16780
J. Phys. Chem. B 2004, 108, 16780-16785
Adsorption from Mixed Ionic Surfactant/Protein Solutions: Analysis of Ion Binding V. B. Fainerman,† S. A. Zholob,† M. E. Leser,‡ M. Michel,‡ and R. Miller*,§ Medical Physicochemical Centre, Donetsk Medical UniVersity, 16 Ilych AVenue, 83003 Donetsk, Ukraine, Nestec Ltd., Nestle´ Research Centre, Vers-chez-les-Blanc, CH-1000 Lausanne 26, Switzerland, and Max-Planck-Institut fu¨r Kolloid und Grenzfla¨chenforschung, Am Mu¨hlenberg 1, 14424 Potsdam, Germany ReceiVed: January 20, 2004; In Final Form: August 4, 2004
A thermodynamic model is derived for the description of the equilibrium behavior of mixtures of a protein with an ionic surfactant adsorbed at the liquid/fluid interface. It is shown that experimental data for the mixtures HSA/CTAB (human serum albumin/cetyl trimethylammonium bromide) and β-LG/SDS (β-lactoglobulin/ sodium dodecyl sulfate) agree satisfactorily with the theoretical estimates. The theoretical calculations of the adsorption behavior are based on the parameters of the individual protein and surfactant solutions. From the comparison between theoretical results and experimental data, quite reasonable estimates for the number of free charges in the protein molecule m were obtained. For the HSA molecule, m is between 5 and 10, and for the β-LG molecule, m is between 2 and 3.
1. Introduction Surfactants can modify surface layers of proteins at liquid/ fluid interfaces. These modifications result in a change of the adsorption as well as rheological characteristics of these layers.1-8 The mechanism of protein-surfactant interaction depends on the surfactant nature and its concentration in the solution bulk.4,9-13 For ionic surfactants, four concentration ranges could be distinguished, in which different interaction mechanisms play the governing role. At low surfactant concentrations, Coulombic interaction between the surface active ion and the oppositely charged ions of the protein molecule is observed.4,11-13 With increasing surfactant concentration, the role of hydrophobic interactions between the nonpolar groups of the surfactant and protein becomes more important. This leads first to a binding of individual surfactant molecules to the protein and, subsequently, to the formation of micelle-like structures. It can be expected that, in the range governed by Coulombic interaction, the surface tension of the mixed protein/surfactant solution is much more strongly changed than for systems where other interactions dominate. This fact can be explained (by analogy with mixtures of surfactants of opposite charges14) by the increase of the average ion concentration in the solution and the increased adsorption activity of the complex. It is also clear that, in the range of hydrophobic binding and formation of micelle-like structures, we cannot expect a variation in surface tension with increasing surfactant concentration.12 The behavior of mixed ionic surfactant/protein solutions is essentially different from that of nonionic surfactant/protein mixtures. In the latter case, at low surfactant concentrations, the behavior of the mixture in the monolayer is governed mainly by competitive adsorption.7,15-25 A first theoretical analysis of competitive adsorption of large and small molecules was presented by Lucassen-Reynders in ref 15. In ref 25, the theoretical model developed in ref 15 was generalized, taking into account the ability of the protein molecule to occupy variable (depending on the surface coverage) area in the surface layer.26 †
Donetsk Medical University. Nestle´ Research Centre. § Max-Planck-Institut fu ¨ r Kolloid und Grenzfla¨chenforschung. ‡
In the proposed study, the theory given in ref 25 is further extended to account for the Coulombic interaction between the protein and surfactant molecules. The theoretical results are compared with experimental surface tension data obtained for solutions of proteins with the addition of ionic surfactants and, also, with data obtained by atomic force microscopy (AFM) and Brewster angle microscopy (BAM).22,23,27,28 2. Theory 2.1. Individual Solutions of Protein. It is known1,17,26 that protein molecules can exist in a number of states of different molar area, varying from a maximum value (ωmax) at very low surface coverage to a minimum value (ωmin) at high surface coverage. The molar area of the solvent, or the area occupied by one segment of the protein molecule ω0, is much smaller than the molar area of an adsorbed protein. The equation of state based on a first-order model for nonideal entropy and nonideal heat of mixing for the surface layer was derived in ref 26
-
(
)
Πω0 ω0 + aPθ2P ) ln(1 - θP) + θP 1 RT ω
(1)
where Π is the surface pressure, R is the gas law constant, T is the temperature, and aP is the intermolecular interaction parameter. n
Γ)
Γi ∑ i)1
(2)
is the total adsorption of proteins in all n states (here the subscript P is omitted for the sake of simplicity). n
θP ) ωΓ )
ωiΓi ∑ i)1
(3)
is the total surface coverage by protein. Here, ω is the average molar area of protein, ωi ) ω1 + (i - 1)ω0 (1 e i e n) is the molar area of protein in state i, assuming the molar area
10.1021/jp0497099 CCC: $27.50 © 2004 American Chemical Society Published on Web 09/30/2004
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J. Phys. Chem. B, Vol. 108, No. 43, 2004 16781
increment ω0, and ω1 ) ωmin, ωmax ) ω1 + (n - 1)ω0. The equations for the adsorption isotherm for each state (j) of the adsorbed protein are
bPcP )
ωΓj (1 - θP)
ωj/ω
[ ()]
exp -2aP
ωj θ ω P
[
(1 - θP)(ωj-ω1)/ω exp 2aPθP Γj ) Γ
n
[
(1 - θP)(ω -ω )/ω exp 2aPθP ∑ i)1 j
1
]
ωj - ω1 ω
]
(5)
ωi - ω1 ω
(
)
ω0 Πω0 ) ln(1 - θP - θS) + θP 1 + aPθ2P + RT ω aSθ2S + 2aPSθPθS (6)
where aPS is a parameter which describes the interaction between the protein and surfactant molecules. For the protein in state 1 and the surfactant, the adsorption isotherm reads25
bPcP )
ωΓ1 (1 - θP - θS)
bScS )
ω1/ω
[ ( )
exp -2aP
θS (1 - θP - θS)
]
ω1 θ - 2aPSθS (7) ω P
exp[-2aSθS - 2aPSθP]
i
ω
1
ωi - ω1
(9)
ω
2.3. Mixture of Protein with Ionic Surfactant. When we consider a protein molecule with m ionized groups available for Coulombic binding of surfactant ions of opposite charge, respective complexes will be formed. The formation of such complexes is determined by the average activity of ions (mean ionic product14) participating in the reaction: (cmP cS)1/(1+m) (assuming the average activity coefficient equal to 1). Other complexes can also be formed (e.g., complexes of the protein with buffer ions); however, these complexes are less surface active, and their contribution to the surface pressure can be neglected. The approach for the description of interfacial layers based on the chemical potentials as developed in ref 29 was used recently for solutions of proteins26 and ionic surfactant mixtures.14 The respective equation of state of the surface layer is given by
(
)
ω0 Πω0 + aPSθ2PS + ) ln(1 - θPS - θS) + θPS 1 RT ω aSθ2S + 2aSPSθPSθS (10)
The adsorption isotherms for the protein/surfactant complex in state 1 and the surfactant unbound by the protein read
c1/(1+m) ) bPS(cmP cS)1/(1+m) ) bPScm/(1+m) P S ωΓ1 ω1 exp -2aPS θ - 2aSPSθS (11) ω1/ω ω PS (1 - θPS - θS)
[ ( )
bS(cScC)1/2 )
θS (1 - θPS - θS)
]
exp[-2aSθS - 2aSPSθPS] (12)
n where ω ) (∑i)1 ωiΓi)/Γ (again the subscript PS is omitted for the sake of simplicity), θPS ) ωΓ, cC is the surfactant counterion concentration (in absence of inorganic salt (cScC)1/2 ) cS), and aSPS is the intermolecular interaction parameter which describes the interaction of the nonassociated surfactant with the protein/ surfactant complex. The subscript PS refers to the protein/ surfactant complex, and the subscript S refers to the surfactant. Note that eq 10 is very similar to eq 6, because it does not contain the additional term in the right-hand side which accounts for the contribution of electrical charges. It was shown in ref 14 that, when expressing the dependence of surface pressure for the ionic surfactant solution via (cScC)1/2, one automatically excludes the contribution of the diffuse part of the electric double layer into the surface pressure, while the remaining small contribution due to the Stern-Helmholtz layer is compensated by the parameter aS. The distribution of protein adsorptions over the states is given by an expression following from eq 11, when written for any arbitrary jth state of the complex
(8)
where θS ) ΓS‚ωS, ΓS is the surfactant adsorption, and the subscript S refers to the values characteristic for the surfactant. The distribution of protein adsorptions over the states is given by the expression25
n
ωj - ω1
(1 - θP - θS)(ω -ω )/ω exp 2apθP ∑ i)1
-
The model given by eqs 1-5 describes the evolution of the states of the protein molecule during the adsorption process, which agrees in many details with known experimental results. It follows from eq 5 that in diluted monolayers all states have the same probability (i.e., the highest fraction of protein molecules could be unfolded to the most possible extent), and therefore, the adsorption layer thickness is minimal. One can also see from eq 5 that, with increasing adsorption, the fraction of states corresponding to the maximum area becomes lower, while those with the minimum area become more probable. This results in a reduced unfolding of the protein molecules, and the adsorption layer thickness increases. The folding-unfolding processes are illustrated in detail by the schematic drawings and by the dependencies of the average molar area on the protein concentration presented recently.1,26 2.2. Mixture of Protein with Nonionic Surfactant. The analysis of the chemical potentials of the components, based on the approximate relation ω0 = ωS, yields the equation of state for a protein/nonionic surfactant mixture25
-
Γj ) Γ
(4)
where cP is the protein bulk concentration and bP ) bPj is the equilibrium adsorption constant for the protein in the jth state (we again omit the subscript j for sake of simplicity). It is assumed that the values of the constants bPj for j ) 1 ... n are equal to each other, and therefore, the adsorption constant for the protein molecule as a whole is ∑bPj ) nbPj.26 From the fact that the bPi are equal to each other, one can calculate the distribution function of adsorptions over various states of the protein molecule from eq 4
[ ( )] [ ( )]
(1 - θP - θS)(ωj-ω1)/ω exp 2apθP
[ ( )] [ ( )]
(1 - θPS - θS)(ωj-ω1)/ω exp 2aPSθPS Γj ) Γ
n
∑ i)1
ωj - ω1
(1 - θPS - θS)(ωi-ω1)/ω exp 2aPSθPS
ω
ωi - ω1 ω
(13)
16782 J. Phys. Chem. B, Vol. 108, No. 43, 2004
Fainerman et al.
Figure 1. Surface tension of HSA (0, data from ref 30) and β-LG (4, data from ref 6; 2, data from ref 31) solutions measured by the pendent drop method; theoretical curve calculated from eqs 1-5.
The set of eqs 6-13 is sufficient to describe the adsorption behavior of mixed solutions of a protein with a surfactant. Therefore, the theoretical description of such a mixture is formulated as follows: Given the known values of T, ω0, ωmin, ωmax, aS, aP, aPS, aSPS, m, bP, bPS, cP, and bS, the dependencies of ω, θP, θS, θPS, and Π on the surfactant concentration cS can be calculated. Assuming the approximations aPS ) aP, aSPS ) 0 (or aSPS ) (aS + aP)/2),14 and bPS ) bP are valid, it becomes possible to calculate the adsorption behavior of mixtures using only the characteristics of the individual solutions of the protein and surfactant. Therefore, out of the parameters necessary for the calculations, there are five parameters corresponding to the individual protein solution (ω0, ωmin, ωmax, aP, and bP), among which the ωmax and ωmin could be determined from the geometrical dimensions of the protein molecule in its ultimately unfolded and folded states, respectively. The value of ω0 is almost the same for all proteins, being in the range of (2-3)‚105 m2/mol. All other parameters can be estimated from the fitting of either (or all, simultaneously) experimental dependencies Π vs cP, Π vs Γ, and Γ vs cP.26 The remaining three parameters, which are related to the individual surfactant solution (ωS, aS, and bS), can be determined by fitting of the experimental dependency Π vs cS. The parameter m is usually known from independent experimental data. However, as will be shown, it can be estimated by fitting the model to the surface tension data of the mixture. Note, the assumption aSPS ) 0 (instead of aSPS ) (aS + aP)/2) is probably more preferable when strong inhomogeneities in the mixed surface layer have to be expected. The protein and surfactant molecules practically do not mix in the surface layer but form domains containing essentially one of the components.22,23,27,28 The assumption bPS ) bP is based on the fact that m is small (10 or 100 times lower than the number of amino acid groups in the protein molecule), and therefore, the adsorption activity of the protein/surfactant complex varies only slightly. Moreover, for cS . cP, the adsorption of nonassociated protein can be neglected. The procedure employed for the calculations according to eqs 6-9 for the protein/nonionic surfactant mixture was described earlier in ref 25. To solve eqs 10-13, a similar but more complicated procedure was used. Note that in the present case the concentration cS enters both adsorption isotherms (eqs 11 and 12).
3. Results and Discussion In Figure 1, the surface tension isotherms for human serum albumin solutions (HSA, data from ref 30) and β-lactoglobulin (β-LG, data from refs 6 and 31) measured by the pendent drop method in the presence of phosphate buffer (0.01 M of Na2HPO4 and NaH2PO4, pH 7.0) are shown. To describe the isotherms theoretically below a critical concentration (shown by the arrows in Figure 1), eqs 1-5 were used. The part of the isotherm corresponding to the postcritical protein concentration is described by the equation of state and adsorption isotherm, assuming protein aggregation in the surface layer.26 In this concentration range, the equations also become dependent on the additional parameter , which accounts for the decrease in the protein molar area at phase transition. The theoretical curves shown in Figure 1 were calculated with the following parameters: 1. For HSA, ω0 ) 2.5‚105 m2/mol, ωmin ) 3.0‚107 m2/mol, ωmax ) 7.5‚107 m2/mol, aP ) 1, bP ) 3‚105 L/mol (or 3‚105‚ 181 ) 5.43‚107 L/mol for the molecule as a whole), and ) 0.1. 2. For β-LG, ω0 ) 3.5‚105 m2/mol, ωmin ) 4.2‚106 m2/mol, ωmax ) 1.5‚107 m2/mol, aP ) 0.3, bP ) 1.7‚106 L/mol (or 1.7‚106‚31 ) 5.27‚107 L/mol for the molecule as a whole), and ) 0.2. Note that the values for ωmin and ωmax agree with the molecular dimensions of HSA and β-LG, representing essentially the adsorption layer thickness for the two proteins.1 The dependencies of Γ on cP and Γ on Π for HSA solutions were obtained in independent experiments.26 Figure 2 illustrates the experimental surface tension isotherm for the cetyl trimethylammonium bromide (CTAB) and HSA/ CTAB mixtures at different CTAB concentrations and a fixed HSA concentration of 5‚10-8 mol/L. The experiments for the individual CTAB and for the HSA/CTAB mixture were performed using the pendent drop method (PAT1, SINTERFACE, Germany) in the presence of the phosphate buffer (0.01 M, pH 7.0, prepared by mixing 0.01 M solutions of Na2HPO4 and NaH2PO4). For comparison, the data for the CTAB in water reported in refs 1,32,33 are also shown in Figure 2. It is seen that in phosphate buffer the surface activity of CTAB becomes much higher, which can be ascribed to the ionization of Na2HPO4 and NaH2PO4 (i.e., to the formation of the H2PO4and HPO42- anions).
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J. Phys. Chem. B, Vol. 108, No. 43, 2004 16783
Figure 2. Surface tension of the HSA (5‚10-8 mol/L) mixed with CTAB (4) and of pure CTAB in buffer (2) as a function of cS; for CTAB in water (9, data from ref 1; ×, data from ref 32; +, data from ref 33). Theoretical curve for individual CTAB solution in buffer calculated from eqs 14 and 15 (thin solid line), and for mixtures calculated from eqs 6-9 (thick solid line); curves calculated from eqs 10-12 (thin lines labeled by m values). Parameters are listed in the text. Curve for CTAB in water (thin dashed line) is reproduced from ref 34.
It should be noted that the protein/ionic surfactant mixture behaves essentially differently from mixed protein/nonionic surfactant solutions. For the system HSA/nonionic (C10DMPO) surfactant, at high C10DMPO concentrations, the surface tension isotherm is almost the same as that for C10DMPO alone, and the curve for the mixture is well described by eqs 6-9.25 In contrast, for the same concentrations, the surface tension of the HSA/CTAB solutions is essentially lower than that for the individual CTAB solution (i.e., the adsorption activity of the protein in the mixture with ionic surfactant becomes higher). The theoretical curve for CTAB in the buffer shown in Figure 2 was calculated using the Frumkin model (see, for example, ref 34)
-
ΠωS ) ln(1 - θS) + aSθ2S RT
bScS )
θS (1 - θS)
exp[-2aSθS]
(14) (15)
Equations 6-13 were derived under the assumption ωS ) ω0. Taking ωS ) 2.5‚105 m2/mol (which is equal to ω0 for HSA), we can obtain the other parameters of eqs 14 and 15 for the CTAB in buffer solution: aS ) -2.4 and bS ) 9.8‚105 L/mol. The theoretical curves for HSA/CTAB mixtures shown in Figure 2 were calculated from the parameters for individual solutions given already, using the two theoretical models: eqs 6-9 and eqs 10-13. It was assumed that aSPS ) 0, aPS ) aP (eqs 10-13), aPS ) 0 (eqs 6-9), and for both cases bPS ) bP. The parameter m in eqs 11-12 was varied in the range between 3 and 20. The best agreement with the experimental results was obtained for the model given by eqs 10-13 and m ) 5-10. This value of m corresponds roughly to the number of free negative charges existing in the HSA molecule.35 With increasing m, the theoretical curves obtained from this model get closer to those obtained when excluding any binding. This situation is quite understandable, because for m . 1, the approximate relation (cmP cS)1/(1+m) = cP holds, and therefore, eq 11 transforms into eq 7. Thus, the proposed theoretical model provides a quite satisfactory description of the experimental data for HSA/CTAB mixtures at physically reasonable values of the parameter m. The adsorption of HSA and CTAB as a function of the surfactant concentration is shown in Figure 3. When increasing
Figure 3. Dependence of adsorption of CTAB (curve 1), HSA (curve 2), and total adsorption of HSA + CTAB (curve 3) in HSA/CTAB mixtures on the CTAB concentration. Dotted lines represent calculations from eqs 6-9; solid lines represent calculations from eqs 10-13 for m ) 7.
the surfactant concentration, an abrupt decrease of the protein adsorption is observed, while simultaneously, the CTAB adsorption becomes much higher. It is seen from Figure 3 that, with the increase of cS, the total adsorption of protein plus surfactant becomes somewhat higher. The curves shown in Figure 3 were calculated for the two given models. For the model corresponding to eqs 10-13, a value of m ) 7 was accepted, which provides the best fit (cf. Figure 2). From these dependencies, it becomes evident why the model described by eqs 10-13 yields lower surface tensions for the mixture, as compared with the model described by eqs 6-9. The adsorption of protein (its complex with the surfactant) and the total adsorption of protein plus surfactant are significantly higher than those in the second case. Figure 4 illustrates the experimental surface tension isotherm for sodium dodecyl sulfate (SDS) and β-LG/SDS mixtures (in phosphate buffer, 0.01 M, pH 7.0) at a different SDS concentration and fixed 10-6 mol/L β-LG.31 For the comparison, the data for the SDS in water are also shown in Figure 4.36,37 In phosphate buffer, the surface activity of SDS is also higher because of the dissociation of Na2HPO4 and NaH2PO4 and the formation of Na+ cations in water (approximate concentration
16784 J. Phys. Chem. B, Vol. 108, No. 43, 2004
Figure 4. The dependence of surface tension of the mixture of β-LG (10-6 mol/L) with SDS (4) and of the individual SDS solution in the buffer (9) on cS; surface tension of SDS in water (], data from ref 36; 2, data from ref 37; 0, data for SDS in buffer, recalculated for average ion activity c/S ) [cS ‚(cS + cNa+)]1/2 14 for cNa+ ) 0.015 M. Theoretical curve for individual SDS solution in buffer calculated from eqs 14 and 15 (thin solid line), for mixtures calculated from eqs 6-9 (thick solid line); curves calculated from eqs 10-12 (thin solid lines labeled by m values). Parameters are given in the text. Curve for SDS in water (thin dashed line) is reproduced from ref 34.
is 0.015 M, because the initial 0.01 M solutions of Na2HPO4 and NaH2PO4 were taken in almost equal proportions). Assuming ωS ) 3.5‚105 m2/mol for SDS (which is equal to ω0 for β-LG), the values for other parameters in eqs 14 and 15 for the SDS in the buffer were obtained: aS ) 0.4 and bS ) 2.39‚104 L/mol. The respective calculated curve is shown in Figure 4. The theoretical curves for the β-LG/SDS mixtures were calculated using the parameters of individual solutions given already, assuming aSPS ) 0, aPS ) aP, and bPS ) bP. The adsorption behavior of β-LG/SDS mixtures is similar to that found for the HSA/CTAB mixtures: The experimental surface tensions for the mixture are essentially lower than for the SDS solution in buffer, and the best fit of the theory is obtained for the model assuming Coulombic binding of the surfactant to the protein, eqs 10-13. The best agreement between experimental and calculated values is obtained for three free positive charges in the β-LG molecule, which is not in contradiction with data obtained by other methods.40 The adsorptions of β-LG and SDS and the total adsorption as a function of the SDS concentration are shown in Figure 5. The results obtained using the model eqs 6-9 disregarding ionic binding (or, on the contrary, for m . 1) agree well with the data obtained for the HSA/CTAB mixture (see Figure 3). However, the calculations made according to the model described by eqs 10-13 show that at a certain SDS concentration a maximum in the adsorption dependence appears, observed both for the adsorption of the protein/surfactant complex and for the total adsorption of the complex and the free surfactant. In this case, the adsorption of the complex becomes significantly higher, while the adsorption of the free surfactant becomes drastically lower as compared with the values calculated for the model without ionic binding. This effect results from the increase of average activity of the interacting ions (cmP cS)1/(1+m) with increasing surfactant concentration. The existence of such a maximum was found experimentally for the mixture of β-LG with nonionic surfactants.38,39 Our results calculated for mixed β-LG/SDS systems agree rather well with AFM data discussed in refs 22 and 23. At surface pressures below 35 mN/m (cf. Figure 4), the surface
Fainerman et al.
Figure 5. Dependence of adsorption of SDS (curve 1), β-LG (curve 2), and total adsorption of β-LG + SDS (curve 3) in β-LG/SDS mixture on SDS concentration. Dotted lines represent calculations from eqs 6-9; solid lines represent calculations from eqs 10-13 for m ) 3.
layer consists of approximately 95% protein/surfactant complexes (cf. Figure 5, solid lines), because it was also obtained in ref 22. The authors describe an intensive replacement of β-LG from the interfacial layer by adsorbing SDS molecules at a higher surface pressure. In the absence of a formation of stable complexes, as is the case when nonionic surfactants are added (dotted curve in Figure 5 and thick curve in Figure 4), a complete displacement of β-LG from the surface layer happens at the surface pressure range between 20 and 30 mN/m. This result agrees very well with the findings for mixed β-LG/Tween 20 solutions shown in ref 23. 4. Conclusions Equations are derived for the thermodynamic description of the equilibrium behavior of mixtures of a protein with an ionic surfactant adsorbed at the liquid/fluid interface. It is shown that experimental equilibrium surface tension data for such mixtures (HSA/CTAB and β-LG/SDS) agree satisfactorily with the theoretical estimates. The surface tension values of the mixture estimated from the model assuming a complex formation are lower than those predicted by the model which disregards complexation. It is essential that the theoretical calculations of the adsorption behavior are based on the parameters of the individual protein and surfactant solutions. From the comparison between theoretical results and experimental data, quite reasonable estimates for the number of free charges in the protein molecule m were obtained. For the HSA molecule, m is between 5 and 10, and for the β-LG molecule, m is between 2 and 3. Acknowledgment. The authors wish to acknowledge detailed comments and criticism by E.H. Lucassen-Reynders. The work was financially supported by projects of the European Space Agency (FASES MAP AO-99-052), the DFG (Mi418/ 11), and the Ukrainian SFFR (Project 03.07/00227). References and Notes (1) Miller, R.; Fainerman, V. B.; Makievski, A. V.; Kra¨gel, J.; Grigoriev, D. O.; Kazakov, V. N.; Sinyachenko, O. V. AdV. Colloid Interface Sci. 2000, 86, 39. (2) Dussaud, A.; Han, G. B.; Ter Minassian-Saraga, L.; Vignes-Adler, M. J. Colloid Interface Sci. 1994, 167, 247. (3) Kra¨gel, J.; Wu¨stneck, R.; Clark, D.; Wilde, P.; Miller, R. Colloids Surf., A 1995, 98, 127. (4) Turro, N. J.; Lei, X.-G.; Ananthapadmanabhan, K. P.; Aronson, M. Langmuir 1995, 11, 2525.
Mixed Ionic Surfactant/Protein Solutions (5) Wu¨stneck, R.; Kra¨gel, J.; Miller, R.; Wilde, P. J.; Clark, D. C. Colloids Surf., A 1996, 114, 255. (6) Kra¨gel, J.; Wu¨stneck, R.; Husband, F.; Wilde, P. J.; Makievski, A. V.; Grigoriev, D. O.; Li, J. B. Colloids Surf., B 1999, 12, 399. (7) Dickinson, E. Colloids Surf., B 1999, 15, 161. (8) Miller, R.; Fainerman, V. B.; Makievski, A. V.; Kra¨gel, J.; Wu¨stneck, R. Colloids Surf., A 2000, 161, 151. (9) Oakes, J. J. Chem. Soc., Faraday Trans. 1 1974, 70, 2200. (10) Jones, M. N. Biochem. J. 1974, 151, 109. (11) McClellan, S. J.; Franses, E. I. Colloids Surf., B 2003, 30, 1. (12) Santos, S. F.; Zanette, D.; Fischer, H.; Itri, R. J. Colloid Interface Sci. 2003, 162, 400. (13) Kelley, D.; McClements, D. J. Food Hydrocolloids 2003, 17, 73. (14) Fainerman, V. B.; Lucassen-Reynders, E. H. AdV. Colloid Interface Sci. 2002, 96 295. (15) Lucassen-Reynders, E. H. Colloids Surf., A 1994, 91, 79. (16) Cohen Stuart, M. A.; Fleer, G. J.; Lyklema, J.; Norde, W.; Scheutjens, J. M. H. M. AdV. Colloid Interface Sci. 1991, 34, 477. (17) Joos, P. Dynamic Surface Phenomena; VSP: Utrecht, The Netherlands, 1999. (18) Joos, P.; Serrien, G. J. Colloid Interface Sci. 1991, 145, 291. (19) Bos, M. A.; van Vliet, T. AdV. Colloid Interface Sci. 2001, 91, 437. (20) Chen, J.; Dickinson, E. Food Hydrocolloids 1995, 9, 35. (21) Murray, B. S. Colloids Surf., A 1997, 125, 73. (22) Mackie, A. R.; Gunning, A. P.; Wilde, P. J.; Morris, V. J. Langmuir 2000, 16, 8176. (23) Mackie, A. R.; Gunning, A. P.; Wilde, P. J.; Morris, V. J. J. Colloid Interface Sci. 1999, 210, 157. (24) Wijmans, C. M.; Dickinson, E. Langmuir 1999, 15, 8344. (25) Fainerman, V. B.; Zholob, S. A.; Leser, M.; Michel, M.; Miller, R. J. Colloid Interface Sci. 2004, 274, 496.
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