Solution Interface

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Surface Shear Rheology of β-Casein Layers at the Air/ Solution Interface: Formation of a Two-Dimensional Physical Gel Grigor B. Bantchev and Daniel K. Schwartz* Department of Chemical Engineering, University of Colorado at Boulder, Boulder, Colorado 80309 Received July 12, 2002. In Final Form: December 30, 2002 A magnetic rod interfacial shear rheometer was used to measure the properties of β-casein adsorbed at the air/solution interface as a function of aging time. Over a wide range of concentrations (1 × 10-6 to 2 × 10-2 wt % β-casein) the initial rheology of the adsorbed surface layer is dominated by a viscous response of the interface. For solutions in the range 5 × 10-3 to 2 × 10-2 wt %, interfacial gelation is observed after ∼15 h of aging, long after the surface tension has stabilized. In particular, although both components of the complex interfacial shear modulus (i.e., the storage and loss moduli) gradually increase with aging time, the ratio of the loss to the storage modulussthe loss tangentsdecreases and drops below unity. The frequency dependence of the shear modulus is consistent with sol-gel transitions observed in bulk systems and described within the context of percolation theory.

Introduction Many proteins adsorb at interfaces and form thin (120 nm) viscoelastic layers.1-3 In fact, it is common to say that proteins form “rigid” layers at an interface4 or that these layers represent a “skin”5 or “gel”6 or form networks.7,8 The typical evidence for the existence of a network in such adsorbed layers is simply that they have much larger viscoelastic shear rheological parameters8 or dilatational viscosity6,7 than monolayers of low-molecularweight surfactants. The interfacial rheology of adsorbed proteins has been studied extensively (see refs 5, 7, 9, and 10 for reviews), but the focus is typically on dilatational properties;7,10 interfacial shear investigations are relatively uncommon.5,11 This is because dilatational properties are regarded as being more directly related to the formation and stabilization of emulsions. For example, interfacial flow during the close approach of idealized oil droplets is purely dilatational. However, more realistic pictures of coalescence must include complex combined * Corresponding author. E-mail: [email protected]. Phone: 303-735-0240. Fax: 303-492-4341. (1) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 415. (2) Russev, S. C.; Arguirov, T. V.; Gurkov, T. D. Colloids Surf. B 2000, 19, 89-100. (3) Boerboom, F. J. G.; de Groot-Mostert, A. E. A.; Prins, A.; van Vliet, T. Neth. Milk Dairy J. 1996, 50, 183. (4) Fisher, L. R.; Mitchell, E. E.; Parker, N. S. J. Colloid Interface Sci. 1987, 119, 592. (5) Murray, B. S. Interfacial rheology of Mixed Food Protein and Surfactant Adsorption Layers with respect to Emulsion and Foam stability. In Proteins at Liquid Interfaces; Mobius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1998; Vol. 7, p 179. (6) Prins, A.; Jochems, A. M. P.; van Kalsbeek, H. K. A. I.; Boerboom, F. J. G.; Wijnen, M. E.; Williams, A.; Prog. Colloid Polym. Sci. 1996, 100, 321. (7) Prins, A.; Bos, M. A.; Boerboom, F. J. G.; van Kalsbeek, H. K. A. I. Relation between surface rheology and foaming behaviour of aqueous protein solutions. In Proteins at Liquid Interfaces; Mobius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1998; Vol. 7, p 221. (8) Benjamins, J.; van Voorst Vader, F. Colloids Surf. 1992, 65, 161. (9) Bos, M. A.; van Vliet, T. Adv. Colloid Interface Sci. 2001, 91, 437. (10) Benjamins, J.; Lucassen-Reynders, E. H. Surface Dilatational Rheology of Proteins Adsorbed at Air/Water Interfaces. In Proteins at Liquid Interfaces; Mobius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1998; Vol. 7, p 341. (11) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1980, 76, 240.

flows. Furthermore, interfacial shear rheology can provide important insights into the structure of the interfacial layers that are not apparent from dilatational rheology. For example, the appearance of non-zero shear elasticity is characteristic of an interfacial gel or “soft solid” whereas liquidlike layers typical of small molecule surfactants have no shear elasticity. However, even liquidlike interfacial layers have non-zero dilatational elasticity related to their compressibility. This dilatational elasticity is often directly related to the equilibrium isotherm and, therefore, does not provide particularly valuable rheological information. Finally, shear rheology is conventionally used to characterize three-dimensional (3D) viscoelastic materials such as gels, and quantitative criteria for gelation (as well as theoretical models) are, therefore, well-established. The caseins are a major component of milk: ∼3 wt %12 and ∼80% of the total protein.13 The most surface-active component is β-casein, which comprises 35% of the caseins. β-Casein has 209 amino acid residues, with MW ) 24 kDa. It contains little or no secondary structure; the exact conformation is controversial. For example, Creamer et al.14 report only 20% R-helix, 0% β-sheet, and 80% random coil, whereas Graham et al.13 report a greater amount of secondary structure: 7% R-helix, 33% β-sheet, 19% β-turns, and 42% aperiodic, claiming the difference to be because of a gentler isolation procedure. Most of the charged residues are located within the first 50, and the remainder are predominantly hydrophobic and prolinerich (34 proline residues, or 16% by number);15 therefore, it is often described as a natural diblock copolymer.16 It lacks cysteine residues so it cannot form intramolecular covalent disulfide bonds, distinguishing it from other milk proteins such as whey proteins. Interfacial gelation of protein layers is considered to be an important factor in emulsion stabilization and the conventional wisdom is (12) Encyclopedia of Chemical Technology; Interscience Encyclopedia, Inc.: New York, 1949; Vol. 4. (13) Graham, E. R. B.; Malcolm, G. N.; McKenzie, H. A. Int. J. Biol. Macromol. 1984, 6, 155. (14) Creamer, L. K.; Richardson, T.; Parry, D. A. D. Arch. Biochem. Biophys. 1981, 211, 689. (15) Nylander, T.; Walhgren, N. M. J. Colloid Interface Sci. 1994, 162, 151. (16) Hunter, J. R.; Kilpatrick, P. K.; Carbonell, R. G. J. Colloid Interface Sci. 1991, 142, 429.

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that interfacial gels are stabilized by intermolecular covalent cross-links consisting of disulfide bonds.17 For this reason, β-casein is not generally considered a contributor toward interfacial gelation. However, there are many examples of 3D gels that form in the absence of covalent cross-linking. These “physical gels” form in both aqueous and nonaqueous solutions and are stabilized by a variety of noncovalent interactions including hydrogen bonding and electrostatic interactions. A common feature in these systems is the formation and entanglement of supermolecular aggregates such as fibers or lamellae. Rheological data are often reported in terms of the complex shear modulus G*(ω) ) G′(ω) + iG′′(ω), where G′ is the elastic or storage modulus and G′′ is the viscous or loss modulus and both are functions of the frequency ω of the oscillatory measurement. The interfacial storage and loss moduli of β-casein are too small to be reliably measured with the torsion disk technique.11 As a result, there are only a few published reports of the complete surface rheology of β-casein (or whole caseinate) at the oil/water interface5,18 or air/water interface.8,19 The viscosity alone has also been reported.20,21 There are severe discrepancies within these data. For example, Murray5 found β-casein to form a highly elastic layer at the oil/ water interface with G′/(ηω) ≡ G′/G′′ ≈ 600, whereas at the other extreme Kiosseoglou18 reported a “purely viscous film”. It is likely that the surface rheology is sensitive to experimental conditions that differ between the two experiments, for example, different oils, pH, casein concentration, ionic strength, and shearing frequency. Regarding the behavior at the air/water interface, Benjamins and van Voorst Vader8 reported G′ ) G′′ ) 0.2 mN/m for sodium caseinate layers (2 h of aging, ω ) 0.084 rad/s, c ) 0.03 wt %, pH ) 5.7, no salt added). We report measurements of the complex shear modulus (i.e., storage and loss moduli) of β-casein layers adsorbed at the air/water interface. We measure the aging effects of the adsorbed layers and find that initially the layer is mainly viscous, but at higher coverage (higher concentration and greater aging times) it manifests predominantly elastic behavior. The frequency dependence of the shear moduli confirms that the observed transition is characteristic of a sol-gel transition described by percolation theory. Percolation theory assumes growth of clusters by formation of cross-links between separate units (in our case noncovalent cross-links between β-casein molecules or aggregates). If we denote the degree of the link formation by p, there are three general regimes. Initially, for small values of p, only finite size clusters are present. The system is called a “sol”. There is a critical (percolation) value of p ) pc, at which one of the clusters reaches an infinite size. This is called the “gel point” (GP), and at this stage the system (called a “critical gel”) has unique properties that can be described with simple scaling laws. For p > pc the system is a gel. For large values of p all the clusters are joined together and there are no loose units or clusters. The critical gel has some divergent properties and its (17) Dickinson, E. J. Dairy Sci. 1997, 80, 2607. (18) Kiosseoglou, V. J. Dispersion Sci. Technol. 1992, 13, 135. (19) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 427. (20) Dickinson, E.; Murray, B. S.; Stainsby, G. J. Colloid Interface Sci. 1985, 106, 259. (21) Semenova, M. G.; Antipova, A. S.; Belyakova, L. E.; Dickinson, E.; Brown, R.; Pelan, G. E.; Norton, I. T. Effect of Pectinate on Properties of Oil-in-Water Emulsions Stabilized by Rs1-Casein and β-Casein. In Food Emulsions and Foams: Interfaces, Interactions and Stability; Dickinson, E., Patino, J. M. R., Eds.; The Royal Society of Chemistry: Cambridge, 1999; p 163.

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precise structure is not well-established (see Winter and Mours22 and Stauffer and Aharony23). Experimental Methods The magnetic rod interfacial rheometer used in the current experiments is significantly more sensitive than the instruments used in previous investigations of casein interfacial rheology. Also, in contrast with torsion wire rheometers, it is capable of frequency-dependent shear experiments. Among the reports described above, only Benjamins and van Voorst Vader8 measured the rheology at multiple frequencies. The determination of ω-dependence is critical for the unequivocal characterization of a gel.22 Our rheometer is based on a concept proposed by Shahin24 and further developed by others.25,26 It is one of a class of instruments where the motion of a floating object is used to apply a lateral stress at the interface27 or a magnetic field is used to generate the force.28,29 The heart of the rheometer is a thin ferromagnetic rod, which floats, due to capillary forces, at the interface of interest. A magnetic force is applied to the rod, and its motion shears the interface between it and the stationary walls of a channel. The displacement of the rod is observed with a linear CCD camera and a comparison of the applied force and detected motion gives the strain/stress relation. In our instrument, the magnetic field causing the external force is produced by two coils with 100 double turns of magnet wire (AWG 20). The distance between the coils is equal to their radius, 25.4 cm. The current through each of the coils is controlled by a separate power supply (Sorensen LS 18-5). The power supplies are controlled by a PC with a D/A card (AT-MIO-16E10, National Instruments). The force acting upon the rod in the center of the apparatus between the two electromagnets is proportional to the difference of the currents in the two coils. To achieve a constant gradient of the magnetic field (and, therefore, a homogeneous force) along the axis, the current in the two coils should have a ratio of 2:1.26 Therefore, for oscillatory measurements, the time-dependent current through the coils had the form 3|cos(ωt)| + cos(ωt) and 3|cos(ωt)| - cos(ωt), respectively, where ω is the circular frequency in rad/s and t is the time. The protein layers are prepared by placing 10 mL of β-casein solution in a glass channel cut along the cylinder axis with an inner diameter of 1.64 cm and length of 15 cm. The cylinder is centered between the two coils along the symmetry axis. The area of the glass in contact with the solution is ∼40 cm2; the air/solution area is ∼26 cm2. Due to these dimensions (which are necessary for sensitive rheological measurements), interfacial adsorption leads to significant depletion of the bulk protein concentration for the experiments using the most dilute solutions. Table 1 shows the initial protein concentrations and various estimates of the final concentrations. Given that the adsorption at the air/water interface has been reported previously (but the adsorption at the glass surface has not), lower and upper limits of the final concentration (Clower and Cupper in the second and third columns of Table 1, respectively) were calculated using the following limiting approximations: (1) the concentration of adsorbed protein on the glass surface is equal to that at the air/water interface or (2) the protein adsorbs only at the air/ water interface. The isotherm used for the calculation was taken from Hunter et al.16 Had we used the data of Graham and Phillips,1 we would have found a slightly weaker effect of adsorption. Our best estimate (Cfinal in the fourth column of Table 1) was made by comparing the final surface pressure of the 1 × 10-4 wt % sample with that of a series of solutions held within (22) Winter, H. H.; Mours, M. Adv. Polym. Sci. 1997, 134, 165. (23) Stauffer, D.; Aharony, A. Introduction to Percolation Theory, 2nd ed.; Taylor & Francis Inc.: Washington, DC, 1992. (24) Shahin, G. T. The Stress Deformation Interfacial Rheometer. Ph.D. Thesis, University of Pennsylvania, 1986. (25) Brooks, C. F.; Fuller, G. G.; Frank, C. W.; Robertson, C. R. Langmuir 1999, 15, 2450. (26) Ding, J.; Warriner, H. E.; Zasadzinski, J. A.; Schwartz, D. K. Langmuir 2002, 18, 2800. (27) Petkov, J. T.; Danov, K. D.; Denkov, N. D.; Aust, R.; Durst, F. Langmuir 1996, 12, 2650. (28) van Vliet, T.; de Groot-Mostert, A. E. A.; Prins, A. J. Phys. E: Sci. Instrum. 1981, 14, 745. (29) Gaub, H. E.; McConnell, H. M. J. Phys. Chem. 1986, 90, 6830.

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Table 1. Initial and Approximate Final Concentrations Following Depletion of the Solution Due to Interfacial Adsorptiona

a

Cinitial

Clower

Cupper

Cfinal

2 × 10-5 wt % 1 × 10-4 wt % 1.1 × 10-3 wt % 5.5 × 10-3 wt % 1.8 × 10-2 wt %

1 × 10-6 wt % 6 × 10-6 wt % 8.6 × 10-4 wt % 5.2 × 10-3 wt % 1.8 × 10-2 wt %

2 × 10-6 wt % 6 × 10-5 wt % 1 × 10-3 wt % 5.4 × 10-3 wt % 1.8 × 10-2 wt %

1 × 10-6 wt % 8.0 × 10-6 wt % 9.0 × 10-4 wt % 5.2 × 10-3 wt % 1.8 × 10-2 wt %

The values from the last column are used in the remainder of the text.

a “deep” sample container where interfacial adsorption resulted in negligible depletion of the bulk concentration. This concentration was chosen for this calculation because the isotherm of β-casein is most sensitive in the range 1 × 10-5 to 1 × 10-4 wt %. We found that the final concentration of this sample was approximately 8 × 10-6 wt %, implying that the adsorption of the protein at the glass/solution interface was about 75% of that at the air/solution interface. Using this value, we calculated approximate final concentrations for all samples used in these experiments; the estimates are reported in the final column of Table 1. The values from this final column are used throughout the remainder of the text. In some cases, sodium dodecyl sulfate (SDS) is introduced into the solution following aging of the protein layer. The surface with an adsorbed protein layer is first allowed to age for 41 h. At that point, 10 µL of 5 × 10-3 M SDS solution are injected into the solution on each end of the channel. The SDS concentration after complete mixing of the surfactant is calculated to be 10-5 M, if the adsorption at the interfaces is neglected. This is approximately 3 orders of magnitude less than the CMC of SDS. The tip of the pipet is washed with deionized water immediately before the injection of the SDS solution to avoid direct deposition of the surfactant at the interface. To decrease water evaporation, the cylinder is placed within a closed acrylic box (∼10 × 2 × 30 cm) with buffer solution on the bottom and with an antireflective glass cover. Under experimental conditions, the change of water level is negligible for about 1 week and the pH changes by only ∼0.01 units per 24 h, so we believe that evaporation and/or CO2 dissolution has a negligible influence on the results. The magnetic rod is placed on the solution surface within the channel. The rod is made from a patterned piece of steel music wire, 2.54-cm long and 0.6 mm in diameter. The patterns are black and white stripes with a periodicity of 0.159 cm made for the purpose of optical detection. Prior to an experiment, the rod is magnetized by placing it in a field of about 6 × 10-2 T modulated with a sinusoidal signal of 5 × 10-2 T and frequency of 0.25 Hz. After magnetization the rod is hydrophobized by one of two methods. In some cases, it is dipped in a warm solution of paraffin in hexanes and removed. After evaporation of the hexanes, the rod remains covered with a thin layer of paraffin that ensures hydrophobicity of the rod. Otherwise, the rod is rendered hydrophobic by deposition of a self-assembled layer of octadecyltriethoxysilane (OTE) using an amine-catalyzed procedure described by Mooney et al.30 We did measure a small difference in the absolute values of the interfacial shear moduli when using rods that were hydrophobized using different methods; we ascribe this to the fact that the contact angle of the interface at the rod surface is slightly modified. This represents a systematic uncertainty in the absolute values of the measured quantities. However, the essential results of the study, for example, relative changes with aging and concentration, were identical. The rod position is detected with a linear-array CCD camera (model Calipso, Ulice Corp., France, www.ulice.com) equipped with a 2048-pixel Sony array sensor with a length of 2.2 cm. A 4× microscope objective is used to focus the rod image onto the sensor. The image obtained with the camera is numerically fitted to a square-wave function (related to the striped pattern on the rod) in real time to obtain the instantaneous position of the rod. The camera is connected to a computer (Athlon 550 MHz, 196 MB RAM) through a parallel port. The slowest step of the measurement involves obtaining the signal from the camera (∼30 (30) Mooney, J. F.; Hunt, A. J.; McIntosh, J. R.; Liberko, C. A.; Walba, D. M.; Rogers, C. T. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 12287.

ms) and fitting it with the rod pattern (∼30-40 ms). The minimum sampling interval is in the range 0.050-0.090 s, limiting the frequency to a maximum of 1/(2 × 0.09) ) 5.6 Hz, corresponding to ω ) 5.6 × 2 × π ) 35 rad/s. An oscillatory force is applied for at least 20 s to achieve a stable response before data are acquired. The length of an individual measurement is the larger of 10 s or 1 period. Whole numbers of periods are measured; the data for the rod position are linearly interpolated to an array of equally spaced points and a Fourier transform (FT) spectrum is calculated. From the spectra we are able to extract the amplitude ()γd/2, where the d is the width of the channel and γ is the strain) and the phase angle δ between the response and the applied stress. From these we calculate the complex dynamic surface modulus G* ) G′ + iG′′, where G′ is the elastic (storage) dynamic surface modulus and G′′ is the viscous (loss) dynamic surface modulus, both in units of mN/m. The explicit formulas used are

G′(total) ) |σ| cos(δ)/|γ| G′′(total) ) |σ| sin(δ)/|γ| where the shear stress σ ) K × ∆A/2 × l, ∆A is the difference in the currents through the coils in Amperes, l is the rod length (2.54 cm), and K is a calibration constant. The calibration of the apparatus (to obtain K) and determination of the bulk (subphase) contribution are made with a buffer solution before each measurement with a protein solution. The calibration follows the method described in the work of Brooks and co-workers.25,31 After measurement of the total G*, the bulk contribution is subtracted assuming simple additivity, that is, G*(layer) ) G*(total) - G*(bulk). The bulk |G*| is of the order of 5 × 10-3 mN/m at 0.2 rad/s and 0.1mN/m at 6.3 rad/s and is found to have a negligible effect on calculations when it is less than 5% of the total G*. The uncertainty in the data was estimated including the following sources: (1) the accuracy of detection of the rod position, (2) the calibration of the microscope magnification, (3) errors in the calculated phase difference related to data transfer delays, and (4) uncertainties in parameters derived from fits, including those used to describe G*(bulk). However, the scatter of the data remained larger than the calculated error bars, with the exception of the highest frequencies, suggesting that there is some fundamental physical issue that limits reproducibility. Also, at low frequencies, after the subtraction of the bulk contribution, we sometimes obtained negative values for G′, a physically impossible result. We attribute this to systematic error involving subtraction of the bulk contribution; that is, G*(bulk) in the presence of the adsorbed protein layer is not identical to G* of the protein-free buffer. The negative values for G′ are most often found when G′ is much less than G′′ and both have relatively low values. We note that negative values for G′ have been previously reported for measurements with a similar apparatus.25 Negative values of the surface viscosity have also been reported,29 obtained again by subtracting a bulk contribution from an apparent total viscosity. In principle, an apparent negative surface viscosity is possible because the presence of a monolayer could decrease the total drag. However, an analogous explanation does not seem sensible in the context of surface elasticity. For measurements of the steady-state interfacial viscosity, the rod is initially positioned near one end of the channel and (31) Brooks, C. F. An Interfacial Stress Rheometer to Study the Shear Rheology of Langmuir Monolayers. Ph.D. Thesis, Stanford University, 1999.

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currents are generated within the coils such that a constant (i.e., time-independent) force is applied to the rod. The speed of the rod is detected when passing through the central part of the channel. After the rod comes to rest at the other end, a force is applied in the opposite direction and the next measurement is made. This process is repeated using a wide range of applied forces resulting in various measured shear rates. For interfacial layers with high viscosity, the range of shear rates measured is approximately 0.3-1.5 s-1, whereas for lower viscosity layers the range is 0.9-5 s-1. The measured shear rates versus applied stress are fitted with a third-order polynomial (shear rate ) b0 + b1σ + b2σ2 + b3σ3). The inverse of the linear coefficient (b1) gives the “total” viscosity. This can be regarded as an extrapolation to the zero shear rate viscosity. Following subtraction of the subphase contribution, the result is reported as the steady-state surface viscosity. In principle, the shear rate versus stress data should pass through the origin and so the parameter b0 should be equal to zero. This constraint was not imposed on the fit, however, because this parameter compensated for small constant forces such as those due to the earth’s magnetic field gradient (and that of other stray magnetic fields) and so forth. β-Casein was obtained from Sigma-Aldrich (Sigma C-6905, min. 90% β-casein by electrophoresis, lyophilized, essentially salt-free, Lot 108H7813) and used as received. Although the product specification is simply >90% β-casein, the actual lot analysis by gel electrophoresis (performed by Sigma) was β-casein 96%, γ-caseins (proteolysis fragments of β-casein) ∼3%, and R-caseins ∼1%. No κ-caseins were detected. Batch solutions are prepared by dissolving approximately 0.01-2 g of β-casein in 100 mL of phosphate buffer solution (water from Millipore UV+ system) with ionic strength of 0.1 M (which is close to the ionic strength of bovine milk) and pH ) 7.4 (Fisher Sci., buffer B82). To the buffer solution is added 0.1 g/L NaN3 to avoid bacterial contamination. The batch solution concentrations (about 0.02 wt %) are below the “CMC” of β-casein32 of 0.17 wt % and are kept in a refrigerator at ∼5 °C (β-casein is less likely to aggregate at low temperature) so we believe that the solutions are essentially aggregate-free. A batch solution is not used for more than a week after preparation. The solutions used in experiments are prepared from the batch solution by dilution in a beaker and are immediately transferred to the channel. The aging of the surface is measured from the time the solution is placed in the channel. All experiments are performed at ambient temperature, 23.5 ( 1 °C. The bulk protein concentrations are reported in weight percent units. In the literature, g/L and mol/L are also used (1 wt % ) 10 g/L ≈ 4.2 × 10-4 mol/L). Surface pressure measurements are made using an R&K tensiometer, a Wilhelmy-type balance, which uses a 3-mm-wide filter paper plate. The balance is calibrated before the measurements using pure Millipore water. To not disturb the surface, the paper remains in the solution throughout an experiment. This does not allow us to recalibrate the apparatus, which can drift 0.2 mN/m over several hours. Thus, the surface tension measurements are prone to slow drift, which is noticeable for very long aging times. The solution is held within a cylindrical glass dish 7.5 cm in diameter (the air/solution interfacial area is 44.2 cm2). For final concentrations above 10-4 wt % (where depletion was not a concern in the rheology experiments) 60 mL of solution was used (glass/solution interfacial area ) 76.2 cm2). For the solution with a final protein concentration of 8 × 10-6 wt % efforts were made to duplicate the adsorption behavior of the rheometer channel. In particular, 17.5 mL of solution was placed within the same dish and glass slides were added to increase the solution/glass area to ∼76 cm2 so that the area/ volume ratios were similar to those within the rheometer channel.

Results and Analysis Adsorption Isotherms of β-Casein Solutions. Our observations of the kinetics of β-casein adsorption (Figure 1) are essentially in agreement with data from the literature.33 The S-like shape of the surface pressure, π (32) Payens, T. A. J.; Brinkhuis, J. A.; van Markwijk, B. W. Biochim. Biophys. Acta Protein Struct. 1969, 175, 434. (33) Sengupta, T.; Damodaran, S. Langmuir 1998, 14, 6457.


Figure 1. Surface pressure vs aging time of β-casein solutions.

vs time, observed for 8 × 10-6 and 1 × 10-4 wt % solutions, is a common feature of protein adsorption; often it is rationalized by association with a 2D phase transitions formation of 2D aggregates,34 micelle-type aggregates,35 gas to liquid expanded phase transitions,36 or simply cooperative adsorption.16 The 8 × 10-6 wt % solution does not reach a steady-state surface pressure after 48 h of aging. For 10-4 wt % and greater concentrations, an essentially constant value of π is observed after 1-8 h of aging (Figure 1). This is consistent with data from the literature,33,37 which also suggest that the amount of adsorbed protein does not change after 5-8 h. This gives us reason to believe that, for concentrations >10-4 wt %, the rheological changes observed at longer times are due to structural rearrangement within the layer and not to continued adsorption. The results shown in Figure 1 are also in agreement with previous reports1 that the final (asymptotic) surface pressure is essentially constant for solution concentrations in the range 10-4 to 5 × 10-2 wt %. The surface concentration in “equilibrium” with 10-4 wt % solution has been reported to be about Γ ) 2.3 mg/ m2, consistent with a complete monolayer.16 Although the surface pressure changes only very slightly above this concentration, radiotracer measurements16 suggest that the adsorbed amount continues to increase with increasing concentration. The increase of the adsorption in this region may be due to rearrangement of the molecules at the interface to a more densely packed configuration or to formation of multilayers. Dependence of G′ and G′′ on Concentration and Aging Time of Solution. Oscillatory shear rheology data discussed in this section are obtained at a frequency of ω ) 1.57 rad/s. At the lowest concentration used, 1 × 10-6 wt %, we observe a very small rheological response (see Figure 2a). In fact, the bulk contribution is larger by an order of magnitude, making the extraction of surface rheology difficult and resulting in large uncertainties. Nevertheless, we observe a slight increase in the loss modulus (G′′); the storage modulus is too small to measure reliably. At 8 × 10-6 wt % we initially observe low values for the shear moduli (Figure 2b). The measured values are within the uncertainty of the apparatus (i.e., G* < G*(bulk)/10). After ∼5 h of aging the values become significant (G* ∼ G*(bulk)) and the viscous component (G′′) is clearly dominant. This is consistent with an essentially liquidlike interfacial layer. A comparison of the time dependence of rheological parameters and surface pressure (Figures 2 (34) Rao, C. S.; Damodaran, S. Langmuir 2000, 16, 9468. (35) Fainerman, V. B.; Miller, R. Langmuir 1999, 15, 1812. (36) Erickson, J. S.; Sundaram, S.; Stebe, K. J. Langmuir 2000, 16, 5072. (37) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 403.


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Figure 3. Dependence of the loss tangent (G′′/G′) at ω ) 1.57 rad/s as a function of aging time for solutions with different concentrations. For concentrations greater than 9 × 10-4 wt %, tan δ drops below 1 after approximately 15-20 h. This is a qualitative demonstration that the interfacial layer has developed predominantly elastic behavior.

Figure 2. Dynamic interfacial shear moduli, G′ (storage, open symbols) and G′′ (loss, filled symbols) components, are shown as a function of aging time for various solution concentrations, measured at a frequency of ω ) 1.57 rad/s. The instrumental sensitivity is estimated to be ∼1 × 10-4 mN/m for G′ and ∼1 × 10-3 mN/m for G′′ at this frequency. (a) 1 × 10-6 wt %; (b) 8 × 10-6 wt %; (c) 9 × 10-4 wt %; (d) 5.2 × 10-3 wt %; (e) 1.8 × 10-2 wt %.

and 1) at this concentration suggests that the increase of the loss modulus is related to the process of adsorption. At concentrations above 9 × 10-4 wt %, the adsorption

is much fastersafter only 0.2 h the surface tension is within 1.5 mN/m of the final value (Figure 1). These dense layers also have much larger surface moduli (Figure 2ce). At concentrations of 9 × 10-4 wt % and higher, a small decrease in the surface modulus is initially observed, but the moduli begin to grow with aging time after about 4 h. For the 9 × 10-4 wt % solution, the layer maintains a predominantly viscous character (i.e., G′′ > G′); however, the loss tangent (G′′/G′) decreases significantly after 10 h of aging. On the other hand, for concentrations of 5.2 × 10-3 wt % and higher, the behavior is initially viscous (G′′ > G′), but about 10 to 20 h after preparation of the surface there is a distinct crossover to elastic behavior where G′ > G′′ (Figure 2d,e). This can be seen more clearly in Figure 3, where the loss tangent (G′′/G′) falls below unity for the two highest concentrations. One might expect that increased bulk concentration will lead to an increase of the surface adsorption and correspondingly the surface modulus of the layer. However, we observed a maximum of the surface modulus at 5.2 × 10-3 wt % and a small decrease of the surface modulus at higher concentrations. There is an interesting correlation between these data and those of Boerboom et al.,3 who studied the layer structure using ellipsometry. They found that while the layer thickness increased with concentration in this range, the density of the layer actually decreased slightly. Frequency Dependence of Surface Rheology. The complex interfacial shear modulus is measured as a function of frequency in the range 0.2-6.3 rad/s. The data are fitted with a simple power law dependence of G′ and G′′ on ω, that is, G′ ) G′0ωn′; G′′ ) G′′0ωn′′. According to the percolation theory of gelation,22 a power-law dependence of G′ and G′′ on ω is expected from polymer systems near the point of the sol-gel transition (gelation point, GP). As the system approaches the GP, the agreement with a simple power law form is predicted to improve and, in fact, the values of n′ and n′′ are predicted to approach each other.22 For solutions of 9 × 10-4 wt % and below, some negative values for G′ were measured at low frequency; they were not included in the fits shown here. However, if they are included, the resulting values for G′0 and n′ are indistinguishable statistically from the current ones. These data and fits are shown in Figures 4-7; the fitting parameters obtained are presented in Table 2 and Figure 8. For the lower concentrations (Figures 4 and 5) G′′ > G′ for all aging times except for the very highest frequencies. There is a systematic trend in the exponents, n′ and n′′,

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Figure 4. Rheological response of a layer adsorbed from 8 × 10-6 wt % β-casein solution. Data are obtained at four values of ω: 0.2, 0.4, 1.6, and 6.3 rad/s. To present the data better, the ω axis for successive data sets is shifted by the factor 10A, where the respective exponent A is annotated next to the data. The error bars represent the standard deviation of multiple measurements (5 at ω ) 0.2; 3 each at ω ) 1.6 and ω ) 6.3 rad/s). Most of the error bars are smaller than the symbols. The power law fits for 3-h aged are summarized in Table 2. For the 40-h fit, G′ ) G′0ω2 and G′′ ) G′′0ω.

Figure 5. Rheological response of a layer adsorbed from 9 × 10-4 wt % β-casein solution. At least two independent measurements were made at each value of ω: 0.2, 0.4, 0.8, 1.6, 3.14, 6.3, and 12.6 rad/s. The ω axis for successive data sets is shifted by the factor 10A, where the respective exponent A is annotated next to the data. The fits for 0.2- and 14-h data are G′ ) G′0ω2 and G′′ ) G′′0ω. The 60-h data were fit to a power law (see Table 2).

Figure 6. Rheological response of an adsorbed layer from 5.2 × 10-3 wt % β-casein solution. The ω axis for successive data sets is shifted by the factor 10A, where the respective exponent A is annotated next to the data. The lines represent fits to power law forms.

obtained from the fits. For layers that are expected to be thin and/or dilute, we find large exponents. With the increase of the bulk concentration and/or the aging time one expects the adsorbed layer to become thicker and/or denser; the data uniformly show a decrease of the exponents. Under conditions where n′′ ≈ 1, we find that n′ ≈ 2. This behavior is typical for classical theories


Figure 7. Rheological response of an adsorbed layer from 1.8 × 10-2 wt % β-casein solution. The ω axis for successive data sets is shifted by the factor 10A, where the respective exponent A is annotated next to the data. The lines represent fits to power law forms.

describing viscoelastic liquids at low frequenciesssuch as the Maxwell, Rouse, or Zimm models.38 We do not know of a popular theory that predicts larger exponents (n′′ > 1 and n′ > 2) as we observe for the most dilute layers. The decrease of the exponents with aging can be qualitatively described within the context of the Rouse and Zimm theories as due to an increase of the friction felt by individual polymer segments. The Zimm model, which assumes intramolecular friction, predicts minimum values of 2/3 for both n′ and n′′.38 A further decrease in the exponents could be achieved if the polymer chains become entangled and the friction on a segment is dominated by intermolecular interactions. According to the Rouse theory, this could lead to a further decrease of the exponents down to 0.5.38 For the two highest concentrations (Figures 6 and 7), G′′ > G′ for all frequencies at short aging times. However, there is a crossover after 10-15 h of aging, after which G′′ < G′ for all frequencies. This is fundamentally inconsistent with the models for viscoelastic fluids described above and is simply a more rigorous demonstration of the gelation mentioned previously (see Figure 3), which considers the entire shear modulus spectrum. Also for these concentrations, it is apparent that n′ > n′′ at the beginning of the experiment and that n′ < n′′ after long aging times (Figure 8). This is similar to the behavior associated with gelation of polymers22 and proteins.39,40 At the GP, according to theory,41 G′ ∼ G′′ ∼ ωn (n ≡ n′ ) n′′ ) const) and G′ ) G′′/tan(nπ/2). The critical value of n is about 0.45 for 5.2 × 10-3 wt % and 0.47 for 1.8 × 10-2 wt % (see the crossover points in Figure 8). So in our case the strict GP occurs when tan δ ) G′′/G′ ) tan(0.45π/2) ≈ 0.85 for 5.2 × 10-3 wt % and 0.91 for 1.8 × 10-2 wt %, which are close to the more conventional criterion tan δ ) 1. We see, indeed, an excellent correspondence between the crossover point between n′ and n′′ (in Figure 8) and the domination of G′ over G′′ (Figure 3). These observations are all consistent with the evolution of a viscoelastic liquid layer to a soft viscoelastic “gelled” (solid) layer. Muthukumar42 derived the connection between n and the fractal dimension for polymer clusters at the GP using (38) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd ed.; John Wiley & Sons: New York, 1980. (39) Ziegler, G. R.; Foegeding, E. A. Adv. Food Nutr. Res. 1990, 34, 203. (40) Michon, C.; Cuvelier, G.; Launay, B.; Parker, A. Sol-Gel Transition of i-Carrageenan and Gelatin Systems: Dynamic Viscoelastic Characterization. In Food Macromolecules and Colloids; Dickinson, E., Lorient, D., Eds.; Royal Society of Chemistry: Cambridge, 1995; p 462. (41) Chambon, F.; Winter, H. H. J. Rheol. 1987, 31, 683. (42) Muthukumar, M. Macromolecules 1989, 22, 4656.


Langmuir, Vol. 19, No. 7, 2003 2679

Table 2. Power Law Fit Parameters for Low Concentrations (see Figures 4 and 5) bulk concentration (wt %)

aging (h)

n′

G′0 (mN/m)

1 × 10-6

5 14 20

8 × 10-6

3 40

2.6 ( 0.4 2.2 ( 0.5

(6 ( 3) × 10-4 (6 ( 5) × 10-4

9 × 10-4

0.3 14 60

1.9 ( 0.2 2.3 ( 0.3 1.0 ( 0.1

(6 ( 2) × 10-3 (1.6 ( 0.8) × 10-3 (5.0 ( 0.8) × 10-2

Figure 8. Best-fit power law exponents for adsorbed β-casein layers as a function of aging time for high solution concentrations as annotated. The arrows indicate crossover points.

Figure 9. Relationship between stress and strain. The experiment was carried out with a 5.2 × 10-3 wt % solution at 40 h of aging, under conditions where G′ > G′′ (after the gelation point). The lines show the best linear fit to the data.

percolation theory. He gave the following formulas:

n ) d/(df + 2)

for the unscreened case

n ) d(d + 2 - 2df)/2(d + 2 - df) for the screened case (Rouse dynamics) where d is the dimensionality and df is the fractal dimension of the polymer network at the GP. The unscreened case predicts n > 0.5 for all df, which is inconsistent with our observations. The screened case predicts (for n ) 0.45-0.47 and d ) 2) that df ) 4(1 - n)/(2 - n) ) 1.4. Values of n < 0.5 are usually observed for physical gels22 in which there is no covalent cross-linking. This is the expected result for β-casein, which can aggregate only through noncovalent interactionsshydrogen bonds, van der Waals, hydrophobic, and electrostatic interactions. Stress-Strain Relation. Figure 9 shows data from the experiment where the strain-stress relation was investigated most thoroughly. The experiment was carried out with a 5.2 × 10-3 wt % solution at 40 h of aging, under conditions where G′ > G′′. The data are fitted very well by straight lines. This, together with the fact that the δ values are independent of the stress, demonstrates that

n′′

G′′0 (mN/m)

1.80 ( 0.09 1.6 ( 0.1 1.53 ( 0.07

(2.1 ( 0.3) × 10-3 (4.6 ( 0.9) × 10-3 (5.3 ( 0.7) × 10-3

1.8 ( 0.2 1.05 ( 0.2

(2.1 ( 0.9) × 10-3 (4.7 ( 1.5) × 10-2

1.05 ( 0.2 1.02 ( 0.2 0.67 ( 0.09

(4.7 ( 1.5) × 10-2 (2.5 ( 0.6) × 10-2 (1.1 ( 0.2) × 10-1

Figure 10. A comparison of our steady-state viscosity data with data from the literature. The data of Murray5 refer to the water/oil interface.

the response of the system is linear over the range of stress applied and that it is appropriate to explain the data (obtained at about 1% strain) with linear models. These results correlate well with the recently published data for shear rheology of different proteins,43 which demonstrate the existence of a linear relationship between stress and strain for strains less than 0.1. The chronological order of the measurements in Figure 9 is shown in the legend. We see that the first and the second measurements at ω ) 0.2 coincide with each other. The second measurement was made after the layer had been subjected to four more experiments, where the stress and strain had reached high values. This demonstrates that the physical connections within the layer that are responsible for the observed viscoelasticity are either not damaged or recover within minutes of their destruction. We emphasize that the results described in the previous sections, which showed the onset of interfacial gelation, were obtained at values of stress within the linear regime shown in Figure 9. Steady-State Viscosity. Figure 10 shows the steadystate interfacial viscosity as a function of aging time for a β-casein solution with a concentration of 9 × 10-4 wt % and a shear rate in the range of 3 × 10-1 to 5 s-1. The data are extrapolated to a shear rate of zero. Also plotted are data from the literature that explored the effect of aging.5,44 Murray5 reported data taken at 2 × 10-4 s-1 and Kragel et al.44 used various shear rates below 9 × 10-3 s-1. The absolute values of viscosity cannot be directly compared due to significant differences in the measurement techniques, subphase chemistry, and the bulk phases present. In both previously published cases, an oscillatory technique was used at a single frequency. Also, both Kragel et al.44 and Murray5 worked at extremely low ionic strength (0.01 and 0.005 M, respectively), resulting in a decreased screening of the electrostatic charges and stronger repul(43) Martin, A.; Bos, M. A.; Stuart, M.; van Vliet, T. Langmuir 2002, 18, 1238. (44) Kragel, J.; Wustneck, R.; Husband, F. A.; Wilde, P. J.; Makievski, A. V.; Grigoriev, D. O.; Li, J. B. Colloids Surf., B 1999, 12, 399.

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the adsorbed protein molecules increased when the molar ratio (R) of the surfactant to protein was >1. Kragel et al.44 also demonstrated significant reduction of the surface viscosity for β-casein films in the presence of nonionic surfactant (Tween 20) at R ) 1 and negligible surface viscosity at R ) 10. The present experiment extends these results to a situation where the protein layer was permitted to form an elastic network prior to the introduction of the surfactant. Discussion

Figure 11. Formation of a gelled β-casein network (left part of the graph) followed by the degradation of the gel by a lowmolecular-weight surfactant (SDS). Dynamic interfacial shear moduli are measured at a frequency of ω ) 1.57 rad/s. The vertical line shows the moment of SDS injection. Note that the two time scales (before and after the injection) are different. The protein concentration was 5 × 10-3 wt % (2.1 × 10-6 M); the SDS concentration was 1 × 10-5 M assuming complete mixing after injection.

sion between moieties with the same charge. Murray’s data were obtained at the oil/water interface. However, the qualitative trends with interfacial aging are instructive. For example, the “viscosities” extracted from the oscillatory data using the expression G′′/ω ) η are larger than the steady-state measurements. (This is true of our oscillatory data as well.) Also, the steady-state measurements do not reflect the increase in the modulus observed for long aging times. A likely explanation involves the large and continuous deformations necessary for the measurements of the steady-state viscosity, which may destroy protein aggregates. Strains above 0.5 have been shown to lead to fractures in formed surface networks.43 We note that Kragel et al.44 also observed a decrease in surface viscosity after ∼1 h of aging. Additional purification of their β-casein did not alter this behavior. This suggests that the decrease in the viscosity (Figure 10) and G* (Figure 2c-e) at early aging times is connected to the molecular reorganization and is not simply an impurity effect. Stability of the Network. Figure 11 shows an experiment designed to investigate the stability of the interfacial network upon exposure to a low-molecularweight surfactant. A 5 × 10-3 wt % β-casein solution is first aged for 40 h. The gelation is shown in Figure 11 (as in Figure 2d) by the crossing of G′ and G′′ at ∼15 h. The anionic surfactant SDS is injected into the sample at the time indicated by a dotted vertical line. The total molar ratio of surfactant to protein molecules in solution was R ≈ 5. Note that the time axis on the graph is rescaled after the injection. There is an immediate increase in both storage and loss moduli. Approximately 0.5 h after introduction of SDS, both moduli decrease dramatically; after 1.5 h the interface loses its gelled character as G′ < G′′, and after 3 h both moduli have decreased by at least an order of magnitude. We interpret the data as (1) the rapid formation of a mixed layer, giving the initial postinjection increase in G*, followed by (2) displacement of the protein by the surfactant, resulting in the decrease of the moduli. The fluidization of β-casein layers by lowmolecular-weight surfactant is generally interpreted in terms of protein solubilization and/or competitive adsorption. Clark and Wilde45 found that the surface mobility of (45) Clark, D. C.; Wilde, P. J. Mobility of Adsorbed Protein Molecules as Studied by Fluorescence Recovery after Photobleaching (FRAP). In Proteins at Liquid Interfaces; Mobius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1998; Vol. 7; p 267.

At low protein concentrations (below the plateau region of the isotherm16) we observed only a gradual increase in surface viscosity with aging time. At these concentrations the protein adsorbs to form a layer that completely covers the interface and all the protein molecules have “trains”s residues lying at the interface.19 We speculate that the increase of viscosity may be related to entanglement of the protein chains. At higher concentrations the adsorbed amount grows.16 Some models assume the formation of multilayers,19 whereas others speculate about reorientation of the β-casein molecules from all “trains” to a “trains” + “tails” configuration.16 Under these conditions the appearance of viscoelastic behavior, and eventually gelation, is observed. The formation of viscoelastic interfacial layers of macromolecules has been known for some time. In fact, the first experimental data related to surface gelation was published by Kim et al.46 They observed the appearance of elastic behavior at the air/solution interface for a sulfonated polystyrene ionomer dissolved in dimethyl sulfoxide. However, in the interfacial rheology literature, the word “gelation” is often used quite loosely. For example, Benjamins and van Voorst Vader8 reported that G′ becomes greater than G′′ with aging for an adsorbed layer of bovine serum albumin. However, the authors did not explore the frequency dependence of this behavior (a typical criterion for gelation is that G′ > G′′ for all frequencies). They also used the fact that the viscoelasticity was large in magnitude to argue that a protein network had formed. This type of criterion suffers from the fact that a “large value” is somewhat arbitrary. Also, we would suggest that it is not necessary for the absolute values of the dynamic moduli to be large; a system can be regarded as having gelled even with small moduli if the real and imaginary parts have appropriate relations. In this manuscript, we explicitly demonstrate the surface gelation of a protein layer using dynamic rheological measurements within the context of the currently accepted formalism for bulk gelation. It is tempting to ascribe interfacial gelation to strong intermolecular interactions between proteins or protein aggregation. In theory, true gelation corresponds to a structure where the size of aggregates diverges. There is good reason to believe that proteins tend to aggregate at interfaces. For example, the details of protein adsorption kinetics at the air/water34 or solid/water47 interfaces have been used as indirect evidence of interfacial aggregation. Also, ATR-FTIR spectroscopy measurements suggest the existence of surface protein aggregates.48 Specifically, these data demonstrate a significant increase in β-sheet content as indicated by an increase in the area of the 1620-cm-1 shoulder of the amide I peak. Such conforma(46) Kim, M. W.; Peiffer, D. G.; Pincus, P. J. Phys. Lett. 1984, 45, L953. (47) Calonder, C.; Tie, Y.; Van Tassel, P. R. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 10664. (48) Ball, A.; Jones, R. A. L. Langmuir 1995, 11, 3542.


tional changes upon surface adsorption are consistent with aggregation but certainly cannot be regarded as proof. Also, the methods mentioned above do not probe the lateral extent of protein aggregates, which is necessary to make the connection with interfacial gelation. Our measurements suggest that the first rheological changes related to thickening or gelation are observed after about 3-4 h of surface aging. We speculate that this corresponds to the initial formation of aggregates of significant size, large enough to affect the rheology, but much smaller than the relevant lateral dimension of the interface (in our case 0.82 cm, the rod-wall distance). After 10-15 additional hours of aging, the aggregate size approaches that of the interface and the layer behaves as a gel. This aging time is much longer than the time needed for the equilibrium adsorption to be achieved (∼5 h),2,33,37 so the observed phenomena cannot be attributed simply to an increase in the amount of adsorbed protein; we must conclude that structural changes occur within the protein film. Of course, the adsorbed amount is an important factor; at lower bulk concentrations, where there is less adsorption,16 we do not observe gel formation at even the longest aging times. As mentioned previously, typical protein gels (interfacial or bulk) are stabilized by covalent (disulfide) cross-links between cysteine residues. Therefore, a protein must have at least two cysteine residues to form extended “linear” aggregates and three or more cysteines to form true crosslinked networks. Although β-casein does not contain any cysteine residues, there is a natural concern that the interfacial rheology could be dominated by a surface-active impurity protein containing multiple cysteine residues. This would require the interfacial accumulation of the impurity to a concentration sufficient to form a covalently linked surface-spanning network. Among the typical impurities found in β-casein samples, both κ-casein and Rs2-casein have at least two cysteines (γ-caseins, as β-casein fragments, clearly contain no cysteine residues). According to the analysis of our sample, κ-casein is not observed, placing an upper limit on κ-casein concentration at the sensitivity of the analysis technique (about one part per thousand). The total R-casein concentration is about 1%; Rs2-casein typically constitutes about one-fifth of the total R-caseins. Therefore, we estimate that cysteinecontaining proteins constitute 0.2-0.3% of our samples. Regarding the relative surface activities of these proteins, competitive adsorption experiments using R- and β-casein mixtures show that the air-water interface is slightly enriched with β-casein.49 Other data suggest that β- and κ-caseins have similar surface activities.10 Thus, one would not expect the fraction of cysteine-containing proteins at the surface to exceed the bulk fraction (0.2-0.3%). This small amount would not be sufficient for the formation of covalently linked aggregates of significant size. The experiment involving degradation of the interfacial gel using SDS directly addresses the nature of the protein network. Although SDS is an efficient denaturant (e.g., it is typically used prior to gel electrophoresis), it is incapable of breaking covalent disulfide cross-links in the absence of a reducing agent. The decline of interfacial shear moduli by more than an order of magnitude upon exposure of the interfacial gel to SDS indicates that connections within the protein film have been severed and individual proteins (or small aggregates) solubilized, that is, displaced from the interface by surfactant. A covalently linked protein network cannot be degraded in (49) Razumovsky, L.; Damodaran, S. Colloids Surf., B 1999, 13, 251.

Langmuir, Vol. 19, No. 7, 2003 2681

this way by SDS; this again suggests that the interconnections within the interfacial gel are noncovalent. At present, we can only speculate about the structure of the interfacial gel that forms. As discussed above, there is no potential for covalent cross-linking, so the film must be classified as a “physical” gel. Previous studies on globular proteins48,50,51 have used β-sheet content (determined from FTIR spectra) as a measure of the degree of aggregation based on a comparison with bulk gelation. By analogy, we could speculate that the β-casein interfacial gel is stabilized by intermolecular H-bonds, leading to the formation of such β-sheets. We would urge caution in this type of speculation, however, based on the fact that β-casein is widely considered to have very little secondary structure, consistent with the fact that it is extremely proline-rich. The secondary structure of β-casein has been difficult to determine accurately and the reported values of β-sheet content range from 0%14 to 33%.13 Another possible driving force for aggregation is the hydrophobic interaction. Such a hypothesis could explain the discrepancy in the previously reported data for the ratio of the measured viscous and elastic components at the oil/water interface (Murray5 G′/G′′ ≈ 600; Kiosseoglou18 “purely viscous response”). It is likely that the oil phase alters the interactions between hydrophobic moieties, strengthening the surface gel or preventing its formation depending on the details of the specific oil phase composition. We note, however, that the observed gelation of β-casein is probably not limited to the air-water interface. In particular, Semenova et al.21 reported a dramatic increase of the shear viscosity of β-casein at the oil interface after 24 h of aging. Unfortunately, they did not measure the shear elasticity or ω-dependence so it is impossible to make a detailed comparison at this time. Conclusions We have exploited the sensitivity of a custom-built magnetic rod interfacial rheometer to measure the surface shear rheology of β-casein layers adsorbed at the air/ solution interface and to trace the changes with the aging time of the layer. We report not only the surface shear viscosity (loss modulus) but also the surface shear elasticity (storage modulus) of adsorbed β-casein layers. For protein layers absorbed from low-concentration solution (1 × 10-6 to 9 × 10-4 wt %), the interfacial rheology is consistent with a viscoelastic 2D liquid. However, layers adsorbed from higher concentration solutions (5.2 × 10-3 to 1.8 × 10-2 wt %) form 2D gels at the interface after 10-20 h of aging. This is contrary to the conventional wisdom regarding β-casein interfacial layers, which lack the capacity to form covalent (disulfide) cross-links. Thus, the interfacial layer of β-casein is an example of a 2D “physical gel”; details of the supramolecular structure are currently unknown. The evolution of the rheology during the 2D gelation process (in particular, the frequency dependence of the complex shear modulus) is quantitatively consistent with the predictions of percolation theories often used to describe bulk gelation of polymer solutions (i.e., the sol-gel transition). These theories provide well-defined quantitative criteria for gelation that are relevant for interfacial layers as well as bulk systems. Such criteria, and the type of data necessary to test them (e.g., frequency-dependent rheology measurements), have (50) Green, R. J.; Hopkinson, I.; Jones, R. A. L. Langmuir 1999, 15, 5102. (51) Green, R. J.; Hopkinson, I.; Jones, R. A. L. Conformational Changes of Globular Proteins in Solution and Adsorbed at Interfaces Investigated by FTIR Spectroscopy. In Food Emulsions and Foams: Interfaces, Interactions and Stability; Dickinson, E., Patino, J. M. R., Eds.; Royal Society of Chemistry: Cambridge, 1999; p 285.

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the potential to unify the disparate and arbitrary standards often applied in the interfacial rheology literature. Acknowledgment. This work was supported by the National Science Foundation (Award No. CTS-0196119) and the U.S. Department of Agriculture (Award No. 2002-


35503-12520). The authors are grateful to Levent Kurnaz for building the initial prototype of the apparatus and to Gerry Fuller and Carlton Brooks for many helpful conversations. LA0262349

Solution Interface

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