Spinodal decomposition in microemulsions

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Spinodal decomposition in microemulsions

D. Roux

To cite this version:

D. Roux. Spinodal decomposition in microemulsions. Journal de Physique, 1986, 47 (5), pp.733-738.

�10.1051/jphys:01986004705073300�. �jpa-00210255�

SPINODAL DECOMPOSITION ^IN MICROEMULSIONS

D. ROUX*

Corporate ^{Research Science} Laboratories, ^Exxon Research and Engineering, Annandale, ^New Jersey 08801, ^U.S.A.

(Requ ^{Ze 9} dgcembre 1985, accepté ^{sous forme} definitive ^{le 28} fgvrier ¹⁹⁸⁶⁾

Résumé

On étudie par, diffusion ^{de la Lumière la}

séparation de ^phase pres d’un point critique ^d’un

mélange microémulsion. ^La décomposition spinodale peut ^{etre observée dans une} large ^{zone autour du} point critique (jusqu’a ^{1K de la} temperature

critique). ^{La position de l’anneau de diffusion a} été mesurée en Fonction ^du temps. ^{L’ inhabituel} ralentissement ^de la decomposition ^a permis ^de

caractériser ^trois regimes successifs:

a) ^{Au tout} début de la decomposition

la position ^{de l’anneau reste fixe}

alors que ^son intensite augmente.

b) ^Puis Le diametre de l’anneau

décroit ^en suivant ^{La loi de}

puissance km ^{03B1 t-1/3.}

c) Enfin l’anneau disparait ^{dans Le}

faisceau central selon la loi km ^a t-1.

Abstract

Light scattering ^{was used to} study phase separation ⁱⁿ critically quenched quaternary ^micro- emulsions. Spinodal decomposition ^was observed in

a large region ^around the critical point (until ^1K

from the critical temperature). ^We measured the parameter km(t) ^i.e., the maximum of the ring ^in- tensity ^{as a} function of time. The unusually ^slow decomposition ^{allowed us to} characterize three

regimes:

a) ^An early stage where the position

of the ring ^{is constant as the in-} tensity ^increases

b) ^An intermediate stage ^{where the} position of ^the ring decreases ^as

a power law km ^{03B1 t-1/3.}

c) ^{A late} stage ^{where the} ring ^merges

in the central

beam ^{following the}

power law km ^{a t-1}

Classification

Physics ^Abstracts

74.70J - 64.60M - 68.10

Spinodal decomposition (SD) ^{in 1 iquids is} generally ^{studied in} binary ^{mixtures very close to}

their critical point. Light scattering ^{is used to} study ^the phase separation ⁱⁿ critically quenched

mixtures. The quench depths ^{in the binary fluids}

must be from 1 to 10 mK from the critical tempera-

ture. For deeper quenches spinodal ¹ decomposition

occurs too fast to be observed. ^{SD is} evidenced by the appearance ^{of a} ring ⁱⁿ scattering figure. ^The radius of the ring (km) ^{decreases with a power law} km ^a t-cI> with cI>

1/3 for ^{the early stage} and 4>

¹

for the later stage. The value of cJ> = 1/3 ^{is in}

agreement ^{with a} coalescence model of domain

growth while, = ¹ corresponds ^to hydrodynamic

effects ^{on the rate} of growth. In ^simple fluids

the behavior predicted by the Cahn’s theory ^has

never been observed. In this theory, ^{a charac-} teristic length ^{of the unstable} fluctuations appears, resulting ^{from a} competition between the fluctuations at large ^{wave vector} (small amplitude)

which are energetically unfavorable and the fluc- tuations at small wave vector (large amplitude)

which are slow. Cahn’s theory predicts ^{the ap-}

pearance ^{of a} ring ^of constant diameter with an

exponential, ^{increase of the} intensity ^{of the} ring. This behavior had never been observed in

binary ^{fluids due to the nonlinear} coupling ^between fluctuations, ^{which occurs} very rapidly. ^{On the} contrary ⁱⁿ polymer ^blends 50r ^{metallic alloys, this}

behavior has been observed.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01986004705073300

734

As we shall see, microemulsions present

an intermediate system ^between binary ^{fluids and} polymers. Microemulsions are multicomponent

mixtures of

6oil, water, surfactant and usually

cosurfactant. ^These mixtures ^{exhibit liquid-}

1 iquid ^critical points. ^The pecul iarity ^of microemulsion critical behavior is the large ^value

of the correlation length E ^which diverges ^when approaching ^{a critical} point. ^The divergence follows a power law E

Eo E-V ^{where e is the}

distance from the critical point (c

(T - Tc)/T )

and v is a universal exponent (v AI 0.6). The prefactor E is _{its value is} around 2-3 ^{not universal} A. 8but In micellar ^{in binary fluids} and microemulsion systems is increased

by a ^factor

of 10 or more depending ^{on the} system. _EO ^is

known to be related to the basic particle ^size (in binary ^{fluids it is a molecular} length). ^The large

value of Eo ⁱⁿ micellar and microemulsion systems

may be interpreted by ^the increasing ^{of the} par- ticle size of the basic object 4which is an aggre- gate of molecules instead of ^a molecule.

According

to the universal relations between prefactors ^a

change ^{of the} scale E ^{has several} experimental implications. ^For example, ^the turbidity ^is higher

than ^{j8 binary fluids and} the surface tension lower.. In the following ^we report ^results concerning spinodal decomposition ^{in microemul-} sions. The most spectacular difference between microemulsions and binary ^{mixtures is the} possi- bil ity ^{to observe the SD as far as one} degree (and

even more) ^{from the critical point. This} property allows us to measure three regimes including ^the

linear regime corresponding ^{to the Cahn’s} theory.

The different regimes ^are separated ^{with cross-over} regions. Further, ^more observation by ^{direct mi-} croscopy provided evidence for macroscopic spinodal

structure.

ExperimentaL

The system studied is a quaternary ^mix-

ture of water, ^sodium dodecylsulfate (SDS), ^penta-

nol and dodecane. At fixed _pressure, the system has four degrees ^of freedom, ^the temperature ^and three

concentrations. ^{The phase} iiagram ^{of this}

system has been studied previously. I ^{At constant}

temperature ^{it exhibits a} critical line beginning

on a critical end-point. The critical

behavior ^of

the system ^{has some} remarkable properties. ^The

experimentally ^measured exponents y and v seems to be dependent ^{on the} proximity of the critical end

point. Far from this point ^{we found} Ising ^{like ex-} ponents. ^As the critical end-point ^is approached

the experimental ^{values of the} exponents ^de-

crease. We have studied several samples along ^the

critical 1 ine and the spinodal decomposition ^seems

to slow down as the critical end-point is ap-

proached. However, the results presented ^here correspond ^{to a} sample ^{not too close to} this criti- cal end-point. ^This sample is defined as in the

preceding paper7 by the ratio of water ^{to surfac-}

tant (W/S-1.55). ^{A schematic cut of the} phase diagram fixing ^{the water over} surfactant ratio and the alcohol/oil ratio is given ^on Figure ^{1. The SD}

was studied in two different ways: with thermal

quenches ^and with shear. In the thermal quench ^the

evolution of the SD was studied as a function of the time with the quench occurring ^{at t}

^{0. This} path ^{starts from the} point Mo at temperature To (see Figure 1). ^The temperature ^is quickly (-1i 5s) ^{increased to} reach the point M1 ^at temperature

Ti, going through ^{the critical} point Pc ^{at tempera-}

ture Tc. ^{Typical values used are} TC.-To. ^{0.1 K and} T1-Tc ^ranging from 0.02 K until 1 K. The second

Figure ^{1: Schematic} representation ^{of a} cut of the four dimensional phase diagram ^of water, SDS, ^{dodecane and} pentanol mixture. The cut corresponds ^{to the} plane ^{defined at}

a fixed value of the water over

surfactant rat io and to a fix val ue of the alcohol over oil ratio. The dashed line corresponds ^to the spinodal ^curve.

way ^we studied SD was to keep ^the sample ^{at the} point ^{M at constant} temperature Ti. ^{The sample}

was in the two-phase region, ^but in order to pre- vent phase separation, ^the sample ^{was stirred. The}

shear flow displaces the coexistence ^curve towards

high temperatures. Spinodal decomposition appears when the shear flow is stopped ^and corresponds ^{to a} relaxation of the system ^{to its} ground ^state. The

same effect ^was utilized previously by Beysens for studying the effect of a periodic quench ^on spinodal decomposition. ^The sample ^is placed ^{in a}

thermostated water bath (AT

^{t 0.01} K). ^{A visual}

observation of the light scattering on a screen

allows us to observe a ring of scattered light just after the quench. ^The intensity ^{of the} ring ^in-

creases with time while its radius decreases.

Figure ² represents photos ^{of the} scattering figure

at different times after the quench. ^{In addition}

to this observation in Fourier space, direct ob- servation under microscope clearly ^{shows SD.}

Figure ^{3 shows two} photos ^{of the} microscopic ^struc-

ture as a function of time. These structures appears after the ring merges into the central beam. One _sees, that even for the long ^{time the} characteristic length ^{continues to} increase with the time. These pictures ^{can be} compared ^with

those obtained by Houessou and collaborators for

a binary mixture where the densities of the two

coexisting phases ^{were matched. For a more} quanti-

tative analysis ^of the evolution of the ring posi-

tion with time, ^we have used the experimental ^set-

up represented ^on Figure ^{4. The} scattering pattern

Figure ^{2: Photos of} the evolution of the scattered

ring ^{as a} function of ^the time. 30s separates ^each picture.

is video-taped ^{and different} spectra corresponding

to different times are digitalized. ^A computer

program allows ^us to obtain the profile ^{of the} ring I(k,t) ^{for each} picture. ^The position ^{of the ring}

is defined as the value km ^{of the intensity maxi-}

mum. Due to the nonlinear response ^of the video

camera no quantitative informations about the evolution of the intensity ^{can be obtained.} Figure

5 presents ^a typical ^{set of data. This} set-up ^is particularly efficient in obtaining ^{the evolution}

at the early stage. Indeed the possibility ^of quick (every ⁴⁰ ms) ^data acquisition ^and storage allowed us to look at the precise development ^of

the ring. Figure ^6a presents the evol ution of the

scattering just after the quench ^{for a thermal} quench ^{of 0.02 K. The first curve} corresponds ^to the profile I(k,0) ^{before the} quench. ^{We have}

verified that this profile ^{can be fit with the}

Ornstein-Zernike (0-Z) expression:

T

where E ^{is the} correlation length ^{of the con-} cent ration fluctuation at the temperature TO’ ^and io ^{is a constant. After the quench, a bump appears}

in the 0-Z profile. ^The intensity ^{of this} bump ^in-

creases with time. This bump corresponds ^{to a} very weak ring ^{which is obtained} by subtracting ^the background scattering. Figure ^6b represents ^the result of this subtraction I’(k,t) = I(k,t)* - I(k,0). ^{This figure} clearly shows that the posi-

tion of the maximum of the ring ^{doesn’t move as the} intensity increases. This result is in

agreement

with the 1 inear regime of Cahn’s theory; ^{it had}

never been observed in liquid mixtures of multi- component systems.

In order to analyze ^{the data in a contin-}

uous manner we have plotted ^the evolution of the

position ^{of the} ring ^{as a function of the time for}

different quench. ^In figure ^{7 we} plot ^{on a} log-log

scale the reduced position ^{of the} ring TV = k -e-V

as a function of the reduced time i

tE , ^where c

-

{TI-Tc)/Tc. T1 is the final temperature ^after

the quench and TC the critical temperature, k ^is

the position ^of cthe ring ^{and v is} the critical

exponent ^{of the} divergence ^{of the} correlation

length ^{in the one} phase domain (from Ref. 7 v =

0.53). ^From Figure 7, three ^different regimes ^can

be seen. Initially ^the position ^{of the} ring ^does

not move as the time and the intensity ^{of the} ring increases. Then, ^the position ^{of the} ring ^de-

creases linearly with time (on ^a log-log plot) ^with

two different slopes. ^{In each case the evolution}

of qm ^{as a function} of ^T may be represented ^{with a}

power law qm = ^a T with f> = ^{0 for} the first step

of the evolution, ,

1/3 ⁱⁿ the second step and ,

=

1 for the last step. Cross-over regions sepa- rates these three different regimes.

We have obtained the same type ^{of results} when we measured SD after stirring ^the sample ^{at a}

constant temperature. ^In this case, the spinodal decomposition appears ^more rapidly but the evolu- tion with the time is the same. Figure ^{8 repre-}

sents this evolution for the reduced position ^of

the ring q ^{as a} function of the reduced time T.

The main difference ^{with the} previous quench ^is

that only ^{the two} last time regimes (f>

^1/3 and,

=

1) ^{was observed.}

736

Figure ^{3: Photos of the direct} microscopic observation of the sample ^{after a} temperature quench. ^The scale is the

same for all the pictures, they ^are

taken at different times after the

quench.

Figure ^{4: Schematic} representation ^{of the} set-up

used to obtain the position ^{of the} ring and its evolution as a function of the time.

Figure ^{5: A} typical evolution of the ring profile

as a function of the time. The data

represent the evolution for a sample quenched ^{at 0.12K from} the critical point. The first profile corresponds ^to

a time of 60s after the quench, ^{the last}

one to 250s. All the axis are in

arbitrary ^units.

Figure ^{6: Evolution of the} profile ^{of the}

scattered light ^{at the} early-stage ^of

the decomposition. ^The temperature quench ^{is 0.02 K from} the critical point

and the profile ^is plotted every 5 ^s.

At t=0 the profile follows the Ornstein- Zernike law. Figure ^6a gives ^the profile directly ^observed I(k,t) ^and Figure ^6b represents the evolution of the profile I’(k,t) = I(k,t) - I(k,0)

where the "background" scattering ^was

subtracted.

Discussion

For spinodal decomposition, ^microemul-

sions follow qualitatively ^{the same} behavior than classical multicomponent ^{mixture. The} main differ- ence is that SD in microemulsions ^occurs more

slowly. ^The large ^value of Co ^{for the system}

studied (co

^{46 A) explains this} behavior. ^Indeed

the reduced time is proportional ^to o -. ^Conse-

quently, ^{a value} of Eo ^{ten times larger than for}

simple ^fluids corresponds Io ^an increase of the time scale by ^{a factor} 10 . In other words, ⁱⁿ microemulsions the diffusion coefficient is reduced

by ^{a factor 10. The} broadening ^{of the time scale}

has two consequences. The first one is to increase the region ^{where SD is} observable (lK ^{above the}

critical point instead of 10 mK as in binary fluids). ^The second consequence ^{is to} allow the observation of three regimes ^for SD, including ^the initial regime predicted by ^{Cahn. For the} long

time evolution, ^{we saw} that the spinodal ^structure

is observable at a macroscopic ^scale. Though ^this

738

Figure ^7: Variation of the reduced position ^{of the} ring q ^{as a function of the reduced}

time for ^a thermal quench. ^Three regimes ^{can be} evidenced ^{following the}

power law qm

T" _{where ,} ^is _equaled successively ^to 0., 1/3 ^{and 1} depending

on T.

Figure ^8: Variation of the reduced position ^{of the} ring qm ^{as a function of} the reduced time T. The sample ^{is at a} temperature above the critical temperature, ^{the SD} is prevented by stirring and appears when stopping ^the stirring.

evolution was less studied, the final (late) stages of the SD is probably controlled by the interfacial tension between the two phases ⁱⁿ equilibrium. ^The

very low value of the intpgfacial tension found in the microemulsions system ^{is one of the reasons}

why these extended structures are observable.

Conclusion

For the first time, spinodal decomposi-

tion has been observed in microemulsion or micellar systems. ^These systems ^{seem to be} very attractive for studying ^the decomposition process ^{at not} only

the early stages ^{but also for} the final stage ^of the decomposition.

Acknowledgment

The author has profited ^from stimulating

discussions with D. Beysens ^and acknowledges ^him

for his interest to this work. He acknowledges also S. A. Safran for a critical reading ^{of the} manuscript.

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