J. Phys. Chem. B 2009, 113, 103–113
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Dilation and Shear Rheology of Mixed β-Casein/Surfactant Adsorption Layers Cs. Kotsmar,*,† J. Kra¨gel,† V. I. Kovalchuk,‡ E. V. Aksenenko,§ V. B. Fainerman,| and R. Miller† Max Planck Institute of Colloids and Interfaces, 14424 Potsdam-Golm, Germany, Institute of Biocolloid Chemistry, Vernadsky AV., 42, 03142 KieV, Ukraine, Institute of Colloid Chemistry and Chemistry of Water, 42 Vernadsky AV., 03680 KieV, Ukraine, and Medical UniVersity Donetsk, 16 Ilych AVenue, 83003 Donetsk, Ukraine ReceiVed: August 12, 2008; ReVised Manuscript ReceiVed: October 14, 2008
The present study deals with dilational and shear rheological properties of adsorption layers of the milk protein β-casein (BCS) mixed with the nonionic dodecyl dimethyl phosphine oxide (C12DMPO) and the positively charged dodecyl trimethyl ammonium bromide (DoTAB), respectively. The drop profile analysis tensiometer PAT-1 was applied for the dilational rheological studies at low frequency harmonic relaxations. A special modification of the setup, consisting of a coaxial capillary combined with a double dosing system, provides exchange of the drop volume during experiments. This arrangement offers a unique protocol for studies of mixed surface layers, formed by sequential adsorption of the individual compounds. The dilational viscoelastic modulus and the dilational viscosity of the mixed layers, built-up in the two different ways, were investigated and compared. The features of the mixed surface layers drawn from the dilational rheology are qualitatively confirmed by the shear rheological parameters measured by torsion shear rheometry ISR-1. Recently derived theoretical models were used for a quantitative description of the equilibrium state and dilational rheology of the surface layers formed by the single components and their mixtures. 1. Introduction Mixed systems containing proteins and low molecular weight surfactant are widely utilized for the stabilization of foams and emulsions in many modern technologies, like food processing, cosmetics, and the pharmaceutical industry.1 The surface and bulk properties of proteins and surfactants in mixed solutions have been studied for many years.2-7 The particular interfacial properties of such mixed layers strongly influence the formation and stabilization of respective foams and emulsions1 and play different roles in these processes.8 The interactions between protein and surfactant molecules in the bulk and at the surface are different, and hence, the resulting complexes are different as well: solubility, surface activity leading to different surface tension values, and surface rheological properties in the adsorbed state.9,10 The interactions stabilizing these complexes are generally of hydrophobic11,12 and/or on electrostatic nature13-15 and will change the conformation of the protein molecules in the bulk and at the surface as well.11,12,15 The presence of complexes in the adsorption layer, even if their amount is very small, can be effectively detected via surface rheological measurements, especially if their surface activity differs sufficiently from that of single components. In the case of shear rheological measurements, the interactions between the adsorbed molecules play a decisive role as well, and they are also subject to changes due to the formed complexes. The increase of surfactant concentration in the mixtures affects the complexation and simultaneously the adsorption of the free surfactant molecules and leads to a gradual displacement of protein molecules (complexes) from the adsorption layer.11,12,16,17 At * Corresponding author. † Max Planck Institute of Colloids and Interfaces. ‡ Institute of Biocolloid Chemistry. § Institute of Colloid Chemistry and Chemistry of Water. | Medical University Donetsk.
sufficiently high surfactant concentrations, which depends on the nature of the protein and the surfactant as well as the pH and ionic strength of the solvent, a significant change of the respective surface layer composition, and consequently of the respective liquid films in foams and emulsions results, i.e. protein molecules can be completely displaced by surfactants.11,12 Therefore, the understanding of the interaction between these two surface-active species, their complex formation and displacement is very important not only from a scientific but also from a practical point of view. The exact mechanism for protein displacement is not yet fully understood, despite extensive studies of the adsorption of protein molecules to various interfaces and their displacement by various surfactants. In the past decade, different mechanisms have been suggested, such as orogenic displacement18 or competitive adsorption combined with protein modification via complexation.19 The random coil structured β-casein (BCS) is the favorite model molecule of polymer scientists20 and is one of the most frequently investigated proteins. Therefore, its adsorption dynamics, thermodynamics and rheological behavior are well-known.21-23 This molecule behaves like a block-copolymer, has a strong tendency for self-assembling,24 and with its disordered and flexible structure differs significantly from other proteins. Dodecyl dimethyl phosphine oxide (C12DMPO) is used as standard nonionic surfactant because of the available high level of purity.25 The surface properties of this surfactant have been extensively studied, for example in refs 25-28. The adsorption and rheological behavior of the cationic surfactant dodecyl trimethyl ammonium bromide (DoTAB) at the water/ air interface has been studied with different methods such as tensiometry29,30 and neutron reflectivity31 and at high-surface oscillation frequencies with excited capillary waves.32 Protein/surfactant mixed layers can be built-up in two different ways, applying simultaneous (sim ads) and sequential
10.1021/jp807197s CCC: $40.75 2009 American Chemical Society Published on Web 12/11/2008
104 J. Phys. Chem. B, Vol. 113, No. 1, 2009 adsorption (sequ ads)11 of the respective components. A sequential adsorption is possible by using a special modification of the drop profile tensiometry. Since its introduction in the early eighties,33 the drop and bubble profile method became an accurate tool to determine contact angles and interfacial tensions, as described in detail in ref 34. Further developments opened its applicability to dilational rheological studies, such as transient35 and low frequency harmonic relaxations.36 A remarkable further step was made by Wege et al.,37 who developed the possibility to exchange the bulk phase in a single pendant drop during drop shape measurements. This idea was later adapted to numerous experimental protocols, such as penetration experiments,38 desorption studies,39 wash off experiments,40 studies on evaporation,41 or even for multilayer formation.42 The aim of this work is to perform adsorption and surface rheological experiments with mixtures of the random coil protein BCS with the nonionic C12DMPO and cationic DoTAB to find out the composition of the interfacial layer at the water/air interface. The layers are formed on two ways, by sequential and simultaneous adsorption of the two components, and this could have an impact on the surface properties, as in the first case the surfactant starts interaction only at the interface while in the second case the two compound interact with each other already in the solution bulk. A second target of the present work is the better understanding of how surfactants can successfully compete with proteins at liquid interfaces, although their adsorption energy is much lower than that of a protein. The mechanism we want to discuss here for the selected mixed systems is based on complex formation (in the bulk or at the interface) and a competitive adsorption at the interface. Equilibrium surface tensions complemented by dilational and shear rheology experiments are performed for this reason. The dilational rheology is measured by oscillating drop profile tensiometry, while the surface shear rheological measurements of the BCS/surfactant mixtures were carried out with a torsion pendulum rheometer,43 which allows to determine the dependence of the shear rheological parameters on the adsorption time. 2. Materials and Methods Ultrapure MilliQ water with a resistivity of 18.2 MΩ · cm was used for the preparation of all solutions. Na2HPO4-NaH2PO4 buffer solution (Fluka, assay > 99%) with pH 7 and a surface tension of 72.2 mN/m at 22 °C was used to prepare the 10-6 mol/L solutions of BCS. The BCS from bovine milk (minimum 90% pure) with a molecular weight of 24 KDa and an isoelectric point around pH 5.2 was purchased from Sigma-Aldrich Chemical Co. (Germany) and used without further purification. C12DMPO (MW ) 246.4 g/mol), synthesized at the MPI by Haage,25 was added at concentrations in the range between 10-6 mol/L and the critical micelle concentration (CMC) at 5 × 10-4 mol/L. DoTAB (MW ) 308.35 g/mol) purchased from Fluka (Switzerland) was used in the concentration range between 10-6 mol/L and the CMC (2 × 10-2 mol/L). The above-mentioned buffer solution was used for the preparation of all surfactant solutions. All experiments were performed at room temperature, 22 °C. The mixed protein/surfactant solutions were prepared in the following way: the respective protein and surfactant solutions were mixed 30 min before starting the measurements to ensure that protein-surfactant complexes are formed. All mixed solutions contained a fixed concentration of 10-6 mol/L BCS, while the concentration of the surfactant was varied. In case of sequential adsorption experiments, solutions of the single components were introduced sequentially into the system with
Kotsmar et al. the help of the special dosing system combined with a coaxial double capillary, as described below. Two different experimental methods were used in the present study. The first one was the drop profile analysis tensiometer34 PAT-1 (SINTERFACE Technologies, Germany), to determine the surface tension and dilational rheological parameters of the different surface layers. The rheological investigations are based on harmonic area oscillations of the drop surface at low frequencies, which are performed by the dosing system. The used setup is equipped with a special dosing system consisting of two syringes (50 µL syringe from ILS, Germany), which are connected to a coaxial double capillary system.37,39 This configuration allows the exchange of the bulk phase in the drop without disturbing its surface layer. The operation of the drop exchange is based on a simple master-slave principle: one syringe, connected to the inner capillary, pumps small quantities of liquid into the drop, while the second syringe, connected to the outer capillary, controls a constant drop size, i.e. sucks excess liquid out of the drop. Thus, new liquid comes into the drop through the inner glass capillary (1 mm diameter) and leaves the drop through the outer plastic capillary (2 mm diameter). This process also creates some convection inside the drop. Thus, the instrument allows performing sequential adsorption experiments of different types of molecules at the same surface/interface. The second experimental method used was surface shear rheometry in order to measure the shear rheological properties of the mixed systems. The instrument used in this study was the torsion pendulum rheometer43 (interfacial shear rheometer ISR-1, SINTERFACE Technologies, Germany). Briefly described, the rheometer makes a small deflection (0.5-3°) of the measuring body, which is a sharp-edged ring with a hydrophobic titanium surface, pending on a 100 µm diameter tungsten torsion wire. The sharp edge of the measuring body touches the surface of the studied solution. The deflection results in a free oscillation of the measuring body, which will be damped by mechanical properties of the surface, and the instrument records the time dependence of this damped oscillation. The important quantities, the damping coefficient, and the circular frequency of the torsion oscillation can be calculated from the shape of the curve and there from the shear elasticity and viscosity of the investigated adsorption layer.21,44 The measuring cell was a cylindrical Teflon vessel with a sharp pointed lip around the inside wall, in order to avoid a curved meniscus on the liquid surface. The mixing of the protein and surfactant solutions was performed in this Teflon vessel. The solution surface was cleaned by suction immediately before the experiment. Then, the solution surface was touched with the sharp edge of the measuring body. When the system has reached mechanical equilibrium, the program automatically starts the measurement. The experiments were carried out with 1° deflection angle, in order to stay in the linear region of the viscoelastic properties and not to destroy the structure of the adsorption layer. The oscillation frequency of the torsion pendulum is 0.1 Hz. Each experiment lasted 500 min, and the deflections were carried out every 15 min during the adsorption process. 3. Theoretical Models of Adsorption and Dilational Rheology Recently developed theoretical models were used for the quantitative description of the equilibrium adsorption state. The models were derived by Fainerman and co-workers,45-47 on the basis of the idea of Joos,48 according to which molecules
Mixed β-Casein/Surfactant Adsorption Layers
J. Phys. Chem. B, Vol. 113, No. 1, 2009 105
can adsorb at the interface in different states requiring different molar areas, varying from a maximum (ωmax) to a minimum value (ωmin). A summary of the required set of equations for the thermodynamics, kinetics, and dilational rheology was given recently elsewhere49 so that we will give here only a very brief summary. The equation of state for a mixture of a protein with a nonionic surfactant was derived recently50 and has the following form:
-
Πω0 ) ln(1 - θP - θS) + θP(1 - ω0 /ωP) + RPθP2 + RT RSθS2 + 2RPSθPθS (1)
where the indices S and P refer to the surfactant and protein molecules, respectively, Π is the surface pressure, R and T are gas law constant and absolute temperature, Γi, Ri, ωi, and bi are adsorption, interaction constant, average molar area for the protein, and adsorption equilibrium constant of component i, θi ) ωiΓi are the surface coverages of the components i, and ω0 is the molar area of a water molecule. The parameter RPS reflects the interaction between the protein and surfactant molecules. The adsorption isotherms for protein molecules adsorbed in state j ) 1 (with minimum molar area ω1 )ωmin) and for the surfactant molecules, respectively, read as follows:
concentration, and aSPS is the parameter which describes the interaction of the nonassociated surfactant with the protein/ surfactant complexes. It was shown that the assumption of an intrinsic compressibility of surfactant in form of the relationship
ωS ) ωS0(1 - εSΠθS)
is improving the quality of data description. Here, ωS0 (ω0 = ωS0) is the molar area of surfactant at zero surface pressure and εS is the two-dimensional relative surface layer compressibility coefficient, which characterizes the intrinsic compressibility of the surfactant molecules in the surface layer. The given sets of eqs 1-3 and 7 or 4-7 are used to fit the experimental dependencies obtained for BCS/C12DMPO and BCS/DoTAB, respectively. The data for the single components are described with the same equations, which reduce to known models. For example, with θP ) 0, eq 1 reduces to the Frumkin adsorption model, suitable to describe the adsorption of both surfactants. The dilational rheology is studied here by the oscillating drop method, which yields the dilational viscoelasticity of the surface layer. For small amplitude perturbations of the surface layer behaves linear, i.e. all time dependent quantities can be written as a superposition. The surface dilational viscoelasticity E is defined as
E) bP1cP )
ωPΓP1 (1 - θP - θS)ω1/ωP
θS exp[-2RSθS - 2RPSθP] (1 - θP - θS)
(3)
The adsorption behavior of a protein mixed with an ionic surfactant is essentially different. For a protein molecule with m ionized groups, the Coulomb interaction with ionic surfactants causes the formation of complexes, which are determined by the average activity of ions (cPmcS)1/(1+m). The resulting equation of state of the surface layer is similar to eq 1:51
-
Πω0 ) ln(1 - θPS - θS) + θPS(1 - ω0 /ω) + RT aPSθPS2 + aSθS2 + 2aSPSθPSθS (4)
The respective equations corresponding to eqs 2 and 3 now read
bPS(cPmcS)1/(1+m) ) bPScPm/(1+m)cS1/(1+m) ωΓ1 ) × (1 - θPS - θS)ω1/ω exp[-2aPS(ω1 /ω)θPS - 2aSPSθS] (5) 1/2
bS(cScC)
∆γ ∆A/A0
(8)
exp[-2RP(ω1 /ωP)θP 2RPSθS] (2)
bScS )
(7)
θS ) exp[-2aSθS - 2aSPSθPS] (1 - θPS - θS) (6)
Here θPS ) ωΓ is the coverage of the interface by adsorbed protein/surfactant complexes, cC is the surfactant counterion
where ∆γ is the variation of the surface tension, ∆A is the variation of the surface area, and A0 is the initial surface area. This is of course a simplified definition. The exact definition requires that ∆γ and ∆A are the Fourier images of the respective time functions, or they can be also presented as complex amplitudes in the case of established harmonic oscillations. The viscoelasticity E is a frequency dependent complex quantity,52 where the real part (Er) is the storage modulus, which depends on the surface composition and the frequency (ν), and is usually referred to the surface dilational elasticity. The imaginary part (Ei) is the so-called loss modulus, which accounts for the contribution of the surface dilational viscosity (η) and also depends on the surface composition and the perturbation frequency.
E ) Er + iEi
(9)
Experimentally, the imaginary contribution to the modulus ε is reflected in a phase difference, φ, between stress (dγ) and strain (dA), which means that the elastic and viscous contributions are given by
Er ) |E| cos φ
and
Ei ) |E| sin φ
(10)
or
Ei ) 2πνη
(11)
where the dilational viscoelastic modulus |E| and the phase angle φ are given by
|E| ) √Er2 + Ei2
and
φ ) arctan(Ei /Er)
(12)
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Kotsmar et al. TABLE 1: Fit Parameters for the Equilibrium Surface Tension and Adsorption Isotherm of BCS Obtained from Fitting the Data to the Model Given by Equations 1 and 2 at θS ) 0 BCS ω0 ω1 ωmax aP bP DP
Figure 1. Adsorption isotherms of the surfactants C12DMPO (9) and DoTAB (2) and their mixtures with BCS built-up in two different ways: BCS/C12DMPO via sequential (0) and simultaneous adsorption (red O); BCS/DoTAB via sequential (4) and simultaneous adsorption (red ]). The horizontal line indicates the equilibrium surface tension value of the 10-6 mol/L BCS solution. The solid curves correspond to the theoretical fitting for C12DMPO and DoTAB, and the dashed line and dotted line are fittings for the BCS/C12DMPO and BLG/DoTAB mixtures, respectively, formed via simultaneous adsorption. The fitting parameters for the protein and surfactants alone and for the mixtures are presented in Tables 1-4.
The viscoelasticity of a surface layer is a function of deformation frequency ν. Assuming a diffusion-controlled exchange of matter mechanism, Lucassen and van den Tempel derived the following expressions for single surfactants solutions:53
( )/(
E ) E0
dΓ dc
iΩ D
1+
dΓ dc
iΩD ) ) E 11++2ζζ ++ 2ζiζ 0
2
(13)
or
|E| ) E0(1 + 2ζ + 2ζ2)-1/2,
φ ) arctan [ζ/(1 + ζ)] (14)
where the surface dilational elasticity E0 (high frequency limit) and the characteristic parameters of the diffusional exchange between bulk and surface ζ and ΩD are given by
E0 ) dΠ/d ln Γ,
ζ)
( ) ΩD Ω
1/2
,
ΩD )
D dc 2 dΓ
2
( )
(15)
i.e. the rheological quantities are given by the thermodynamic parameters and the diffusion coefficient D. The circular frequency of the generated drop area oscillation is given by Ω ) 2πν. For mixed protein/surfactant adsorption layers, the resulting relations are similar in structure, however, very complex. The theory contains the diffusion coefficients and relevant thermodynamic parameters and their derivatives related to all components. The interested reader may find more details on the formalism in ref 54.
2.2 × 105 m2/mol 3.0 × 106 m2/mol 4.0 × 107 m2/mol 1.1 1.0 × 102 m3/mol 1.0 × 10-10 m2/s
4. Results and Discussion 4.1. Adsorption Isotherms. Figure 1 shows the adsorption isotherms of the surfactants C12DMPO and DoTAB and their mixtures with BCS measured by profile analysis tensiometry. The mixed adsorption layers were built up in two different ways, with sequential and with simultaneous adsorption of the different components. A detailed description of sequential adsorption experiments is given in ref 11. In brief, a droplet was formed with the outer capillary from the 10-6 mol/L BCS solution, and then we waited until the adsorption kinetics reached the plateau region, i.e. the equilibrium state. The adsorption energy of protein molecules like BCS is very large; they adsorb very strongly to the surface.40 The existence of a protein layer can be probed by performing low frequency surface layer oscillations, leading to the results discussed below. The first bulk exchange experiment with the pure pH 7 buffer solution washes out the proteins from the drop bulk. The proteins adsorbed in the surface layer obviously do not desorb but remain at the interface since the measured surface tensions remain almost constant during this subphase exchange. The result of this exchange is a drop covered by a protein layer containing no protein molecules in the drop volume. The second exchange of the drop bulk was made with surfactant solutions at different concentrations. The surfactant molecules penetrate into the protein adsorption layer, adsorb, and modify the surface structure by forming protein/surfactant complexes. The higher the surfactant concentration, the lower the new surface tension plateau for the mixed adsorption layer. These surface tension plateau values are presented in Figure 1 as experimental points for the sequential adsorption experiments. The low frequency harmonic oscillations of the drop surface area were performed at this stage of the experiments at five different frequencies to obtain the dilational viscoelastic properties of the adsorption layers. In the case of simultaneous adsorption of the mixed protein/ surfactant layers, the two components were mixed and the drop was formed from these solutions via the outer capillary. When the adsorption kinetics reached equilibrium, harmonic oscillations were performed. The kinetic curves of these experiments were discussed recently in ref 11. One can see in Figure 1, that the isotherms of the respective mixtures built-up in the two different ways do not differ significantly, indicating that the composition of the mixed layers is very similar. Despite these tensiometric data, the surface dilational investigations showed that the compositions of the layers differ. On the other hand, by comparison of the isotherms of the mixtures containing the nonionic C12DMPO and the cationic DoTAB, one can see that the isotherms of BCS/C12DMPO mixtures merge with the isotherm of the pure surfactant already before reaching its CMC. It suggests that BCS is displaced from the surface layer by the C12DMPO already before reaching this concentration value. The surface rheological data also support these findings for both ways of mixed layer formation (see
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J. Phys. Chem. B, Vol. 113, No. 1, 2009 107
TABLE 2: Fit Parameters for the Equilibrium Surface Tension and Adsorption Isotherm of C12DMPO and DoTAB Obtained from Fitted the Data with a Frumkin Model Given by Equations 1, 3, and 7 at θP ) 0 ωS0 aS εS bS DS
C12DMPO
DoTAB
2.5 × 10 m /mol 0 8.0 × 10-3 m/mN 1.9 × 102 m3/mol 3.0 × 10-10 m2/s
2.1 × 105 m2/mol 0 8.0 × 10-3 m/mN 1.2 m3/mol 1.0 × 10-10 m2/s
5
2
TABLE 3: Fit Parameters for the Equilibrium Surface Tension and Adsorption Isotherm of BCS/C12DMPO Mixtures Obtained from Fitting the Data with the Model Given by Equations 1-3 and 7 BCS ω0 ω1 ωmax aPS bP DP
2.2 × 105m2/mol 3.0 × 106m2/mol 2.7 × 105m2/mol 1.1 1.0 × 102m3/mol 1.0 × 10-10 m2/s
C12DMPO ωS0 aS aSPS εS bS DS
2.5 × 105m2/mol 0.0 0.0 9.0 × 10-3m/mN 1.96 × 102m3/mol 3.0 × 10-10 m2/s
below). Ellipsometric and foam film measurements using the simultaneous adsorption route showed the same results.12 For the BCS/DoTAB mixtures, the curves meet the pure DoTAB isotherm only around its CMC (Figure 1), showing that the ionic surfactant with the same hydrocarbon chain length cannot displace the BCS as effectively as the nonionic C12DMPO. The surface activity of DoTAB molecules is also much smaller, as compared to that of C12DMPO, due to the charged headgroup. The curves on the figure represent the theoretical fitting for the surfactants and for the mixtures formed via simultaneous adsorption. In addition to the experimental surface tension isotherms, Figure 1 contains the fitted curves calculated with the parameters given in Tables 1-4. The set of model equations discussed above describe the studied systems perfectly. The fitting parameters for the individual BCS (Table 1) and surfactants (Table 2) and for the mixtures of BCS/C12DMPO (Table 3) and BCS/DoTAB (Table 4) differ slightly from those discussed recently.55,56 The reason for this is that the used concentration of BCS (10-6 mol/L) is just above the critical region of concentration (c* ) 4 × 10-7 mol/L), where the adsorption layer is saturated with the protein molecules and where the formation of a second layer or surface aggregation starts. To be able to describe properly the surface dilational rheological data of the mixed BCS/surfactant and BCS/surfactant solutions, we assumed that the concentration of 10-6 mol/L of the protein is still located in the precritical region, so that the rheological parameters of BCS can be described well (see below). For drop shape experiments, as performed here, due to the target of comparing the sequential and simultaneous adsorption routes, the losses of molecules in the bulk due to adsorption at the drop surface can be significantly lower than the initial values. This fact is an additional argument for our assumption that the chosen BCS concentration falls into the precritical concentration region (below 4 × 10-7 mol/L).
TABLE 4: Fit Parameters for the Equilibrium Surface Tension and Adsorption Isotherm of BCS/DoTAB Mixtures Obtained from Fitting the Data with the Model Given by Equations 4-7 BCS ω0 ω1 ωmax aPS bPS DPS DoTAB ωS0 aS aSPS εS bS m DS
2.2 × 105 m2/mol 3.0 × 106 m2/mol 4.0 × 107 m2/mol 1.1 1.0 × 102 m3/mol 1.0 × 10-10 m2/s 2.1 × 105 m2/mol 0.0 0.0 8.0 × 10-3 m/mN 1.2 m2/mol 8.0 3.0 × 10-10 m2/s
As one can see, the obtained values for the interaction aSPS between the protein/surfactant complex and the free surfactant are zero for both studied surfactants. This means that there is no extra interaction as compared to the individual protein adsorption layer, which was expected for the random coil protein, i.e. no significant structure changes were induced by the interacting surfactants as potential reason for an increased interfacial interaction. 4.2. Dilational Rheology of Single Component Solutions. 4.2.1. BCS. For these investigations, we used always the same five oscillation frequencies: 0.005, 0.01, 0.02, 0.04, and 0.1 Hz. At these frequencies, the measured elasticities and viscosities are sensitive to the respective contributions given by the surfactant and protein molecules at the rather low bulk concentrations used in the present studies. Figure 2 shows the real (Er) and imaginary (Ei) part of the complex viscoelasticity E(Ω) of a 10-6 mol/L BCS solution vs oscillation frequency ν. The real part increases and levels off at a sufficiently high frequency reaching the value of the limiting viscoelastic modulus. The viscosity values decrease with increasing frequency and it is expected, that the values reach zero beyond a sufficiently high frequency.53 The curves of theoretical fitting are also shown in Figure 2. One can see that the absolute values obtained from the experiments are similar to those related to the theoretical fitting. In the Er values in both cases an increase with the frequency rise can be observed, since the experimental Ei data show a slight increase and the theoretical values related to the imaginary part slightly decrease with increasing frequency in the used range. Note that the curves are calculated from the available theory based on the thermodynamic model for protein adsorption at liquid interfaces (eqs 1 or 4) and a diffusional mechanism for the relaxations induced by the harmonic area perturbations (eqs 9-15). It is known that proteins do not relax according to a diffusional exchange mechanism; however, for any other mechanism, theories do not exist. Hence, the diffusion coefficient Dp given in the tables are effective values and can be lower or larger (as in the present case) than the physically reasonable value. 4.2.2. C12DMPO. The dilational viscoelastic properties of C12DMPO solutions were studied systematically for example by Wantke et al.27 and Kovalchuk et al.28 in a broad concentration range between 10-5 and 4 × 10-4 mol/L at by using the oscillating bubble method. While Wantke et al.27 measured at frequencies between 1 and 500 Hz, Kovalchuk et al.28 used the oscillating bubble method under microgravity conditions in the
108 J. Phys. Chem. B, Vol. 113, No. 1, 2009
Figure 2. Real Er (9) and imaginary Ei (0) part of the complex viscoelasticity E of a 10-6 mol/L BCS solution vs oscillation frequency. The curves represent the theoretical fitting obtained from eqs 9-15.
Figure 3. Real and imaginary part of the complex viscoelasticity as a function of C12DMPO concentrations at two oscillation frequencies 0.01 (90) and 0.1 Hz (2∆): Er filled symbols, Ei open symbols. The curves are theoretical fittings using eqs 9-15.
frequency range of 0.01-100 Hz. The results obtained in these two works are in good agreement with each other. The data presented in Figure 3 obtained here with the PAT-1 at low frequencies in the range between 0.01 and 0.1 Hz also agree with those in literature. The values, calculated via eqs 6 and 7, show at 0.01 Hz a maximum in Er at about 2 × 10-5 mol/L, which shifts to higher concentrations with increasing frequency. The curves in Figure 3 represent the theoretical dependencies as calculated for the Frumkin adsorption model. 4.2.3. DoTAB. The viscoelastic parameters Er and Ei for DoTAB solutions, shown in Figure 4, have much lower values as those observed for the nonionic C12DMPO. As we can see, the locations of the maxima on the concentration axis for 0.01 and 0.1 Hz are well predicted by the model; however, the absolute values differ slightly from the calculated dependencies. For our further discussion, the most important fact is the location of the maximum in Er and Ei, respectively, so that we can use the obtained results. 4.3. Protein/Surfactant Mixtures. 4.3.1. Dilational Rheology of BCS/C12DMPO Mixtures. The dilational viscoelastic moduli and viscosities of BCS/C12DMPO mixed adsorption
Kotsmar et al.
Figure 4. Real and imaginary part of the complex viscoelasticity as a function of DoTAB concentrations at two oscillation frequencies 0.01 (90) and 0.1 Hz (2∆): Er filled symbols, Ei open symbols. The curves are theoretical fittings using eqs 9-15.
layers, formed via the simultaneous and sequential adsorption route are presented in Figures 5 and 6, respectively. The absolute values of the viscoelastic modulus for the mixtures increase with increasing frequency as it was also observed for the pure C12DMPO solutions (Figure 3). For easier comparison, the scales on the axes of Figure 5a and b are identical. Small additions of C12DMPO to the BCS solution do not influence the values in the sim ads route. The curves at all frequencies slightly decrease up to a C12DMPO concentration of around 4 × 10-5 mol/L. With further increasing concentrations, the values increase, pass through a maximum, and finally decrease. The surfactant dominates the surface layer. The values obtained in the sequ ads route do not differ significantly from those of the sim ads route, except for the smallest amounts of surfactant
