Length Dependence of Demixing and Micelle Formation in a Model for Tenside-Water Mixtures

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Length Dependence of Demixing and Micelle Formation in a Model for Tenside-Water Mixtures

D. Stauffer, D. Woermann

To cite this version:

D. Stauffer, D. Woermann. Length Dependence of Demixing and Micelle Formation in a Model for Tenside-Water Mixtures. Journal de Physique II, EDP Sciences, 1995, 5 (1), pp.1-3.

�10.1051/jp2:1995108�. �jpa-00248131�

J.

Phys.

II £Fance 5

(1995)

1-3 _JANUARY 1995, PAGE 1

Classification

Physics

Abstracts

05.50 68 10 82.35 82.65

Short Communication

Length Dependence of Demixing and Micelle Formation in

_a

Model for Tenside-Water Mixtures

D. Staul$er

(~)

and D. Woermann

(~)

(~)Institute

for Theoretical

Physics, Cologne University,

50923

K61n, Germany (~)Institute

for

Physical Chemistry, Cologne University,

50923

Kiln, Germany

(Received

24 November 1994,

accepted

25

November1994)

Abstract. Monte Carlo simulations of _a

Larson-type

model for

oil-water-amphiphile

_mix-

tures determine the characteristic micelle concentration CMC and the oil-water

phase separation

temperature Tc. These data agree

partially

with experimental data _{on aqueous} solutions of the

non-ionic tensides CH3

(CH2)1-1 (O

CH2 CH2

O)j

H

Microemulsions of

oil,

water and

amphiphiles

have been simulated

successfully

_on lattices with various

approximations

like the Widom model

iii.

Even _more realistic _are off-lattice molecular

dynamics

studies

[2j. Numerically

in between _are

Larson-type

models [3j ^where

amphiphilic self-avoiding

chains _are dissolved in _an

Ising

solvent _{on a} cubic lattice. These Monte Carlo simulations have shown [4j that the CMC

(characteristic

micelle

concentration) decays exponentially

with

increasing length

of the

hydrophobic

tail of the

amphiphilic

chains.

It _is the aim of this

study

to compare simulations with

experimentally

determined "critical"

micelle concentrations

(CMC)

and

phase separation,

_as a function of both head and tail size.

In

particular, experiments

with non-ionic tensides of the

type CH~ (CH2)~-i (O CH2 CH2 O)jH

dissolved in water reveal _a characteristic

dependence

of the

demixing temperature

_on the ratio

if

_j. That _means it is found

experimentally

that for

j

₌ 3 to 8 and ₁₌ 6 to

12,

the

demixing

temperature Tc

is

roughly

the _same for different _i and _j,

provided

the ratio of

i/j

is the _same.

We used the model of reference

[4],

^without a head-head

repulsion,

but with _a head

containing

more than _one site. Thus the whole

amphiphilic

chain _on the

simple

cubic lattice _consists of

j consecutive

hydrophilic

head

sites,

followed

by

_i

hydrophobic

tail sites. The

hydrophilic

monomers are

represented by Ising spins I,

the

hydrophobic

_ones

by Ising spins

-I. These

chains

reptate

like

slithering

snakes in the solvent

represented again by Ising spins

+I

(water)

and -I

(oil)

in

binary

mixtures without

oil,

all solvent sites _are +I. The interaction between nearest

neighbors

is taken into account in _an

(apart

front the chain

reptation)

standard Glauber

@

Les Editions de

Physique

1995

JOURNAL DE

PHYSIQUE

II N°1

ooi

CMC

~~'

_o k

D O

~

_

_~~

@Xp,C8Ej 001

Fig

I.

Comparison

of

theory

and experiment for

C,Ej

tensides dissolved in water at T

= 3 At

this CMC

m the simulations, half of the chains _are assembled in micelles, the other half isolated.

simulation at

temperature T, using

lattice sizes from

50~

_to

600~

_{and up to}

30,000 reptation attempts

_per chain.

The CMC is defined [4j here _as that volume concentration of

amphiphilic

chains at which half of the chains _are isolated and in

equilibrium

with the other half of the cha~ns assembled in

micelles,

I-e- in clusters of two _{or more}

adjacent

chains. The CMC is not _a "critical"

concentration in the _sense of _a

sharp phase

transition.

Figure

I shows the

experimental

_{[5] as} well _as the simulated CMC'S for tail sizes ₁

= 6 and

8,

for various head sizes j. We _see that the

slight

increase of the

experimental

CMC with

increasing

head

length

_j is very well

reproduced by

the simulation.

However,

the

exponential decay

of the CMC with

increasing

tail

length

I is

stronger

ⁱⁿ the

experiments

than in the

simulation.

(This discrepancy

also appears for ₁

=

12,

not shown in this

Fig.).

The

experimental

tenside solutions show _a lower critical

temperature,

_an effect not

explained by

the

present

^model.

Therefore,

instead _we simulated the oil-water

demixing temperature

_[6j

Tc

at _a fixed volume concentration often

percent polymer

chains.

Indeed,

_we found that for _a

fixed

if

_{j =} I the six critical temperatures for

j

= 2 _to 7 all _{were near} 4.0 + 0.2 in units of

J/kB,

where J is the

Ising

interaction energy. For

i/j

= 2 and _j

=

2, 3,

4 the transition

temperature

went down to 3.2 + 0.I. At _{i + j}

=

12,

it _was about

2.3, 2.7,

and

3.4, respectively,

for _{j =}

2,3,

and 5.

(Without amphiphilic chains, Tc

₌

4.51.)

The

experimental

critical temperatures, for

1 =

6, 8,10,12

and _j

=

3, 4, 5, 6,

8 follow

roughly

_a

straight

line

Tc

= 404

431/j

K and thus decrease about half _as fast with

increasing i/j

_as the simulated values. Thus the

computer

model follows

qualtitatively

but not

quantitatively

the

experimentally

observed trends _{as a}

function of head and tail size. This

dependence

_on

i/j only

has to be contrasted with the temperature ^{where the}

amphiphilic

chains

separate

out of the solvent for _i

=

I;

there the

demixing temperature

^increases

roughly linearly

_[7j with the cha~n

length

I _{+ j.}

N°i LENGTH DEPENDENCE OF DEMIXING AND MICELLE FORMATION 3

Acknowledgments

We thank

Graduiertenkolleg

^Scientific

Computing

for

partial _support.

References

(Ii Gompper G.,

Schick M,

Self-assembly

of

amphiphilic

systems, Phase Transitions and Critical Phenomena, C. Domb and J. L. Lebowitz

Eds.,

vol.16

(Academic Press,

New York,

1994).

[2] Karaborni S

,

Esselink K

,

Hilbers P A. J., Smit B., Karthauser J

, van Os N

M.,

Zana

R.,

Science 266

(1994)

254 with earlier literature of that group

[3] ^{Larson R}

G.,

J. Chem.

Phys.

96

(1992)

7904, with earlier literature of the author.

[4] Stauffer D., Jan N.,

Pandey

R. B.,

Marangoni

D.

G.,

Smith-Palmer

T,

J Chem.

Phys

100

(1994)

6934.

[5] Mitchell D. J,

Tiddy

G J. T.,

Waring L,

Bartock T., McDonald M.

P.,

J. Chem. Sac

Faraday

Trans. f 79

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975,

Schubert K V., Strey R., Kahlweit M., J. Colloid

Interface

So 141

(1991)

91 [6] Sahimi M., ^Nowroozi P.,

Phys.

Rev. Lent 73

(1994)

l182.

[7] ^Jan N, Staulfer D., J. Phys f France 4

(1994)

345;

for _a review _see

Boyden

S

,

Jan N

,

Ray T.,

preprint for Nuouo Cim.