J. Chern. Soc., Furuduy Trans. I, 1988, 84(1), 151-163 Temperature Dependence of Adiabatic Compressibility of Aqueous Solutions of Alkyltrimethylammonium Bromides Ryszard Zielinski'f and Shoichi Ikeda" Department of Chemistry, Faculty of Science, Nagoya University, Nagoya 464, Japan Hiroyasu Nomura and Shigeo Kato Department of Chemical Engineering, School of Engineering, Nagoya University, Nagoya 464, Japan The adiabatic compressibility of aqueous solutions of octyl-, decyl-, dodecyl- and tetradecyl-trimethylammonium bromides has been determined from measurements of density and ultrasound velocity at different temperatures ranging from 20 to 45 "C at 5 "C intervals. Based on the theoretical treatment in which the adiabatic compressibility is given as a function of concentration, the _apparent adiabatic cpmpressibilities of the surfactant in the monomeric (8,) and micellar (8,) forms are obtajned from the experimental results at each temperature.The values for 8, increase with increased temperature, and its temperature coefficient is constant for methyl, octyl and decyl derivatives, but changes sharply betw_een 30 and 40 "C for the dodecyl and tetradecyl derivatives. The value of 8, increases linearly with increased temperature, and its temperature coefficient inp-eases with increasing alkyl chain length. The linear changes of 8, and 8, with temperature are related to the change of hydrophilic hydration, while the sharp change of 8, for dodecyl and tetradecyl derivatives is attributed to the change of hydrophobic hydration. Several papers have appeared on the temperature dependence of the partial molar volume of surfactants in aqueous ~olutions,~-~ but the temperature dependence of the adiabatic compressibility of surfactant solutions has received considerably less attention.Nomoto and Endo5 have studied the temperature dependence of the adiabatic compressibility of aqueous solutions of polyoxyethylene dodecyl ether containing, on average, six oxyethylene groups. Vikingstad et a1.6 have reported pressure and temperature effects on the partial molar volume and adiabatic compressibility of sodium decanoate micelles, while De Lisi et aZ.' have examined temperature dependence of adiabatic compressibility of nonyl- and decyl-trimethylammonium bromides. Backlund et aL8 have investigated the temperature dependence of ultrasound velocity in aqueous solutions of hexadecyltrimethylammonium bromide.In a previous paperg we developed a simple theoretical treatment, in which the adiabatic compressibility of aqueous solutions of surfactants is given as a function of concentration, in order to obtain the apparent adiabatic compressibilities of the surfactant in both monomeric and micellar forms. We then applied it to the experimental results obtained from aqueous solutions of several surfactants at 25 "C. In the present work we measure the density and ultrasound velocity in aqueous solutions of alkyltrimethylammonium bromides in which alkyl = octyl, decyl, dodecyl or tetradecyl, and we derive the partial molar volume and the apparent adiabatic compressibilities of these surfactants in both monomeric and micellar forms at different temperatures.The temperature is varied from 20 to 45 "C at 5 "C intervals. t Permanent address : Department of General and Analytical Chemistry, Institute of Commodity Sciences, Academy of Economics, 60-967 Poznan, Poland. 151152 Compressibility of Surfactants Methods of Calculation In aqueous solution a surfactant can exist in either the monomeric or the micellar form. If the weight concentrations of monomer and micelle are c, and cm, the total concentration of surfactant, c (g ~ m - ~ ) , is given by c = C,+C,. (1) If the apparent specific volume of monomer and micelle are u", and u", (cm3 g-l) respectively, the density of the aqueous solution of the surfactant, p (g cmd3), is given (2) by P = PO + (1 - 61 P O ) c1+ (1 - u"m P O ) c m where po is the density of the solvent.By differentiating eqn (2) with respect to pressure, P, at constant entropy, S, the adiabatic compressibility of the solution, j? (bar-,), can be derived as a function of the c_oncent_rations. If the apparent adiabatic compressibilities of monomers and micelles are p1 and pm, respectively, and the changes in concentrations of monomer and micelle with pressure, P, take place only through a change in volume of solution with pressure, i.e. (ac,/ap)s = 8; c, (aCm/aP)s = B m c m - then the adiabatic compressibility of the solution, /I, is given by where Do is the adiabatic compressibility of the solvent. According to the Laplace equation and expanding the terms to the first power of concentrations, the ultrasound velocity in the solution, u (m s-l), is expressed by where uo is the ultrasound velocity in the solvent, and u, = l/p, is the specific volume of the solvent.In eqn (2), (3) and (9, the concentrations of monomer and micelle must be given as functions of total Concentration of surfactant. In most cases the pseudo-phase model holds well for the micelle f~rmation,'~-'~ which leads to c, = c, cm = 0 c < c.m.c. (6) c, = c.m.c. c, = c-c.m.c. c 3 c.m.c. (7) where c.m.c. is the critical micelle concentration. We can then expect to have two straight line segments intersecting at the c.m.c., if we plot the density, the adiabatic compressibility or the ultrasound velocity against the total concentration, and if the apparent specific volumes and the apparent compressibilities of the surfactant in the monomeric and micellar forms are independent of concentration.R .Zieliriski, S. Ikeda, H. Nornura and S. Kato 153 Experimental Materials Samples of tetramethylammonium bromide (C'TAB), octyltrimethylammonium bro- mide (C,TAB), decyltrimethylammonium bromide (C,,TAB), dodecyltrimethylam- monium bromide (C,,TAB) and tetradecyltrimethylammonium bromide (Cl,TAB) were the same as those used previo~sly.~ They were used as supplied, without further purification, but after having been dried in vacuo at room temperature for at least 48 h. All solutions were prepared by weighing, using distilled and degassed water. The surfactant concentrations were converted to g cm-3 at each temperature. Measurements Density measurements were carried out, using Ostwald type pyknometers of 20 cm3 capacity.Pyknometers were calibrated at each temperature using distilled and degassed water. The densities of the solutions were calculated from the generally accepted values of the density of water13 and were corrected for the density of air. Uncertainties in the solute concentration and the weighing (mainly the latter) can produce errors in the values of density, ca. 5 x Measurements of ultrasound velocity, u, ( f: 0.15 m s-l) were made using an ultrasonic interferometer working at a frequency of 5.0 MHz. Errors in ultrasound velocity measurements can arise mainly from variations of temperature, T. Since the temperature coefficient of ultrasound velocity, du/dT, in water varies from ca.3.0 m s-l K-' at 20 "C to ca. 1.4 m s-l K-l at 45 "C, the uncertainty of 0.01 "C in the temperature of the solutions during ultrasound velocity measurements produces an error in the values of u of ca. f3.0 x lo-, m s-' at 20 "C andf 1.4 x m s-' at 45 "C. This allows us to calculate the adiabatic compressibilities of the surfactant solutions to an accuracy of better than 0.03 %. g ~ m - ~ . Results The densities of aqueous solutions of alkyltrimethylammonium bromides (C,TAB) at each temperature are plotted as a function of the surfactant concentration. A typical plot for octyltrimethylammonium bromide is shown in fig. 1. Each plot can be divided into two straight line segments with a break point corresponding to the c.m.c. The straight line segments can be described by means of eqn (2).From their slopes the values of the apparent specific volumes of the surfactant in the monomeric form, v"', and that in the micellar form, v",, can be derived at each temperature. We introduce the apparent molar volumes of monomer and micelle by - Vl = M,v", vm = M#, - where M, is the molecular weight of the surfactant. In general, for dilute electrolyte solutions, the apparent molar volume is approximately equal to the partial molar volume. Values of the apparent molar volumes of the surfactants at various temperatures are tabulated in table 1. The change in the apparent molar volume upon micellization, APm, is defined as the difference between the values of the apparent molar volume of the surfactant above and below the c.m.c.: Values of AP, for the surfactants at various temperatures are presented in fig. 2. - - - AV,,, = Vm- Vl. (10)154 Compressibility of Surfactants Fig. 0 50 100 150 concentration/g dm-3 1. Density of aqueous solutions of octyltrimethylammonium bromide as a function of concentration at several temperatures. Symbols: A, 20; V, 25; 0, 30; 0, 35; 0, 40; H, 45 "C. Table 1. Apparent molaL volume of alkyltrimethylammonium bromides in monomeric ( and micellar (V,) forms in water at various temperatures (in cm3 mol-') C,TAB C,TAB C,,TAB C,,TAB C,,TAB T/ "C Pl Vl 'm Vl 'm '1 'm Vl Vm 20 - 223.7 228.1 253.4 260.7 279.9 293.6 305.9 326.2 25 115.2 225.0 228.8 255.0 262.2 283.4 296.2 309.6 329.4 30 115.3 226.3 229.4 256.4 263.4 285.7 297.7 312.0 328.9 35 115.7 227.0 230.4 258.3 264.5 287.1 299.4 315.2 331.8 40 116.1 228.1 231.4 260.5 266.4 288.6 300.2 318.0 332.5 45 116.5 229.3 232.1 261.2 267.2 291.9 301.4 320.4 335.7 Formation of micelles brings about an increase in the apparent molar volume of alkyltrimethylammonium bromides, which indicates that the structure of the micelles is looser than that of the monomers at each temperature.The change in the apparent molar volume due to micelle formation decreases with increased temperature, and this decrease seems to be linear in the range of temperatures investigated. A similar tendency was also observed for nonyl- and decyl-trimethylammonium bromide^,^ sodium dodecyl sulphate,' sodium decanoate6 and sodium sulphonate.2 One can suppose that the decrease in AVm with increased temperature may be brought about by dehydration of the ionic head group.R .Zieliriski, S. Ikeda, H. Nomura and S . Kato 155 24 20 16 d I - 0 E rn $ 12 1 2 --.. 4 8 4 0 15 20 25 30 35 4 0 45 5 0 T/OC Fig. 2. Change in the apparent molar volume upon micellization for alkyltrimethylammonium bromides in aqueous solutions as a function of temperature. Symbols: A, C,TAB; V, C,,TAB; 0, C,,TAB; 0, C,,TAB. In aqueous solution the apparent molar expansion, ii = (avi/aT),, (i = 1 or m) is ex- pected to be a Fseful and sensitive measure of the structural solute-solvent interactions.14 The value of Ei increases with the length of the alkyl chain from 0.212 cm3 mol-' K-' for the octyl to 0.576 cm3 mol-' K-' for the tetradecyl derivative in the monomeric form (i = I), and from 0.193 cm3 mol-1 K-' for the octyl to 0.380 cm3 mol-1 K-' for the tetradecyl derivative in the micellar form (i = m).The higher value for the monomer would suggest stronger hydration for the monomer than for the micelle. Fig. 3 and 4 are representative examples of the changes in the ultrasound velocity in aqueous solutions of octyl- and dodecyl-trimethylammonium bromides with the surfactant concentration at temperatures ranging from 20 to 45 "C. Each plot can be divided into two straight line segments, which correspond to the monomeric and micellar forms of the surfactant in aqueous solution. We can assign the intersection point on each plot to the c.m.c. It should be noted that in the case of octyltrimethylammonium bromide the plots near the c.m.c deviate from straight lines at each temperature, so that the c.m.c.values have to be estimated by linear extrapolation from both sides. A similar deviation can be observed on the plot of ultrasound velocity in aqueous solutions of sodium octyl sulphate at 25 "C published by Bloor et all5 It should be noted that there is a general tendency, especially for higher homologues, that a positive deviation from the straight line or a curvature, concave upward, occurs at the highest micelle concentrations examined. Typical examples of the changes in the adiabatic compressibility of aqueous solutions of octyl- and dodecyl-trimethylammonium bromides with the surfactant concentration at different temperatures are shown in fig. 5 and 6. Each plot can be divided into two straight line segments corresponding to the monomeric and micellar forms of the156 Compressibility of Surfactants 1570 - 1560 - 1550 - 1530 1520 E \ 1510 Y 7 .. 1 5 0 0 v 0 50 100 150 concentration/g dm-3 Fig. 3. Ultrasound velocity in aqueous solutions of octyltrimethylammonium bromide as a function of concentration at several temperatures. Symbols are the same as in fig. 1. ii-r--y 1: 1534 1508 '""k d4---+- 1484 v 1'"g6 1482 I I I I I 0 10 20 30 40 concentration/g dm-3 Fig. 4. Ultrasound velocity in aqueous solutions of dodecyltrimethylammonium bromide as a function of surfactant concentration at several temperatures. Symbols are the same as in fig. 1.R. Zieliriski, S. Ikeda, H. Nomura and S. Kato 157 4.001 I 1 I 0 50 loo 150 concentration/g dm-3 Fig. 5. Adiabatic compressibility of aqueous solutions of octyltrimethylammonium bromide as a function of surfactant concentration at several temperatures.Symbols are the same as in fig. 1. 425 I 0 10 20 30 40 concentration/g dm-3 Fig. 6. Adiabatic compressibility of aqueous solutions of dodecyltrimethylammonium bromide as a function of surfactant concentration at several temperatures. Symbols are the same as in fig. 1.158 Compressibility of Surfactants Table 2. Apparent adiabatic compressibility of alkyltrimethylammonium bromides in monomeric &) and micellar c6,) forms in water at various temperatures (in bar-') C,TAB C,TAB Cl,TAB C,,TAB C,,TAB T/"C B l Bl Bm Bi B m Bi Bm Bl B m 20 -0.33" -0.64 3.36 -0.98 3.69 -1.70 3.88 -2.49 4.04 25 -0.12 -0.17 3.47 -0.55 3.78 - 1.48 4.04 -2.62 4.18 30 0.16 0.24 3.49 -0.19 3.90 - 1 .1 1 4.20 -2.71 4.22 35 0.45 0.59 3.49 0.37 4.03 -0.17 4.31 -0.75 4.39 40 0.72 0.93 3.61 0.83 4.15 0.56 4.40 -0.25 4.51 45 0.83 1.22 3.66 1.18 4.27 0.77 4.63 0.61 4.65 - - - 4.66 - - - - 50 - a Extrapolated value. surfactant. One can draw straight lines by means of eqn (3). It is seen that the plot of the adiabatic compressibility of octyltrimethylammonium bromide as a function of surfactant concentration has a curvature near the c.m.c. at each temperature. Also there is a general tendency, especially for higher homologues, that a negative deviation from the straight line or a curvature, convex upward, occurs at the highest micelle concentration examined. The slopes of the plots for the monomeric forms are negative for all homologues, while the sign of the slope above the c.m.c.depends on the length of alkyl chain and temperature. At a given temperature, the slope of the plot for the micellar form increases with increasing number of carbon atoms. For a given number of carbon atoms in the alkyl chain, the slope increases with increased temperature. Because of deviation from linearity at the highest concentration, all numerical values of the slope are based on the straight line parts of an experimental curve. The apparent _adiaba_tic compressibilities of the surfactants in the monomeric and micellar forms, P1 and am, can be estimated using eqn (3), and their values at different temperatures are listed in table 2. For comparison, some data on tetramethylammonium bromide are also included.The temperature dependence of Bl and Brn for alkyltri- methylammonium bromides are shown in fig. 7 and 8. At 20 "C the values of bl are negative and they increase with increased temperature. The negative values can be attributedjo the effect of water of hydration around the monomer, and the gradual increase in P1 with rising temperature must be caused by th_e partial dehydration of the monomer. It is seen that the temperature dependence of /I1 varies with the length of the hydrocarbon chain of the alkyltrimethylammonium bromide. For the octyl and decyl derivatives it is linear, whereas for the dodecyl and tetradecyl derivatives it is sigmoidal. The values of P1 decrease non-linearly at each temperature as the number of carbon atoms in alkyl chain increases.The value of Pm increases linearly with increased temperature for all the derivatives, and its temperature coefficient is larger for higher homol_ogues. The temperature coefficient of Pm for all the derivatives is + or less of that of PI for the octyl and decyl derivatives. The values of Prn are positive but lower than the adiabatic compressibility of liquid hydrocarbons having the same number of carbon atoms.16* l7 However, while the apparent adiabatic compressibility of the micelles increases with increasing length of the alkyl chain, the adiabatic compressibility of hydrocarbons in the liquid state decreases. The change in apparent adiabatic compressibility of surfactants due to micelle formation can be expressed by ABm = /Tm -&. (1 1)R.Zieliriski, S. Ikeda, H. Nomura and S. Kato 159 1.5 1.0 0.5 - - 0.0 'f' -0.5 - 2 3 6 - -1.0 -1.5 -2.0 - -2.5 - - - b P --- - - 2-4 -3.0 I I I 1 I I I I 15 20 25 30 35 40 45 50 T/"C Fig. 7. Apparent adiabatic compressibility of alkyltrimethylammonium bromides in the monomeric form as a function of temperature. Symbols are the same as in fig. 2. 4.801 4.60 4.40 4.20 I s " 4.00 2 t G 2 P \ 3.8 0 3.60 3.40 3.20 15 20 25 30 35 40 45 50 T/"C Fig. 8. Apparent adiabatic compressibility of alkyltrimethylammonium bromides in the micellar form as a function of temperature. Symbols are the same as in fig. 2. 6 FAR II60 Compressibility of Surfactants 15 20 25 30 35 40 45 50 Fig. 9. Change in the apparent adiabatic compressibility upon micellization for alkyltri- methylammonium bromides in aqueous solution as a function of temperature.Symbols are the same as in fig. 2. T/"C The Yalues of ADm are shown as a function of temperature in fig. 9. A gradual d_ecrease in ADm with rising temperature can be mostly attributed to the increase in PI, gnd, therefore, to the dehydration of the ionjc head groups, but the sharp decrease in ADm is attributable to the sudden increase in P1 caused by partial destruction (melting) of the hydrophobic hydration. The apparent adiabatic compressions of the surfactant in the monomeric and micellar forms, El and Em, can be calculated from the values of the corresponding apparent molar volumes, Fl and Tm, and the apparent adiabatic compressibilities, Bl and Bm : El = TJ1 (1 2) Km = VmPm. (13) (14) - - - The change in the apparent molar compression, AKm, due to micelle formation can be expressed by CI - - AKm = Km - Kl.The values of kl, Km and AKm at various temperatures are tabulated in table 3. At a given temperature El decreases with the number of carbon atoms of alkyl chain, whereas Em increases. Similar observations were reported by Vikingstad et al.l8 for aqueous solutions of the homologous series of sodium alkanoates containing 6-1 3 carbon atoms in hydrocarbon chain, at 25 "C. For a given surfactant both Kl and K,,, increase with increased temperature, but the increase in Kl is larger. A similar tendency was reported by Vikingstad et for sodium decanoate. According to Cabani et al.lg the negative values of El at low temperaturesR. Zieliriski, S. Ikeda, H.Nomura and S. Kato 161 Table 3. Apparent molar compressions and the change in apparent molar compression due to micelle formation of alkyltrimethylammonium bromides in water at various temperatures (1 OP4 cm3 mol-' bar-,) C,TAB C,,TAB C,,TAB C,,TAB T/"C kl km Akm k, km Akm k, km Akm kl Em Akm 20 -14 77 91 -25 96 121 -48 114 162 -76 132 208 25 - 4 79 83 -14 99 113 -42 120 162 -81 137 218 30 5 80 75 - 5 103 108 -32 125 157 -84 140 224 35 13 81 68 10 107 97 - 5 129 134 -24 146 170 40 21 84 63 22 1 1 1 89 16 132 116 8 150 142 45 28 85 57 31 114 83 22 140 118 20 156 136 can be interpreted as a result of higher resistance to pressure of the structured water around the surfactant in the monomeric form than that of water in the bulk. Increasing the temperature brings aboyt a loosening of str-uctured water around the monomer and, therefore, an increase in Kl.An increase in K, can be attributed to the loosening of hydration +ell around polar head group as a result of an increase in temperature. The value of AKm increases with increasing alkyl chain length and decreases with increased temperature. Discussion The most probable explanation for the present results may be given by assuming two types of hydration, i.e. hydrophilic (or ionic) and hydrophobic, on the monomeric surfactant ion, and a single type of hydration, i.e. hydrophilic, on the surfactant ions forming micelles. The hydrophilic hydration occurs around the ionic head group which directs the hydrogen or oxygen atom of the water molecule towards the ionic group. The hydrophobic hydration is caused by strong association of water molecules or formation of hydration shell ('iceberg structure ') around alkyl chains.For the octyl and decyl derivatives the hydrophilic hydration is so extensive in the monomeric forms that there is no room for hydrophobic hydration around the hydrocarbon moiety. On the contrary, the hydrophilic hydration itself is strongly influenced by the hydrocarbon moiety, so that the compressibility further increases with increased temperature, as the alkyl chain become? longer. The contribution of one methylene group of the hydrocarbon chain to the ap,/aT coefficient is (4.2 0.7) x lo-* bar-l K-l. For the dodecyl and tetradecyl derivatives, the hydrophobic hydration is strong around the terminal methyl and methylene groups of the hydrocarbon moiety.The structure of the hydration shell around them is partially destroyed by melting at around 30-40 "C. Above and below this temperature range the apparent adiabatic com- pressibility of these higher homologues seems to vary with temperature in a manner similar to that of the lower homologues. On the other hand, the apparent adiabatic compressibility of the surfactant in _the micellar form increases linearly with increased temperature, and its rate of change, t)Pm/ aT, is 1.1 x bar-l K-' for the octyl derivative, while its average rate is 2.5 x lop6 bar-l K-l for the higher homologues. These increases in the apparent adiabatic conipressibilities of micelles can be attributed mostly to increased loosening of the micellar structure as well as to the gradual dehydration of the ionic head group with increased temperature.The lower rate of change for the octyl derivative can be attributed to the partial 6-2162 Compressibility of Surfactants penetration of water into the micelle interior. The micelle has an aggregation number as low as 2320921 for the octyl derivative in water at 25 "C. Furthermore, an increase in temperature generally causes a decrease in the micelle aggregation number for ionic surfactants.22'23 The low hydrophobicity of short alkyl chain and the small size of the micelle makes the micelle structure relatively loose and penetrable to water. Penetration of water molecules into the micelle interior has been discussed by several workers, and the existence of some bound water in the micelle interior in the vicinity of a few carbon atoms near the ionic head group was suggested by them.24-30 The temperature coefficient of the adiabatic compressibility of water, @?o/aT, in the same range of temperatures has an average value of - 1.2 x lo-' bar-' K-l.It seems reasonable to suppose that the lower value of the C@,,,/aTcoefficient for the octyl derivative can be, at least partially, caused by penetration of water molecules into the micellar interior. For the higher homologues there is almost a common micellar structure so that the rate of change in the apparent adiabatic compressibility with temperature may correspond to that of the structural loosening of the micelle, but its degree of loosening would be lower than that of liquid hydrocarbon^.'^ It is relevant to point out here again the observed difference in the types of micelle formation between the octyl derivative and higher derivatives.While it is not necessarily sharp, as seen in fig. 3 and 5, for the octyl derivative, micelle formation is clearly manifest with the higher homologues. The former behaviour means that the micelle formation does not take place like pseudo-phase formation because the size of the micelles is not sufficiently large, so that it is less sharp. For the latter, the micelle size is sufficiently large that micelle formation is well approximated by the pseudo-phase model. 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