MCT interfaces

Colloids and Surfaces A: Physicochem. Eng. Aspects 413 (2012) 136–141

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Adsorption and shear rheology of ␤-lactoglobulin/SDS mixtures at water/hexane and water/MCT interfaces V. Ulaganathan a,∗ , B. Bergenstahl b , J. Krägel a , R. Miller a a b

MPI of Colloids and Interfaces, D-14476 Potsdam/Golm, Germany Department of Food Technology, Lund University, 22100 Lund, Sweden

a r t i c l e

i n f o

Article history: Received 3 November 2011 Received in revised form 17 February 2012 Accepted 18 February 2012 Available online 25 February 2012 Keywords: Adsorption Shear rheology Water/oil interface Hexane MCT ␤-Lactoglobulin SDS

a b s t r a c t The adsorption and shear rheological behavior is studied of ␤-lactoglobulin (BLG) alone and in mixtures with sodium dodecyl sulphate (SDS) at water/hexane and water/MCT interface. At a low ratio of SDS in the mixture, the adsorbed layer at the interface comprises mostly of protein–surfactant complexes while at a higher SDS/BLG mixing ratio the surfactant dominates at the interface and governs the interfacial properties. The adsorption and shear rheological behavior complement each other and confirm the stepwise replacement of BLG by SDS. The molecular scheme at the two studied interfaces is similar, but the quantitative properties differ due to the differences in the polarity of the oils. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Emulsions find many applications in various industries especially in food and pharmaceutical products. The stability of emulsions depends on various factors and especially on the surface active components which play an important role by adsorbing at the involved interfaces. The amphiphilic substances such as surfactants and proteins adsorb at the large interfacial area of emulsions providing stability against coalescence. In general, the surfactants reduce the interfacial energy and thus make it easier to disperse the oil droplets in the matrix liquid. Ionic surfactants provide in addition electrostatic stabilization against coalescence. The proteins can unfold at the interface and cross-link among themselves forming an adsorption layer of high viscosity even at low bulk concentration. Therefore, the adsorbed proteins provide mechanical stability and also steric repulsion between the dispersed droplets which again prevents coalescence [1,2]. The low molecular weight surfactants adsorb quickly at the interface reducing the interfacial tension, whereas the proteins adsorb slower due to much lower molar bulk concentrations and can additionally unfold at the interface. Mixtures of protein and ionic surfactant can form complexes which could contribute to higher viscosities at the interface while at

∗ Corresponding author. Tel.: +49 331 567 9454; fax: +49 331 567 9202. E-mail address: [email protected] (V. Ulaganathan). 0927-7757/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2012.02.027

higher surfactant concentrations the interfacial viscosity becomes reduced by displacing protein complexes from the interface. This knowledge can be used to achieve emulsions of desired properties [3]. Proteins or polymers in a stationary system diffuse from its aqueous phase, whereas in case of agitated systems it is driven by convection, and adsorb at the interface. The molecular properties of a protein, such as size and shape would determine its diffusion coefficient. Thus, the time required for the interfacial tension to reach equilibrium depends on the nature of protein and its concentration in the aqueous bulk phase [4]. At the interface the protein molecules orient themselves in such a way that the hydrophobic parts are directed towards the nonpolar phase and the hydrophilic parts towards the polar phase (water). In this way it reduces the free energy and thus the interfacial tension. The number of contacts made by the protein at the interface influences the interfacial tension and the surface hydrophobicity of protein is an important feature. The more the protein is spread the more it would cover the interface but not necessarily reduce the interfacial tension as it is the case for heat treated BLG [3,5]. Rheological properties are very important for many applications. Shear rheology is essentially sensitive to structure formation in the interfacial layer. The slow formation of interfacial structures can also be studied with this technique. The number of studies of the shear rheology of layers between two immiscible liquids, in

V. Ulaganathan et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 413 (2012) 136–141

contrast to layers at the water/air surface, is very small and routine measurements are feasible only since recently due to the availability of the required experimental tools [6]. This is the main reason why we present here adsorption and shear rheology data for ␤lactoglobulin (BLG) in absence and presence of different amounts of sodium dodecyl sulphate (SDS) studied at two water/oil interfaces.

2. Materials and methods Mixtures of BLG with the anionic surfactant SDS were chosen to study the dynamics of adsorption layer formation at the water/oil interface with hexane and medium chain triglycerides (MCT) as oil phases. BLG is a globular protein from bovine milk with a molecular weight of 18.4 kDa and isoelectric point of 5.3. SDS has a molecular weight of 288.38 g/mol. Both chemicals were purchased from Sigma–Aldrich. The stock solutions are prepared in 10 mM sodium phosphate buffer, pH 7, prepared by mixing appropriate stock solutions of Na2 HPO4 and NaH2 PO4 with Milli-Q water. 100 ml of 10−6 mol/l BLG was prepared and used as stock solution which is stored for maximum one week in a refrigerator after which it was discarded and a fresh stock is prepared. Hexane was purchased from Aldrich and purified with alumina oxide. The interfacial tension of NaH2 PO4 /Na2 HPO4 buffer was 72.5 and 49.0 mN/m at the water/air and water/hexane interface, respectively. The MCT Delios® V was purchased from Cognis and had an interfacial tension against NaH2 PO4 /Na2 HPO4 buffer of 26.0 mN/m. All experiments were performed at 20 ◦ C and pH 7. All glassware used were flushed with water, dried and then immersed in concentrated sulfuric acid for 2 h, subsequently flushed well with water, rinsed with Milli-Q water and then dried and stored in clean place. The instruments used here are the interfacial shear rheometers MCR 301 and ISR-1 and the drop Profile Analysis Tensiometer PAT-1 for measuring the interfacial tension. The MCR 301 and ISR-1 work with different principles as described briefly below. The working principle of PAT-1 can be found for example in [7].

137

shear stress, T,  and interfacial shear rate is given by the surface co-ordinates of the Boussinesq surface stress tensor which reads: T = [ − ( − )div v ]P + 2D

(1)

where,  is the interfacial tension,  is the interfacial dilational viscosity and  is the interfacial shear viscosity. v is the interfacial velocity vector, div the interfacial divergence operator, D is the surface deformation rate tensor, and P is a projection tensor that transforms every vector into its component tangential to the interface. For the studied liquid–liquid interface the corresponding Boussinesq number, Bo is considered which is the ratio of interfacial drag to the sub-phase drag: Bo =

S bulk R

(2)

Here, R is a characteristic distance of the flow geometry. For Bo  1 the interfacial flow is not coupled to the flow in the sub-phases. In this case, bulk viscosity effects may be neglected and the interface may be considered as an isolated two-dimensional fluid. For very small Boussinesq numbers, Bo  1, the interfacial flow is dominated by the bulk phase stresses. For intermediate values of Bo, bulk phase contributions to the interfacial viscosity are relevant [9]. The contribution of bulk phase must be separated from the total measured quantities by a certain hydrodynamic analysis in the complete measuring cell. Therefore all discussed interfacial rheological (G* calculated from G , G ) data are bulk phase corrected data. 2.2. Damped free oscillations performed by ISR-1 The torsion pendulum technique is mostly preferable in interfacial shear rheology since it allows experiments with very small mechanical deformations of the adsorption layer. The principle is based on an instantaneous movement of the torsion head; the pendulum performs damped oscillations with a damping factor ˛ and a radian frequency factor ˇ: ˛=

Ft + (S /HS ) 2It



(3)

Et + (GS /HS ) − ˛2 It

2.1. Forced oscillations performed by MCR 301

ˇ=

In general, the instrument operates with CSR – controlled shear rate, CSS – controlled shear stress modes, CSD – controlled shear deformation or strain and CSS – controlled shear stress modes which include all the tests like rotational, oscillation, creeps and recovery. These modes influence solely the dynamics of the instrument control. The rheological quantities are therefore calculated from measured torque or angular velocity with respective correction factors.. In our experiments we used direct strain oscillation mode (DSO) for amplitude, time and frequency sweeps. This mode is based on position control of measuring body and the amount of desired deformation is directly induced on to the measuring system. Compared to the other conventional modes the DSO mode is the most suitable for weak interfacial structures since the strain is precisely controlled. This needs a regular check of inertia of device and measuring system and a motor adjustment to have access to reliable measurements for torque values as low as 10 nN m. The measured torque is interpreted as G , which is storage modulus and G , which In our results the complex interfacial shear elasticis loss modulus. 

Et and It are the elasticity of the torsion wire and the moment of inertia of the measuring system, respectively, which represent the main physical parameters of the torsion pendulum itself as well as the friction of the clean solvent interface Ft , and in addition the modulus of interfacial shear elasticity and viscosity GS and ␩S , respectively. The constants Et , It and Ft are determined by calibration measurements. If the values of the constants are known, the shear rheological properties ␩S and GS can be calculated from ␣ and ␤, which are determined by fitting of the measured oscillation curve. Et and It can be measured by performing two experiments with the measuring body in air. A measurement with the pure solvent yields the value of Ft . The geometry parameter HS is obtained from the outer diameter of the measuring body and the inner diameter of the measuring vessel. From the difference of these values compared with those for the oscillations in the pure solvent, the rheological parameters can be obtained. The acting shear stress S is given by

ity, G∗ = G 2 + G 2 is used to have one single parameter for the ease of comparing the results [8]. Not only static interfacial properties such as interfacial tension would influence dynamic processes, but also the type and rate of deformation of the interface. The relationship between interfacial

M S= 4



1 r12

+

1 r22

(4)



(5)

where M is the transferred torque, r1 is the outer radius of the edge of the bicone and r2 is the inner radius of the measuring vessel [10]. With a single experiment the technique provides information on both interfacial shear parameters simultaneously, shear viscosity

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25

and elasticity. Their values are obtained from the damping coefficient and the angular frequency by Fourier analysis of the measured curves.

The adsorption studies for the protein/surfactant mixtures were performed by Profile Analysis Tensiometer (PAT-1). For the data analysis, Eqs. (6)–(8) were considered which were derived for the adsorption of ionic surfactants mixed with proteins: ˘ω0∗ RT

= ln(1 − PS − S ) + PS

=

1/(1+m)

0 1.00E-06

0



(1 − PS − S )

bS (cS cC )1/2 =



exp −2aPS (ω1 /ω)PS − 2aSPS S

S 1 − PS − S

1.00E-04



  exp −2aS S − 2aSPS PS

(7) 50 45

(8)

The subscripts 0, S, P, PS, indicate solvent, surfactant, protein, protein–surfactant complex, respectively, and asps describes the interaction between surfactant and protein–surfactant complex. The subscript 1 indicates the state where no surfactant has interacted with the protein yet. We also assumed aS = 0 as there is no interaction between SDS molecules at the interface (due to electrostatic repulsion). We used the software protein IX for fitting the theoretical model to the experimental adsorption isotherm data of the BLG/SDS mixtures (shown in Fig. 1). For the interaction constants in Table 1 we have aS < aPS < aSPS , i.e. the interaction between protein–surfactant complex and surfactant is the highest. Figs. 2 and 3 allow the comparison of BLG adsorption at the water/MCT and water/hexane interfaces, respectively. In ref. [12], the onset of the formation of a secondary layer of BLG at concentrations above 10−6 M was postulated. Therefore, in our present investigations we have chosen a concentration of 3 × 10−7 M to study the rheology of adsorbed layers. The adsorption kinetics between water/hexane and water/MCT interface at the same concentration are more or less similar. The oscillations performed in the end of each experiments show the possibility for studying the dilational rheology by the instrument PAT-1. The amplitudes of the interfacial tension response at perturbations with the same area amplitude are a measure of the dilational interfacial elasticity. Additional systematic studies are pending and will not further be discussed here. Using the MCR 301 rheometer, the complex shear elasticity, G* of the mixed BLG/SDS adsorption layers were studied, the results of which are shown below in Figs. 4 and 5. The numbers in Figs. 4(a)

35 30 25 20 15 10 0

10000

20000

30000

Time (s) 50

(b)

45

(mN / m)

molar area at the interface 2-dimensional surface layer compressibility coefficient surface coverage

(a)

40

40 35 30 25 20 15 10 0

10000

Time (s)

20000

30000

Fig. 2. Dynamic interfacial tension for 3 × 10−7 M BLG at the water/hexane interface with (a) no surfactant and (b) 5 × 10−7 M SDS.

28 26 24

(mN / m)

ω0 P +ωS0 S P +S

ω ε 

1.00E-02

Fig. 1. Equilibrium interfacial tension isotherm comprising of interfacial tension values corresponding to concentration of SDS mixed at a fixed amount of 10−6 mol/l BLG; data points represent the isotherm obtained at water/MCT interface () and at water/hexane interface (), respectively, while the lines represent the fitting with the theoretical model, using the parameters given in Table 1.

interaction parameter adsorption equilibrium constant surfactant counter-ion concentration number of ionized groups on protein molecule gas law constant temperature surface concentration bulk concentration surface pressure

ω0∗

1.00E-03

C (mol / L)

A detailed description of the theoretical model was given in by Fainerman et al. [11]. The following symbols are used: a b cc m R T c ˘

1.00E-05

(6)

m/(1+m) 1/(1+m) cS

ω1 /ω

5

ω

= bPS cP

ω 1

10

1 − ω 

2 + aPS PS + aS S2 + 2aSPS PS S

bPS (cPm cS )

15

(mN / m)

−

(mN / m)

3. Results

20

22 20 18 16 14 12 10 0

5000

10000

15000

20000

Time (s) Fig. 3. Dynamic interfacial tension for 3 × 10−7 M BLG at the water/MCT interface.

V. Ulaganathan et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 413 (2012) 136–141

139

Table 1 Parameters obtained by fitting the theoretical adsorption models to the data of SDS and BLG mixtures, shown in Fig. 1. SDS

Water/hexane Water/MCT

12

BLG

ωS (m2 /mol)

aS

ε

bS (m3 /mol)

ω0 (m2 /mol)

ωmin (m2 /mol)

ωmax (m2 /mol)

aPS

bPS (m3 /mol)

aSPS

m

3.8 × 10+5 3.8 × 10+5

0 0

0.01 0.01

1.5 × 10+2 1.5 × 10+2

4.0 × 10+5 4.0 × 10+5

4.5 × 10+6 4.5 × 10+6

2.0 × 10+7 2.0 × 10+7

0.5 0.1

2.5 × 10+4 1.0 × 10+5

1 0

5 5

(a)

1.8

(b)

2

1.6

1

8 6

1

3

2

3

4

5

4

4

2

5

0 0

200

400

600

Time (min)

800

1000

Gs (mPa.m)

G* (mPa.m)

10

0.4 0

200

400

600

800

1000

Time (min) Fig. 6. Increase in GS of 3 × 10−7 mol/l BLG mixed with different concentrations of SDS at water/hexane interface and measured by damped oscillations performed by the ISR-1 at a deflection angle of 0.75◦ ; the data points represent corresponding concentrations of SDS in the mixtures: () No added SDS, () 5 × 10−7 mol/l, () 1 × 10−5 mol/l.

layer, passing through a maximum and then decreases with higher concentration. In Figs. 6 and 7 the ISR-1 was used to measure the shear elasticity and viscosity by producing free damped oscillations. This instrument is very sensitive to even low elasticity of the interfacial layer. Here there is a threshold value of GS = 1.5 mPa m for the sensitivity of the torsion wire used and hence the experiments are conducted until this value is reached for each ratios of protein–surfactant mixtures. The similar trend observed in Figs. 4 and 5 could be seen here. The above Fig. 8 shows that though the two instruments ISR-1 and MCR 301 have different ranges of sensitivity and work with different physical principles, they complement each other when the same conditions of the adsorbed layers are kept. Here the conditions such as bulk concentration, pH, temperature and frequency of oscillations were in both cases identical so that a comparison of the results was possible.

(b)

(a)

1.4

2 3

6 5

1

1.2 1

2

3

4

1

4 3

Gs (mPa.m)

G* (mPa.m)

1

0.6

and 5(a) indicate the concentrations in the mixed solutions while the BLG concentration was fixed at 3 × 10−7 mol/l. As mentioned above, this fixed BLG concentration is below the onset of a secondary adsorption layer formation and was therefore used for all shear rheological measurements. The experiments with the MCR 301 were carried out at controlled strain oscillations. The optimum strain amplitude was determined from an amplitude sweep at a low frequency of 0.7 Hz. An amplitude of 0.2% strain was further used in order to stay in the linear visco-elastic regime. In case of water/MCT interface the protein or protein–surfactant complex network was too weak to be measured at these conditions. So, the experiments were carried out by aging the interface for 18 h after which the layer was in a visco-elastic regime. Still the kinetics of structure formation (see Fig. 5) was very slow as compared with that at the water/hexane interface (see Fig. 4). Here section (b) in both Figs. 4 and 5 present the qualitative values of different ratios of the BLG and SDS mixtures, being the values of G* obtained at final time of each experiment. The columns show the effect of concentration of surfactant in the mixtures. Clearly at low surfactant concentration there is an increase in elasticity of the

4

2 1 0 1080

1.2

0.8

1200

Fig. 4. (a) Increase in G* of 3 × 10−7 mol/l BLG mixed with different concentrations of SDS at water/hexane interface and measured under controlled strain forced oscillations performed by MCR 301 at 0.2% deformation and 0.7 Hz frequency; (1) no added SDS, (2) 7 × 10−7 mol/l, (3) 9 × 10−7 mol/l, (4) 1 × 10−6 mol/l, (5) 1 × 10−5 mol/l; (b) qualitative trend of total increase in the G* values as observed in (a).

7

1.4

0.8 0.6 0.4 0.2

1280

1480

1680

1880

2080

2280

Time (min) Fig. 5. (a) Increase in G* of 3 × 10−7 mol/l BLG mixed with different concentrations of SDS at water/MCT interface and measured after 18 h of aging, under controlled strain forced oscillations performed by MCR 301 at 0.2% deformation and 0.7 Hz frequency; (1) no added SDS, (2) 5 × 10−7 mol/l, (3) 7 × 10−7 mol/l, (4) 1 × 10−6 mol/l; (b) qualitative trend of total increase in the G* values observed in (a).

0

0

500

1000

1500

Time (min) Fig. 7. Increase in GS of 3 × 10−7 mol/l BLG mixed with different concentrations of SDS at water/MCT interface and measured by damped oscillations performed by the ISR-1 at a deflection angle of 0.75◦ ; the data points represent corresponding concentrations of SDS in the mixtures: () no SDS, () 1 × 10−5 mol/l, () 1 × 10−4 mol/l.

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G* and Gs (mPa.m)

4.5 4

3.5 3

2.5 2

1.5 1

0.5 0

1

10

100

1000

10000

Time (min) Fig. 8. The open symbols (, ) are GS values obtained from ISR-1 and the closed symbols (, 䊉) are G* values obtained from MCR 301; the square symbols are for 3 × 10−7 M BLG at water/MCT interface and circle symbols are for 1 × 10−5 M SDS mixed with 3 × 10−7 M BLG at water/hexane interface.

4. Discussion The adsorption kinetics studied by drop profile analysis tensiometry gives good information about the composition of the mixed adsorbed layer at the interface. With increasing the concentration the surfactant dominates, step by step, the interface by replacing gradually the protein, i.e. the higher the concentration of the surfactant the greater the dominance over the protein at the interface which is reflected by the surface tension isotherms in Fig. 3. For mixtures of the protein at low surfactant concentrations there is not much effect on equilibrium surface tension but a considerable effect can be observed on the shear elasticity and viscosity of the adsorbed layer. The reason for this is that shear rheology is very sensitive to the intermolecular interactions between the molecules adsorbed at the interface. Here even the low surfactant concentrations could induce some changes in the protein conformation which cannot be appreciated by surface tension measurements. At pH 7, BLG has a negative net charge as the pH is higher than the iso-electric point of 5.3. When SDS binds to the few yet available positive sites the protein becomes more hydrophobic due to the addition of the hydrophobic chains of the surfactant molecules. This results in more hydrophobic and thus more surface active protein/surfactant complexes. With increasing SDS concentrations, however, after a complete compensation of available positively charged groups in the protein molecule, a hydrophobic interaction between surfactant and protein sets in, which now leads to an opposite effect of increased hydrophilization of the formed complexes. The effect of different SDS concentrations in the mixtures with BLG can be seen in Figs. 4–7. Though the results obtained from MCR 301 and ISR-1 have different ranges of sensitivities they complement each other (cf. Fig. 8) and confirm the complex formation behavior of BLG/SDS mixtures. The higher shear viscosity at lower concentrations of SDS in BLG/SDS mixtures are due to ionic interaction and unfolding of the protein molecule in the formed protein–surfactant complex, i.e. the cross-linking of the BLG/SDS complexes at the interface gets stronger [13,14]. The subsequent decrease in hydrophobicity due to further hydrophobic binding of SDS leads to an increase in the total charge (even with a sign change) and consequently an ionic repulsion of adsorbed complexes appears. Finally, the complexes are very hydrophilic and have, therefore, so low interfacial activity that they are progressively replaced from the interface, as it was also discussed for example in refs. [15,16] for other protein/surfactant mixtures studied at the water/air interface. The measured shear rheological parameters depend on the number of bonds formed between the molecules, and their strength [17,18]. The conformation of BLG at the water/hexane interface

is expected to be different from that at water/MCT, as hexane is less polar than MCT. This could be one reason why intermolecular interactions and rate of structure formation at the water/MCT interface is very slow as compared to the water/hexane interface. The reproducibility is more pronounced in the damped oscillations performed by ISR-1 with the protein prepared from the same stock solution than with MCR 301. At such low SDS concentrations we are at the low sensitivity region of MCR 301. Thus obtained rheological data can essentially be analyzed qualitatively. The combinations of the two rheometers, however, provide a maximum range of shear visco-elasticity data for the studied interfacial layers. 5. Conclusion The results obtained support the idea about protein–surfactant interaction and complex formation and their contribution to the mechanical properties of the layers formed at the water/oil interface. While qualitatively, the phenomena are similar to the water/air interface, the specificity of the oil, in particular its polarity controls the strength of the self-assembling and anchoring at the interface. This knowledge is useful in preparing protein layers of desired properties and ultimately emulsions of desired stability. The shear rheology has various applications in emulsion and foam stability of many systems in food industries, medical, pharmaceutical industries, etc. Further studies are, however, required in the future in particular for liquid–liquid interfaces which would allow a more detailed understanding of the interactions between the adsorbed molecules at the respective interfaces and the role of the oil’s specific properties. References [1] J.W. Goodwin, Macromolecules and Surfactants, John Wiley & Sons Ltd., 2004. [2] M.S. Brent, Rheological properties of protein films, Current Opinion in Colloid and Interface Science 16 (2011) 27–35. [3] E. Dickinson, D.J. McClements, Advances in Food Colloids, 1st ed., Blackie Academic & Professional, London, New York, 1996. [4] P.C. Hiemenz, R. Rajagopalan, Principles of Colloid and Surface Chemistry, 3rd ed., Marcel Dekker, New York, 1997. [5] K.P. Das, J.E. Kinsella, Effect of heat denaturation on the adsorption of [beta]-lactoglobulin at the oil/water interface and on coalescence stability of emulsions, Journal of Colloid and Interface Science 139 (1990) 551–560. [6] R. Miller, R. Wüstneck, J. Krägel, G. Kretzschmar, Dilational and shear rheology of adsorption layers at liquid interfaces, Colloids and Surfaces A: Physicochemical and Engineering Aspects 111 (1996) 75–118. [7] G. Loglio, P. Pandolfini, L. Liggieri, A.V. Makievski, F. Ravera, Determination of interfacial properties by the pendant drop tensiometry: optimisation of experimental and calculation procedures, in: L.L.R. Miller (Ed.), Bubble and Drop Interfaces, Brill Publications, Leiden, 2011, pp. 7–38. [8] P. Erni, P. Fischer, E.J. Windhab, V. Kusnezov, H. Stettin, J. Läuger, Stress- and strain-controlled measurements of interfacial shear viscosity and viscoelasticity at liquid/liquid and gas/liquid interfaces, Review of Scientific Instruments 74 (2003). [9] L.E. Scriven, Dynamics of a fluid interface equation of motion for Newtonian surface fluids, Chemical Engineering Science 12 (1960) 98–108. [10] J. Krägel, S. Siegel, R. Miller, M. Born, K.H. Schano, Measurement of interfacial shear rheological properties: an apparatus, Colloids and Surfaces A: Physicochemical and Engineering Aspects 91 (1994) 169–180. [11] V.B. Fainerman, S.A. Zholob, M.E. Leser, M. Michel, R. Miller, Adsorption from mixed ionic surfactant/protein solutions: analysis of ion binding, Journal of Physical Chemistry B 108 (2004) 16780–16785. [12] V. Pradines, J. Krägel, V.B. Fainerman, R. Miller, Interfacial properties of mixed ␤-lactoglobulin–SDS layers at the water/air and water/oil interface, Journal of Physical Chemistry B 113 (2008) 745–751. [13] R. Miller, V.B. Fainerman, A.V. Makievski, J. Krägel, D.O. Grigoriev, V.N. Kazakov, O.V. Sinyachenko, Dynamics of protein and mixed protein/surfactant adsorption layers at the water/fluid interface, Advances in Colloid and Interface Science 86 (2000) 39–82. [14] E. Dickinson, Adsorbed protein layers at fluid interfaces: interactions, structure and surface rheology, Colloids and Surfaces B: Biointerfaces 15 (1999) 161–176. [15] C. Kotsmar, V. Pradines, V.S. Alahverdjieva, E.V. Aksenenko, V.B. Fainerman, V.I. Kovalchuk, J. Krägel, M.E. Leser, B.A. Noskov, R. Miller, Thermodynamics adsorption kinetics and rheology of mixed protein–surfactant interfacial layers, Advances in Colloid and Interface Science 150 (2009) 41–54. [16] V.B. Fainerman, R. Miller, V.I. Kovalchuk, Influence of the two-dimensional compressibility on the surface pressure isotherm and dilational elasticity of

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