air interface at different pH values

Colloids and Surfaces A: Physicochem. Eng. Aspects 404 (2012) 17–24

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Surface dilatational behavior of ␤-casein at the solution/air interface at different pH values R. Wüstneck a , V.B. Fainerman b , E.V. Aksenenko c , Cs. Kotsmar d , V. Pradines e , J. Krägel a , R. Miller a,∗ a

Max Planck Institute of Colloids and Interfaces, 14424 Potsdam/Golm, Germany Donetsk Medical University, 83003 Donetsk, Ukraine Institute of Colloid Chemistry and Chemistry of Water, 03680 Kiev, Ukraine d University of California at Berkeley, Berkeley, CA 94720-1462, USA e Laboratoire de Chimie de Coordination, 31077 Toulouse cedex 04, France b c

a r t i c l e

i n f o

Article history: Received 20 December 2011 Received in revised form 29 February 2012 Accepted 13 March 2012 Available online 31 March 2012 Keywords: ␤-Casein Dynamic surface visco-elasticity Solution–air interface pH effects Oscillating bubble tensiometry

a b s t r a c t The surface tension and dilatational visco-elasticity isotherms for ␤-casein determined at pH 7 and 9 are essentially the same, but differ remarkably from those measured at the isoelectric point (i.e.p.) of the protein at pH 5. A recently developed thermodynamic model is applied to the experimental data, which were not only obtained at equilibrium, but also under quasi-equilibrium conditions. It turned out that such a model can be adequately applied to data obtained not too far from the equilibrium state of a protein adsorption layer. The change in the model parameters allows to understand slow changes in the structure of the adsorption layer. Even at pH 5, where ␤-casein is most hydrophobic and in its most compact conformation, the data point to the fact that conformational changes may happen at the interface upon adsorption. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Modeling of the adsorption behavior in thermodynamic equilibrium is a great challenge. This is an even more complex task when the model has to agree at the same time with the equation of state and the visco-elastic properties of the surface layer. Nevertheless, such a thermodynamic approach was presented for example by Kotsmar et al. [1] for mixtures of surfactants and proteins. Some proteins, however, are not easily included into the model. For instance ␤-casein (␤CS) with its flexible molecular structure provides many possibilities of interfacial conformations due to the large variety of inter- and intramolecular interactions. ␤CS is one of the two main protein fractions of mammalian milk and, along with ␣-casein, accounts for ∼35% of the casein fraction. ␤CS has a molecular weight of ∼24 kDa and an unusual primary structure with a high density of charged amino acids and five phosphorylated serine residues at the N-terminal side of the molecule. Its isoelectric point (i.e.p.) is between 4.9 and 5.2 [2], and therefore in milk (pH ∼ 6.6) it is negatively charged. ␤CS contains relatively hydrophobic molecular parts, which consist of a high number of not interacting proline peptides, and it does not contain disulfide

∗ Corresponding author. Tel.: +49 331 5679252; fax: +49 331 5679202. E-mail address: [email protected] (R. Miller). 0927-7757/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.colsurfa.2012.03.050

bridges. As a result, compared with typical globular proteins, ␤CS is classified as an intrinsically unstructured (random coil) protein [3] with no characteristic denaturation temperature, although the various conformational states of ␤CS are less chaotic and random-like than widely believed. Several studies at neutral pH suggest that it has a relatively high residual secondary structure [4–7]. Being adsorbed the N-terminal hydrophilic residues are extended into the aqueous solution phase, whereas the C-terminal hydrophobic parts of the molecule are strongly attached to the surface and are less flexible anchored in the interfacial layers. Therefore BCS adsorption layers where frequently described by a two-layer model consisting of a densely packed protein-rich inner layer and a diluted outer layer (4–5 nm) [8]. The present work will focus on the improvement of the thermodynamic adsorption model in order to cover also this important protein. Another aspect is to include also dynamic properties into the considerations, because these properties are of large practical interest in food processing. We will demonstrate, however, that presently there is not really a consistent theory to describe such properties. Therefore the second focus of this work will be the discussion of experimental data for a possible further theoretically improvement. Such data will allow defining the aspects to be taken into consideration in such a model refinement. Data will be presented for 3 different pH-values of the BCS solutions for which no systematic literature data exist.

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2. Theory We use the most recent state of the art models for the description of the adsorption layer properties of BCS at pH 5, 7 and 9, including the surface tension as well as the dilatational elasticity as functions of the protein bulk concentration.

P ≈ 

2.1. Equilibrium adsorption layer of protein solutions

˘ω0 = ln(1 − ) + (1 − ω0 /ω) + a 2 , RT

(1)

The following symbols are used here: ˘ is the surface pressure, R is the gas law constant, T is the temperature, a is the intermolecular interaction parameter, ω0 is the molar area of the solvent and the area occupied by one segment of the protein molecule (the area n increment),  =  is the total adsorption of proteins in all n i=1 i

n

ω  is the total surface coverage states (1 ≤ i ≤ n),  = ω = i=1 i i by protein molecules, ω is the average molar area of the adsorbed protein, and ωi = ω1 + (i − 1)ω0 is the molar area in state i, assuming ω1 = ωmin , ωmax = ω1 + (n − 1)ω0 . In Refs. [9,10] it was assumed that the surface activity of the reorientable surfactant molecules increases with increasing molar area ωj , according to a power law with the constant exponent ˛. It was also assumed that ˛ = 0 for protein solutions, which leads to a coexistence of adsorption states with different molecular areas. In the present case, we assume ˛ > 0, which promotes the adsorption in states with larger areas. The adsorption isotherms for each adsorbed state (j) of the protein are:

bj c =



ωj ˛

(ωj /ω1 ) (1 − )

ωj /ω

exp −2a

ω   j

ω

 .

(2)

Here c is the protein bulk concentration and bj are the equilibrium adsorption constants for the protein in the jth state. When all bj are identical for any j, the adsorption constant for the protein molecule as a whole is bj = nbj = b, which leads to the following distribution function of adsorptions over all states of the protein molecules [9,10]: ˛

j = 

(ωj /ω1 ) (1 − )

n

˛

(ωj −ω1 )/ω

(ωj /ω1 ) (1 − ) i=1

exp[2a((ωj − ω1 )/ω)]

(ωi −ω1 )/ω

exp[2a((ωi − ω1 )/ω)]

m  i−1  b2 c i=1

The properties of protein adsorption layers at the solution/air or solution/oil interface are rather different from those of lowmolecular weight surfactants. A review [9] summarized the various theoretical models for the adsorption behavior of proteins, derived via statistical, scaling and thermodynamic approaches. Taking into account first-order non-ideality corrections for both enthalpy and entropy, the equations of state and adsorption isotherm for protein solutions can be formulated in terms of fractions of the surface area coverage, as it was presented in [9,10]. Assuming that protein molecules can absorb in n states of different molar area, varying between a maximum ωmax and a minimum area ωmin , the following equation of state was obtained [1]: −

includes the assumption that the formation of the second and any subsequent layer affects the surface pressure not significantly [9]. On the basis of a Langmuir type isotherm for multiple (m) adsorption layers, a rough approximation for the total adsorption  P in the first, second and subsequent layers can be obtained:

. (3)

Eqs. (1)–(3) describe the evolution of the protein adsorption states with increasing total adsorption, which reflects in many details known experimental results [9,10]. The model proposes that with increasing total adsorption, the number of adsorbed protein molecules occupying larger areas progressively decreases at the expense of those requiring smaller areas at the interface. With increasing protein concentration, for many proteins the formation of bilayers (or multilayers) at liquid interfaces is observed. The isotherm equation for such a multilayer adsorption can be derived by assuming that the coverage of the second and subsequent layers is proportional to the adsorption equilibrium constant b2 , and also to the coverage of the previous layers. This

1 + b2 c

.

(4)

Eq. (4) shows that the adsorption in the first layer is assumed to be identical to that given by Eqs. (1)–(3). This approximation is of course rather crude, as it ignores both the non-ideality of enthalpy and entropy of the mixed surface layer. However, the adsorption parameter b2 in Eq. (4) takes these effects approximately into account. In many experiments it was shown that above a certain protein concentration, c*, the surface tension only slightly increases, while the adsorption often exhibits a strong increase. To such a critical bulk concentration, critical values of adsorption  * and surface pressure ˘* refer. This was explained in [11,12] by a condensation (aggregation) of the protein molecules in the surface layer or by the formation of a secondary layer adjacent to the surface. Both effects change the average molar area of adsorbed molecules. The equations of state and adsorption isotherm for such surface layers were discussed in [9]. Here, in contrast to [9], we assume that in the postcritical range  P >  *, monomers and aggregates are independent kinetic units. Hence, the following approximation for the surface pressure can be used (na is the aggregation number):



˘ = ˘∗ 1 +

1 P −  ∗ na ∗



.

(5)

One can see from Eq. (5), which is similar to what was proposed for micellar solutions [13], that the increase in surface pressure in the post-critical concentration range is proportional to the increase in protein adsorption, with a proportionality factor equal to the inverse aggregation number, i.e. the surface pressure increase is proportional to the adsorption of kinetic entities (monomers and aggregates). For na = 1, i.e. in absence of any aggregate formation, the model almost coincide with Eq. (1) (see also Ref. [13]). With increasing na the changes in surface pressure calculated from Eq. (5) become progressively less significant. 2.2. Surface dilatational rheology of adsorbed layers The surface dilatational modulus is defined by an expression originally proposed by Gibbs as the increase in surface tension  for a small increase in surface area A: E=

d . d ln A

(6)

The expressions for the dilatational modulus of adsorbed layers of a single surfactant or protein assuming a diffusion controlled exchange of matter mechanism and harmonic oscillations of the surface area, including a finite curvature of the interface, were derived by Joos [14]. In particular, for the adsorption of a protein from solution at the surface of a bubble we have:



E = E0 1 − i

D dc (1 + r) ˝r d

−1

,

(7)

where E0 =

d˘ , d ln 

(8)

is the surface dilatational elasticity. Here D is the diffusion coefficient of the protein in the solution, ˝ = 2f is the angular frequency of the surface oscillations, 2 = i˝/D, and r is the radius of the bubble. For a plane interface (r → ∞) Eq. (7) becomes equal to the

R. Wüstneck et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 404 (2012) 17–24

expression derived by Lucassen and van den Tempel [15,16]. For low oscillation frequencies f (below 0.1 Hz) and values for r close to those used in this study, Eq. (7) yields a slight decrease of the modulus and increase of the phase angle for bubbles as compared with a flat surface. The surface dilatational modulus can be presented as a complex quantity: E = Er + iEi

(9)

which can be split into the visco-elasticity modulus |E| and the phase angle between stress (d) and strain (dA):

|E| =

Er2 + Ei2 ,

= arctan

E  i

Er

.

(10)

All these expressions apply for protein solutions below the critical point. The protein adsorption layer above the critical point should be regarded to as a composite surface [17], for the limiting elasticity E0 is given by: E0 = E0∗

P ∗

(11)

The superscript * refers to the values in the critical point, and  P is the total adsorption (monolayer and multilayer) above the critical point. In this range the formation of a second and subsequent layers are discussed, the presence of which increases the elasticity of the entire interfacial layer.

3. Experimental details 3.1. Materials The ␤CS from bovine milk (minimum 90% pure) was purchased from Sigma–Aldrich Chemical Co. (Germany) and used without further purification. The necessary ␤CS concentration was adjusted by diluting a stock solution with buffer 30 min before starting the measurements. Ultrapure MilliQ water with a resistivity of 18.2 M cm was used for the preparation of all solutions. A Na2 HPO4 –NaH2 PO4 buffer (Fluka, assay ∼99%) of pH 7 with a surface tension of 72.2 mN/m at 22 ◦ C was used to prepare the ␤CS solutions by mixing appropriate stock solutions (0.01 mol/l of Na2 HPO4 (Lot# 001442217) and NaH2 PO4 (Lot# BC885121). The preparation of solutions at pH 5 only Na2 HPO4 was used and titrated with NaOH. Similarly, the solutions at pH 9 were prepared by titrating NaH2 PO4 with HCl. To follow the kinetics of interfacial structure formation the drop and bubble profile tensiometer PAT-1 (SINTERFACE Technologies, Berlin) was programmed in a way that after an initial period of rather fast dynamic interfacial tension changes some series of harmonic drop volume oscillations were generated at frequencies of 0.01, 0.02, 0.04, 0.1, and 0.2 Hz, and the resulting interfacial area and tension oscillations recorded. Previously it was proven that at these frequencies and sufficiently small amplitudes of area deformation guaranteed a linear response [18]. Some minutes of rest were left between the different series of oscillations. The surface dilation visco-elasticity, i.e. the real part Er and imaginary part Ei were determined from the amplitudes of the surface area and surface tension oscillations, and from the phase shift between area and tension changes, respectively. The imaginary part is a measure of the dilatational viscosity,  = Ei × f, with f being the frequency of oscillation. All measurements were carried out at 22 ◦ C over a time interval of 20 h.

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3.2. Bubble profile analysis tensiometry The pendant drop and buoyant bubble profile tensiometry is a routine method to record dynamic interfacial tensions over time. Most devices are equipped with a computer driven dosing system in order to realize harmonic oscillations of the drop area to determine the interfacial dilatational visco-elasticity. For slow adsorption processes it is reasonable to combine both techniques, i.e. to interrupt the recording of the dynamic interfacial tension changes and to superimpose some drop area oscillation experiments. The dilatational rheology parameters obtained from such experiments are related then to an average time characteristic for the interval during which the oscillations were performed. This experimental protocol was first proposed by Noskov et al. [18] to determine the dynamic visco-elasticity of ␤CS layers by using capillary wave spectroscopy. Typical studies of the visco-elasticity of interfacial layers are performed in such a way that first the adsorption equilibrium is established and only thereafter harmonic oscillations of the drop or bubble surface area are generated to gain the dilatational rheological parameters [18,19]. A shortcoming of this procedure is that no information is obtained during the long period of formation of the adsorption layer. In the present work experiments were performed such that the dynamic interfacial tension was followed over a long period time whereas the drop/bubble area was subjected to harmonically oscillations at different adsorption times interrupting the monitoring of the adsorption process. Fig. 1 shows the dependence of the dynamic surface tension of a typical experiment chosen to determine interfacial rheological parameters under dynamic conditions. There is an initial strong decrease of  within the first seconds after creating a fresh air bubble surface. The measurements of (t) were then repeatedly interrupted by some cycles of interfacial area oscillation at five different frequencies. In Fig. 1 the superposition of two experiments are shown. One experiment is a usual measurement of the dynamic surface tension decrease, and the other represents the dynamic surface tensions interrupted by repeatedly generated drop area oscillations. Both curves agree very well so that we can conclude

Fig. 1. Dynamic surface tension of a 5 × 10−7 mol/l ␤CS solution at pH 5 at the air/solution interface, green symbols ( ) – surface tensions obtained at A = const., ) – measurements with repeated intermediate drop area oscillared symbols ( tions, the zoom shows one cycle of oscillation consisting of 5 frequencies, the mean drop area was 25.28 ± 0.02 mm2 , the amplitude 1.95 ± 0.06 mm2 .

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that the adsorption process is not affected by the intermediate drop oscillations. During the initial period of about 10,000 s, the resulting surface tension oscillations showed a significant trend down at each frequency and, therefore, the visco-elasticity was not determined via Fourier analysis. 3.3. Data acquisition and experimental protocols The acquisition of equilibrium interfacial tensions is a long lasting problem which requires special experimental tools, because at low bulk concentrations proteins adsorb very slowly. One way to overcome this problem is to increase of the experimental time, which however is limited by the biological nature of the protein. The extension of measurements to several hours [20], or as reported by Hunter et al. to more than 48 h [21] seems feasible. In our studies the experimental time was up to 20 h, which was obviously insufficient at low protein concentrations so√that equilibrium data were obtained by extrapolation via the (1/ t) plot [22]. An additional problem is the use of the drop profile method for very diluted solutions due to the depletion of proteins during adsorption. The protocol with bubbles formed in a cuvette containing the solution shows much smaller depletion effects [23]. Therefore, in the present work we used air bubbles formed at the tip of a U-shaped capillary immersed into the cell filled with the protein solution. A solution volume of about 20 ml was found to be sufficient to exclude depletion effects at the bubble surface. The influence of pH and ionic strength on the interfacial behavior of ␤CS has been addressed in some publications, however, without any systematic plan [24–28]. Therefore, in the present work we present adsorption data of ␤CS at three pH values: 9, 7, and 5. Using the protocol shown in Fig. 1 (red symbols) the following data were obtained: • Equilibrium adsorption isotherms from dynamic interfacial tensions after 20 h at different ␤CS concentrations (c) and three different pHs. • Dependencies of the real and imaginary part of the elastic dilatational modulus (Er and Ei ) for different c, f, pH, measured at different adsorption times t. • Dependencies of Er and Ei on the film pressure (˘, with ˘ =  0 − ,  0 is the interfacial tension of the pure solvent) for different f, pH, and t, while the corresponding values for ˘ were calculated from the experimental surface tensions determined after each oscillation cycle.

The experiments show that the critical pressure ˘* does not vary much with adsorption time, i.e. remains constant in the range of experimental error. Thus, we can conclude that the conformation of the protein in its most compact form is given by ω1 . This means, that ω1 does not depend on the age of the adsorption layer. This fact is very important as the parameters b and ω1 depend indirectly on each other. Any shift with respect to the protein concentration must therefore be accounted for only by adapting the value of b. Furthermore it was assumed that a and ˛ are not changed under the conditions of the experiment, because the shapes of the isotherms are very similar. Only in the range of very low adsorption times there are rather strong changes. The adjustment of the remaining model parameters which govern the slope of the isotherm in the post-critical range is rather trivial. We mentioned above that the theoretical model should not reflect only the (quasi-)equilibrium surface state, but at the same time the visco-elastic properties of the surface layer. Even when for these properties only a qualitative agreement can be expected, the position of the maximum of Er in the pre-critical concentration range and the deepness and position of the subsequent minimum can be easily adjusted. Usually this goes on the account of a worsening of the approximation of the ˘(c) isotherm. This means that from the many independent model parameters the majority, if not all, are fixed by their effect on the dependencies ˘(c) and E(c), i.e. by their definite physical meaning. 4. Results and discussion 4.1. Thermodynamic equilibrium isotherms of ˇCS at different pH In Fig. 2 the measured equilibrium surface pressure isotherms ˘(c) are shown for ␤CS at different pH values. Remarkable is the shift of the isotherm at pH 5 to higher concentrations, which indicates the lower adsorption activity of ␤CS as compared to pH 7 and pH 9, where the isotherms nearly coincide. The lines are the isotherms calculated by using the parameter set given in Table 1 for 72,550 s. The agreement between the experimental and calculated isotherms is quite good, and the post-critical range is correctly included into the model isotherms. The Frumkin parameter, a, reflexes the hydrophobic interaction between adsorbed molecules. Its value should be largest at the i.e.p. Thus, ω1 at pH 5 can be chosen smaller in comparison to pH 7

3.4. Parameter selection and strategy of approximation by using a thermodynamic approach The selection of meaningful parameters is of central importance in such a complex model as we are using here. Information about the minimum and maximum area per molecule at the interface can be usually found in literature, however, values at different pH are scarce. Here specific knowledge is needed about the behavior of the protein at different pH, i.e. the ␤CS molecule becomes more compact in the vicinity of the i.e.p. Therefore, at pH 5 the values for both limiting areas per molecule ω1 and ωm should be smaller than those at pH 7 or pH 9. As mentioned above, there is no theoretical model for surface layers under dynamic conditions. However, it seems adequate to use equilibrium models for adsorption layer when they are in a quasi-equilibrium state. In the presented experiments the dilational rheology data are acquired during the adsorption process, providing a rough idea about the dynamics of the adsorption layer formation. When assuming a quasi-equilibrium state for the time range between 15,550 and 72,550 s, at a certain time moment also a quasi-equilibrium adsorption isotherm can be constructed.

Fig. 2. Adsorption isotherms of ␤CS in phosphate buffer at pH 5 ( ), pH 7 ( ), and pH 9 ( ), symbols – experimental values, lines – calculated from Eqs. (1)–(4) for data below, and from Eq. (5) for data above the kink point, the parameter values were taken from Table 1.

R. Wüstneck et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 404 (2012) 17–24 Table 1 Variation of the model parameters for the thermodynamic equilibrium on pH, and surface age; the best fit values were calculated from Eqs. (1)–(4) for data below the kink point, and from Eq. (5) for data above the kink point. t (s) pH 5 a ˛ ω0 (105 m2 /mol) ω1 (106 m2 /mol) ωm (107 m2 /mol) na ˘* (mN/m) b2 (103 m3 /mol) b = n × bj (104 m3 /mol) m pH 7 a ˛ ω0 (105 m2 /mol) ω1 (106 m2 /mol) ωm (107 m2 /mol) na ˘* (mN/m) b2 (103 m3 /mol) b = n × bj (104 m3 /mol) m pH 9 a ˛ ω0 (105 m2 /mol) ω1 (106 m2 /mol) ωm (107 m2 /mol) na ˘* (mN/m) b2 (103 m3 /mol) b = n × bj (104 m3 /mol) m

15,550

25,550

35,550

45,550

72,550

1.3 0.5 2 4.4 1.3 5 21.0 1.00 4.4 2

1.3 0.5 2 4.4 1.3 12 23.5 1.20 5.28 3

1.3 0.5 2 4.4 1.3 10 24.0 1.1 4.62 3

1.3 0.5 2 4.4 1.3 10 23.5 1.20 5.14 3

1.3 0.5 2 4.4 1.3 20 23.5 1.30 5.46 3

1.1 0.6 2.2 4.8 3.7 10 22.0 8.0 3.2 1

1.1 0.6 2.2 4.8 3.7 10 21.5 7.2 9.6 2

1.1 0.6 2.2 4.8 3.7 10 22.0 6.0 4.0 2

1.1 0.6 2.2 4.8 3.7 10 22.0 3.5 5.1 3

1.1 0.6 2.2 4.8 3.7 30 22.5 6.0 12.2 3

1.00 0.75 2.2 5.0 4.00 20 19.0 8.0 11.70 1

1.00 0.75 2.2 5.0 4.0 20 21.8 7.20 11.52 2

1.00 0.75 2.2 5.0 4.0 10 20.0 7.40 11.84 2

1.00 0.75 2.2 5.0 4.0 30 20.0 12.00 11.50 2

1.00 0.75 2.2 5.0 4.0 40 22.5 10.00 16.00 3

and pH 9 as the molecules are more compact at the i.e.p. Consequently ωm at pH 7 and pH 9 becomes higher. It is the highest at pH 9 because the molecules become more stretched with increasing molecular charge. With these assumptions the best approximation of the experimental data by the theory is obtained. There are big differences in the adsorption constants b between the isotherm at pH 5 in comparison to the other isotherms. Also the increasing tendency to aggregate and multilayers, with na and m in

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the post-critical concentration range, are easily visible for pH 7 and pH 9. Fig. 3a–c shows the dependencies of the real Er and imaginary part Ei of the visco-elasticity modulus E. The imaginary part is relatively small in comparison to the real part. Therefore the surface dilatational rheological behavior of the ␤CS films is essentially elastic, independent of the pH. Only in the post-critical region the imaginary parts start to increase. A quantitative discussion of Ei is therefore irrelevant and only trends can be given. In this respect, the data measured here are in quite good agreement with the predictions by the model, i.e. are very small and more or less in the range of the sensitivity of the instrument. The surface rheological characteristics are qualitatively well described, but there are pronounced discrepancies between the experimental and the model curves. The weak frequency dependences of the modules are correctly reflected. The maxima in the pre-critical range do not agree in their position. Also the deepness of the following minima is not perfectly reflected. In [18] two maxima of the modulus were reported, whereas the second is only very shallow. The reason for this discrepancy may be that either we did not trace the necessary concentration range in small enough steps, or that the scattering of the experimental results was too large to detect such a weakly pronounced second maximum. The increase of the modules in the post-critical range is correctly reflected. The values of the imaginary modules are close to those obtained for the highest frequency, 0.2 Hz. Here the model fails and we can conclude that the surface dilatational rheology is not correctly described by our present thermodynamic approach and a refinement is required. 4.2. Dynamic surface tension and dynamic modules of ˇCS In Fig. 4 the dynamic surface tension, and the real and imaginary parts of the visco-elasticity are shown in dependence on time for different ␤CS concentrations. This figure is constructed from data for pH 5 and pH 7. Data for pH 9 (data not shown) are very similar to those for pH 7. The dynamic surface tension at low concentrations slowly decreases and obviously equilibrium is not reached within 20 h, while for higher concentrations a stationary plateau of (t) is observed. At highest concentrations the dynamic surface tension

Fig. 3. Real and imaginary parts of the surface visco-elasticity in dependence of frequency, 0.01, 0.02, 0.04, 0.1, and 0.2 Hz, symbols – experimental valued after 72,550 s adsorption time, curves calculated dependencies by using the parameter values given in Table 1 and a diffusion coefficient of D = 10−10 m2 /s; red curves for 0.01 Hz, and green curves for 0.2 Hz; solid lines – below the critical point (calculated from Eqs. (6)–(9)), dotted lines – above the critical point (calculated from Eq. (11)).

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Fig. 4. Dynamic surface tension , and the real and imaginary part of the modulus Er and Ei for ␤CS solutions at pH 5 and pH 7. pH 7: and

3 × 10−7 mol/l. pH 5:

10−8 ,

4 × 10−8 ,

5 × 10−8 ,

4 × 10−9 ,

2 × 10−8 ,

7 × 10−8 ,

7 × 10−8 , 3 × 10−7 mol/l, symbols – experimental values, lines are only guides for the eye.

decreases rapidly, adopting an equilibrium tension depending on the protein concentration. At the same time the visco-elasticity reveals an interesting behavior. At low concentrations the values are also very small. At higher concentrations (>10−8 at pH 7, and >2 × 10−8 mol/l at pH 5) a maximum in Er occurs. Actually this means that with increasing adsorption time a mechanically stable surface structure is formed, which further is destroyed again, as indicated by a decreased elasticity value. At longer adsorption times and further increase of surface coverage the layer is obviously reorganized. Our explanation is that with the start of the ␤CS adsorption the molecules in the vicinity of the interface enter the surface layer where they undergo conformational changes at low surface coverage, i.e., with a rather large average area per molecule close to the maximum area. These conditions obviously offer the best prerequisite to form mechanically stable structures by intermolecular interaction. With increasing adsorption time further molecules enter the interface thus changing the conditions for structure formation. The new adsorbing molecules cannot easily rearrange at the interfacial. The interaction between the molecules of different conformations however is deteriorated in comparison to those at low concentrations, thus weakening the mechanical stability of the adsorption layer. This explanation is supported by the lower maximum values realized at higher ␤CS concentrations (see pH 5). The maximum becomes smaller and shifted to lower adsorption times. Above a certain protein concentrations no maximum is observed and the elasticities increase and adopt high values when a saturated layer starts to be formed. As this scenario takes also place at pH 5 it means that the most compact ␤CS molecules partly loosen their conformation. The maximum at pH 5 is higher than that found at pH 7, which however needs to be verified by more measurements.

4.3. Dynamic interfacial behavior beyond 2 h adsorption time Analyzing the dynamic behavior of the investigated ␤CS layer we have to realize that the discussed structures were studied close to equilibrium. Therefore, no distinct differences are expected. For faster processes additional methods are required. As we know nothing about changes of the model parameters during the adsorption process we assumed as a first approximation that the parameters a, ˛, ω0 and ωm are constant (see Table 1). Note, the model reveals mainly the tendencies for the respective parameters, such as the interaction a, of aggregate given by na in the pre-critical, and the number of layers m formed in the postcritical range. As the aggregation obviously needs some time the value of na increases slowly in the pre-critical range. This tendency is better expressed in the formation of multilayers after definite adsorption times. Obviously this process is governed by hydrophobic interaction. Therefore 3 layers are formed already at low adsorption times at pH 5 and at pH 9 only close to the equilibrium (see Table 1). Fig. 5 shows adsorption isotherms determined at certain adsorption times. The corresponding model parameters are given in Table 1. All experimental isotherms correspond to a kind of quasiequilibrium and are sufficiently well described by the model independent of the surface age. Fig. 6 shows the analogous graph for the modules measured at a surface age of 25.550 s. This figure stands for all other dependencies obtained at different pH values and in the adsorption time range from 9.550 to 72.550 s. The agreement between experimental and calculated values is qualitative, whereas at low concentrations the model strongly fails. In the post-critical range the experimental points are independent of frequency and hence the model fails in describing the findings at highest concentrations. In conclusion, the

R. Wüstneck et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 404 (2012) 17–24

Fig. 5. Dynamic adsorption isotherms of ␤CS at pH 7 and after an adsorption time 9550, 15,550, 25,550, 35,550, 45,550, and of 72,550 s, symbols – experimental values, curves in the same color – fitted dependencies using the parameters given in Table 1; solid lines – below the critical point (calculated from Eqs. (6)–(9)), dotted lines – above the critical point (calculated from Eq. (11)).

Fig. 6. Er and Ei for an adsorption time of 25.550 s at pH 7 for different protein 0.02, concentrations and frequencies, symbols – experimental values ( 0.01, 0.04, 0.1, 0.2 Hz), red curves – 0.01 Hz, green curves – 0.2 Hz, fitted curves calculated using the parameters given in Table 1; solid lines – below the critical point (Eqs. (6)–(9)), dotted lines – above the critical point (Eqs. (11)), respectively.

results shown here are in good qualitative agreement with those shown in Fig. 4. 5. Conclusions A method to characterize simultaneously the adsorption isotherm and the visco-elastic behavior was tested under equilibrium and dynamic conditions. This method combines two sets of measurements in one by inserting harmonic drop area oscillations during the overall adsorption process. It was shown that these

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oscillations under the given experimental conditions only negligibly influence the establishment of the equilibrium adsorption state. The thermodynamic model for the adsorption and visco-elastic behavior was further improved by including the entropy of mixing in the pre-critical region of adsorption, by accounting for the number of molecules in aggregates formed during the adsorption process, an additional adsorption constant for these aggregates, and the number of layers formed in the post-critical concentration range. By using the Frumkin interaction parameter and the entropy of mixing a wide range of possible shapes of the adsorption isotherms can be adequately described even for flexible protein molecule like ␤CS. Both parts of the adsorption isotherm (precritical and post-critical range) are quantitatively described. In contrast, the visco-elastic behavior is only qualitatively captured. In comparison with the real part of the modulus the imaginary part is small. Therefore the interfacial ␤CS layers behave essentially elastic. The imaginary part starts to rise up only in the range of the transition between pre- and post-critical region, whereas even there the viscous part remain small. The dynamic surface elasticity Er exhibits a maximum in a certain range of protein concentrations. This discloses a behavior which is not reflected by the dynamic surface tension. At low protein surface coverage no maximum can be found and the elasticity of the adsorption layer is small. Starting with a certain concentration a mechanically stable structure at the interface is formed whereas the protein concentration in a definite range of adsorption times provides optimal conditions for intermolecular interaction between molecules at the interface. At longer adsorption times the elasticity and therefore the mechanical strength of the layer decreases, obviously by further adsorbing protein molecules. This can be explained by a further incorporation in the interfacial layer of molecules which cannot take an optimal conformation and interact with earlier adsorbed protein molecules. The condition for an effective interaction deteriorates for all subsequently adsorbed molecules. The adsorption layer looses the rigidity, but creates better conditions (new area) for the adsorption of further molecules. In accordance with the protein concentration the elasticity stays at a low level or increases again when the post-critical range is reached. These processes take place at all pH values investigated, i.e. also in the vicinity of the i.e.p. of ␤CS at pH 5. This means that even molecules in the most compact conformational structure provide better conditions for intermolecular interaction. At higher ␤CS concentrations the maximum is shifted to smaller adsorption times and disappears totally at sufficiently high concentrations. The dynamic behavior was characterized in a wide range of adsorption time, whereas reliable information was provided only at surface pressures in the vicinity of equilibrium. Therefore, this method is suitable to characterize long-time adsorption behavior, for instance long time properties of protein foams. It is inapplicable to investigate processes in the short time region, for instance to follow the mass transfer processes in protein/surfactant foams within the time scale of the adsorption layer formation. Here other methods must help. Acknowledgements The work was financially supported by projects of the DFG (Wü187/12-2 and Mi418/20-1), the European Space Agency (FASES MAP AO-99-052, PASTA), and the German Space Agency (DLR 50WM1129). We kindly thank Sabine Siegmund for performing the experiments. References [1] R. Miller, E.V. Aksenenko, V.S. Alahverdjieva, V.B. Fainerman, Cs. Kotsmar, J. Krägel, M.E. Leser, J. Maldonado-Valderrama, B.A. Noskov, V. Pradines, C.

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