Surfactant Mixtures

J. Phys. Chem. C 2007, 111, 2715-2723

2715

Surface Properties and Foam Stability of Protein/Surfactant Mixtures: Theory and Experiment Julia Maldonado-Valderrama,*,† Alberto Martıń-Molina,† Antonio Martıń-Rodriguez,† Miguel A. Cabrerizo-Vı´lchez,† Marıá J. Ga´ lvez-Ruiz,† and Dominique Langevin‡ Grupo de Fı´sica de Fluidos y Biocoloides, UniVersidad de Granada, Facultad de Ciencias, Campus de FuentenueVa, sn, 18071, Granada, Spain, and Laboratoire de Physique des Solides, UMR 8502, UniVersite´ Paris-Sud, Bat, 510, 91405, Orsay Cedex, France ReceiVed: October 25, 2006; In Final Form: December 1, 2006

This research work deals with the surface behavior of mixed protein/surfactant systems and its relation with foam stability. In particular, a novel procedure of analysis of the experimental data is proposed, which provides a direct correlation between both phenomena. Accordingly, the results presented might constitute a promising tool in the control of foam stability, which has a crucial technological application. The surface characterization is performed by studying the surface pressure isotherms of mixed systems. The qualitative information extracted from the experimental curves is importantly verified by the application of a thermodynamic model to the mixed system, which was previously probed with the individual components. Moreover, the model provides the concrete composition of the surface-adsorbed layer in which the surfactant seems to displace the protein from the surface. Subsequently, the surface tension arises as a key factor in determining which species dominate the surface, and the findings appear in agreement with the theoretical conclusions. Also, the displacement of the protein by the surfactant, previously inferred experimentally and theoretically, is observed in situ by means of the evolution of the surface pressure in the sequential adsorption. Finally, this structural characterization of the surface is correlated with the measurements of the foam stability. This last feature provides a direct connection between fundamental properties and industrial magnitudes and constitutes a main achievement of this work.

Introduction Foam stability is a topic of widespread relevance in the literature because of the multiple applications in many different scientific areas such as cosmetics, detergents, food, and so forth. Foams are dispersions of air bubbles in a liquid media that contains a surface-active agent, also called foaming agent.1 This surface-active agent tends to place itself at the surface, protecting the bubbles from collapse. The composition and properties of the adsorbed layer determine the stability and physical properties of the resulting foam.2 In this sense, a direct relationship between the viscoelastic properties of the adsorbed layer and the resulting foaming properties of the system is frequent in the literature.3,4 Likewise, the structural properties of the surface-adsorbed layers are determinant in the resulting viscoelasticity.5 Accordingly, it should be interesting to investigate the relation between static surface properties, which are more accessible experimentally, and the stability of the corresponding foam. In this sense, the composition of the adsorbed surface layers should play a crucial role. Undoubtedly, the possible correlation of these phenomena has enormous technological interest because it would contribute to the control of technological variables. Moreover, to our knowledge few literature studies show a direct connection between both topics. Proteins and surfactants are widely used foaming agents in the literature, and therefore their structure upon adsorption onto * Corresponding author. Address: Departamento de Fı´sica Aplicada, Facultad de Ciencias, Universidad de Granada, Campus de Fuentenueva, sn, 18071, Granada, Spain. E-mail: [email protected]. Phone/Fax: 0034958246175/ 0034958243214. † University of Granada, Spain. ‡ University of Paris XI, France.

a surface is a question of increasing interest. The structural properties of adsorbed layers of proteins and surfactant are very different because of important differences in the molecular structure of both types of emulsifiers.2 Also, it is unusual to find “real” systems in which the interfacial layer comprises a single component, but it is more likely to comprise a mixture of materials. Despite its enhanced interest, the behavior of mixed systems is less known and still presents unsolved questions. In this sense, Peter Wilde and co-workers have thoroughly studied the composition of mixed adsorbed layers by applying several experimental techniques.2,6 However, because of the many and complex phenomena acting in these systems, the use of theoretical models in the interpretation of these systems is still scarce in the literature. Regarding the theoretical treatment of surface systems, Fainerman and co-workers have developed within the last few decades a thermodynamic model that enables the extraction of structural information on the basis of accessible experiments such as surface pressure isotherms.7 This model has been used extensively toward the better understanding of adsorbed protein layers.8,9 Likewise, the model has been extended recently to account for the behavior of mixed systems composed of proteins and surfactants.10,11 Accordingly, the first aim of this work was the application of this novel theoretical treatment to the experimental adsorption data in order to obtain structural information of the mixed adsorbed layer of a model protein and a surfactant, namely, β-casein and Tween 20. β-casein is a major fraction of milk proteins and a key ingredient in the emulsification of dairy products. The surface properties of β-casein have been studied widely in the literature by using different experimental devices such as monolayers,12,13

10.1021/jp067001j CCC: $37.00 © 2007 American Chemical Society Published on Web 01/20/2007

2716 J. Phys. Chem. C, Vol. 111, No. 6, 2007

Maldonado-Valderrama et al.

dilatational14,15 and shear rheology,16 and thin liquid films.17 Likewise, its model structure enables the application of theoretical treatments to the data.7-9,18 As a result, the static and dynamic properties of β-casein adsorbed layers as well as its confinement in thin liquid films are reasonably well-known aspects in the literature. Conversely, despite the generalized use in the literature of Tween 20 as a non-ionic emulsifying agent its interfacial structure is not as well documented as that of β-casein. Accordingly, the foaming and surface properties of Tween 20 on its own are analyzed prior to the study of the mixture in this research work. In summary, first the surface behavior of the individual systems is presented separately; β-casein was studied in previous works,7,19 whereas Tween 20 is studied hereby. Once this is clarified, the surface behavior of the mixed system is analyzed and compared to that of the individual systems by looking mostly into a very accessible property such as the surface pressure. To this end, the competitive adsorption of protein and surfactant is studied by looking into the dynamic adsorption curves and the adsorption isotherms of mixed solutions. Second, the theoretical model provides quantitative information of the composition of the mixed adsorbed layer. Next, the surface interaction arising from this analysis is probed by testing the sequential adsorption of the two species. Finally, the foam stability of the mixture is related to the surface properties encountered in this manner.

TABLE 1: Input Parameters for the Frumkin Isotherm (eqs 1-2), from Reference 21 parameter

Tween 20

b a ω

21.9 ×103 m3/mol -0.25 2.5 × 105 m2/mol

fitting parameters and allows a better data fitting than the Frumkin equation, which treats molecular interactions to first order only. On the basis of Fainerman’s model, a numerical procedure to study the adsorption of proteins at fluid interfaces was developed in a previous work.8 Similarly, in this work we have employed an analogous iterative method to solve eqs 1 and 2 for the case of Tween 20 by using the corresponding parameters found in the literature and shown in Table 1. By following a similar procedure, Fainerman et al. have recently extended the theoretical formalism to account for the adsorbed layer of mixtures of proteins and non-ionic surfactants in a thermodynamic model. Although they are described in detail in refs 10 and 11, the main equations are briefly summarized hereafter. The equation of state of the mixed protein/non-ionic surfactant adsorbed layer, assuming ω0 * ωs is

-π(θpω0 + θsωs) RT(θp + θs)

(

) ln(1 - θp - θs) + θp 1 -

apθ2p + asθ2s + 2apsθpθs (3)

Theoretical Background The adsorption behavior of an individual non-ionic surfactant obeys the Frumkin equation of state along with the adsorption isotherm:20,21

π)-

RT [ln(1 - θs) + asθ2s ] ωs

b s cs )

)

ω0 + ω

θs (1 - θs)

exp(-2asθs)

(1)

(2)

Where π ) γ - γ0 is the surface pressure of the solution, γ and γ0 are the surface tensions of the solvent and solution, respectively, R is the gas constant, T is the temperature, and the subscript “s” refers to the surfactant. Thus, cs is the surfactant bulk concentration in the solution, ωs is the molar area of the surfactant, and θs is the surface coverage of surfactant. Also, bs is the adsorption coefficient, which provides information about the strength of the interaction between the adsorbing species and the surface, and as is the Frumkin interaction parameter that indicates whether the adsorbing molecules exhibit attractive or repulsive (lateral) interactions.22 A thermodynamic model proposed recently by Fainerman and co-workers describes the adsorbed layers of proteins at fluid interfaces by assuming that proteins can exist in the surface layer in a number of states with different molar areas, varying from a minimum ωmin at high surface coverage, to a maximum ωmax at low surface coverage. The incremental value is chosen equal to the molar area of the solvent ω0 and assuming that n is the total number of possible states of an adsorbed protein molecule in the ith state is ωi ) ωmin + (i - 1)ω0. Where ω1 ) ωmin and the maximum molar area of an adsorbed protein is ωmax ) ωmin + (n - 1)ω0. With these premises, Fainerman et al. derived a thermodynamic formalism that describes the protein adsorbed layer very satisfactorily.7 Although there is no direct proof of the existence of these different states (in particular with Brewster angle microscopy), the equation introduces additional

Where, similar to the pure protein layer, ω is the mean molar area of the protein in the mixed adsorbed layer and ω0 is the area of the solvent. The adsorption of the protein in the i state n is denoted by Γi so that Γ ) ∑i)1 Γi is the total adsorption. Also, the total surface coverage degree of the protein in the n adsorbed layer is defined by θp ) ωΓ ) ∑i)1 ωiΓi and in the i state reads θi ) Γiωi. Regarding the surfactant, ωs is the molar area and Γs is the adsorption of the surfactant so that θs ) Γsωs is the surface coverage in the adsorbed layer. Finally, a is a Frumkin type interaction parameter (ap for the protein, as for the surfactant, and aps for the mixture). The adsorption isotherm for each of the i states of the protein molecule in the mixed adsorbed layer reads

b pc p )

ωiΓi (ωi /ω)(1 - θp - θs)ωi/ω exp[-2ap(ωi /ω)θp - 2apsθs] (4)

and for the surfactant

bscs )

θs (1 - θp - θs)

exp[-2asθs - 2apsθp]

(5)

Finally, the distribution of adsorptions over the states is equal to that given for the adsorbed layer of proteins ωj - ω 1

(1 - θp - θs) Γj ) Γ

n

(1 - θp - θs) ∑ i)1

[

exp 2apθp

ω

ωi - ω1 ω

[

exp 2apθp

so that the adsorption in state 1 (Γ1) reads11

]

ω j - ω1 ω

]

ωi - ω1 ω

(6)

Protein/Surfactant Mixtures

J. Phys. Chem. C, Vol. 111, No. 6, 2007 2717

θp

Γ1ω )

n

(1 - θp - θs) ∑ i)1

[

ωi - ω 1 ω

]

ωi - ω1

exp 2apθp

ω

(7)

and the expression of the mean molar area occupied by the protein in the mixed surface layer can be written as ωj - ω1

n

ω)

ωi(1 - θp - θs) ∑ i)1 n

(1 - θp - θs) ∑ i)1

ω

ωi - ω 1 ω

[

exp 2apθp

[

ω

]

ωi - ω1

exp 2apθp

]

ωj - ω1

ω

(8)

The set of eqs 3-5, 7, and 8 completely describes the surface layer formed by a mixture of protein and a non-ionic surfactant. However, prior to the use of this set of equations, one should obtain the values of the parameters from the previous application of the model to the adsorption of the pure components: ω0, ωs, ωmax, ωmin, bp, bs, ap, and as. In this manner, the only free parameter in the fitting procedure is the Frumkin interaction parameter for the mixed system: aps. To facilitate the resolution of the above theoretical treatment, the set of equations that describe the adsorption of mixed protein/non-ionic surfactants (eqs 3-5, 7, and 8) has been numerically solved and the details of the implementation are presented in the Appendix. Experimental Section Materials. Lyophilized, essentially salt-free bovine milk β-casein (90+)% by electrophoresis was purchased from SIGMA Chemical Co. β-casein is a model protein studied widely in the literature.23 It presents a random coil, an asymmetric configuration, and has an extremely flexible structure. It is made up of 209 aminoacids, and it has a molecular weight of 23.8 kDa. The first 50 aminoacid residues contain a negative charge at pH 7 so that this part of the molecule is hydrophilic. The rest of the molecule is basically made up of neutral residues that are responsible for the hydrophobic character. As a result, β-casein has a marked amphiphilic character that makes it very surface-active. It was stored at -18 °C and used without further purification. Polyethylene glycol sorbitan monolaurate (or polyoxyethylenesorbitan monolaurate) was also purchased from SIGMAAldrich and used without further purification. This is a nonionic surfactant, soluble in water with a molecular weight of 1228 g/mol. Its chemical composition is C58H114O26, and its generical name is Tween 20 (or polysorbate 20). The aqueous subphase used in all of the solutions is a 0.05 M buffer Tris of final pH 7.4. Solutions were prepared by successive dilution from a concentrated solution. The mixed solutions were formed by adding the desired amount of protein to the surfactant solution so that the final concentration of protein in all of the mixtures is constant (0.1 g/L ∼ 5 × 10-3 mol/m3) and the concentration of surfactant ranges between 10-5 and 1 mol/m3. Solutions were prepared daily, and 0.054 µS MilliQ+ purified water was used for buffer preparation and all other purposes. All experiments were performed at T ) 23 °C. The surface tension (γ0) of the clean surface was measured before each experiment to ensure the absence of surface-active contaminants obtaining values of 72.5 ( 0.5 mJ/m2. Experimental Set-Up. Surface Tension. The surface tension measurements have been performed in a pendant drop film

balance based on axisymmetric drop shape analysis (ADSA), which is described in detail by Cabrerizo-Vı´lchez et al.24 The solution droplet is formed at the tip of a coaxial double capillary, connected independently to a double microinjector that enables a subphase exchange that substitutes the bulk solution for clean buffer once the desired amount of protein (or surfactant) reaches the interface. The program fits the experimental drop profile to the Young-Laplace equation of capillarity by using ADSA and provides as output the drop volume V, the interfacial tension γ, and the interfacial area A. The drop is formed in a glass cuvette (Hellma) that is kept in a thermostatized cell at T ) 23 °C. The adsorption process is measured by recording the change of interfacial tension at a constant interfacial area of 28 mm2 for very long periods of time (10 h) for each of the fixed bulk concentrations. Three kinds of experiments have been performed. First, the adsorption process of the two systems has been studied by varying the bulk concentration several orders of magnitude. Second, the competitive adsorption was evaluated by monitoring the surface tension of the mixed solutions. The solutions were prepared with varied amounts of surfactant and a fixed amount of protein, 0.1 g/L ∼ 5 × 10-3 mol/m3. It will be shown that this concentration provides a saturated surface layer that facilitates the evaluation of the role played by Tween 20 in the mixed system over a wide range of surfactant concentrations. Finally, the subphase exchange enabled the study of the sequential adsorption. Once a steady layer of protein had been adsorbed on the surface, the remaining protein bulk solution was exchanged by that of the surfactant. The evolution of the surface tension after the exchange provides structural information of the mixed surface layer. Foam Stability. Foam stability has been studied using a specially designed vertical foam column. The foaming solution is placed in a hollow rectangular prism of section of 2.56 × 10-2 m2 and height of 1 m. The column is made of plexiglass and is connected to a fritted glass filter of porosity 40-100 µm at the bottom. The air flux is blown into the column through the filter by means of a flowmeter. The flow rate is kept constant in all of the experiments at 5 × 10-4 m3/s. The experiments are performed with the following protocol: the column is filled with 200 mL of solution and, subsequently, the flowmeter is connected. Once the foam has reached a height of around 0.8 m, the air flow is stopped. The stability of the foam formed is estimated by measuring the lifetime of the foam (t1/2), time taken by the foam to decay to half the original height after the air flow is stopped. These results, though qualitative in character, allow a comparison of the foam stability of the different solutions.25,26 Results and Discussion Surface Characterization. This first section deals with the surface behavior of the mixed protein/non-ionic surfactant systems in comparison to that of the individual components. Because the ultimate aim of this work is to obtain structural information of the surface layers formed by mixtures of β-casein and Tween 20, several experiments were performed. On one hand, the adsorption behavior is studied by evaluating the competitive adsorption from the mixed solution from an experimental and a theoretical point of view. On the other hand, the characteristics of the sequential adsorption of the protein and the surfactant are analyzed. CompetitiVe Adsorption. Let us first study the adsorption behavior of the mixed solutions and compare it to that of the individual components. The range of concentrations in which


Figure 1. Surface pressure isotherms of β-casein (solid squares), Tween 20 (solid triangles), and the mixture of 5 × 10-3 mol/m3 β-casein and Tween 20 (hollow circles).

the surface pressure varies has been determined for the sole surfactant, and the same interval of surfactant concentrations has been used for the mixed system. Figure 1 shows the measured surface pressure isotherms for Tween 20 and for the mixed system as a function of the surfactant concentration. To facilitate comparisons, Figure 1 also shows the surface pressure isotherm of β-casein, in which the x axis corresponds to protein concentration. These experimental data are taken from refs 8 and 9 and were obtained by recording the adsorption at constant surface area until the rate of change of surface pressure was negligible (approximately 10 h). Let us briefly comment on the isotherm of β-casein. This is a highly surface-active protein, which affects the surface tension at very low bulk concentrations, but the maximum surface pressure (saturated layer) is not high, being around 22 mJ/m2. This feature is consistent with the flexible structure of β-casein reported in the literature14 and suggests the formation of a loosely packed surface layer and possibly multilayers at high surface coverage.15,27 Conversely, the maximum surface pressure of Tween 20 is very high (36 mJ/m2). This relates to the higher compaction of the surfactant monolayer.6 From the surface pressure isotherm of the surfactant, one can also obtain its critical micelle concentration (cmc), which according to Figure 1 is 2 × 10-2 mol/m3, in agreement with literature results.13 Regarding the π-c curve obtained for the mixed system, Figure 1 shows how the system behaves either like the sole protein at low surfactant concentrations or like the sole surfactant at higher surfactant concentrations. Hence, at low surfactant concentrations, the surface pressure remains practically constant and coincides with that of the sole protein at the concentration used in the mixture. Accordingly, within this interval, it might be assumed that the final adsorbed layer is composed basically of protein and that the presence of surfactant does not significantly affect the surface tension. At a well-defined surfactant concentration, 10-2 mol/m3, the behavior of the mixed system changes abruptly. From this concentration on, the surfactant seems to control the adsorption process, and the isotherm recorded for the mixed system practically coincides with that of the sole surfactant. The surface pressure increases very steeply in a narrow range of surfactant concentration and the saturation also occurs at the cmc of Tween 20. These experimental results suggest that the surface layer at this high concentration of Tween 20 is composed essentially of surfactant. The surfactant might therefore have forced the protein molecules out of the surface layer, possibly underneath. Further information on the underlying mechanisms can be found in the analysis of the dynamic behavior.


Figure 2. Dynamic adsorption curves of β-casein, Tween 20, and the mixed system. β-casein (solid squares) 5 × 10-3 mol/m3, Tween 20: (solid up-triangles) 10-3mol/m3, (solid down-triangles) 10-2 mol/m3, (solid side-triangles) 10-1 mol/m3, mixtures of 5 × 10-3 mol/m3 β-casein + Tween 20: (hollow up-triangles) 10-3 mol/m3, (hollow down-triangles) 10-2 mol/m3, (hollow side-triangles) 10-1 mol/m3.

Figure 2 shows the time evolution of the surface pressure of the pure and the mixed systems for the protein at the concentration used in the mixed system (5 × 10-3 mol/m3) for the pure surfactant and for the mixed systems at a very low surfactant concentration (10-3 mol/m3), an intermediate concentration just below its cmc (10-2 mol/m3) and a concentration well above the cmc (10-1 mol/m3). The surface pressure increases steeply and reaches rapidly a practically constant value for β-casein. Consequently, at this concentration, the protein molecules adsorb very rapidly on to the surface and provide a saturated surface layer in agreement with the results presented in Figure 1. Concerning Tween 20, the rate of increase of the surface pressure increases significantly with the bulk concentration of surfactant. For the mixed systems, the general trends perfectly match the behavior seen in the adsorption isotherms. At the two smallest surfactant concentrations, the dynamic curve practically matches that of the sole protein, whereas at the highest surfactant concentration, it coincides with that of the sole surfactant. Furthermore, the rate of increase of the surface pressure is higher for the β-casein than for the Tween 20 at the lowest concentrations considered in the mixture. Conversely, the rate is higher for Tween 20 than for β-casein at the largest surfactant concentration. However, the change seen here also coincides with the moment where the surface pressure of the surfactant overcomes that of the protein, in which case the same behavior is expected. Theoretical Treatment. The experimental curves were fitted with the theoretical model presented above and the results are shown in Figure 3. First, Figure 3a shows the experimental data for Tween 20 at the air-water interface along with the theoretical fitting given by eqs 1 and 2 and the parameters displayed in Table 1. The theoretical curve was obtained by numerically solving the system of eqs 1 and 2 as detailed in the theoretical background. Note that the input parameters are not free parameters but data that were found in the literature for a similar surfactant (see ref 21). It is worth mentioning that the correlation between theory and experiment is satisfactory within the range of applicability of the model, which excludes the surface saturation interval.21 This feature confirms that the selected parameters can be used in the subsequent analysis of the mixture.


J. Phys. Chem. C, Vol. 111, No. 6, 2007 2719

Figure 3. (a) Experimental surface pressure isotherm of Tween 20 at the air-water interface (solid triangles) and theoretical fitting with eqs 1 and 2 and parameters from Table 1 (solid line). (b) Experimental surface pressure isotherm of 5 × 10-3 mol/m3 β-casein and Tween 20 at the air-water interface (hollow circles) and theoretical fitting with eqs 3-5, 7, and 8 and parameters from Table 2 (dashed line).

TABLE 2: Input and Fitting Parameters for the Adsorption of Mixed Systems According to Equations 3-5, 7, and 8a parameter

β-casein/Tween 20

bs bp as ap aps ω0 ωmin ωmax ωs

21.9 × 103 m3/mol 10 m3/mol -0.25 1.00 0.375 2.5 × 105 m2/mol 4.5 × 106 m2/mol 4.5 × 107 m2/mol 2.5 × 105 m2/mol

a Input parameters with subscript p and s correspond to the sole protein7 and to the sole surfactant (Table 1), respectively. aps is the fitting parameter.

Let us comment on the conclusions derived from the application of the model to the surface pressure isotherm of Tween 20, which to our knowledge has not been investigated in the literature in spite of being a widely used surfactant. The value of the molecular area of Tween 20 is given in Table 1 and is 0.4 nm2/molec. This value is twice the molecular area reported in the literature for widely used ionic surfactants such as SDS.28,29 The value of the molecular area of the adsorbed species seems to have a relation with the subsequent stability of the foam, and this feature will be further analyzed below. Besides, Tween 20 shows a negative Frumkin interaction parameter a (Table 1). Although the interpretation of this parameter is complicated because it can depend on the bulk concentration,30 some aspects can be elucidated. Namely, the negative sign has already been considered in the literature for a wide variety of systems.22,31,32 In particular, for the case of non-ionic surfactants it implies a sort of repulsion between the adsorbed species, that is, a diminishing capability of adsorption with increasing surface coverage.22 Furthermore, this feature is completely consistent with the high value encountered for the molar area of Tween 20 adsorbed in these conditions. According to Paul et al., a large area per molecule indicates that there are repulsive interactions preventing the adsorbed species from packing more tightly at the interface.31 Regarding the theoretical treatment of the surface pressure isotherm of β-casein, this has been studied in detail in refs 7 and 19. β-casein unfolds upon contact with the surface, and this feature is accounted for in the theoretical treatment. Namely, the fitting quantifies this unfolding by the minimum and maximum values of the molar area (ωmin and ωmax in Table 2). At low surface pressure, molecules adopt a maximum unfolded

state, whereas at high surface pressures, the molecules occupy a minimum surface area. Hence, once the individual systems have been analyzed and the required parameters have been obtained, we proceed with the theoretical analysis of the mixed system. The algorithm designed for the numerical solution of the system of equations that describe the mixed adsorbed layer (eqs 3-5, 7-8), is explained in detail in the Appendix. Figure 3b shows the surface pressure isotherm obtained for the mixture of β-casein and Tween 20 along with the theoretical curve given by the system of eqs 3-7 and the parameters displayed in Table 2. The parameters with subscript “s” are those derived from the Frumkin isotherm and also displayed in Table 1. Similarly, the parameters with subscript “p” correspond to the surface pressure adsorption curve obtained for β-casein at the air-water interface studied previously.7,9 Accordingly, and as already mentioned in the theoretical section, the only fitting parameter in the model of mixed protein/non-ionic surfactant adsorbed layer is the Frumkin type interaction parameter aps, which accounts for the possible interaction occurring between protein and surfactant in the surface. The election of the value of this parameter was done by taking into account the conclusions derived from the analysis of the experimental curves presented above. According to the results shown in Figure 1, there is no critical aggregation concentration, different from the critical micelle concentration of the surfactant. This feature strongly suggests that there is not any specific interaction between protein and surfactant in these experimental conditions. Taking this into consideration, the value of the parameter aps is taken as aps ) (ap + as)/2.10 The use of this value for aps in the theoretical formalism provided the better correlation with the experimental data. The results are shown in Figure 3b in which it can be appreciated that a reasonable correspondence is achieved between theory and experiment. Likewise, the numerical resolution of the system of equations that describe the adsorbed layer of β-casein/Tween 20 system provides, apart from the theoretical dependence of π-c, the dependence of other parameters that contain relevant structural information about the surface layer. In particular, Figure 4a shows the theoretical dependences of the surface coverage of protein and surfactant with the surface pressure of the mixed adsorbed layer. It can be easily appreciated in this figure that, in the absence of surfactant (θs ) 0), the surface layer is completely covered with protein (θp ) 0,86). While the surface pressure of the mixed solution increases, the surface coverage of Tween 20 increases at the expense of the surface coverage



Figure 4. (a) Theoretical surface coverage of protein (solid triangles) and surfactant (hollow triangles) in the adsorbed mixed layer. (b) Theoretical mean surface molar area of the protein (ω) in the mixed adsorbed layer (solid squares).

Figure 5. Surface pressure of 5 × 10-3 mol/m3 β-casein (solid squares). Subphase exchange by PBS (hollow squares), subphase exchange by 10-3 mol/m3 Tween 20 (down triangles), and subphase exchange by 10-1 mol/m3 Tween 20 (up triangles).

of the protein. As shown by Figure 4a, at high enough surface pressure, the surfactant seems to have displaced the protein from the surface. This finding is completely consistent with the experimental results discussed in the previous section and quantifies the encountered behavior. Furthermore, it is interesting to evaluate the variation of the molar area of the protein during the displacement process. Such variation is plotted in Figure 4b as a function of the surface pressure and it shows a clear decreasing tendency. Concretely, the mean molar area of the surface protein varies from a value of 8.12 × 106m2/mol to a slightly lower one of 6.05 × 106m2/ mol. The low value is consistent with the high surface coverage expected at this protein concentration. Furthermore, the compacting of the molecule shown in Figure 4b is in agreement with the proposed displacement of the protein by the surfactant because the return to the bulk might induce a folding of the hydrophobic segments into the molecule that would explain the encountered decrease in the molar area. Sequential Adsorption. Taking into consideration the conclusions derived from the study of the adsorption performed above, it was interesting to deepen into the process of displacement of the adsorbed protein by the surfactant. To this end, the sequential adsorption of the two components in the mixed system was investigated. This can be done by arranging several consecutive experiences that are represented in Figure 5 and explained in detail below. First, the β-casein was adsorbed freely onto the surface. Once a protein-saturated surface layer is achieved, the subphase is

depleted of protein by exchanging the bulk solution by PBS. The stability of the protein surface layer formed before the exchange is verified by the absence of effect of the subphase exchange in the surface pressure, which remains constant. Thus, it can be concluded that the protein is well attached to the surface in agreement with previous works33 and literature results.34 In this manner, the evolution of the surface pressure after a subphase exchange by a solution of Tween 20 provides direct information of the effect of the surfactant on the protein surface layer. Figure 5 shows the experimental results of exchanging the protein subphase by a surfactant solution at two different bulk concentrations; one below (10-3 mol/m3) and one above (10-1 mol/m3) the cmc of Tween 20. It can be seen in the figure how the presence of Tween 20 in the bulk solution has an important effect on the surface layer. In particular, the increase in surface pressure obtained for the two concentrations clearly indicates that the Tween 20 is able to penetrate into the surface layer formed by β-casein. Furthermore, in view of the results relating the adsorption of the mixed system, this penetration into the surface layer might produce a complete displacement of the protein by the surfactant at the highest surfactant concentration. This surface phenomenon has also been encountered by other authors in the literature and studied in detail by Wilde et al.2,6 Hence, these findings provide experimental evidence of the ability of the surfactant to displace the protein from the surface at high surfactant concentrations, as predicted by the experimental isotherm in Figure 1 and quantified by the model in Figure 4. Furthermore, these experimental results prove that it is not the component that reaches first the surface that controls the adsorption behavior in the mixed system, as suggested by the dynamic curves of the mixed system, but rather the surface pressures of each of the component. Accordingly, this final experiment appears of major importance in the interpretation of the underlying mechanisms because it allows us to conclude that the surface behavior is dominated by the component that creates the higher surface pressure. Foam Stability. Figure 6 shows the half-life of the foams formed by Tween 20 within the same range of concentrations used in the surface characterization, alone or mixed with a constant protein concentration of 5 × 10-3mol/m3. Tween 20 solutions only provide appreciable amounts of foam above the cmc, in agreement with the results reported by Liu et al. for the same system.35 Even above the cmc, the stability of the foam is poor and t1/2 is of the order of a few minutes, roughly independent of the concentration of surfactant. Moreover, the resulting foam shows a very poor stability and disappears within a few minutes. This feature is consistent with the large value


Figure 6. Half-life of the foam formed by Tween 20 (solid line) and the mixture of 5 × 10-3 mol/m3 β-casein + Tween 20 (dashed line).

of the molecular area of Tween 20 (Table 1). Although equilibrium parameters cannot in principle account for a dynamic property such as foam stability, it is proven that surfactants with low molecular areas such as SDS provide very stable foams owing to the formation of a compact and resistant surface layer.36,37 As a consequence, the large value of the molecular area encountered for Tween 20, along with the repulsion between molecules at the surface revealed by the negative Frumkin parameter, might well explain the formation of a fragile surface layer and might be in part responsible for the instability of the foam shown in Figure 6. The low stability shown by Tween 20 solutions certainly contrast with the very stable foam formed by β-casein at a concentration of 5 × 10-3 mol/m3, which presents a half-life of 2000 s in these experimental conditions and in the absence of surfactant. According to Saint-James et al. the percolation and confinement of protein aggregates in foam films appears decisive in the behavior of protein foams.26

J. Phys. Chem. C, Vol. 111, No. 6, 2007 2721 Once the stability of the foam formed by the individual systems has been presented, we can address the properties of the foam formed by the mixed system. Figure 6 shows the evolution of the lifetime of the foam of the mixed system with increasing concentration of surfactant in the mixture. It can be clearly appreciated in this figure how the stability of the foam formed by the mixture completely reproduces the behavior encountered in the surface properties of the mixed system. Namely, the stability of the foam formed by the mixture of β-casein with low concentrations of Tween 20 corresponds to that of the sole protein, whereas the lifetime of the foam formed by the mixture approaches that of the sole surfactant upon increasing the concentration of Tween 20 in the mixture. This behavior agrees with the surface characterization performed on the basis of the sequential and competitive adsorption but also aggress with that found by Kra¨gel et al. in a study in which the surface shear rheology and the foam film thickness of the mixed system formed by β-casein and Tween 20 were evaluated.16 By means of those experimental techniques, these authors also state that at sufficiently high concentrations the surfactant completely displaces the protein from the surface. In view of all of these results, it could be concluded that the surface film formed by a mixed solution of β-casein and Tween 20 is composed essentially of Tween 20, at high enough concentrations of Tween 20 in the mixture. The protein seems to place itself underneath the surface layer so that the properties of the surface layer do not seem to be affected by the presence of the protein. Furthermore, the stability of the foam formed by the mixed system perfectly reproduces the displacement mechanism of the protein by the surfactant predicted by the surface characterization and even visualized theoretically in Figure 4. As a final remark, let us stress that this work confirms that the stability of foams depends on the surface behavior of the foaming solutions. This work proposes novel insight into the

Figure 7. Flux diagram summarizing the algorithm for the resolution of the system of equations shown in the Appendix.



behavior of mixed solutions and proposes a few ideas and tools to better control and predict foam properties. Conclusions The surface behavior of the mixed system formed by β-casein and Tween 20 is evaluated by looking into the competitive and the sequential adsorption of the system onto the air-water interface. On one hand, evaluation of the competitive adsorption is made through the surface pressure isotherms. The adsorption isotherm completely matches that of β-casein at low surfactant concentrations in the mixture, whereas it coincides with that of Tween 20 at higher surfactant concentration in the mixture. Moreover, the cmc of the surfactant is not affected by the presence of the protein in the bulk solution indicating that protein/surfactant complexes do not form. The resulting Frumkin interaction parameter obtained from the best fitting of the experimental data accounts for the lack of interaction. Moreover, the theoretical analysis shows how the degree of surface coverage of the protein diminishes while that of the surfactant increases. According to these predictions, once the surfactant concentration is high enough, no proteins remain at the surface. On the other hand, the sequential adsorption of β-casein and Tween 20 evidence the displacement of the protein by the surfactant. Moreover, it shows that the surface pressures of each component control the adsorption behavior of the mixture. Finally, the results concerning the surface properties are in line with the foaming properties of the system: the foams formed by mixtures of β-casein/Tween 20 show the same stability as the protein foam at very low concentration of surfactant and the same stability as the surfactant foam when the Tween 20 concentration in the mixture is large enough. Acknowledgment. Financial support from Plan Propio de la Universidad de Granada, Consejerıá de Innovacioń, Ciencia y Empresa de la Junta de Andalucıá: Ayudas para apoyar grupos de investigacioń y desarrollo tecnolo´gico and proyecto FQM 392, FEDER and Ministerio de Ciencia y Tecnologıá, plan nacional de Investigacioń cientı´fica, Desarrollo e Innovacioń Tecnolo´gica (I+D+I), projects MAT2004-06872-C03-01 and AGL2004-01531. A.M.-M. thanks the Programa Ramoń y Cajal, 2005, Ministerio de Educacioń y Ciencia (RYC-2005-000829). Finally, Dr. E. H. Lucassen-Reynders is gratefully acknowledged for her helpful comments. Appendix Numerical Solutions of the Model. The general procedure used to solve the system of eqs 3-8 is based on an iterative method, analogous to those used in the solution of the individual components (see ref 8). The method consists of the following steps, which are summarized in Figure 7: 1. Enter start paramenters: ωstart ) (ωmax + ωmin)/2, θstart p , . and θstart s in start, θstart, and θstart. 2. Define ωin, θin p , and θs as ω p s out 3. Calculate ω with in-parameters in eq 7. 4. Compare the value obtained in step 3 with ωin, and use the iterative method applying the corresponding mix equation until the difference between ωin and ωout is minimal

ωmix ) λωout + (1 - λ)ωin The value obtained in this step is named ω4.

(A1)

in 5. Calculate θs with ω4, θin p , and θs in eq 4 rewritten as

[

θs ) 1 - θp θp exp(-2ap(ω1/ω)θp - 2apsθs) bpcp

n

(1 - θp - θs) ∑ i)1

ωi - ω 1 ω

[

exp 2apθp

]

ω/ω1

]

ωi - ω1 ω

(A2)

6. Compare the value obtained in step 5 for θs with θin s , and use the iterative method applying the corresponding mix out equation until the difference between θin s and θs is minimal. in ) λθout θmix s s + (1 - λ)θs

(A3)

The value obtained in this step is named θs6. 7. For a given value of π, estimate θp with ω4, θs6, and θin p in eq 3 rewritten as

θp ) 1 - θs - exp

[

-π(θpω0 + θsωs) RT(θp + θs)

(

- θp 1 -

)

ω0 ω

]

apθ2p - asθ2s - 2apsθpθs (A4) 8. Compare the value obtained in step 7 for θp with θin p and use the iterative method applying the corresponding mix out equation until the difference between θin p and θp is minimal out in θmix p ) λθp + (1 - λ)θp

(A5)

The value obtained in this step is named θp8. 9. Compare the new set of values ω4, θs6, and θp8 with ωstart, start mix mix and define ωmix θp , and θstart s 4 , θs6 , and θp8 by means of the following equations: start ωmix 4 ) λ′ω4 + (1 -λ′)ω

(A6)

start θmix s6 ) λ′θs6 + (1 - λ′)θs

(A7)

start θmix p8 ) λ′θp8 + (1 - λ′)θp

(A8)

mix mix start, θstart, and θstart. 10. Rename ωmix 4 , θs6 , and θp8 as ω p s 11. Repeat steps 2-9 until the differences between ω4, θs6, start and θp8 and ωstart, θstart p , and θs , respectively, are minimal simultaneously for the value of π chosen in step 7. 12. Calculate cs with eq 5 rewritten as

cs )

θs exp[-2asθs - 2apsθp] bs(1 - θp - θs)

(A9)

Accordingly, varying the previous process for different values of surface pressure, the theoretical isotherm π(cs) shown in Figure 3b is obtained. Because of the high number of iterations in this process, the mixing parameters were adequately changed along the computational procedure in order to optimize the convergence process. Finally, it is worth noting that this kind of iterative method has been successfully employed in the past for solving numerically a similar thermodynamic model of protein adsorption as well as equations systems based on integral equations.8,38 References and Notes (1) Weaire, D.; Hutzler, S. The Physics of Foams; Oxford Univ. Press: Oxford, U.K., 1999.

Protein/Surfactant Mixtures (2) Mackie, A.; Wilde, P. AdV. Colloid Interface Sci. 2005, 117, 3. (3) Holmberg, K.; Jo¨nsson, B.; Kronberg, B.; Lindman, B. Surfactants and Polymers in Aqueous Solutions, 2nd ed.; Wiley: Chichester, U.K., 2003. (4) Langevin, D. AdV. Colloid Interface Sci. 2000, 88, 209. (5) Ravera, F.; Ferrari, M.; Santini, E.; Liggieri, L. AdV. Colloid Interface Sci. 2005, 117, 75. (6) Wilde, P.; Mackie, A. R.; Husband, F.; Gunning, P.; Morris, V. AdV. Colloid Interface Sci. 2004, 63, 108-109. (7) Fainerman, V. B.; Lucassen-Reynders, E. H.; Miller, R. AdV. Colloid Interface Sci. 2003, 106, 237. (8) Maldonado-Valderrama, J.; Martıń-Molina, A.; Ga´lvez-Ruiz, M. J.; Martıń-Rodriguez, A.; Cabrerizo-Vı´lchez, M. A. J. Phys. Chem. B. 2004, 108, 12940. (9) Maldonado-Valderrama, J.; Fainerman, V. B.; Aksenenko, E.; Ga´lvez-Ruiz, M. J.; Cabrerizo-Vı´lchez, M. A.; Miller, R. Colloids Surf., A 2005, 261, 85. (10) Miller, R.; Fainerman, V. B.; Leser, M. E.; Michel, M. Colloids Surf., A 2004, 233, 39. (11) Fainerman, V. B.; Zholob, S. A.; Leser, M.; Michel, M.; Miller, R. J. Colloid Interface Sci. 2004, 274, 496. (12) Maldonado-Valderrama, J.; Ga´lvez-Ruiz, M. J.; Martıń-Rodriguez, A.; Cabrerizo-Vı´lchez, M. A. Colloids Surf., A 2005, 323, 270-271. (13) Rodriguez-Ninõ, M. R; Wilde, P.; Clark, D. C.; Rodriguez-Patino, J. M. J. Agric. Food Chem. 1998, 46, 2177. (14) Benjamins, J.; Lyklema, J.; Lucassen-Reynders, E. H. Langmuir 2006, 22, 6181. (15) Maldonado-Valderrama, J.; Fainerman, V. B.; Galvez-Ruiz, M. J.; Martin-Rodriguez, A.; Cabrerizo-Vilchez, M. A.; Miller, R. J. Phys. Chem. B 2005, 109, 17608. (16) 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. (17) Casç ao-Pereira, L. G.; Johanson, C.; Radke, C. J.; Blanch, H. W. Langmuir 2003, 19, 7503. (18) Douillard, R.; Aguie´-Beghin, V. Colloids Surf., A 1999, 149, 285. (19) Miller, R.; Fainerman, V. B.; Aksenenko, E. V.; Leser, M. E.; Michel, M. Langmuir 2004, 20, 771.

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