22 eV}

prior

^to

freezing,

^shifts

after a

crystallization/melting cycle

towards lower

frequencies (at 0 °C)

^to occupy ^a

position

^{with which}

a

higher

activation _energy is associated.

4.5.2 In this new

position,

^at

temperature T=Tf,

the relaxation

frequencies

^{of the water emulsion and}

of the ice

dispersion

^are identical.

Somehow,

^the

emulsion remembers its former state. In this sense we

Weight fraction : 0.25

Emulsifying medium : 1 portion of surf actant for 11 portions ^{of oil}

Weight fraction : 0. 30

Emulsifying medium : 1 portion of surfactant for 3 portions ^{of oil}

FIG. 4. ^- (a) ^Cole-Cole plot ^and Smyth plot ^{of ice} dispersions. (b) ^Cole-Cole plot ^and Smyth plot ^{of water emulsions.}

can

speak

^{of a} memory

effect, though

^{the term} may be

inadequate.

4.5.3 The maintenance

of

the emulsion at a

posi-

tive temperature ^{tends in course of time to}

bring

^the

line of

absorption

^{back to the}

position initially

^occu-

pied prior

^{to the}

crystallization/melting cycle.

4.6 Further

experiments

have been conducted on

emulsions made _up with a different

emulsifying

830

medium

(a

mixture of vaseline and

Span 85).

^The

behaviour is in every

point

^{similar to the one des-}

cribed above.

Figure

⁶ illustrates this result

(Table II).

In

particular,

the shift of the line of

absorption

towards lower

frequencies

^{can be}

observed, together

with a simultaneous increase of the activation _energy and also the return to the initial

position

^{- 0.22 eV}

as ever ^- after

cancelling

^{of the} memory

effect.

5. Discussion. ^- 5.1 INFLUENCE OF IMPURITIES. ^-

It seems that the differences observed in

samples

^at

different moments -

prior

^to

freezing,

then after the

freezing/melting cycle

^{- cannot} be attributed to any diffusion of

impurities

^of

emulsifying

medium in the

disperse phase during

its maintenance either in the solid or in the

liquid

state, ^or

during

its successive

changes

^{in state.}

Effectively,

the variation of the activation _energy of the

liquid

^{water emulsion cannot}

be accounted for

by

^the

possible

dissolution of

impu-

rities since the

experiment

^shows

that,

for emulsions of _aqueous saline

solutions,

^the energy remains constant and

equal

^to 0.22 eV when concentration varies

(see § 2.1). Besides,

^the

frequency

^{at maximum}

absorption

^{of the}

liquid

^water emulsion decreases

whereas,

^{in the case of}

aqueous

^saline

solutions,

^this

frequency

^{increases as the salt}

proportion

^increases.

Finally,

^{if such were the} case, ^one

might

expect ^an alteration of the

properties

studied when the emul-

sifying

^{medium was}

replaced by

^{another one of}

quite

different nature, ^{as in} this case the environment of the

droplets

^is

thoroughly

^altered.

However,

^{as has} been

mentioned above,

the behaviour of the systems remains

unchanged

^as

regards

^the activation _energy and the memory

effect (indeed

^{a variation of}

8’ s

^and

Ed

is

observed,

but this results from the alteration of the dielectric

permittivity

^{of the}

emulsifying medium).

FIG. 6. - Lines of absorption : (1) prior ^to crystallization; (2) after the crystallization-melting cycle. ^Water weight fraction : 0.22.

Span ⁸⁵ weight ^{fraction in} the emulsifying medium : 0.05.

TABLE II

5.2 STRUCTURE OF LIQUm ^{WATER. -}

Likewise,

variations in the behaviour of a water emulsion

prior

to

crystallization,

then after the

freezing/melting phase,

pose the

problem

of the fusion

phenomenon

^of crys- talline

samples dispersed

in the form of small systems and

undoubtedly,

^the very

complex problem

^{of the}

structure of

liquid

^water is connected with it. This structure is as yet

insufficiently

known and various

points

of view have been stated in the literature. From the _many models

proposed,

^{it is}

possible

^{to draw}

four main _groups, which we will sum up

shortly.

5 . 2 .1 Medium

arrangement

model. - The

simplest

model divised

by

^{J. A.}

Pople [10]

and termed distorted

hydrogen

bond model consists in

attributing

^no spe- cific structure to water but instead

only

^{a medium}

arrangement of molecules. This model describes water

as a continuous lattice of linked molecules in which all four

hydrogen

^{links on} each molecule can bend

or twist

independently

^{from one} another. The dis- tortion of the links leads to the

breaking

^{of the}

long-

range order

existing

within the

crystal

^{- with the}

short-range

^order

undergoing

little alteration. The scheme represents ^a

transposition

^{of the}

crystal

^lattice

of ice

Ih

^{to the case of}

liquid

^water.

The other three types of structural models that follow are

quoted

^more

frequently

and all three intro- duce elements of

arranged

structure, ^{for which reason}

they

^{are termed mixture models of water.}

5.2.2 Patterns in cage ^{or water} clathrates. ^- These involve consideration of water as a water

hydrate [11],

that

is,

^an

interstitial

solution of non-linked molecules within a labile

medium, frequently

assimilated with dodecahedra. In such a structure, there exist cages located within the

polyhedra

^or in the interstices formed

by

^their arrangement and filled

by

^molecules

of free water.

5.2.3

Flickering

clusters models. ^- The first of

these, proposed by

^H. S. Frank and W. Y. Wen

[12]

assumes that the formation of

hydrogen

links within water is

essentially

^a

cooperative phenomenon. Thus,

the _presence of a

pair

^{of atoms linked}

by

^a

hydrogen

bond would increase the

probability

^of formation of other links of the same nature with

neighbouring

molecules. This in return would ensure

greater

^sta-

bility

^{of the}

existing

system.

Taking

^this

hypothesis

into account and

owing

^{to the structure} of the mole- cule

H20,

^{one can} then foresee the formation in

places

^of

flickering

clusters. These would be labile structures of various extents,

consisting

^{of a} system of

strongly

^linked

molecules,

of which the

greatest possible

^{number are four-link ones. These structures}

are

separated

^{from one} another within the

liquid by

free molecules which make _up the remainder of the system.

Relying

^on the idea of

flickering clusters,

statistical patterns ^{have been}

developed,

among which can be mentioned that of G.

Nemethy,

^{H. A.}

Sheraga [13], recently improved by

^{B. R.}

Lentz,

^{A. T.}

Hagler,

H. A.

Sheraga [14] relating

^{to a}

hexagonal

arrange- ment of molecules within the cluster ^- which arran-

gement is identical to that of ice

Ih.

^But in these various

schemes,

^the structures should not be considered ^as stable

crystalline configurations

^{but as} labile forms liable to very

quick

fluctuations.

5.2.4

Near-crystalline models,

^or models with

defects

ⁱⁿ the lattice. ^- At the basis of such models is the idea that water possesses ^{a structure} similar to that of ice

Ih. Thus,

^{E. Forslind}

[15]

^utilizes

it,

^consi-

dering

^a

crystalline

^structure very ^{near to} that of ice

Ih

^-

though slightly

^{loose - marred}

by

^the

presence of molecules

occupying

interstitial sites.

Likewise,

^{C. M.}

Davis,

^T. A. Litowitz

[16]

^and

G. E. Walrafen

[17]

^{conceive water as a mixture.}

The former assume a mixture with an open ^structure

- one molecule is linked

by hydrogen bridges

^with

four

neighbouring

^{molecules - and with a denser}

structure in which molecules are linked

only

^with

some

neighbouring molecules, generally

^{two. The}

latter assumes a mixture with free molecules and tetrahedral clusters of molecules.

5.2.5 The

different

^theories

constituting

^these

four _groups

generally

^{have a common}

point

^{the exis-}

tence of tetrahedral arrangements of certain mole-

cules,

^{as in ice.}

However, they

^differ

widely

^{in the}

sense that two of these _groups ^- 1 and 4 ^- start from the idea that the structure of

crystal

^determines

that of the

liquid,

whereas the other two ^- 2 and 3 ^-

assume the formation of labile combinations results from local fluctuations of _energy.

However,

^{none of}

these theories refers to the occurrence of a critical temperature ^{above which the}

orderly

structures would

be destroyed.

^{It seems} that their authors assume the

validity

^{of the}

description

^at any

temperature

^above

melting

temperature

and,

^of course, at any tempera-

ture within the _range of

supercooling.

5. 3 DISCUSSION OF THE « MEMORY EFFECT » FROM

« BULK » PROPERTIES OF WATER. ^- 5 . 3 .1 The _process

of melting

^{can be} considered as a process of a

complete

destruction of

long-range

order within the

crystalline

arrangement.

However,

^one may think that in the

case of

ice,

^the transformation does not affect the whole of the lattice. From the

melting

theories which

involve order-disorder transformations

[18],

the coexis- tence of normal

liquid

^{with more} associated

liquid constituting

^a metastable

phase

^{can be}

predicted.

Intermediary elements,

^{with a structure near that of} the solid at

0 °C, might

^be

preserved

^{in the}

liquid

- still at 0 OC ^-

immediately

after the

change

ⁱⁿ

state. The

liquid

^{could then be} assimilated to a mixture of

species.

The maintenance of the

sample

^{for a}

certain time at

positive

temperatures

would,

^because

of thermal

agitation,

^entail

gradual

transformation of these unstable structures,

coming

from the solid at 0 OC. Parallel to this

disappearance,

^the memory

effect

^would

dwindle, entailing

normalization of the dielectric

properties

^{of the}

liquid.

^{After the return to}

initial

equilibrium,

^{there is no hindrance to}

conceiving

the structure of water

by

^{means of the} theoretical models mentioned above.

5. 3. 2 As

regards

^{the variation}

of

activation energy observed on

liquid samples,

^the

following

^{facts can}

be recalled :

a)

The activation _energy of relaxation of the water emulsion is in fact

equal

^to the activation _energy of

conductivity

^{of water}

(see § 2.2).

^Its value under normal conditions ^- without _any thermal treatment

or after return to initial

equilibrium

^- is 0.22 eV.

b)

^The variation with

temperature

of the conducti-

vity

associated with the

perturbed

^zones

appearing during

^the

phenomenon

^of

premelting

of ice micro-

crystals

^is very

important

ⁱⁿ the immediate

vicinity

of

Tf.

^This amounts to

associating

with these zones a

high

apparent activation _energy at 0 OC.

If there

effectively

^{exists a} direct link between the structure of ice at 0 OC and that at the same tempe-

rature of the

liquid resulting

^{from its}

melting,

^the

activation _energy of the system ^should present ^an

intermediary value, necessarily higher

than 0.22 eV.

5. 3. 3 As

regards

^the

possible relationship

^between

ice at 0 OC and

liquid

^water

resulting

^{from it at the}

same

temperature,

^{it seems}

interesting

^{to sum} up the works of M. V.

Kurik,

^{V. A.}

Shayuk [19] dealing

with the _process of

melting

of molecular

crystals.

Starting

^{from the} appearance ^or

disappearance

^of

optical anisotropy during

the fusion of such

crystals,

then in the course of a slow

heating

^that

follows,

^the

authors note the existence of two

transitions,

^{with a}

slight lag

ⁱⁿ temperature. ^The

melting

^of

crystal

^is

manifested,

^not

by

instantaneous _passage to the iso-

tropic liquid phase,

^but

by

^the appearance of a

half-liquid, half-crystalline

intermediate

phase

^{- a}

mesophase

^{- cancelled}

by ^the passing

^{of the}

higher

transition temperature. The interval

separating

^the

so-called

melting

temperature ^-

crystal/mesophase

transition ^- from the temperature ^{related to the} second transition ^-

mesophase/liquid

^- varies from 2 °C to 23 OC

according

^to the bodies studied. The

question

^is whether there is _any

analogy

between the

mesophase

^{and the}

perturbed

^{zones of ice at 0 °C}

(the

^structure

being probably nocrystalline).

832

5.4 LET us POINT OUT that F.

Broto,

^{D. Clausse}

[20] using

^another

experimental

^{method - differen-}

tial

enthalpic analysis

^{- have}

observed,

too, ^a memory

effect

^on

systems

^{identical to ours. For an emulsion} that has never

undergone

any former

change

ⁱⁿ state,

supercooling

breakdown of

liquid

^{water occurs at}

a more

probable temperature

^{T* = -}

(39

^±

0.5)

^OC.

After monothermal

crystallization,

^then

melting, immediately

^followed

by

^further

cooling,

^the

experi-

ment shows that there exist two more

probable

^values

of

crystallization

temperature : ^{the current value of}

supercooling

breakdown T* and a

higher

^value

T** = -

(34

±

0.5)

^{OC. If} the emulsion is main- tained for a few

days

^{at a}

sufficiently high positive temperature

^- around 10 OC ^- the

higher

^threshold

T** no

longer

appears ^at the next

cooling.

^{The water}

of the emulsion

crystallizes again

^{at the more}

probable temperature

^T*.

Although

^the process utilized differs

substantially

from dielectric measurements, ^{we are} entitled to make a

comparison

between the _memory

effects observed,

^and also about the _way these

disap-

pear

through

maintenance at a

positive temperature

for a few

days

^- the order of

magnitude being

^the

same.

5.5 TRANSITORY ^{« MEMORY} EFFECTS ». ^- Transi- tory memory

effects

^-

disappearing

^{with an increase}

in temperature ^- have also been noticed in the case

of

metastability

^and

polymorphism

^of

organic

^bodies

[21, 22]. They

have been accounted for

by

^the

adsorp-

tion of molecules in the

organic product/medium

interface. This

adsorption

^on the medium would create

orderly layers

^{liable to} become similar to the structure of the solid. Their destruction could

only

occur above a critical temperature

higher

^{than the}

fusion

temperature

^{of the}

product,

which would be characteristic of the media present.

5.6 CONCLUSION. ^- If the first

interpretation

^can,

to a certain extent, ^account for the differences observ-

ed,

^{one should be aware of the}

difficulty

that exists in

postulating

such slow structural

changes,

^as

they

take about ten

days

^to

evolve,

^{even in such a fluid}

network as water.

On the other

hand,

^{the act of}

freezing

^followed

by melting

may also

modify

^the arrangement of molecules within the

emulsifying

medium. The walls around each

droplet

^can

undergo configurational

^molecular

changes

^that

might

^{take as}

long

^{as ten}

days

^{to smooth}

out

again definitively.

^This

implies

^{that the}

orienting

effects should stretch out from the

droplets’

^walls

into their interior. As the ratio of

surface/volume

^of

the

disperse particles

is rather

high,

^{one can}

actually

assume an

orienting

effect in the environment. For

instance,

^one such influence

during freezing

^{of water}

dispersed

^{within a} medium has been evidenced

by

M.

Vignes,

^{K. M.}

Dijkema [22]. Therefore,

^this

possibility

^{cannot be ruled out}

categorically, though

in this case the

identity

of relaxation

frequencies

at 0 °C between the water emulsion and the ice dis-

persion

^{cannot be}

easily

understood.

References

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Séan. Acad. Sci. 279B (1974) ^461.

[2] LAGOURETTE, B., ^J. Physique ³⁷ (1976) ^945.

[3] LAGOURETTE, B., BONED, C., ROYER, R., ^J. Physique ³⁷ (1976)

955.

[4] ^HANAI, T., Kolloid Z. 177 (1961) ^57.

[5] LAFARGUE, C., CLAUSSE, M., LACHAISE, J., C. R. Hebd. Séan.

Acad. Sci. 274B (1972) ^540.

[6] CLAUSSE, M., ^{C. R.} Hebd. Séan. Acad. Sci. 274B (1972) ^887.

[7] CLAUSSE, M., ^Colloid Polym. ^{Sci. 253} (1975) ^1020.

[8] LAGOURETTE, B., Thèse de Doctorat ès Sciences, ^Pau (1977).

[9] SMYTH, ^C. P., Dielectric behaviour and structure (Mac ^Graw Hill) ^1955.

[10] POPLE, ^J. A., Proc. R. Soc. 205 (1951) ^163.

[11] PAULING, L., Hydrogen Bonding (Ed. by ^D. Hadzi, Pergamon Press, London) ^1959.

[12] ^{FRANK, H. S., WEN, W. Y., Discuss} Faraday Soc. 24 (1957) ^133.

[13] NEMETHY, G., SHERAGA, ^H. A., ^{J. Chem.} Phys. ³⁶ (1962)

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[14] LENTZ, ^B. R., HAGLER, ^A. T., SHERAGA, ^H. A., ^J. Phys. ^Chem.

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[15] FORSLIND, E., ^Acta Polytech. 115 (1952) ^3.

[16] DAVIS, ^C. M., LITOVITZ, ^T. A., ^{J. Chem.} Phys. ⁴² (1965) ^2563.

[17] WALRAFEN, ^G. E., ^{J. Chem.} Phys. ⁴⁷ (1967) ^114.

[18] UBBELOHDE, ^A. R., Melting ^and crystal ^structure (Clarendon Press, Oxford) ^1965.

[19] KURIK, ^M. V., SHAYUK, ^V. A., ^Sov. Phys. Solid State 17 (1975)

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