J . Phys. Chem. 1990, 94, 4755-4756
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COMMENTS -3
Conductivity of Microemuisions: Refinement of Charge Fluctuation Model
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Sir: Recently, Eicke et a1.l explained the conductivity of microemulsions on the basis of the charge fluctuation model (CFM) by taking into account the Born energy of charging the spheres in a dielectric medium. This theory applies to microemulsions of relatively low water content in which the continuous phase is a nonconductive oil, and the percolation does not take place. The fluctuation model considers the statistical distribution of charges over the microemulsion droplets. As a consequence, some droplets are negatively charged, some are neutral, and others are positive. The total charge is zero; Le., the microemulsion dispersed phase is electroneutral. The conductivity of microemulsion will depend on the number concentration and charges of droplet units, on their size, and on the viscosity of the medium. The simple fluctuation theory overestimates the conductivity by approximately 2 orders of magnitude. The introduction of the Born energy, which suppresses the charge fluctuations, results in realistic values of the conductivity. According to the original expression derived by Eicke et aI.,l the “specific conductivity” (conductivity/volume fraction of microemulsion droplets) is inversely proportional to the cube of droplet radius. In the Aerosol OT-water-isooctane microemulsions, an excellent agreement between the theory and experiments was found for droplets with radius above 7 nm. Below this limit the experimental data are significantly lower than theoretical predictions. In addition, for radius r < 2.7 nm the trends are opposite; theory predicts an increase in specific conductivity by lowering the size of droplets while the experiments showed an abrupt decrease to extremely low conductances. The aim of this Comment is to propose a refined theoretical treatment by distinguishing the Born radius of droplets from the Stokes radius. It will be demonstrated that such an approach improves the concordance between the theory and experiments over the whole range of sizes of microemulsion droplets. Microemulsion droplets consist of a water core (pool) and a shell of surfactant molecules and are dispersed in the oil phase. The Born radius ( r B )corresponds to the water part of a microemulsion droplet because the charge is distributed only in this space. The radius of the whole droplet (rd)is essentially the Stokes radius determining the friction coefficient of the moving units. This parameter can be determined by means of the dynamic light scattering method via diffusion coefficient. The thickness of surfactant shell ( 1 ) causes a significant difference in rB and rd, especially for small droplets: rd = rB
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(1)
Consequently, in the original work by Eicke et al.,I one should replace r in their eqs 2 and 3 by rd and by rB in eq 8 . The basic relationship describing quantitatively the conductivity, K , of microemulsions is then
where C i s the droplet number concentration, k Bthe Boltzmann constant, T the thermodynamic temperature, to the permittivity of vacuum, c, the relative permittivity of the medium around the water core of droplet, and 9 the viscosity of the oil phase. (1) Eicke, H.-F.; Borkovec, M.; Das-Gupta, 8. J . Phys. Chem. 1989, 93, 314.
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Figure 1. Dependence of specific conductivity on the radius of microemulsion droplets as determined by dynamic light scattering for the system AOT-water-isooctane. Experimental data (0)were taken from ref 1. Dashed line represents predictions according to the original work by Eicke et al.’ Full line was calculated on the basis of eq 4. The following values were used: T = 298 K,cr = 1.96, Q = 0.47 CP = 4.7 X IOJ Pa s, and I = 2.1 nm.
The volume fraction of microemulsion droplets 4 is related to the radius of the whole droplet (rd) and to the droplet number concentration (C) by
4 = 4rd3rC/3
(3)
Equations 1-3 result in (4)
It is obvious that ( 4 ) when plotted vs rd has a maximum and that it follows the pattern of the experimental results. Equation 4 can be used to predict the specific conductivity K / $ without adjusting the values of various parameters. The viscosity q applies to the oil phase and could be easily measured, and radius rd is obtainable by dynamic light scattering. The thickness of the shell (0 should be approximately equal to the radius of droplets in the absence of water, and the relative permittivity tr corresponds to the medium surrounding the water core. It is approximately equal to that of oil. In our calculations we have used the same values of these parameters as Eicke et al.:I q = 0.47 cP, t, = 1.96, T = 298 K. These authors find the droplet radius in the absence of water to be 2 nm. In our calculations the value of 1 = 2.1 nm was found to better fit the experimental conductivity data. The difference of 0.1 nm may well be due to experimental errors or imperfections of the model. The length of surfactant (AOT) chain was estimated2 as 1.24 nm, which is considerably lower than the thickness of surfactant shell as obtained in this study. This discrepancy may be explained by considering the ”association” (intermingling) of isooctane molecules with the tails of surfactant chains resulting in a higher value of the effective Stokes radius. However, such a hypothesis would require further studies. Figure 1 represents the original experimental data by Eicke et aI.,l the prediction based on their simplified treatment of size parameters (re = r d ) and our calculations based on eq 4. The agreement of experiments with the improved version of the charge (2) Eicke, H.-F.; Shepherd, J. C. W.Helu. Chim. Acra 1974, 57, 1951.
0022-3654/90/2094-4155$02.50/0 0 1990 American Chemical Society
Additions and Corrections
4756 The Journal of Physical Chemistry, Vol. 94, No. 1 1 . 1990
fluctuation model is obvious. It is really surprising to obtain such an agreement especially since no parameters were adjusted to fit the experimental data. This finding opens the possibilities of various applications of the simple and inexpensive conductivity method. For example, by fitting the experimental conductivity data, one can obtain all parameters of interest (C,tr, rd, rB,0 for a given system. On the other hand, the applicability of the charge fluctuation concept seems to be verified and could be extended to other problems such as the distribution of electrophoretic mobilities of colloid particles.
Laboratory of Physical Chemistry Faculty of Science University of Zagreb, P.O. Box 163 41001 Zagreb, Yugoslavia Centro Ricerche e Sviluppo Montefluos, 20021 Bollate, Italy
1990, Volume 94
Linda R. De Young and Ken A. Dill*: Partitioning of Nonpolar Solutes into Bilayers and Amorphous n-Alkanes. Page 805. Figure 3 should be replaced by the following corrected figure.
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Alba Chittofrati
Received: September 11, 1989; In Final Form: December 18, 1989
ADDITIONS AND CORRECTIONS
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Nikola Kallay*
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Figure 3. Dependence of the mole fraction bilayer/water partition coefficient of hexane on temperature at various concentrations (mole percent) of cholesterol in the membrane: DLPC with ( 0 )O%, ( 0 )20%, and (A)40% cholesterol; DMPC with ( 0 )0%, (W) IO%, (0) 20%. (0) 30%,and (A)40% cholesterol; and DPPC with ( 0 )0%, ( 0 ) 20%, and (A) 40% cholesterol. Hexane partitioning increases with increasing temperature.
