Sodium

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Langmuir 2001, 17, 278-287

Interpretation of the Activity of a Hydrotrope in Lecithin/ Sodium Xylenesulfonate/Water Microemulsions Ge´za Horva´th-Szabo´* Department of Colloid Chemistry, Eo¨ tvo¨ s University, P.O. Box 32, H1518 Budapest 112, Hungary

Stig E. Friberg† Chemistry Department, Clarkson University, Potsdam, New York 13699-5810 Received October 21, 1999. In Final Form: August 22, 2000 Activity changes of sodium xylenesulfonate (SXS) in lecithin/SXS/water microemulsion phase were determined by equilibrating it with the SXS/water solution through a semipermeable membrane, which retained the lecithin while the water and SXS were free to move. The activity of the SXS in the microemulsion phase was calculated from its equilibrium concentration measured in the SXS/water phase. The activity changes were interpreted by both the surface excess approach and Hall’s thermodynamic description. The calculation of the adsorbed amount of SXS took the electrostatic exclusion effect into consideration. Combining the microemulsion with water leads to the formation of vesicles. A relation between the size of these vesicles and the composition of the microemulsion droplets is suggested by considering a depletion effect.

Introduction There are two main approaches in the description of the properties of microemulsions. The first approach regards them as a two-phase system and uses the phase equilibrium method for their description,1-3 whereas the second approach traces their origin back to the molecular interactions and uses the methods of the thermodynamics of multicomponent solutions.4,5 The properties of interfaces play a significant role in both of the descriptions and numerous contributions have been made investigating the composition and structure of these intermediate regions.6 It follows from these two descriptions that the essential role of the accumulation of surface-active molecules at interfaces may be described either in terms of adsorption or association. Because microemulsions are in thermodynamic equilibrium,4 it is necessary to use equilibrium measurements for the experimental investigation of this adsorption (mentioning here only one of the thermodynamic terms), because otherwise additional assumptions are necessary for the interpretation of the results. Surface-active molecules also play an important role at vesicle formation. Vesicle formation has been observed when lecithin/sodium xylenesulfonate (SXS)/water microemulsions were diluted by water, resulting in compositions within the microemulsion/lamellar-liquid-crystal two-phase region.7 Because these vesicles are not equi* To whom correspondence should be address. E-mail: ghszabo@ usa.net. † Permanent address: 641 Spring Hill Estates, Eminence, KY 40019. (1) Overbeek, J. Th. G. Faraday Discuss. 1978, 65, 7. (2) Prince, L. M. Emulsions and Emulsion Technology; Marcel Dekker: New York 1974; Part I, Chapter 3, p125-77. (3) Ruckenstein, E.; Krishnan, R. J. Colloid Interface Sci. 1980, 76, 201. (4) Danielsson, J.; Lindman, B. Colloid Surf. 1981, 3, 391. (5) Zemb, T. N.; Hyde, S. T.; Derian, P. J.; Barnes, I. S.; Ninham, B. W. J. Phys. Chem. 1987, 91, 3814. (6) Biais, J.; Clin, B.; Lalanne, P. In Microemulsions: Structure and Dynamics; Friberg, S. E., Bothorel, P., Eds.; CRC Press: Boca Raton FL, 1987; p 1. (7) Campbell, S. E.; Zhang, Z.; Friberg, S. E.; Patel, R. Langmuir 1998, 17, 590.

librium structures, the description of the different kinetic processes related to the dilution is necessary to understand their formation. This description should involve the thermodynamic characterization of the initial and final states of this dilution process, as well as the characterization of the structures present in these states. The target of the present contribution is 2-fold. First, the thermodynamic characterization of the initial state of the vesicle formation by the determination of the activity of SXS in the lecithin/SXS/water microemulsion phase diagram within the concentration range next to the microemulsion/lamellar-liquid-crystal two-phase region. Second, the determination of the SXS content of the microemulsion droplets from the activity data. To obtain the SXS content of the droplets, the SXS activity is explained by the above-mentioned two main approaches: (i) on the basis of the two-phase model, where the classical formalism of the adsorption description is used; and (ii) on the basis of a thermodynamic theory developed by Hall, which has been applied successfully for micelles.8 The amount of the SXS adsorbed on the surface of the microemulsion droplets is calculated from both models, and information is obtained for the composition of the microemulsion droplets in the initial state of vesicle formation. This composition is used for the interpretation of the vesicle sizes. Materials and Methods Materials. Materials is included methanol, anhydrous, 99.8% (Aldrich, Milwaukee, WI); diethyl ether, 99%, anhydrous (Aldrich); acetone, 99.9% HPLC grade (Aldrich); lecithin, L-alfaphospatidylcholine (egg lecithin, grade purified for intravenous injection, Kabi, Sweden); n-heptane, HPLC grade (Fisher, Loughborough, UK); and distilled water; SXS, containing less than 9.5% sodium sulfate (Aldrich). The SXS was recrystallized from methanol/ether and acetone/water mixtures. The detailed process was published elsewhere.9 Regenerated cellulose mem(8) Hall, D. G. J. Chem. Soc., Faraday Trans. 1 1981, 77, 1121. (9) Horva´th-Szabo´, G.; Friberg, S. E. J. Colloid Interface Sci., submitted for publication.

10.1021/la9913912 CCC: $20.00 © 2001 American Chemical Society Published on Web 12/29/2000

Hydrotrope in Lecithin/SXS/Water Microemulsions

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branes (CelluSepTM, molecular weight cut off (MWCO) 60008000, and AmiKa Corp. MWCO 500) were used for the dialysis. Refractive Index Measurements. An Abbe-refractometer was used for the determination at 25 ( 0.1 °C. Light Scattering Experiments. The static light scattering of the samples was determined by a Brookhaven Instrument System with a Lexer-laser (model 85) operating at a wavelength of 514.5 nm at 25 ( 0.1 °C. The intensities at 90° were referenced to that of the benzene. Partial Molar Volume Determination. An A-PAAR DMA60 instrument with 601 cell at 25 ( 0.002 °C was used for the highprecision density measurements of SXS solutions. The partial molar volume was calculated from the density data. The detailed procedure was published elsewhere.9 Activity Determination of SXS in Water Solution. The vapor pressures of SXS/water solution were measured with a VAPRO 5520 type vapor pressure osmometer (Wescor Inc., Logan, UT) at 25 ( 1 °C. Prior to the experiment, the instrument was calibrated with NaCl solutions using their activity data.10 The detailed procedure was described elsewhere.9 UV-Vis Adsorption Measurements. An HP8452A photometer was used. The concentration of the SXS was calculated with a calibration curve based on the light absorption of SXS solution at the 268-nm peak. Activity Determination of SXS in the Microemulsion. A compartments of a two-compartment system containing microemulsion (lecithin/SXS/water) in compartment R and electrolyte (SXS/water) in compartment β were separated by a semipermeable membrane permeable only for the electrolyte and solvent. The establishment of osmotic membrane equilibrium means that the chemical potentials of both the solvent (1) and electrolyte (2) are identical in the two compartments. Mathematically, this is expressed by the following equation for the electrolyte: 0

R

R

R

0

0

µ2 + RT ln a2 + (P - P )V2 ) µ2 + RT ln a2 + β

(Pβ - P0)V2β (1) where µ20 is the standard chemical potential, a2 is the activity, V2 is the partial molar volume, PR and Pβ are the pressures of phases R and β, and the other symbols have their usual meanings. If the pressure of phase R equals the reference pressure P0, one obtains

a2R a2β

(

)

Pβ - P0 β V2 ) exp RT

(2)

where the pressure difference Pβ - P0 across the membrane is experimentally measurable. This equation was used for the determination of the activity of the SXS in the microemulsion by determining (i) the pressure difference, (ii) the activity of the SXS in phase β, and (iii) the partial molar volume of SXS in the following manner: (i) The microemulsion was equilibrated (through a semipermeable membrane) with an SXS/water solution using a concentration ratio of these two components identical to their ratio used for the microemulsion preparation. A QixStep (5 mL) cell with regenerated cellulose membrane (CelluSep, MWCO 6000-8000) was used for the equilibrium. The cell was shaken gently, so the air occupying around onequarter of the volume of the cell maintained a well-mixed condition. The results of the pre-experiments showed 48 h to be sufficient for equilibrium to the effect that the SXS concentration was the same within the experimental error during a 6 h period. The microemulsion, which had previously reached osmotic membrane equilibrium (with the above-described SXS/water solution), and the equilibrium SXS/water solution were filled into the internal and external part, respectively, of an Adair type homemade osmometer with the same membrane as used previously in the QixStep cell. The change of the height of the liquid was detected by a microscope. (ii) The concentration of the SXS in the β phase was determined by light scattering and refractivity index measurements. Its activity was calculated by using the activity coefficient vs concentration function, which (10) Hamer, V. J.; Wu, Y. J. Phys. Chem. Ref. Data 1972, 1, 1047.

was previously determined.9 (iii) The partial molar volume of SXS was determined by density measurements on its solution. Determination of SXS Concentrations in the Microemulsions. Microemulsion (0.8 g) was placed in a QixStep (1 mL) cell. Regenerated cellulose membranes (CelluSep, MWCO 6000-8000, and AmiKa Corp., MWCO 500) were used for the dialysis against 800 g distilled water in an Erlenmeyer flask. The water was vigorously stirred, resulting in a continuous shaking of the liquid in the cell. Approximately 795 g water was removed after 24 h. Its mass was measured, and the UV-Vis absorbance recorded. Another 800 g water was added again into the flask and the procedure was repeated. The concentration of the SXS in both water samples was calculated from the measured absorbance values using a previously determined calibration curve. The amount of the SXS was calculated from concentration of SXS and the total masses of water samples used. The method was checked by measuring the SXS concentration of microemulsion samples of known composition. The deviation between the calculated and measured SXS amounts was below 0.2%. Determination of the Amount of Water in the Microemulsions. The mass of around 1.5 g microemulsion was measured by an analytical balance, and placed into a vacuum desiccator with dried silicagel at 25 °C. The mass of the dried sample was measured again after 21 days. Determination of the Molality of the Lecithin Aggregates in the Microemulsion. The following formula was used to calculate the molality of lecithin aggregates (i.e., microemulsion droplets):

WLEC VLEC,MASS × mLEC ≈ 1000 WW VLECNA

(3)

where WLEC/WW is the mass ratio of lecithin and water, NA is the Avogadro’s number, VLEC (cm3) is the volume of one lecithin aggregate, and VLEC,MASS (cm3/g) is the apparent mass volume of the lecithin in the microemulsion. This formula includes the following approximation:

moles of lecithin ≈ 1 apparent mass volume of lecithin NA geometrical volume of one aggregate VLEC is calculated assuming 20 nm for the diameter of lecithin aggregates as measured earlier.7 The apparent mass volume (eq 4) is defined as the ratio between the apparent molar volume of the lecithin, VLEC,Φ (cm3/mole), and the relative molar mass of the lecithin aggregate, MLEC. At the calculation of the apparent mass volume the lecithin is regarded as the solute component in the mixed solvent SXS/water. By using the expression for the calculation of apparent molar volumes in mixed solvents,19 the following expression is obtained for the apparent mass volume:

VLEC,MASS )

(

)

WSXS + WW d - d* 1 1d WLEC d*

(4)

where d is the density (g/cm3) of the lecithin/SXS/water system, d* is the density (g/cm3) of SXS/water before the dissolution of the lecithin, and (WSXS + WW)/WLEC is the ratio between the joint mass of SXS and water in the microemulsion and the lecithin. (11) Benzing, D. W.; Russel, W. B. J. Colloid Interface Sci. 1981, 83, 178. (12) Vilker, V. L.; Colton, C. K.; Smith, K. A. J. Colloid Interface Sci. 1981, 79, 548. (13) Tamashiro, M. N.; Levin, Y.; Barbosa, M. C. Eur. Phys. J. B 1998, 1, 337. (14) Chattoray, D. K.; Birdi, K. S. In Adsorption and the Gibbs Surface Excess; Plenum Press: New York, 1984; p 54. (15) Schay, G. In Surface and Colloid Science; Matijevic, E., Ed.; Wiley: New York, 1969; Vol. 2, p 155. (16) Mukerjee, P.; Anavil, A. In Adsorption at Interfaces; Mittal, K. L., Ed.; ACS Symposium Series No. 8; American Chemical Society: Washington DC, 1975; p 107. (17) Vink, H. J. Chem. Soc., Faraday Trans. 1990, 86, 2607. (18) Hall, D. G. Colloids Surf. 1982, 4, 367. (19) Horva´th-Szabo´, G.; Hoiland, H. Langmuir 1998, 14, 5539.

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Figure 1. The investigated part of the phase diagram of lecithin/SXS/water system. The concentrations are expressed in weight fractions. Dotted line: phase boundary7 in the presence of Na2SO4. Solid-line: phase boundary in the absence of Na2SO4 using recrystallized SXS. The crosses mark the equilibrium concentrations of the microemulsion samples used for the calculations.

Results and Discussion The position of the boundary of the phase range of the microemulsion (prepared with SXS containing no additional salt) in the phase diagram was redetermined, because in our earlier investigations the SXS also contained some amount of Na2SO4.8 The position of the boundary was shifted toward higher SXS and higher lecithin concentrations (Figure 1). The former observation shows that the presence of salt facilitates the stabilization of the microemulsion at low lecithin concentration (if the salt were indifferent, the boundary would have been shifted in the opposite direction). The latter implies that the salt destabilizes the microemulsion at high lecithin concentration. These trends appear to be antagonistic. Because in the present caseswith the concentration of SXS as high as 2 m or soswe can reject the possibilities of essential changes in the electrostatic stabilization forces (if there are any) against the aggregation of the microemulsion droplets, there are two remaining options for the explanation. (i) The activity of SXS was changed by the presence of the other salt; and (ii) the salting in or salting out phenomena was modified by the presence of the other salt, resulting in modified interaction between the SXS and lecithin molecules. The osmotic membrane equilibrium was used for the determination of the SXS activity. This method is generally applicable in the case of colloids or microphases,11-13 but its use is exceptional for microemulsions, because of the potential transport of their monomers. Our use of the osmotic membrane equilibrium is based on the fact that transport of SXS and lecithin takes place on different time scales with the SXS reaching its equilibrium distribution rapidly, long before the concentration of lecithin is significantly changed. Although it follows from the size of the microemulsion droplets7 that the applied membrane

Horva´ th-Szabo´ and Friberg

Figure 2. The refractive index increment of lecithin, ∆n/∆CLEC, plotted against the concentration of the SXS in water. The lecithin was solved in the SXS/water mixture. A first-order function was fitted to the points.

(MWCO 6000-8000) should prevent the transport of the droplets, a small amount of lecithin was found in compartment β, revealing a small concentration of lecithin monomer (probably associated with SXS) to be present in the microemulsion. The determination of the amount of the transported lecithin was necessary for two reasons: First, it must be established that the amount is negligible compared to the total amount of lecithin in the R compartment, so that the lecithin content would not change noticeably in the microemulsion. Second, the presence of lecithin could cause an error in the concentration determination of the SXS by refractive index measurements. What follows is a solution to the problem of determining the SXS concentration in the presence of a small amount of lecithin. Because the lecithin causes a strong light absorption over the same wavelength range where the characteristic peaks of the SXS are present, refractive index and light scattering measurements were combined for the determination of the concentration. The refractive index vs concentration function n(CSXS) was measured for SXS/water solutions. At certain SXS/water concentrations, some samples were also prepared with lecithin in the concentration range 0-5% and in this range the refractive index was a linear function of the lecithin concentration. From these data, the refractive index increments of lecithin ∆n/∆CLEC were calculated at different SXS concentrations. The dependence of these increments on the SXS concentration is also linear (Figure 2). In addition, the relative (against benzene) light scattering intensity, ISXS(CSXS), of SXS/water solutions was determined in the 0.15-0.35 g/g concentration range (Figure 3), and at certain SXS/water concentrations the scattering intensities of samples prepared with lecithin (concentration range 0-1.5%) were also determined. The relative scattering intensity from the SXS/water solutions was independent of the SXS concentration (Figure 3), whereas it was a linear function of the lecithin concentration. The scattered light intensity increment of lecithin (∆I/∆CLEC) was calculated at different


Langmuir, Vol. 17, No. 2, 2001 281

increment of lecithin ∆I/∆CLEC |CSXS,FIRST-APPROX were calculated.OncetheCSXS,FIRST-APPROX,∆I/∆CLEC |CSXS,FIRST-APPROX, and the scattered light intensity of the sample Iβ were known, and the linear superposition principle was applied, the concentration of the lecithin CLEC,FIRST-APPROX was determined by the following equation:

Iβ ) ISXS|CSXS,FIRST-APPROX + (∆I/∆CLEC|CSXS,FIRST-APPROX) CLEC,FIRST-APPROX Combining this value with the ∆n/∆CLEC |CSXS,FIRST-APPROX value, the refractive index shift caused by the lecithin, ∆nLEC, was calculated by

∆nLEC ) (∆n/∆CLEC|CSXS,FIRST-APPROX) × CLEC,FIRST-APPROX

Figure 3. The relative light scattering intensity of SXS/water solutions as plotted against the concentration of the SXS in water. The 90° scattered intensities of the samples were referenced to that of the benzene. A first-order function was fitted to the points.

Applying again the linear superposition principle, the difference nβ - ∆nLEC is the part of the refractive index caused by the presence of SXS. The concentration of the SXS was determined using the inverse of the n(CSXS) function, and an improved approximation CSXS,SECOND-APPROX for the SXS concentration was acquired. This value was subsequently iteratively improved. The partial molar volume of the SXS in water was calculated from the apparent molar volume data of SXS in water. The latter was obtained from high-precision density measurements.9 A linear equation was fitted to the apparent molar volume data in the 0.1-4 molal range, giving VSXS,Φ ) 133.44 + 1.1397 × mSXS function, where VSXS,Φ (cm3/mole) is the apparent molar volume of SXS and mSXS (mole/kg) is the molality of the solution. The determination of the partial molar volume, VSXS, is based on the following equation:

(

VSXS ) VSXS,φ + mSXS

Figure 4. The scattering increment of lecithin, ∆I/∆CLEC, plotted against the concentration of SXS. The 90° scattered intensities of the samples were referenced to that of the benzene. A second-order function was fitted to the points.

SXS concentrations and fitted with the function Y ) A + BX + CX2 (Figure 4). The following routine was used for the simultaneous concentration determination of lecithin and SXS. The refractive index nβ and the relative scattered light intensity Iβ of the solutions from the β compartment were both measured. An approximate concentration of the SXS (CSXS,FIRST-APPROX) was calculated by using the function n(CSXS). The CSXS,FIRST-APPROX was used as an independent variable, and both the refractive index increment of lecithin ∆n/∆CLEC |CSXS,FIRST-APPROX and the scattering

)

∂VSXS,φ ∂mSXS

(5)

from which VSXS ) 133.44 + 2.2794 × mSXS. The equilibrium concentration of the SXS was within the molality range 1.5-2.2 in our investigations; hence, its partial molar volume is within the range 136.9-138.5 cm3/moles. The equilibrium pressure differences Pβ - P0 (see Activity Determination of SXS in the Microemulsion in Material and Methods) in the Adair osmometer were less than the pressure of 10 cm water for all of the investigated samples along the phase region boundary. These data together with the partial molar values in eq 2 show that the activity difference of SXS between the microemulsion phase and the equilibrated SXS/water phase is well below 0.01%, which is negligibleswithin the precision of the methods used. In other words, the effect of the evolving osmotic pressure on the chemical potential of SXS in the microemulsion (eq 1) results in negligible SXS activity differences between the microemulsions and SXS/water phases under the conditions of our membrane equilibrium experiments. Hence, the activity of SXS in the microemulsion was equated to the activity of the equilibrated SXS/water solution. The effect of the small amount of lecithin on the activity of SXS in β phase (SXS/water) was not taken into consideration. The concentration of lecithin in the β phase increases with the SXS concentration (Figure 5), showing an increasing extent of lecithin transport through the membrane. It may be concluded that either the equilibrium monomer concentration of the lecithin (or small lecithin/ SXS association structures) is increased simultaneously with the increased SXS concentration, or the lecithin

282



composition of the microemulsion phase was also measured, finally the activity coefficient of SXS in the microemulsion was calculated. In the following section we first discus the models before presenting our interpretation of the changes of the coefficients and vesicle size. Two-Phase Model. In this model it is assumed that the microemulsion contains monodisperse nonpenetrable particles formed from lecithin molecules in equilibrium with a liquid phase (SXS/water). On the surface of the lecithin SXS is adsorbed, resulting in a depletion from the water. The following equation is used for the calculation of adsorption:14

ΓSXSw )

t 1 Ww (m t - mSXS) A 1000 SXS

(6)

where ΓSXSw is the relative surface excess of the SXS with respect to water, Wwt is the total amount of water in the liquid phase, A is the area of the interface, and mSXSt and mSXS are the molal concentrations of SXS in the bulk before and after the adsorption, respectively. Applying this equation for the R compartment and introducing the activity, the following formula is obtained: Figure 5. The concentration of lecithin in β phase as a function of the equilibrium SXS concentration.

transport is diffusion limited having its supply from the microemulsion droplets, the concentration of which are also increased (along the phase line) with the increasing SXS concentration. The water concentration also changed in the microemulsion at the condition of the osmotic membrane equilibrium, and it was determined by measuring the dried mass of microemulsion. The increment measuring technique described above is not applicable for the determination of the SXS concentration in the microemulsion, because the concentration of lecithin is similar to that of SXS. Hence, another method was used for the determination involving dialysis against a large amount of water to remove the SXS from the microemulsion. With this method there also is a possibility for an adventitious lecithin transport into the water to cause an error in the SXS concentration determination using light absorbance measurements. This obstacle can be overcome by the application of a membrane for which the MWCO is smaller than the MW of lecithin but higher than the MW of SXS molecules. However, this approach increased the equilibration time to 1 week, which made the determination too tedious to be practical. Instead, a high MWCO membrane was here also used, becausesas our measurements showedsthe perturbing effect of the lecithin transport was within the measuring uncertainty. The arguments include the following. During the first 2 h there was no measurable SXS transport out from the cell; instead, a fast water transport was observed to increase the volume of the sample by around 50%. At the same time, the turbidity of the sample increased strongly, showing that the dilution moved the composition from the microemulsion to the two-phase region including the liquid crystal. The entire SXS transport occurred under this condition where the concentration of the lecithin monomers must be considerably lower that in the microemulsion region. Combining all of the above results, the concentration of SXS in the β phase (SXS/water) is evaluated and, together with the activity coefficient vs concentration function, the activity of the SXS in the R phase (lecithin/ SXS/water) can be calculated. Because the equilibrium

ΓSXSw )

(

t a(mSXS) a(mSXSt) 1 Ww t A 1000 γ[a(m γ[a(mSXS)] SXS )]

)

(7)

where the γ(a) function describes the dependence of the activity coefficient of SXS on its activity (the activity and the activity coefficient are both known), and the a(mSXS) function describes the dependence of the activity of SXS on its molality. The γ and a are mean quantities (γ(, a(). At equilibrium, the chemical potentials are uniform in the system. The constancy of the chemical potential of a component is equivalent to the constancy of its activity within the same phase (because µ° and P are constant) providing that the component investigated is composed from an electrically neutral combination of ions. One of the advantages of using the results of activity measurements becomes obvious at this point. In concentrated systems (in this case at high lecithin/liquid ratio)swhen there is no place in the liquid where one could define the bulk concentrationsthe local concentration of the solute changes with the distance, resulting in a changed local activity coefficient in agreement with the constancy of activity as it is visible in Figure 6. Because there is no bulk concentration in the liquid, eq 6 is not applicable. However, using eq 7, one can refer to a plane placed in a hypothetical bulk liquid because the activity is constant. Because this plane is in the bulk (at a large hypothetical distance), the activity coefficient of SXS is now also independent of the distance. After some rearrangement of eq 7, one obtains the following formula at a certain lecithin concentration:

ΓSXSw )

LEC

(

)

Cw × a(mSXSt) R 1 (8) t 1000 γ[a(mSXS )] γ[R × a(mSXSt)] where LECΓWSXS (mol/g) is the relative surface excess (referred to the surface of 1 g lecithin) of the SXS with respect to water, Cw is the mass of the water in the microemulsion divided by the mass of lecithin, the values of functions a(mSXSt) and R × a(mSXSt) calculated at a given mSXSt are independent variables of the γ(a) function, and R is equal to a(mSXS)/a(mSXSt), or more clearly, R ) aSXS,ME/


Figure 6. Schematic of the distribution of concentration, activity, and activity coefficient of SXS in the concentrated lecithin dispersion. The local concentration of the solute changes with the distance, resulting a changing local activity coefficient in agreement with the constancy of the activity. Using eq 5, one can refer to a plane placed in a hypothetical bulk liquid at constant activity.

a(mSXSt). This ratio is the experimentally measured activity (aSXS,ME) of the SXS in the microemulsion (after the adsorption) divided by the activity [a(mSXSt)] of SXS in the liquid phase before the adsorption. In accordance with our previous considerations, aSXS,ME was obtained from the osmotic membrane equilibrium, combining it with the equilibrium concentration of SXS (mSXS) and calculating its activity with the expression: aSXS,ME ≡ aSXSR = aSXSβ ) γ(mSXSβ)mSXSβ. The quantity a(mSXSt) was not measured but calculated from the measured total moles nt of the SXS in the microemulsion phase (microemulsion in osmotic membrane equilibrium) referenced to the mass of the water in the microemulsion phase by using the previously known activity vs concentration function of SXS, i.e., aSXSt ) γ(mSXSt)mSXSt. The activity coefficient vs molality function of SXS is presented in Figure 7 and the fitted polynomial was used for the numerical calculations. Because the right-hand side (rhs) of eq 8 contains only measurable or calculable quantities, it is operable. This equation was used for the calculation of the adsorption of SXS on lecithin at a fixed lecithin concentration. The R values and the Γ values are presented in Figures 8 and 9 as the function of the lecithin and SXS concentrations. The function of the surface excess of SXS has a maximum similar to the excesses measured on apolar surfaces in binary mixtures of organic components.15 This behavior is observed only in a few cases for ionic surfactants.16 The phenomenon is related to the high solubility of SXS and to the fact that the hydrotropes having no critical micelle concentration (cmc), contrary to the surfactantsshas a continuously increasing activity with increasing concentration. Hall’s Model. This model was introduced to describe the properties of polyelectrolytes and micelles in the presence of supporting electrolyte. The basis of this theory is the description of the Donnan equilibrium between the solution of interest and a polyion-free electrolyte solution. The chemical potentials of an electrically neutral combination of polyions, counterions, and coions are related to measurable quantities. The electrostatic interactions between polyions are implicitly included in the description and no artificial distinction was made between bound and

Langmuir, Vol. 17, No. 2, 2001 283

Figure 7. The activity coefficient vs molality function of SXS. The fitted third-order polynomial was used for the numerical calculations (Y ) 0.7884 - 0.2242X + 0.03236X2 + 0.001235X3).

Figure 8. The experimentally measured activity of the SXS in the microemulsion after the adsorption referenced to the calculated activity of SXS in the liquid phase before adsorption, plotted against the concentration of the lecithin in the microemulsion.

free counterions.17 Also, the treatment is not restricted to any particular polyion geometry. Applying this model to our case, the lecithin is one of the components of the continuous liquid phase. The xylenesulfonate associates with the associated lecithin molecules charging them. The presence of charged associates modifies the activity coefficient of the electrolyte in the system. The assumption of the fully dissociated state of the SXS adsorbed on the surface on the lecithin aggregates will be used. The following expression8,18 is valid for the activity coefficient of the small electrolyte

284



activity coefficient, which is partly compensated by the increase of the SXS concentration by negative adsorption. The following form is obtained from eq 10:

[

R* ) 1 -

Figure 9. The relative Gibbs surface excess (referred to the surface of 1 g lecithin) of SXS with respect to water as a function of the equilibrium SXS concentration.

(1:1 type) in the presence of polyions:

1 [c3 + RZcp] log γ/( ) log γ( + log 2 [c3 + Zcp]

(9)

where γ*( and γ( are the mean ionic activity coefficients of the added salt in the presence and in the absence of the lecithin aggregates, respectively; c3 is the number of moles of electrolyte divided by the same of solvent;8 cp stands for the number of moles of polyion divided by the same of solvent; Z is the charge of the polyion; and R is the osmotic coefficient in the absence of added salt. According to Hall’s considerations, RZ is approximately equal to twice the amount of the electrostatically excluded co-ions by an isolated polyion.8,18 Because in our case one part of the xylenesulfonate belongs to the macroion together with its Na+ ions, ensuring the electroneutrality (i.e., this is the combination of ions which plays the role of one of the electrically neutral components introduced by Hall), the rest of the SXS can be treated as the added electrolyte (i.e., this is the other neutral combination of ions). In other words, the total concentration of SXS equals c3 + ZcP. Taking this equation into consideration and introducing the notation mSXSt for the total molality of the SXS in the microemulsion, and furthermore regarding that the concentration used in eq 9 is identical to molalitiessapart from a constant multipliersone obtains:

(

γ(SXS/ ) 1 +

mLEC

(2ZEX - Z) mSXSt

)

1/2

γ(SXS

(10)

where γ*(SXS and γ(SXS are the ionic activity coefficients of SXS in the presence and in the absence of the lecithin aggregates, respectively; mLEC is the molality of the lecithin aggregates; Z is the number of the charges of a lecithin aggregate; and ZEX is equal to the number of the electrostatically excluded co-ions by an aggregate. The form of the equation is in agreement with expectation, namely: with increasing adsorption the SXS “disappears” from the solution resulting in a decrease in its measured

mLEC

(2Zex - Z) t

mSXS

]

mSXSt

1/2

mSXSt - ZmLEC

(11)

where R* ) aSXS,ME/aSXS. In the above equation, aSXS,ME is the experimentally measured activity of the SXS in the microemulsion, and aSXS is the activity of SXS in the absence of the lecithin. The former quantity was calculated from γSXSβ × mSXSβ expression using the experimentally measured equilibrium concentration of SXS on the other side of the membrane. The last mentioned quantity is calculated by using the mSXSt - ZmLEC expression as the independent variable in the activity coefficient vs SXS concentration γ(mSXS) plot, and by multiplying it with (mSXSt - ZmLEC), in this manner taking into consideration the amount of the salt theoretically divided into the bound (adsorbed) and supporting electrolyte parts. Both mSXSt and mLEC are referenced to the mass of the water in the microemulsion phase. By using eqs 3 and 4, the mLEC is obtained for eq 11. For the calculation of the electrostatic exclusion of coions (ZEX in eq 11) by one polyion, the following model is used: (i) The overlap between the double layers of the individual polyions is neglected (the average distance between the lecithin aggregates is around 60 nm at the highest concentration of lecithin, while the thickness of the electrical double layer is around 0.28 nm); (ii) the charges are homogeneously distributed on the surface of the spherical particle; (iii) the particle is penetrable by the solvent and the ions, therefore there will be exclusion both from the internal part of the sphere and from its surrounding volume; and (iii) the Gouy expression is applicable. Because in our case, κa (1/κ is the thickness of the electrical double layer and a is the radius of the sphere) is between 30 and 40, the flat double layer model is a reasonable approximation. Using the flat double layer model the exclusion has been calculated by Schofield and Talibuddin20 and Van Den Hul and Lyklema.21 Unfortunately their results are applicable only to high surface charge density and at infinite surface potential limit.22,23 Because in our case these assumptions are not a priori applicable (there are no previous data on the surface charge density), the calculation of the exclusion is necessary under arbitrary surface charge condition. The starting point to this is the expression given by Van Den Hul and Lyklema21 for the number of excluded co-ions. It has the following form for the case of 1:1 type electrolytes:

∫0∞[1 - exp(

Γex ) n∞

)]

eφ(x) dx kT

(12)

where Γex is the number of excluded ions per unit area, n∞ is the number density of the negative ions at infinite distance from the surface, φ is the electric potential, and x is the distance from the surface. Introducing y ) eφ/ (kT), the following form is obtainable (a similar formula was published recently26,27) from the previous equation: (20) Schofield, R. K.; Talibuddin, O. Discuss. Faraday Soc. 1948, 3, 51. (21) Van Den Hul, H. J.; Lyklema, J. J. Colloid Interface Sci. 1967, 23, 500. (22) Shone, M. G. T. Trans. Faraday Soc. 1962, 58, 805. (23) Van Den Hul, H. J. J. Colloid Interface Sci. 1981, 86, 173. (24) Hiemenz, P. C.; Rajagopalan, R. Principles of Colloid Chemistry, 3rd. ed.; Marcel Dekker: New York, 1997. (25) Friberg, S. E.; Shah, D. O. Unpublished results.


Γex )

n∞ κ

∫yy

∞

0

n∞

(2y)dy ) κ [2 exp(2y)]

exp

0

Langmuir, Vol. 17, No. 2, 2001 285

(13)

y0

where y0 and y∞ apply to surface and in the bulk, respectively. Because the overlap of the double layers is negligible, φ∞ ) 0 at y∞ ) 0 (i.e., this is the reference for the potential) as well. For the calculation of the surface potential y0 ) eφ0/(kt), from the surface charge σ0, the Gouy theory is used, which has the following form in our case:24

[ ()

σ0 ) x(2kTn∞) exp

( )]

y0 -y0 - exp 2 2

(14)

where ) r0 is the dielectric constant of the medium. Equation 13 combined with eq 14 gives the number of excluded ions in the case of arbitrary charge density. However, it seems to be reasonable to consider also the contribution of the internal exclusion to the Donnan effect. Considering that the overlap of the inside double layer from the opposite sides of the sphere is negligible (compare the 0.28 nm double layer thickness to the 20 nm aggregate diameter), and accepting that the flat double layer model is applicable, the following model is appropriate. The surface area of an aggregate (ALEC) is outstretched on a plane with the same surface. This plane is immersed into the equilibrium electrolyte solution of SXS. Now there are two reference points (x ) +∞ and x ) -∞) for the zero potential. Therefore, it is necessary to separate the surface charge into two equal parts for the internal and external exclusions, which means that σ0 in eq 14 has the following relation with the charge of the macroion:

σ0 )

-Ze 2ALEC

(15)

where ALEC is the surface area of the lecithin aggregate. Combining eqs 13, 14, and 15, the following formula arises for the number of electrostatically excluded ions from both sides of the charged surface of an aggregate:

ZEX )

x

4ALEC

{

r0kTn∞ 2

2e

[

1 - exp arc sinh

]}

σ0 8r0kTn∞

(16)

where n∞ is the number of SXS molecules in 1 m3 liquid in the bulk, and for r the dielectric constant of the water was used as an approximation. Because this equation gives the number of excluded co-ions from a negative surface having σ0 surface charge density in the case of a flat double layer for 1:1 type electrolyte, it is the exact mathematical solution (given the model) of the problem studied earlier by Schofield.20 For the calculation of n∞ in the previous equation, the following formula is used:

n∞ )

106NAFmSXS,BULK 1000 + mSXS,BULKMSXS

(17)

where NA is Avogadro’s number, F (g/cm3) is the density of the liquid in the bulk, mSXS,BULK is the molality of SXS in the bulk, and MSXS is the relative molar mass of SXS. For the calculation of the bulk liquid density the molality vs density function was determined. The number of (26) Lyklema, Academic Press: (27) Lyklema, Academic Press:

J. Fundamentals of Interface and Colloid Science; New York, 1995; Vol. 2. J. Fundamentals of Interface and Colloid Science; New York, 1993; Vol. 1.

Figure 10. The number of the electrostatically excluded xylenesulfonate (XS) ions divided by the number of the XS ions on the surface (of a microemulsion droplet) as a function of the XS ions on the droplet at different equilibrium concentration of SXS. So essentially, the ratio negative/positive adsorption of SXS is computed. The droplet radius is 10 nm.

excluded ions divided by the number of the charges on the surface of a microemulsion droplet is plotted in Figure 10 vs the surface charge. In agreement with the two phase model:

mSXS,BULK )

aSXS,ME γ(aSXS,BULK)

(18)

where aSXS,ME is the experimentally measured activity in the microemulsion and γ is calculated from the measured activity using the known γ(a) dependency. By using equations 18, 17, 16, 3, and 4 in eq 11, all of the quantities except Z may be calculated; hence Z is definite. However, because eq 11 is an implicit function of Z, it was solved numerically at fixed lecithin concentrations by using the “solve” function of the Mathematica programming system by iterations. These equations have three roots. One of them provides results with physical meaning in the range of the data of our system. Using these together with the 10 nm radius data of lecithin aggregates,8 the resulting surface area of the SXS on lecithin is plotted against the concentration of SXS in Figure 11. According to this the surface area of one adsorbed SX ion varies between 0.045 and 0.110 nm2. One can compare these data to the surface areas of a benzene molecule in a parallel (0.18 nm2) and perpendicular (0.15 nm2) position to the surface.29 These results may indicate multilayer adsorption, the strong electrostatic repulsion (28) One should not be confused by the fact that for the calculation of the exclusion the flat double layer description was used, whereas here the strong curvature of the dividing surface is discussed. The possibility of the simplification of the double layer description is one thing (it is connected with the thickness of the double layer compared with its curvature), and the dependence of the surface area of the adsorbed material on the curvature of the dividing surface is another (it has nothing to do with the thickness of the double layer). (29) Endo, T.; Iida, T.; Furuya, N.; Yamada, Y.; Ito, M. M. J. Chem. Software 1999, 5, 81.

286



Figure 11. The surface area and surface concentration of SXS on the microemulsion droplets calculated from Hall’s model and plotted against the equilibrium concentration of SXS. The small surface area values indicate multilayer adsorption.

of the layers of SX ions being suppressed by the counterions. From the structure of SX ion follows that the layerto-layer distance (perpendicular position) is around 0.72 nm, while the double layer thickness is around 0.28 nm. In other words, around 9/10 of the electrical potentials originating from one layersvanishes at the position of charges of the next layer. Comparison of the Two Models. The thermodynamic description of adsorption does not differentiate between the adsorbed and repelled amounts of SXS because it is based on the analysis of bulk concentration data, without using any assumption about the detailed structure of the adsorption layer. However, Hall’s model requires a structural description, discriminating between the number of bound and repelled ions. Hence it is also necessary to make a similar distinction in the case of surface excess treatment, to create the correct conditions for the comparison. One can separate the surface excess amount into two parts, using the electrostatic exclusion picture described above:

ΓSXSW ) *ΓSXSW - EXΓSXSW

(19)

where ΓSXSW is the relative surface excess of SXS, EXΓSXSW is the electrostatic exclusion, and *ΓSXSW is the surface excess that would be measured had there been no exclusion. The latter quantity is comparable with the number of adsorbed charge (Z) of Hall’s model. For the calculation of the EXΓSXSW, eqs 15 and 16 were used but for one side exclusion only because the lecithin is nonpenetrable in the two-phase description. That is why the multiplier 4 in eq 16 was changed to 2 and the divisor 2 in eq 15 was removed. To calculate the exclusion the knowledge of surface charge is necessary which, in this case, can be calculated from *ΓSXSW. However, because the latter is calculable from ΓSXSW only if one already knows the exclusion, the method becomes a vicious circle. The problem was solved by iteration setting EXΓSXSW as zero at the first step of the iteration process. The surface area

Figure 12. The surface area of SXS on lecithin calculated from the surface excess of SXS (*ΓSXSW) considering the electrostatic exclusion as well (dotted line), and the surface area calculated from the Gibbs surface excess of SXS (ΓSXSW) (solid-line) against the equilibrium concentration of SXS.

of SXS was calculated from the resulting “corrected” surface excess of SXS, (*ΓSXSW), and is presented in Figure 12 together with the surface area calculated from the surface excess of SXS, (ΓSXSW), using 10 nm as the radius of the lecithin aggregate. Comparing these data with the surface area calculated from Hall’s model, it is obvious that (i) the surface excess model results in smaller number of ions on the surface than Hall’s model; (ii) the surface area data of the Hall’s model is realistic with multilayer adsorption only; and (iii) the models predict qualitatively different dependence of the adsorbed SXS on its equilibrium concentration. For the interpretation of the smaller number of adsorbed ions of the surface excess model, the following factors must be considered. The surface excess description always underestimates the number of ions in the adsorption layer. It follows from the “excess” properties of the description. In Figure 13, a schematic concentration distribution is presented in the liquid phase from the solid surface. If the concentration distribution is characterized by the CFIKJ function, then the following equation is valid for the following areas:

BCFIGB - IJKI ) BCDEFGB

(20)

The “true” value for the adsorbed material concentration (in the adsorption layer model) is the concentration difference between points A and D. The calculation based on the surface excess picture results in an adsorption layer concentration equivalent with the concentration difference between B and D points. The difference is inherent in the amount of material in ABGHA volume. In the case of high bulk concentration, as in our case, this “underestimation” can be significant. To achieve estimation about its magnitude, the approximate value of the thickness of the adsorption layer would be necessary. For the interpretation of the qualitatively different dependence of the adsorbed amount of SXS on equilibrium concentration, the following considerations may be ap-


Figure 13. The schematics of the concentration distribution of SXS (CFIKJ function) in the liquid phase plotted against the distance from the solid surface. The thickness of the adsorption layer is AH. The concentration in the adsorption layer is defined by the following equation for the areas: BCFIGB - IJKI ) BCDEFGB. The “true” value for the adsorbed material concentration in the adsorption layer is the concentration difference between points A and D. Calculations based on the surface excess picture result in an adsorption layer concentration equivalent with the concentration difference between B and D points.

plied. At the calculation of the surface area, the relative surface excess of SXS is referenced to the dividing surface (DS), the geometrical position of which is defined by the zero surface excess of the water ΓW ) 0. For flat DS, its geometrical position has no influence on the numerical value of the surface area calculated from the excess. For highly curved28 DS, small change in its radius may cause considerable differences in the surface area of the adsorbed materials (while the relative excess remains the same, because it is defined thermodynamically). The small radii of the microemulsion droplets are in this critical range. However, because the geometrical position of the dividing surface cannot be found thermodynamically, one must accept the fact that the comparison of our models itself has also been based on model assumptions (e.e., the DS was positioned to the fixed aggregate size). Explanation of the Increasing Vesicle Size on the Basis of Hall’s Model. According to our previous investigation,7 the size of vesicles produced by dilution from microemulsion along the phase boundary line of the phase diagram is increasing with increasing lecithin concentration. Because according to our present measurements, the equilibrium concentration of SXS also increases simultaneously with the increasing lecithin concentration along the phase boundary line of the microemulsion region of the phase diagram, the microemulsion from which larger vesicles were formed has higher equilibrium SXS concentration. Because the amount of the associated SXS is presented in similar fashion in Figure 11, the higher values on the x-axes belong to larger vesicle sizes. It means that the larger vesicles were formed from the microemulsion droplets with the smaller surface concentration of SXS. The formation of vesicles can be described by the following elementary steps: (i) the dilution of the SXS/ water electrolyte, (ii) the desorption of SXS from the surface of the lecithin, (iii) the aggregation of the primary lecithin particles (originating from the microemulsion)

Langmuir, Vol. 17, No. 2, 2001 287

and the formation of secondary aggregates, and (iv) the coalescence within the secondary aggregates and vesicle formation. Item (i) is the fastest step. The SXS desorption takes relatively a long time according to the results measured by pressure jump technique.25 Item (iii) is necessarily present, because the system is not in thermodynamic equilibrium (its composition is on one of the tie lines between the liquid crystal and SXS/lecithin/ water-solution phase ranges). It is reasonable to assume that step (iii) happens simultaneously with step (ii). If not every collision of the microemulsion droplets results in aggregation (i.e., the system is in the slow coagulation range), then the speed of the aggregation of the primary lecithin aggregates (hence the size of secondary aggregates) is a function of the height of the energy barrier that prevents the aggregation. The sizes of the secondary aggregates and vesicles are interpretable by the following mechanism. The desorption rate of the SXS from the lecithin surface is higher for the higher surface density of SXS, producing a more concentrated shell of electrolyte than the electrolyte concentration in the bulk. Furthermore, this shell has a longer lifetime for a higher surface density because the flux of electrolyte has a supply for a longer time. The ion flux repels the approaching objects because in the approaching volume region of the two particles, the local electrolyte concentration is higher than the concentration of the surrounding electrolyte, giving a transient depletion stabilization (the osmotic flux of water into this region repels the particles) for the particles. Consequently, the particles with higher surface concentration of SXS have higher stability and form smaller secondary aggregates. We think that the above-mentioned process offers a potential explanation for the dependence of the vesicle size on the microemulsion composition. Conclusion The microemulsions investigated are concentrated systems in two senses. At first the concentration of the hydrotrope is high in the continuous phase, forming a strongly nonideal solution, and in addition the concentration of the dispersed phases itself is also high, further modifying the properties of the continuous phase. That is why the knowledge of the activity of the hydrotrope is necessary to determine its distribution in the system. It was possible to separate the continuous phase from the microemulsion droplets experimentally under equilibrium conditions by semipermeable membrane for the lecithin/SXS/water system. The activity of SXS in the microemulsion was measurable by using the Donnan equilibrium. The SXS activity was evaluated both on the basis of the Gibbs excess function and on the basis of Hall’s model. For a correct comparison of the two approaches, the surface excess amounts of SXS were corrected using the electrostatic exclusion effect. The models predict qualitatively different dependence of the adsorbed SXS on its equilibrium concentration. The amount of SXS bound to the surface of the lecithin was used for the interpretation of the changing size of vesicles formed from the microemulsion by dilution. A depletion effect is proposed to describe the dependence of the vesicle size on the composition of microemulsion droplets. Acknowledgment. Ge´za Horva´th-Szabo´ expresses his sincere gratitude for the help and support of Professor Johan Sjo¨blom. The authors acknowledge the thorough work of Reviewer 1, who helped improve the content of this paper. Financial support from OTKA Project T025878 is acknowledged. LA9913912

Sodium

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