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Fluorescence probing study of the effect of medium chain-length alcohols on the properties of tetradecyltrimethylammonium bromide aqueous micelles
CHEMICAL PHYSICS LETTERS
Volume 76, number 1
FLUORESCENCE
PROBING
ON THE PROPERTIES
P. LIANOS
OF THE EFFECT
OF MEDIUM
CHAIN-LENGTH
OF TETRADECYLTRIMETHYLAMMONHJM
BROMIDE
ALCOHOLS
AQUEOUS
MICELLES
and R. ZANA
Centre de Recherchcs
Recewed
STUDY
15 November 1980
ntr les Macron~ol&ules,
CNRS. 6 7083 Strasbourg, Cedtq
France
26 June 1980; IJI final form 19 August 1980
The tluorescence decay of mrcclle-mcorporated py rcne hns been used to dsrermme the m~celle aggegaaon number upon addltlon of butanol, pcntanol and hexanol. The changes of 11,of the monomer pyrens fluorescence MetIme, and the polanry of the probe mKrocn%onment
are discussed m terms of rhe alcohol solubihzanon
III the mwzllc
n
of
pabsnde
layer,whrch mcrcases the mIcelIe zonlzatlon degree.
1. Introduction
In the first part [l] of this senes studymg the effect of alcohol on the nucellar properties with the use of fluorescent probes, we investigated the formation of rmcelles of cetyltnmethylammonrum brormde (CTAB) in the presence of 1-butanol. Pyrene was used as fluorescent probe and the mam results were as follows: (1) part of the added butanol was adsorbed in the micelle pahsade layer, that is, m the layer contammg the polar heads of the aggregated surfactant molecules, (3) this adsorption (or solubdization) resulted in a large decrease of the surfactant aggregation number; (3) the environment of the micelle-solubdized pyrene became less polar as the alcohol &solved m the rrucelles; and (4) the composition of the mixed CTAB + I-butanol micelles was deternuned. In the present work we have largely extended the domain by studymg the effect of me&urn chamlength alcohols, 1-butanol, 1-pentanol and l-hexanol, on the properties of tetradecylrnmethylammonium brormde (TTAB) aqueous rrucelles with particular emphasis on the effect of the surfactant and alcohol concentrations on the surfactant awegahon number, on the fluorescence hfeme of the micelle-solubilized pyrene and on the effective polanty of the ennronment of the probe. As shown below, the results gve a good picture of the effect of alcohol on Ehe rmcellar structure, wluch 62
is consstent with a recently developed model [2]. Future extensions of this work \vlll apply to microemulsions wluch are thermodynarmcally stable, transparent, monophaslc systems generally obtamed by addmg od to the ternary system [3] H?O/surfactant + co-surfactant. Microemulnons are of conslderable practlcal importance, particularly m the process of tertiary od recovery.
2. Materials and methods All alcohols used were obtamed from Fluka (punssimum grade). Pyrene (Fluka, punssunum) was used without further purifkation while TTAD (Aldrich) was recrystalhzed three times from ethylacetate. The cntical rmcellar concentration (CIVIC)in the absence of alcohol was deternuned by conductivity to be 3.6 X 1O-3 M, m excellent agreement with reported values. The mtroduction of pyrene m the micelles was done as previously reported [ 11. The polarity sensitive vibronic structure of the monomer pyrene fluorescence spectrum was used to detect the adsorptlon of alcohol m the pabsade layer of the micelle. The ratio of the intensltles of the first over the third (f1/13) vibronic peak of the above spectrum
increases
with
the effective
polarity
of
the micro-
ennronment of the probe taking the lowest value in ahphailc hydrocarbon and among the highest m aque-
Volume
76, number
1
CHEhIlCAL
PHYSICS
15 November
LETTERS
1980
200 0
9I.I.I. 02
03
-
cfi(M/P) 06
0
004
Fg 1. Effect of alcohol on the fluorescence decay tune of monomer pyrene mcorporarcd at 10m5 hl mo 3YrAB mrccks
FI_~ 2. (a) Decrease of the surfactant
- X - butanol, -o- pentanol, and -cl- hekanol. Surfactant concentration 0.05 hI.
solution of
the pmsencc of rncreasm_e amounts
ITi\B
he%rnol. (b)
-X
-
aggregatton of alcohol
liutanol. -e-
Increase of 11 wth
CWI?) 1 . I 016 Q20
QO8 012
number
n III
III a 0.05 M
pcntanol; and -o-
mcreasing TTAB
concentm
tron for a mr_\turc water +0.1 hl pentanoL
tlon of alcohol (pentanol) was fixed at 0.2 ikl and the concentration was mcreased from 0.0 to 0.2 hi
TTAB
wrth mcreasing surfactant explained by the solubilrzatron of alcohol m the mrcellar palisade layer. We have calculated the average number tr,& of alcohol molecules per aggregated surfactant molecule in each mrcelle from the estimated partitton coefficient K of I-pentanol between the aqueous and the mrcekr phase accordmg to the following equation 12,151 vahd for farrly dilute solutrons: and its decay hme decreased
concentration.
(table 3). Thus IS eqmvalent to dissolving the surfactant m a new solvent (water + 0.2 bl pentanol mixture). The CMC for TTAB III ths nuxture is below 0.001 hi [2], thus nucelles were formed at ah hsted values of C. A monotonic mcrease of II was then observed wth increasmg C (fig. 2b and table 3, column 2). As seen in table 3 (cohnnn 6) this fact was not observed m the absence of alcohol where a relatrvely small increase of PI was observed only for C> 0.15 M. krspecnon of table 3 reveals an mterestmg feature. The effective polanty of the probe environment mcreased Table
agam
is
li’ = (CA- Cv/)/C\~(C+ CA =
chlk*
-
C&&C +
chI)
-
qfr) ,
3
TTAB concentratron W-l
Ratiolr/Is of the monomer pyre”2 fluorescence
Surfmzt~r aggregatton number, n
0.008
0.01 0.02 0.05 0.1 0.2 a) These values have been calculated depends
n&
on CA_ The equonon
IS
Decxr) rune of the free monomer pyrcne (ns)
Rat10 n*/n 4
-
n III the absence of alcohol
1.95
100
27
1.30
293
1.51
-
29 33 50 71 110
1.31 1.31 1.34 1.36 1.46
181 254 246 224 207
1.46 1.27 0.95 0.71 0.49
68 65 66 66 85
0.0
case
l3us
assummg
the part~tron coefiicrcnt
K = 13/(1 7 4.4
CA)
has
been proposed
K constant
and equal to 3.2 M-t.
--
In fact it is likely that K
[ 171 \rhxh > wlds K = 6.9 hl-' for CA = 0.1 XI.In thst
calculated to be lugher. particularly at low surfactant concentratrons, and to decrease upon mcreasmgC from 8.8
to 0.7. These numerical
changes
do not affect
the dtscusnon
grren m the text.
65
where chl and cw are the concentrations of miceUe and water solubtied alcohol in mole per liter of solution. The results for the water + 0.3 M pentanol rnncture are shown in table 3 (column 5; K was taken equal to 3.2 M-l [2]). It is seen then that nA/n, that is the average number of alcohol molecules around each surfactant molecule, decreases ~th increasmg C. Thisin turn, mcreasesthe amount of water in the
micelle palisade layer and therefore its dielectnc constant and the average number of bound bromide ions [2]. Thus on the one hand the effective polarity mcreases and on the other the increased encounters with Br- result m decreased 7. At low C the values of II&Z are so high that the micelIes can be considered as saturated with alcohol. For this reason II/I3 changes only slightly for C < 0.1 M, even though n&z decreases substantially in this range, but increases more rapidly at h&er surfactant concentration (table 3, column 3). This initial slow increase of the effective polarity rmght give the unpression that the bulk phase rather rhan the mice&u
surface
dete -es
it.
How-
ever, as seen from table 3, I J13 for pyrene lssolved in the water + 0.2 M pentanol nuxture, in the absence of TTAB, IS much higher (1.95) than any of the observed values m the presence of micelles. Increase of II/13 and decrease of 7 with increasing C for a pven alcohol concentration was also observed with butanol and hexanol as can be seen from table 2. The decrease of n upon mcreasmg CA at low surfactant concentration and the near constancy or mcrease of pzwith CA at C> 0.1 M, for the TT&lpentanol and TTAB-I-hexanol systems, can be now explamed as follows. At low surfactant concentration the repulsions between micelles are weak as the mter-
micellar lstance is large. In the presence of a large excess of alcohol, the average number of micellesolu@lized alcohol molecules per micelhzed surfactant molecule nA/n is large. This results m a large mcrease of the Ionization degree p which breaks down the origmal micelles into smaller ones [2]. The imtially weak repulsions between miceUes do not hinder this process much. At high surfactant concentration, the repulsions between miceUes are strong. In the expenmental contitsons of this work the alcohol is no longer m excess and nA/n is much smaller. Neverthe-
less the solubtiation of alcohol into the miceUes results in an increase of p, although smaller than at low C. and therefore the electrostatic repulsions between
66
15 November 1980
CHEhlICAL PHYSICS LETTERS
Volume 76, number 1
micelles become even stronger. Micelles then have to grow by partial mergmg in order to mcrease the intermicellar &stance, and thus reduce their mutual repulsions. The effects just discussed will be the more pronounced the longer the alcohol chain length, as the alcohol partition coefficient between micelies and the aqueous phase mcreases by a factor of 3 per additional methylene‘group As mentioned
121.
above, increase of the surfactant aggregatlon number with mcreasmg C was not observed m the absence of alcohol at moderate surfactant concentrations (table 3, column 6) contrary to what was observed in the presence of alcohol. n is m fact determined by the difference &! - & between the standard chemical potentials of the surfactant in the aqueous and nucellar phase, respectively [ 161. in pure water thus lfference depends only slightly on the surfactant concentration. In the presence of alcohol, however, which ptitions between aqueous and the micellar phase in a manner depending on both micellar
and alcohol
concentrations
and alcohol
chain
length, the alcohol mole fraction in the micelles is large and & is changed, which m turn results in changes of TV.
Acknowledgement The authors are extremely grateful to Professor G. Laustriat (FacultC de Pharmacie, Laboratoire de Phynque, Strasbourg) for making available his facilities for all measurements of the present work.
References t11 P. Llanos and R. Zana, Chen Phys. Letters 72 (1980) 171.
[21 R. Zana, S. YN,C. Strazlelle and P. Llanos, J. Collold Interface Sci., to be pubhshed.
t31 K.L. Mittal, ed., hkellization, solubtiatlon and microemulsions, Vols. 1 and 2 (Plenum Press, New York, 1977). 141 P. Lianos and S. Ceorghiou, Photochem. PhotobioL 30 (1979) 355.
r51 K. Kalyanasundaram and J.K. Thomas, J. Am. Chem sot. 99 (1977) 2039.
[61 K_ Kal>ans.undaram, J.K.
Chsm.
Sot
Rev. 7 (1978) 453;
Thomas, Accounts Chem. Res. 10 (1977) 133.
Volume 76, number
1
CHEMICAL PHYSICS LETTERS
[ 71 S. Atrk, hl. Nam and L.A. Smger, Chem. Phys. Letters 67 (1979) 75. [8] PP. Infelta and M. GrZtzel, J. Chem. Phys. 70 (1979) 179. [9] J.B. Brrks, Photophysrcs of aromatrc molecules (WdeyInterscrence, New York, 1970). [lo] R. McNeil and J.K. Thomas, J. Colloid Interface Sci. 73 (1980) 522. [ 1 l] P. Lurnos, AK hInkhopadyay and S. Georghrou, Photothem [
Photobml,
to
be
pubbshed.
121 P. Lianos and S. Georgh~ou, Photochrm. PhotobloL 29
(1979) 843. [13] P. Lianos, B. Luu and D. Gerard, 3. Chrm. Phys., to be pubhshed.
15 November
1980
1141 E. Vtkmgstad and 0. Kvammen, J. Collotd Interface Sci 74 (1979) 16, J. Larsen and L. Teplcy, J. ColIoid Interface Sci. 49 (1974) 113. J. Rassing and E. Wyn ]lSl J. Gettmps, D. HaB. P. Job@. Jones, J. Chem. Sot. Faraday Trans. II 74 (1978) 1957. tl6] C.Tanford, J. Phys. Chem. 78 (1974) 2*9; J. Israelachvrli, D. MttcheU and 8. Ninham. J. Chem. Sot. Faraday Trans. II 72 (1976) 1525; E. Ruckenstein and R. NCI~ZU~J~, J. Phyr Chem 79 (1975) 2622. J_ CoUoid [I71 S. Yrv, R. Zana, 1X”. Ulbncht and H. Hoffmnann, Interface SIX, to be published.
67
Volume 76, number 1
FLUORESCENCE
PROBING
ON THE PROPERTIES
P. LIANOS
OF THE EFFECT
OF MEDIUM
CHAIN-LENGTH
OF TETRADECYLTRIMETHYLAMMONHJM
BROMIDE
ALCOHOLS
AQUEOUS
MICELLES
and R. ZANA
Centre de Recherchcs
Recewed
STUDY
15 November 1980
ntr les Macron~ol&ules,
CNRS. 6 7083 Strasbourg, Cedtq
France
26 June 1980; IJI final form 19 August 1980
The tluorescence decay of mrcclle-mcorporated py rcne hns been used to dsrermme the m~celle aggegaaon number upon addltlon of butanol, pcntanol and hexanol. The changes of 11,of the monomer pyrens fluorescence MetIme, and the polanry of the probe mKrocn%onment
are discussed m terms of rhe alcohol solubihzanon
III the mwzllc
n
of
pabsnde
layer,whrch mcrcases the mIcelIe zonlzatlon degree.
1. Introduction
In the first part [l] of this senes studymg the effect of alcohol on the nucellar properties with the use of fluorescent probes, we investigated the formation of rmcelles of cetyltnmethylammonrum brormde (CTAB) in the presence of 1-butanol. Pyrene was used as fluorescent probe and the mam results were as follows: (1) part of the added butanol was adsorbed in the micelle pahsade layer, that is, m the layer contammg the polar heads of the aggregated surfactant molecules, (3) this adsorption (or solubdization) resulted in a large decrease of the surfactant aggregation number; (3) the environment of the micelle-solubdized pyrene became less polar as the alcohol &solved m the rrucelles; and (4) the composition of the mixed CTAB + I-butanol micelles was deternuned. In the present work we have largely extended the domain by studymg the effect of me&urn chamlength alcohols, 1-butanol, 1-pentanol and l-hexanol, on the properties of tetradecylrnmethylammonium brormde (TTAB) aqueous rrucelles with particular emphasis on the effect of the surfactant and alcohol concentrations on the surfactant awegahon number, on the fluorescence hfeme of the micelle-solubilized pyrene and on the effective polanty of the ennronment of the probe. As shown below, the results gve a good picture of the effect of alcohol on Ehe rmcellar structure, wluch 62
is consstent with a recently developed model [2]. Future extensions of this work \vlll apply to microemulsions wluch are thermodynarmcally stable, transparent, monophaslc systems generally obtamed by addmg od to the ternary system [3] H?O/surfactant + co-surfactant. Microemulnons are of conslderable practlcal importance, particularly m the process of tertiary od recovery.
2. Materials and methods All alcohols used were obtamed from Fluka (punssimum grade). Pyrene (Fluka, punssunum) was used without further purifkation while TTAD (Aldrich) was recrystalhzed three times from ethylacetate. The cntical rmcellar concentration (CIVIC)in the absence of alcohol was deternuned by conductivity to be 3.6 X 1O-3 M, m excellent agreement with reported values. The mtroduction of pyrene m the micelles was done as previously reported [ 11. The polarity sensitive vibronic structure of the monomer pyrene fluorescence spectrum was used to detect the adsorptlon of alcohol m the pabsade layer of the micelle. The ratio of the intensltles of the first over the third (f1/13) vibronic peak of the above spectrum
increases
with
the effective
polarity
of
the micro-
ennronment of the probe taking the lowest value in ahphailc hydrocarbon and among the highest m aque-
Volume
76, number
1
CHEhIlCAL
PHYSICS
15 November
LETTERS
1980
200 0
9I.I.I. 02
03
-
cfi(M/P) 06
0
004
Fg 1. Effect of alcohol on the fluorescence decay tune of monomer pyrene mcorporarcd at 10m5 hl mo 3YrAB mrccks
FI_~ 2. (a) Decrease of the surfactant
- X - butanol, -o- pentanol, and -cl- hekanol. Surfactant concentration 0.05 hI.
solution of
the pmsencc of rncreasm_e amounts
ITi\B
he%rnol. (b)
-X
-
aggregatton of alcohol
liutanol. -e-
Increase of 11 wth
CWI?) 1 . I 016 Q20
QO8 012
number
n III
III a 0.05 M
pcntanol; and -o-
mcreasing TTAB
concentm
tron for a mr_\turc water +0.1 hl pentanoL
tlon of alcohol (pentanol) was fixed at 0.2 ikl and the concentration was mcreased from 0.0 to 0.2 hi
TTAB
wrth mcreasing surfactant explained by the solubilrzatron of alcohol m the mrcellar palisade layer. We have calculated the average number tr,& of alcohol molecules per aggregated surfactant molecule in each mrcelle from the estimated partitton coefficient K of I-pentanol between the aqueous and the mrcekr phase accordmg to the following equation 12,151 vahd for farrly dilute solutrons: and its decay hme decreased
concentration.
(table 3). Thus IS eqmvalent to dissolving the surfactant m a new solvent (water + 0.2 bl pentanol mixture). The CMC for TTAB III ths nuxture is below 0.001 hi [2], thus nucelles were formed at ah hsted values of C. A monotonic mcrease of II was then observed wth increasmg C (fig. 2b and table 3, column 2). As seen in table 3 (cohnnn 6) this fact was not observed m the absence of alcohol where a relatrvely small increase of PI was observed only for C> 0.15 M. krspecnon of table 3 reveals an mterestmg feature. The effective polanty of the probe environment mcreased Table
agam
is
li’ = (CA- Cv/)/C\~(C+ CA =
chlk*
-
C&&C +
chI)
-
qfr) ,
3
TTAB concentratron W-l
Ratiolr/Is of the monomer pyre”2 fluorescence
Surfmzt~r aggregatton number, n
0.008
0.01 0.02 0.05 0.1 0.2 a) These values have been calculated depends
n&
on CA_ The equonon
IS
Decxr) rune of the free monomer pyrcne (ns)
Rat10 n*/n 4
-
n III the absence of alcohol
1.95
100
27
1.30
293
1.51
-
29 33 50 71 110
1.31 1.31 1.34 1.36 1.46
181 254 246 224 207
1.46 1.27 0.95 0.71 0.49
68 65 66 66 85
0.0
case
l3us
assummg
the part~tron coefiicrcnt
K = 13/(1 7 4.4
CA)
has
been proposed
K constant
and equal to 3.2 M-t.
--
In fact it is likely that K
[ 171 \rhxh > wlds K = 6.9 hl-' for CA = 0.1 XI.In thst
calculated to be lugher. particularly at low surfactant concentratrons, and to decrease upon mcreasmgC from 8.8
to 0.7. These numerical
changes
do not affect
the dtscusnon
grren m the text.
65
where chl and cw are the concentrations of miceUe and water solubtied alcohol in mole per liter of solution. The results for the water + 0.3 M pentanol rnncture are shown in table 3 (column 5; K was taken equal to 3.2 M-l [2]). It is seen then that nA/n, that is the average number of alcohol molecules around each surfactant molecule, decreases ~th increasmg C. Thisin turn, mcreasesthe amount of water in the
micelle palisade layer and therefore its dielectnc constant and the average number of bound bromide ions [2]. Thus on the one hand the effective polarity mcreases and on the other the increased encounters with Br- result m decreased 7. At low C the values of II&Z are so high that the micelIes can be considered as saturated with alcohol. For this reason II/I3 changes only slightly for C < 0.1 M, even though n&z decreases substantially in this range, but increases more rapidly at h&er surfactant concentration (table 3, column 3). This initial slow increase of the effective polarity rmght give the unpression that the bulk phase rather rhan the mice&u
surface
dete -es
it.
How-
ever, as seen from table 3, I J13 for pyrene lssolved in the water + 0.2 M pentanol nuxture, in the absence of TTAB, IS much higher (1.95) than any of the observed values m the presence of micelles. Increase of II/13 and decrease of 7 with increasing C for a pven alcohol concentration was also observed with butanol and hexanol as can be seen from table 2. The decrease of n upon mcreasmg CA at low surfactant concentration and the near constancy or mcrease of pzwith CA at C> 0.1 M, for the TT&lpentanol and TTAB-I-hexanol systems, can be now explamed as follows. At low surfactant concentration the repulsions between micelles are weak as the mter-
micellar lstance is large. In the presence of a large excess of alcohol, the average number of micellesolu@lized alcohol molecules per micelhzed surfactant molecule nA/n is large. This results m a large mcrease of the Ionization degree p which breaks down the origmal micelles into smaller ones [2]. The imtially weak repulsions between miceUes do not hinder this process much. At high surfactant concentration, the repulsions between miceUes are strong. In the expenmental contitsons of this work the alcohol is no longer m excess and nA/n is much smaller. Neverthe-
less the solubtiation of alcohol into the miceUes results in an increase of p, although smaller than at low C. and therefore the electrostatic repulsions between
66
15 November 1980
CHEhlICAL PHYSICS LETTERS
Volume 76, number 1
micelles become even stronger. Micelles then have to grow by partial mergmg in order to mcrease the intermicellar &stance, and thus reduce their mutual repulsions. The effects just discussed will be the more pronounced the longer the alcohol chain length, as the alcohol partition coefficient between micelies and the aqueous phase mcreases by a factor of 3 per additional methylene‘group As mentioned
121.
above, increase of the surfactant aggregatlon number with mcreasmg C was not observed m the absence of alcohol at moderate surfactant concentrations (table 3, column 6) contrary to what was observed in the presence of alcohol. n is m fact determined by the difference &! - & between the standard chemical potentials of the surfactant in the aqueous and nucellar phase, respectively [ 161. in pure water thus lfference depends only slightly on the surfactant concentration. In the presence of alcohol, however, which ptitions between aqueous and the micellar phase in a manner depending on both micellar
and alcohol
concentrations
and alcohol
chain
length, the alcohol mole fraction in the micelles is large and & is changed, which m turn results in changes of TV.
Acknowledgement The authors are extremely grateful to Professor G. Laustriat (FacultC de Pharmacie, Laboratoire de Phynque, Strasbourg) for making available his facilities for all measurements of the present work.
References t11 P. Llanos and R. Zana, Chen Phys. Letters 72 (1980) 171.
[21 R. Zana, S. YN,C. Strazlelle and P. Llanos, J. Collold Interface Sci., to be pubhshed.
t31 K.L. Mittal, ed., hkellization, solubtiatlon and microemulsions, Vols. 1 and 2 (Plenum Press, New York, 1977). 141 P. Lianos and S. Ceorghiou, Photochem. PhotobioL 30 (1979) 355.
r51 K. Kalyanasundaram and J.K. Thomas, J. Am. Chem sot. 99 (1977) 2039.
[61 K_ Kal>ans.undaram, J.K.
Chsm.
Sot
Rev. 7 (1978) 453;
Thomas, Accounts Chem. Res. 10 (1977) 133.
Volume 76, number
1
CHEMICAL PHYSICS LETTERS
[ 71 S. Atrk, hl. Nam and L.A. Smger, Chem. Phys. Letters 67 (1979) 75. [8] PP. Infelta and M. GrZtzel, J. Chem. Phys. 70 (1979) 179. [9] J.B. Brrks, Photophysrcs of aromatrc molecules (WdeyInterscrence, New York, 1970). [lo] R. McNeil and J.K. Thomas, J. Colloid Interface Sci. 73 (1980) 522. [ 1 l] P. Lurnos, AK hInkhopadyay and S. Georghrou, Photothem [
Photobml,
to
be
pubbshed.
121 P. Lianos and S. Georgh~ou, Photochrm. PhotobloL 29
(1979) 843. [13] P. Lianos, B. Luu and D. Gerard, 3. Chrm. Phys., to be pubhshed.
15 November
1980
1141 E. Vtkmgstad and 0. Kvammen, J. Collotd Interface Sci 74 (1979) 16, J. Larsen and L. Teplcy, J. ColIoid Interface Sci. 49 (1974) 113. J. Rassing and E. Wyn ]lSl J. Gettmps, D. HaB. P. Job@. Jones, J. Chem. Sot. Faraday Trans. II 74 (1978) 1957. tl6] C.Tanford, J. Phys. Chem. 78 (1974) 2*9; J. Israelachvrli, D. MttcheU and 8. Ninham. J. Chem. Sot. Faraday Trans. II 72 (1976) 1525; E. Ruckenstein and R. NCI~ZU~J~, J. Phyr Chem 79 (1975) 2622. J_ CoUoid [I71 S. Yrv, R. Zana, 1X”. Ulbncht and H. Hoffmnann, Interface SIX, to be published.
67