Volume Properties of Decylammonium Chloride and Micelle-Forming

Micelle-Forming Local Anesthetic Mixtures in the Micelle. Hitoshi Matsuki,* Hiroshi Kamaya, and Issaku Ueda. Department of Anesthesia, DVA Medical Cen...
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Langmuir 1998, 14, 4030-4035

Volume Properties of Decylammonium Chloride and Micelle-Forming Local Anesthetic Mixtures in the Micelle Hitoshi Matsuki,* Hiroshi Kamaya, and Issaku Ueda Department of Anesthesia, DVA Medical Center, and University of Utah School of Medicine, Salt Lake City, Utah 84148

Michio Yamanaka Department of Chemistry, Faculty of Science, Kyushu University Ropponmatsu, Ropponmatsu, Fukuoka 810, Japan

Shoji Kaneshina Department of Biological Science and Technology, Faculty of Engineering, The University of Tokushima, Minamijosanjima, Tokushima 770, Japan Received December 16, 1997. In Final Form: April 9, 1998 The densities of aqueous solutions of a decylammonium chloride (DeAC)-dibucaine hydrochloride (DC‚ HCl) mixture and a DeAC-tetracaine hydrochloride (TC‚HCl) mixture were measured as a function of the total molality and composition of the mixture at 298.15 K under atmospheric pressure. The molar volumes of the mixture in the monomeric and micellar states of both systems were evaluated by applying the thermodynamic equations to the apparent molar volumes obtained from the density data. They varied linearly with composition between the values of pure components. The volume of mixed micelle formation also showed the linear dependence on the composition. These facts indicate that the DeAC and the anesthetic molecules mix ideally in both the monomeric and micellar states from the viewpoint of volume. On the other hand, the micellar composition was calculated from the composition dependence of the critical micelle concentration values. The shape of the phase diagram of micelle formation was slightly distorted cigartype due to the nonideal interaction between DeAC and the anesthetic molecules in the mixed micelle. Ideal mixing of volume in the micellar state indicates that the nonideal interaction is not so strong that it affects the molar volume of the micelle.

Introduction 1,2

Anesthetic molecules expand cell membranes. The action of anesthetics is reversed by high pressure.3-5 The phenomena show that the volume function of the anesthetics in membranes is a significant factor in molecular mechanism of anesthesia. The volume change of anesthetics from aqueous solution to hydrophobic environments such as phospholipid bilayers and micelles has been reported in connection with a model study of pressureanesthetic antagonism. This quantity was evaluated from thermodynamic analysis of the pressure dependence of the partition coefficient of the anesthetic between both states6,7 or by comparing the volumes occupied by the anesthetics in both states with each other.6,8 However, most studies of volume change are concentrated in * On leave from the Department of Biological Science and Technology, Faculty of Engineering, The University of Tokushima, Minamijosanjima, Tokushima 770, Japan. Correspondence should be addressed to this address. Fax: +81-886-55-3162. E-mail: [email protected] (1) Matubayasi, N.; Ueda, I. Anesthesiology 1983, 59, 541. (2) Ueda, I.; Kamaya, H. Anesth. Analg. 1984, 63, 929. (3) Johnson, R. H.; Brown, D. E.; Marsland, D. A. J. Cell. Comp. Physiol. 1942, 20, 269. (4) Lever, M. J.; Miller, K. W.; Paton, W. D. M.; Smith, E. B. Nature 1971, 231, 368. (5) Halsey, M. J.; Wardley-Smith, B. Nature 1975, 257, 811. (6) Kaneshina, S.; Kamaya, H.; Ueda, I. Biochim. Biophys. Acta 1982, 685, 307. (7) Kaneshina, S.; Kamaya, H.; Ueda, I. J. Colloid Interface Sci. 1983, 93, 215.

inhalation anesthetics; similar volume studies on local anesthetics have hardly been performed except for alcohols such as benzyl alcohol.8 There are also few studies which cover all mixing ratios of the anesthetic to the membrane molecules. Partial molar volume is an important thermodynamic quantity to describe the volume behavior of molecules. Density measurement is a superior method for determining the value of the partial molar volume from experimental data directly. Molar volumes of some anesthetics in pure liquid and their partial molar volumes in water and in phospholipid bilayers have been reported.9-12 In previous papers,13,14 we measured the densities of aqueous local anesthetic solutions and characterized their volume behavior thermodynamically. The present paper reports the volume properties of the cationic surfactant decylammonium chloride (DeAC) and a local anesthetic in their (8) Kaneshina, S.; Kamaya, H.; Ueda, I. Biochim. Biophys. Acta 1984, 777, 75. (9) Kita, Y.; Bennet, L. J.; Miller, K. W. Biochim. Biophys. Acta 1981, 647, 130. (10) Kita, Y.; Miller, K. W. Biochemistry 1982, 21, 2840. (11) Mori, T.; Matubayasi, N.; Ueda, I. Mol. Pharmacol. 1984, 25, 123. (12) Fukushima, K.; Kamaya, H.; Ueda, I. J. Pharm. Sci. 1990, 79, 893. (13) Matsuki, H.; Hashimoto, S.; Kaneshina, S.; Yamanaka, M. Langmuir 1994, 10, 1882. (14) Matsuki, H.; Yamanaka, M.; Kaneshina, S. Bull. Chem. Soc. Jpn. 1995, 68, 1833.

S0743-7463(97)01385-1 CCC: $15.00 © 1998 American Chemical Society Published on Web 06/30/1998

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Langmuir, Vol. 14, No. 15, 1998 4031

mixed micelle from density measurements of aqueous DeAC and anesthetic mixtures. The hydrophobic local anesthetics dibucaine hydrochloride (DC‚HCl) and tetracaine hydrochloride (TC‚HCl) are selected for this purpose because (i) both anesthetics form micelles in the aqueous solution and this enables us to study the volume of anesthetic in the micelle in the whole range of composition and (ii) the information concerning the miscibilities of the DeAC and DC‚HCl and the DeAC and TC‚HCl systems in the micellar state has been already reported from surface tension measurements.15 Volume quantities concerning mixed micelle formation of DeAC and the anesthetic are calculated by applying the thermodynamic equations to the density data. Volume behavior and miscibilties of DeAC and the anesthetic in the micelle are discussed on the basis of the molar volumes of the mixtures between aqueous solution and micelle and of the composition of the micelle. Experimental Section Materials. Dibucaine (2-butoxy-N-[2-(diethylamino)ethyl]4-quinolinecarboxamide) hydrochloride and tetracaine (2-(dimethylamino)ethyl 4-(butylamino)benzoate) hydrochloride were purchased from Sigma Chemical Company. The anesthetics were purified by repeated recrystallizations from an ethanol and carbon tetrachloride mixture for dibucaine and from ethanol for tetracaine, respectively. Decylammonium chloride was synthesized by the method reported previously15 and recrystallized four times from ethanol. The purities of the anesthetics and surfactant were checked by elemental analysis and by measuring the surface tension of their aqueous solutions in the vicinity of the critical micelle concentration. Water was distilled twice after deionization, where the second distillation was carried out from dilute alkaline permanganate solution. Density Measurements. The densities of the aqueous surfactant-anesthetic solutions were determined with a vibrating tube density meter (Anton Paar DMA60/602) under atmospheric pressure.13 The temperature of the U-shaped glass tube was maintained at 298.15 ( 0.001 K by circulating water thermostated by a PID temperature controller (Yamashita Giken Co. Ltd. (Tokushima, Japan)). The output of the density meter was transmitted by RS232C interface to a personal computer, and it was converted into density value right away. The experimental error for the value of density was within 0.002 kg m-3 (2 ppm).

Results The total molality of DeAC and the anesthetic mt and the mole fraction of the anesthetic in the total components X2, defined by

mt ) m 1 + m 2

(1)

X2 ) m2/mt

(2)

and

were employed as concentration variables, since it is advantageous to consider the interaction of two components in molecular aggregates.16 Here m1 and m2 are the molalities of DeAC and the anesthetic, respectively. The density F of the aqueous solutions of the mixtures was measured as a function of mt and X2. Tables 1 and 2 demonstrate the results of density measurements for the DeAC-DC‚HCl system and the DeAC-TC‚HCl system, respectively. The F values of pure DC‚HCl and TC‚HCl solutions increased linearly with (15) Matsuki, H.; Hashimoto, S.; Kaneshina, S.; Yamanaka, M. Langmuir 1997, 13, 2687. (16) Motomura, K.; Aratono, M. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Marcel Dekker: New York, 1993; p 99.

Table 1. Experimental Densities for Aqueous Solutions of the DeAC-DC‚HCl System mt (mmol kg-1)

F (kg m-3)

0 10.332 20.120 29.788 39.256 48.416 59.398 70.568 81.115

997.045 996.995 996.952 996.906 996.862 996.826 996.770 996.650 996.505

X2 ) 0 (DeAC) 90.055 996.381 99.224 996.246 111.148 996.090 120.042 995.960 130.050 995.828 139.080 995.689 151.202 995.525 154.154 995.480 160.993 995.403

4.931 9.877 15.781 20.808 30.326 40.502 50.850 59.454

997.067 997.091 997.124 997.148 997.206 997.253 997.312 997.347

5.697 10.404 15.351 20.338 29.321 40.483 50.580 59.970

mt (mmol kg-1)

mt (mmol kg-1)

F (kg m-3)

170.680 190.377 202.188 210.226 219.759 231.523 240.983 251.425

995.248 994.990 994.824 994.719 994.590 994.431 994.297 994.166

X2 ) 0.160 64.854 997.350 69.670 997.362 74.997 997.336 80.354 997.313 84.613 997.303 90.128 997.283 100.311 997.257 120.248 997.166

129.811 150.237 160.051 179.025 199.412 219.078 240.592 259.587

997.146 997.054 997.033 996.956 996.873 996.809 996.727 996.659

997.135 997.211 997.288 997.373 997.507 997.677 997.836 997.977

X2 ) 0.330 64.927 998.048 69.739 998.100 75.038 998.151 80.177 998.188 90.105 998.261 99.598 998.329 110.183 998.404 118.883 998.464

129.389 140.197 150.206 170.644 199.338 219.151 239.230 260.181

998.535 998.612 998.662 998.820 999.012 999.139 999.278 999.409

5.069 9.969 14.994 19.936 20.248 25.147 31.378 40.970 49.193 54.869 59.474

997.175 997.304 997.434 997.564 997.570 997.696 997.859 998.108 998.323 998.473 998.583

X2 ) 0.500 64.546 998.712 70.242 998.846 79.674 999.028 93.561 999.286 100.712 999.413 109.915 999.588 119.708 999.751 129.696 999.925 139.523 1000.106 150.458 1000.285 159.375 1000.451

169.948 180.475 191.662 199.876 203.505 210.225 220.095 224.519 231.100 243.464 249.915

1000.632 1000.780 1000.990 1001.136 1001.191 1001.298 1001.481 1001.539 1001.649 1001.852 1001.960

5.409 10.104 15.530 20.368 30.178 40.556 50.641 61.056

997.242 997.415 997.615 997.789 998.148 998.526 998.892 999.263

X2 ) 0.670 65.006 999.409 70.174 999.585 75.389 999.761 80.771 999.927 90.066 1000.205 100.517 1000.516 110.631 1000.804 129.618 1001.344

141.846 160.088 170.436 179.096 199.979 220.655 240.288 260.101

1001.684 1002.196 1002.480 1002.720 1003.285 1003.838 1004.362 1004.880

4.082 9.968 15.195 20.129 30.073 39.963 50.422 60.113

997.267 997.512 997.756 997.989 998.452 998.918 999.397 999.853

X2 ) 0.840 70.623 1000.337 74.931 1000.522 85.114 1000.968 89.438 1001.148 100.202 1001.590 120.279 1002.376 130.610 1002.787 140.217 1003.148

149.279 159.992 179.841 199.879 219.500 238.851 260.279

1003.494 1003.907 1004.655 1005.395 1006.119 1006.821 1007.583

9.973 10.103 14.964 15.408 20.679 24.999 30.310 40.679 61.143

997.558 997.563 997.825 997.847 998.119 998.334 998.620 999.151 1000.205

X2 ) 0.920 65.555 1000.420 69.908 1000.643 75.646 1000.930 81.003 1001.205 90.298 1001.634 100.427 1002.109 110.176 1002.543 120.274 1002.991 129.484 1003.410

139.446 156.725 159.586 179.431 199.677 219.144 239.012 259.012

1003.831 1004.576 1004.717 1005.564 1006.412 1007.219 1008.056 1008.843

5.047 15.030 15.449 25.146 30.874 35.341 36.972 45.100 52.595 54.975

997.331 997.899 997.922 998.470 998.795 999.044 999.142 999.597 1000.028 1000.152

X2 ) 1 (DC‚HCl) 59.171 1000.374 65.229 1000.733 75.179 1001.278 80.941 1001.599 83.078 1001.710 85.520 1001.834 85.535 1001.837 95.022 1002.334 103.178 1002.763 105.311 1002.867

111.054 115.313 132.647 140.163 160.879 183.328 199.253 203.173 224.735 250.518

1003.141 1003.373 1004.263 1004.597 1005.581 1006.686 1007.449 1007.641 1008.611 1009.799

F (kg m-3)

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Matsuki et al.

Table 2. Experimental Densities for Aqueous Solutions of the DeAC-TC‚HCl Systema mt (mmol kg-1)

F (kg m-3)

10.318 18.481 29.801 39.140 49.515 59.849 70.038 80.191 89.352

997.074 997.096 997.127 997.149 997.176 997.200 997.202 997.145 997.091

9.777 18.402 29.676 39.068 48.977 56.154 67.204 68.282 78.891

mt (mmol kg-1)

mt (mmol kg-1)

F (kg m-3)

X2 ) 0.160 99.769 997.028 109.715 996.964 119.580 996.901 130.703 996.866 138.517 996.817 150.366 996.717 160.542 996.680 174.187 996.596 177.491 996.574

189.350 201.497 210.864 218.522 229.797 236.652 248.713

996.499 996.432 996.374 996.323 996.260 996.219 996.148

997.149 997.239 997.355 997.451 997.551 997.621 997.729 997.738 997.815

X2 ) 0.330 89.331 997.849 99.134 997.874 109.241 997.899 119.571 997.923 128.347 997.955 136.513 997.976 149.803 997.997 158.726 998.030 167.033 998.049

179.164 186.753 196.800 208.328 217.476 229.892 238.688 249.794

998.074 998.093 998.114 998.139 998.162 998.190 998.208 998.235

9.465 19.059 29.064 39.712 49.526 59.373 68.407 79.106 91.333

997.216 997.390 997.570 997.762 997.934 998.106 998.261 998.445 998.620

X2 ) 0.500 100.116 998.722 110.848 998.838 120.712 998.955 132.735 999.087 140.054 999.167 150.977 999.286 152.708 999.296 160.929 999.391 169.576 999.476

180.277 188.996 200.303 210.390 219.481 231.790 241.275 251.744

999.589 999.693 999.812 999.919 1000.008 1000.137 1000.233 1000.340

9.061 19.635 29.507 38.582 49.678 59.349 68.463 78.489 88.904

997.277 997.546 997.798 998.032 998.309 998.550 998.776 999.019 999.273

X2 ) 0.670 99.231 999.504 108.824 999.709 119.296 999.925 126.047 1000.075 135.246 1000.255 150.044 1000.525 157.115 1000.675 168.339 1000.890 176.722 1001.048

187.644 199.014 206.683 219.739 229.695 238.821 250.161

1001.254 1001.468 1001.614 1001.851 1002.036 1002.204 1002.407

9.626 19.391 29.423 39.913 49.467 59.623 69.055 79.601 89.760

997.363 997.688 998.021 998.367 998.679 999.010 999.315 999.649 999.973

X2 ) 0.840 99.575 1000.282 110.094 1000.603 118.945 1000.876 125.452 1001.074 136.097 1001.393 151.526 1001.825 156.493 1001.969 166.659 1002.249 176.404 1002.520

187.214 196.673 208.143 217.641 228.541 235.299 250.216

1002.812 1003.070 1003.375 1003.633 1003.916 1004.097 1004.489

9.626 20.012 29.516 39.345 49.431 59.452 69.838 80.011 91.110

997.400 997.785 998.134 998.493 998.861 999.222 999.597 999.960 1000.353

X2 ) 0.920 100.079 1000.671 107.424 1000.937 117.958 1001.301 127.795 1001.640 137.037 1001.948 147.709 1002.301 157.265 1002.614 167.674 1002.949 178.912 1003.303

189.254 199.844 211.673 220.677 230.332 236.773 250.980

1003.630 1003.964 1004.333 1004.618 1004.911 1005.104 1005.535

2.961 9.595 10.168 14.002 29.658 34.574 44.243 58.459 59.413 59.666

997.163 997.431 997.452 997.607 998.236 998.434 998.810 999.376 999.416 999.420

X2 ) 1 (TC‚HCl) 69.627 999.824 73.458 999.969 85.419 1000.435 89.431 1000.590 99.466 1000.976 104.118 1001.172 106.498 1001.249 115.941 1001.616 119.081 1001.723 126.722 1002.016

136.424 146.514 150.577 156.867 167.048 183.223 201.955 223.888 251.211

1002.373 1002.748 1002.904 1003.122 1003.490 1004.072 1004.736 1005.493 1006.390

F (kg m-3)

a The densities of the DeAC solution (X ) 0) are included in 2 Table 1.

Figure 1. Apparent molar volume versus total molality curves of the DeAC-DC‚HCl system at constant composition: (1) X2 ) 0, (2) 0.160, (3) 0.330, (4) 0.500, (5) 0.670, (6) 0.840, (7) 0.920, and (8) 1. The break point indicated by the arrow corresponds to the cmc.

Figure 2. Apparent molar volume versus total molality curves of the DeAC-TC‚HCl system at constant composition: (1) X2 ) 0, (2) 0.160, (3) 0.330, (4) 0.500, (5) 0.670, (6) 0.840, (7) 0.920, and (8) 1. The break point indicated by the arrow corresponds to the cmc.

increasing mt while that of pure DeAC solution decreased with increasing mt. Regular variation of the F values with X2 was observed for both systems. From the F value given in Tables 1 and 2, the apparent molar volume φt of the mixtures at constant X2 was evaluated by the following equation

φt ) (1/F - 1/FW)/mt + M/F

(3)

where FW and M are the density of water (kg m-3) and the molar mass of the mixture (kg mol-1), respectively. Here M is defined by

M ) X1M1 + X2M2

(4)

where M1 and M2 refer to the molar masses of DeAC and the anesthetic, respectively. In Figures 1 and 2 are shown the φt versus mt curves of both systems at various X2. All φt versus mt curves of both systems had a break point at the concentration corresponding to the critical micelle concentration (cmc). The φt values of TC‚HCl and DeAC were almost constant below the cmc while that of DC‚HCl decreased slightly with increasing mt. At the cmc, their values began to increase and approached certain values

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Langmuir, Vol. 14, No. 15, 1998 4033

asymptotically in the high-concentration region above the cmc. For the mixtures, the φt versus mt curves all showed similar behavior to that above for pure components, and the shape of the φt versus mt curves of both systems varied regularly with X2 from DeAC (X2 ) 0) to the anesthetic (X2 ) 1). We fitted the following equations to the φt values by the least-squares technique:

φt ) A0 + A1mt + A2(mt)2 + A3(mt)3 (mt < Ct)

(5)

and

φt ) B0 + B1/mt + B2/(mt)2 + B3/(mt)3 (mt > Ct)

(6)

where Ct is the total molality at the cmc and Ai (i ) 0, 1, 2, 3) and Bj (j ) 0, 1, 2, 3) are best fit parameters of the curves. Discussion

Figure 3. Partial derivative of mtφt with respect to total molality versus total molality curves of the DeAC-DC‚HCl system at constant composition: (1) X2 ) 0, (2) 0.160, (3) 0.330, (4) 0.500, (5) 0.670, (6) 0.840, (7) 0.920, and (8) 1.

Although decylammonium and local anesthetic cations are weak electrolytes, we assumed in this study that DeAC and the anesthetics are uni-univalent electrolytes on account of their relatively high pKa values, as described previously.15,17 By analyzing the behavior of the φt versus mt curves given in Figures 1 and 2 thermodynamically, two important quantities about volume, the molar volume of the mixtures in the monomeric state VW t and that in the 18-20 The VW and , can be obtained. micellar state VM/NM t t M/NM values were evaluated from the derivative of the V t quantity mtφt with respect to mt at constant T and p at a concentration below the cmc and that in a sufficiently high concentration range above the cmc, respectively:18 W W VW t ) X1V1 + X2V2 ) [∂(mtφt)/∂mt]T,p,X2 (mt < Ct) (7)

and M M M VM/NM t ) V /(N1 + N2 ) ) [∂(mtφt)/∂mt]T,p,X2 (mt . Ct) (8) W where VW 1 and V2 are the partial molar volumes of monomeric DeAC and the anesthetic, VM is the molar volume of the micelle, NM t is the sum of the aggregation number of DeAC molecules NM 1 and anesthetic molecules M M NM 2 in the micelle. The quantities V and Nt are defined as the excess quantities with reference to the dividing spherical interface which is located around the micelle, so as to make the excess number of water molecules zero.21 From eqs 5 and 6, we obtain the following equations

Figure 4. Partial derivative of mtφt with respect to total molality versus total molality curves of the DeAC-TC‚HCl system at constant composition: (1) X2 ) 0, (2) 0.160, (3) 0.330, (4) 0.500, (5) 0.670, (6) 0.840, (7) 0.920, and (8) 1.

[∂(mtφt)/∂mt]T,p,X2 ) B0 - B2/(mt)2 - 2B3/(mt)3 (mt > Ct) (10)

4A3(mt)3 (mt < Ct) (9)

The evaluated ∂(mtφt)/∂mt values of both systems are depicted in the form of a ∂(mtφt)/∂mt versus mt plot in Figures 3 and 4. The ∂(mtφt)/∂mt versus mt curves of both systems were similar to the φt versus mt curves in the concentration range below the cmc. However, a discontinuous change due to micelle formation was observed on all curves at the cmc. The ∂(mtφt)/∂mt values reached constant values with increasing mt in the concentration range above the cmc. The magnitude of the discontinuous changes of the mixtures at the cmc became smaller with increasing X2 although their ∂(mtφt)/∂mt values increased with X2.

(17) Kamaya, H.; Hayes, J. J., Jr.; Ueda, I. Anesth. Analg. 1983, 62, 1025. (18) Yamanaka, M.; Kaneshina, S. J. Solution Chem. 1990, 19, 729. (19) Yamanaka, M.; Kaneshina, S. J. Solution Chem. 1991, 20, 1159. (20) Yamanaka, M.; Matsuki, H.; Kaneshina, S. Bull. Chem. Soc. Jpn. 1995, 68, 2159. (21) Motomura, K.; Yamanaka, M.; Aratono, M. Colloid Polym. Sci. 1984, 262, 948.

M M Figure 5 shows the VW t versus X2 and V /Nt versus X2 curves of both systems. Here the ∂(mtφt)/∂mt values at the cmc and those at 250 mmol kg-1 were taken as the VW t and VM/NM t values, respectively. The overall composition X2 in the aqueous solution is equal to the monomer composition XW 2 at concentrations below the cmc, and it is approximately equal to the micellar composition XM 2 defined by

[∂(mtφt)/∂mt]T,p,X2 ) A0 + 2A1mt + 3A2(mt)2 +

and

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Matsuki et al.

Figure 5. Molar volumes of monomer and micelle versus M M composition curves: (1) VW t ; (2) V /Nt ; (s) DeAC-DC‚HCl system; (---) DeAC-TC‚HCl system.

XM 2

)

M NM 2 /Nt

(11)

at sufficiently high concentrations above the cmc. Hence, M M the plots of VW t and V /Nt against X2 in Figure 5 are W regarded as the plot of Vt against XW 2 and the plot of M W M M VM/NM t against X2 , respectively. The Vt and V /Nt values of both systems increased linearly between those of pure DeAC and the anesthetic. According to the thermodynamics on the basis of surface excess quantities,22-24 the VM/NM t value can be approximately given hM by the mean partial molar volume of DeAC V 1 and the M h 2 in the micelle anesthetic V M M h 1 + XM hM VM/NM t ≈ X1 V 2 V 2

(12)

Present results indicate the following relations. W,0 W,0 + XW VtW ≈ XW 1 V1 2 V2

(13)

M M,0 h 1 + XM h M,0 VM/NM t ≈ X1 V 2 V 2

(14)

and

where the superscript 0 represents the pure component. These relations mean that the partial molar volumes of DeAC and local anesthetic in the aqueous solution and micelle are almost equal to the molar volumes of pure DeAC and local anesthetic, respectively. Therefore, we can say that the molar volumes of monomer and micelles of both mixtures behave ideally. Yamanaka et al. reported similar behavior in the mixture of dodecyltrimethylammonium chloride (DTAC) and DC‚HCl20 and those of alkyltrimethylammonium halides.18,19 The volume of mixed micelle formation from DeAC and the anesthetic monomers ∆M WV is defined by the equation21

Figure 6. Volume of micelle formation versus composition curves: (1) DeAC-DC‚HCl system; (2) DeAC-TC‚HCl system.

values in Figure 5. Here we assumed that the V1W and V2W values at sufficiently high concentrations are the same as those at the cmc.25,26 The evaluated ∆M WV values of both systems are plotted against X2 in Figure 6. A linear decrease of ∆M WV values between those of pure DeAC and the anesthetic was found in both systems. By using eqs 13 and 14, eq 15 can be expressed as the following form in both systems M M ∆M h M,0 - VW,0 h M,0 - VW,0 WV ≈ X1 (V 1 1 ) + X2 (V 2 2 )

(16)

This means that the volumes of mixed micelle formation of both systems are nearly ideal; in other words, the DeAC and the anesthetic molecules are miscible ideally in their mixed micelle from the viewpoint of volume. M Finally, we compared the XW 2 value with the X2 value in order to consider the miscibility of DeAC and the anesthetic in their mixed micelle. The Ct values determined from the break points in Figures 1 and 2 are drawn in the form of the Ct versus X2 plot in Figure 7. The Ct values of both systems (open circles) were in good agreement with those obtained from the previous surface tension study15 (closed circles). They increased with increasing X2. The XM 2 values are calculated by applying the equation16,21

XM 2 ) X2 - 2(X1X2/Ct)(∂Ct/∂X2)T,p

(17)

W The ∆M and VM/NM WV values were evaluated from Vt t

to the Ct versus X2 curves in Figure 7. The calculated XM 2 values and X2 (namely XW 2 ) values construct the diagrams called the phase diagram of micelle formation. The resulting diagrams of both systems are shown in Figure 7. The XM 2 values of both systems were smaller than the XW 2 values over the whole range of composition, and both diagrams had a cigar shape. The micelle is more abundant in DeAC than in the aqueous solution although DeAC and the anesthetic molecules mix completely in the micellar state. The thinner phase diagram of the DeACDC‚HCl system than that of the DeAC-TC‚HCl system implies that greater quantities of DC‚HCl than TC‚HCl exist in the mixed micelle. The more hydrophobic DC‚

(22) Motomura, K. J. Colloid Interface Sci. 1978, 64, 348. (23) Motomura, K. Adv. Colloid Interface Sci. 1980, 12, 1. (24) Motomura, K.; Iwanaga, S.; Uryu, S.; Matsukiyo, H.; Yamanaka, M.; Matuura, R. Colloids Surf. 1984, 9, 19.

(25) Musbally, G. M.; Perron, G.; Desnoyers, J. E. J. Colloid Interface Sci. 1976, 54, 80. (26) De Lisi, R.; Perron, G.; Desnoyers, J. E. Can. J. Chem. 1980, 58, 959.

M M W M W M ∆M WV ) V /Nt - (X1 V1 + X2 V2 )

(15)

Volume Properties of Surfactant and Local Anesthetic

Langmuir, Vol. 14, No. 15, 1998 4035

tension study15 that there exists nonideal interaction between DeAC and the anesthetic in their mixed micelle. Because the VM/NM t values of both systems behave ideally as given in Figure 5, the nonideal interaction is not so strong that it affects the VM/NM t values. Conclusions

Figure 7. Critical micelle concentration versus composition curves: (1) DeAC-DC‚HCl system; (2) DeAC-TC‚HCl system; (s) Ct versus X2; (---) Ct versus XM 2 . Open circles and closed circles indicate the results from the present study and those from the surface tension measurements,15 respectively.

HCl than TC‚HCl partitions larger quantities into the micelle, and the result correlates with their anesthetic potency.15 Further, the phase diagrams of both systems showed a slightly distorted shape, especially in the low composition region. We have clarified from the surface

The volume study on local anesthetics gives us important information, since the volume function of local anesthetic molecules is closely related to the anesthetic mechanisms. Volume properties of mixed micelles formed by DeAC and a micelle-forming local anesthetic were investigated by measuring the densities of aqueous solutions of DeAC and the anesthetic mixtures. The molar volumes of the mixtures in the monomeric and micellar states were calculated from the thermodynamic analysis of apparent molar volumes. The ideal mixing of the DeAC and the anesthetic molecules in both states was shown from the linear variation of the molar volume of both states; namely, the volumes of mixed micelle formation were almost ideal. The phase diagrams of micelle formation showed that the DeAC and the anesthetic molecules interact nonideally in their mixed micelle. However, the nonideal interaction does not affect the molar volume of the micelle. Acknowledgment. This study was supported in part by DVA Medical Research Funds. LA971385A