J. Phys. Chem. 1980, 84, 589-593
sending us reports of their work in advance of publication. References a n d Notes (1) E. E. Tucker and S. U. Christian, J. Phys. Chem., 83, 426 (1979). (2) F. Franks in “Water, A Comprehensive Treatise”, F. Franks, Ed., Vol. 4, Plenum Press, New York, Chapter 1. (3) A. Bendaim, J. Wilf, and M. Yaacobi, J. Phys. Chem., 77, 95 (1973). (4) H. L. Friedmanand C. V. Krishnan, J. Solution Chem., 2, 119 (1973). (5) C. V. Krishnan and H. L. Friedman, J. Solution Chem., 3, 727 (1974). (6) P. S. Ramanathan, C. V. Krishnan, and H. L. Friedman, J. Solution Chem., 1, 237 (1972). (7) H. L. Friedman, C. V. Krishnan, and C. Jolicoeur, Ann. N. Y. Acad. Sci., 204, 79 (1973). (8) W. H. Streng and W.-Y. Wen, J . Solution Chem., 3 , 865 (1974). (9) W. McMiliani and J. Mayer, J. Chem. Phys., 13, 276 (1945).
589
(10) J. J. Kozak, W. S.Knight, and W. Kauzmann, J . Chem. Phys., 48, 675 (1968). (11) J. H. Dymund and E. 8. Smith, “The Virial Coefficients of Gases”, Oxford University Press, London, 1969. (12) B. Y. Okamoto, R. H. Wood, and P. T. Thompson, J . Chem. Soc., Faraday Trans. 7 , 74, 1990 (1978), Table 9. (13) (a) L. R. Pratt and D. Chandler, J . Chem. Phys., 67, 3683 (1977); (b) J . Solution Chem., 9, 1 (1980). (14) 2. S. Belousova and Sh. D. Zaalishvili, Russ. J. Phys. Chem., 41, 1290 (1967); Sh. D. Zaalishvili, 2. S. Belousova, and V. P. Verkhova, /bid., 45, 149, 894, 902 (1971). (15) (a) W.-Y. Wen and S. Saito, J. Phys. Chern., 68, 2639 (1964). (b) For a relatively recent review, see ref 2, pp 77-78. (16) C. Pangali, M. Rao, and B. J. Berne, J. Chem. Phys., 71, 2975, 2982 (1979). (17) D. Levesque, J. J. Weis, and G. N. Patey, phys. Lett., 86A, 115 (1978).
Thermal Transpiration Effects for Gases at Pressures above 0.1 torr Isao Yasumoto Department of Chemistry, Yonago Technical College, Yonago, 683, Japan (Received Aprll 12, ‘1979) Publication costs assisted by Yonago Technical College
Thermal transpiration effects have been measured by a relative method with a high-sensitivity mercury U-tube manometer for helium, neon, argon, krypton, xenon, hydrogen, deuterium, oxygen, nitrogen, carbon monoxide, nitric oxide, carbon dioxide, nitrous oxide, hydrogen sulfide, ammonia, hydrogen chloride, water vapor, methane, hydrogen bromide, acetylene, ethylene, ethane, methyl chloride, methyl alcohol, ethyl alcohol, propane, n-butane, and isobutane in a pressure range from 10 to 0.1 torr (1.3 X lo3-13 Pa). The Takaishi-Sensui equation was applied to the data obtained. Values of constants in their equation, A, B, and C, were determined for the gases mentioned above. Empirical relations were obtained between the diameters of molecules and the values of constants A and C.
Introduction The importance of applying the corrections due to thermal transpiration effects for gases has been amply demonstrated in such cases as in adsorption studies and low pressure measurements, where the temperature difference exists between the part of a system in which the pressure is to he measured and a pressure measuring device. Many investigators L-12 measured the effects for noncondensable gases, and obtained experimental curves or empirical equations. However, few measurements of the effects for condensable eases have been made because of technical difficulties. Recentlv, Takaishi and SensuilO DroDosed from their hydrogen measurement one of the mosi useful empirical equations, which is a modification of that due to Liang,4 and is expressed as
The equation has the following excellent advantage: when it is difficult to measure the effect for an appropriate gas under the condition of Tl < T2,we can estimate the effect by using the equation whose constants A, B, and C were obtained under the condition T1> T2. The aim of this study is to examine the general adaptability of the equation. When a high-sensitivity mercury U-tube manometer was used, measurements of the effelcts for a number of condensable gases as well as noncondensable ones have been made by the so-called relative method4 under a variety of temperature conditions in a pressure range from 10 to 0.1 torr. The data obtained were found to be fitted with the Takaishi-Sensui equation. In connection with the diameters of molecules, discussion has been made on the values A, B, and C which were obtained for a variety of gases used.
(1 - (Pi/P2))/(1 - (T1/7’2)”2)= 1/(AX2
Water Vapor. The Takaishi-Sensui equation states that thermal transpiration values, P,/ Pa, are described as a function of the ratio of the product P2d and the mean temperature T. The adaptability of this equation was examined experimentally for water vapor, one of the most condensable gases. The equation was found correct for explaining the results. The experimental procedure and the results are presented below. The experimental arrangements used are illustrated in Figure 1. The pressure difference was measured between the upper ends of a capillary tube and a wide tube which were joined together at their lower ends to form a U-tube. This was installed in a brass box 80 mm wide, 300 mm
-
+ BX + CX112+ 1)
for T , < T2and
(1 - (P2/P1))/(1- (7‘2/TJ1/’)= 1/(AX2 + B X
+ CX1I2+ 1) for Tl > T2with X = P,(d/T) and T = ( T , + T2)/2,where
PI and P2 and T1and T’, denote pressure and temperature in the respective parts of a two-part system which are connected by a narrow tube, and d denotes the diameter of the connecting tube along which the temperature gradient exists. A , B, and C are specific constants for an appropriate gas.
0022-3654/80/2084-0589$0 1.OO/O
Experimental Section
0 1980 American
Chemical Society
590
The Journal of Physical Chemistry, Vol. 84, No. 6, 1980
Yasumoto
JC-
*
-'r P h o t o c o u p l e r
LED T L R l O 3 T L P B O l
Thyristoi SF5Fl I
I
It// L E D "
TLRlOJ
747
Figure 2. Switching circuit: (Tr, and Tr,) 2SC372, (TI2) 2SC503, (D,)
1S1661, (J, K, S, R, X, and Y) terminals. Figure 1. Schematic diagram of the apparatus: (A) Pyrex tube 40.2 mm in diameter, (B) capillary, (U) U-tube, (G and G') manometers, (U,) traps, (CJ taps, (Pt,) platinum needle electrode with the terminal J, (R2) platinum needle electrode with the terminal K, (L) terminal connected to mercury, (SI) mercury surfaces, (R) mercury reservoir, (X and Y) terminals.
long, and 5 mm thick. The U-tube was heated in an electric furnace to the preset temperature T1of 723,625, and 522 K controlled within f 3 K during a run. The temperature was measured with a chromel-alumel junction at the lower side in the box, and was approximately by 10 K higher than that at the upper. Room temperature T2 was maintained at about 293 K. The fluctuation of T2was less than h0.3 K during a run. Three kinds of glass capillary were used for the measurement. They were all 600 mm in length, but different (0.55, 1.12, and 2.04 mm) in diameter. The diameters were measured by the mercury filling method. The wide tube was approximately 600 mm in length, and 40.2 mm in diameter, which was measured by the water filling method. When the pressure in the system was lower than 3 torr, parts U1 and Uz were always cooled with ice to minimize the error due to the presence of mercury vapor. The mercury vapor drag effect due to these cooled parts was estimated with the equation which was proposed by Takaishi and Sensui,13and the effect was considered negligible. This estimation was also ascertained by comparing the values which were obtained by measurements with and without refrigeration. The two manometers, G and G', are essentially the same as those used by Meyer and Wade.14 This was previously improved by the present author,15 and has been further improved by using platinum needle electrodes, a modified heating system, and a wide U-tube, 35 mm in diameter, in this study. The manometer has an ordinary sensitivity of 2 X torr, and has an excellent advantage for measuring the absolute pressure of the gas. Details of the manometer and a switching circuit are shown in Figures 1 and 2, respectively. A constant reference height platinum needle electrode Ptl is sealed with a lime glass, and is fixed in one arm of the manometer. On the other arm a micrometer head is installed to measure the variable mercury column height. The head has graduations of 0.002 mm and a total travel of 25 mm with an accuracy of 0.002 mm over the entire range. The low end of the spindle of the head is joined together by silver solder with one end of a platinum needle electrode Pt2. In order to keep the height of the mercury surface S1automatically constant, the heater of a tungsten filament which was controlled by the switching circuit was used as a heating system. When the heater heats the nitrogen around it, the mercury surfaces S1 and S2 rise in the manometer. When the surface S1 makes an electrical
4
A717 Figure 3. NAND RS flip-flop: (Tr, and Tr,) 2SC372, (S and R) terminals.
contact with the electrode Pt,, a gate trigger current is diverted through the parallel path by a transistor Tr2,then the thyristor is turned off, and the heater current is then switched off as a result. The atmosphere cools the nitrogen, and the mercury surface S1 drops below the point of Ptl. Then, the thyristor is turned on to regenerate the cycle. The amplitude of the up and down oscillation of S1 was controlled within 0.1 mm by the heating system, and the period of the oscillation was approximately 8 s. Two phototransistors, LED (1) and (2), serve as a visual signal of the on-off contacts between Ptl and S1 and between Ptzand S2,respectively. By adjusting the micrometer, the on-off signal between Ptz and Sz can be made synchronous to that between Ptl and S1. The flip-flop circuit which is shown in Figure 3 was found useful for obtaining the highest sensitivity of 1 X torr of the manometer. The spaces above both mercury surfaces S1 and S2 were pumped down to 1 X torr, and the micrometer was carefully adjusted so that both LED (3) and (4) were turned on with a equal frequency, then the highest adjustment was attained. The initial reading was thus obtained. Absolute pressures can be measured directly by subtracting the initial reading from succeeding micrometer readings. The whole apparatus was evacuated to below 1 X torr, and then an appropriate amount of water vapor was admitted into the apparatus. When the U-tube was held at the temperature T1, parts U1and U2 at 0 "C, and the rest of the apparatus at T,, a pressure difference slowly developed across the U-tube and attained a stationary value in about 4 h due to the thermal transpiration of water vapor. Then, the thermal transpiration was calculated by using the measured values of P I ,P2, T1, and T2. It was plotted against X,as shown in Figure 4, where the pressure and diameter are expressed in units of torr and mm, respectively. The plotted points were found to lie almost on a single curve. When the experimentaldata were substituted into the Takaishi-Sensui equation, the best-fitting values for A , B , and C were obtained as follows: A = 1.5 X lo6.
The Journal of Physical Chemistry, Vol. 84, No. 6, 1980 591
Thermal Transpiration Effects for Gases
1 ,.o F
Capillary 0 5 5 0 m m in d i a m e t e r
l
\
0723K @
-....
P
.. -.
v
-I
C723K
\
fd625K
A522K
2 0 4 m m r d ameter 3 7 2 3 K El625K 3 522K
1
n
8522K
Ca(,illary
7 0.5r -
625K
I I 2 m m ir diameter
Capillary
\
% %
O L _ _ - L 10
\
-%A=.-
1 o-4 X = Pz.d /
10-~
7
.
\
lo-*
Torr-mrn .deg
-'
V
Figure 4. Thermal transpiration of water vapor.
F F.E
l'Oi
He O 7 7 J K
977K
Ne C 7 7 3 K ,
h77K
0773K
077K
Kr 0 7 7 3 K
@77K
Ar
Xe
B773K
a b s o l u t e method e U 7 7 K
7
7
"
10-~
10-~ X=Pz.d/T
: T o r r . m m . deg-'1
Flgure 6. Thermal transpiration of hydrogen, deuterium, oxygen, nitrogen, carbon monoxide, nitric oxide, methane, carbon dioxide, nitrous oxide, hydrogen sulfide, water vapor, hydrogen chlorkle, ammonia, and hydrogen bromide. The broken lines LY and represent the curves obtained for hydrogen and methane, respectively, under the condition of T i (673K) and T2 (room temperature) by Takaishi and Sensul, while 7 ,6, and 6 represent the curves obtained for oxygen, nitrogen, and methane, respectively, under the condition of T , (77K) and T2 (300 K) by Furuyama.
0195K
1 0 ~
10-4 i o
I
- a
X=Pz.d/i
: T o r r . mm.deg-']
Figure 5. Thermal transpiration of helium, neon, argon, krypton, and
xenon. The broken line LY represents the experimental curve obtained for helium under the experimental condition of T i (77K) and T2 (300 K) by Furuyam,a, while 10, 7,and 6 represent the curves obtained for neon, argon, arid krypton, repsectively, under the condition of T i (673 K) and T 2 (room temperature) by Takaishi and Sensui.
B = 1.0 X lo2, and C = 6.5 X 10. When the above values were used, a correction was made for thermal transpiration across the wide, 40.2-mm in diameter tube. Then, the values were determined as follows: A =: 1.5 X lo6 (torr mm deg-1)-2,B = 1.0 X lo2 (torr rnm deg -l)-l, and C = 6.2 X 10 (torr mm deg-')-lI2. Gases. In order to examine the adaptability of the Takaishi-Sensui equation, the effects for a variety of gases were measured for Tl > T2and Tl < T2. The equation was found suitable for explaining the results. For Tl > T2,the apparatus and the experimental procedure, which are the same as used for water vapor, were applied to the measurements. For TI< T,, a new IJ-tube was prepared, which was constructed of a capillary tube 350 mm long and 0.55 mm in diameter and a wide tube about 350 mm in length and 40.2 mm in diameter, and was dipped in liquid nitrogen. The gases which were used were supplied by the Takachiho Shoji co.,and they were sealed in respective glass vessels. The nominal purities of gases in vol % are as follows: helium, 99.999; neon, 99.99; argon, 99.999; krypton, 99.95; xenon, 99.9; hydrogen, 99.999; deuterium, 99.5; oxygen, 99.9; nitrogen, 99.999; carbon monoxide, 99.9; nitric oxide, 99.9; carbon dioxide, 99.99; nitrous oxide, 9%9;hydrogen sulfide, 99.0; ammonia, 99.5; hydrogen chloride, 99.5; methane, 99.95; hydrogen bromide, 99.8; acetylene, 99.6; ethylene, 99.8; ethane, 99.7; methyl chloride, 99.5; propane, 99.9; n-butane, 99.7; and isobutane 99.9. Methyl and ethyl alcohols of a spectrograde reagent of 99.5 vol % were used after distilling under a reduced pressure. The temperature T1was applied to these gases as follows: 773 and 77 K to helium, neon, argon, krypton, hydrogen, deuterium, oxygen, nitrogen, and carbon monoxide; 773 K to xenon, carbon dioxide, and water vapor; 683 K
X=Pz
*
.
d / T [ T o r r rnm deg-'1
Figure 7. Thermal transpiration of acetylene, ethylene, ethane, rnethyl
alcohol, methyl chlorie, ethyl alcohol, propane, n-butane, and isobutane.
to nitric oxide, nitrous oxide, hydrogen sulfide, hydrogen chloride, and hydrogen bromide; 623 and 77 K to methane; 623 K to ethane, methyl chloride, propane, n-butane, and isobutane; 583 K to methyl and ethyl alcohols; 513 K to acetylene and ethylene; and 403 K to ammonia. The resultr, are plotted in Figures 5-7. As is seen, points referring to different temperature conditions lie also on respective smooth curves. To examine the reliability of the data which were obtained, an absolute method4 was applied to some gases. The data obtained by this method were also plotted in Figures 5 and 6. The agreement of these data with those obtained by the relative method was sufficient in the range of X applied. Then, the values for A , B, and C in the Takaishi-Sensui equation were determined. They are summarized in Table I, together with those obtained by Takaishi and SensuilO and Furuyama.12 The experimental curve for helium agreed as a whole with the curve obtained by Furuyama, and the curve for neon agreed well with that obtained by Takaishi and Sensui. The curves for argon, krypton, oxygen, and nitrogen agreed well in the region of larger values of X with those obtained by the other authors. However, in the region of smaller values of X the curves obtained by the present author stood apart from theirs. The curve for hydrogen was approximately parallel to and situated lower than that obtained by Takaishi and Sensui. The curve for methane agreed well in the region of larger values of X with the curve obtained by Takaishi and Sensui, but, however, it deviated gradually from their curve in the
592
The Journal of Physical Chemistry, Vol. 84, No. 6, 1980
TABLE I: Values of the Constants in the Empirical Equations
gas He Heb Ne Nea Ar Ara Kr Kr" Xe H2 HZ a D2
1.0 1.1 1.6 2.65 9.0 10.8 15 14.5 22 2.0 1.24 2.5
0 2
10
OZb
NZ NZb
co cob
NO NO COZ NZO HZS NH,C HC1 CH, CH,a CH,b H Br CZHZ CZH, CZH, CH,OH CH3Cl C,H,OH C3H8 n-C'lH,o i-C,H,o a
10-5 A , (torr m m deg-')-'
Reference 1 0
8.6 10 10 10 10
10 9.7 17 17 17 15 15 15 14.5 16 22 22 22 30 30 35 40 40 50 50
IO-ZB, (torr mm deg-l )- 1 4.0 1.1 5.0 1.88 7 .O 8.08
1.0 15.0 5.0 6.3
8.00 3.1 7.0 17 7.6 20 7.6 20 7.6 18 8.0 8.0 8.0 1.0 1.0 1.0 15.0 22 5.0 5.0 5.0 1.5 1.5 3.0 6.0 6.0 6.5 6.5
Reference 12.
Yasumoto He Ne
C,
(torr mm deg-'1 ) - I / 2 16 22 25 30.0 50 15.6 70 13.7 90 20 10.6 30 38
10 40 8 40 8 40 9 64 64 64 62 62 62 13 16 80 80 80 90 90
:507
P
A
NH3 0 HCI
HBr CZHZ
A
CzH4
Ar ; I
Hz0
Hz 0 02 Q
Nz0 E
0
4
i
1
0
E
E
0
HzS 0 CZHB
N2
k 25'
c
CHICI
u
0 U
1000
500
CaHsOH CH IO
1500
2000
(C*)* (A? Flgure 8. Plot of A vs. (cT*)*.
f
1501
2
4
6
6 (A) Flgure 9. Plot of C vs. u. Symbols denote the same gases as are
represented by those in Figure 8.
100 120 120 150 150
Estimated values.
region of smaller values of X . It disagreed with the curve obtained by Furuyama. Discussion It is considered that thermal transpiration values, Pl/Pz, will be represented as a function of Xld, where X denotes the mean free path length of a molecule, which is expressed as X = kT/(2ll2 ra2P),where u designates the diameter of a molecule. This formula has the variables P and T , which vary from P1to Pz and from T1to T,, respectively, in the connecting tube along which the temperature gradient exists. However, a description of the exact functional form for X by using them is very difficult in this case. For this reason only an approach which uses the empirical equation is practical. According to the estimation which was proposed by Takaishi and Sensui,lothe values for A , B, and C should be proportional to ( o ~ )u2, ~ ,and a, respectively. However, the experimental results which were obtained by the above authors were different from their own estimation. This was caused by their narrow range of a. As shown in Figure 8, the values for A were roughly proportional to ( u ~ )except ~ , for those of ethyl alcohol, propane, and butane, where the diameter a is expressed in unit of A. The value of u is calculated from the viscosity data at 293 K with the use of the well-known formula, = ( m k T / r ) 1 / 2 ( l / r a 2 ) , where q, m, and k denote the viscosity of a gas, the mass of the molecule, and Boltzmann's constant, respectively. The points for ethyl alcohol, pro-
X Flgure 10. Curves obtained for helium, hydrogen, nitrogen, and water vapor.
pane, and butane deviated from the line which was obtained. The reason for the deviation is not as yet understood. As shown in Figure 9, a plot of C vs. u lies almost on a linear line. It is found that the value of C becomes large with increasing in the value of u. The equation for C was proposed before by Takaishi and SensuilO as follows: C = (110/0) - 14. Their equation states that C becomes small with increasing CT.This contradicts the experimental results which were obtained by the present author. The equations of the lines which were obtained for A and C are expressed as follows: A = 3 9 ( ~ X ~ )lo2 ~ (torr mm deg-1)-2= 0.22(a2)2 (Pa mm deg-1)-2 and C = 28 a - 56 (torr mm deg-')-liZ = 2.4a - 4.8 (Pa mm deg-1)-1/2. As is known from the Takaishi-Sensui equation, the effect of constant A is more important than B and C on thermal transpiration at higher pressures. However, constant C becomes dominant at lower pressures. The relation between B and a was not determined from this experiment. However, the numerical values of B lay between 100 and 800 in Table I. Then, assuming the value of B to be 500 (torr mm deg-')-l, introducing the function f(X) = 1/(AX2+ BX + CX1/2+ l),where A and C are the values which were calculated with the equations of the above lines, plotting
J. Phys. Chem. 1980, 84, 593-598
TABLE 11: Calculated Values of A and C
10-5~, (torr mm deg-')-'
llas
-.-
He Ne Ar Kr Xe H, 0, N,
co NO co L
N,O H,S 3"
HCI. H,O CH,, HBr C A C;H[; C,H[, CH,,OH CHiCl C,H,OH C,H, n-C.,H,, i-C,H,,
0.869 1.75 6.76 11.5 21.4 2.17 6.47 7.63 7.45 7.08 17.0 17.2 18.5 14.2 14.9 15.6 11.5 22.5 20.9 22.9 29.6 30.2 37.5 48.5 57.4 88.5 88.5
C,
(torr mm deg-1)-1'2 4.83 16.5 45.6 60.1 79.6 20.5 44.5 48.7 48.1 46.8 71.9 72.3 74.6 66.3 67.7 69.3 59.9 81.3 78.7 81.9 91.0 91.7 99.9 110 117 137 137
593
well with the respective experimental curves, and the curves obtained for oxygen, nitrogen, carbon monoxide, nitric oxide, carbon dioxide, nitrous oxide, hydrogen sulfide, ethane, methyl and ethyl alcohols,propane, n-butane, and isobutane agreed as a whole with the respective experimental curves. However, the curves obtained for water vapor, hydrogen chloride, and ammonia were approximately parallel to and situated lower than their experimental curves. The curves obtained for the rare gases did not agree with the respective experimental curves. The values of A and C calculated for the gases are summarized in Table 11. Some representative results are shown in Figure 10. Acknowledgment. The author thanks Professor Emeritus Nobuji Sasaki, Kyoto University, and Professor Tetsuo Takaishi, Toyohashi University, for their interest and encouragement in this work. References and Notes (1) M. Knudsen, Ann. Phys., 31, 205, 633 (1910). (2) I. Langmuir, J. Am. Chem. Soc.,40, 1361 (1918). (3) F. C. Tompkins and D. E. Wheeler, Trans. Faraday Sac., 29, 1248 (1933). (4) S. Chu Liang, J . Appl. Phys., 22, 148 (1951). (5) J. M. Los and R. R. Fergusson, Trans. Farachy Soc., 48, 730 (1952). (6) G. L. Kington and J. M. Holmes, Trans. Farachy Soc., 49, 417 (1953). (7) M. J. Bennett and F. C. Tompkins, Trans. Faraday Soc., 5:3, 185 (1957). (8) A. J. Rosenberg and C. S. Martei, Jr., J. phys. Chem., 62,457 (1958). (9) H. H. Podgurski and F. N. Davis, J. fhys. Chem., 65, 1343 (1961). (IO) T. Takaishi and Y. Sensui, Trans. Faraday Soc., 59, 2503 (1963). (1 1) T. Edmonds and J. P. Hobson, J. Vac. Sci. Techno/.,2, 182 (1965). (12) S. Furuyama, Bull. Chem. Soc. Jpn., 50, 2797 (1977). (13) T. Takaishi and Y. Sensui, Vacuum, 20, 495 (1970). (14) D. E. Meyer and W. H. Wade, Rev. Sci. Insfrum., 33, 1283 (1962). (15) I . Yasumoto, Shinku, 13, 232 (1970).
the function against X for all the gases used, and comparing the pilotted curves with the experimental curves, we obtained interesting results shown below. The curves obtained for hydrogen, methane, hydrogen bromide, acetylene, ethylene, and methyl chloride agreed
Characterization of Micellar Solutions Using Surfactant Ion Electrodes Kalldas M. Kale, E. L. Cussler, and D. F. Evans" Department of Chemical Engineering, Carnegie-Melion University, Pittsburgh, Pennsylvania 152 13 (Received February 16, 1979) Publication costs assisted by the National Institute of Health
Surfactant ion electrodes were used to investigate the dimerization, aggregation, and micelle formation occurring at 25 "C in aqueous solutions of sodium dodecyl sulfate, decyltrimethylammonium bromide, tetradecyltrimethylammonium bromide (TTAB),and orange I1 (4-[ (2-hydroxy-l-naphthalenyl)azo]benzenesulfonicacid monosodium salt) as a function of added electrolyte. The surfactant electrodes, which contained a liquid membrane ion exchanger, permitted a direct determination of the surfactant monomer activity. Analysis of these data gave an association constant of lo00 for orange 11, an estimated fractional charge on the DTAB micelle of 0.78, a dimerization constant of 400 (L/M) for TTAB, and a second break above the commonly accepted critical micelle concentration for sodium dodecyl sulfate, a break which may result from an ordering of the micelles. Introduction Many experimental techniques for studying micellar systems such as light scattering or sedimentation yield information primarily about aggregates. Other methods such as osmotic pressure or conductance give data which combine contributions of micelles, surfactant monomers, and counterions. In contrast, surfactant ion electrodes provide a direct measure of the surfactant monomer activity done. Above the critical micelle concentration (cmc), such measurements allow determination of the activity of the surfactant monomer in equilibrium with the micelle. When used with other ion electrodes specific for the 0022-3654/80/2084-0593$0 1.OQ/O
counterion, surfactant ion electrodes provide data which are difficult to obtain by any other technique and thus constitute an unexploited method for studying micellar solutions. This paper examines the behavior of four micellar systems in order to demonstrate how premicellar dimerization, aggregation processes, and micelle reorganization can be studied with surfactant ion electrodes. This examination includes a dye, two cationic detergents, and an anionic detergent. Experimental Section The surfactants, sodium dodecyl sulfate (SDS) (B.D.H. @ 1980 American Chemical Society
