β-Casein and Symmetrical Triblock Copolymer (PEO−PPO−PEO

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β-Casein and Symmetrical Triblock Copolymer (PEO-PPO-PEO and PPO-PEO-PPO) Surface Properties at the Air-Water Interface Arayik Hambardzumyan,† Ve´ronique Aguie´-Be´ghin,† Mohamed Daoud,‡ and Roger Douillard*,† INRA/URCA, UMR FARE, Centre de Recherche en Environnement et Agronomie, 2 Espl. Roland Garros, BP 224, 51686 Reims, Cedex 2, France, and Service de Physique de l’Etat Condense´ C.E.A. Saclay, 91191 Gif/Yvette Cedex, France Received July 19, 2003. In Final Form: October 16, 2003 A comparison of β-casein and symmetrical triblock copolymer (PEO-PPO-PEO and PPO-PEO-PPO) adsorption layer properties at the air-water interface has been carried out by bubble tensiometry and ellipsometry. It has been verified that the equation of state parameters (π ∼ Γy) obtained from surface pressure (π) and ellipticity in Brewster conditions (FjB), which is proportional to the surface concentration (Γ) data, are the same as those obtained from dilational modulus  and π data. These two consistent approaches give further support to the theoretical model of block copolymers which has been previously developed for protein adsorption at fluid interfaces. It is shown that the interfacial behavior of the copolymer adsorption layer changes strongly as a function of the length of the hydrophilic and hydrophobic block sequences. The theoretical model may be used for the interpretation of the adsorption properties of the synthetic copolymers only when the size of the blocks is large enough. In the case of block copolymers, the coil is in a self-avoiding walk conformation (y ) 3) whatever the temperature, while in the case of β-casein, the polypeptide chain is partly collapsed at room temperature due to thermolabile noncovalent bonds. At the end of the first semidilute regime, there is clear evidence for a crossover toward a second semidilute regime for synthetic copolymers as well as for β-casein but it is presently only partially characterized.

Introduction The adsorption of proteins at the air-liquid and liquidliquid interfaces plays a significant role in the stabilization of foams and emulsions.1-6 The relationships between structure and properties are of major importance for the understanding of the mechanism of the adsorption of these molecules.7,8 It was demonstrated that small differences in protein structure can induce major changes in surface properties. For instance, the genetic variants A, B, and C of β-lactoglobulin (globular whey protein) differ in their amino acid sequence at only three positions along the protein chain, but their adsorption behaviors9 and emulsion properties10 are significantly different. The substitution of an aspartic acid residue in variant A by a glycine in variant B at position 64 appears to increase the rate * Corresponding author. Tel: 33 (0)3 26 77 35 94. Fax: 33 (0)3 26 77 35 99. E-mail: [email protected]. † INRA/URCA, UMR FARE, Centre de Recherche en Environnement et Agronomie. ‡ Service de Physique de l’Etat Condense ´ C.E.A. Saclay. (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) Aluko, R. E.; McIntosh, T.; Reaney, M. Food Res. Int. 2001, 34, 733. (4) Schokker, E. P.; Bos, M. A.; Kuijpers, A. J.; Wijnen, M. E.; Walstra, P. Colloids Surf., B 2002, 26, 315. (5) Caessens, P. W. J. R.; Visser, S.; Gruppen, H.; van Aken, G. A.; Voragen, A. G. F. Int. Dairy J. 1999, 9, 347. (6) Dickinson, E. An Introduction to Food Colloids; Oxford University Press: Oxford, 1992. (7) Caessens, P. W. J. R.; de Jongh, H. H. J.; Nordh, W.; Gruppen, H. Biochim. Biophys. Acta 1999, 1430, 73. (8) Dickinson, E. Colloids Surf., B 2001, 20, 197. (9) Mackie, A. R.; Husband, F. A.; Holt, C.; Wild, P. J. Int. J. Food Sci. Technol. 1999, 34, 509. (10) Euston, S. R.; Robyn, L.; Hirst, R. L.; Hill, J. P. Colloids Surf., B 1999, 12, 193.

of adsorption and the surface dilational modulus in the case of variant B.9 Although variant C has poorer emulsification properties than variants A and B, its stability to coalescence is larger.10 The physicochemical properties, including conformation of the protein and consequently its surface properties, can be changed also by chemical modifications.11-15 The adsorption of proteins at fluid interfaces is currently interpreted in the frame of the polymer theories8,16-28 using theoretical models, which are, for instance, multiblock copolymers.22,28,29 Each block is made of a sequence A of ZA hydrophobic and of a sequence B of ZB hydrophilic (11) Krause, J. P.; Kra¨gel, J.; Schwenke, K. D. Colloids Surf., B 1997, 8, 279. (12) Krause, J. P. Ind. Crops Prod. 2002, 15, 221. (13) Matsudoni, N.; Kato, A.; Kobayashi, K. Agric. Biol. Chem. 1988, 52, 1973. (14) Kato, A.; Tanaka, A.; Lee, Y.; Matsudoni, N.; Kobayashi, K. J. Agric. Food Chem. 1987, 35, 285. (15) Darewicz, M.; Dziuba, J.; Caessens, P. W. J. R.; Gruppen, H. Biochimie 2000, 82, 191. (16) Ligoure, C. J. Phys. II 1993, 3, 1607. (17) Leclerc, E.; Daoud, M. Macromolecules 1997, 30, 293. (18) Zheng, Y. C. J. Chem. Phys. 2000, 112, 8665. (19) Baranowski, R.; Whitmore, M. D. J. Chem. Phys. 1995, 103 (6), 2343. (20) Marques, C. M.; Joanny, J. F. Macromolecules 1989, 22, 1454. (21) Ligoure, C. Macromolecules 1996, 29, 5459. (22) Aguie´-Be´ghin, V.; Leclerc, E.; Daoud, M.; Douillard, R. J. Colloid Interface Sci. 1999, 214, 143. (23) Vilanove, R.; Poupinet, D.; Rondelez, F. Macromolecules 1988, 21, 2880. (24) Poupinet, D.; Vilanove, R.; Rondelez, F. Macromolecules 1989, 22, 2491. (25) Sedev, R. Colloids Surf., A 1999, 156, 65. (26) Alexander, S. J. Phys. 1977, 38, 983. (27) Mun˜oz, M. G.; Monroy, F.; Ortega, F.; Rubio, R. G.; Langevin, D. Langmuir 2000, 16, 1083. (28) Aschi, A.; Gharbi, A.; Bitri, L.; Calmettes, P.; Daoud, M.; Aguie´Be´ghin, V.; Douillard, R. Langmuir 2001, 17, 1896. (29) Hambardzumyan, A.; Aguie´-Be´ghin, V.; Panaı¨otov, I.; Douillard, R. Langmuir 2003, 19, 72-78.

10.1021/la030294c CCC: $27.50 © 2004 American Chemical Society Published on Web 01/06/2004

Surface Properties of β-Casein and Copolymers

monomers. The structure of the interfacial layer is determined as a function of R (R ) ZA/ZB) and of the surface concentration using scaling law arguments. The power law form of the equation of state (π ∼ Γy, where π is the surface pressure and Γ is the surface concentration) points to the signification of the exponent y. It was shown that this exponent is directly related to the fractal dimension of the two-dimensional organization of the polymer at the interface and it can be conveniently determined from the relation between the dilational modulus, , and the surface pressure:  ) yπ.22,28-30 In the case of β-casein, a very good agreement was found between the theoretical model covering several semidilute regimes in the interfacial layer and the experimental data.28,29-30 However, the question arises of the reasons for this agreement: is it fortuitous or does it correspond really to the physicochemical nature of the adsorbed β-casein? To answer this question, some elements may be found in the comparison of the adsorption properties of β-casein, which can be modeled as a diblock30 or as three irregular alternating hydrophilic-hydrophobic diblocks (multiblock),28 and of synthetic triblock copolymers PEO-PPO-PEO (hydrophilic-hydrophobic-hydrophilic; PEO, poly(ethylene oxide); PPO, poly(propylene oxide)). The adsorption behavior of the latter has been well characterized.27,31-36 Thus, Mun˜oz et al.27 reported that despite the solubility of these polymers, the central more hydrophobic PPO block may act as an anchoring element at the air-water interface, while the more hydrophilic lateral PEO blocks dissolve in the bulk solution at sufficiently high surface concentration. According to these authors, when the “interchain space” between flat adsorbed polymer at the interface is less than the Flory radius of the molecule in the solution, the chains stretch away from the surface into the solvent, while remaining attached to the interface by an anchoring hydrophobic block. This structure is commonly called a polymer brush. Ellipsometric measurements indicate that the thickness of the adsorbed copolymer layer is growing with the number of PEO segments in the chain in agreement with the simple brush model.25,27,34-36 Very recently the results were confirmed, also by a neutron reflectivity study of PEOPPO-PEO adsorption layers at the air/water interface.36 Referring to these data on β-casein and on these organic block copolymers, the goal of this work is to compare the properties (or the equation of state) of β-casein and of synthetical triblock copolymers PEO-PPO-PEO and PPO-PEO-PPO adsorbed at the air/liquid interface by tensiometry and ellipsometry measurements in order to understand the mechanism of the adsorption of protein. This comparison should give some elements of the diblock or multiblock copolymer behavior of β-casein. Material and Methods Materials. High-purity water (Elgastat Maxima-HPLC) was used throughout this work. 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 (30) Puff, N.; Cagna, A.; Aguie´-Be´ghin, V.; Douillard, R. J. Colloid Interface Sci. 1998, 208, 405. (31) Nystro¨m, B.; Walderhaug, H. J. Phys. Chem. 1996, 100, 5433. (32) Sedev, R.; Ne´meth, Zs.; Ivanova, R.; Exerova, D. Colloids Surf., A 1999, 149, 141. (33) Alexandridis, P.; Hatton, T. A. Colloids Surf., A 1995, 96, 1. (34) Barnes, T. J.; Prestidge, C. A. Langmuir 2000, 16, 4116. (35) Sedev, R.; Exerowa, D. Adv. Colloid Interface Sci. 1999, 83, 111. (36) Sedev, R.; Steitz, R.; Findenegg, G. H. Physica B 2002, 315, 267. (37) Mercier, J. C.; Maubois, J. L.; Poznanski, S.; Ribadeau-Dumas, B. Bull. Soc. Chim. Biol. 1968, 50, 521.

Langmuir, Vol. 20, No. 3, 2004 757 Table 1. Chemical Properties of the Triblock Copolymers PEOxPPOyPEOx polymers

M (g/mol)

PEO %

x-y-x

I II III IV V

2000 2900 5800 8350 5000

12 46 36 84 100

2-30-2 13-30-13 20-70-20 76-30-76 N(PEO) ) 113

PPOyPEOxPPOy polymers

M (g/mol)

PEO %

y-x-y

VI VII VIII

3300 2700 2000

12 46 58

25-7-25 14-24-14 8-22-8

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 β-casein in buffer solution is E1cm1% ) 4.6 at 278 nm. The PEO-PPO-PEO and PPO-PEO-PPO triblock copolymers (Synperonic), available in a range of molecular mass and of PPO/PEO ratios, were obtained from Sigma-Aldrich. Their molecular masses and structures are given in Table 1. The monodispersity of these compounds was verified by gel permeation chromatography. Surface Tension Measurements. A bubble (or drop) tensiometer (IT Concept, Longessaigne, France) was used38-40 for static and dynamic surface tension measurements. 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. The needle is attached to a syringe whose plunger is precisely controlled by a micrometer screw driven by an electric motor. 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.41 The surface pressure, π, is, as usual, the difference between the surface tension of the pure solvent γ0 and that of the solution with surface-active molecules γ. Dilational Modulus. The surface dilational modulus, , is defined as the ratio between the variation of surface tension, dγ, and the relative change in surface area, dA/A ) d ln(A):42-44

)

dπ dγ )d ln(A) d ln(A)

(1)

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 two times a second. A Fourier transform of the data was performed, and only the first harmonic was retained. It was verified that the calculated dilational modulus was independent of the relative variation of the area (∆A/A) when this quantity was less than 15% of the mean area.29 (38) Cagna, A.; Esposito, G.; Rivie`re, C.; Housset, S.; Verger, R. 33rd International Conference on Biochemistry of Lipids, Lyon, France, 1992. (39) Saulnier, P.; Boury, F.; Malzert, A.; Heurtault, B.; Ivanova, T.; Cagna, A.; Panaı¨otov, I.; Proust, J. E. Langmuir 2001, 17, 8104. (40) McLeod, C. A.; Radke, C. J. J. Colloid Interface Sci. 1993, 160, 435. (41) Labourdenne, S.; Gaudry-Rolland, N.; Letellier, S.; Lin, M.; Cagna, A.; Esposito, G.; Verger, R.; Rivie`re, C. Chem. Phys. Lipids 1994, 71, 163. (42) 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. (43) Langevin, D. Adv. Colloid Interface Sci. 2000, 88, 209. (44) 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.

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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.29,42-47 In the experimental conditions retained, the viscous component is negligible.29 Ellipsometry. All the measurements were done using a spectroscopic phase modulated ellipsometer (UVISEL, Jobin Yvon, Longjumeau, France). It was equipped with a xenon arc lamp. Both the polarizer and the analyzer were set to the 45° configuration angle. The photoelastic modulator, activated at the 50 kHz frequency, was set to the 0° configuration orientation. The incidence angle is set to 53.4°. All measurements were done at the air/liquid interface in an air-conditioned room at 20 ( 1 °C. The two ellipsometric angles Ψ and ∆48-50 are linked to the two reflectivity coefficients rp and rs, respectively, in the directions parallel and perpendicular to the incidence plane, leading to the determination of the complex ellipticity, F, by

F ) rp/rs ) tan Ψ exp(i∆) ) F˜ + iFj

(2)

For an ideal dioptre, at a particular angle θΒ (Brewster angle), the reflection of the wave with the electric field parallel to the incidence plane vanishes, ∆ ) π/2 and F ) 0, and θΒ is defined as tan θΒ ) n2/n0, where n0 and n2 are the refractive indexes of air and substrate, respectively. For a real dioptre, the complex ellipticity measured at this angle is very sensitive to any structure present at the interface. Experimentally, ∆ * π/2 and the ellipticity passes through a positive minimum value which is due to the roughness of the interface (capillary waves on a liquid surface). When an adsorption layer occurs with a thickness much smaller than the wavelength λ, at the Brewster angle, the coefficient of ellipticity FjB is negative and equal to

FjB ≈ tan Ψ sin ∆

(3)

The sign ≈ means that the roughness and the anisotropy are negligible compared to the contribution of the adsorption layer.48-51 From the Drude equation52 and as a first approximation, the Brewster angle ellipticity is proportional to the surface concentration and increases as a function of the square of the layer index:53

FjB ∼ Γ

(4)

Theoretical Background for Polymer Adsorption. A model has been developed for proteins and other copolymers at interfaces assuming an alternating hydrophilic/hydrophobic multiblock structure.17,22,28-30 A basic feature of this thermodynamic model is that it assumes a quasi-equilibrium state. Using the scaling law approach of polymers, the thermodynamic model allows one to make a description of the variation of the surface pressure (π) as a function of the surface concentration (Γ):

π = kBTΓy

(5)

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 polymer at the beginning of its adsorption at the interface, and Γ is the surface concentration defined as

Γ ) m/A

(6)

where m is the mass of polymer adsorbed at the interface of area A. (45) Lucassen-Reynders, E. H.; Cagna, A.; Lucassen, J. Colloids Surf., A 2001, 186, 63. (46) Ca´rdenas-Valera, A. E.; Bailey, A. I. Colloids Surf., A 1993, 79, 115. (47) Benjamins, J.; Cagna, A.; Lucassen-Reynders, E. H. Colloids Surf., A 1996, 114, 245. (48) Azzam, R. M. A.; Bashara, N. M. Ellipsometry and Polarized Light; Elsevier Science B.V.: Amsterdam, 1987. (49) Pe´ron, N.; Cagna, A.; Valade, M.; Marchal, R.; Maujean, A.; Robillard, B.; Aguie´-Be´ghin, V.; Douillard, R. Adv. Colloid Interface Sci. 2000, 88, 19. (50) Keddie, J. L. Curr. Opin. Colloid Interface Sci. 2001, 6, 102.

Figure 1. Theoretical model of the variation of the surface pressure (Π) as a function of the surface concentration (Γ) in log scale in each of the three cases (I, II, and III) of the phase diagram (ref 22). Cases I, II, and III correspond to small, medium, and large values of R (the ratio of the number of hydrophobic (ZA) to that of hydrophilic (ZB) monomers in the blocks). Insert: Variation of the dilational modulus, , as a function of the surface pressure in the same cases. The slopes of the lines in cases I, II, and III are the y values of eqs 5 and 7. Abbreviations: Γ/pol, overlap concentration of the polymer / chains; Γblock , overlap concentration of the block sequences; Γ/A, overlap surface concentration of the A block sequences; Γ/B, overlap surface concentration of the B block sequences; Γ// A, overlap surface concentration of the monomers of the A block sequences with thickness growth in a quasi-melt. When the surface concentration increases, the interface enters in successive semidilute regimes whose natures are determined as a function of the surface concentration and of the ratio (R) between the hydrophobic (ZA) and hydrophilic (ZB) monomers of the hydrophobic (A) and hydrophilic (B) sequences, respectively (Figure 1) (the ratio ZA/ZB ) R is the parameter of the chemical structure of the polymer).22 A key parameter of the model is the exponent y (eq 5) linked to the fractal dimension of the blocks in the dilute regime and to the regime of the interface. It is also the proportionality coefficient between  and π28-30 (Figure 1 insert):

 ) yπ

(7)

When the two-dimensional blocks impose their behavior to the interfacial layer, y g 3. When the surface tension properties of the interface are dominated by three-dimensional coils forced to form quasibrushes (they are forced to have an extension in a direction perpendicular to the interface), y ) 1. A very good agreement was found between the experimental variation of  as a function of π for β-casein and the theoretical predictions in the case of a polymer where the hydrophobic and the hydrophilic blocks have the same order of length (case II of Figure 1).28,30 However, the experimental determination of y using eq 5 has not yet been performed with other multiblock copolymers.

Results and Discussion In the first part, a comparison is made of two experimental approaches to the equation of state, in the case of (51) Meunier, J. J. Phys. 1987, 48, 1819. (52) Drude, P. The Theory of Optics; Longmans, Green, and Co.: New York, 1920. (53) Sausse, P.; Aguie´-Be´ghin, V.; Douillard, R. Langmuir 2003, 19, 737.

Surface Properties of β-Casein and Copolymers

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Figure 2. Time course of the surface tension during β-casein adsorption when the area of the bubble is submitted to a sinewave deformation. A is the area of the bubble (mm2). This allows simultaneous determination of the surface tension and dilational modulus.

polymers adsorbed at a fluid interface, using either the surface pressure as a function of the surface concentration, approximated by the ellipticity, or the dilational modulus as a function of the surface pressure. These approaches concern β-casein and symmetric triblock copolymers of general structure PEO-PPO-PEO. In the second part, we compare the surface properties of β-casein and of triblock copolymers with the general structures PEOPPO-PEO or PPO-PEO-PPO. Experimental Approaches to the Equation of State. The surface tension and dilational modulus of adsorption layers of β-casein and of two PEO-PPO-PEO copolymers (2-30-2 or polymer I, and 76-30-76 or polymer IV, Table 1) were determined during the time course of a slow adsorption at the air/buffer interface (Figure 2). It was verified that the measured properties were independent of the initial bulk concentration and of the frequency used in the case of the dilational modulus as previously described.29 In addition to the dilational modulus, we also measured the surface pressure and the ellipticity in Brewster conditions. For the equation of state approach, the surface pressure and ellipticity data were obtained using a Wilhelmy plate and a spectroscopic ellipsometer operated on a single Petri dish. The dilational modulus and the corresponding surface pressure data were obtained using a bubble tensiometer as previously described29 (Figure 2). The results plotted in Figures 3-5 deserve several comments. Due to the theoretical scaling law approach, the interest is focused on linear parts of the log(π)/log(FjΒ) (eq 5) or /π (eq 7) plots. In the log-log plot used for the surface concentration and pressure data, the slope dπ/dFjB is the same as the one obtained from dπ/dΓ since FjB and Γ are proportional to each other, even if the proportionality constant is unknown. Values of y. In the case of β-casein (Figure 3), the surface concentration approach gives two clear values of 4.5 ( 0.7 and 0.40 ( 0.01 which compare favorably with the values of 5.2 ( 0.3 and 0.66 ( 0.07 obtained from the dilational modulus approach. A value of 0.40 ( 0.06 at surface pressures below 0.1 mN/m is also ascribed in the surface concentration approach but has no counterpart in the dilational modulus one; it could correspond to the dilute regime. For polymer I (Figure 4), a single value of 3 ( 1

Figure 3. Brewster ellipticity |FjB| (b) and dilational modulus  (O) as a function of the surface pressure π for β-casein adsorption layers formed at the air-aqueous buffer interface. (a)  and |FjB| as a function of π. (b) The log scale variation of π as a function of |FjB|; the insert details the region of π between 10 and 20 mN/m. The β-casein volume concentration in the bulk was 10 mg/L at 20 °C. Errors on values of the exponents were calculated from three repetitions.

merges from the surface concentration approach for π in the range 0-20 mN/m. The same value is obtained in the π range from 0 to 6 mN/m in the dilational modulus approach (y ) 2.7 ( 0.1) where a transition toward other regimes is also obvious for surface pressures larger than 6 mN/m. For polymer IV (Figure 5), two values of 2.7 ( 0.1 and ∼0.5 from the dilational modulus approach and 2 ( 1 and 0.38 ( 0.05 from the surface concentration one are obtained, respectively, but a transition between two semidilute regimes is clearly noticed in the  case, in the π range from 5 to 10 mN/m, while it is very slightly observed in the FjB case. It can be concluded that the two approaches give consistent results for the semidilute regimes. This is also a confirmation that the dilational modulus approach deals with data obtained in conditions where the equilibrium hypothesis applies during the oscillation of the area. Scattering of the Experimental Data. The ellipticity data have a much larger scattering than the dilational modulus ones, either plotted as a function of the surface pressure or in log-log plots. Thus, the dilational modulus approach

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Figure 4. Brewster ellipticity |FjB| (b) and dilational modulus  (O) as a function of the surface pressure π for PEO-PPOPEO (2-30-2) (polymer I) adsorption layers formed at the airwater interface. (a)  and |FjB| as a function of π. (b) The log scale variation of π as a function of |FjB|. The copolymer volume concentration in the bulk was 5 × 10-4 g/L at 20 °C. Errors on values of the exponents were calculated from three repetitions.

allows a more accurate description of the phenomena than the surface concentration one with the presently available technique. Transitions between Semidilute Regimes. The transition range covers 7 mN/m for β-casein and 6 mN/m for polymer IV in the  approach. It seems practically instantaneous in the Γ approach, but this is probably due to the log-log plot (Figure 3 insert). For β-casein, the transition range is more subtle since a slight curvature is observed at 15 mN/m (Figure 3 insert), while in the  approach, it is clearly shown by the decrease of the dilational modulus from 28 to 10 mN/m in the surface pressure range from 7 to 15 mN/m. Similarly, no transition is noticed for polymer I in the Γ approach while a transition is expected in the range 6-22 mN/m in the other approach. These differences may be due to the previously noticed scattering of the ellipticity data or to the fact that a slope difference in the Γ approach is less easy to notice than an ordinate difference ( approach) or to the difference of methods used for surface tension recording (Wilhelmy plate and Petri dish or bubble tensiometer). Nevertheless, it may be concluded that the dilational modulus approach provides a more detailed

Hambardzumyan et al.

Figure 5. Brewster ellipticity |FjB| (b) and dilational modulus  (O) as a function of the surface pressure π for PEO-PPOPEO (76-30-76) (polymer IV) adsorption layers formed at the air-water interface. (a)  and |FjB| as a function of π. (b) The log scale variation of π as a function of |FjB|. The copolymer volume concentration in the bulk was 5 × 10-4 g/L at 20 °C. Errors on values of the exponents were calculated from three repetitions.

picture of the behavior of the adsorption layers of the polymers under investigation. Absolute Values of Ellipticity. Comparing the data for β-casein and for the block polymers, we find that the values of the ellipticity are roughly 3 times smaller for the polymer than for the protein (Figures 3-5). This is directly linked with the equation of state of these molecules (Figure 6). This may be due to the fractal dimension of the organic polymer which is smaller than that of the protein (see below) and to the structure of the molecules which include more hydrophilic segments in the case of β-casein than in the case of the organic polymers. In this respect, it should be stressed that the ellipticity reached in the case of polymer IV is larger than in the case of polymer I which has less hydrophilic segments. On the contrary, if the data are drawn with respect to the PPO contribution to the ellipticity (Figure 6 insert), the value reached in the case of polymer IV is smaller than in the case of polymer I. Thus, a part of the hydrophilic segments must contribute to the 2-D structure of the block copolymers that is responsible for the slope of the log π/log Γ relation (eq 5). Dilational Modulus and Surface Pressure Comparison of β-Casein and Triblock Copolymer Surface Properties. According to the results of the preceding

Surface Properties of β-Casein and Copolymers

Figure 6. Comparison of the equations of state of β-casein (4) and of PEO-PPO-PEO copolymers I (2-30-2) (0) and IV (7630-76) (b). π versus |FjB| is shown in logarithmic scale. Insert: the same data are plotted as a function of the PPO contribution to the Brewster ellipticity for the block copolymers.

Figure 7. Relationship between the dilational modulus, , and the surface pressure, π, for the PEO-PPO-PEO triblock copolymers I (4), II (b), III (0), and IV (O) and for PEO, polymer V (×) (Table 1). The dilational modulus and the surface pressure were recorded simultaneously during the adsorption of these polymers at the air-water interface at 20 °C. The frequency and amplitude of oscillations were 0.1 s-1 and 10% of the initial area, respectively. The concentration of the copolymer in the bulk was 1 mg/L.

section, the comparison of the surface properties which are linked to the equation of state is focused on experimental data presenting the evolution of  versus π. In the first step, the main properties of two kinds of triblocks, PEO-PPO-PEO and PPO-PEO-PPO, and of a homopolymer PEO (Table 1) are reported. Then these properties are compared with those of β-casein to check their possible similarities. Effects of the Structure of Synthetic Polymers on Their Surface Properties. The data of Figures 7 and 8 show that PEO (polymer V) has surface properties since it may produce a surface pressure of 7 mN/m and a dilational modulus of nearly 10 mN/m with a bulk concentration of

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Figure 8. Relationship between the dilational modulus, , and the surface pressure, π, for the PPO-PEO-PPO triblock copolymers VI (4), VII (b), VIII (O), and V (×) (Table 1). The dilational modulus and the surface pressure were recorded simultaneously during the adsorption of these copolymers at the air-water interface at 20 °C. The frequency and amplitude of oscillations were 0.1 s-1 and 10% of the initial area, respectively. The concentration of these copolymers in the bulk was 1 mg/L.

Figure 9. Effect of the percentage of PPO in the triblock polymers on the maximum surface pressure (b) and on the maximum of the dilational modulus (O). The maximum value data were extracted from Figures 7 and 8.

1 mg/L. These surface properties are well-known from the literature.54,55 The polymers which are mostly built of 88% PPO, either polymer I with its PEO motifs at each end or polymer VI with its PEO block in the middle of the chain, exhibit large surface properties with a modulus close to 25 mN/m and a maximum surface pressure of also 25 mN/m (Figure 9). When the percentage of PEO blocks is increased in the polymer chain, the maximum surface pressure and the maximum dilational modulus tend to decrease and finally get close to those of the homopolymer PEO, polymer V (Figure 9). Some details of the relations between  and π seem to be linked with the details of the structure such as the molecular mass and the relative situation of the PEO and PPO blocks (Figures 7 and 8). (54) Kim, M. W.; Cao, B. H. Europhys. Lett. 1993, 24, 229. (55) Baekmark, T. R.; Elender, G.; Lasic, D. D.; Sackmann, E. Langmuir 1995, 11, 3975.

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Figure 10. Effect of the size of the PEO blocks on the equation of state. π versus |FjB| is shown in linear scale. PEO-PPO-PEO copolymers I (2-30-2) (b) and IV (76-30-76) (O). Insert: the same data are plotted as a function of the PPO contribution to the Brewster ellipticity for the block copolymers.

Figure 11. Schematic representation of the conformation of β-casein in the adsorption layer in the first semidilute regime. The hydrophobic and hydrophilic sequences are drawn in gray and black lines, respectively.

Thus, the general trend seems to be that PPO blocks induce the formation of a stiff layer (high pressure, high modulus) while PEO blocks which have more affinity for water induce the formation of a smooth layer (low pressure, low modulus), as evidenced from the data of Figures 4 and 5 replotted in Figure 10 either as a function of total surface concentration or scaled with respect to the PPO surface concentration (Figure 10 insert). Analogies with the Multiblock Copolymer Model. This model22 developed for large multiblock copolymers such as β-casein (Figure 11) provides an interpretation of some features of the equation of state for surface-adsorbed macromolecules. The slope of the line joining the origin to any point of the experimental data in the /π representation is equal to the slope of the tangent to the equation of state curve in log-log coordinates (Figure 1). Thus the linear part, starting from the origin, of all the curves of Figures 7 and 8 means that all the equations of state begin with a power law with exponent y of 2.7 ( 0.3 and 2.9 ( 0.1, respectively. These values of y are approximately equal to the theoretically predicted value of 3 for an interface in a purely 2-D semidilute regime for polymers forming 2-D coils in a selfavoiding walk (or excluded volume) conformation in the dilute regime. The same value holds experimentally for PPO or PEO coils. Thus, the use of this exponent is not very useful for the understanding of the effect of introducing more or less hydrophobic blocks in the structure of the polymer.

Hambardzumyan et al.

At the end of the purely 2-D regime, the theoretical model states that when a crossover occurs toward a regime dominated by the formation of quasi-brushes in the liquid phase (the thickness of the adsorption layer increases) there is a sharp decrease of  at practically constant π toward either a line with a slope equal to 1 or toward the x axis and then to the first bisectrix (Figure 1). The experimental data are expected to be smoothed because of the nonideality and especially the finite size of the actual polymers. Such a behavior is clearly observed only with polymer IV, with a minimum slope of 0.38 ( 0.05 (Figure 5). For the other copolymers, a quasi-brush growth is probably not to be expected because their hydrophilic blocks are too small. This 0.38 ( 0.05 value of the experimental exponent may be interpreted only as a “smoothing” of the zero value consistent with the increase of thickness of the hydrophobic coils before the formation of quasi-brushes in the water phase.22 This situation may occur only if the diameter of the hydrophilic coils is smaller than that of the hydrophobic ones at the end of the first semidilute regime of the blocks. This condition is fulfilled in the theory when R > 0.398ZB1/5, a value calculated as in ref 22 for a ZAZBZA triblock taking into account a numerical prefactor of 2 for the area covered by the hydrophilic loops. Using the number of chemical monomers for ZA and ZB, R ) 0.39 and 0.398ZB1/5 ) 0.95 for polymer IV (76-30-76). Thus the theoretical condition is not fulfilled by this triblock structure. However, the actual lengths of the hydrophilic and of the hydrophobic blocks are probably not those corresponding strictly to the chemical nature of the blocks since PEO has some affinity for the interface (Figures 7 and 8) and also for steric reasons, since a few EO units in the vicinity of the linkage with PPO may be expected to stick to the interface. Finally, the length of the block sticking to the interface will be longer than that of the only PPO block. Assuming that 14 EO units of each block contribute to the central PPO block, then R ) 0.93 and 0.398ZB1/5 ) 0.91. Consequently when at least 14 EO units contribute to the structure of the central block, the theory predicts a behavior similar to the one observed experimentally. The polymer is then in the conformation expected to exhibit a thickness growth of the hydrophobic coils before the formation of quasibrushes in the water phase, and in these conditions, the experimental data are similar to the /π representation of region III of Figure 1. Another reason for the differences between the theoretical model and the block copolymer behavior may be the small size of the hydrophobic blocks which may be ejected from the interface and stretch in the air when the surface pressure increases. To conclude this section, it can be stressed that the interface behavior of PEO-PPO triblocks is influenced by both the PEO and the PPO blocks and that their properties are moderately described by the multiblock theoretical model. An important feature is their behavior as 2-D excluded volume polymers in the first semidilute regime (Figure 12). In the case of β-casein, the properties of the polymer in this semidilute regime are between a θ polymer behavior and an excluded volume behavior.28 Moreover, at the end of this semidilute regime, both for β-casein and for block polymer IV, a crossover is noticed toward a regime tentatively identified as the increase of the thickness of the hydrophobic coils before the formation of quasi-brushes. Effects of Temperature. The effect of temperature on the equation of state representation of the surface properties of polymers IV (76-30-76) and III (20-7020) was monitored between 20 and 60 °C (Figure 13). No

Surface Properties of β-Casein and Copolymers

Figure 12. Schematic representation of the conformation of block copolymers adsorbed at the air/water interface: (a) PEOPPO-PEO I (2-30-2), (b) PPO-PEO-PPO VI (25-7-25), and (c) PEO-PPO-PEO IV (76-30-76). The hydrophobic and hydrophilic sequences are drawn in gray and black lines, respectively.

effect is noticed on the slope of the first semidilute regime which remains close to 2.9. On the contrary, in the case of β-casein, the same treatment induces a decrease of the slope of the same regime from 4.8 to 3.3,29 indicating a decrease of the fractal dimension of the 2-D coils of the protein probably driven by the rupture of hydrogen bonds. The fact that the slope of 2.9 ( 0.1 is constant for the triblock polymer is in favor of a polymer structure where no interactions occur between the statistical units, as expected from the chemical structure. This result is consistent both with the structure of the polymer and with the theoretical model used to interpret the data. The second significant feature of the effect of temperature on the surface properties is the increase of the smoothing of the crossover between the first semidilute regime and the second one which is suspected to occur for a surface pressure larger than 10 mN/m (Figure 13a). In the case of polymer III (20-70-20), the data which can be attributed to the second semidilute regime, for π larger than 10 mN/m, display a slope which decreases steadily between 10 and 60 °C. At 40 °C, this slope is close to 1 and the data coincide with the first bisectrix. Considering only the results at 40 °C, it could have been concluded that the data are completely consistent with the theoretical model of multiblock copolymers.22 If this was true, a temperature change should not have modified the coincidence between the data and the first bisectrix. It must be concluded that this coincidence is somehow fortuitous and that the data for π larger than 10 mN/m do not comply with the case of a quasi-brush regime of the hydrophilic blocks associated with a constant contribution of the hydrophobic blocks.

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Figure 13. Effect of temperature on the /π patterns of PEOPPO-PEO copolymers IV (76-30-76) (a) and III (20-70-20) (b). The temperature was (O) 20 °C, (b) 40 °C, and (4) 60 °C for (a) and ranged from 10 to 60 °C for (b).

Conclusion The comparison of the surface properties of β-casein and block PEO-PPO polymers points to several important results. (i) The experimental equation of state approaches using the surface concentration or the dilational modulus measurements give very close results for the exponents characterizing the various regimes. However, the surface concentration results exhibit a larger scattering of the data than those of the dilational modulus approach. Moreover, the logarithmic plot of the equation of state does not allow one to observe in detail the crossover range between various regimes. (ii) The surface properties of the PEO-PPO-PEO or PPO-PEO-PPO triblocks are dominated by the ratio between their PEO and PPO units. Some small differences may be linked to the detail of their structure. The theoretical multiblock copolymer model may apply to the interpretation of their properties only when the size of their blocks is large enough, a situation which does not seem to be often encountered in this study. (iii) At surface pressures between 0.1 and 10 mN/m, the ellipticity is roughly 3 times smaller for the polymer than for the protein. (iv) As expected from their chemical structures, the PEO and PPO copolymers behave like 3-D and 2-D excluded volume polymers while β-casein exhibits significant attractions between its monomers (probably hydrogen bonds). (v) For the synthetic copolymers as well as for β-casein, a crossover is clear toward a second semidilute regime which is presently not well characterized. Acknowledgment. The authors thank Re´gion Champagne-Ardenne (France) for financial support of this work. LA030294C