Effect of Frequency and Temperature on Rheological Properties of β

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Effect of Frequency and Temperature on Rheological Properties of β-Casein Adsorption Layers Arayik Hambardzumyan,† Ve´ronique Aguie´-Be´ghin,† Ivan Panaı¨otov,‡ and Roger Douillard*,† Equipe Parois et Mate´ riaux Fibreux, UMR FARE, INRA/URCA, Centre de Recherche Agronomique, 2 Espl. Roland Garros, BP 224, 51686 Reims Cedex 2, France, and Biophysical Chemistry Laboratory, University of Sofia, J. Bourchier str. 1, 1126 Sofia, Bulgaria Received July 1, 2002. In Final Form: October 4, 2002 The rheological behavior of adsorption layers of β-casein formed at the air/water interface was studied by bubble tensiometry. It was observed that in some instances, the dilational modulus, , has only an elastic component while in other cases it has both an elastic and a viscous component. The conditions where the elastic modulus is significant have been defined. In these conditions, the measured dilational modulus is practically equal to a physical quantity measured in equilibrium conditions. Until a surface pressure, π, of about 5 mN/m, it is proportional to the surface pressure. Referring to a multiblock polymer model, the proportionality coefficient y ( ) yπ) is directly related to the fractal dimension of the polymer forming a pancake at the interface. An increase of temperature from 10 to 60 °C results in a decrease of y from 6.6 to 3.3, indicating that in these conditions the two-dimensional polymer changes from a partly collapsed structure to that of a two-dimensional self-avoiding walk. These results show that even with the flexible polypeptide chain of β-casein, interactions between amino acids contribute significantly to the structure of the adsorption layer formed at the air-aqueous buffer interface at room temperature.

Introduction The adsorption of amphiphilic macromolecules at fluid interfaces is an important matter in the food industry, in cosmetics, and in material manufacturing for instance.1-5 The understanding of the relations between the structure of the macromolecules and their surface properties is a challenge which has been addressed for a long time.5-10 Several theories and models for polymer adsorption at the air-liquid and liquid-liquid interfaces have been proposed and tested extensively in the past few years.11-27 * Corresponding author. Tel: 33 (0)3 26 77 35 94. Fax: 33 (0)3 26 77 35 99. E-mail: [email protected]. † Centre de Recherche Agronomique. ‡ University of Sofia. (1) Kinsella, J. E.; Whitehead, D. M.; Brady, J.; Bringe, N. A. In Developments in Food Chemistry 4; Fox, P. F., Ed.; Elsevier Applied Science: London, 1989; pp 55-95. (2) De Wit, J. N. In Developments in Food Chemistry 4; Fox, P. F., Ed.; Elsevier Applied Science: London, 1989; pp 285-321. (3) Dickinson, E. An introduction to food colloids; Oxford University Press: Oxford, 1992. (4) Dickinson, E. Int. Dairy J. 1999, 9, 305. (5) Halling, P. J. CRC Crit. Rev. Food Sci. Nutr. 1981, 13, 155. (6) Darewicz, M.; Dziuba, J.; Caessens, P. W. J. R.; Gruppen, H. Biochimie 2000, 82, 191. (7) Caessens, P. W. J. R.; de Jongh, H. H. J.; Nordh, W.; Gruppen, H. Biochim. Biophys. Acta 1999, 1430, 73. (8) Krause, J. P.; Kra¨gel, J.; Schwenke, K. D. Colloids Surf., B 1997, 8, 279. (9) Euston, S. R.; Hirst, R. L.; Hill, J. P. Colloids Surf., B 1999, 12, 193. (10) Krause, J. P. Ind. Crops Prod. 2002, 15, 221. (11) Ligoure, C. J. Phys. II France 1993, 3, 1607. (12) Leclerc, E.; Daoud, M. Macromolecules 1997, 30, 293. (13) Zheng, Y. C. J. Chem. Phys. 2000, 112, 8665. (14) Baranowski, R.; Whitmore, M. D. J. Chem. Phys. 1995, 103 (6), 2343. (15) Marques, C. M.; Joanny, J. F. Macromolecules 1989, 22, 1454. (16) Dickinson, E. Colloids Surf., B 2001, 20, 197. (17) Ligoure, C. Macromolecules 1996, 29, 5459. (18) Sedev, R. Colloids Surf., A 1999, 156, 65. (19) Currie, E. P. K.; Wagemaker, M.; Cohen Stuart, M. A.; van Well, A. A. Physica B 2000, 283, 17. (20) Alexander S. J. Phys. 1977, 38, 983. (21) Halperin, A. Macromolecules 1991, 24, 1418.

In recent years, a model has been developed for proteins and other macromolecules at interfaces, assuming an alternatinghydrophilic/hydrophobicblockstructure.12,17-20,24 A basic feature of this thermodynamic model is that it assumes a quasi-equilibrium. A convenient method to compare the properties of the model and that of an authentic block copolymer is to determine the variations of the dilational modulus versus the surface pressure.24,28 A very good agreement has been found between the experimental pattern for β-casein and the theoretical predictions in the case of a polymer where the hydrophilic and the hydrophobic blocks have the same order of length.24,28 This is not completely surprising since β-casein is a flexible linear amphiphilic polyelectrolyte of 24 kDa molecular mass and it carries a moderate net charge (-15e) at neutral pH. It has little ordered secondary structure and no intramolecular covalent cross-links. The highly nonuniform distribution of hydrophilic and hydrophobic residues in this protein produces a distinctly amphiphilic molecular structure that resembles that of a simple watersoluble surfactant or a block copolymer.16 In addition, it has been frequently used for model studies of protein adsorption and its properties in adsorption layers are well documented.28 Moreover, the interpretation of the data in the frame of the multiblock theory showed that the two-dimensional hydrophobic pancakes are partly collapsed because of attractions between the monomers. Moreover, these noncovalent attractions can be ruptured by GuHCl,28-30 (22) Mun˜oz, M. G.; Monroy, F.; Ortega, F.; Rubio, R. G.; Langevin, D. Langmuir 2000, 16, 1083. (23) Daoud, M.; de Gennes, P. G. J. Phys. 1977, 38, 85. (24) Aguie´-Be´ghin, V.; Leclerc, E.; Daoud, M.; Douillard, R. J. Colloid Interface Sci. 1999, 214, 143. (25) Vilanove, R.; Poupinet, D.; Rondelez, F. Macromolecules 1988, 21, 2880. (26) Poupinet, D.; Vilanove, R.; Rondelez, F. Macromolecules 1989, 22, 2491. (27) Dickinson, E. Colloids Surf., B 1999, 15, 161. (28) Aschi, A.; Gharbi, A.; Bitri, L.; Calmettes, P.; Daoud, M.; AguieBeghin, V.; Douillard, R. Langmuir 2001, 17, 1896.

10.1021/la020599b CCC: $25.00 © 2003 American Chemical Society Published on Web 12/07/2002

Effect of Frequency and Temperature on Rheology

leading to the conformation of a two-dimensional selfavoiding walk. Some results indicate that the attractions are probably not hydrophobic interactions but rather van der Waals attractions or hydrogen bonds.28 However, this tentative conclusion is not completely supported by experimental results. Referring to a multiblock polymer model,17,20,22,24-26 the proportionality coefficient y ( ) yπ) is a key parameter in the understanding of the formation and of the structure of the polymer adsorption layers at the air-liquid interface. Moreover, the theory assumes a quasi-equilibrium state where  is a purely elastic quantity. Nevertheless, the dilational modulus  is a complex number and incorporates a real and an imaginary part which correspond to the elasticity and viscosity, respectively.31-36,47,48 Moreover, it has been shown that the imaginary part of the dilational modulus may change according to the experimental conditions.33-35 In a previous work,28 it was checked that a frequency change does not modify the modulus which for this reason was assumed to be purely elastic. In the present work, a detailed analysis of the effect of frequency is performed on the viscous and elastic parts of the dilational modulus to specify accurately conditions where viscosity can be neglected. This treatment of data is then used to evaluate the effect of temperature on the purely elastic component of the dilational modulus and on the coefficient y and finally to get an insight into the nature of the interactions between monomers. Material and Methods Materials. β-Casein was obtained from the skimmed milk of a single cow homozygous for the three major caseins (Rs1B, βB, and κB), purified according to the method of Mercier et al.,37 and freeze-dried. Acid-precipitated casein was fractionated by ion exchange chromatography on a DEAE column (5 PW, Waters) using a NaCl gradient in a 20 mM imidazole buffer at pH 7 including 3.3 M urea and 1 mM dithiothreitol (DTT). The fraction corresponding to β-casein was rechromatographed in the same conditions, and its purity was checked by polyacrylamide gel electrophoresis. The extinction coefficient used to determine the volume concentration of this protein is E1% 1cm ) 4.6 at 278 nm. Surface Tension Measurements. For measurement of static or dynamic surface tension, a bubble tensiometer (IT Concept, Longessaigne, France) was used.38-41 The surface tension was measured through shape analysis of an air bubble formed at the tip of a stainless steel needle dipped in the solution thermostated in a optical glass cuvette.42 The needle is attached to a syringe (29) Zhou, J.-M.; Fan, Y.-X.; Kihara, H.; Kimura, K.; Amemiya, Y. FEBS Lett. 1997, 415, 183. (30) Calmettes, P.; Durand, D.; Receveur, V.; Desmadril, M.; Minard, P.; Douillard, R. Physica B 1995, 213/214, 754. (31) Miller, R.; Fainerman, V. B.; Makievski, A. V.; Kra¨gel, J.; Grigoriev, D. O.; Kazakov, V. N.; Sinyachenko, O. V. Adv. Colloid Interface Sci. 2000, 86, 39. (32) Langevin, D. Adv. Colloid Interface Sci. 2000, 88, 209. (33) Boury, F.; Ivanova, T.; Panaı¨otov, I.; Proust, J. E. Langmuir 1995, 11, 599. (34) Panaı¨otov, I.; Ivanova, T.; Proust, J.; Boury, F.; Denizot, B.; Keough, K.; Taneva, S. Colloids Surf., B 1996, 6, 243. (35) Bois, A. G.; Panaiotov, I.; Baret, J. F. Chem. Phys. Lipids 1984, 34, 265. (36) Benjamins, J.; Lucassen-Reynders, E. H. In Proteins at Liquid Interfaces; Mo¨bius, D., Miller, R., Eds.; Elsevier Science: London, 1998; No. 7, pp 341-384. (37) Mercier, J. C.; Maubois, J. L.; Poznanski, S.; Ribadeau-Dumas, B. Bull. Soc. Chim. Biol. 1968, 50, 521. (38) Cagna, A.; Esposito, G.; Rivie`re, C.; Housset, S.; Verger, R. 33rd International Conference on Biochemistry of Lipids, Lyon, France, 1992. (39) McLeod, C. A.; Radke, C. J. J. Colloid Interface Sci. 1993, 160, 435. (40) Lucassen-Reynders, E. H.; Cagna, A.; Lucassen, J. Colloids Surf., A 2001, 186, 63. (41) Saulnier, P.; Boury, F.; Malzert, A.; Heurtault, B.; Ivanova, T.; Cagna, A.; Panaı¨otov, I.; Proust, J. E. Langmuir 2001, 17, 8104.

Langmuir, Vol. 19, No. 1, 2003 73 whose plunger is precisely controlled by a micrometer screw driven by an electric motor. The area of the bubble can be made to oscillate periodically at a chosen amplitude and frequency. This was achieved by regulating the electric motor driving the piston in the syringe feeding the bubble, so as to produce approximately sinusoidal oscillations of the bubble volume. The bubble is illuminated with a beam of parallel light. The image is recorded by a CCD camera and is digitized to allow the analysis of its shape. The interfacial tension γ is determined by analyzing the profile of the bubble according to the Laplace equation:

∆F 1 d(x sin θ) 2 ) -g z x dx b γ

(1)

where x and z are the Cartesian coordinates at any point of the bubble profile, b is the curvature radius at the apex of the bubble (x ) z ) 0), θ is the angle of the tangent to the bubble profile formed with the x axis, g is the acceleration of gravity, and ∆F is the difference of volumetric mass between the two fluids. The surface pressure is, as usual, the difference between the surface tension of the pure solvent γ0 and that of the solution with surface active molecules γ: 45

π ) γ0 - γ

(2)

Dilational Modulus. The surface dilational modulus, , is defined as the ratio between the variation of the surface tension, dγ (or the surface pressure dπ), and the relative change in surface area, dA/A ) d ln(A):27,28,31,42

)

dγ dπ )d ln(A) d ln(A)

(3)

It was determined during periodical deformations of the area of the bubble performed by moving the plunger of the syringe. The area and the surface tension were calculated 2 times per second. A Fourier transform of the data was performed, and only the first harmonic was retained.40-42

Rheological Model The surface dilational modulus (or viscoelastic modulus) is a complex number and incorporates a real and an imaginary part, which correspond to the elasticity and viscosity, respectively.31-34 The complex nature of the dilational modulus implies the occurrence of the equilibrium and nonequilibrium parts of the surface pressure in the relaxation process. To describe the surface pressure change, ∆π ) π(t) πi (Figure 1), during the compression c of duration T with a constant velocity (U ) dA/dt) followed by a relaxation r, it is assumed that at any time the total surface pressure change can be represented as the sum of an equilibrium ∆πe and a nonequilibrium ∆πne contribution.33,34

∆π ) ∆πe + ∆πne

(4)

The equilibrium part, ∆πe, is related to the equilibrium surface dilational elasticity Ee:

UT ∆πe ) Ee Ai

(5)

where Ai is the initial interface area before the compression and UT/Ai t ∆A/Ai, the corresponding strain (see Figure (42) Benjamins, J.; Cagna, A.; Lucassen-Reynders, E. H. Colloids Surf., A 1996, 114, 245. (43) Lucassen, J.; van den Tempel, M. J. Colloid Interface Sci. 1972, 41, 491. (44) Lucassen, J.; Giles D. J. Chem Soc., Faraday Trans. 1 1975, 171, 217. (45) Mellema, M.; Clark, D. C.; Husband, F. A.; Mackie, A. R. Langmuir 1998, 14, 1753.

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UT EneUt ∆π ) Ee + (1 - et/τ) Ai Ai

(8)

τ ∆π A ) Ee + Ene (1 - et/τ) Ut i t

(9)

or

In the frame of the rheological model presented above (Figure 1), the relaxation of the adsorption layer (T < t < ∞) can be represented by33

π(t) - π∞ t ln )π0 - π∞ τ

(10)

This equation permits the determination of the specific time of relaxation τ,35 which allows one, with [9], to obtain graphically the values of the equilibrium and nonequilibrium parts of the elasticity. Theoretical Background for Polymer Adsorption Figure 1. Rheological model and theoretical behavior of the monolayer. Ee is the equilibrium elasticity, Ene is the nonequilibrium elasticity, and τ is the relaxation time associated with the nonequilibrium component. The deformation velocity, U, is constant during the compression, c, between t ) 0 and t ) T, and it is zero during the relaxation, r, for t > T, U ) 0. πi and π0 are the surface pressures before and after compression of the monolayers, respectively. τ is the specific time of relaxation.

1). This elastic behavior is represented by the upper branch of the mechanical model in Figure 1.33,34 The nonequilibrium part of the total surface pressure change ∆πne is associated with the accumulation of elastic energy during the compression. Dissipation of this accumulated energy occurs during compression as well as relaxation. In the case of polymer adsorption layers, the relaxation processes may be described by several characteristic times36,47,48 but usually a single-exponential decay is convenient for the phenomenological analysis of small deformations of protein layers.33-35 Thus, Boury et al.33 had shown that the viscoelastic behavior can be described with Maxwell’s equation:

d∆πne ∆πne U + ) Ene dt τ Ai

(6)

where ∆πne is the applied stress, Ene is the nonequilibrium surface dilational elasticity, and τ is the specific time of relaxation. This viscoelastic behavior is represented by the lower branch of the mechanical model in Figure 1. The two branches of the mechanical model are coupled in parallel according to eq 4 which corresponds to the addition of stresses. The solution of eq 6 using the initial condition ∆πne ) 0 at t ) 0 is

∆πne )

EneUt (1 - et/τ) Ai

(7)

From eqs 4, 5, and 7, we obtain the following equation describing the viscoelastic behavior of the monolayer: (46) de la Fuente Feria, J.; Rodrı´guez Patino, J. M. Langmuir 1994, 10, 2317. (47) Ca´rdenas-Valera, A. E.; Bailey, A. I. Colloids Surf., A 1993, 79, 115.

In the current theory of adsorption of proteins at the air/water buffer interface, the polymer chain is assumed to be made of N diblocks of two sequences A and B of ZA and ZB monomers, respectively (the ratio ZA/ZB ) R is the usual parameter for the chemical structure of the polymer). The monomers of the A and B sequences have different chemical natures, say, A is hydrophobic and B is hydrophilic. For the sake of simplicity, it will be assumed that the liquid is a good solvent for the B sequences and that the junctions between the hydrophilic and the hydrophobic blocks stick strictly to the interface plane. Once adsorbed, the polymer adopts a conformation where the hydrophobic sequences form two-dimensional pancakes in contact with the gas and with the liquid and where the hydrophilic sequences form three-dimensional coils in the liquid phase. The conformations of the pancakes and coils are defined as random self-avoiding walks or as partially or completely collapsed coils and are characterized by a radius and a thickness in the two-dimensional case. Such a definition implies that each block has a fractal structure where the fractal dimension (D) is the reverse of the Flory exponent, ν:

R = aZν

(11)

D ) 1/ν

(12)

where R is the radius of the block, a is the size of a monomer (in an ideal polymer, the size of the statistical unit is the size of a monomer), and Z is their number in the block. The sign = means that all numerical coefficients are purposely ignored in the relation. When the surface concentration increases, the polymer molecules and the blocks overlap. The interface enters in successive semidilute regimes whose natures are determined as a function of the ratio R and of the surface concentration using scaling law arguments. The succession of surface regimes as a function of the total surface concentration may occur in three different ways according to the value of R (R ) ZA/ZB).24 At intermediate values of R (hydrophilic and hydrophobic blocks having the some order of size), the phase diagram is influenced by the properties of both sides of the interface. In the semidilute regimes, using a scaling law approach, the surface pressure was found to be24 (48) Mun˜oz, M. G.; Monroy, F.; Ortega, F.; Rubio, R. G.; Langevin, D. Langmuir 2000, 16, 1094.

Effect of Frequency and Temperature on Rheology

π = kBTΓy

Langmuir, Vol. 19, No. 1, 2003 75

(13)

where kB is the Boltzmann constant, T is the absolute temperature, y is an exponent characteristic of the regime of the interface and of the fractal dimension of the block in the dilute regime, and Γ is the surface concentration defined as

Γ ) m/A

(14)

where m is the mass of polymer (protein) adsorbed at the interface of area A. Equation 13 is similar to expressions which have been derived for adsorbed polymers using self-consistent field theories19,49-52 or scaling law approaches.17,20,22 When the two-dimensional blocks impose their behavior to the interfacial layer, y g 3. When the properties of the interface are dominated by the three-dimensional coils forced to form quasi-brushes (they are forced to have an extension in a direction perpendicular to the interface), y ) 1. Assuming that adsorption or desorption is not significant during one oscillation (m is constant), we have, combining [3], [13], and [14],

 ) yπ

(15)

Thus, representing  as a function of π gives an evaluation of y which has a significance in the state eq 13 and is directly related to the fractal dimension of the twodimensional blocks.12,22,24 Results and Discussion At first, the effect of the relative amplitude of bubble area change (∆A/A) on the surface pressure change was checked starting from an adsorption layer with a surface pressure around 20 mN/m. The duration of the deformation was of the order of 1 s. The relation between the surface pressure change and the relative variation of the area is linear until, at least, a value of 0.15 for ∆A/A (Figure 2). For experimental means, it is difficult to reduce the area of the bubble by more than 15%. It is assumed that the same linearity holds for smaller values of the surface pressure of the adsorption layer. A standard value of ∆A/A ) 0.1 was used throughout this work. Deformation and Relaxation of Adsorption Layers. It is necessary to evaluate the relaxation time of a compressed adsorption layer in order to choose a perturbation process with a larger characteristic time, allowing the measurement of the quasi-equilibrium properties of the layer. Using a 1 s perturbation on layers with different surface pressures, it was observed that at a surface pressure below 11-12 mN/m, no relaxation occurs; the layer is practically purely elastic in these conditions (Figure 3a). This behavior is no longer true at larger surface pressures (19 mN/m), where a significant relaxation is observed (Figure 3b). The relaxation time is there of the order of 10 s. The amplitude of the relaxation is also a function of the compression rate (Figure 4). The characteristic time of relaxation τ was measured (eq 10) in the different cases. (49) Dickinson, E.; Horne, D. S.; Pinfield, V. J.; Leermakers, F. A. M. J. Chem. Soc., Faraday Trans. 1997, 93, 425. (50) Leermakers, F. A. M.; Atkinson, P. J.; Dickinson, E.; Horne, D. S. J. Colloid Interface Sci. 1996, 178, 681. (51) Halperin, A. Eur. Phys. J. B 1998, 3, 359. (52) Faure´, M. C.; Bassereau, P.; Carignano, M. A.; Szleifer, I.; Gallot, Y.; Andelman, D. Eur. Phys. J. B 1998, 3, 365.

Figure 2. Relation between the surface pressure change (∆π) and the relative variation of the area (∆A/A) of adsorption layers of β-casein formed at the air/buffer interface. The deformation of the area was performed in less than 1 s. The pressure before deformation was close to 19 mN/m.

Its value was used for the graphical determination (Figure 5) of the nonequilibrium and equilibrium parts of the dilational modulus (Table 1). These data show that the nonequilibrium part of the dilational modulus decreases when the velocity of compression decreases, while the equilibrium part remains practically constant. When the compression reaches 60 s, the surface pressure relaxation is of the order of the background noise. Thus, it is clear that any perturbation process with a characteristic time larger than 60 s should lead to the observation of practically the equilibrium properties of the layer (∆πne ∼ 0.25 mN/m). To confirm this conclusion, the dilational modulus was measured during the formation of the adsorption layer at surface pressures between 0 and 20 mN/m at several frequencies (Figure 6). No differences are observed for periods ranging from 10 to 40 s until the surface pressure is close to 12 mN/m. The 10 s period curve is slightly different from the two others between 16 and 20 mN/m. These results are in good agreement with those of Figure 4 where the surface pressure was 23 mN/m. It can be concluded that when β-casein is used in the experimental conditions of this work, the dilational modulus measured at a surface pressure smaller than 20 mN/m is obtained in quasi-equilibrium conditions when the period of the sine wave deformation is equal to or larger than 20 s. This conclusion is consistent with previous observations that no slower relaxation mode occurs in β-casein adsorption layers.36,45 From a more general standpoint, for quasi-equilibrium measurements using a sine wave deformation it can also be concluded that the period can be chosen by measuring the relaxation time at a high surface pressure (Figures 3 and 4) or by measuring the dilational modulus at several frequencies (Figure 6) and choosing the value where the relation between the modulus and the pressure is not affected by the frequency especially at high surface pressure. Concerning the relaxation mechanisms, they can be ascribed to (i) diffusional interchange with the bulk solution and (ii) relaxation phenomena in the surface layer. Relaxation of surface tension by diffusion is the most

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Figure 4. Effects of the velocity of compression on the evolution of the surface tension of β-casein adsorption layers formed at the air/buffer interface. The β-casein concentration in the bulk is 10 mg/L. The time of compression T was (9) 1 (s), (4) 10 (s), (2) 20 (s), (O) 40 (s), and (×) 60 (s). ∆πne is the nonequilibrium and ∆πe the equilibrium part of the surface pressure variation after compression of the adsorption layer.

Figure 3. Effects of a fast compression (1 s) on the surface tension (γ) evolution of adsorption layers of β-casein at surface pressures of 11 mN/m (a) and 19 mN/m (b).

common relaxation mechanism in soluble monolayers and has been modeled quantitatively for single-surfactant solutions.43,44 However, in the case of β-casein, it was shown that the dilational viscosity in time scales from 1 to 1000 s cannot be explained by diffusional relaxation.36 In contrast, several relaxation processes can take place other than diffusion, for example, (i) slow reorientation of molecules after adsorption; (ii) complex formation and phase transition in the surface; and (iii) formation or destruction of three-dimensional structures, either in the surface or in the adjoining solution.36,46 The data of the present study do not give information in favor of one mechanism or another. Effects of the Temperature on the Dilational Modulus. To check the effect of temperature on the relaxation behavior of β-casein adsorption layers, deformations were performed on layers with surface pressures of 7.6 and 8.5 mN/m at 10 and 60 °C (Figure 7). Similar experiments were carried out also at higher surface pressures of 17.8 and 17.2 mN/m at 10 and 60 °C, respectively (Figure 8). The elastic deformations at all

Figure 5. Graphical determination of the equilibrium and nonequilibrium parts of the elasticity. The measurements were recorded during the relaxation (T < t < ∞) of β-casein adsorption layers at the air-buffer interface with a velocity of compression of 0.45 (b) and 0.025 (O) mm2 s-1, respectively. These data are those of Figure 4 for T ) 20 and T ) 60 s, respectively. They are plotted according to [9].

pressures are much smaller at 60 °C than at 10 °C. This should indicate that hydrogen bonds, van der Waals attractions, and other attractions broken by temperature have a major role in the elastic behavior of the layer. Moreover, no viscous component is detected at surface pressures of 7.6 and 8.5 mN/m (Figure 7), while a nonequilibrium component of the same order of magnitude and with a similar decay time (∼20 s) occurs at 17.8 and 17.2 mN/m (Figure 8) whatever the temperature.

Effect of Frequency and Temperature on Rheology

Langmuir, Vol. 19, No. 1, 2003 77

Table 1. Kinetics and Rheological Parameters of β-Casein Adsorption Layer Relaxationa T (s)

t (s)

Ee (mN/m)

Ene (mN/m)

∆πe (mN/m)

∆πne (mN/m)

∆A/Ai

1 10 20 40 60

24 42 48 73 17

6.9 7.0 7.0 7.1 7.0

6.3 5.9 5.3 3.4 2.9

0.82 0.63 0.63 0.64 0.63

0.76 0.53 0.48 0.31 0.26

0.12 0.09 0.09 0.09 0.09

a The adsorption layer in quasi-equilibrium before compression had a surface pressure of 23 mN/m.

Figure 8. Effect of temperature on the surface tension (γ) change after a fast compression (1 s) of β-casein adsorption layers at surface pressures of 17.8 mN/m (O) at 10 °C and 17.2 mN/m (0) at 60 °C. The β-casein concentration in the bulk is 1 mg/L. ∆πe is the equilibrium and ∆πne the nonequilibrium part of the surface pressure variation after compression of the adsorption layer. The surface tension of the aqueous buffers is 74.2 and 65 mN/m at 10 and 60 °C, respectively.

Figure 6. Effect of frequency on the relationship between the dilational modulus, , and the surface pressure, π. The dilational modulus and the surface pressure were recorded simultaneously during the adsorption of β-casein from a 10 mg/L solution. The frequencies were (O) 0.1, (×) 0.05, and (∆) 0.025 s-1.

Figure 9. Effect of temperature on the relationship between the dilational modulus, , and the surface pressure, π. The dilational modulus and the surface pressure were recorded simultaneously during the adsorption of β-casein from a 10 mg/L solution. The period of the oscillation is 20 s. The temperatures were (b) 10 °C, (4) 20 °C, (O) 40 °C, and (+) 60 °C. Inset: effect of temperature on the value of y.

Figure 7. Effect of temperature on the surface tension (γ) change after a fast compression (1 s) of β-casein adsorption layers at surface pressures of 7.6 mN/m (O) at 10 °C and 8.5 mN/m (0) at 60 °C. The β-casein concentration in the bulk is 10-2 mg/L. The surface tension of the aqueous buffers is 74.2 and 65 mN/m at 10 and 60 °C, respectively.

Thus, finally, temperature does not seem to modify much the effect of surface pressure on the relaxation behavior of the layers. As a consequence, it is accepted that the

same frequency can be used to determine the relation between the dilational modulus and the surface pressure in quasi-equilibrium conditions whatever the temperature between 10 and 60 °C. The period used was 20 s (as determined in the preceding section) at 20 °C. Temperature has an important effect on the relation between the dilational modulus and the surface pressure (Figure 9). Referring to the theory24 for surface pressures between zero and a maximum close to 7 mN/m, the linear part of these curves is indicative of a semidilute regime of the two-dimensional polymer blocks. The next decrease of the dilational modulus corresponds to a crossover between the previous two-dimensional-dominated

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semidilute regime and a semidilute regime dominated by the behavior of quasi-brushes. In the theory, this transition is very short but it is smoothed with real polymers. The slope y corresponding to the two-dimensional semidilute regime at low surface pressure is significantly lowered by the temperature increase. Referring to the thermodynamic model,14,22,24-26 this lowering of the slope y is indicative of a decrease of the fractal dimension of the blocks forming the two-dimensional pancakes at the border between air and water. These results completely confirm and extend previous limited data28 on the effect of temperature on the y exponent of β-casein layers. At 10 °C, y ) 6.6, a value which is intermediate between that of θ conditions (y ) 8) and that of a two-dimensional self-avoiding walk (y ) 3). Increasing the temperature until 60 °C leads to a value of y ) 3.3, which is close to that of a self-avoiding walk. Thus, in the first case attractions between the monomers result in a partially collapsed chain while in the second case these noncovalent bonds are mostly broken. Concerning the nature of these bonds, the two-dimensional blocks at the interface are expected to be enriched in hydrophobic side chains which are at the origin of the driving force for adsorption. However, since the bonds are ruptured by a temperature increase, they are not dominated by hydrophobic interactions. It should be concluded that these bonds are largely hydrogen bonds or van der Waals interactions.

Hambardzumyan et al.

compression (or expansion) of the surface area of the adsorption layers. Consequently, at these surface pressures, the adsorption layers of β-casein are viscoelastic. Moreover, it is possible to measure only the elastic part of the viscoelastic modulus, by choosing a period equal to or larger than the relaxation time of the adsorption layers (∼20 s). In a second step, the effect of temperature was examined on the dilational behavior of β-casein adsorption layers. The elastic deformations decrease with temperature at all surface pressures, while at surface pressures larger than 17 mN/m the nonequilibrium component is of the same order of magnitude and has a similar decay time (∼20 s) whatever the temperature. The /π curves measured at different temperatures show that the slope y decreases significantly when the temperature increases. Referring to the block copolymer model, this slope variation is indicative of a decrease of the fractal dimension of the two-dimensional blocks. It can be inferred from this change of fractal dimension that the attractions between the monomers observed at 10 °C (y ) 6.6) are ruptured by the temperature increase. This may suggest that the attractions between monomers are probably dominated by hydrogen bonds or van der Waals attractions. Moreover, hydrophobic interactions do not play a major role in this phenomenon since they would have been increased by a temperature rise.

Conclusions In this work, the surface rheological behavior of β-casein adsorption layers was studied at the air/aqueous buffer interface. The results show that at high surface pressure (g16 mN/m), a significant relaxation is observed after a

Acknowledgment. The financial support and a postdoctoral grant to A.H. of Re´gion Champagne-Ardenne are gratefully acknowledged. LA020599B