J. Phys. Chem. 1993,97, 9073-9074
9073
COMMENTS Comment on "Unusual Thermal Diffusion of Ionic Surfactants" N. Takeyama' and K. Nakashima 10.0
Department of Applied Chemistry, Faculty of Science and Engineering, Saga University, Saga 840, Japan Received: April 5. 1993; In Final Form: June 24, I993 In an earlier paper Leaist and Hui' successfully dealt with the Soret effect of aqueoussodium dodecyl sulfate (NaDS), a micelleforming electrolyte. The results were analyzed by using the chemical equilibrium model for micellization.2 We agree with the main features of their discussion, except for the importance of the Wagner effect:3s4the contribution to the heat of transport of NaDS, Ht,made by the change in enthalpy, AH, of the micelle formation
n D S + qNa+ -t NaqDSiV)
(1) where n is the aggregation number and q is the average number of sodium counterions bound to a micelle. Leaist and Hui did not include the Wagner effect, because the standard enthalpy change of reaction 1 is known to be very small. Here we will show that the Wagner effect might be important near the critical micelle concentration (cmc), 0.008 mol kg-1 at
25 'C. According to the theory of the Wagner effect by Agar and Lin? Ht is expressed as follows:
v7' t 0.01
"0
Figure 1. Heat of transport Hs of aqueous sodium dodecyl sulfate at 25 OC: (0)measured by Leaist and Hui (Table I of ref 1); curve (1) drawn by Leaist and Hui's data in ref 1; curve (2) calculated by taking into account the Wagner effect with LW= 6.5 kJ mol-' by means of eq 2. The limiting diffusion coefficient of DS-,D- = 0.72 X 10-9 m2 s-1 at 25 O C cited in ref 1, is corrected by 0.61 X 1 V m2 s-I described by Leaist in ref 2. cmc 1.0
4 I
I I-t1
(2)
I
where tl is the fraction of total NaDS diffusing in monomeric form, t, (= 1 - t l ) is that in micellar form, HI*is the heat of transport of the monomer, H,* is that of total n-mer, 8' is the differential distribution coefficient of the monomer to total NaDS in molality, which is defined by (dml/dm)T at a constant temperature Tin terms of the molality of the monomer, ml, and the total molality of NaDS, m, and AH is the change in enthalpy of reaction 1. Here AH equals TAS with the change in entropy of reaction 1, AS. This comes from the equilibrium condition of AG = 0 for the change in the Gibbs energy of reaction 1, The Wagner effect is in the last term on the right-hand side of eq 2. In Figure 1, the measured points of H* by Leaist and Hui are shown by open circles in the range of concentration under consideration. They find that Ht remarkably decreases from HI*= 11.5 kJ mol-' below thecmc to H,*/n= 1.9kJ mol-' above the cmc. The broken curve (1) is calculated by Leaist and Hui's procedure with using numerical data described therein.1v2 The main problem is in disagreement between the open circles and the broken curve (1) above the cmc. Prior to the explanation of the solid curve (2), we present Figure 2, in which the broken curve of rl and the lambda-shaped solid curve of (ti - 8') are drawn against m. The curve of t~ versus m obviously yields the sharp decrease of H+ at the cmc in Figure 1. In addition to this fact, we pay attention to the curve of (tl - 81) versus m, starting from the cmc through the maximal peak at 0.008 35 mol kg-1 followed by the concave curve in the higher concentration. With the aid of eq 2, we may evaluate the contribution of the last term on the right-hand side by using the calculated values of (tl - 81) to know the value of AH = 6.5kJ mol-' on an average. Although the standard enthalpy of micellization of NaDS is very small, AH,* = 2 (Flockhart and Ubbelohdes), -0.04 (Goddard and Bensod), and 0.2kJ mol-' (Flockhart'), the valueof AHremains unknown. In this regard, we should consider some contribution
I
H* = [tlH1* + tn(Hn*/n)l-
( t l - Bl)m
0.02
m / m o l kg-1
I
I
m /mol kg-1
Figure 2. Calculated curves of t l and (tl - 81)versus m: curve of t1 drawn by eq 7 of ref 1; curve of ( t l - 81) drawn by eq 7 of ref 1 and eq 12 of ref 2 on the scale of total molality, using Leaist and Hui's data in ref 1 and the corrected value of D- = 0.61 X 10-9 m2 s-I at 25 OC.
of nonideal enthalpy of micellization under the condition of AH = TAS. Assuming AH = 6.5 kJ mol-', we can draw the solid curve ( 2 ) in Figure 1 by using eq 2 with the values of HI*and H.*/n described above. This curve is fairly fit to the measured points of H* by Leaist and Hui.' Consequently, the maximal value of the Soret coefficient, om, = 48 X 10-3 K-1 at 0.012mol kg-*calculated by Leaist and Hui,' decreases to 34 X 10-3 K-1 at 0.0133 mol kg-1, which is nearer to their measured value of 32.0 X 10-3 K-1 at 0.010mol kg-l. Although we may point out that the experimental results near the cmc reported by Leaist and Hui can be explained by the contribution of the Wagner effect just above the cmc, the essence of the present problems clearly exists in the validity of AH = 6.5 kJ mol-L used, together with its nature, and also in the remarkable diminution of Ht at the cmc, that is approximately attainable to H I * - (H,*/n) = 9.6kJ mol-'. These problems should be clarified by taking into account ion-ion interactions, inclusively of hydrophobic interaction.
0022-3654/93/2097-9073S04.00/0 Q 1993 American Chemical Society
9074 The Journal of Physical Chemistry, Vol. 97, No. 35, 1993 References and Notes
Additions and Corrections (4) Agar, J. N.; Lin, J. J. Solution Chem. 1987, 16, 973.
(1) Leaist, D. G.; Hui, L. J . Phys. Chem. 1989, 93, 7547. (2) Lcaist, D.G. J. Colloid Inrerface Sci. 1986, 111, 230. (3) Wagner, C.Ann. Phys. 1929, 3,629.
( 5 ) Flockhart, B. D.; Ubbelohde, A. R. J. Colloid Sci. 1953, 8, 428. (6) Gcddard, E. D.;Benson, G. C. Can. J. Chem. 1957, 35, 986. (7) Flockhart, B. D.J. Colloid Sci. 1961, 16, 484.
ADDITIONS AND CORRECTIONS
1992, Volume 96 M. L. McKee,' M. E. Squillacote,' and D. M. Stanbury': Ab Initio Investigationof Dihydrogen Transfer from cis- 1,2-Diazene Page 3272. An error was committed in converting units in the last paragraph of the section Experimental Correlations. The gas-phase rate constant given as 5 X 10s atm-1 s-1 should be corrected to 8 X lo2atm-I s-l, and the corresponding AG*of 9.7 kcal/mol should be corrected to 13.5 kcal/mol. These corrections lead to closer agreement between theory and experiment and thus actually strengthen the conclusions of the paper.
