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A dielectric method to investigate the interfacial composition of micellar aggregates
Colloids and Surfaces A: Physicochemical and Engineering Aspects 140 (1998) 313–320
A dielectric method to investigate the interfacial composition of micellar aggregates G. Briganti *, A. Bonincontro INFM, Physics Department, ‘‘La Sapienza’’ University, P.A. Moro 5, 00185 Rome, Italy Received 10 February 1997; accepted 21 April 1997
Abstract The aggregation state of micellar solutions is mainly determined by the specific chemical and physical conditions within the interfacial region constituted by the polar head terminations and solvent molecules. In particular the mutual head group interactions and their interactions with solvent and cosolvent molecules strongly affect the overall shape, size and size distribution function of micellar solutions. It then becomes evident how important the determination of the composition and structural arrangement of the interfacial region is. Permittivity measurements of an heterogeneous system allow the evaluation of the permittivity of the suspended particles using one of the available mixture equations. If the suspended particles are constituted by separated regions with different dielectric properties it is possible to iterate the procedure to extract information on each of the regions. In the case of micellar aggregates there is the hydrocarbon core region, equivalent to an oil liquid phase, and an interfacial region, constituted by the polar head group terminations, solvent and cosolvent molecules. By comparing the interfacial permittivity with the permittivity of mixtures composed by the solvent and free head groups, it is possible to evaluate the composition of the micellar interface. We apply this methodology on two different surfactant mixtures: C E in water and in 12 6 water–urea (2, 4 and 6 M ); octyl-b--glucopyranoside in water and in water–glyclne (0.3 and 0.6 M ). The results obtained concerning the conformation and composition at the interface are consistent with the overall behaviour of the solutions studied by many other different techniques supporting the proposed procedure. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Mesoscopic solution; Dielectric spectroscopy
1. Introduction Most of the molecular thermodynamic theories suggest that the micellar thermodynamic state, i.e. shape and size distribution function, is strongly affected by the properties of the micellar interface [1,2]. Changing temperature and solvent composition, shape and size of non-ionic surfactant solutions [3] as well as of zwitterionic surfactant solutions [4] change. In both cases rescaling vari* Corresponding author. 0927-7757/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S0 9 2 7 -7 7 5 7 ( 9 7 ) 0 0 28 8 - 4
ables with temperature allows the solvent composition to be found. These results suggest that the overall thermodynamic properties of the surfactant solution can be divided in the contributions due to three different regions, namely the bulk solvent region, the oil core region and the interfacial one, containing the head group terminations and the solvent molecules. A very exhaustive analysis of the free energy associated with the formation of micelles with different size and shape was recently developed by Blankschtein and Puvvada [2]. The contribution
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due to the oil core formation can be evaluated through measurable thermodynamic quantities, i.e. free energy of solubilization of the hydrocarbon tails and interfacial tension oil core–bulk solvent, and computing the hydrophobic tail conformation compatible with the micellar shape. In contrast, the contributions due to head group terminations depend on the area per polar head and on the repulsive excluded volume head–head interactions. It is difficult to ascertain the connection between the area per polar head group and of the head– head interaction with any directly measurable quantity. In this work we wish to show that dielectric measurements supply this demand. Then, combining these measurements with the one required for the model describing the oil core, a complete prediction of the solution behaviour can be obtained. The following paragraph concerns the methodology used for the determination of the interfacial composition. The methodology is then applied on two different surfactant solutions with an extended comparison with other experimental results. This section is divided into two subsections, the first concerns binary mixtures, with examples on water–C E and water–OBG (octyl-b--glucopi12 6 ranoside) solutions, a non-ionic and a zwitterionic surfactant molecule, respectively. The second subsection shows the analysis of results obtained from ternary solutions with cosolvent molecules (water–urea–C E and water–glycine–OBG solu12 6 tions). The last paragraph is devoted to a discussion of reliability of our method in the light of the proposed experimental results.
2. Method The sample preparations is reported in Ref. [5] for C E water and water–urea solutions, and in 12 6 Ref. [6 ] for water–OBG and water–glycine–OBG solutions. Permittivity measurements in our experiments were carried out by means of an impedance analyser HP 4194 A in the frequency range from 10 to 100 MHz. The cell consists of a section of a cylindrical wave guide excited far beyond its cutoff frequency mode; its general properties are
described elsewhere [6 ]. Cell constants were determined by calibration with reference liquids according to a standard procedure [7]. The temperature was controlled to within 0.1°C. The frequency range used in our dielectric measurements is above the Maxwell–Wagner dispersion [8] and below the solvent relaxation [9]. Thus the experimental results can be analysed in terms of an appropriate mixture equation in order to estimate the permittivity of the micelle. In particular, the Polder–van Santen equation, derived from the original Wagner equation, was used because its validity extends over a wide concentration range. For prolate ellipsoids the equation can be written as follows [10]:
G H
w 4 e=e − 2 (e −e )e* 1 2 1 2e* +(1−2d)(e −e* ) 3 1 1 2 1 1 + , (1) e* +2d(e −e* ) 1 2 1 where d is a parameter which decreases from 0.33, for spherical particles, to zero increasing the axial ratio of the particles. This parameter can be obtained from quasielastic light scattering measurements of the hydrodynamic radius R [10]. For h C E solutions the axial ratios were taken from 12 6 Ref. [3]. According to Eq. (1), the dielectric permittivity of the solution, e, is a linear function of the volume fraction of the solute, W , and depends 2 on the dielectric constants of solvent, e , and 1 solute, e , and on e*. This last quantity lies 2 1 between e and e, and is related to the modification 1 of the intrinsic properties of the solvent due to solvent–solute interactions. It has been found that up to 25% in W , e*=e in most systems and, in 2 1 1 particular, in micellar solutions [9]; for solutions up to 45% in W a small correction ( less than 10%) 2 due to e* change is necessary, but still a reasonable 1 estimation of e can be obtained. 2 In Eq. (1) the computation of the volume fraction of the suspended particles, knowing the mole fraction (x) of the monomers in solution, implies a model for the solution. Our analysis is based on the following assumptions: (1) the solution is monodisperse with aggregates
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of aggregation number equal to the average aggregation number of the real solution; (2) the volumes of all the monomers are equivalent. Since the aggregate shape and dimension, i.e. the factor d in Eq. (1), contribute little to the determination of the solute permittivity in the data treatment, we can use these approximations in our analysis. The same assumptions are used in the determination of the monomer partial molar volume and of the first cumulant approximation of R . Using these two conditions the volume h fraction appearing in Eq. (1) is the monomer volume fraction. Indeed N monomers occupy, on average, the same volume as N/n aggregates of aggregation number n. In Fig. 1 the section of a micelle (spherical or cylindrical ) of C E is sche12 6 matized; under the previous conditions the monomer volume can be visualized by the cone dotted in the polar head region and dark in the oil core region. The method then develops in three steps. In the first we determine the dielectric constant of the suspended particles, parametrizing the monomer volume V used in the definition of the solute 1
Fig. 1. A section of a spherical or cylindrical C E nonionic 12 6 micelle is shown. The dark cone on the right side illustrates the oil core volume per monomer, the dotted region the volume available to the head group termination and to solvent molecules. The dashed rectangular region visualizes the actual structuaral properties of the water–PEO solution at the micellar interface.
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volume fraction. This parameter defines the overall conformation of the polar head terminations; the oil core properties can be obtained by the theory for micellar formation of Ref. [2]. In the case of C E micelles of Fig. 1, V defines the conforma12 6 1 tion of the PEO polar termination as well as of the area per polar head group. In Fig. 2 the permittivity experimental results of C E are visu12 6 alized for different choices of the value of V , the 1 lines indicate the corresponding linear trends where Eq. (1) can be applied. The second step of our analysis is not novel. Asami et al. [11] used the same methodology to obtain the permittivity of a double layer. From the previous determinations we know the micellar permittivity, the one of the oil core (equivalent to the corresponding oil permittivity), the total monomer volume V, and the tail volume from Ref. [2]. The shape factor of the oil core is the same as the one of the micelle. We can then evaluate the interfacial permittivity applying again Eq. (1) to an idealized solution composed, in this case, of the oil cores dispersed in a mixture, constituted by the solvent molecules and the head group terminations. The third step of our analysis concerns the comparison of the obtained interfacial permittivity
Fig. 2. Permittivity of C E micellar solution e divided by the 12 6 water permittivity e at 25°C as a function of the hydrated 1 monomer volume fraction w . The different curves correspond 2 ˚3 to different values of the monomer hydrated volume: 1000 A ˚ ˚ ˚ 3 (,), 1982 A ˚ 3 (%), (#), 1200 A3 ($), 1500 A3 (( ), 1770 A ˚ 3 (&), 3470 A ˚ 3 (6). 2500 A
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with the one of a solution composed by solvent molecules and free polar head groups. The dashed region of Fig. 1 visualizes the solute network at the water–C E micellar interface. The micellar 12 6 interface is randomly oriented with respect to the polarizing field, averaging the orientational distribution of the interfacial water–polymer solution as in the case of pure water–polymer solutions. Then the dielectric responses of the pure water– polymer solutions should be very similar to the one of the interfacial mixture. Then the intercept between the permittivity trend with polymer concentration of solvent-free polar head solutions and of the interfacial one, obtained with our parametric procedure, represents a good approximation of the composition at the micellar interface.
3. Results and discussion 3.1. Water surfactant mixtures In Fig. 3 the interfacial permittivity in water–C E solutions, obtained for different 12 6 values of V (data from Fig. 2) and the experimen1 tal permittivity of water–PEO solutions are reported as a function of PEO polymer concentration. Following our hypothesis the concentration of the intercept between the two curves corresponds to the equivalent interfacial concen-
Fig. 3. Micellar crown permittivity (full symbols) in water solution as a function of PEO unit molar concentration at three different temperatures (5, 25 and 45°C which correspond to T −T of 46.6, 26.6 and 6.6). The empty symbols refer to c PEO–water solutions at the same temperatures.
tration. The number of PEO units per polar head group is known, six in our case, and then the available volume for the hydrophilic termination results from our procedure. The comparison of our results on water–C E 12 6 solutions with results from other techniques supports our analysis. Light scattering [12] and SANS measurements [13] have given for the micellar ˚ , respectively. minor radius values of 30 and 32 A At the same temperature the volume of the interfacial mixture we estimate, using the theoretical ˚ 2 [2], is value for the area per polar head of 63 A compatible with a micellar minor radius of about ˚ . Subtracting the mass of the hydration water 31 A computed from the micellar molecular weight determined by Zimm plot light scattering analysis [12], we evaluate an aggregation number for spherical micelle of about 45 at 18°C. Theoretical evaluations of the oil core dimension give, using the liquid oil density for the oil core, the same aggregation number we previously estimated [2]. Our estimation of the aggregation number is significantly smaller than the direct evaluations from Zimm analysis, from a combination of light and neutron scattering measurements [13] and from fluorescence quenching experiments [14,15] which give 140. At low temperature and concentration the micellar shape is generally considered spherical [2,3,12,13]. The aggregation number of 140 is not consistent with this shape — indeed the micellar density will be too high. In our opinion the first two experimental evaluations of the aggregation number are overestimated because they are related to the total mass of the hydrated micelle and the water contribution is relevant. The fluorescence quenching result is obtained with drastic approximations and it is affected by the enviromental condition of the micellar interface, as observed by the direct measurements of the fluorescence decay time of the pyrene [14,15]. Our aggregation number on the other hand might be underestimated because we did not consider any effect due to the oil core on the dielectric properties of the interface. Similar measurements were performed on solutions of water and OBG. Addition, in this case we define the volume of the hydrocarbon core in accordance with Blankschtein’s model [2], whereas
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the total volume of hydrated OBG was obtained from experimental determination of the partial molar volume [6 ]. The oil core/monomer volume fraction estimated in this way is about 38% of the total micellar volume. This implies a thickness of ˚ in good the head group region of about 4 A agreement with X-ray data from crystallized samples [16 ]. Differently from C E , in this case 12 6 the conformation of the head groups practically does not affect the monomer volume and V is 1 fixed. The comparison of the permittivity of the interfacial region with the water–glucose permittivity indicates that the glucose concentration at 25°C is about 6.1 mol l−1, that corresponds to a water–glucose molecular ratio of 4 at the micellar interface, in agreement with the literature [17]. The solubility of glucose in water is 4.3 mol l−1, and our results indicate that zwitterionic head terminations strongly interact with the oil core interface and the degree of hydration at the micellar interface can exceed the precipitation threshold, up to a maximum of 6.1 mol l−1. Recent results of sound velocity suggest that the London force field generated by the oil core region acts on the head groups and on the solvent molecules, overcoming the local binary interactions between solvent molecules and head group terminations [18]. This finding might justify the anomalous concentration observed at the OBG micellar interface, and indeed the electrostatic interactions could stabilize the very high concentration of glucose in the micellar interface.
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of non-ionic and zwitterionic surfactant solutions in binary solvents is of wide interest and our technique is specific for this purpose. The same micellar solutions studied as binary mixtures were analysed in the presence of a cosolvent. In the case of water–C E solutions we 12 6 added urea, a specific component generally used for protein denaturation. In water–OBG solutions the cosolvent was glycine, one of the most common aminoacid which has a strong electric dipole moment. Regarding C E solutions in presence of urea, 12 6 it is known that the thermodynamic properties (phase separation as well as shape and size of the micelle) rescale with the reduced temperature T −T, where T s are the lower consolute critical c c temperatures for the different content of urea in the solvent mixtures [3]. With an equivalent procedure as the one applied in the binary mixtures we obtain, at similar rescaled temperatures, the interfacial permittivity. The results for 6 M urea in the buffer mixtures are shown in Fig. 4 and compared with water–6 M urea–PEO permittivity. In the case of ternary solutions the dielectric contribution due to the interface depends on the specific interfacial composition, therefore our determination of the available volume per polar head groups requires other independent information. Looking to Fig. 4 it is possible to state that
3.2. Ternary mixtures: cosolvent contributions Ternary surfactant solutions can be divided into two categories: two surfactant species in a homomolecular solvent (in the presence of a cosurfactant), one surfactant specie in a binary solvent (the in presence of a cosolvent). The interactions between surfactants and biopolymers are the subject of continuous investigations [19]. Most of them deal with the capability to separate biopolymers from their natural matrices by selective solubilization. To avoid drawbacks occurring in presence of ionic detergents, non-ionic or zwitterionic surfactants are preferred [20]. Then the study
Fig. 4. Micellar crown permittivity (full symbols) in 6 M water–urea solution as a function of PEO unit molar concentration at three different temperatures (18.2, 35.6 and 54°C which correspond to T −T of 47.4, 30 and 11.6). The empty c symbols refer to water–6 M urea–PEO solutions at the same temperatures.
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the permittivities of water–urea–PEO solutions with an urea content lower then 6 M, the urea buffer concentration of these micellar solutions, never crosses the evaluated interfacial permittivity. This clearly indicates that the urea concentration at the interface cannot be lower the bulk concentration, therefore urea desorbtion from the interface is excluded. On the other hand adsorbtion of urea is compatible with our results. In Fig. 5 the temperature dependence of the volume per polar head is reported as a function of temperature for all the investigated concentrations of urea in the solvent. Looking at the figure some statements can be asserted. Equivalent linear trends are observed in all the cases, suggesting that mainly water molecules are involved in the temperature-induced dehydration of the interface; increasing temperature cause the urea concentration at the interface to increases. The volume per polar head increases with urea concentration and saturates at about 4 M. Since the hydrodynamic radii of the aggregates coincide, at the same rescaled temperature the area per polar head group must increase with urea concentration, remaining constant above 4 M. This is not surprising since the solubility of the hydrocarbon tail increases with urea and the interfacial tension decreases. In water–glycine–OBG solutions the micellar permittivities obtained in the first step of our
˚ 3) estimated by our Fig. 5. Monomer hydrated volume V (A h method (see text) as a function of T −T (C ). (#) Water soluc tion, ($) 2 M water–urea solution, (+) 4 M water–urea solution, (%) 6 M water–urea solution.
analysis at 0.0, 0.3 and 0.6 M glycine concentrations coincide at all the investigated temperatures. Since the head group conformation cannot significantly change the interfacial volume per monomer, the interfacial composition might change only by substituting water molecules with the glycine, the volume ratio between water and glycine being about 1/3. Dielectric measurements carried out on water– glucose, water–glycine and water–glycine–glucose solutions show that the dielectric constant of water linearly decreases with glucose concentration with a slope of 4.4 mol−1, whereas the addition of glycine linearly increases the water permittivity with a slope of 23.6 mol−1. Both results are in full agreement with data from the literature [10]. Concerning the water–glycine–glucose solutions, the dielectric measurements were carried out at two different glucose concentrations (0.8 and 1.6 M ) and at five different glucose glycine ratios ranging from 0.25 to 2. The contributions of glucose and glycine to the permittivity of the ternary solutions linearly add, and then significant interactions between glucose and glycine molecules in water solutions must be excluded. In any case, the substitution of three water molecules with one glycine molecule implies a permittivity increment of the interfacial region of about 100. This value is absolutely incompatible with our results. This means that glycine does not coordinate within the primary shell of glucoside micelle. In addition, given the coincidence of the dielectric results of water–OBG and water–glycine–OBG solutions, we can conclude that the water content into the interfacial region is not affected by the presence of glyclne. It is interesting to compare the temperature dependence of the water–glucose and the interfacial water-OBG permittivity, see Fig. 6. For water–glucose solutions the slopes are nearly constant with glucose concentration, whereas in the case of the interfacial permittivity of water–OBG micelle the slope is evidently higher. This finding is in agreement with the observed micellar growth with temperature [21]. Again it is associated with dehydration of the interface and then with a dipper decrease with temperature of the interfacial permittivity than the one of water-glucose solutions.
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Fig. 6. Dependence on temperature of permittivities of water (curve 1); waterglucose at different molarities (curve 2, 0.5 M; curve 3, 1.5 M; curve 4, 2.5 M; curve 5, 3.5 M ) and of the micellar interface (curve 6).
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The main limitations of the method are detailed below. (1) The dimension of the interfacial region: if the volume of the interface is less than 10% the sensibility of the method is not enough to obtain reliable evaluation of the interfacial permittivity. (2) The method is not applicable to ionic surfactant solutions or in presence of high ionic strength: in these cases the electrical conductivity becomes predominant. (3) If the chemical composition of the polar heads induces strong structural arrangements of the solvent molecules at the interface the main hypothesis of our method falls.
Acknowledgment 4. Concluding remarks The method we present gives the composition at the micellar interface. In binary mixtures the evaluated compositions are quite well defined, under the general hypothesis of dielectric equivalence between the interfacial region and water-free polar head solutions. From these results it is possible to estimate the conformational properties of the head group, when unknown. Indeed the composition corresponds to a specific volume per polar head group, that is defined by the area per polar head and by the thickness of the interface. If one of the parameters is known, the other is completely defined. Our analysis strictly follows bases of Blankschtein model that separates the free energy of micellar formation in different independent contributions due to the oil core and micellar interface. For binary mixtures our results completely matches the theoretical predictions. In ternary mixtures this procedure can give unambiguous information on the degree of absorbtion of cosolvent molecules at the interface, but quantitative evaluations require other independent data. Nevertheless, from the temperature dependence of the interfacial permittivity, a lot of information on the structural properties of micellar solutions in presence of cosolvent molecules can be obtained.
The research was supported by a grant of the Istituto Nazlonale di Fisica della Materia.
References [1] R. Kjellander, E. Florin, J. Chem. Soc. Farad. Trans. 1 77 (1981) 2053. [2] S. Puvvada, D. Blankschtein, J. Chem. Phys. 92 (1990) 6053. [3] G. Briganti, S. Puvvada, D. Blankschtein, J. Phys. Chem. 95 (1991) 8989. [4] B. Carvalho, G. Briganti, S.H. Chen, J. Phys. Chem. 93 (1989) 4282. [5] G. Briganti, A. Bonincontro, J. Non-Cryst. Solids 172 (1994) 1173. [6 ] A. Bonincontro, G. Briganti, A. D’Aprano, C. La Mesa, B. Sesta, Langmuir 12 (1996) 3206. [7] A. Bonincontro, A. Glansanti, F. Pedone, G. Risuleo, Biochim. Biophys. Acta 1115 (1991) 49. [8] P.A. Bottomley, J. Phys E, Sci. Instrum. 11 (1978) 413. [9] L.K.H. Van Beek, in: J.B. Birks, Progress in Dielectrics, Heywood, London, 1967, p. 69. [10] J.B. Hasted, Aqueous Dielectrics, Chapman and Hall, London, 1973. [11] K. Asami, Y. Takahashi, S. Takashima, Biochim. Blophys. Acta 1010 (1989) 49. [12] W. Brown, R. Rymden, J. Phys. Chem. 60 (1987) 775. [13] M. Zulauf, K. Weckstrom, J.B. Hayter, V. Degiorgio, M. Corti, J. Phys. Chem. 89 (1985) 3411. [14] R. Zana, C. Weill, J. Phys. Lett. 46 (1985) 953. [15] M. Almgren, J. Alsins, Prog. Colloid Polym. Sci 81 (1990) 9.
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[16 ] G.A. Jeffrey, S. Bhattacharjee, Carbohydr. Res. 115 (1983) 53. [17] A. Suggett, J. Sol. Chem. 5 (1976) 33. [18] G. Briganti, G. D’Arrigo, Progress Colloid Polym. Sci. (1997) in press. [19] E.D. Goddard, Colloids Surf. 19 (1986) 255.
[20] K.P. Ananthapadmanabhan, in: E.D. Goddard, K.P. Ananthapadmanabhan, Interactions of Surfactants with Polymers and Proteins, CRC Press, Boca Raton, FL, 1993, p. 319. [21] D. Blankschtein, G.M. Thurston, G.B. Benadek, J. Chem. Phys. 85 (1986) 7268.
A dielectric method to investigate the interfacial composition of micellar aggregates G. Briganti *, A. Bonincontro INFM, Physics Department, ‘‘La Sapienza’’ University, P.A. Moro 5, 00185 Rome, Italy Received 10 February 1997; accepted 21 April 1997
Abstract The aggregation state of micellar solutions is mainly determined by the specific chemical and physical conditions within the interfacial region constituted by the polar head terminations and solvent molecules. In particular the mutual head group interactions and their interactions with solvent and cosolvent molecules strongly affect the overall shape, size and size distribution function of micellar solutions. It then becomes evident how important the determination of the composition and structural arrangement of the interfacial region is. Permittivity measurements of an heterogeneous system allow the evaluation of the permittivity of the suspended particles using one of the available mixture equations. If the suspended particles are constituted by separated regions with different dielectric properties it is possible to iterate the procedure to extract information on each of the regions. In the case of micellar aggregates there is the hydrocarbon core region, equivalent to an oil liquid phase, and an interfacial region, constituted by the polar head group terminations, solvent and cosolvent molecules. By comparing the interfacial permittivity with the permittivity of mixtures composed by the solvent and free head groups, it is possible to evaluate the composition of the micellar interface. We apply this methodology on two different surfactant mixtures: C E in water and in 12 6 water–urea (2, 4 and 6 M ); octyl-b--glucopyranoside in water and in water–glyclne (0.3 and 0.6 M ). The results obtained concerning the conformation and composition at the interface are consistent with the overall behaviour of the solutions studied by many other different techniques supporting the proposed procedure. © 1998 Elsevier Science B.V. All rights reserved. Keywords: Mesoscopic solution; Dielectric spectroscopy
1. Introduction Most of the molecular thermodynamic theories suggest that the micellar thermodynamic state, i.e. shape and size distribution function, is strongly affected by the properties of the micellar interface [1,2]. Changing temperature and solvent composition, shape and size of non-ionic surfactant solutions [3] as well as of zwitterionic surfactant solutions [4] change. In both cases rescaling vari* Corresponding author. 0927-7757/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S0 9 2 7 -7 7 5 7 ( 9 7 ) 0 0 28 8 - 4
ables with temperature allows the solvent composition to be found. These results suggest that the overall thermodynamic properties of the surfactant solution can be divided in the contributions due to three different regions, namely the bulk solvent region, the oil core region and the interfacial one, containing the head group terminations and the solvent molecules. A very exhaustive analysis of the free energy associated with the formation of micelles with different size and shape was recently developed by Blankschtein and Puvvada [2]. The contribution
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due to the oil core formation can be evaluated through measurable thermodynamic quantities, i.e. free energy of solubilization of the hydrocarbon tails and interfacial tension oil core–bulk solvent, and computing the hydrophobic tail conformation compatible with the micellar shape. In contrast, the contributions due to head group terminations depend on the area per polar head and on the repulsive excluded volume head–head interactions. It is difficult to ascertain the connection between the area per polar head group and of the head– head interaction with any directly measurable quantity. In this work we wish to show that dielectric measurements supply this demand. Then, combining these measurements with the one required for the model describing the oil core, a complete prediction of the solution behaviour can be obtained. The following paragraph concerns the methodology used for the determination of the interfacial composition. The methodology is then applied on two different surfactant solutions with an extended comparison with other experimental results. This section is divided into two subsections, the first concerns binary mixtures, with examples on water–C E and water–OBG (octyl-b--glucopi12 6 ranoside) solutions, a non-ionic and a zwitterionic surfactant molecule, respectively. The second subsection shows the analysis of results obtained from ternary solutions with cosolvent molecules (water–urea–C E and water–glycine–OBG solu12 6 tions). The last paragraph is devoted to a discussion of reliability of our method in the light of the proposed experimental results.
2. Method The sample preparations is reported in Ref. [5] for C E water and water–urea solutions, and in 12 6 Ref. [6 ] for water–OBG and water–glycine–OBG solutions. Permittivity measurements in our experiments were carried out by means of an impedance analyser HP 4194 A in the frequency range from 10 to 100 MHz. The cell consists of a section of a cylindrical wave guide excited far beyond its cutoff frequency mode; its general properties are
described elsewhere [6 ]. Cell constants were determined by calibration with reference liquids according to a standard procedure [7]. The temperature was controlled to within 0.1°C. The frequency range used in our dielectric measurements is above the Maxwell–Wagner dispersion [8] and below the solvent relaxation [9]. Thus the experimental results can be analysed in terms of an appropriate mixture equation in order to estimate the permittivity of the micelle. In particular, the Polder–van Santen equation, derived from the original Wagner equation, was used because its validity extends over a wide concentration range. For prolate ellipsoids the equation can be written as follows [10]:
G H
w 4 e=e − 2 (e −e )e* 1 2 1 2e* +(1−2d)(e −e* ) 3 1 1 2 1 1 + , (1) e* +2d(e −e* ) 1 2 1 where d is a parameter which decreases from 0.33, for spherical particles, to zero increasing the axial ratio of the particles. This parameter can be obtained from quasielastic light scattering measurements of the hydrodynamic radius R [10]. For h C E solutions the axial ratios were taken from 12 6 Ref. [3]. According to Eq. (1), the dielectric permittivity of the solution, e, is a linear function of the volume fraction of the solute, W , and depends 2 on the dielectric constants of solvent, e , and 1 solute, e , and on e*. This last quantity lies 2 1 between e and e, and is related to the modification 1 of the intrinsic properties of the solvent due to solvent–solute interactions. It has been found that up to 25% in W , e*=e in most systems and, in 2 1 1 particular, in micellar solutions [9]; for solutions up to 45% in W a small correction ( less than 10%) 2 due to e* change is necessary, but still a reasonable 1 estimation of e can be obtained. 2 In Eq. (1) the computation of the volume fraction of the suspended particles, knowing the mole fraction (x) of the monomers in solution, implies a model for the solution. Our analysis is based on the following assumptions: (1) the solution is monodisperse with aggregates
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of aggregation number equal to the average aggregation number of the real solution; (2) the volumes of all the monomers are equivalent. Since the aggregate shape and dimension, i.e. the factor d in Eq. (1), contribute little to the determination of the solute permittivity in the data treatment, we can use these approximations in our analysis. The same assumptions are used in the determination of the monomer partial molar volume and of the first cumulant approximation of R . Using these two conditions the volume h fraction appearing in Eq. (1) is the monomer volume fraction. Indeed N monomers occupy, on average, the same volume as N/n aggregates of aggregation number n. In Fig. 1 the section of a micelle (spherical or cylindrical ) of C E is sche12 6 matized; under the previous conditions the monomer volume can be visualized by the cone dotted in the polar head region and dark in the oil core region. The method then develops in three steps. In the first we determine the dielectric constant of the suspended particles, parametrizing the monomer volume V used in the definition of the solute 1
Fig. 1. A section of a spherical or cylindrical C E nonionic 12 6 micelle is shown. The dark cone on the right side illustrates the oil core volume per monomer, the dotted region the volume available to the head group termination and to solvent molecules. The dashed rectangular region visualizes the actual structuaral properties of the water–PEO solution at the micellar interface.
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volume fraction. This parameter defines the overall conformation of the polar head terminations; the oil core properties can be obtained by the theory for micellar formation of Ref. [2]. In the case of C E micelles of Fig. 1, V defines the conforma12 6 1 tion of the PEO polar termination as well as of the area per polar head group. In Fig. 2 the permittivity experimental results of C E are visu12 6 alized for different choices of the value of V , the 1 lines indicate the corresponding linear trends where Eq. (1) can be applied. The second step of our analysis is not novel. Asami et al. [11] used the same methodology to obtain the permittivity of a double layer. From the previous determinations we know the micellar permittivity, the one of the oil core (equivalent to the corresponding oil permittivity), the total monomer volume V, and the tail volume from Ref. [2]. The shape factor of the oil core is the same as the one of the micelle. We can then evaluate the interfacial permittivity applying again Eq. (1) to an idealized solution composed, in this case, of the oil cores dispersed in a mixture, constituted by the solvent molecules and the head group terminations. The third step of our analysis concerns the comparison of the obtained interfacial permittivity
Fig. 2. Permittivity of C E micellar solution e divided by the 12 6 water permittivity e at 25°C as a function of the hydrated 1 monomer volume fraction w . The different curves correspond 2 ˚3 to different values of the monomer hydrated volume: 1000 A ˚ ˚ ˚ 3 (,), 1982 A ˚ 3 (%), (#), 1200 A3 ($), 1500 A3 (( ), 1770 A ˚ 3 (&), 3470 A ˚ 3 (6). 2500 A
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with the one of a solution composed by solvent molecules and free polar head groups. The dashed region of Fig. 1 visualizes the solute network at the water–C E micellar interface. The micellar 12 6 interface is randomly oriented with respect to the polarizing field, averaging the orientational distribution of the interfacial water–polymer solution as in the case of pure water–polymer solutions. Then the dielectric responses of the pure water– polymer solutions should be very similar to the one of the interfacial mixture. Then the intercept between the permittivity trend with polymer concentration of solvent-free polar head solutions and of the interfacial one, obtained with our parametric procedure, represents a good approximation of the composition at the micellar interface.
3. Results and discussion 3.1. Water surfactant mixtures In Fig. 3 the interfacial permittivity in water–C E solutions, obtained for different 12 6 values of V (data from Fig. 2) and the experimen1 tal permittivity of water–PEO solutions are reported as a function of PEO polymer concentration. Following our hypothesis the concentration of the intercept between the two curves corresponds to the equivalent interfacial concen-
Fig. 3. Micellar crown permittivity (full symbols) in water solution as a function of PEO unit molar concentration at three different temperatures (5, 25 and 45°C which correspond to T −T of 46.6, 26.6 and 6.6). The empty symbols refer to c PEO–water solutions at the same temperatures.
tration. The number of PEO units per polar head group is known, six in our case, and then the available volume for the hydrophilic termination results from our procedure. The comparison of our results on water–C E 12 6 solutions with results from other techniques supports our analysis. Light scattering [12] and SANS measurements [13] have given for the micellar ˚ , respectively. minor radius values of 30 and 32 A At the same temperature the volume of the interfacial mixture we estimate, using the theoretical ˚ 2 [2], is value for the area per polar head of 63 A compatible with a micellar minor radius of about ˚ . Subtracting the mass of the hydration water 31 A computed from the micellar molecular weight determined by Zimm plot light scattering analysis [12], we evaluate an aggregation number for spherical micelle of about 45 at 18°C. Theoretical evaluations of the oil core dimension give, using the liquid oil density for the oil core, the same aggregation number we previously estimated [2]. Our estimation of the aggregation number is significantly smaller than the direct evaluations from Zimm analysis, from a combination of light and neutron scattering measurements [13] and from fluorescence quenching experiments [14,15] which give 140. At low temperature and concentration the micellar shape is generally considered spherical [2,3,12,13]. The aggregation number of 140 is not consistent with this shape — indeed the micellar density will be too high. In our opinion the first two experimental evaluations of the aggregation number are overestimated because they are related to the total mass of the hydrated micelle and the water contribution is relevant. The fluorescence quenching result is obtained with drastic approximations and it is affected by the enviromental condition of the micellar interface, as observed by the direct measurements of the fluorescence decay time of the pyrene [14,15]. Our aggregation number on the other hand might be underestimated because we did not consider any effect due to the oil core on the dielectric properties of the interface. Similar measurements were performed on solutions of water and OBG. Addition, in this case we define the volume of the hydrocarbon core in accordance with Blankschtein’s model [2], whereas
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the total volume of hydrated OBG was obtained from experimental determination of the partial molar volume [6 ]. The oil core/monomer volume fraction estimated in this way is about 38% of the total micellar volume. This implies a thickness of ˚ in good the head group region of about 4 A agreement with X-ray data from crystallized samples [16 ]. Differently from C E , in this case 12 6 the conformation of the head groups practically does not affect the monomer volume and V is 1 fixed. The comparison of the permittivity of the interfacial region with the water–glucose permittivity indicates that the glucose concentration at 25°C is about 6.1 mol l−1, that corresponds to a water–glucose molecular ratio of 4 at the micellar interface, in agreement with the literature [17]. The solubility of glucose in water is 4.3 mol l−1, and our results indicate that zwitterionic head terminations strongly interact with the oil core interface and the degree of hydration at the micellar interface can exceed the precipitation threshold, up to a maximum of 6.1 mol l−1. Recent results of sound velocity suggest that the London force field generated by the oil core region acts on the head groups and on the solvent molecules, overcoming the local binary interactions between solvent molecules and head group terminations [18]. This finding might justify the anomalous concentration observed at the OBG micellar interface, and indeed the electrostatic interactions could stabilize the very high concentration of glucose in the micellar interface.
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of non-ionic and zwitterionic surfactant solutions in binary solvents is of wide interest and our technique is specific for this purpose. The same micellar solutions studied as binary mixtures were analysed in the presence of a cosolvent. In the case of water–C E solutions we 12 6 added urea, a specific component generally used for protein denaturation. In water–OBG solutions the cosolvent was glycine, one of the most common aminoacid which has a strong electric dipole moment. Regarding C E solutions in presence of urea, 12 6 it is known that the thermodynamic properties (phase separation as well as shape and size of the micelle) rescale with the reduced temperature T −T, where T s are the lower consolute critical c c temperatures for the different content of urea in the solvent mixtures [3]. With an equivalent procedure as the one applied in the binary mixtures we obtain, at similar rescaled temperatures, the interfacial permittivity. The results for 6 M urea in the buffer mixtures are shown in Fig. 4 and compared with water–6 M urea–PEO permittivity. In the case of ternary solutions the dielectric contribution due to the interface depends on the specific interfacial composition, therefore our determination of the available volume per polar head groups requires other independent information. Looking to Fig. 4 it is possible to state that
3.2. Ternary mixtures: cosolvent contributions Ternary surfactant solutions can be divided into two categories: two surfactant species in a homomolecular solvent (in the presence of a cosurfactant), one surfactant specie in a binary solvent (the in presence of a cosolvent). The interactions between surfactants and biopolymers are the subject of continuous investigations [19]. Most of them deal with the capability to separate biopolymers from their natural matrices by selective solubilization. To avoid drawbacks occurring in presence of ionic detergents, non-ionic or zwitterionic surfactants are preferred [20]. Then the study
Fig. 4. Micellar crown permittivity (full symbols) in 6 M water–urea solution as a function of PEO unit molar concentration at three different temperatures (18.2, 35.6 and 54°C which correspond to T −T of 47.4, 30 and 11.6). The empty c symbols refer to water–6 M urea–PEO solutions at the same temperatures.
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the permittivities of water–urea–PEO solutions with an urea content lower then 6 M, the urea buffer concentration of these micellar solutions, never crosses the evaluated interfacial permittivity. This clearly indicates that the urea concentration at the interface cannot be lower the bulk concentration, therefore urea desorbtion from the interface is excluded. On the other hand adsorbtion of urea is compatible with our results. In Fig. 5 the temperature dependence of the volume per polar head is reported as a function of temperature for all the investigated concentrations of urea in the solvent. Looking at the figure some statements can be asserted. Equivalent linear trends are observed in all the cases, suggesting that mainly water molecules are involved in the temperature-induced dehydration of the interface; increasing temperature cause the urea concentration at the interface to increases. The volume per polar head increases with urea concentration and saturates at about 4 M. Since the hydrodynamic radii of the aggregates coincide, at the same rescaled temperature the area per polar head group must increase with urea concentration, remaining constant above 4 M. This is not surprising since the solubility of the hydrocarbon tail increases with urea and the interfacial tension decreases. In water–glycine–OBG solutions the micellar permittivities obtained in the first step of our
˚ 3) estimated by our Fig. 5. Monomer hydrated volume V (A h method (see text) as a function of T −T (C ). (#) Water soluc tion, ($) 2 M water–urea solution, (+) 4 M water–urea solution, (%) 6 M water–urea solution.
analysis at 0.0, 0.3 and 0.6 M glycine concentrations coincide at all the investigated temperatures. Since the head group conformation cannot significantly change the interfacial volume per monomer, the interfacial composition might change only by substituting water molecules with the glycine, the volume ratio between water and glycine being about 1/3. Dielectric measurements carried out on water– glucose, water–glycine and water–glycine–glucose solutions show that the dielectric constant of water linearly decreases with glucose concentration with a slope of 4.4 mol−1, whereas the addition of glycine linearly increases the water permittivity with a slope of 23.6 mol−1. Both results are in full agreement with data from the literature [10]. Concerning the water–glycine–glucose solutions, the dielectric measurements were carried out at two different glucose concentrations (0.8 and 1.6 M ) and at five different glucose glycine ratios ranging from 0.25 to 2. The contributions of glucose and glycine to the permittivity of the ternary solutions linearly add, and then significant interactions between glucose and glycine molecules in water solutions must be excluded. In any case, the substitution of three water molecules with one glycine molecule implies a permittivity increment of the interfacial region of about 100. This value is absolutely incompatible with our results. This means that glycine does not coordinate within the primary shell of glucoside micelle. In addition, given the coincidence of the dielectric results of water–OBG and water–glycine–OBG solutions, we can conclude that the water content into the interfacial region is not affected by the presence of glyclne. It is interesting to compare the temperature dependence of the water–glucose and the interfacial water-OBG permittivity, see Fig. 6. For water–glucose solutions the slopes are nearly constant with glucose concentration, whereas in the case of the interfacial permittivity of water–OBG micelle the slope is evidently higher. This finding is in agreement with the observed micellar growth with temperature [21]. Again it is associated with dehydration of the interface and then with a dipper decrease with temperature of the interfacial permittivity than the one of water-glucose solutions.
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Fig. 6. Dependence on temperature of permittivities of water (curve 1); waterglucose at different molarities (curve 2, 0.5 M; curve 3, 1.5 M; curve 4, 2.5 M; curve 5, 3.5 M ) and of the micellar interface (curve 6).
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The main limitations of the method are detailed below. (1) The dimension of the interfacial region: if the volume of the interface is less than 10% the sensibility of the method is not enough to obtain reliable evaluation of the interfacial permittivity. (2) The method is not applicable to ionic surfactant solutions or in presence of high ionic strength: in these cases the electrical conductivity becomes predominant. (3) If the chemical composition of the polar heads induces strong structural arrangements of the solvent molecules at the interface the main hypothesis of our method falls.
Acknowledgment 4. Concluding remarks The method we present gives the composition at the micellar interface. In binary mixtures the evaluated compositions are quite well defined, under the general hypothesis of dielectric equivalence between the interfacial region and water-free polar head solutions. From these results it is possible to estimate the conformational properties of the head group, when unknown. Indeed the composition corresponds to a specific volume per polar head group, that is defined by the area per polar head and by the thickness of the interface. If one of the parameters is known, the other is completely defined. Our analysis strictly follows bases of Blankschtein model that separates the free energy of micellar formation in different independent contributions due to the oil core and micellar interface. For binary mixtures our results completely matches the theoretical predictions. In ternary mixtures this procedure can give unambiguous information on the degree of absorbtion of cosolvent molecules at the interface, but quantitative evaluations require other independent data. Nevertheless, from the temperature dependence of the interfacial permittivity, a lot of information on the structural properties of micellar solutions in presence of cosolvent molecules can be obtained.
The research was supported by a grant of the Istituto Nazlonale di Fisica della Materia.
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