Shear and Dilatational Relaxation Mechanisms of Globular and

Langmuir 2004, 20, 10159-10167

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Shear and Dilatational Relaxation Mechanisms of Globular and Flexible Proteins at the Hexadecane/Water Interface Erik M. Freer,† Kang Sub Yim,‡ Gerald G. Fuller,‡ and Clayton J. Radke*,† Chemical Engineering Department, University of California, Berkeley, California 94720-1462, and Chemical Engineering Department, Stanford University, Stanford, California 94305-5025 Received June 15, 2004. In Final Form: August 19, 2004 Proteins adsorbed at fluid/fluid interfaces influence many phenomena: food emulsion and foam stability (Murray et al. Langmuir 2002, 18, 9476 and Borbas et al. Colloids Surf., A 2003, 213, 93), two-phase enzyme catalysis (Cascao-Pereira et al. Biotechnol. Bioeng. 2003, 83, 498; 2002, 78, 595), human lung function (Lunkenheimer et al. Colloids Surf., A 1996, 114, 199; Wustneck et al.; and Banerjee et al. 2000, 15, 14), and cell membrane mechanical properties (Mohandas et al. 1994, 23, 787). Time scales important to these phenomena are broad, necessitating an understanding of the dynamics of biological macromolecules at interfaces. We utilize interfacial shear and dilatational deformations to study the rheology of a globular protein, lysozyme, and a disordered protein, β-casein, at the hexadecane/water interface. Linear viscoelastic properties are measured using small amplitude oscillatory flow, stress relaxation after a sudden dilatational displacement, and shear creep response to probe the rheological response over broad experimental time scales. Our studies of lysozyme and β-casein reveal that the interfacial dissipation mechanisms are strongly coupled to changes in the protein structure upon and after adsorption. For β-casein, the interfacial response is fluidlike in shear deformation and is dominated by interfacial viscous dissipation, particularly at low frequencies. Conversely, the dilatational response of β-casein is dominated by diffusion dissipation at low frequencies and viscous dissipation at higher frequencies (i.e., when the experimental time scale is faster than the characteristic time for diffusion). For lysozyme in shear deformation, the adsorbed protein layer is primarily elastic with only a weak frequency dependence. Similarly, the interfacial dilatational moduli change very little with frequency. In comparison to β-casein, the frequency response of lysozyme does not change substantially after washing the protein from the bulk solution. Apparently, it is the irreversibly adsorbed fraction that dominates the dynamic rheological response for lysozyme. Using stress relaxation after a sudden dilatational displacement and shear creep response, the characteristic time of relaxation was found to be 1000 s in both modes of deformation. The very long relaxation time for lysozyme likely results from the formation of a glassy interfacial network. This network develops at high interfacial concentrations where the molecules are highly constrained because of conformation changes that prevent desorption.

Introduction Over the past quarter century, many properties of adsorbed biomolecular films have been investigated at fluid/fluid interfaces.1-31 These studies focus on both * To whom correspondence should be addressed. Tel.: 510-6425204. Fax: 510-642-4 778. E-mail: [email protected]. † University of California. ‡ Stanford University. (1) Murray, B. S.; Cattin, B.; Schuler, E.; Sonmez, Z. O. Langmuir 2002, 18, 9476. (2) Borbas, R.; Murray, B. S.; Kiss, E. Colloids Surf., A 2003, 213, 93. (3) Cascao-Pereira, L. G.; Hickel, A.; Radke, C. J.; Blanch, H. W. Biotechnol. Bioeng. 2003, 83, 498. (4) Cascao-Pereira, L. G.; Hickel, A.; Radke, C. J.; Blanch, H. W. Biotechnol. Bioeng. 2002, 78, 595. (5) Lunkenheimer, K.; Winsel, K.; Fruhner, H.; Fang, J.; Wantke, K. D.; Siegler, K. Colloids Surf., A 1996, 114, 199. (6) Wustneck, R.; Wustneck, N.; Grigoriev, D. O.; Pison, U.; Miller, R. Colloids Surf., B 1999, 15, 275. (7) Banerjee, R.; Puniyani, R. R.; Bellare, J. R. J. Biomater. Appl. 2000, 15, 140. (8) Mohandas, N.; Evans, E. Annu. Rev. Biophys. Biomol. Struct. 1994, 23, 787. (9) Atkinson, P. J.; Dickinson, E.; Horne, D. S.; Richardson, R. M. J. Chem. Soc., Faraday Trans. 1995, 91, 2847. (10) Benjamins, J.; Cagna, A.; Lucassen-Reynders, E. H. Colloids Surf., A 1996, 114, 245. (11) Benjamins, J.; Vader, F. V. Colloids Surf. 1992, 65, 161. (12) Beverung, C. J.; Radke, C. J.; Blanch, H. W. Biophys. Chem. 1999, 81, 59. (13) Cicuta, P.; Stancik, E. J.; Fuller, G. G. Phys. Rev. Lett. 2003, 90, 236101-1. (14) Dickinson, E.; Horne, D. S.; Phipps, J. S.; Richardson, R. M. Langmuir 1993, 9, 242.

fundamental (surface pressure isotherms,15,32 rheology,11,13,17,18,24-26,28,31,33 thin film forces,34 and struc(15) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 415. (16) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 427. (17) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1980, 76, 227. (18) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1980, 76, 240. (19) Grigoriev, D. O.; Fainerman, V. B.; Makievski, A. V.; Kragel, J.; Wustneck, R.; Miller, R. J. Colloid Interface Sci. 2002, 253, 257. (20) Hambardzumyan, A.; Aguie-Beghin, V.; Panaiotov, I.; Douillard, R. Langmuir 2003, 19, 72. (21) Harzallah, B.; Aguie-Beghin, V.; Douillard, R.; Bosio, L. Int. J. Biol. Macromol. 1998, 23, 73. (22) Lu, J. R.; Su, T. J.; Thomas, R. K.; Penfold, J.; Webster, J. J. Chem. Soc., Faraday Trans. 1998, 94, 3279. (23) Lu, J. R.; Su, T. J.; Thomas, R. K. J. Colloid Interface Sci. 1999, 213, 426. (24) Freer, E. M.; Yim, K. S.; Fuller, G. G.; Radke, C. J. J. Phys. Chem. B 2004, 108, 3835. (25) Mellema, M.; Clark, D. C.; Husband, F. A.; Mackie, A. R. Langmuir 1998, 14, 1753. (26) Murray, B. S. Curr. Opin. Colloid Interface Sci. 2002, 7, 426. (27) Patino, J. M. R.; Sanchez, C. C.; Nino, M. R. R. Food Hydrocolloids 1999, 13, 401. (28) Cascao-Pereira, L. G.; Theodoly, O.; Blanch, H. W.; Radke, C. J. Langmuir 2003, 19, 2349. (29) Cascao-Pereira, L. G.; Johansson, C.; Blanch, H. W.; Radke, C. J. Colloids Surf., A 2001, 186, 103. (30) Tupy, M. J.; Blanch, H. W.; Radke, C. J. Ind. Eng. Chem. Res. 1998, 37, 3159. (31) Williams, A.; Prins, A. Colloids Surf., A 1996, 114, 267. (32) Fainerman, V. B.; Miller, R.; Wustneck, R. J. Colloid Interface Sci. 1996, 183, 26.

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ture)9,14,22,23 and applied (emulsions and foam stability)1,2 aspects of protein adsorption. Unlike simple amphipathic molecules, proteins typically reconfigure (denature) upon adsorption to the fluid/fluid interface.12,16,24,30,35 Partial unfolding of the protein molecules gives rise to unique interfacial properties (e.g., interfacial gelation,12 irreversible adsorption,15,24,36 and multilayer formation).9,14,16,22,37 Particularly, it is the formation of interfacial protein gels that is believed to stabilize thin liquid films resulting in long-lived emulsions and foams. Emulsion and foam stability have been linked to both dilatational and shear rheological properties, most likely because the deformations occurring in droplet (bubble) collision and film drainage are a combination of both shear and dilatation. Thus, the viscoelastic properties and the relaxation time scales need to be studied in both deformation modes. Our recent rheological studies of adsorbed proteins indicate that dilatation and shear deformation probe different molecular properties of the interface.24 Shear deformation is sensitive to conformational changes and the resulting intermolecular interactions between the adsorbed molecules through transient physical junctions.38 Dilatational deformation measures the relaxation of molecules undergoing compression or expansion.24,39,40 For irreversibly adsorbed molecules (e.g., insoluble monolayers), the dilatational storage modulus is also comprised of a static contribution independent of strain rate.24,39,40 Hence, dilatational deformation detects the intrinsic softness or hardness of the molecules at the interface, in addition to their dynamic rearrangement. The majority of rheological studies on adsorbed protein films have investigated either interfacial shear or dilatational moduli at a single frequency.10,17,24,28,41-43 Singlefrequency experiments are useful in detecting structural changes of the adsorbed layer with changes in other variables (i.e., surface pressure, interface age, temperature).10,17,24,28,41-43 However, specific relaxation mechanisms that include diffusion exchange or surface relaxation must be determined from the rheologic response at different experimental time scales (i.e., the frequency spectrum of the interfacial moduli). Therefore, we focus here on the linear viscoelasticity of adsorbed protein layers over broad experimental time scales ranging from 20 s to 2 h in both shear and dilatational deformation. We show that diffusion exchange and surface relaxation dominate at different experimental time scales for dilatation. For interfacial shear, however, only in-plane relaxation is observed for all experimental times scales. Methods Materials. Hen-egg-white lysozyme (Seikagaku Corp., Tokyo, Japan, lot LF1121) and β-casein from bovine milk (Sigma Chemical Co., St. Louis, MO, lot 30K7442) are used as received. (33) Bantchev, G. B.; Schwartz, D. K. Langmuir 2003, 19, 2673. (34) Cascao-Pereira, L. G.; Johansson, C.; Radke, C. J.; Blanch, H. W. Langmuir 2003, 19, 7503. (35) Rao, C. S.; Damodaran, S. Langmuir 2000, 16, 9468. (36) Svitova, T. F.; Wetherbee, M. J.; Radke, C. J. J. Colloid Interface Sci. 2003, 261, 170. (37) Rotenberg, Y.; Boruvka, L.; Neumann, A. W. J. Colloid Interface Sci. 1983, 93, 169. (38) Larson, R. L. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1999; Chapter 3. (39) Monroy, F.; Rivillon, S.; Ortega, F.; Rubio, R. G. J. Chem. Phys. 2001, 115, 530. (40) Monroy, F.; Ortega, F.; Rubio, R. G. Phys. Rev. E 1998, 58, 7629. (41) Naumann, C. A.; Brooks, C. F.; Fuller, G. G.; Knoll, W.; Frank, C. W. Langmuir 1999, 15, 7752. (42) Naumann, C. A.; Brooks, C. F.; Fuller, G. G.; Lehmann, T.; Ruhe, J.; Knoll, W.; Kuhn, P.; Nuyken, O.; Frank, C. W. Langmuir 2001, 17, 2801. (43) Naumann, C. A.; Brooks, C. F.; Wiyatno, W.; Knoll, W.; Fuller, G. G.; Frank, C. W. Macromolecules 2001, 34, 3024.

Freer et al. The 100 mM phosphate buffer solutions (pH 7.0 ( 0.1) are made with distilled water further purified using a Milli-Q filtration unit (to greater than 18.2 MΩ cm resistivity). Sodium phosphate dibasic heptahydrate and monobasic monohydrate are from EM Science (Gibbstown, NJ) and are of analytic grade. They are also used as received. Hexadecane (Mallinckrodt Baker, Inc., Paris, KY) was purified using an alumina (Fisher Scientific, Fair Law, NJ) and silica gel (J.T. Baker, Phillipsburg, NY) adsorption column. The interfacial tension of the purified hexadecane against the phosphate buffer solution remained constant at a value of 53.3 mN/m for 24 h. All experiments were conducted at 23 °C. Interfacial Tension. To determine the dynamic interfacial tension of the hexadecane/water interface we use pendant-drop tensiometry. Details of this apparatus are given elsewhere.44-46 Image acquisition and regression of the interfacial tension are performed with commercially available Dropimage software (Rame´-Hart, Inc.) by fitting the Laplace equation to the drop shape. Typical precision in tension is (0.5%. Results are later reported in terms of the dynamic surface pressure, π, which is defined as the difference between the clean hexadecane/water tension (53.3 mN/m) and the tension with protein present. Interfacial Dilatational Rheology. We measure the surface dilatational storage modulus, E ′, and the surface dilatational loss modulus, E ′′, by subjecting the oil/water interface to an infinitesimal periodic-area deformation. Additionally, we measure the interfacial dilatational relaxation modulus, E(t), after an infinitesimal step-strain deformation. Modification of the pendant-drop tensiometer enables sinusoidal variations in the drop surface area.47 Oscillation hardware consists of a 50-mL gastight syringe mechanically coupled to a linear piezoelectric actuator from Physik Instrumente (model P-840.3). Actuator motion is forced using a Hewlett-Packard function generator (model 3325 A) that is computer controlled with National Instruments LabView software. The piezoelectric actuator is capable of subnanometer resolution ensuring the smoothest possible drop-volume oscillation. Further details of the oscillating-drop rheometer are available.44-46 We report the complex interfacial dilatational modulus, E*(ω), which is defined as the linear proportionality factor between a periodically applied strain and the response stress

∆γ j ei[ωt+φ(ω)] ) E*(ω)

∆A iωt e A0

(1)

where A0 is the unperturbed oil-drop interfacial area, ∆A is the amplitude of the interfacial area change, ∆γ j is the amplitude of the isotropic oil/water interfacial stress measured from axisymmetric drop shape analysis (ADSA), ω is the oscillation frequency, and φ is the phase angle difference between the applied strain and the response stress. The isotropic interfacial stress, γ j , is distinguished from the thermodynamic interfacial tension, γ, in that it generally includes nonequilibrium contributions.48 Because the drop area oscillates periodically, the dilatational modulus exhibits two elements: an elastic part accounting for the recoverable energy stored in the interface (storage modulus, E ′) and a viscous part accounting for energy lost through relaxation processes (loss modulus, E ′′). The interfacial storage and loss moduli correspond to the real and imaginary components of the complex dilatational elasticity: E* ) E ′ + iE ′′. The frequency dependencies of the dilatational moduli are determined by varying the oscillation frequency from 0.1 to 3.14 rad/s. Equation 1 and equation 2 to follow demand small strains so that the interface lies in the linear viscoelastic regime. We set ∆A/A0 at 0.025 because nonlinear effects are observed above a relative strain of about 3.0%. (44) Freer, E. M.; Svitova, T. F.; Radke, C. J. J. Pet. Sci. Eng. 2003, 39, 137. (45) Freer, E. M.; Radke, C. J. J. Adhes. 2004, 80, 481. (46) Freer, E. M. Interfacial Rheology of Macromolecules. Ph.D. Thesis, University of California, Berkeley, CA, 2004. (47) Lunkenheimer, K.; Kretzschmar, G. Z. Phys. Chem. 1975, 256, 593. (48) Edwards, D. A.; Wasan, D. T.; Brenner, H. Interfacial Transport Processes and Rheology; Butterworth-Heinemann: Boston, 1991; Chapters 3 and 4.

Protein Relaxation at Hexadecane/Water Interface

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To determine the dilatational relaxation modulus, E(t), we measure the stress relaxation after a sudden strain displacement. In these experiments, the interface is instantaneously deformed (expanded or compressed) and then held constant while the interfacial stress is measured (through ADSA). The dilatational relaxation modulus is calculated as a function of time from the following expression

E(t) ) ∆γ j (t)

A0 ∆A

(2)

where ∆γ j is the difference between the static tension prior to interfacial deformation and the measured isotropic interfacial stress. The dilatational relaxation modulus, E(t), is related to the complex dilatational modulus, E*(ω), via a Fourier transform.49 The advantage of the step-strain technique is that the interfacial stress decays to a steady value within 2 h for the systems investigated in this work. Acquiring the same information using the oscillatory technique requires a very long time, because of the low frequencies needed to probe slow stress relaxation. We assert the interfacial concentration is nearly constant (as is required by eq 2), because the surface pressure changes negligibly during the relaxation experiment (i.e., after 24 h of interface aging when the step-strain experiment is performed) as shown later.24 Interfacial Shear Rheology. To probe the interfacial shear rheology we use a recently developed interfacial stress rheometer.50 In this apparatus, a thin magnetized rod oscillates at the oil/water (or air/water) interface between two vertical glass walls. Rod motion is forced by an oscillating magnetic field. The position of the rod is detected by an optical microscope and a photodiode array, allowing determination of the surface strain, , defined as the amplitude of the rod displacement divided by the distance between the rod and the vertical glass wall. For small periodic rod displacements, the complex interfacial shear modulus, G*(ω), is ascertained as the linear proportionality constant between the applied stress and the response strain

σei[ωt+φ(ω)] ) G*(ω)eiωt

(3)

where σ is the interfacial shear stress and, again, φ(ω) is the phase lag between the applied stress and the measured strain response. Analogous to the complex dilatational modulus, the complex interfacial shear modulus is comprised of two contributions: G* ) G ′ + iG ′′, where the storage modulus, G ′, accounts for the recoverable energy stored in the interface and the loss modulus, G ′′, accounts for energy lost through shear dissipation processes. The frequency dependencies of the shear moduli are determined by varying the oscillation frequency from 0.0157 to 3.14 rad/s. In addition, to ensure that these experiments are performed in the linear viscoelastic regime, is set at 0.02 because, again, above this relative strain, nonlinear effects are evident. To investigate longer relaxation modes in shear deformation the creep response is determined.51 In the creep experiments, the strain response is measured after a sudden stress is applied to the magnetic needle. The surface creep compliance, J(t), is the proportionality constant between the shear stress and shear strain and is defined as

(t) ) σJ(t)

(4)

As discussed above, the applied stress is set such that the strain is slowly varying enough so as to remain in the linear regime. Washout. To investigate the contribution of diffusion to the dilatational response45 of lysozyme and β-casein reversibly adsorbed at the oil/water interface, we utilize continuous flow tensiometry.36 After aging the interface for 24 h, 20 cell volumes of protein-free water (interfacial tension 72 mN/m) were flushed through the optical cuvette of the tensiometer, resulting in a (49) Morrison, F. A. Understanding Rheology; Oxford University Press: New York, 2001; Chapter 8. (50) Brooks, C. F.; Fuller, G. G.; Frank, C. W.; Robertson, C. R. Langmuir 1999, 15, 2450. (51) Brooks, C. F.; Thiele, J.; Frank, C. W.; O’Brien, D. F.; Knoll, W.; Fuller, G. G.; Robertson, C. R. Langmuir 2002, 18, 2166.

Figure 1. Dynamic surface pressures of lysozyme (5.0 mg/L) and β-casein (8.5 mg/L) each at 0.35 µM. negligible bulk protein concentration in the buffer solution. Similar results for washout of lysozyme and β-casein aged at the hexadecane/water interface for 12 h are presented elsewhere.24 Washing away the reversibly adsorbed proteins decreases the surface pressure of lysozyme and β-casein by only 2 and 3 mN/m, respectively, indicating that most, but not necessarily all, of the protein molecules are irreversibly adsorbed from the water phase at the oil/water interface.

Results Dynamic Surface Pressure. Figure 1 shows the dynamic surface pressures for lysozyme (5.0 mg/L) and β-casein (8.5 mg/L) at the same molar concentration, 0.35 µM, on a semilogarithmic scale. Adsorption of these two proteins has been previously discussed in detail elsewhere in terms of three dynamic adsorption regimes: induction, monolayer saturation, and interfacial gelation.12,24 Most relevant to this study is that the long-time adsorption dynamics of lysozyme and β-casein are substantially different. Lysozyme shows a slow continuing increase after the initial rapid surface-pressure change characteristic of interfacial gelation.12 Contrastingly, β-casein reaches a relatively steady surface pressure at long interface-aging times. Slow surface-pressure changes observed at later times have been attributed to adsorption barriers and surface relaxation.12,52 To quantify the physical differences between the interfacial structures of lysozyme and β-casein, the frequency responses in both the shear and the dilatational moduli are measured. Interfacial Rheology. We previously reported that the dilatational and shear moduli change slowly with interface age (continued adsorption) at the hexadecane/ water interface.24 Slow changes in the interfacial moduli mark the formation of an interfacial glass/gel that results from protein conformation rearrangement at the interface. Here, we investigate the frequency response of the shear and dilatational moduli after 24 h of interface aging. Figures 2 and 3 show the dilatational and shear moduli on logarithmic and semilogarithmic scales, respectively, for lysozyme after aging at the interface for 24 h. For both shear and dilatation moduli, the response spans two frequency decades. Data collected after washout in Figure 2 are discussed later. As observed from the order of magnitude difference between E ′ and E ′′ in Figure 2, the interfacial dilatational response is primarily elastic. E ′ slightly increases whereas E ′′ slightly decreases with (52) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 403.

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Figure 2. Oscillatory dilatational response versus frequency for 0.35 µM (5.0 mg/L) lysozyme aged at the hexadecane/water interface for 24 h in 100 mM phosphate buffer. pH ) 7.0. E ′ and E ′′ prior to washout are shown as closed and open circles, respectively. E ′ and E ′′ after washout are shown as closed and open squares, respectively. The frequency responses of the complex dilatational viscosity before and after washout are shown as open triangles and open diamonds, respectively. Power-law fits to |κ*| before and after washout are shown as solid and dashed lines, respectively.

Figure 3. Oscillatory shear response versus frequency for 0.35 µM (5.0 mg/L) lysozyme aged at the hexadecane/water interface for 24 h in 100 mM phosphate buffer. pH ) 7.0. G ′ and G ′′ are shown as closed and open circles, respectively. The complex shear viscosity is shown as closed triangles with a power-law fit shown as a solid line.

increasing oscillation frequency. This is a characteristic trend observed at frequencies higher than the characteristic time of diffusion exchange or network relaxation as captured, for example, in the Lucassen and van den Temple (LVDT)53 or Maxwell39 models, respectively. We also report in Figure 2 the magnitude of the complex interfacial dilatational viscosity, |κ*| ) [(E ′/ω)2 + (E ′′/ω)2]1/2. The complex interfacial dilatational viscosity change is inversely proportional to the frequency, reflecting a shear-thinning behavior for lysozyme at the interface. Similar to the dilatational response, the shear storage modulus, G ′, is 1 order of magnitude larger than the shear loss modulus, G ′′, over the frequency range shown in Figure 3. However, in contrast to the dilatational response, both G ′ and G ′′ increase monotonically over the identical frequency range. This trend suggests different dissipation mechanisms between shear and dilatational deformation over the measured frequency range. In addition to the shear moduli in Figure 3, the frequency dependence of (53) Lucassen, J.; van den Temple, M. Chem. Eng. Sci. 1972, 27, 1283.

Freer et al.

Figure 4. Oscillatory dilatational response versus frequency for 0.35 µM (5.0 mg/L) β-casein aged at the hexadecane/water interface for 24 h in 100 mM phosphate buffer. pH ) 7.0. E ′ and E ′′ prior to washout are shown as closed and open circles, respectively. E ′ and E ′′ after washout are shown as closed and open triangles, respectively. Solid and dashed lines correspond to the LVDT model before and after washout, respectively.

Figure 5. Oscillatory shear response versus frequency for 0.35 µM (5.0 mg/L) β-casein aged at the hexadecane/water interface for 24 h in 100 mM phosphate buffer. pH ) 7.0. G ′ and G ′′ are shown as closed and open circles, respectively. The complex shear viscosity is shown as closed triangles with a power-law fit shown as a solid line.

the interfacial shear viscosity, |η*| ) [(G ′/ω)2 + (G ′′/ω)2]1/2, is shown as solid triangles. Analogous to |κ*|, the interfacial shear viscosity, |η*|, decreases with a power-law exponent nearly identical to that observed for |κ*|, confirming a shear-thinning behavior of adsorbed lysozyme in both shear and dilatational deformation. Companion interfacial dilatational and shear moduli for β-casein are shown in Figures 4 and 5, respectively, as a function of oscillation frequency after 24 h of interface aging. As opposed to lysozyme, E ′ and E ′′ for β-casein are the same order of magnitude within the measured frequency range. However, both are 1 order of magnitude smaller than the magnitudes of E ′ and E ′′ observed for lysozyme. In Figure 4, the dilatation storage modulus of β-casein increases monotonically with frequency. The dilatational loss modulus initially decreases somewhat and then increases at higher frequencies (i.e., beyond 1 rad/s). Note that the interfacial dilatational storage modulus in Figure 4 for β-casein is more than 1 order of magnitude smaller than that for lysozyme. Data collected after washout and the absence of |κ*| data in Figure 4 are discussed later.


Figure 6. Step-strain dilatational response for lysozyme (open diamonds), β-casein prior to washout (open circles), and β-casein after washout (open triangles) after a step compression of the interfacial area (|∆A/A0| ) 0.025). The interface was aged for 24 h before compression in 100 mM phosphate buffer. pH ) 7.0. The static moduli E∞ are labeled. Solid lines correspond to the LVDT model before and after washout.

Figure 5 shows the frequency response of the shear moduli for β-casein. The shear loss modulus is larger than the storage modulus for the frequency range investigated, characteristic of fluidlike monolayers.38 As with the dilatational storage modulus, the shear moduli for β-casein are 1 order of magnitude smaller than those observed for lysozyme in Figure 3. The frequency dependence of the interfacial shear viscosity is also shown in Figure 5. Similar to that of lysozyme, the interfacial shear viscosity decreases with a power-law dependence, indicating shear thinning. The pseudoplasticity of lysozyme, however, is stronger than that of β-casein as shown through the scaling exponents of the interfacial viscosities listed in Figures 3 and 5. To investigate relaxation processes occurring on longer time scales, we report the dilatational relaxation modulus, E(t), as calculated from the relaxation of the interfacial stress using eq 2. Figure 6 displays the dilatational relaxation modulus, E(t), for lysozyme and β-casein as open diamonds and triangles, respectively, after aging the interface for 24 h. Data measured after washout are discussed later. Consistent with the interfacial dilatational moduli in Figures 2 and 3, E(t) is 1 order of magnitude larger for lysozyme than for β-casein. Nevertheless, for both lysozyme and β-casein, the modulus decays to a nonzero value denoted by E∞ in Figure 6, where the subscript ∞ indicates the zero-frequency limit (i.e., t f ∞). Hence, the interfacial tension after relaxation is not the same as the initial value before drop compression. The static dilatational modulus, E∞, arises from an interfacial-tension change with an interfacial-area change at a constant adsorbed amount of an irreversibly adsorbed species.24 Accordingly, the static modulus is given by the slope of the surface pressure-area isotherm according to the Gibbs elasticity: E∞ ) -dπ/d ln A.24 Similar to E(t), the interfacial creep compliance, J(t), is measured to investigate relaxation processes occurring on long experimental time scales during shear deformation. In Figure 7, the interfacial creep compliances for β-casein and lysozyme are shown on different ordinate scales as open triangles and circles, respectively. Lysozyme exhibits a classic viscoelastic response. There is an initial large sudden strain representing the solidlike behavior and then a slow decay to a constant slope representing

Langmuir, Vol. 20, No. 23, 2004 10163

Figure 7. Shear creep response for lysozyme (open circles) and β-casein (open triangles) after a step stress. The interface was aged for 24 h in 100 mM phosphate buffer. pH ) 7.0. Dashed lines correspond to the four-parameter Burger model.

fluidlike behavior. Conversely, the response of β-casein is almost entirely fluidlike, and the adsorbed layer gives little resistance to shear deformation. It is interesting to note that the time scales of relaxation for E(t) observed in Figure 6 are similar to those observed for J(t) in Figure 7 for lysozyme as discussed later. Interfacial Rheology: Washout. The frequency responses of the dilatational moduli measured after washout of lysozyme and β-casein are shown in Figures 2 and 4 as squares (open and closed) and triangles (open and closed), respectively. Additionally, the interfacial dilatational viscosity data for lysozyme after washout are shown as open triangles in Figure 2. The magnitudes and frequency responses of E ′ and |κ*| change very little after washout. This result suggests that reversible diffusion exchange does not appreciably contribute to the dilatational response of lysozyme. However, E ′′ decreases after washout indicating that the small reversibly adsorbed fraction contributes significantly to the viscous dissipation within the interfacial region. In contrast to lysozyme, E ′ for β-casein in Figure 4 increases substantially and is independent of oscillation frequency after washout. The dilatational loss modulus of β-casein decreases after washout, but similar to the response prior to washout, E ′′ increases with increasing oscillation frequency. E(t) for β-casein after washout is shown in Figure 6 as open triangles. The response is essentially constant, and E(t) ) E∞ for all times consistent with the oscillatory experiments after washout shown in Figure 4. A caveat of the stress-relaxation technique is that the protein surface concentration must not change appreciably during the course of the experiment (quasi-equilibrium). This condition is fulfilled when the interfacial-stress change due to compression is faster than the interfacial-tension change due to aging. For lysozyme prior to washout, E(t) decays to a steady value, E∞. After washout, E(t) initially relaxes similar (t < 1000 s in Figure 6) to that observed prior to washout. After 1000 s, however, the surface pressure upon washout changes very slowly on the same time scale as the asymptotic decay in E(t). Therefore, E(t) does not decay to a steady value for lysozyme after the washout experiments were performed. For this reason we are unable to compare E(t) before and after washout for lysozyme. Discussion Interfacial dilatational stress relaxation can occur through both in-plane surface relaxation for the irrevers-

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Table 1. Parameters of the Modified LVDT Model for β-Casein Adsorbed at the Hexadecane/Water Interface E∞,a mN/m β-casein (pre-washout; oscillation) β-casein (pre-washout; step-strain) β-casein (post-washout; oscillation) β-casein (post-washout; step-strain) a

E 0, mN/m

0.6 ( 0.2 8.5 ( 0.2

τD, s

κ, (mN‚s)/m

26.8 ( 2 0.83 ( 0.08

0.6 ( 0.2 11.1 ( 0.2 18.5 ( 1 NA 17 ( 0.2

NA

NA

0.4 ( 0.1

17 ( 0.2

NA

NA

NA

Determined from Figure 6.

ibly adsorbed molecules13,39,40,45,51 and diffusion exchange for the reversibly adsorbed moelcules.45,54 Because E* . G* for both lysozyme and β-casein, any diffusion exchange with the bulk solution arising from surface concentration gradients in shear deformation is negligible.55 Therefore, stress relaxation in shear deformation occurs primarily through surface relaxation. In addition, the material functions E* and E(t) as well as G* and J(t) contain complementary relaxation information, respectively. Therefore, physical models can be investigated over broad experimental time scales. In the following sections, we investigate the physical mechanisms of stress relaxation for β-casein and then lysozyme. β-Casein. The considerable change observed in the dilatational response of β-casein after washout shown in Figures 4 and 6 suggests that diffusion exchange contributes significantly to the relaxation process. To confirm this assertion, we model the data using a modified form of the classical LVDT diffusion-exchange model originally devised for reversibly adsorbed surface-active molecules53

1+Ω E ′ ) E∞ + E0 1 + 2Ω + 2Ω2

(5)

Ω + κω E ′′ ) E0 1 + 2Ω + 2Ω2

(6)

and

where Ω ) (τDω)-1/2 is a dimensionless parameter consisting of the ratio of the experimental and diffusion time scales, τD is the characteristic time for diffusion, E0 ) -dγ/d ln Γ is the Gibbs elasticity for reversibly adsorbed species, Γ is the interfacial concentration of the reversible surface-active species, and κ is the interfacial dilatational viscosity. Our embodiment of the LVDT relaxation mode in eqs 5 and 6 includes the static modulus of irreversibly adsorbed proteins, E∞, which is directly determined from the experimental data for E(t f ∞) and is independent of the chosen relaxation model. At high frequencies (i.e., Ω f 0) the protein film behaves as an insoluble monolayer. Therefore, an additional term, κω, is added to E ′′ to account for viscous dissipation at higher frequencies.56 Equations 5 and 6 fit to β-casein E ′ and E ′′ data before and after washout are shown in Figure 4 as solid and dashed lines, respectively. The regressed parameters τD, E0, and κ are given in Table 1 with E∞ determined directly from the dilatational relaxation modulus (see Figure 6). (54) Johnson, D. O.; Stebe, K. J. Colloids Surf., A 1996, 114, 41. (55) Barentin, C.; Ybert, C.; di Meglio, J. M.; Joanny, J. F. J. Fluid Mech. 1999, 397, 331. (56) Wantke, K. D.; Fruhner, H. J. Colloid Interface Sci. 2001, 237, 185.

Prior to washout, the frequency response is dominated by diffusion exchange (i.e., in the limit of t f ∞ the dilatational storage modulus approaches E∞ ) 0.63 mN/m) with a small contribution to E ′′ from viscous dissipation at higher frequencies as indicated by the magnitude of κ in Table 1. After washout, E ′ increases to 17 mN/m, and the frequency independence of the dilatational modulus (E ′ ) E∞) suggests that indeed diffusion exchange with the bulk solution contributes to the dilatational response prior to washout. The increase in E ′ after washout is discussed later. Conversely, upon washout, E ′′ decreases with a slight linear increase with frequency in Figure 4, verifying the proposed modification of eq 6 with the viscous dissipation contribution from the insoluble monolayer (i.e., κω). The smaller value of κ measured after washout likely results from desorption of the reversibly adsorbed protein molecules. To consider diffusion exchange over longer experimental time scales and to validate extrapolation of eqs 5 and 6 to low frequencies, we investigate the dilatational relaxation modulus E(t), within the LVDT framework57

E(t) ) E∞ + E0 exp(2t/τD) erfc(x2t/τD)

(7)

Equation 7 is shown in Figure 6 as solid lines for β-casein both before and after washout. The model fits the data well over the entire relaxation time scale prior to washout, suggesting again that diffusion dissipation is the only contributing relaxation mode. The parameters E0 and τD regressed using eq 7 are listed in Table 1 with E∞ again determined asymptotically from the E(t) data. They compare well with those regressed from the oscillatory data using eqs 5 and 6. After washout, E(t) is constant and equal to E∞, confirming that surface relaxation does not contribute to the measured dilatational storage modulus for the irreversibly adsorbed fraction on the measured time scale.45 In addition, E ′ in Figure 4 is equal to E∞ in Figure 6, establishing consistency between the two rheological techniques after washout. To explain the increase in E ′ after washout, we investigate how the structure of the protein-laden interface changes with π as inferred through the static dilatational modulus.24 We measured the static dilatational modulus as a function of surface pressure by performing step-strain experiments at different interface aging times. Results are shown for β-casein in Figure 8. Each datum in this figure represents a single step-strain experiment (cf., Figure 6) with Figure 1 giving the corresponding surface pressure for the particular aging time. The static dilatational modulus for β-casein in Figure 8 changes nonmonotonically with surface pressure. E∞ initially increases, reaches a maximum at approximately π ) 14 mN/m, and then decreases to 0 at a surface pressure of 32 mN/m that corresponds to the steady-state surface pressure in Figure 1 (π for t > 1 h). Proposed schematic conformations of β-casein adsorbed at different surface pressures are sketched in Figure 8. For low surface pressures, the adsorbed protein molecules exhibit loops and trains due to partial unfolding.16 As the surface pressure increases, the protein molecules suffer compression (the area occupied per molecule decreases), and loops and tails exude into the continuous phases resulting in thickening of the interfacial layer.27 Thus, protein molecules are considered as elastic chains where (57) Loglio, G.; Rillaerts, E.; Joos, P. Colloid Polym. Sci. 1981, 259, 1221.


Langmuir, Vol. 20, No. 23, 2004 10165 Table 2. Parameters of the Burger’s Model for β-Casein and Lysozyme Adsorbed at the Hexadecane/Water Interface GM, mN/m

GV, mN/m

τv, s

η, (mN‚s)/m

β-casein 0.2 ( 0.01 0.012 ( 0.001 193 ( 2 2.87 ( 0.01 lysozyme 11.21 ( 0.05 14.9 ( 0.1 393 ( 7 22 000 ( 100

parameter Burger’s model has been used successfully to represent the creep response of viscoelastic monolayers51

J(t) )

Figure 8. Static modulus versus surface pressure for 0.35 µM (5.0 mg/L) β-casein in 100 mM phosphate buffer. pH ) 7.0. β-Casein conformations are (a) train and (b) loops and tails, and (c) β-casein molecules are squeezed beyond the collapse surface pressure of 29 mN/m and exchanged with the bulk solution. The dotted line around the protein molecules represents the average area occupied by the individual molecules.

the interprotein interactions change with the molecule conformation.58 The conformational changes of β-casein in Figure 8, and for lysozyme shown later in Figure 10, are continuous in π where the illustrations exemplify configurations at a single surface pressure. At low surface pressures, β-casein adsorbs in a mostly train conformation (conformation a in Figure 8).16 At higher surface concentrations loops and tails extend into the bulk phases (conformation b in Figure 8). It has been suggested that the maximum in E∞ occurs through the conformation transition from mostly train to mostly loops and tails.16,59 Beyond π ) 29 mN/m the monlayer collapses (dE∞/dπ ) ∞) and protein molecules are squeezed into the subphase, as illustrated in Figure 8 (conformation c).16 Additionally, at the steady-state surface pressure, E∞ is approximately 0, indicating reversible exchange of the protein molecules with the bulk solution.60 Multilayers may form at these high surface pressures and contribute to the observed response.16 As discussed above, β-casein is practically irreversibly adsorbed at the oil/water interface after 24 h of interface aging, but some fraction of the protein molecules do desorb after washout. Interestingly, we find that the surface pressure directly after washout for β-casein decreases to the collapse pressure (29 mN/m), indicating that some small fraction of adsorbed protein layers at E∞ close to zero in Figure 8 (i.e., after 24 h of aging) is reversibly adsorbed.15 Apparently, near the collapse surface pressure, β-casein molecules overcome desorption barriers and exchange reversibly with the bulk solution, as supported through the LVDT analysis above. At the surface pressure of 29 mN/m, the dilatational static modulus is 15 mN/m, which is consistent with E ′ and E∞ reported after washout in Figures 4 and 6, respectively. Therefore, E ′ and E∞ increase after washout because some β-casein molecules desorb from the interface. To determine the long-time response of β-casein in shear deformation, we model the creep compliance. A four(58) Stoyanov, S. D.; Paunov, V. N.; Rehage, H.; Kuhn, H. Phys. Chem. Chem. Phys. 2004, 6, 596. (59) Benjamins, J.; Feijter, J. A. D.; Evans, M. T. A.; Graham, D. E.; Phillips, M. C. Faraday Discuss. 1975, 218. (60) Van den tempel, M.; Lucassen-Reynders, E. H. Adv. Colloid Interface Sci. 1983, 18, 281.

1 t 1 + + (1 - e-t/τv) η GM GV

(8)

where η is the zero-shear viscosity, GM and GV are the elastic moduli of the Maxwell and Voigt-Kelvin elements, respectively, and τv is the charaterisitc time of the VoigtKelvin element. Equation 8 is regressed to the experimental data in Figure 7 for β-casein. The parameters are listed in Table 2. Equation 8 is shown in Figure 7 as a dashed line. The zero-shear viscosity is 3 mN s/m, which is a factor of 3 larger than κ. Although β-casein exhibits some elastic behavior in shear deformation (finite G ′), the J(t) data establish that the response is primarily viscous on long time scales. For β-casein, the dilatational and shear responses are dominated by different mechanisms that have different characteristic times: diffusion exchange and surface relaxation, respectively. Lysozyme. The dilatational and shear moduli for globular lysozyme are much larger than those for the flexible β-casein. In contrast to β-casein, there is little change in the dilatational moduli for lysozyme after washout, suggesting that diffusion exchange does not significantly contribute to the interfacial relaxation processes. Additionally, the dilatational and shear moduli exhibit only a weak dependence on frequency for the oscillatory experiments as indicated by the power-law coefficients for |κ*| and |η*| shown in Figures 2 and 3. However, significant changes in E(t) and J(t) are observed at long experimental times signifying that the characteristic relaxation time is greater than the time scale amenable to the oscillatory technique. Therefore, as opposed to β-casein, E(t) and E* probe different relaxation modes. In the linear-response regime, E(t) can be directly transformed into the frequency domain, E*(ω), by61

∫t∞[E(t) - E∞] sin(ωt) dt

E ′(ω) ) E∞ + ω

(9)

and

E ′′(ω) ) ω

∫t∞[E(t) - E∞] cos(ωt) dt

(10)

This transformation allows direct comparison of data measured using the step-strain and oscillatory techniques. Integration of eqs 9 and 10 is possible only at small frequencies (i.e., when 1/ω is much less than the time step to collect each data point) and, thus, is possible only if the characteristic relaxation time is large. Therefore, the same procedure could not be used for β-casein (i.e., τD ) 10 s). The transformation of E(t) into E*(ω) for lysozyme was performed by numerically integrating the experimental data in Figure 6. Figure 9 shows E ′ and E ′′ over five frequency decades. E ′ and E ′′ acquired from oscillatory experiments (cf., Figure 2) are shown as closed and open (61) Tschoegl, N. W. The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction; Springer-Verlag: New York, 1989; Chapters 4 and 11.

10166


Freer et al.

Figure 9. Combined oscillatory and step-strain dilatational response versus frequency for 0.35 µM (5.0 mg/L) lysozyme aged at the hexadecane/water interface for 24 h in 100 mM phosphate buffer. pH ) 7.0. E ′ and E ′′ are shown as closed and open symbols, respectively. E ′ and E ′′ measured using the oscillatory technique and E ′ and E ′′ converted to the frequency domain from the step-strain data are shown as triangles and circles, respectively. Solid lines correspond to the Maxwell model.

triangles, respectively, whereas E ′ and E ′′ converted from step-strain experiments are shown as closed and open circles, respectively. Combination of the two techniques allows comparison with theoretical models over a very broad frequency range. Therefore, it is possible to separate relaxation modes occurring on very different time scales.45,61 Figure 9 shows a sharp peak in E ′′ at approximately 10-3 rad/s where the majority of change in E ′ occurs, contrasting the relatively broad changes at higher frequencies. The sharp changes in the dilatational moduli shown in Figure 9 suggest that a single relaxation mode dominates the response at low frequencies. As discussed above, we found that for lysozyme the frequency response of the dilatational moduli is dominated by the irreversibly adsorbed protein molecules. The frequency response of E ′ and E ′′ for insoluble monolayers of complex macromolecules has been successfully modeled using the generalized linear viscoelastic model (GLVE).39,40,45 For a single relaxation mode, the GLVE model reduces to the Maxwell model61

τM2ω2 E ′ ) E∞ + EM 1 + τM2ω2

(11)

τMω E ′′ ) EM 1 + τM2ω2

(12)

and

where τM is the characteristic surface relaxation time and EM is the high-frequency limiting modulus (i.e., ω f ∞). Again, the static dilatational elasticity of irreversibly adsorbed proteins, E∞, must be included to capture the zero-frequency response. The parameters EM and τM were regressed to the data in Figure 9 as 37 ( 2 mN/m and 1180 ( 60 s, respectively. The static dilatational modulus was determined directly from Figure 6 with a value of 16.3 (1 mN/m. Equations 11 and 12 are shown as solid lines in Figure 9. The Maxwell model well captures the dominant changes in E ′ and E ′′ at low frequencies. However, multiple relaxation modes in the GLVE model

Figure 10. Static modulus versus surface pressure for 0.35 µM (5.0 mg/L) lysozyme in 100 mM phosphate buffer. pH ) 7.0. Lysozyme conformations are (a) partially unfolded and globular, (b) partially unfolded and aggregated, and (c) multilayer. The dotted line around the protein molecules represents the average area occupied by the individual molecules.

and, hence, several parameters may be required to fit the data over the entire frequency range. It is important to note that fitting the data for lysozyme in Figure 6 to the LVDT model resulted in significant error. Therefore, diffusion exchange does not measurably contribute to the interfacial dilatational response for lysozyme. Similar to Figure 8 for β-casein, the dilatational static modulus for lysozyme is shown in Figure 10 as a function of surface pressure. Initially, lysozyme adsorbs in a compact globular state, resembling the native bulk conformation,10,24 and E∞ increases with surface concentration. A maximum is reached at 78 mN/m, and then E∞ decreases monotonically to 20 mN/m at a surface pressure of 28 mN/m. The overall large magnitude of E∞ results from rigidity of the adsorbed protein molecule that is stabilized by strong hydrophobic interactions and disulfide bridges. Possible conformations of lysozyme adsorbed at different surface pressures are illustrated in Figure 10. The structural transitions include a change from globular to partially unfolded (conformation a in Figure 10) and partially unfolded aggregated (conformation b in Figure 10), and at high surface pressures multilayer adsorption is likely (conformation c in Figure 10).22 The decrease in E∞ at higher surface pressures is believed to occur through partial unfolding and subsequent conformation changes that result in loss of intrinsic rigidity of the protein molecule.24,28 Unfolding conformational changes of the protein molecules upon adsorption results in strong kinetic barriers to desorption.36,62 This is due to the unfavorable interactions of the exposed hydrophobic groups with the bulk solution and to interprotein aggregation. Unlike β-casein, a collapse pressure is not observed, indicating that lysozyme is strongly bound to the interface. Analogous experiments investigating long relaxation time scales in shear deformation are shown in Figure 7 for lysozyme. Similar to the shear moduli, there is 1 order of magnitude difference in J(t) for lysozyme and β-casein. The slow relaxation mode observed for E(t) in Figure 6 is apparent in Figure 7. J(t) for lysozyme was also fit to the four-parameter Burger’s model, shown as a solid line in Figure 7. Parameters regressed to eq 8 are given in Table 2. The zero-shear viscosity for lysozyme is 4 orders of magnitude larger than that for β-casein, emphasizing the (62) Anderson, R. E.; Pande, V. S.; Radke, C. J. J. Chem. Phys. 2000, 112, 9167.


glassy nature of the lysozyme interfacial network.51 Interestingly, the characteristic relaxation times of the Maxwell elements in shear (τM ) η/GM ) 1962 s) and dilatational (τM ) 1180 s) deformation are comparable, suggesting that the same relaxation mode dominates the rheological response in both modes of deformation. The very long relaxation time observed for lysozyme in both shear and dilatation is characteristic of highly concentrated insoluble monolayers that form a gel-like network or an interfacial glassy phase.39,40,45,51 Comparison of β-Casein and Lysozyme. To explain the differences in the relaxation mechanisms and the relaxation time scales between β-casein and lysozyme, we consider the differences in kinetic desorption barriers and conformation changes between the two protein molecules. For both β-casein and lysozyme there is an initial rapid increase in the surface pressure in Figure 1 with interfacial concentration. Additionally, after 1 h of interface aging, the surface pressure and dilatational moduli reach nominally steady values for β-casein but not for lysozyme.24 The nominally steady surface pressure and the decay of the static dilatational modulus toward zero for β-casein (reversible exchange) indicates that the adsorption layer approaches an equilibrium state. This reversible adsorption is observed only near and beyond the collapse pressure. The collapse pressure represents the point where protein molecules begin to squeeze out of the primary adsorption layer upon further compression (upon an increase in surface concentration).15 Apparently, at the collapse pressure, the work required to compress the β-casein molecules (further conformational changes) becomes comparable to the energetic barriers for desorption. Because the native protein conformation for β-casein in bulk solution is random, desorption barriers are likely not strongly coupled to significant conformation change. For lysozyme, the dynamic changes in the surface pressure and rheological properties are substantially different than those observed for β-casein. We previously demonstrated for lysozyme at the oil/water interface that an interfacial network forms from continued slow conformational rearrangement of the protein molecules.24 Upon adsorption, lysozyme slowly changes conformation, exposing hydrophobic groups, as the surface concentration increases. The conformation changes at the interface are consistent with computer models of globular protein adsorption62,63 as well as with adsorption isotherm modeling for macromolecules.64,65 It is likely that the strong irreversibility (i.e., complete absence of both diffusion exchange and a collapse pressure) is correlated to unfolding upon adsorption. Therefore, in contrast to β-casein, desorption of unfolded lysozyme (interfacially denatured) is highly unfavorable even at high surface pressures. Additionally, the slow adsorption dynamics and changes in the rheological properties can be explained in terms of irreversible adsorption. Because lysozyme is highly effective at reducing the interfacial tension between oil and water, it adsorbs at high interfacial concentrations. Although lysozyme unfolds, disulfide bonds limit conformational flexibility. Therefore, unlike β-casein at high interfacial concentrations, a glassy phase forms because (63) Leonhard, K.; Prausnitz, J. M.; Radke, C. J. In preparation. (64) Defeijter, J. A.; Benjamins, J. J. Colloid Interface Sci. 1982, 90, 289. (65) Fainerman, V. B.; Miller, R.; Kovalchuk, V. I. Langmuir 2002, 18, 7748.

Langmuir, Vol. 20, No. 23, 2004 10167

the adsorbate molecules cannot slide along their own contours (i.e., the motion of a single adsorbed protein requires the cooperative motion of other adsorbed protein molecules over large length scales). Additionally, after partial unfolding, exposed hydrophobic groups interact with hydrophobic groups on adjacent molecules forming junctions.24 It is the formation of these hydrophobic junctions, conformational constraints from disulfide bridges, and irreversible adsorption that lead to slow glassy dynamics. Additionally, constraining protein molecules to the interface, as opposed to the diffusion mechanism, limits the degrees of freedom (in-plane rearrangement) and contributes to the slowness of the reorganization of the interfacial network. This mechanism for the formation of an interfacial gel/glass has been observed for another globular protein and interfacially adsorbed colloidal particles.13 Conclusions Our rheological studies of lysozyme and β-casein at the oil/water interface indicate that the dissipation mechanisms of two proteins are strongly coupled to changes in the protein structure upon/after adsorption. For β-casein, the interfacial response is fluidlike in shear deformation and dominated by viscous dissipation, particularly at low frequencies. Above the monolayer-collapse surface pressure for β-casein, subsequently adsorbed protein molecules are less strongly bound to the interfacial layer and adsorb reversibly. Accordingly, the dilatational response is dominated by diffusion dissipation at low frequencies and viscous dissipation at higher frequencies (i.e., ωτD > 1). These mechanisms are confirmed by investigating the rheological response after washing away the protein from the aqueous solution. This result emphasizes that care must be taken when directly comparing dilatation and shear deformations for molecules that are near the collapse surface pressure. For lysozyme, the adsorbed protein layer is primarily elastic (G ′ > G ′′) with a weak frequency dependence in shear deformation. Similarly, the interfacial dilatational moduli change very little with frequency for the oscillatory experiments. In contrast to the results for β-casein, the frequency response of lysozyme does not change significantly after washout. The irreversibly adsorbed fraction dominates the dynamic rheological response. As observed from experiments investigating long time scales [i.e., E(t) and J(t)], it is apparent that the dilatational and shear responses are dominated by the longest relaxation mode. The characteristic time of this mode is similar in both dilatation and shear. The very long relaxation time results from the formation of a glassy interfacial network that forms at high interfacial concentrations and arises from protein unfolding and interprotein aggregation. Therefore, irreversibility and large interfacial moduli (E* and G*) go hand-in-hand. The greater are the values of E* and G*, the greater is the stress in the interface upon expansion/ compression. Large interfacial stresses require large adsorption/desorption activation barriers, otherwise the stress is readily dissipated through sorption and diffusion if the interfacial strain rate is slower than the characteristic time of diffusion. Therefore, interfacial relaxation mechanisms depend strongly on adsorption/desorption activation barriers, which in turn depend on the stability of the native protein conformation. LA0485226

Shear and Dilatational Relaxation Mechanisms of Globular and

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