Tracer Electrophoresis. II. The Mobility of the Micelle of S(3)

48

D.

STIO'rER AND

I<.J. MYSELS

Vol. 59

which connects the first, or Henry, terms of the two series. For higher potentials, when nonlinear terms become important, a correction factor must be introduced. Appendix I gives a method of estimating this correction factor. The results thus obtained from[ B~~+are I, also shown in Fig. 3 as Qr. They are some 10% higher than Q~~ and even somewhat higher than QOverbeek. The average f potential and the total particle charge are unaffected by the electrophoretic motion under the assumptions of the Booth theory. Hence the assumption of an undistorted spherical double layer in t8he calculation of Qf, cannot cause the difference between&Booth and Qr. The discrepancy must therefore lie in the neglected higher terms of the series. The series for converges faster than the one for Q. It appears therefore that the error produced by neglecting higher terms is lesser in calculation of from u than Q from u. Since the calculation of Q R=&ea/aDkT (4) from{ involves few inaccuracies we feel that Qf (for R= 1 and a in cm., Q= 0.1401a X lo8at 25" should be closer to the truth than&Booth. in water). This inverted series can be used readily As already mentioned,{ is not sensitive to in calculations. Figure 3 shows the values it yields changes in KU, but this is no longer true for Q which upon taking successively into account the first. changes by about 1% when K changes by 1% or a term (QHeruy), the second (QOverbeek) and the by 0.5%. third (&Booth). Comparison with Other Calculations of Charge. -When ion atmosphere effects are negligible, the mobility of an ion is equal to the force exerted by its charge in unit field divided by its friction factor. The latter may be calculated

either from Stokes law or by multiplication of the friction factor of the monomeric ion by the cube root of the degree of association. These two calculations give results within 20% of each other but the values of the charge thus calculated for our case decrease (from 10.4 and 8.7 to 8.7 and 7.3, respectively) instead of increasing as the concentration of NaCl increases and amount to only 50 to 25% of Qr. This emphasizes the danger of considering micelles as ideal electrolytes even under conditions of infinite dilution with respect to micelles. From the slope of light scattering plots one can compute a charge p which is an effective thermodynamic charge.IS For our case the charge p is essentially constant at about 14." The ratio of IO!i Q C and p gives an indication of the activity coefficients to be expected in these solutions. The Degree of Ionization.-The micellar charge can be also expressed as a degree of ionization, a= Q/n, where n is the number of anions in the micelle. CY is slightly less sensitive to errors in a I 1 I I 0 than Q since a is related directly to n3. Summary of Results.-Table I summarizes the properties of micelles of sodium lauryl sulfate a t the CMC as they emerge from the present discussion. It may be noted that while both the size and charge(18) J. T. Edsall, H. Edelhoch, R. Lontie and P. R. Morrison, J . JOURNAL, 68, Am. Chem. Soc., 73, 4641 (1950): K. J. Mysels, THIS 303 (1954).

series converges somewhat regularly, which seems to be the case here. The inverted series should therefore give quite reliable results. We have also investigated the effect of changing q* and KQ on[Booth. A 10% change of q* changes{Booth by about 0.7%. This shows that our assumption of constant X values does not introduce any significant error. A 10% change of KU shifts{Booth by Only 0.1%. Therefore, our computation of K cannot introduce any significant error. Furthermore, moderately large variation in a, i e ., in the radius of curvature of the micelle surface, is immaterial. Hence, the spherical model of the micelle can be replaced by an ellipsoidal one without changing the calculated[ potential significantly. The Micellar Charge by Booth's Method.-The mobility can also be expanded in terms of the charge Qe of the particle. Booth has computed the coefficients of such a series up to the term in the case of symmetrical electrolytes. This series is similar to that of u in[, equation 1. However, the numerical solution is more difficult. We have inverted it and obtained a series of the same form as ( 2 ) with stars omitted from X", Y* and Z*, and with Cb0 replaced by

spectively, in terms of u is different. It is therefore of interest to compare them more closely. The Micellar Charge from[ Potential.-For low potentials the relation between the charge Q and the[ potential is given byR= (1

-k

K~)@O

(5)

~

t

i

~

.

.

4 0

Jan., 1955THEC A L C U L A T I O Nmxaa

MOBILITY OF MICELLE OF SODIUM LAIJRYL SULFATETABLE Immoles/l.

O F Z E T A P O T E N T I A L A N D C H A R G E OF x 104, a, nb cm.2v.-Isec.-I em. X 10-8

4925'

MICELLES OFM a

SODIUM L.4URYL sULF.4TE AT{Booth,

CMC,'

mv.

4.55 21.5 8.12 80 89 01 5.29 22 1 4.26 3.84 23.0 995 .03 3.13 3.63 23.4 .05 2.27 1045 3.42 24.0 .1 1.46 112" Best line of reference 5. * Degree of association, reference 11. hj,drtztion layer. Degree of ionization= Qr/n.0

101.2 0.61 92.3 0.86 80.9 1.32 75.0 1.69 68.3 2.40 Hydrated radius from n, with

Qt a'j 22.9 0.28; 25.1,281,285 28.5,295 30.9 36.3 .324 density 1.14 and 1.5 A".

increase upon the addition of salt, the degree of ionization remains constant within the uncertainty of the determination. Structural Consequences.-In this section we shall assume that the polar heads of the anions are distributed uniformly over the spherical surface of the micelle. This is equivalent to assuming an essentially liquid interior of the micelle. However, a more highly organized micelle, in which the polar heads are closer together, would only make the argument more cogent. The n charges of all the anions, or the nativ …… 此处隐藏：7448字，全部文档内容请下载后查看。喜欢就下载吧 ……