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Adsorption of Proteins at the Solution/Air Interface Influenced by Added Nonionic Surfactants at Very Low Concentrations for Both Components. 3. Dilational Surface Rheology V. B. Fainerman,† E. V. Aksenenko,‡ S. V. Lylyk,† M. Lotfi,§,∥ and R. Miller*,∥ †

Medical University Donetsk, Donetsk 83003, Ukraine Institute of Colloid Chemistry and Chemistry of Water, Kyiv (Kiev) 03680, Ukraine § MPI Colloids and Interfaces, Potsdam D-14424, Germany ∥ Sharif University of Technology, Teheran 11365-11155, Iran ‡

ABSTRACT: The influence of the addition of the nonionic surfactants C12DMPO, C14DMPO, C10OH, and C10EO5 at concentrations between 10−5 and 10−1 mmol/L to solutions of β-casein (BCS) and β-lactoglobulin (BLG) at a fixed concentration of 10−5 mmol/L on the dilational surface rheology is studied. A maximum in the viscoelasticity modulus |E| occurs at very low surfactant concentrations (10−4 to 10−3 mmol/L) for mixtures of BCS with C12DMPO and C14DMPO and for mixtures of BLG with C10EO5, while for mixture of BCS with C10EO5 the value of |E| only slightly increased. The |E| values calculated with a recently developed model, which assumes changes in the interfacial molar area of the protein molecules due to the interaction with the surfactants, are in satisfactory agreement with experimental data. A linear dependence exists between the ratio of the maximum modulus for the mixture to the modulus of the single protein solution and the coefficient reflecting the influence of the surfactants on the adsorption activity of the protein. ionic surfactants with more flexible proteins like β-casein (BCS) there is a sharp maximum in the dilational elasticity. Experimental results on the dilational rheology of protein− nonionic surfactant mixtures were reported in refs 13−17; some of these results and the relevant theoretical models of the corresponding surface layers were discussed previously.18,19 The influence of the addition of the nonionic surfactants C12DMPO, C14DMPO, C10OH, and C10EO5 at concentrations from 10−5 to 10−1 mmol/L to BCS and BLG solutions, respectively, at a fixed concentration of 10−5 mmol/L on the surface tension was studied in ref 19. It was shown that a significant change (3−7 mN/m) of the surface tension at the water/air interface occurs at very low surfactant concentration (10−5 to 10−3 mmol/L). All measurements were performed with the buoyant bubble profile method, in which the bubbles are formed in a large volume of the studied solution. The application of theoretical models to mixed systems is still limited due to the extreme complexity of the equations. To achieve agreement between theory and experiment, we made a supposition about the influence of the concentration of nonionic surfactant on the adsorption activity of the protein. The surface tension values calculated using the proposed

1. INTRODUCTION The interest in dilational surface rheology of protein solutions and their mixtures with surfactants is due mainly to the fact that these systems are frequently used as foam and emulsion stabilizers, in which the stabilization mechanism is governed mainly by the rheological characteristics.1−4 Moreover, the dilational surface rheology turns out to be more sensitive to the conformation of macromolecules at the liquid interface than the interfacial tension. Tensiometry allows following the formation of adsorption layers over a certain time interval, and dilational rheology provides information on the response of the interfacial layer to small perturbations. These results make it possible to estimate the surface layer composition using the rheological data. In mixed protein−surfactant adsorption layers, the nature of the surfactant importantly influences the dilational behavior of the mixture. Moreover, the method of formation of mixed interfacial layers (sequential or competitive adsorption) essentially affects the dilational properties of the mixed interface, as it follows from refs 5−8. Regarding the effect of nonionic surfactants, the monotonous decrease of the dilational modulus with increasing surfactant concentration is found for globular proteins. These results indicate the transition from a protein-dominated interface to a surfactant-dominated interface via competitive adsorption but also the possibility of an orogenic displacement mechanism.9−12 For mixtures of non© 2015 American Chemical Society

Received: January 6, 2015 Revised: January 28, 2015 Published: January 28, 2015 3768

DOI: 10.1021/acs.jpcb.5b00136 J. Phys. Chem. B 2015, 119, 3768−3775

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The Journal of Physical Chemistry B

positive Δγ value corresponds to the maximum ΔA, it could be supposed that the liquid inertia during the air inflow into the suppressed bubble elongates it, making the bubble more spherical.

modified model agree well with all experimental data. The model provides correction coefficients for the protein adsorption equilibrium constant. The largest correction of this constant was found for the BCS + C14DMPO mixtures. The solutions of proteins and surfactants studied here were the same as in ref 19. The dilational rheology of individual solutions and their mixtures after equilibration of the system was studied using the buoyant bubble profile method at surface area oscillation frequencies in the range 0.005−0.5 Hz. It is shown that, depending on the surfactant concentration, the dilational viscoelasticity modulus increases and in some cases exhibits a maximum. The maximum value of this modulus is higher than that observed for the pure protein solution. The ratio between the maximum modulus for the mixture and its value for pure protein solution correlates with a coefficient proposed in ref 19 that describes the increase of the adsorption activity of protein in its mixture with surfactants. Also, the conditions are determined at which the results of theoretical calculations agree satisfactorily with the experimental viscoelasticity modulus.

3. THEORY The adsorption isotherm for a protein in its mixture with a nonionic surfactant as derived in ref 19 differs from that proposed in ref 21. This modified adsorption isotherm assumes a linear dependence of the protein adsorption equilibrium constant on the concentration of the added nonionic surfactant. In physical terms this is due to the fact that the polar groups of the nonionic surfactant molecules can bind to the amino acid groups in the protein molecule by van der Waals interactions, which changes the conformation and hence the hydrophobicity of the protein molecules. The adsorption isotherm for the mixture of a protein with a nonionic surfactant, assuming the influence of the surfactant on the adsorption activity of the protein, reads BP,1c P =

2. MATERIALS AND METHODS The materials and methods used in this study were described in refs 18 and 19. All solutions were prepared in phosphate buffer (10 mmol/L of Na2HPO4 and NaH2PO4, pH 7.0) using MilliQ water. The proteins BLG and BCS were purchased from SIGMA. The nonionic surfactants dodecyl dimethyl phosphine oxide (C12DMPO) and tetradecyl dimethyl phosphine oxide (C14DMPO) were synthesized at the MPI. The oxyethylated alcohols C10EO5 and C12EO5 and decyl alcohol (C10OH) were also purchased from SIGMA. The experiments were performed with the drop/bubble profile analysis tensiometer PAT-1 (SINTERFACE Technologies, Germany). A buoyant bubble was formed at the bottom tip of a vertical Teflon capillary of 3 mm outer diameter and kept in the solution until its equilibration (30 000 s for the most diluted solutions and not less than 15 000 s for the highest concentrations). Rapid equilibrium is established by using the method of buoyant bubble and the possible resulting convective mass transfer.19 After the bubble was equilibrated, harmonic oscillations with an amplitude of ±7% and frequency in the range 0.005−0.5 Hz were imposed on the bubble surface. At high oscillation frequencies, the PAT-1 tensiometer performed ten surface tension measurements per second. The surface dilational viscoelasticity is defined as the surface tension γ increase in response to a certain relative surface area increase A: E = dγ/d ln A. The viscoelasticity is a complex quantity E = Er + i·Ei, where Er and Ei are the real (elasticity) and imaginary (viscosity) constituents of the viscoelasticity, respectively, and the phase angle ϕ between stress (dγ) and strain (dA) is defined as ϕ = arctg(Ei/Er). The viscoelasticity modulus and its constituents were calculated via a Fourier transformation of the experimental quantities. The measurements and calculation procedure were explained in more detail in ref 20. Reference experiments with pure solvent (Milli-Q water or phosphate buffer in Milli-Q water) have shown that within this oscillation frequency range, the viscoelasticity modulus values are about zero and do not exceed 0.6 mN/m. The highest modulus values were observed at high frequencies. These maximum modulus values correspond to the average surface tension deviations of Δγ = ±0.04 mN/m during the oscillations. This observed effect could possibly be ascribed to distortions of the bubble shape caused by variations of the bubble volume: as the maximum

ωP ΓP,1 ωP,1/ ωP

(1 − θP − θS)

⎡ ⎛ ωP,1 ⎞⎤ θP + aPSθS⎟⎥ exp⎢− 2⎜aP ⎢⎣ ⎝ ωP ⎠⎥⎦ (1)

Here BP,1 is the protein adsorption equilibrium constant in the mixture, cP is the protein concentration, ωS is the molar area of the nonionic surfactant, aP and aPS are the intermolecular protein−protein and protein−surfactant interaction parameters, and the subscripts S and P refer to the surfactant and protein, respectively. The total adsorption of proteins in all n states (1 ≤ i ≤ n) is given by ΓP = Σni=1ΓP,i. ωP is the average molar area of the adsorbed protein, ωP,i = ωP,1 + (i − 1)ω0 is the molar area in state i, ωP,1 = ωmin and ωmax = ωP,1 + (n − 1)ω0, and ω0 is the molar area of the solvent or the area occupied by one segment of the protein molecule (area increment). The parameter θP = ωPΓP = Σni=1ωP,iΓP,i represents the partial surface coverage by protein molecules, and θS = ωS·ΓS refers to the surface coverage by surfactant molecules (ΓS is the adsorption of surfactant molecules). The parameter aPS describes the mutual interaction between protein and surfactant molecules. The parameter BP,1 in the left-hand side of eq 1 is determined by the expressions BP,1 = bP,1

at cS < c0

(2a)

BP,1 = bP,1[1 + aX (cS − c0)]

at c0 < cS < cm

(2b)

BP,1 = bP,1[1 + aX (cm − c0)]

at cS > cm

(2c)

where aX is an adjustable parameter that accounts for the influence of the surfactant concentration cS on the activity of the polymer. Therefore, at low surfactant concentrations corresponding to condition 2a the parameter BP,1 is equal to the adsorption equilibrium constant of the individual protein bP,1. Condition 2b corresponds to the variation of this constant with the increase in surfactant concentration, and condition 2c implies the fixed value of the protein adsorption activity at surfactant concentrations above a certain critical value cm. All other equations used in this study to describe the protein− nonionic surfactant mixtures are those presented in refs 19 and 21. An expression for the diffusion controlled exchange of surfactants or proteins caused by harmonic oscillations of the surface area of the bubble or drop surface was derived by Joos.22 In particular, for the adsorption from solution at the 3769


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The Journal of Physical Chemistry B surface of a bubble the following expression for the complex viscoelasticity was obtained:

{

E(ω) = E0 1 − i

D dc (1 + κr ) ω r dΓ

−1

}

(3)

where E0 = dΠ/d ln Γ is the limiting elasticity, Π = γ0 − γ is the surface pressure, γ and γ0 are the surface tension of the solution and pure solvent, respectively, D is the diffusion coefficient of the protein or surfactant in the solution, ω = 2πf is the angular frequency of the surface area oscillations at frequency f given in Hz, κ2 = iω/D, and r is the radius of curvature of the interface. For a planar interface (r → ∞) eq 3 transforms into the expression derived in refs 23 and 24. The surface elasticity of mixed surface layers was discussed in ref 5, where a procedure was developed to calculate the rheological characteristics of mixed adsorbed layers. When performing these calculations, it is sufficient to know the dependencies of surface pressure Π and adsorptions of the system ΓP and ΓS as functions of the bulk concentrations cP and cS. These dependencies can be obtained from the equation of state of the surface layer, and the adsorption isotherms for the protein and surfactant. The complex viscoelasticity is determined by the expression E(ω) =

1 ⎛ ∂Π ⎞ ⎜ ⎟ B ⎝ ∂ ln ΓS ⎠

⎡ iω ⎢ a + ⎢⎣ DS SS Γ P

Γ iω aSP P DP ΓS

−

⎤ ω (aSSaPP − aPSaSP)⎥ ⎥⎦ DSDP

+

Γ 1 ⎛ ∂Π ⎞ ⎡ iω aPS S + ⎟ ⎢ ⎜ B ⎝ ∂ ln ΓP ⎠Γ ⎢⎣ DS ΓP S

−

Figure 1. Dependence of the viscoelasticity modulus for mixtures of 10−5 mmol/L BLG solution with C12DMPO and for individual C12DMPO solutions at two oscillation frequencies. Experimental points: (■, □) mixture; (◆, ◇) individual C12DMPO solution; filled symbols, f = 0.1 Hz; open symbols, f = 0.01 Hz. Calculation results: solid curves (1, 3), f = 0.1 Hz; dashed curves (2, 4), f = 0.01 Hz; red curves (1, 2), mixture; black curves (3, 4), individual C12DMPO; green curve (5), calculations using the reorientation model with parameters listed in Table 1; blue curve (6), calculations with increased bS value. For details, see text.

⎤ ω (aSSaPP − aPSaSP)⎥ ⎥⎦ DSDP

iω aPP DP

(4)

where E = Er + i·Ei, aSS = (∂ΓS/∂cS)cP, aSP = (∂ΓS/∂cP)cS, aPS = (∂ΓP/∂cS)cP, aPP = (∂ΓP/∂cP)cS, and B = 1 + (iω/DS)1/2aSS + (iω/DP)1/2aPP − (ω/(DSDP)1/2)(aSSaPP − aPS aSP). The corresponding expression for the viscoelasticity modulus |E| was obtained in ref 5. The partial derivatives in eq 4 are determined from the adsorption characteristics of the protein and surfactant using the expressions presented in ref 19 and the values listed in Tables 1−3 therein. It was shown by the calculations that the viscoelasticity modulus increases with the increase of ωmin, aP, aPS, bP,1, aS, and bS values, while the increase of ω0, ωmax, and ωS leads to a decrease of the viscoelasticity modulus. It should be noted that the addition of surfactant can affect the model adsorption parameters of protein. With the increased surfactant concentration, the viscoelasticity modulus of the mixture usually exhibits a maximum, which is accompanied by the increase of its imaginary part Ei.

Figure 2. Dependence of the viscoelasticity modulus for mixtures of 10−5 mmol/L BLG solution with C10OH and for individual C10OH solutions at two oscillation frequencies. Experimental points: (■, □) mixture; (◆, ◇) individual C10OH solution; filled symbols, f = 0.1 Hz; open symbols, f = 0.01 Hz. Calculation results: solid curves (1, 3), f = 0.1 Hz; dashed curves (2, 4), f = 0.01 Hz; red curves (1, 2), mixture; black curves (3, 4), individual C10OH. For details, see text.

these surfactants. The viscoelasticity modulus for pure BLG coincides (to within the measurement error of ±2 mN/m) with those measured for mixtures with surfactants added at concentrations below 10−5 mmol/L, which are equal to 33 and 37.6 mN/m, respectively. The results thus obtained for pure BLG and surfactants agree with those published in the literature. The data for C10EO5 solutions are close to those reported in ref 20. In ref 25, BLG solutions at a fixed concentration of 10−5 mmol/L were investigated with the emerging bubble method. At a frequency of 0.1 Hz the following values for the viscoelasticity modulus at different

4. RESULTS AND DISCUSSION The dependencies of the viscoelasticity modulus on the surfactants’ concentrations at the oscillation frequencies 0.1 and 0.01 Hz for mixtures of BLG (at a fixed concentration of 10−5 mmol/L) with C12DMPO, C10OH, and C10EO5 are illustrated by Figures 1−3, respectively. Also shown in these figures are the dependencies for the individual solutions of 3770


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diffusion coefficient was estimated from a best fit between the calculated results and experimental data; the optimum values were found to be in a quite realistic range of 10−10 to 10−9 m2/s. It is seen that Frumkin’s model provides a satisfactory description for the dependence of the viscoelasticity modulus on the concentration of individual surfactants. It should be noted that for the C12DMPO and C10EO5 solutions at low concentrations the reorientation model yields better agreement with experimental data. These dependencies for the frequency of 0.1 Hz calculated with the equations of state and adsorption isotherm for the reorientation model were already presented in refs 20 and 21 with the relevant values of parameters listed in Table 1 and are also shown in Figures 1 and 3. Table 1. Adsorption Characteristics of the Individual Surfactants According to the Reorientation Model Figure 3. Dependence of the viscoelasticity modulus for mixtures of 10−5 mmol/L BLG solution with C10EO5 and for individual C10EO5 solutions at two oscillation frequencies. Experimental points: (■, □) mixture; (◆, ◇) individual C10EO5 solution; filled symbols, f = 0.1 Hz; open symbols, f = 0.01 Hz. Calculation results: solid curves (1, 3), f = 0.1 Hz; dashed curves (2, 4), f = 0.01 Hz; red curves (1, 2), mixture; black curves (3, 4), individual C12DMPO; green curve (5), calculations using the reorientation model with parameters listed in Table 1; blue curve (6), calculations with increased ωmin and bS values. For details, see text.

1 + ζ + iζ 1 + 2ζ + 2ζ 2′

(5)

where the high frequency elasticity limit E0, the characteristic frequency ωD, and the parameter ζ are given by E0 = −

dγ d ln Γ

ωD =

2 D ⎛⎜ dc ⎞⎟ 2 ⎝ dΓ ⎠

ζ=

C10EO5

C12DMPO

C14DMPO

3.5 7.5 2.8 3.0 388

2.5 4.8 1.3 3.0 175

3.0 6.0 1.5 3.0 4360

The calculations for the protein−surfactant mixtures were performed using the Frumkin adsorption model. The viscoelastic characteristics were calculated from eq 4 for the parameter values listed in Tables 1−3 of ref 19; the characteristic parameters of eq 2 are listed in Table 3 of ref 19, and the diffusion coefficient was taken to be 10−11 m2/s. This diffusion coefficient value for BLG, obtained for mixtures at all surfactant concentrations, is very realistic. Convective mass transfer at the investigated oscillation frequencies has virtually no effect on the rate of adsorption and desorption, which justifies the use of diffusion as relaxation mechanism. Note that in ref 25 a smaller diffusion coefficient had to be used to obtain agreement between theory and experiment. The inflection points on the calculated curves correspond to the critical concentration cm in eq 2c. The theoretically calculated values of the viscoelasticity modulus for the mixtures with C12DMPO and C10OH are in a satisfactory agreement with the experimental data; however, for the BLG mixtures with C10EO5 the maximum on the theoretical curve is significantly shifted toward higher concentrations. This shift is probably ascribable to the fact that for the surfactant the Frumkin model is used rather than the more rigorous reorientation model. It is possible to shift the isotherm toward lower concentration by increasing the value of the surfactant adsorption equilibrium constant bS. This is illustrated in Figure 1 for the BLG mixtures with C12DMPO in which the corrected curve was calculated for the frequency 0.1 Hz with a bS value increased by a factor of 3 as compared to its value listed in Table 2 of ref 19. It is seen that the maximum becomes in fact shifted toward lower concentrations. However, for the BLG mixtures with C10EO5 this shift was found to be insignificant: a similar increase of the bS value results in a shift of the viscoelasticity maximum from 2.5 × 10−2 to 10−2 mmol/L, while the experimentally observed maximum for 0.1 Hz is located at 2 × 10−4 mmol/L. This difference in the behavior between C12DMPO and C10EO5 could possibly be related to changes in the protein molecule structure caused by the addition of C10EO5. The penetration of the surfactant molecule into the BLG globule leads to an increase of its size, and hence, the area of the protein molecule.

surface age were obtained: at 10 000 s, 21 mN/m; at 30 000 s, 43 mN/m; at 80 000 s, 52 mN/m. The slightly higher values obtained here at longer adsorption times can be explained by differences in shape and size of the bubble. It is seen that the addition of surfactants leads to an increase of the viscoelasticity modulus, which attains its maximum at concentrations between 10−4 and 10−3 mmol/L and then decreases. The most significant increase of the modulus was observed for the BLG mixtures with C10EO5. The value of the phase angle ϕ for the mixtures of BLG with surfactants in the studied frequency range are 4−7, 5−10, and 10−15° for the surfactants concentration of 0.1, 1, and 10 mmol/L, respectively. Lower values of the phase angle refer to higher frequencies. Note that no influence of the surfactant type on the ϕ values was observed. Shown in Figures 1−3 are also the calculated values of the viscoelasticity modulus for individual surfactants and their mixtures with BLG. For the surface of an individual surfactant solution, assuming a purely diffusion controlled adsorption mechanism (without an adsorption barrier), the surface viscoelasticity takes the form23,24 E(iω) = E0

parameter ωmin [105 m2/mol] ωmax [105 m2/mol] α ε [10−3 m/mN] b [103 m3/mol]

⎛ ωD ⎞1/2 ⎜ ⎟ ⎝ ω ⎠ (6)

The calculations according to eq 5 were performed using the equations of state and adsorption isotherm derived for Frumkin’s model assuming an intrinsic compressibility of molecules in the surface layer. The parameters of these equations are listed in Table 2 of ref 19. The value of the 3771


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The Journal of Physical Chemistry B This effect becomes apparent for the state of the protein molecule at a minimum area ωmin. The red solid curve (1) in Figure 3 was calculated for f = 0.1 Hz with ωmin = 4.5 × 106 m2/ mol.19 The calculations with an increased value ωmin = 6 × 106 m2/mol yield the blue curve (6) that is seen to be in a much better agreement with the experimental data. It should be noted that this increase of ωmin (in addition to some other parameters that were slightly changed to obtain the best fit of the calculated values to all experimental data) does not virtually affect the dependence of the surface tension of the BLG mixture with C10EO5 on the surfactant concentration. This is illustrated by Figure 4, where the experimental data and calculated results reproduced from Figure 6 of ref 19 are shown along with the curve calculated with the corrected ωmin value.

Figure 5. Dependence of the viscoelasticity modulus for mixtures of a 10−5 mmol/L BCS solution with C14DMPO and for individual C14DMPO solutions for two oscillation frequencies. Experimental points: (■, □), mixture; (◆, ◇), individual C14DMPO solution; filled symbols, f = 0.1 Hz; open symbols, f = 0.01 Hz. Calculation results: solid curves (1, 3), f = 0.1 Hz; dashed curves (2, 4), f = 0.01 Hz; red curves (1, 2), mixture; black curves (3, 4), individual C14DMPO; green curve (5), calculations using the reorientation model with parameters listed in Table 1; blue curve (6), calculations with increased ωmin and bS values. For details, see text.

Figure 4. Dependencies of equilibrium surface tension isotherms for BLG mixtures with C10EO5 (■) and for BCS mixtures with C12DMPO (□) at a fixed protein bulk concentration of 10−5 mmol/L on the surfactants’ concentration. The experimental points and dashed calculated curves are reproduced from ref 19; solid curves are calculated with corrected ωmin values for the proteins.

The experimental results for the 10−5 mmol/L BCS solutions with additions of nonionic surfactants are shown in Figures 5−7. Similar to that of BLG solutions, the viscoelasticity modulus for the individual 10−5 mmol/L BCS solution coincides (to within the experimental error) with those values measured for mixtures with the surfactants at concentrations below 10−5 mmol/L. These modules are equal to 29 and 31 mN/m at frequencies 0.01 and 0.1 Hz, respectively, which is quite close to the values 25−30 mN/m measured for the same BCS concentration at pH 7 using the oscillating bubble method in ref 26. The experimental values of the viscoelasticity modulus for both mixtures exhibit maxima at surfactant concentrations of about 10−3 mmol/L. The magnitudes of these maxima are essentially larger (especially for the BCS mixture with C14DMPO) than those for the mixtures with BLG. For the mixture with C10EO5 the modulus does not exhibit any pronounced maximum and decreases monotonously with increasing surfactant concentration, while the same addition to BLG results in an increase of the viscoelasticity modulus and the existence of an appreciable maximum. The phase angle values for the surfactant mixtures with BCS are approximately the same as those for the mixtures with BLG except for the BSC/C14DMPO mixture, where at a concentration of 5 × 10−3 mmol/L the phase angle was found to be as large as 10−20°.

Figure 6. Dependence of the viscoelasticity modulus for mixtures of a 10−5 mmol/L BCS solution with C12DMPO and for individual C12DMPO solutions for two oscillation frequencies. Experimental points: (■, □), mixture; (◆, ◇), individual C12DMPO solution; filled symbols, f = 0.1 Hz; open symbols, f = 0.01 Hz. Calculation results: solid curves (1, 3), f = 0.1 Hz; dashed curves (2, 4), f = 0.01 Hz; red curves (1, 2), mixtures; black curves (3, 4), individual C12DMPO; green curve (5), calculations using the reorientation model with parameters listed in Table 1; blue curve (6), calculations with increased ωmin and bS values. For details, see text.

Figure 8 illustrates the equilibrium surface tension isotherms for BCS + C10EO5 mixtures at a fixed BCS bulk concentration of 10−5 mmol/L; also shown are data for pure C10EO5 solutions measured by the buoyant bubble method. As compared with the calculations that disregard the increase of the BCS adsorption activity caused by the presence of the surfactant (curve 2), the values obtained assuming this dependence are only by 1.3−1.5 mN/m lower (curve 3), while for the BLG + 3772


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19. It is known that the influence of coadsorbed surfactants on the structure of adsorbed protein depends on the kind and chemical structure of the surfactant.27−30 In this regard, the very weak influence caused by C10EO5 could be explained by the fact that the polar group of this molecule is quite large. To verify this supposition, we have studied mixed solutions of BCS and C12EO5. It appears that the presence of this surfactant does not result in any additional decrease in surface tension: the observed differences were within the experimental error range, i.e., aX = 0. Also, the dependence of the viscoelasticity modulus on the C12EO5 concentration is different from those obtained for all other mixtures: this dependence does not exhibit any extrema and the modulus remains constant and equal to its value for individual BCS (ca. 30 mN/m at 0.1 Hz) up to a C12EO5 concentration of 10−3 mmol/L. For higher C12EO5 concentrations the viscoelasticity modulus becomes lower, which is caused by the competitive adsorption of the surfactant. For the individual solutions the maximum of the modulus is attained at a concentration of 2 × 10−3 mmol/L; for the frequency of 0.1 Hz the modulus value is 24 mN/m. The experimental and theoretical dependencies for the individual C12DMPO and C10EO5 solutions shown in Figures 6 and 7 are reproduced from Figures 1 and 3, respectively. The dependence for the individual C14DMPO solutions shown in Figure 5 exhibits good fitting by the reorientation model with parameters listed in Table 1 and differs significantly from that obtained using Frumkin’s model. The theoretical curves for mixtures in Figures 5−7 were calculated with the parameters listed in Tables 1−3 of ref 19. However, the minimum adsorption area for the BCS molecule ωmin in mixtures with C12DMPO and C14DMPO was increased to 6 × 106 m2/mol (instead of 4.4 × 106 m2/mol). For mixtures with C10EO5 this increase was much less significant, i.e., up to 5 × 106 m2/mol only, because of a very weak influence of C10EO5 molecules on the BCS activity. Similar to that in BLG solutions, the interaction of surfactant molecules with BCS molecules can result in an increase of its volume and adsorption area ωmin in the state with minimal area. Therefore, in the calculations all other parameters were either taken to be equal to their values determined in the previous publications or slightly varied (bP,1, ωmax, ω0) to keep other dependencies unchanged. This is illustrated by Figure 4, where the experimental results and calculated dependence of surface tension for BCS mixtures with C12DMPO are reproduced from Figure 3 in ref 19. Also shown in Figure 4 is the calculated curve for the corrected value ωmin = 6 × 106 m2/mol (solid curve), which is almost identical to the curve obtained for the noncorrected value (dashed curve). The increase of ωmin for the BCS molecules by approximately 106 m2/mol is quite probable: as the C12DMPO molar area is 2.5 × 105 m2/mol,19 the aggregation of the protein molecule with four or five C12DMPO molecules would be sufficient. The theoretical calculations for BCS mixtures with C14DMPO were performed with two sets of parameters. The red curves (1 and 2) in Figure 5 were obtained with the corrected ωmin value, and to calculate the blue curve (6) for 0.1 Hz, the bS value was also increased by a factor of 3. The curve obtained with this second set (i.e., with both ωmin and bS values increased) is closer to the experimental dependence. Similar calculations were made for BCS mixtures with C12DMPO; these are illustrated by Figure 6. It is seen that the blue curve (6) obtained with both ωmin and bS values increased also exhibits better agreement with the experimental data. For BCS mixtures with C10EO5 (see Figure 7) the calculations were

Figure 7. Dependence of the viscoelasticity modulus for mixtures of a 10−5 mmol/L BCS solution with C10EO5 and for individual C10EO5 solutions for two oscillation frequencies. Experimental points: (■, □), mixture; (◆, ◇), individual C10EO5 solution; filled symbols, f = 0.1 Hz; open symbols, f = 0.01 Hz. Calculation results: solid curves (1, 3), f = 0.1 Hz; dashed curves (2, 4), f = 0.01 Hz; red curves (1, 2) for mixtures calculated with increased ωmin values; black curves (3, 4), individual C12DMPO; green curve (5), calculations using the reorientation model with parameters listed in Table 1. For details, see text.

Figure 8. Equilibrium surface tension isotherms for a fixed BCS concentration of 10−5 mmol/L BCS mixed with C10EO5 (■) and for individual C10EO5 solutions (□, ◇). The experimental points and theoretical dependence for individual C10EO5 solutions are represented by the thin line (1) and reproduced from ref 19; the bold black line (2) represents the dependence for mixtures calculated using the parameters listed in Tables 1 and 2 in ref 19; the bold blue line (3) represents the dependence for mixtures calculated using the same parameters and eqs 1 and 2 with the values of the parameters involved in eq 2 listed in the text. The horizontal dotted line corresponds to the surface tension value for the 10−5 mmol/L individual BCS solution.

C10EO5 system this decrease is 2 times larger (see ref 19). For the dependence shown in Figure 8 by curve 3, which was obtained using the model equations, eqs 1 and 2, and others derived in ref 19, the values of aX = 103 L/mmol, cm = 2 × 10−4 mmol/L, and c0 = 0 were found; this yields the coefficient describing the protein activity increase k = [1 + aX(cm − c0)] = 1.2, which is much lower than for other systems studied in ref 3773


Article

The Journal of Physical Chemistry B made with the increase of ωmin only to 5 × 106 m2/mol and bS unchanged; this was sufficient to obtain good agreement with the experimental data. There is a certain relation between the change of the viscoelasticity modulus and the increase of the adsorption activity of proteins due to the influence caused by the presence of surfactants in the mixture. Figure 9 illustrates the ratio of the

the modulus is not so pronounced. For BCS mixtures with C10EO5 only a slight increase of the modulus with increasing concentration was observed, while for BLG mixtures with C10EO5 this increase is essentially higher. As can be seen, the rheological behavior of mixtures of proteins with surfactants is affected by the protein structure and the type of the polar group of surfactants. BLG is a typical globular protein, and BCS is a typical flexible protein. To understand the mechanism of the surfactants’ effect, we require more research on the structure of the complexes. The viscoelasticity modulus was calculated using the theoretical model developed in ref 19, which takes into account the surfactant influence on the adsorption activity of proteins. The model assumes that the increase of the equilibrium adsorption activity of a protein is proportional to the surfactant concentration in the solution. The values of the viscoelasticity modulus calculated using this model, with the additional assumption that the presence of surfactant affects the minimum molar area of adsorbed protein molecules, are in a satisfactory agreement with the experimental data for all systems studied. It is shown that a linear dependence exists between the ratio of the maximum |E| value for the mixture to that of the individual protein solution and the value of the coefficient k that expresses the impact of surfactant molecules on the adsorption activity of proteins. A linear dependence exists also between this ratio and the difference between the surface tension calculated disregarding the influence of the surfactant on the protein adsorption activity and its original value. A maximum value of the modulus (twice as large as that for the individual protein solution) was found for BCS mixtures with C14DMPO, for which k = 2.7, while the surface tension decrease amounts to 6 mN/m.

Figure 9. Dependencies of the ratio of the maximum value of the viscoelasticity modulus for the mixture of protein with surfactant Emax to that of the individual protein solution E0 on the difference Δγ between the surface tension (calculated disregarding the influence of the surfactant on the protein adsorption activity) and its original value (■, □, curve 1), and also as a function of the coefficient k (◆, ◇, curve 2). Filled and open symbols correspond to the frequencies 0.1 and 0.01 Hz, respectively.

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AUTHOR INFORMATION

Corresponding Author

*R.M.: MPI Colloids and Interfaces, Potsdam−Golm Science Park, 14424 Potsdam, Germany. Email: [email protected]. Tel: +49-331-5679252.

maximum values of the viscoelasticity modulus for the mixture to that of the individual protein solution as a function of the coefficient k = [1 + aX(cm − c0)] and of the maximum difference Δγ between the surface tension calculated disregarding the influence of the surfactant on the protein adsorption activity and its original value. In Figure 8 this is the difference between the values of the bold black line (2) and the bold blue line (3) at the surfactant concentration of 4 × 10−4 mmol/L; for other systems these values could be calculated from the corresponding plots presented in ref 19. It is seen that both these dependencies for two oscillation frequencies are approximately straight lines. The maximum value of the modulus (approximately twice as large as that for the individual BCS solution) was found for the BCS mixture with C14DMPO: for this case k = 2.7 and Δγ = 6 mN/m.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was financially supported by projects of the DFG SPP 1506 (Mi418/18-2), the DLR (50WM1129), and the COST actions CM1101 and MP1106.

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REFERENCES

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5. CONCLUSIONS The influence of the addition of the nonionic surfactants C12DMPO, C14DMPO, C10OH, and C10EO5 at concentrations between 10−5 and 10−1 mmol/L to BCS and BLG solutions, respectively, at a fixed concentration of 10−5 mmol/L on the dilational surface rheology is studied. It is shown that a significant change of the viscoelasticity modulus occurs, and a maximum at very low surfactant concentration (10−4 to 10−3 mmol/L) appears for BCS mixtures with C12DMPO and C14DMPO, while for all other studied mixtures the increase of 3774


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