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Adsorption of Proteins at the Solution/Air Interface Influenced by Added Nonionic Surfactants at Very Low Concentrations for Both Components. 2. Effect of Different Surfactants and Theoretical Model V. B. Fainerman,† M. Lotfi,‡,§ A. Javadi,‡,∥ E. V. Aksenenko,⊥ Yu. I. Tarasevich,⊥ D. Bastani,§ and R. Miller*,‡ †

Medical University Donetsk, Donetsk 83003, Ukraine MPI Colloids and Interfaces, Potsdam D-14424, Germany § Sharif University of Technology, Tehran, Iran ∥ Chemical Engineering Department, University of Tehran, Tehran, Iran ⊥ Institute of Colloid Chemistry and Chemistry of Water, Kyiv (Kiev) 03680, Ukraine ‡

ABSTRACT: The influence of the addition of the nonionic surfactants dodecyl dimethyl phosphine oxide (C12DMPO), tetradecyl dimethyl phosphine oxide (C14DMPO), decyl alcohol (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 surface tension is studied. It is shown that a significant decrease of the water/air surface tension occurs for all the surfactants studied at very low concentrations (10−5−10−3 mmol/L). All measurements were performed with the buoyant bubble profile method. The dynamics of the surface tension was simulated using the Fick and Ward−Tordai equations. The calculation results agree well with the experimental data, indicating that the equilibration times in the system studied do not exceed 30 000 s, while the time required to attain the equilibrium on a plane surface is by one order of magnitude higher. To achieve agreement between theory and experiment for the mixtures, a supposition was made about the influence of the concentration of nonionic surfactant on the adsorption activity of the protein. The adsorption isotherm equation of the protein was modified accordingly, and this corrected model agrees well with all experimental data. theoretical data calculated using the model13 for the protein/ surfactant mixture. It should be noted that in this model the values of the equilibrium adsorption constants were the same as those for the individual solutions. The studies in ref 12 at quite low concentrations of the surfactants and proteins in their mixed solutions were performed with the buoyant bubble profile tensiometry. It was found that because of a significant acceleration of the diffusional fluxes of surfactants and proteins to the surface of a spherical bubble the time to reach adsorption equilibrium becomes dramatically reduced. It was due to this very method that a significant decrease of the equilibrium surface tension was found for protein/surfactant mixtures. In the present study, we compare the results calculated assuming the diffusional kinetics of adsorption from the solution onto the bubble surface with those onto a plane surface; these values are also compared with relevant experimental data. It is shown that for the adsorption onto a bubble surface from very diluted protein−surfactant mixed solutions the equilibration time is by one order of magnitude

1. INTRODUCTION Protein and low molecular weight surfactant mixtures are widely studied due to their major industrial applications. Added surfactants influence the interfacial properties of the proteins and their surface activity, rheological behavior, and adsorption dynamics. The effects caused by the additions of nonionic surfactants were studied in a number of publications1−12 using various surfactants. The influence of added surfactants was studied for β-lactoglobulin, lysozyme, and β-casein. The results reported in ref 11 are of particular interest: the addition of C12EO5 to solutions of lysozyme induces some degree of globular structure deformation. The evidence for the deterioration of the globular framework is the inhomogeneous distributions of lysozyme volume fractions across the interface. It was noted in ref 12 that in all known studies the protein concentration was high enough (equal or above 10−4 mmol/L), and therefore no noticeable influence of the additions of nonionic surfactant at very low concentrations could be detected. In ref 12, it was reported that at C12DMPO concentrations between 10−4 and 10−3 mmol/L the surface tension decrease of the mixtures amounts to about 3−5 mN/m as compared with the experimental values measured for both individual β-lactoglobulin and β-casein solutions, and with the © 2014 American Chemical Society

Received: July 26, 2014 Revised: October 5, 2014 Published: October 7, 2014 12812

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lower than that for the adsorption onto a plane surface. The effect caused by the additions of C12DMPO, C14DMPO, C10OH, and C10EO5 to the β-lactoglobulin and β-casein solutions on the surface tension of the respective mixed solutions was processed using a theoretical model modified to account for the variation of the protein adsorption equilibrium constant caused by the presence of the surfactant. This effect was assumed to be proportional to the surfactant concentration. It was shown that this influence can increase the protein adsorption equilibrium constant several times, and the maximum increase was found for β-casein solutions with the addition of C14DMPO.

c(r , 0) = c10 c(r , 0) = c 20

ΓP(t ) = 2

ΓS(t ) = 2

Let us consider briefly the model of diffusion controlled adsorption from the solution as presented in ref 14. The diffusion of the surfactant and protein in the two phases is governed by the Fick equations, which in spherical coordinates read:

⎛ ∂ 2c ∂c 2 ∂c ⎞ = D2⎜ 2 + ⎟ ∂t r ∂r ⎠ ⎝ ∂r

for

R1 < r < R 2

(1)

(2)

where c = c(r,t) is the surfactant concentration at time t and distance r from the center of the cell (chosen as the origin of the coordinate system), and Di (i = 1 and 2) are the diffusion coefficients of the surfactant in the ith phase. The temporal variation of the adsorption Γ caused by the incoming/outgoing diffusive fluxes is

dΓ ∂c = − D1 dt ∂r

r = R1−

+ D2

∂c ∂r

r = R1+

bP,1c P =

=0 r=0

and

∂c ∂r

(3)

=0 r = R2−

DP [c0P t − π

∫0

DS [c0S t − π

∫0

t

c P(0, t − t ′) d( t ′ )] ±

c0PDP t r (6)

t

cS(0, t − t ′) d( t ′ )] ±

c0SDS t r

ωP ΓP, j ωP,1/ ωP

(1 − θP − θS)

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

(8) Here bP,1 is the adsorption equilibrium constant, 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, respectively, 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, where ωP is the average molar area of the adsorbed protein, ωP,i = ωP1 + (i − 1)ω0 is the molar area in state i, ωP1 = ωmin, and ωmax = ωP1 + (n − 1)ω0, where ω0 is the molar area of the solvent or the area occupied by one segment of the protein molecule (area increment). The value θP = ωPΓP = Σni=1ωP,iΓP,i represents the partial surface coverage by protein molecules, and θS = ωSΓS 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

This equation is the boundary condition at the interface r = R1. The boundary conditions at r = 0 and at r = R2 follow from the symmetry of the system and the fact that the system is closed:

∂c ∂r

(5)

(7) Here DP and DS are the diffusion coefficients for the protein and surfactant, respectively, t is the time, c0P and c0S are the corresponding bulk concentrations, and r is the radius of curvature. The signs “−” or “+” before the second term on the right-hand side correspond to diffusion inside a drop and outside a drop or bubble, and t′ is a dummy integration variable. For flat interfaces, this term vanishes. Using eqs 6 and 7, and the corresponding adsorption isotherms as boundary conditions, the dependencies ΓP(t) and ΓS(t) for a protein/surfactant mixture can be calculated. It should be noted that eqs 6 and 7 describe the effects related to the drop radius only within the range smaller than the time necessary for the diffusion through a liquid layer equal to the drop radius. For a bubble located within a large solution volume the diffusion layer thickness can exceed the bubble radius, and therefore, the temporal interval within which the calculations with eqs 6 and 7 remain valid could be also somewhat larger than that corresponding to the diffusion from a drop. In ref 12, for the analysis of the experimental results, a relatively rigorous thermodynamic model13 was used which accounts for the mutual influence of the components of the protein/surfactant mixture only via the attraction interaction coefficient, while the values of the equilibrium adsorption constants are taken to be the same as in the individual solutions. The comparison with experimental data in ref 12 has shown that the theoretical calculations result in surface tension values higher than the observed ones. Therefore, it was supposed in ref 12 that the presence of the nonionic surfactant leads to an increase of the protein equilibrium adsorption constant. The polar groups of the nonionic surfactant molecules could be bounded to the amino acid groups in the protein molecule by electric, covalent, or van der Waals interactions, which increase the hydrophobicity of the protein molecules. If this effect is disregarded, then the adsorption isotherm equation for the protein reads:12,13

3. THEORY

0 < r < R1

R1 < r < R 2

for

and

All studied solutions were prepared in phosphate buffer (10 mmol/L, Na2HPO4 and NaH2PO4, pH 7.0) using Milli-Q water (surface tension of 72.0 ± 0.2 mN/m at 25 °C during a time of up to 70 000 s). To prevent any chemical degradation of the proteins in the aqueous solutions, 0.5 g/L sodium azide (NaN3) was added to the phosphate buffer solution. The proteins β-lactoglobulin (BLG, molecular weight of 18.4 kDa) and β-casein (BCS, molecular weight of 24 kDa) both from bovine milk were purchased from Sigma and used without further purification. The nonionic surfactants dodecyl dimethyl phosphine oxide (C12DMPO) and tetradecyl dimethyl phosphine oxide (C14DMPO) were synthesized at the Max Planck Institute (MPI). The oxyethylated alcohols C10EO5 and C12EO5 and decyl alcohol (C10OH) were purchased from Sigma and used without further purification. The experiments were performed with the drop/bubble profile analysis tensiometer PAT-1 (SINTERFACE Technologies, Germany). The temperature in the measuring cell of 25 mL volume was kept constant at 25 °C. A geometry of a buoyant bubble formed at the bottom tip of a vertical Teflon capillary of 3 mm outer diameter was used. The measurement procedure is explained in more detail in ref 12.

for

and

The adsorption kinetics of a surfactant/protein mixture on a spherical interface was analyzed in ref 14, where the general relationship between the dynamic adsorption Γ(t) and the subsurface concentration ci(0,t) proposed by Ward and Tordai15 was employed. The corresponding equations for the time dependence of the adsorptions from a mixed solution of protein and surfactant onto a spherical interface have the following form:14

2. MATERIAL AND METHODS

⎛ ∂ 2c ∂c 2 ∂c ⎞ = D1⎜ 2 + ⎟ ∂t r ∂r ⎠ ⎝ ∂r

0 < r < R1

for

(4)

It was assumed that the initial distribution of the surfactant in each phase is homogeneous; therefore, the initial conditions for the set of eqs 1 and 2 are 12813

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surfactant molecules. Other equations involved in the theoretical model derived in refs 12 and 13 are as follows. The equation of state for protein/nonionic surfactant mixtures with the approximation ω0 ≅ ωS reads

−

Πω0* = ln(1 − θP − θS) + θP(1 − ω0 /ωP) + aPθP 2 + aSθS2 RT + 2aPSθPθS

(9)

Here, Π is the surface pressure, R is the gas law constant, and T is the absolute temperature. Small differences between ω0 and ωS can be accounted for by introducing the mean molar area ω0* =

ω0θP + ωS0θS θP + θS

(10)

The adsorption isotherm for the surfactant reads bScS =

θS exp[− 2aSθS − 2aPSθP] (1 − θP − θS)

Figure 1. Dynamic surface tension of 10−5 mmol/L individual BCS solution (black lines 1−4) and mixed solutions at two C12DMPO concentrations: 10−3 mmol/L (red lines 5−7) and 10−2 mmol/L (green lines 8−10); data reproduced from ref 12. Bold solid lines (4, 7, 10), experimental data; bold dashed lines (3, 6, 9), calculations for bubble with eqs 1−5 for the individual BCS solution and eqs 6 and 7 for mixtures; thin dashed lines (1, 5, 8), calculations for plane interface with eqs 1−5 for the individual BCS solution and eqs 6 and 7 for mixtures; thin black solid line (2), calculations for plane interface with eqs 6 and 7 for the individual BCS solution.

(11)

where bS is the adsorption equilibrium constant. The surfactant’s molar area ωS and the corresponding adsorption ΓS depend on the surface pressure Π and the total surface coverage θ = θP + θS and is given by ωS = ωS0[1 − ε Πθ ],

θS = ΓSωS0[1 − ε Πθ ]

(12)

with ωS0 = ωS at Π = 0. The eqs 12 take into account the intrinsic compressibility ε of surfactant molecules in the surface layer. Assuming that the influence of the surfactant on the protein adsorption equilibrium constant is proportional to the surfactant concentration in the solution cS, eq 8 becomes

toward the bubble located in the center of the measuring cell at the tip of a vertical capillary. This convective flow in the large measurement cell can arise due to several effects: temperature gradients caused by a nonuniform heating of the cell; diffusion of surfactant to the free upper surface of the cell; adsorption leading to the decrease of surface tension; and evaporation of water from the upper surface of liquid resulting in a lower local temperature. The calculations for the individual BCS solution were made for two values of the bubble radius: the actual value used in the buoyant bubble experiments, r = 1.6 mm, and r = 50 mm which corresponds to a plane surface (for any r > 30 mm, the value does not affect the results). The BCS diffusion coefficient was taken equal to the value found for the actual bubble. The calculated kinetic curves are shown in Figure 1 by bold and thin dashed lines, respectively. It is seen that the theoretical curve for the actual bubble radius agrees well with the experimental values; according to the calculations, the equilibrium is attained after 30 000 s. The kinetic curve calculated assuming a plane surface is significantly shifted toward larger times, as compared with those for the spherical surface; for this curve, the time necessary to attain the equilibrium is by a factor of 10 larger than that for the actual bubble. To compare two different calculation procedures, the values for r = 50 mm were also calculated using the Ward− Tordai eq 6. These values, shown in Figure 1 by the thin solid line, agree with the results obtained from the Fick equation (thin dashed line). The calculations for the mixtures were performed using eqs 6 and 7 for the actual bubble with a radius of 1.6−1.7 mm and diffusion coefficient values of 5 × 10−10 m2/s and 10−9 m2/s for the BCS and C12DMPO, respectively. These results shown by bold dashed lines provide a good agreement with the experiment. In these calculations, the value of the protein adsorption equilibrium constant for the mixture was increased by a factor of 1.7, that is, to 2.0 × 103 L/mmol instead of 1.2 × 103 L/mmol used for the individual solution (see Table 1).

̃ cP bP,1(1 + a*cS)c P ≡ bP,1 =

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

(13) ̃ Here bP,1 = bP,1(1 + a*cs) is the modified, or “effective”, adsorption equilibrium constant for the protein, where a* is an adjustable parameter which accounts for the influence of the surfactant on the surface activity of the protein. In the present study, we assume that this effect occurs within the surfactant concentration range below a certain concentration cm, above which the expression in the parentheses remains equal to its maximum value (1 + a*cm).

4. RESULTS AND DISCUSSION Figure 1 shows the dynamic surface tension curves of the individual BCS solution at a bulk concentration of 10−5 mmol/ L (black curves) in the absence and presence of two amounts of C12DMPO: 10−3 and 10−2 mmol/L (red and green curves, respectively). The experimental data shown by bold solid lines are reproduced from ref 12. Also shown in Figure 1 by bold dashed lines are the theoretical curves calculated using eqs 1−5 for the individual BCS solution and eqs 6 and 7 for the mixtures. The values of model parameters for individual BCS and C12DMPO used in these calculations were taken from ref 12. The parameters for weak protein solutions (with concentrations below the critical one) are listed in Table 1, while the parameters involved in the equation of state and Frumkin adsorption isotherm16 for C12DMPO and the other surfactants studied here are listed in Table 2. The value of the diffusion coefficient for BCS obtained from the best fit of the calculated kinetic curve to the experimental data is 6 × 10−10 m2/s. This rather high value could be possibly attributed to the convective transfer of protein molecules 12814

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Table 1. Main Parameter Values of the Theoretical Adsorption Model for the Proteins BCS and BLG at the Aqueous Solution/ Air Interface12 protein

ω0 (×105 m2/mol)

ωmin (×106 m2/mol)

ωmax (×107 m2/mol)

bP,1 (×103 L/mmol)

aP

BCS BLG

2.0 2.3

4.4 4.5

4.7 2.0

1.2 31.0

1.3 0.0

theoretical model. Figure 3 shows the equilibrium surface tension of pure BCS solution at the concentration of 10−5 mmol/L (horizontal dotted line), as well as of mixtures BCS/ C12DMPO and BCS/C14DMPO at various concentrations. The results for the pure C12DMPO and C14DMPO solutions, also shown in Figure 3, were also measured via the buoyant bubble method. The theoretical isotherms for these surfactants (thin solid lines) were calculated using the Frumkin model equations with the parameters listed in Table 2; for all the substances, the intrinsic compressibility coefficient in the adsorption layer is ε = 0.003 m/mN. The negative values of the constant a for C14DMPO (and C10EO5, see below) are attributable to the fact that for these surfactants the Frumkin model does not provide a perfect description. The reorientation model16 actually provides a much better description for the adsorption isotherms for these surfactants. However, for this model there are problems in the theoretical formulation for the case of protein/surfactant mixture; in particular, regarding the definition of the average molar area of the surfactant molecule, and the area of one segment of the protein molecule. The model for mixtures implies these areas to be rather close to each other; at the same time it is assumed in the reorientation model that these areas can be quite different, which introduces the ambiguity to the model formulation. In ref 17, to simulate the adsorption kinetics for protein/surfactant mixtures, the model proposed in ref 13 for the protein and Frumkin’s equations for the surfactant solution are also used. In Table 2, the aPS values refer to the intermolecular protein/surfactant interactions; the values without and in parentheses correspond to the BSC/surfactant and BLG/surfactant systems, respectively. It is seen from Figure 3 that the experimental results for both C12DMPO and C14DMPO are well fitted by the theoretical curves; note that

Table 2. Parameter Values of the Frumkin Model for the Studied Surfactants surfactant

ω0 (×105 m2/mol)

aS

b (L/mmol)

aPS

C12DMPO C14DMPO C10OH C10EO5

2.45 2.5 1.7 2.65

0.35 −0.44 1.11 −1.1

260 5600 28.6 802

2.0 (1.0) 1.5 (1.7) (0.7)

This was done to take into account the surfactant influence on the protein adsorption activity; this fact is discussed below. In the calculations for a plane interface (r = 50 mm), the same values of the diffusion coefficient were assumed. The results are shown in Figure 1 by thin dashed lines; the curves are also shifted toward the longer time range. At the C12DMPO addition concentration of 10−2 mmol/L, the time necessary to attain the equilibrium is by a factor of about 30 longer than that for the bubble. These results support the applicability of the present method which is based on a bubble formed in a large volume of the studied solution, which was used also in ref 12, and indicate the reliability of the results in what regards the adsorption equilibrium. Figure 2 shows the dynamic surface tension curves of the individual BCS solution at a bulk concentration of 10−5 mmol/ L (curves 1 and 1* were obtained for two different samples) and seven mixed solutions at different C14DMPO concentrations in the range from 2 × 10−5 to 5 × 10−3 mmol/L. As can be seen, even at very low C14DMPO concentrations, the dynamic and equilibrium surface tensions of the mixtures are lower (note the experimental error is less than 0.5 mN/m) than those of the individual protein solution. Now we consider the equilibrium surface tension of mixtures and compare them with the calculations according to the given

Figure 2. Dynamic surface tension of 10−5 mmol/L BCS solutions at different concentrations of added C14DMPO listed in the figure. 12815

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Table 3. Parameters of eq 13 for the Protein/Surfactant Mixtures

Figure 3. Equilibrium surface tension isotherms for BCS+C12DMPO (solid red square) taken from ref 12 and BCS+C14DMPO (solid blue square) mixtures at BCS bulk concentration 10−5 mmol/L; (open red square) and (open blue square) are the data for individual C12DMPO taken from ref 12 and C14DMPO solutions measured using the buoyant bubble method; the equilibrium surface tension of individual 10−5 mmol/L BSC solution is shown by dotted horizontal line. The results of theoretical calculations are shown by red (C12DMPO systems) and blue (C14DMPO systems) lines. Thin solid lines, individual surfactants, calculations using Frumkin’s model; thin dashed lines, calculations using eq 8 with parameters listed in Tables 1 and 2; bold solid lines, calculations using eq 13 with parameters listed in Tables 1−3.

protein+surfactant

a* (×104 L/mmol)

cm (×10−4 mmol/L)

k = 1 + a*cm

BCS+C12DMPO BCS+C14DMPO BLG+C12DMPO BLG+C10OH BLG+C10EO5

0.56 1.7 0.3 0.2 0.2

1.25 1.0 1.85 1.5 2.5

1.7 2.7 1.55 1.3 1.5

Figure 4. Equilibrium surface tension isotherms for BLG+C12DMPO mixtures at BLG bulk concentrations 10−5 mmol/L (solid red square) taken from ref 12 (open red square); the data for individual C12DMPO solutions are taken from ref 12; the equilibrium surface tension of individual 10−5 mmol/L BLG solution is shown by dotted horizontal line. Thin solid line, individual surfactant, calculations using Frumkin’s model; thin dashed line, calculations using eq 8 with parameters listed in Tables 1 and 2; bold solid line, calculations using eq 13 with parameters listed in Tables 1−3.

the experimental results for C12DMPO were reproduced from ref 12 and are very close to those published in previous studies based on measurements with the ring18 and drop profile tensiometry.19 For the individual C14DMPO, the experimental surface tension values are by several mN/m lower than those reported in these publications, because here the buoyant bubble method was used which totally prevents any surfactant losses due to its adsorption. The calculated surface tension isotherms for BCS/C12DMPO and BCS/C14DMPO mixtures at a fixed BCS concentration of 10−5 mmol/L using the model12 with eq 8 and the parameters listed in Table 1 for BCS and Table 2 for the surfactants are shown in Figure 3 by dashed red and blue lines, respectively. For these mixtures, the data calculated by the model with eq 8 are inconsistent with the experimental data: the theoretical values exceed essentially the experimental ones. Therefore, instead of using eq 8 to describe the adsorption of the protein, eq 13 was used where the corrected adsorption equilibrium constant b̃P,1 was introduced. The calculated results are shown in Figure 3 by thick solid red and blue lines, respectively. The values of a*, the limiting concentration cm, and the coefficient k ̃ value at the = 1 + a*cm which governs the increase of the bP,1 concentration cm and above are listed in Table 3. Similarly to mixed BCS solutions, the measurements and calculations were performed for BLG solutions with a protein concentration of 10−5 mmol/L. The experimental values of equilibrium surface tension for the BLG/C12DMPO, BLG/ C10OH, and BLG/C10EO5 systems are shown in Figures 4−6, respectively, by filled symbols. Also shown in these figures are the isotherms for the individual surfactant solutions measured

by the buoyant bubble method (open symbols), and the surface tension of individual 10−5 mmol/L BLG solution (horizontal dotted line). The results for the individual C10OH solutions are sufficiently close to the values reported in refs 20 and 21, while the data for the C10EO5 solutions are virtually coincident with those obtained in ref 22, also using the buoyant bubble method. Some differences in surface tension of C10OH solutions from the values reported in refs 20 and 21 could be ascribed to the fact that in these publications the drop shape method was used. It is known that the adsorption at the surface of a drop results in a depletion of the solution in the drop bulk, while for bubble in a large solution volume the losses of surfactant caused by adsorption are negligibly small.23 The surface tension isotherms for mixtures calculated with eq 8 are shown by thin dotted curves. For all the systems studied, the theoretical results at very low surfactant concentrations are higher than the experimental values. If eq 13 is used for the calculations, which implements the correction of the BLG adsorption equilibrium constant (thin solid curves), the agreement with the experimental data becomes much better. The values of ̃ are parameters in eq 13 involved in the corrected constant bP,1 listed in Table 3. By comparing the k values for various systems, one can see that the highest values of this coefficient were 12816

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2.7. For the BLG solutions, the corrected adsorption equilibrium constant also becomes higher than the bP,1 value, while this increase is not so large: for mixtures of BLG and BCS with C12DMPO the k values are 1.55 and 1.7, respectively, while for the BLG mixtures with C10OH and C10EO5 these values are even smaller, 1.3 and 1.5, respectively. Nevertheless, it is seen that the increase of the “effective” adsorption equilibrium constant for the BCS and BLG solutions occurs when small amounts of surfactants are added. This variation of the “effective” adsorption equilibrium constant on the surfactant concentration could probably depend both on the structure of the protein and on the kind of surfactant, and is governed by the interaction between the polar groups of the surfactant molecules with the polar groups of the amino acids involved in the protein structure. This interaction results in the realignment of the intermolecular interactions between individual polar groups and in the formation of intergroup molecular bonds of different nature. The van der Waals interaction between the phosphor atoms involved in the polar groups of CnDMPO and the oxygen or hydrogen atoms involved in the polar groups of protein amino acids is possible. The hydrogen atoms involved in the polar groups of C10OH and C10EO5 can also bind with the oxygen atoms involved in the polar groups of protein amino acids. It should be noted that the energy of interatomic attraction, defined by the attractive (negative) term of the van der Waals equation, for the P−O or P−H bonds is approximately 2 times higher than that for the H−O bond.24 Also the structure of the protein molecule and the size of the polar headgroup of the surfactant molecule should be taken into account. Of all the surfactants studied here, the weakest intermolecular interaction is possibly that of the C10OH, while the relatively small effect observed for the proteins mixtures with C10EO5 could probably be explained by the large size of its polar headgroup. It should be noted that the studies of the BCS solutions with the additions of C10EO5 and C12EO5 have shown an insignificant decrease of the surface tension at surfactants concentrations within the range of 10−5−10−3 mmol/L. This could also be related to the size of the polar group in these molecules. Among all the surfactants studied, the polar group of the CnDMPO molecule possesses the best possible properties for the binding, due to its compact shape and the presence of phosphor. For a detailed elucidation of the nature of interactions, the influence of the type of polar group and the protein structure, additional studies are necessary, which should involve quantum chemical calculations. It was shown that the dilational viscoelasticity is most sensitive to the composition of mixed adsorption layers and can reflect best the interactions between the components adsorbed at a liquid interface.25 Therefore, ongoing work is dedicated to the dilation rheology of mixed protein/surfactant systems at the same very low concentrations as studied here.

Figure 5. Equilibrium surface tension isotherms for BLG+C10OH mixtures at BLG bulk concentrations 10−5 mmol/L (solid green square); (open green square) the data for pure C10OH solutions measured using the buoyant bubble method; (open green circle) the data are taken from refs 20 and 21; the equilibrium surface tension of individual 10−5 mmol/L BLG solution is shown by dotted horizontal line. Thin solid line, individual surfactant, calculations using Frumkin’s model; thin dashed line, calculations using eq 8 with parameters listed in Tables 1 and 2; bold solid line, calculations using eq 13 with parameters listed in Tables 1−3.

Figure 6. Equilibrium surface tension isotherms for BLG+C10EO5 mixtures at BLG bulk concentrations 10−5 mmol/L (solid green square); (open green square) the data for pure C10EO5 solutions measured by using the buoyant bubble method; (open green circle) the data from ref 22; the equilibrium surface tension of individual 10−5 mmol/L BLG solution is shown by dotted horizontal line. Thin solid line, individual surfactant, calculations using Frumkin’s model; thin dashed line, calculations using eq 8 with parameters listed in Tables 1 and 2; bold solid line, calculations using eq 13 with parameters listed in Tables 1−3.

5. CONCLUSIONS The influence of the addition of the nonionic surfactant C12DMPO, C14DMPO, C10OH, and C10EO5 at concentrations from 10−5 to 10−1 mmol/L to BCS and BLG solutions at a fixed concentration of 10−5 mmol/L on the surface tension is studied. It is shown that a significant change (3−7 mN/m) of the surface tension at the water/air interface occurs at very low surfactant concentration (10−5−10−3 mmol/L) for all studied surfactants. All measurements were performed with the buoyant bubble profile method, where the bubbles are formed in a large volume of the studied solution. The kinetic adsorption curves

obtained by fitting the data for BCS solutions with the addition of C12DMPO and, especially, C14DMPO for which the ̃ exceeds the bP,1 value by a factor of corrected constant bP,1 12817

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from individual BSC solutions, and from protein/C12DMPO mixed solutions at the bubble surface are calculated using the Fick and Ward−Tordai equations. The calculation results agree well with the experimental data, indicating that the equilibration times in the system studied do not exceed 30 000 s. At the same time, the values calculated for the adsorption on a plane surface with the same diffusion coefficient show that the adsorption process is significantly slower, and the time required to attain the equilibrium is by one order of magnitude higher than that for the adsorption at the bubble surface. Calculations of the equilibrium surface tension with an earlier derived theoretical model for protein/surfactant mixtures do not propose any reduction of surface tension at the very low studied surfactant concentrations. Therefore, to achieve agreement between theory and experiment, the supposition was made about the influence of the concentration of nonionic surfactant on the adsorption activity of the protein. The adsorption isotherm equation of the protein was modified accordingly: a correction was introduced which assumes the increase of the equilibrium adsorption activity of protein proportionally to the surfactant concentration in the solution. This effect is probably caused by the interaction between the polar groups of the nonionic surfactant with the polar groups of amino acids involved in the protein structure, which results in an increase of the hydrophobicity and adsorption activity of the protein. The values calculated using the proposed modified model agree well with all the experimental data, and provides correction coefficients of the protein adsorption equilibrium constant. The largest correction of this constant (by a factor of 2.7) was found for the BCS+C14DMPO mixtures, and the smallest one (by a factor of 1.3) for the BLG+C10OH mixtures.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 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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dx.doi.org/10.1021/la502964y | Langmuir 2014, 30, 12812−12818