Critical composition in organized surfactant solutions

C&ids and Surfaces A: Physicochemical and Engineering Aspects, 79 (1993) 15 1- 155 Elsevier Science Publishers B.V., Amsterdam

Critical composition

151

in organized surfactant

solutions

Kozo Shinoda, Nobuyoshi Yamaguchi and Masakatsu Usui Department of Physical Yokohama 240, Japan

Chemistry,

(Received 27 May 1992; accepted

Faculty of Engineering,

24 September

Yokohama

National University, Tokiwadai,

1992)

Abstract Micellar organized solutions are systems in which the size of the solvent molecule and the organized aggregate are widely different. The solubility of the small water molecules in the surfactant phase is large while the solubility of the large surfactant micellar aggregates in water is very small. There is in aqueous non-ionic surfactant systems a good correlation between the experimental critical compositions and the values estimated from the aggregation number of the micelles close to the respective critical temperatures. The critical compositions of some non-ionic surfactants in the aqueous solutions in weight fractions are: R,(OCH,CH,),OH, 0.117; R,(OCH,CH,),OH, 0.071; R,,(OCH,CH2),0H, 0.012; R,2(OCH2CH2)60H, 0.020; R,,(OCH,CH,),OH, 0.0087; R,,(OCH,CH,),OH, 0.0049. Thus, the surfactant phase has the capability to incorporate large amounts of water. Furthermore, there is a linear decrease in the plot of the logarithm of the critical compositions vs the hydrocarbon chain length of the surfactants. This characteristic property of an organized solution, i.e. a marked asymmetry in the critical composition, is explained by the large aggregation number for the micelles close to the lower critical consolute temperature, and decreases geometrically with the increase of hydrocarbon chain length of the surfactants. At the lower critical consolute temperature the aggregation number of the micelles increases geometrically with the hydrocarbon chain length. The upper critical solution temperature in R,,(CH,CH&OH-H,O is 300°C and the critical composition is about 0.37 wt%. The system is now no longer a typical organized solution and the aggregation number is about 3. Keywords: Critical composition; non-ionic surfactant.

hexaoxyethylene

hexadecyl

ether; hexaoxyethylene

Introduction A micellar

solution

is a self-organized

liquid-liq-

uid mixture of small solvent molecules and large micellar aggregates. Marked deviations in the critical composition in an organized solution have been pointed out in previous work [ 1,2]. In order to elucidate the deviations in the critical compositions in micellar solutions, the critical compositions of long hydrocarbon chain surfactants were carefully determined. The characteristic properties of an organized solution are exemplified by the

tetradecyl

ether; liquiddhquid

solubility

curve;

H,0PC16H,,(OCH,CH2),0H solution system. In this system the critical composition is below 0.5 wt%, that is the solubility of water in the hexaoxyethylene hexadecyl ether phase was 99.5 wt%. The entropy of mixing of small molecules and large organized particles is estimated, and the critical composition is calculated from the entropy and the enthalpy of mixing so as to compare them with the experimental values. Experimental Materials

Correspondence to: K. Shinoda, Dept. of Physical Chemistry, Faculty of Engineering, Yokohama National University, Tokiwadai, Yokohama 240, Japan. 0927-7757/93/$06.00

0

1993 -

Elsevier Science Publishers

Diethylene glycol monohexyl ether, tetraethylene glycol monooctyl ether, pentaethylene glycol B.V. All rights reserved

K. Shinoda et al./Colloids

152

A: Physicochem.

Eng. Aspects 79 (1993)

50

C~HI~(OCHZCH~)~OH

appeared to contain (diether), because the

surface tension vs the concentration ous solution showed a minimum.

Ca Hir(OCH2CHd+OH I~H~~(OCH&H~ISOH

curve in aqueThe compound

was purified by repeated solvent (cyclohexane) extraction at the three-phase region, i.e. the HLB temperature [3]. At this temperature most surfactant was in the surfactant phase and an oleophilic impurity, such as the diether, was preferentially dissolved in the oil phase.

1.5-15.5

60

monododecyl ether, hexaethylene glycol monododecyl ether, hexaethylene glycol monotetradecyl ether and hexaethylene glycol monohexadecyl ether were obtained from Nikko Chemicals Co. Ltd. C1,H,,(OCH2CH2),0H a small amount of impurity

Surfaces

40

G 0 F 30

C,0H22(OCH2CH2)40H

3 z ti E I-” 20

Procedures

Liquid-liquid solubility curves, i.e. cloud point curves were determined by observing the phase equilibria in a series of ampoules containing systems with slightly different compositions. The temperature was controlled to 0.002”C.

01

0

Hz0

Results Liquid-liquid solubility curves of water vs -(OCH,CH,),OH are shown in Fig. 1. GHz.+ I The arrows indicate the critical compositions. Data for RIO(OCH,CH,),OH given by Lang and Morgan [4] and for R,(OCH,CH,),OH and R14(0CH,CH2),0H given by Corti et al. [S] are included. The cloud point curves are flat at the critical compositions particularly for short-chain surfactants. Therefore the critical compositions were determined by observing the change in phase volumes for the aqueous and surfactant phases with temperature for a series of ampoules containing systems with slightly different compositions. At temperatures above the solubility curve a surfactant phase separates from the aqueous solution below the critical composition, whereas above the critical composition a water phase separates from the surfactant phase, and the water phase occupies a large volume fraction of the system.

t

I

02

weight

I

fraction

I

04

I

Surfactant

5

Fig. I. Liquid-liquid solubility curves in aqueous non-ionic surfactants close to the lower critical solution temperature. The arrows indicate the critical compositions.

The critical compositions steadily decrease with the hydrocarbon chain length of non-ionic surfactants as shown in Fig. 2. When the critical composition lies below 1 wt% for long-chain surfactants more than 13 carbon atoms, a water phase separation from a surfactant phase above the cloud point curve is usually observed. Since the densities of water and surfactant phases are very close in balanced R,EO,OHtype surfactant solutions (EO represents the ethylene oxide group -OCH,CH,-), the volume fraction is very close to the weight fraction. Discussion Small water molecules and large solvated surfactant aggregates mix randomly in micellar solution. At the critical point the interfacial tension between

K. Shinoda et al./Colloids Surfaces A: Physicochem. Eng. Aspects 79 (1993) I

3, \

\\

‘P \

\\

\\

\\ 0

I

I

I

\

’

’ P

\

0

‘\

mixing may be close to that of the surface areas of the solvated micelle and the solvent molecule. Therefore, the solubility of a micellar aggregate is far smaller than that of the solvent in the solution and the critical composition is thus markedly deviated

toward

position

will deviate

the solvent

axis. The critical com-

further

to the solvent

axis

with an increase in the aggregation number of the micelle, i.e. the micelle surface area. This is a qualitative argument for the location of the critical composition in micellar solutions of long hydro-

0 \

153

151-155

\

01

carbon

\ \

chain non-ionic

surfactants.

\

Entropy of mixing in organized

!

I

6

8

hydrocarbon

chain

I

1

I

IO

12 length

I4 of

I

16

18

RiOCHI)HJ,OH

Fig. 2. The change of critical compositions of pure polyoxyethylene alkyl ethers as a function of the hydrocarbon chain length. Non-ionic surfactants whose micellar shape is oblate or lamellar were studied.

the water and the surfactant phases is zero. Above the cloud point the interfacial tension is slightly positive [l], while below the lower critical solution temperature the extrapolated interfacial tension between the water and the surfactant phases is slightly negative. The reason for this is the linear decrease in interfacial tension with temperature close to the critical temperature [l]. (see Fig. 3 in Ref. 1.) Below the lower critical solution temperature the interface thus increases and the aggregation number of the surfactant phase changes from being infinite to being finite. At the critical temperature the interfacial energy of mixing of solvent molecules with the organized aggregate will be about kT/2. Since the micellar surface is very large compared with the molecular surface of the solvent, the energy of mixing per solvated micellar aggregate is much larger than that of a solvent molecule. Roughly speaking, the ratio of the energies of

micellar solution

Since the aggregated molecules are not chemically bound and the micelle is in the liquid state, the amphiphile molecules exchange within the micelle. The free volume of an aggregated particle v,~ may be considered to be proportional to the aggregation number N, i.e. v,,,~= NV,, just as the free volume of a liquid is proportional to the number of molecules. The total free volume of the solvent is N,v,,; after mixing with the micelles it will be N,v,, + N,v,~, where N, is the number of solvent molecules and N, is the number of micellar aggregates, because all amphiphile aggregates are in contact with solvent. The free volume available to the amphiphiles changes from N,v,, to N,v,, + N,v,, (where N, = N,N). The entropy of mixing of a micellar solution is then given as ASmix= -kink

lnCN,v,,l(N,v,,+N,v,,)I

+ N, lnCNm%fIW1vlf + Nmvmf)l} (1) ASmix = - k{N, lnCN1vldN1vlf + N,Nvx)l + N, lnCN,NMN1vlf+ N,Nvx)I} (2) Since the micellar surface, particulary in a lamellar micelle, is proportional to the aggregation number, we may say that the free volume of the micelle is proportional to the surface area of the micelle. This means that the entropy and the energy of mixing are functions of the surface fraction

K. Shinoda et al./Colloids

154

rather than the volume fraction. Actually, as the micelle surface is covered with hydrophilic groups, the use of surface fraction seems more appropriate than the use of volume fraction. The partial

molal entropy

8, + 0,(1 - Nv2r/vlf)]

where

8, are the surface

solvent and the micelles, gas constant. Critical composition

fractions

respectively,

and R is the

in organized micellar solutions

= A,@B

(4)

where A, is the micellar area and B’ is the enthalpy of mixing per unit area. The partial molal Gibbs free energy of organized particles is obtained from Eqns (3) and (4) just like the partial molal free energy, entropy and enthalpy in polymer solution. AG,/RT=ln

a,=ln

that

8, + 8,(1 -NV&,,)

(5)

+ A,tIfB’/RT, where a, is the micelle activity, T is the absolute temperature and T, is the critical temperature. Differentiating Eqn (5) with the surface fraction twice, at the critical point

of the surfactant.

= l/&l - (1 - Nv,rlv,,) -2A,%,B’IRT,=O

(6)

(d In a~/8~),,,

= -1/d;t,+2A,B’/RT,=O

(7)

+N”*(v*/v,)“*]~~~,~w,,

emc

=

=

where O,, is the surface

fraction

of component

(10)

are very close, so that the volume fractions 4, are very close to the weight fractions w,. Based on the lattice model, Kjellander [6] derived formally a similar relationship from the revised Flory-Huggins entropy. While the phenomena in the critical region are too complex to be accounted for by a simple equation, the trend in the changes of the critical compositions derived from the aggregation numbers agreed reasonably well with the experimental values as shown in Table 1 [7-91. The critical composition is a function of the free volumes (entropic contribution) and the surfaces (enthalpic contribution) of two mixing species. The aggregation of the non-ionic surfactants we have studied may be lamellar or oblate spheroidal close to the respective cloud points [lo]. The agreement is good, but that may be fortuitous considering the assumptions in the theory and the experimental errors. However, it is clear that the critical composition is markedly deviated toward the solvent axis in organized solution and that it furthermore with

the increase

chain length of the surfactant, size of the organized particles.

in the hydrocarbon i.e. the increasing

on the critical composition

(9) 1

H,O-R,,,(OCH,CH,),OH system is due to the enhanced solubility of water in the surfactant

(8)

l/Cl + N”*(v*r/vir)“*]

If v2r/rlf =

The upper critical solution temperature (UCST) in the H,O-R,,(CH,CH,O),OH system Lang and Morgan [4] carefully studied the phase diagram of some non-ionic surfactants. The lower critical solution temperature (LCST) in the

Eqn (7) in Eqn (6) N1’*(v2flVlfP2

in

be much

In the case of balanced R,EO,OH-type surfactants the densities of the water and surfactant phases

The effect of temperature

Q&nc

force

may

v,/Vi

decreases

(8 ln a,/%Jr,P

Introducing

of water

of the

Since solvent molecules and aggregated particles randomly mix, and the enthalpy of mixing of organized particles with the solvent is proportional to the square of Q1 (the surface fraction of the solvent), the partial molal enthalpy of mixing of the micelle is AH,

than

151-155

and 8,, is the surface fraction

the free volume

f&,=l/[l 8, and

point

Eng. Aspects 79 (1993)

of the micelles at the critical point. Due to the stronger intermolecular smaller

(3)

A: Physicochem.

at the critical

water,

of a micelle is

AS, = - R[ln

Surfaces

K. Shinoda et al./Colloids TABLE

Surfaces

A: Physicochem.

Eng. Aspects 79 (1993)

151-155

155

1

Comparison

of critical

Surfactant

compositions

with those calculated

Critical temp.

from the aggregation

Critical composition ( wt%)

(“C)

number

Calculated critical composition

close to the respective Aggregation number

critical

temperature Ref.

( wt%)

R,EO,OH R,EO,OH

9 44

11.7 13

This work

R,EO,OH R,EO,OH R,EO,OH

40 39 68

I 7.1

c71 This work

R,,EO,OH R,,EO,OH R,,EO,OH R,,EO,OH

20.5 300” 44 61

2.1 37” 2.3

R,,EO,OH R,,EO,OH R,,EO,OH

28 51 48

1.2 2.0

R,,EO,OH R,,EO,OH R,,EO,OH

43 42 57.5

0.87

R,,EO,OH R,,EO,OH

37.1 35

0.49

6.5b

compositions

181 c41 M

1330 (50°C)

PI 181 This work This work

1.6b

4400 (45°C)

c91 This work

0.92b

11700 (40°C)

181 c51

1.5

This work 16600 (34°C)

0.77b

were calculated

181

and compositions. with the aid of Eqn (10).

phase. It is caused by the progressive iceberg formation of water molecules surrounding the ethylene oxide chains and the hydrocarbon chains at low temperature [l 11. The aggregation number of a micelle is large at the LCST and the critical composition (weight fraction 0.022) is markedly deviated towards the water axis. By contrast, at the UCST, 570 K (about 3OO”C), which is nearly twice the room temperature, the self organizing tendency will be only a half number consequently much critical composition is about gation number estimated by

210 (60°C)

2.7b

aUpper critical solution temperature b Critical

[51

and the aggregation smaller. Actually, the 0.37 wt%. The aggreEqn (10) is 3.

1 2 3 4 5 6 7 8 9 10

Acknowledgements 11

Financial support from the Japan Society for the Promotion of Science is acknowledged. Discussions and linguistic revision by Docent K. Fontell are gratefully acknowledged.

K. Shinoda, J. Phys. Chem., 89 (1985) 2429. K. Shinoda, Langmuir, 7 (1991) 2877. K. Shinoda and S. Friberg. Emulsions and Solubilization, John Wiley, New York 1986, Chapter 1. J.C. Lang and R.D. Morgan, J. Chem. Phys., 73 (1980) 5849. M. Corti, C. Miner0 and V. Degiorgio, J. Phys. Chem., 88 (1984) 309. R. Kjellander, J. Chem. Sot., Faraday Trans. 2, 78 (1982) 2025. M. Corti, V. Degiorgio and M. Zulauf, Phys. Rev. Lett., 48 (1982) 1617. R.R. Balmbra, J.S. Clunie, J.M. Corkill and J.F. Goodman, Trans. Faraday Sot., 60 (1964) 979. R.R. Balmbra, J.S. Clunie, J.M. Corkill and J.F. Goodman, Trans. Faraday Sot., 58 (1962) 1661. D.J. Mitchell, G.J.T. Tiddy, L. Waring, T. Bostock and M.P. McDonald, J. Chem. Sot., Faraday Trans. 1, 79 (1983) 975. K. Shinoda, Adv. Colloid Interface Sci., 41 (1992) 81.