Static and Dynamic Properties of a Whey Protein Isolate and

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Ind. Eng. Chem. Res. 2002, 41, 2652-2661

Static and Dynamic Properties of a Whey Protein Isolate and Monoglyceride Mixed Films at the Air-Water Interface Juan M. Rodrı´guez Patino,* Ma. Rosario Rodrı´guez Nin ˜ o, and Cecilio Carrera Sa´ nchez Departamento de Ingenierıá Quı´mica, Facultad de Quı´mica. Universidad de Sevilla, C/Prof. Garcıá Gonza´ lez, s/nu´ m. 41012-Seville. Spain

The static and dilatational properties of mixed emulsifiers are of interest due to their importance in relation to dispersion formation and stability. In this work, we have used different and complementary interfacial techniques (surface film balance, Brewster angle microscopy, and interfacial dilatational rheology), to analyze the static (structure, morphology, reflectivity, and miscibility) and dynamic (surface dilatational properties) characteristics of whey protein isolate (WPI) and monoglyceride (monopalmitin or monoolein) mixed films spread on the air-water interface. The static and dynamic characteristics of the mixed films depend on monolayer composition and the surface pressure. At higher surface pressures, collapsed WPI residues may be displaced from the interface by monoglyceride molecules with important repercussions on the interfacial characteristics of the mixed films. A close relationship between interfacial dilatational rheology and changes in molecular structure, interactions, miscibility, and relaxation phenomena has been established from the frequency dependence of the surface dilatational properties. Introduction The formation of stable colloidal dispersions (emulsions, foams, etc.) is extremely important in the paint, petroleum, cosmetic, pharmaceutical, and food industries.1-4 To stabilize food emulsions and foams, emulsifiers (lipids, phospholipids, and proteins) must be placed at the interface, so they can form a film around droplets or bubbles, respectively. The chemical and physical properties of surface-active molecules are of great interest because they determine the colloidal stability of dispersed systems.5 However, the presence of proteins and lipids in the same system can result in instability as both types of surface-active molecules compete to form different types of adsorbed layers.6 The distribution of protein and lipids in food emulsions and foams is determined by competitive and cooperative adsorption between the two types of emulsifiers at the fluid-fluid interfaces, and by the nature of protein-lipid interactions, both at the interface and in bulk phase.6 Interactions between molecules of emulsifiers could affect the film structure and morphology7-9 and the relaxation phenomena in mixed films.10,11 Information about these phenomena would be very helpful in the prediction of optimized formulations for food foams and emulsions. In addition, nonequilibrium processes occurring in systems containing fluid-fluid interfaces with a surfactant present are of great practical significance for food-dispersed systems6,12-14 and many other technologies and natural phenomena.1,12,15-17 Monolayers at the air-water interface are interesting systems for studying two-dimensional structures of amphiphilic substances. Rheological interfacial properties have a role in the long-term stability of dispersed systems (emulsions and foams) and the stability of the * To whom correspondence should be addressed. Telephone: +34 95 4557183. Fax: +34 95 4557134. E-mail: [email protected].

emulsion or foam in the production stage.18-21 Moreover, the surface rheology is also of interest because of its extreme sensitivity to the nature of intermolecular interactions at the interface22-26 and/or because of its relationships with relaxation phenomena at the interface.27,28 In fact, different surface dilatational characteristics, including nonlinear viscoelastic behavior, were observed for monoglyceride27 and protein28 spread films depending on the amplitude and the frequency of the oscillation. The aim of this work was to analyze the static (structure, morphology, relative reflectivity, and miscibility) and surface dilatational properties of mixed food emulsifiers (WPI and monoglycerides) at the air-water interface. So far, there are only a few experimental results available on surface rheological behavior of mixed surfactants adsorbed at fluid-fluid interfaces.12-14,29-31 However, as far as we know, there have been few studies of interfacial rheological properties of oil-soluble emulsifiers (monoglycerides and phospholipids) and proteins spread at the air-water interface. In this work, we have observed that there exist close relationships between surface dilatational properties and structural characteristics and relaxation phenomena11 in WPI-monoglyceride mixed films. Experimental Section Chemicals. Synthetic 1-monohexadecanoyl-rac-glycerol (monopalmitin, DIMODAN PA 90) and 1-mono(cis9-octadecanoyl) glycerol (monoolein, RYLO MG 19) were supplied by Danisco Ingredients with over 95-98% purity. Whey protein isolate (WPI), a native protein with very high content of β-lactoglobulin (protein 92 ( 2%, β-lactoglobulin > 95%, R-lactalbumin < 5%) obtained by fractionation, was supplied by Danisco Ingredients (Brabran, Denmark). The sample was stored below 0 °C, and all work was done without further purification. Samples for interfacial characteristics of WPI films were

10.1021/ie010882q CCC: $22.00 © 2002 American Chemical Society Published on Web 04/27/2002

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prepared using Milli-Q ultrapure water and were buffered at pH 7. To form the surface film, monoglyceride was spread in the form of a solution, using hexane: ethanol (9:1, v:v) as a spreading solvent. Analytical grade hexane (Merck, 99%) and ethanol (Merck, >99.8%) were used without further purification. The water used as subphase was purified by means of a Millipore filtration device (Milli-Q). To adjust subphase pH, buffer solutions were used. Acetic acid/sodium acetate aqueous solution (CH3COOH/CH3COONa) was used to achieve pH 5, and a commercial buffer solution called trizma ((CH2OH)3CNH2/(CH2OH)3CNH3Cl) for pH 7. All these products were supplied by Sigma (>99.5%). Ionic strength was 0.05 M in all the experiments. Surface Film Balance. Measurements of surface pressure (π)-area (A) isotherms of WPI-monoglyceride mixed films at the air-water interface were performed on a fully automated Wilhelmy-type film balance. The method has been described previously for pure10,32 and mixed components.7,8 Before each measurement, the film balance was calibrated at 20 °C. Mixtures of particular mass ratiossranging between 0 and 1, expressed as the mass fraction of monoglyceride in the mixture, Xswere studied. To allow the quantitative adsorption of the protein on the interface, the monolayer was not under any surface pressure during the spreading process. Thus, the WPI necessary to form the mixed film should be spread before the monoglyceride. Aliquots of aqueous solutions of WPI (1.623 × 10-4 mg/µL) at pH 7 were spread on the interface by means of a micrometric syringe. To allow for spreading, adsorption, and rearrangements of the protein, 30 min were allowed to elapse before measurements were taken. The spreading method adopted in these experiments ensured the quantitative spreading of the protein on the interface as was discussed in a previous paper.32 Afterward, a monoglyceride solution in hexane:ethanol mixture was spread at different points on the WPI film. The monoglyceride solutions were spread on the subphase by means of a micrometric syringe at 20 °C. To allow for spreading and WPI-monoglyceride interactions, 30 min were allowed to elapse before compression was performed. To ensure interactions and homogeneity, the mixed film was compressed near the collapse point of the mixture and then expanded immediately to avoid the collapse. After 30 min at the maximum area, a new π-A isotherm was performed. The compression rate was 3.3 cm.min-1, which is the highest value for which isotherms were found to be reproducible in preliminary experiments. From the repetitivity of these π-A isotherms it can be inferred that the results presented in this work are under static behavior. The π-A isotherm was measured at least six times. The reproducibility of the results was better than (0.5 mN/m for surface pressure and (0.005 nm2/molecule for area. All isotherms were recorded continuously by a device connected to the film balance and then analyzed off-line. Brewster Angle Microscopy (BAM). A commercial Brewster angle microscope (BAM), BAM2, manufactured by NFT (Go¨ttingen, Germany) was used to study the morphology of the monolayer. The BAM was positioned over the film balance. Further characteristics of the device and operational conditions have been described elsewhere.33,34 The surface pressure measurements, area, and gray level as a function of time were carried out simultaneously by means of a device connected between the film balance and BAM. These

measurements were performed during sinusoidal compression and expansion of the monolayer. To measure the relative thickness (d) of the film a previous camera calibration is necessary in order to determine the relationship between the gray level (GL) and the relative reflectivity (I), according to a procedure described previously.33,34 At the Brewster angle

I ) |Rp|2 ) Cd2

(1)

where C is a constant and Rp is the p-component of the light. In all BAM images, the light regions are protein rich and the dark regions are monoglyceride rich. The imaging conditions were adjusted to optimize both image quality and quantitative measurement of reflectivity. Thus, generally as the surface pressure or the protein content increased, the shutter speed was also increased. Surface Dilatational Rheology. To obtain surface rheological parametersssuch as surface dilatational modulus, elastic and viscous components, and loss angle tangentsa modified Wilhelmy-type film balance (KSV 3000) was used as described elsewhere.27,28 In this method, the surface is subjected to small periodic sinusoidal compressions and expansions by means of two oscillating barriers at a given frequency (ω) and amplitude (∆A/A) and the response of the surface pressure is monitored (π). Surface pressure was directly measured by means of two roughened platinum plates situated on the surface between the two barriers. The surface dilatational modulus derived from the change in surface tension (dilatational stress), σ (eq 2), resulting from a small change in surface area (dilatational strain), A (eq 3), may be described by eq 4.35

σ ) σo sin(ωt + θ)

(2)

A ) Ao sin(ωt)

(3)

E)

dσ dπ )dA/A d(ln A)

(4)

where t is the time, σo and Ao are the stress and strain amplitudes, respectively, θ is the phase angle between stress and strain, π ) σο - σ is the surface pressure, and σο is the surface tension in the absence of protein and/or monoglyceride. The dilatational modulus is a complex quantity and is composed of real and imaginary parts (eq 5). The real part of the dilatational modulus or storage component is the dilatational elasticity, Ed ) |E| cos θ. The imaginary part of the dilatational modulus or loss component is the surface dilatational viscosity, Ev ) |E| sin θ. The ratio (σo/Ao) is the absolute modulus, |E|, a measure of the total unit material dilatational resistance to deformation (elastic + viscous). For a perfectly elastic material the stress and strain are in phase (θ ) 0) and the imaginary term is zero. In the case of a perfectly viscous material, θ ) 90° and the real part is zero. The loss angle tangent can be defined by eq 6. If the film is purely elastic, the loss angle tangent is zero.

E ) (σo/Ao)(cos θ + i sin θ) ) Ed + iEv

(5)

Tan θ ) Ed/Ev

(6)

Measurements were performed at least three times. The reproducibility of these results was better than 5%.

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Figure 1. Surface pressure-area isotherms (compression curve) for (A) monopalmitin-WPI and (B) monoolein-WPI mixed monolayers on buffered water at pH 7 and at 20 °C. Mass fraction of monoglyceride in the mixture (X): (4) 0, (s) 0.2, (- - -) 0.4, (-‚-) 0.6, (-‚‚-) 0.8, and (O) 1.

Results Structural and Morphological Characteristics of WPI-Monoglyceride Mixed Films at the AirWater Interface. Results derived from π-A isotherms at pH 7 (Figure 1) in the Wilhelmy-type trough are in good agreement with those obtained in the same trough with pure WPI28 and monoglycerides27 in the Langmuirtype trough with the same WPI, monoglyceride, and WPI-monoglyceride mixed films36 spread on similar subphases at pH 5 and 7. We did not observe any difference in π-A isotherms at pH 5 (data not shown). Briefly, the results of π-A isotherms (Figure 1) confirm that WPI monolayers at the air-water interface adopt a liquid-expanded-like structure and the collapse phase. WPI collapses at a surface pressure of ca. 31 mN/m, a surface pressure higher than the equilibrium surface pressure (πe ≈ 25.9 mN/m). The equilibrium surface pressure (πe) is the maximum surface pressure to which a spread monolayer may be compressed without the possibility of monolayer collapse. Thus, at π > πe, the WPI monolayer is in a metaestable state. WPI retains elements of the native structure, not fully unfolded at the interface. Most amino acid residues in WPI adopt loop conformation at the air-water interface. However, the loop conformation is more condensed at higher surface pressures and is displaced toward the bulk phase at the collapse point. These data are in agreement with those deduced for globular proteins.37,38 Different structures can be deduced for monopalmitin monolayer as a function of surface pressure (Figure 1A). The liquidexpanded phase (LE) (at π < 5 mN/m), a first-order phase transition between liquid-condensed (LC) and liquid-expanded structures (at 5 < π < 30 mN/m), the liquid-condensed structure (at π > 30 mN/m), and, finally, the solid (S) structure near to the monolayer collapse at a surface pressure of about 53.1 mN/m were observed. This collapse pressure is higher than the equilibrium surface pressure (πe ≈ 48.5 mN/m). In

Figure 2. Molecular area (A) and excess free energy (B), for monopalmitin-WPI mixed monolayers on buffered water at pH 7 and at 20 °C, as a function of surface pressure (mN/m): (0) 5, (O) 10, (4) 15, (3) 20, and ()) 25. The mean area (Ai) is indicated by means of a continuous line.

contrast with monopalmitin monolayer, monoolein monolayer (Figure 1B) presents only the liquid-expanded structure and collapses at the equilibrium surface pressure (πe ≈ 45.7 mN/m). These results were reproducible within experimental error as were those obtained previously with monopalmitin and monoolein,33,39 WPI,28,36 and β-lactoglobulin.39 The structure in WPI-monopalmitin (Figure 1A) and WPI-monoolein (Figure 1B) mixed films at surface pressures lower than that for WPI collapse (πC = 31 mN/ m), adopts a structural polymorphism, as for pure monopalmitin or a monoolein monolayer. These data are in agreement with those deduced for β-lactoglobulinmonopalmitin mixed films.39 Moreover, a monolayer expansion was observed (Figure 1) as the monoglyceride content in the mixture was increased. At surface pressures higher than that for WPI collapse, the π-A isotherms for mixed monolayers were parallel to that of monoglyceride (monopalmitin or monoolein), which demonstrates that the arrangement of the monoglyceride hydrocarbon chain in mixed monolayers is practically the same in the entire WPI-monoglyceride ratio.36 The interactions between components in mixed monolayers can be studied from the point of view of miscibility between components on the mixed monolayer.40,41 In Figures 2 and 3 we show the molecular area (A), the mean area (Ai)scalculated according to the additivity rule42 in eq 7sand the excess free energyscalculated according to the equation derived by Goodrich43 and Pagano and Gershfel,44 eq 8sfor WPI-monopalmitin (Figure 2) and WPI-monoolein (Figure 3) mixed films. The continuous lines in Figures 2 and 3 correspond to an immiscible monolayer.

Ai ) A1X1 + A2X2

(7)

∫0πAexc dπ

(8)

∆Gexc )

where A is the molecular area at a given surface pressure for the mixed monolayer, A1 and A2 are the molecular areas of pure components, X1 and X2 are the


Figure 3. Molecular area (A) and excess free energy (B), for monoolein-WPI mixed monolayers on buffered water at pH 7 and at 20 °C, as a function of surface pressure (mN/m): (0) 5, (O) 10, (4) 15, (3) 20, and ()) 25. The mean area (Ai) is indicated by means of a continuous line.

mass fractions of pure components in the mixed monolayer, and Aexc is the excess areasAexc ) A - (A1X1 + A2X2). For WPI-monopalmitin mixed monolayers the excess area (Figure 2A) was negative at surface pressures higher than 5 mN/m and for X < 0.8. However, the excess free energy was negative for every surface pressure and film composition. The minimum ∆Gexc value was observed at 25 mN/m, for a mass fraction of monopalmitin in the mixture of 0.2. That is, from a macroscopic point of view, the mixed monolayer is more stable (from a thermodynamic point of view) than the same monolayer with separation between its components. For WPI-monoolein mixed monolayers the excess area (Figure 3A) was practically zero. However, the excess free energy adopts a positive or a negative value, depending on the film composition. The minimum ∆Gexc value was observed at 25 mN/m for a mass fraction of monoolein in the mixture of 0.2 and the maximum ∆Gexc value for a mass fraction of monoolein in the mixture of 0.8. That is, the thermodynamic stability of the mixed film compared to that of pure components is lower for WPI-monoolein than for WPI-monopalmitin mixed films. Finally, it can be seen that the collapse pressure (πc) for mixed monolayers (Figure 1) is similar to that for pure monoglycerides and does not depend on the monolayer composition. However, the pH did not have any significant effect on the existence of interactions between film-forming components. This was deduced from the comparison (data not shown) between the A-X plot, ∆Gexc-X relationshipsat surface pressures lower that that of WPI collapsesand in the πC-X dependencesat the highest surface pressure. Results of BAM, in particular the relative reflectivity as a function of surface pressure (Figure 4) and morphology (Figure 5) obtained with WPI, monoglyceride, and WPI-monoglyceride mixed films (at a mass fraction of monoglyceride in the mixture of 0.5 and at pH 7, as an example), clearly show, at a microscopic level, the same structural characteristics as those deduced from

Figure 4. Relative reflectivity (arbitrary units) as a function of surface pressure during the compression for (4) monopalmitinWPI and (O) monoolein-WPI mixed monolayers on buffered water at pH 7. Monoglyceride mass fraction in the mixture: 0.5. The line fit for monopalmitin (continuous line), monoolein (dotted line), and WPI (dashed line) pure monolayers are included in plots A and B. Temperature: 20 °C. Shutter speed: 1/250 s.

the π-A isotherms. The domains that residues of WPI (Figure 5A) and monoolein (Figure 5B) molecules at every surface pressure, and monopalmitin with a liquidexpanded structure (image not shown) adopt at the airwater interface appeared to be of uniform reflectivity, suggesting homogeneity in thickness and film isotropy. In this region the I-π plot is a continuous line without any significant reflectivity peak (Figure 4). For monopalmitin monolayer a first-order phase transition between LE and LC structures, with circular LC domains in a homogeneous LE environment (Figure 5C), was observed at 5 < π < 30 mN/m. The existence of reflectivity peaks in the I-π plot (data not shown) was observed when a circular LC domain passed through the spot where this measurement was performed. This phenomenon denotes morphological film anisotropy and differences in film thickness at a microscopic scale. The LC structure was observed at π > 30 N/m, with circular and anisotropic domains which grow with surface pressure. Finally, the collapse phase was observed at a surface pressure of about 53.1 mN/m, characterized by a homogeneous morphology after fusion of LC circular domains (Figure 5D) and the presence of monolayer fracture in different zones of the interface (Figure 5E). The relative intensity decreased at higher surface pressures as the monolayer collapsed (Figure 4A). For comparison purposes, a continuous line was deduced by fitting the I-π data, derived from different measurements for pure components (Figure 4). The I-π plot for compression of WPI-monopalmitin mixed monolayer at 0.5 in mass fraction of monopalmitin in the mixture and at pH 7 (as an example) is shown in Figure 4A. In this figure, we only include the results of a measurement to add clarity (six I-π plots were recorded for compression-expansion cycles with different shutter speeds for the same monolayer). These data followed essentially the same trends as for mixtures

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Figure 5. Visualization of pure and WPI-monoglyceride mixed films (at a mass fraction of monoglyceride in the mixture of 0.5) at the air-water interface and at pH 7. The shutter speed was 1/50 s in all images except in image H (shutter speed: 1/500 s). The horizontal direction of the image corresponds to 630 µm and the vertical direction to 470 µm. Key: (A) WPI at 18.5 mN/m (LElike structure), (B) monoolein at 18 mN/m (LE expanded structure), (C) monopalmitin at 9 mN/m (transition between LE f LC structures), (D) monopalmitin at 52 mN/m (at the collapse point), (E) monopalmitin at 49.7 mN/m (fracture near the collapse point), (F) squeezing out phenomena at 28 mN/m in WPI-monopalmitin mixed film (near the WPI collapse), (G) frontier between collapsed WPI and monopalmitin in a WPI-monopalmitin mixed film at 43 mN/m, and (H) domain of collapse WPI in a WPI-monoolein mixed film at 43 mN/m.

with different mass fraction of monopalmitin. Briefly, at π < 20-22 mN/m, the I-π plots were the same as for pure components. In this region, LC domains of monopalmitin existed in an environment of homogeneous LE monopalmitin and LE-like WPI domains, during the compression. The main difference was observed in the region near WPI collapse (π ≈ 30 mN/m), because the relative reflectivity of the mixed film was lower than for pure WPI. This suggests that as the surface pressure or the content of monopalmitin in the mixture (data not shown) increases, WPI residues are more easily displaced from the interface toward a sublayer beneath the monopalmitin monolayer. Figure 5F shows a characteristic squeezing out phenomenon. In fact, many LC domains of monopalmitinsthe dark domains are due to monopalmitin with an LC structure, as confirmed by turning the analyzer from 60 to 120° (data not shown)sare floating over a sublayer of collapsed WPI moleculesscharacterized by a completely white image. However, some peaks with a relative

Figure 6. Surface pressure dependence of (A) surface dilatational modulus (E, mN/m), (B) surface dilatational elasticity (Ed, mN/ m), and (C) loss angle tangent (Tan θ) for WPI-monopalmitin mixed monolayers at pH 7 and at 20 °C. Frequency: 50 mHz. Amplitude: 5%. Monolayer composition (XMP, monopalmitin mass fraction): (O) 0, (4) 0.2, (3) 0.4, ()) 0.6, (0) 0.8, and (+) 1.

reflectivity similar to that for a collapsed WPI monolayer were observed at π > 30 mN/m. Figure 5G shows the frontier between a region of collapsed WPI molecules and closely packed LC domains of monopalmitin near its collapse (π ) 43 mN/m). For WPI-monoolein monolayer (Figure 4B) at 0.5 in mass fraction of monoolein in the mixture and at pH 7 (as an example), and a surface pressures lower than that for WPI collapse (≈31 mN/m), the I values were similar to that for WPI or monoolein as the monoolein mass fraction approached 0 or 1, respectively. At surface pressures higher than 30 mN/m the I-π plots approached that for pure monoolein monolayer. However, some peaks with a relative reflectivity similar to that for a collapsed WPI monolayer were observed. In fact, some white spots were also observed (Figure 5H) due to the presence of collapsed WPI molecules. Finally, at the collapse point, the reflectivity peaks disappeared in the I-π plot and the relative reflectivity decreased to a value close to that for pure monoolein monolayer (Figure 4B). SurfacedilatationalcharacteristicsofWPI-monoglyceride mixed films at the air-water interface. The Effect of Surface Pressure. The surface viscoelastic properties of WPI-monopalmitin and WPImonoolein mixed films spread on the air-water interface at pH 7 (as an example) are shown in Figures 6 and 7, respectively. We did not observe any difference in the surface pressure dependence of surface rheological parameters at pH 5 (data not shown). It can be seen that (i) the values for the surface dilatational modulus


Figure 8. Surface dilatational modulus (E) as a function of monolayer composition for (A) WPI-monopalmitin and (B) WPImonoolein mixed monolayers on buffered water at pH 7. Temperature: 20 °C. Frequency: 50 mHz. Amplitude: 5%. Surface pressure: (O) 10 mN/m and (∆) 20 mN/m. Figure 7. Surface pressure dependence of (A) surface dilatational modulus (E, mN/m), (B) surface dilatational elasticity (Ed, mN/ m), and (C) loss angle tangent (Tan θ) for WPI-monoolein mixed monolayers at pH 7 and at 20 °C. Frequency: 50 mHz. Amplitude: 5%. Monolayer composition (XMO, monoolein mass fraction): (O) 0, (4) 0.2, (3) 0.4, ()) 0.6, (0) 0.8, and (+) 1.

(E) were very similar to those for the dilatational elasticity (Ed), (ii) from the values of the loss angle tangent (Tan θ) for monoglyceride, WPI, and WPImonoglyceride it can be concluded that these films behaved as viscoelastic at every surface pressure, (iii) for monoolein monolayer Tan θ decreased with surface pressure to a low value close to zero, (iv) the value for E or Ed increased with surface pressure and is a maximum at the collapse point of the mixed film, and (v) the surface dilatational modulus of WPI-monoolein mixed films (Figure 7A) is lower than that for WPImonopalmitin mixed films (Figure 6A), especially at the collapse point of the mixed films. The surface dilational modulus vs interfacial composition is shown in Figure 8. It can be seen that for WPImonopalmitin mixed films (Figure 8A) at X > 0.2 and at surface pressures lower than the WPI collapse (at 10 and 20 mN/m) and for WPI-monoolein mixed films (Figure 8B) at 20 mN/m, the surface dilational modulus of mixed films is lower than that of an ideal mixture between WPI and monoglyceride (solid line). However, for WPI-monoolein mixed films (Figure 8B) at π ) 10 mN/m the surface dilatational modulus is similar to that of an ideal mixture between WPI and monoolein. The difference between E of the mixed film and that for an ideal mixture between WPI and monoglyceride is higher for WPI-monopalmitin than for WPI-monoolein mixed films. This phenomenon is practically similar to that observed for the excess area (Figure 2). Effect of Frequency. Changes in surface dilatational properties for WPI-monopalmitin and WPI-

Figure 9. Frequency dependence of (A) surface dilatational modulus and (B) loss angle tangent for WPI-monopalmitin mixed monolayers on buffered water at pH 7 and at the collapse point. Temperature: 20 °C. Amplitude: 5%. Monolayer composition (XMP, monopalmitin mass fraction): (O) 0, (4) 0.2, (3) 0.4, ()) 0.6, (0) 0.8, and (+) 1.

monoolein mixed monolayers at pH 7 (as a example) and at the collapse point, as a function of frequency of oscillation over a range of 1 to 200 mHz, are illustrated in Figures 9 and 10, respectively. We did not observe any difference in the frequency dependence of surface rheological parameters at pH 5 (data not shown). (i) It can be seen that in the range 1 mHz < ω < 50 mHz, the dilatational modulus increased with the frequency,

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Figure 10. Frequency dependence of (A) surface dilatational modulus and (B) loss angle tangent for WPI-monoolein mixed monolayers on buffered water at pH 7 and at 20 °C. Amplitude: 5%. Monolayer composition (XMO, monoolein mass fractions): (O) 0, (4) 0.2, (3) 0.4, ()) 0.6, (0) 0.8, and (+) 1.

especially for WPI-monopalmitin mixed films (Figure 9A), but at higher frequencies E is practically constant (Figure 9A and 10A). (ii) The dilatational modulus and its elastic component are essentially the same at frequencies lower than 50 mHz, a phenomenon that explains the low values of Tan θ in this region (Figure 9B and 10B). (iii) Significant differences between both rheological parameters were observed at frequencies higher than 50 mHz, mainly due to the decrease of the elastic component at increasing frequencies (data not shown). As a consequence of this behavior, the value of Tan θ increased with frequency (Figure 9B and 10B). Moreover, the value of the viscous component exceeded that of the elastic component at higher frequencies (ω = 200 mHz). Discussion In this paper, we report on structural, morphological, and surface dilatational characteristics of monopalmitin-WPI and monoolein-WPI mixed monolayers spread on water at pH 5 and 7 and at 20 °C. The structural characteristics and morphology of monoglyceride-WPI mixed films are dependent on surface pressure and monolayer composition. However, the aqueous phase pH has no significant effect on WPI-monoglyceride interactions at the air-water interface. From the π-A isotherm of mixed monolayers (Figure 1)sincluding the application of the additivity rule on miscibility (Figures 2A and 3A) and the quantification of interactions between monolayer components by the excess free energy (Figures 2B and 3B)s it has been shown that, at a macroscopic level, monoglyceride-WPI mixed monolayers form a mixed monolayer at the airwater interface with few interactions between filmforming components, at surface pressures lower than that for the WPI collapse (π ≈ 31 mN/m). That is, at surface pressures lower than that for WPI collapse, the

attractive interactions in the WPI-monopalmitin mixed monolayer increase (eq 8) with the surface pressure. In this system there is a minimum in the ∆Gexc-X relationship (Figure 2B), which corresponds to a monoglyceride ratio in the mixture of 0.2. Moreover, at higher surface pressures the value of the minimum in the ∆Gexc-X relationship is higher. The data for WPImonoolein mixed films (Figure 3B) suggest that the filmforming components are practically immiscible at the air-water interface. At the highest surface pressures, at the collapse point of the mixed film, immiscibility between monolayer forming components is deduced45 due to the fact that the collapse pressure of mixed monolayers is similar to that of pure monoglyceride monolayer (Figure 1). That is, at higher surface pressures, collapsed WPI residues may be displaced from the interface by monoglyceride molecules. These results suggest that the composition of mixed monolayers was very dependent on the surface pressure as was observed for the same system in the Langmuir-type trough.36 Results of BAM, in particular the relative reflectivity as a function of surface pressure (Figure 4) and morphology (Figure 5), suggest that at surface pressures lower than that for WPI collapse a mixed monolayer of monoglyceride and WPI may exist. At surface pressures higher than that for WPI collapse, mixed monolayers were dominated by the presence of monoglyceride (monopalmitin or monoolein) at the interface. However, BAM images (Figure 5) also demonstrated that, even at the highest surface pressure, a monoglyceride (monopalmitin or monoolein) monolayer is unable to displace completely WPI molecules from the air-water interface. The surface dilatational modulus depends on the monolayer structure (Figures 6A and 7A). For pure and mixed films the more condensed the structure is (at higher π), the higher the surface dilatational modulus of the monolayer becomes until the collapse is reached. That is, more condensed monolayer structures may lead to an increase in the forces of interaction between molecules at the interface, which is consistent with the observed increase in E. The lower collapse pressure in the monoolein and WPI-monoolein mixed films (Figure 1B) could be due to a reduction in the interactions between molecules in the film, which could explain the differences in E values between monopalmitin and monoolein at the collapse point. Thus, the dilatational modulus is not just determined by the interactions between spread monoglyceride and WPI molecules (which depend on the surface pressure), but the structure of the spread molecule also plays an important role. Thus, for the more condensed monopalmitin and WPI-monopalmitin mixed monolayers (Figure 1A), E is higher than for the more expanded monoolein and WPI-monoolein mixed monolayers (Figure 1B), at every surface pressure (Figures 6 and 7). The purely elastic behavior for pure monoolein film at the collapse pressure (see that in Figure 7C Tan θ is practically zero) may be due to the fact that monoolein collapses with the formation of lenses.10 At surface pressures lower than that for WPI collapse, the results can been explained if WPI and monopalmitin molecules are immiscible at the interface, or there exist minor interactions between film-forming components, as was deduced from π-A isotherms (Figure 1) and Brewster angle microscopy (Figures 4 and 5). From BAM, it was observed that domains of WPI and


monoglyceride exist at the interface with a variable extension and a random distribution (Figures 4 and 5), which is in agreement with a reduction in the surface dilatational modulus (Figure 8) in relation to an ideal mixture of these emulsifiers. The lower E values for mixed films in relation to those for an ideal mixture between WPI and monoglyceride at surface pressures close to the WPI collapse may also be associated with the displacement of WPI by monopalmitin from the interface, as was observed by BAM (Figure 5F). At surface pressures higher than that for WPI collapse the E-π (Figures 6A and 7A) and Ed-π (Figures 6B and 7B) plots for mixed films were parallel to that of monoglycerides, which demonstrated again that at higher surface pressures the mixed films were practically dominated by monoglyceride molecules. However, the data in Figures 6 and 7 also demonstrate that the small amounts of WPI collapsed residues at the interfacesas deduced at a microscopic level from I-π plots (Figure 4) and BAM images (Figure 5)shave an effect on the surface dilatational properties of the mixed films. In fact, the values of E and Ed for mixed films are lower than those for a pure monoglyceride (monopalmitin or monoolein) monolayer, even at the collapse point of the mixed films. Thus, the mechanical properties of the mixed films also demonstrated that, even at the highest surface pressure, a monoglyceride monolayer is unable to displace completely WPI molecules from the air-water interface. From the effect of frequency on surface dilatational properties at the collapse point (Figures 9 and 10), it can be concluded that monoglyceride and WPI-monoglyceride mixed monolayers present rheological behavior in dilatational conditions that is essentially elastic at low frequencies (ω < 50) and viscoelastic at higher frequencies (ω > 50). As a consequence of the viscoelastic behavior, the loss tangent angle increased with frequency (Figures 9B and 10B). These results are in good agreement with those obtained for pure WPI adsorbed46 and spread27 films and for monopalmitin and monoolein under dilatational deformation in a ring trough23 and in a Langmuir film balance.26 These findings may be associated with the effect of the rate of deformation on the structure and relaxation phenomena in the monopalmitin present in the mixed film, because at the collapse point the mixed film is practically dominated by monopalmitin (Figures 1, 4, and 5). For WPI-monopalmitin mixed monolayers different relaxation mechanisms may be operative, as a function of surface pressure and the time scale considered, as was discussed in a previous paper.11 In fact, the elastic behavior observed for WPI-monoglyceride mixed monolayers in the frequency range of 1-50 mHz, should be associated with monoglyceride monolayer collapse. This relaxation process requires a time of the same order of magnitude as the scale of the oscillationsin our experiments between 1.7 and 16.7 min. On the other hand, the magnitude of relaxation in surface pressure is the same for all mixed films, but lower than those for pure monoglyceride,11 as observed for the frequency dependence of E (Figures 9A and 10A). Again, the reason for this behavior must be associated with the immiscibility between both components at the air-water interface. The effect of the frequency on the surface dilatational modulus, in the range 1 mHz < ω < 50 mHz, for WPI-

monoolein (Figure 10A) is lower than that for WPImonopalmitin (Figure 9A) mixed monolayers. This phenomenon may be associated with different relaxation phenomena observed for WPI-monoglyceride mixed films11 and, in particular, for pure monopalmitin and monoolein monolayers at the collapse point.10 In fact, at surface pressures higher than πe, the relaxation phenomena could be mainly due either to nucleation and growth of critical nucleissuch as was observed for monopalmitin monolayers (at the collapse point)sor to a complex mechanism including competition between collapse by formation of lenses10 and monolayer desorptionssuch as was deduced for monoolein monolayers. At higher surface frequencies (50 < ω < 200 mHz), the viscoelastic behavior of the mixed monolayer is more complex and should be associated with formation/ destruction of LC domains in monopalmitin coupled with LC-S and LC-LE phase transitions and the formation/destruction of 3-D collapse structures (with the formation of crystalline nuclei and the existence of monolayer fractures). We do not reject the possibility that islands of collapsed WPI could be displaced and reabsorbed within the interface during the sinusoidal compression-expansion cycle. We have observed recently by means of long-term relaxation phenomena in WPI-monoglyceride mixed films11 that the time required for organization/reorganization changes in the monolayer structure is of the same order of magnitude or higher than the time scale of the deformation. However, the surface dilatational properties are very sensitive to the presence of small islands of collapsed WPI at the collapse point of the mixed film. In fact, the surface dilatational properties depend not only on the frequency of the area oscillation, but also depend on the monolayer composition (Figures 9A and 10A). To check whether the level of frequency can produce any effect on the degree of intermolecular interactions and, as a consequence, on the monolayer structure, we present in Figure 11 the results from a sinusoidal deformation for WPI-monoglyceride mixed films at a mass fraction of monoglyceride in the mixture of 0.6 and at two frequencies (50 and 200 mHz). At 50 mHz and at 20 mN/m (Figure 11A) the LC and LE monopalmitin monolayer structures [MP (LE f LC)], the LE expanded monoolein structure [MO (LE)], and WPI with a liquidexpanded-like structure [WPI (LE-like)] are constant during the compression-expansion cycle. The results indicate that for WPI-monopalmitin mixed films transition between LE and LC phases and the breaking of intermolecular interactionssmainly between LC domains and, most probably, with change in domain size during the compression-expansion cyclesare both operatives in this frequency regime. At the same experimental conditions LE monoolein monolayer structure [MO (LE)] and WPI with LE-like structure [WPI (LElike)] are constant during the compression-expansion cycle (Figure 11A). Thus, at these experimental conditions the effect of frequency may be due to a monoolein monolayer loss due to desorption.10,11 At the same frequency (50 mHz) and at the collapse point (Figure 11B) for WPI-monopalmitin mixed films, a change between LC and S structures (that is, a secondorder phase transition takes place, and LC domains merge toward a solid structure with the compression and then this structure relaxes back to LC domains with the monolayer expansion (see Figure 5)), a first-order phase transition between LE and LC phases, and a

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phenomena by desorption and collapse should be ruled out in this frequency regime. Interestingly, at high frequencies E does not depend on the frequency (Figures 9A and 10A), which is in agreement with the fact that the relaxation phenomena by desorption and collapse have a relaxation time higher than that of the frequency of the oscillation (Figure 11C). Conclusions

Figure 11. Dynamic surface pressure response to a sinusoidal change in area for (O) WPI-monopalmitin and (4) WPI-monoolein mixed monolayers on buffered water at pH 7 and at 20 °C. Monolayer composition: 0.6 in mass fraction of monoglyceride. Amplitude of the area deformation 5%. Key: (A) surface pressure ) 20 mN/m, frequency ) 50 mHz; (B) surface pressure at the collapse point, frequency ) 50 mHz; (C) surface pressure at the collapse point, frequency ) 200 mHz. The equilibrium surface pressure for monopalmitin (πe MP) and monoolein (πe MO) and the collapse pressure for monopalmitin (πC MP) and WPI (πc WPI) are indicated by means of arrows. The transitions between structures and monolayer collapse during a sinusoidal compression-expansion cycle for monopalmitin (MP), monoolein (MO) and WPI are indicated in the figures. Key: (LE) liquid-expanded structure, (LC) liquid-condensed structure, (LE f LC) transition between LE and LC structures, (S) solid structure, (LE-like) liquidexpanded-like structure, and (C) monolayer collapse.

displacement of collapsed WPI including the formation of multilayers are produced during the compressionexpansion cycle. In addition, as monopalmitin collapses at a surface pressure (53.1 mN/m) higher than πe (48.5 mN/m), the monolayer is in a metaestable state at π > πe. However, for WPI-monoolein mixed films (Figure 11B) only desorption of monoolein takes place. All these relaxation phenomena coupled with the displacement and the formation of multilayers of collapsed WPI may be operatives during the time scale of the compression-expansion cycle. The same relaxation phenomena, including the overcompression of the collapsed monopalmitin monolayer, were observed for WPI-monopalmitin mixed films at the collapse point and at a frequency of 200 mHz (Figure 11C). As monoolein in WPI-monoolein mixed films collapses at π = πe (46.1 mN/m), a competition between monolayer collapse and desorption was observed under these experimental conditions.10 However, relaxation phenomena by desorption and collapse have a higher relaxation time10,11 than that due to the period of oscillation (Figure 11C). Thus, long-term relaxation

In this work, we have used a unique device that incorporates different interfacial techniques, such as surface film balance, Brewster angle microscopy, and interfacial dilatational rheology, to analyze the static (structure, morphology, relative film thickness, and miscibility) and dynamic characteristics (surface dilatational properties) of WPI-monoglyceride mixed films spread on the air-water interface. The static and dynamic characteristics of WPI and monoglycerides (monopalmitin and monoolein) mixed films depend on the monolayer composition and the surface pressure. At surface pressures lower than that for WPI collapse, a mixed monolayer of monoglyceride and WPI may exist. At surface pressures higher than that for WPI collapse, the mixed monolayers were practically dominated by monoglyceride molecules. That is, at higher surface pressures, collapsed WPI residues may be displaced from the interface by monoglyceride molecules. However, the small amounts of WPI collapsed residues has an effect on the surface dilatational properties of the mixed films. The surface dilatational modulus increases as the monolayer is compressed and is a maximum at the highest surface pressures, at the WPI-monoglyceride collapse point. The surface dilatational modulus is higher for WPI-monopalmitin than for WPI-monoolein mixed film at every surface pressures. A close relationship between interfacial dilatational rheology and changes in molecular structure, interactions, miscibility, and relaxation phenomena has been established from the frequency dependence of the surface dilatational properties, as a function of the monolayer composition. Acknowledgment This research was supported in part by the EU through Grant FAIR-CT96-1216 and by the DGICYT through Grant PB97-0734. Literature Cited (1) Becher, P., Ed. Encyclopedia of Emulsion Technology; Marcel Dekker: New York, 1985. (2) Exerowa, D., Kruglyakov, P. M., Eds. Foam and Foam Films: theory, Experiment, Application; Elsevier: Amsterdam, 1998. (3) Gunstone, F. D., Padley, F. B., Eds. Lipid Technologies and Applications; Marcel Dekker: New York, 1997. (4) Sjo¨blom, J.,Ed. Emulsions and Emulsion Stability; Marcel Dekker: New York, 1996. (5) Dickinson, E. An Introduction to Food Colloids; Oxford University Press: Oxford, England, 1992. (6) Bos, M.; Nylander, T.; Arnebrant, T.; Clark, D. C. In Food Emulsions and their Applications; Hasenhuette, G. L., Hartel, R. W., Eds.; Chapman & Hall: New York, 1997. (7) Rodrı´guez Patino, J. M.; Carrera, C.; Rodrı´guez Ninõ, Ma. R. Analysis of β-Casein-Monopalmitin Mixed Films at the AirWater Interface. J. Agric. Food Chem. 1999, 47, 4998. (8) Rodrı´guez Patino, J. M.; Carrera, C.; Rodrı´guez Ninõ, Ma. R. Is Brewster Angle Microscopy a Useful Technique to Distinguish

Ind. Eng. Chem. Res., Vol. 41, No. 11, 2002 2661 Between Isotropic Domains in β-Casein-Monoolein Mixed Monolayers at the Air-Water Interface? Langmuir 1999, 15, 4777. (9) Rodrı´guez Patino, J. M.; Rodrı´guez Ninõ, Ma. R.; Carrera, C.; Cejudo, M. The Effect of pH on Monoglyceride-Caseinate Mixed Monolayers at the Air-Water Interface. J. Colloid Interface Sci. 2001, 240, 113. (10) Carrera, C.; Rodrı´guez Ninõ, Ma. R.; Rodrı´guez Patino, J. M. Relaxation Phenomena in Monoglyceride Films at the AirWater Interface. Colloids Surf., B. 1999, 12, 175. (11) Rodrı´guez Patino, J. M.; Rodrı´guez Ninõ, Ma. R.; Carrera, C. Long-Term Relaxation Phenomena in Whey Protein Isolated and Monoglyceride Mixed Films at the Air-Water Interface. Submitted for publication in Ind. Eng. Chem. Res. (12) Dukhin, S. S., Kretzschmar, G., Miller, R., Eds. Dynamic of Adsorption at Liquid Interfaces; Elsevier: Amsterdam, 1995. (13) Murray, B. S. In Proteins at Interfaces; Mo¨bius, D., Miller, R., Eds.; Elsevier Science BV: Amsterdam, 1998. (14) Murray, B. S.; Dickinson, E. Interfacial Rheology and the Dynamic Properties of Adsorbed Films of Food Proteins and Surfactants. Food Sci. Technol. Int. 1996, 2, 131. (15) Baszkin, A.; Norde, W. Physical Chemistry of Biological Interfaces; Marcel Dekker: New York, 2000. (16) Malhotra, A. K.; Wasan, D. T. Interfacial Rheological Properties of Adsorbed Surfactant Films with Applications to Emulsion and Foam Stability. Surf. Sci. Ser. Thin Solid Films 1988, 29, 829. (17) Mittal, K. L., Kumar, P., Eds. Emulsions, Foams, and Thin Films; Marcel Dekker: New York, 2000. (18) Dickinson, E. Adsorption Protein Layers at Fluid Interfaces: Interactions, Structure and Surface Rheology. Colloids Surf. B 1999, 15, 161. (19) Dickinson, E. Milk Protein Interfacial Layers and the Relationship to Emulsion Stability and Rheology. Colloid Surf. B 2001, 20, 197. (20) Walstra, P. Principles of Emulsion Formation. Chem. Eng. Sci. 1993, 48, 333. (21) Wilde, P. J. Interfaces: Their Role in Foam and Emulsion Behaviour. Curr. Opin. Colloid Interface Sci. 2000, 5, 176. (22) Lucassen-Reynders, E. H.; Benjamins, J. In Food Emulsions and Foams: Interfaces, Interactions and Stability; Dickinson, E., Rodrı´guez Patino, J. M., Eds.; Royal Society of Chemistry: Cambridge, England, 1999. (23) Rodrı´guez Ninõ, Ma. R.; Wilde, P. J.; Clark, D. C.; Rodrı´guez Patino, J. M. Surface Rheological Properties of Monostearin and Monoolein Films Spread on the Air-Water Interface. Ind. Eng. Chem. Res. 1996, 35, 4449. (24) Rodrı´guez Ninõ, Ma. R.; Wilde, P. J.; Clark, D. C.; Rodrı´guez Patino, J. M. Surface Dilational Properties of Protein and Lipids Films at the Air-Water Interface. Langmuir 1998, 14, 2160. (25) Rodrı´guez Ninõ, Ma. R.; Wilde, P. J.; Clark, D. C.; Rodrı´guez Patino, J. M. Rheokinetic Analysis of Bovine Serum Albumin and Tween 20 Mixed Films on Aqueous Solutions. J. Agric. Food Chem. 1998, 46, 2177. (26) Ruı´z, D. M.; Gonza´lez, N. I.; Rodrı´guez Patino, J. M. Aqueous Subphase pH Influence on Nonionizable Material Monolayers. Structural and Rheological Characteristics. Ind. Eng. Chem. Res. 1998, 37, 936. (27) Rodrı´guez Patino, J. M.; Carrera, S. C.; Rodrı´guez Ninõ, Ma. R.; Cejudo, M. Structural-Dilatational Characteristics Relationships of Monoglyceride Monolayers at the Air-Water Interface. Langmuir 2001, 17, 4003. (28) Rodrı´guez Patino, J. M.; Carrera, S. C.; Rodrı´guez Ninõ, Ma. R.; Cejudo, M. Structural and Dynamic Properties of Milk Proteins Spread at the Air-Water Interface. J. Colloid Interface Sci. 2001, 242, 141.

(29) Benjamins, J.; Lucassen-Reynders, E. H. In Proteins at Liquid Interfaces; Mo¨bius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1998. (30) Bos, M. A.; van Vliet, T. Interfacial Rheological Properties of Adsorbed Protein Layers and Surfactants: A Review. Adv. Colloid Interface Sci. 2001, 91, 437. (31) Miller, R.; Fainerman, V. B.; Makievski, A. V.; Kra¨gel, J.; Grigoriev, D. O.; Kazakov, V. N.; Sinyachenko, O. V. Dynamics of Proteins and Mixed Protein/Surfactant Adsorption Layers at the Air/Fluid Interface. Adv. Colloid Interface Sci. 2000, 86, 39. (32) Rodrı´guez Ninõ, Ma. R.; Carrera, S. C.; Rodrı´guez Patino, J. M. Interfacial Characteristics of β-Casein Films at the AirWater Interface. Colloids Surf. B 1999, 12, 161. (33) Rodrı´guez Patino, J. M.; Carrera, C.; Rodrı´guez Ninõ, Ma. R. Morphological and Structural Characteristics of Monoglyceride Monolayers at the Air-Water Interface Observed by Brewster Angle Microscopy. Langmuir 1999, 15, 2484. (34) Rodrı´guez Patino, J. M.; Carrera, C.; Rodrı´guez Ninõ, Ma. R. Structural and Morphological Characteristics of β-Casein Monolayers at the Air-Water Interface. Food Hydrocolloids 1999, 13, 401. (35) Lucassen, J.; van den Tempel, M. Dynamic Measurements of Dilational Properties of a Liquid Interface. Chem. Eng. Sci. 1972, 27, 1283. (36) Rodrı´guez Patino, J. M.; Rodrı´guez Ninõ, Ma. R.; Carrera, C.; Cejudo, M. Whey Protein Isolate-Monoglyceride Mixed Monolayers at the Air-Water Interface. Structure, Morphology, and Interactions. Langmuir 2001, 17, 7545. (37) Graham, D. E.; Phillips, M. C. Proteins at Liquid Interfaces III. Molecular Structures of Adsorbed Protein Films. J. Colloid Interface Sci. 1979, 70, 427. (38) Phillips, M. C.; Evans, M. T. A.; Graham, D. E.; Oldani, D. Structure and Properties of Protein Films Adsorbed at the AirWater Interface. Colloid Polym. Sci. 1975, 253, 424. (39) Cornec, M.; Narsimhan, G. Adsorption and Exchange of β-Lactoglobulin onto Spread Monoglyceride Monolayers at the Air-Water Interface. Langmuir 2000, 16, 1216. (40) de la Fuente, J.; Rodrı´guez Patino, J. M. Binary Mixture of Monostearin-Distearin Monolayers at the Air-Water Interface. AIChE J. 1995, 41, 1955. (41) de la Fuente, J.; Rodrı´guez Patino, J. M. Mixed Monolayers of Acylglycerols on Sugar Aqueous Solutions. AIChE J. 1996, 42, 1416. (42) Gaines, G. L. Insoluble Monolayers at Liquid-Gas Interface; Wiley: New York, 1966. (43) Goodrich, F. C. Proceedings of the 2nd International Congress on Surface Activity; Butterworth: London, 1956. Vol. 1. (44) Pagano, R. E.; Gershfel, N. L. Physical Chemistry of Lipid Films at the Air-Water Interface: II. J. Phys. Chem. 1972, 76, 1238. (45) Joos, P.; Demel, R. A. The Interaction Energies of Cholesterol and Lecithin in Spread Mixed Monolayers at the Air-Water Interface. Biochim. Biophys. Acta 1969, 183, 447. (46) Serrien, G.; Geeraerts, G.; Ghosh, L.; Joos, P. Dynamic Surface Properties of Adsorbed Protein Solutions: BSA, Casein and Buttermilk. Colloids Surf. 1992, 68, 219.

Received for review October 26, 2001 Revised manuscript received January 30, 2002 Accepted February 18, 2002 IE010882Q

Static and Dynamic Properties of a Whey Protein Isolate and

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