10248
Langmuir 2002, 18, 10248-10254
Rheological Study of Lysozyme and PEG2000 at the Air-Water and Dichloromethane-Water Interfaces under Ramp Type or Sinusoidal Perturbations A. Malzert, F. Boury,* P. Saulnier, J. P. Benoıˆt, and J. E. Proust INSERM ERIT-M 0104 “Inge´ nierie de la Vectorisation Particulaire”, Immeuble IBT, 10, rue Andre´ Boquel, 49100 Angers, France Received July 10, 2002. In Final Form: October 1, 2002 The dilational rheological properties of interfacial films of poly(ethylene glycol) (PEG2000) and hen egg-white lysozyme (HEWL) were studied respectively at the dichloromethane (DCM)-water and airwater interfaces by means of the pendant drop method. In both cases, the observed interfacial behaviors were approached by a model corresponding to a two-dimensional viscoelastic solid. The interfacial layers were characterized by three physical constants: Ee, the equilibrium elasticity, Ene, the nonequilibrium elasticity, and τ, the relaxation time. Because the interfacial dilational properties of the films were studied by using a ramp type perturbation approach or a sinusoidal variations approach, identical rheological physical constants values were obtained for PEG2000 and HEWL. From these studies, the interactions within the interfacial layer and those between the interfacial film and adjacent phases can be indirectly accessed and estimated.
Introduction Areas where interfacial rheology is thought to be important are numerous and diverse, including, for example, drug delivery, lung function,1 detergency, and food technology.2 Interfacial tension measurements and rheological studies can be a useful way to study dynamic interfacial properties such as adsorption and desorption, provide indirect evidence of the conformation of interfacial layers, and better understand its interactions with the adjacent phases.2-6 The common idea of all the related experiments is to apply a controlled perturbation to the surface in order to simultaneously follow the related surface pressure variations. These surface perturbations can be very small (for example, thermal fluctuations7 or capillary waves8,9) when the interest is the characterization of dynamic behavior with a characteristic time between 10-6 and 1 s. The deformations can be also more important (for example, moving barrier, ring method, canal method, or drop deformation)10-12 when the viscoelastic characteristic time is on the order of 1-103 s. * To whom correspondence should be addressed. E-mail:
[email protected] (1) Panaiotov, I.; Ivanova, T.; Proust, J. E.; Boury, F.; Denizot, B.; Keough, K.; Taneva, S. Colloids Surf., B 1996, 6, 243. (2) Dickinson, E. Colloids Surf., B 1999, 15, 161. (3) Murray, B. S.; Ventura, A.; Lallemant, C. Colloids Surf., A 1998, 143, 211. (4) Prokop, R. M.; Hair, M. L.; Neumann, A. W. Macromolecules 1996, 29, 5902. (5) Saulnier, P.; Boury, F.; Malzert, A.; Heurtault, B.; Ivanova, T.; Cagna, A.; Panaı¨otov, I.; Proust, J. E. Langmuir 2001, 17, 8104. (6) Ornebro, J.; Nylander, T.; Eliasson, A. C. J. Cereal Sci. 2000, 31, 195. (7) Earnshaw, J. C. In Polymer Surfaces and Interfaces II; Feast, H. S. M. W. J., Richards, R. W., Eds.; Wiley: Chichester, New York, 1993; p 101. (8) Langevin, D.; Bouchiat, A. M. C. R. Seances Acad. Sci., Ser. B 1971, 272, 1422. (9) Sauer, B. B.; Yu, H. Macromolecules 1989, 22, 786. (10) Miller, R.; Wustneck, J.; Kra¨gel, J.; Kretzschmar, G. Colloids Surf., A 1996, 111, 75. (11) Williams, A.; Prins, A. Colloids Surf., A 1996, 114, 267. (12) Benjamins, J.; Lucassen-Reynders, E. H. In Proteins at Liquid Interfaces; Mo¨bius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1998; p 341.
The dynamic response of a surface film to a dilational mechanical stress in the time scale of 1-103 s can be studied by means of two experimental approaches. The first one is called ramp type perturbation approach and consists of a continuous and monotonic area deformation upon compression of a surface layer. This approach has already been successfully used in the past to better understand the behavior of phospholipids,1 polymers,13 or proteins14 at various interfaces. The second approach seems very close to the common three-dimensional (3D) rheology field and is widely related in the literature dealing with interfacial dilational rheology12,15-18 and also with interfacial shear rheology.19 A sinusoidal interfacial perturbation is applied in order to follow the interfacial tension response. Relative area variation and surface tension are considered as the input and the output of the interfacial system, respectively, from which it is possible to evaluate a transfer function (complex function) often called complex elasticity modulus E. The real part of this function found with various notations in the literature (′;3,12 r;20 E′;16 Ed;17,18 G′ 19) characterizes a conservative monolayer behavior. The imaginary part (′′;3,12 i;20 E′′;16 Ev;17,18 G′′ 19) characterizes a dissipative monolayer behavior and often defines the dilational (shear) monolayer viscosity with η ) ′′/ω (where ω ) 2πf and f is the frequency of the oscillations). Unfortunately, these functions depend not only on the monolayer behavior but also on the experimental condi(13) Malzert, A.; Boury, F.; Saulnier, P.; Benoit, J. P.; Proust, J. E. Langmuir 2001, 17, 7837. (14) Boury, F.; Ivanova, T.; Panaiotov, I.; Proust, J. E.; Bois, A.; Richou, J. Langmuir 1995, 11, 1636. (15) Chen, P.; Prokop, R. M.; Susnar, S. S.; Neumann, A. W. In Proteins at Liquid Interfaces; Mo¨bius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1998; p 303. (16) Myrvold, R.; Hansen, F. K. J. Colloid Interface Sci. 1998, 207, 97. (17) Rodriguez Nino, M. R.; Wilde, P. J.; Clark, D. C.; Rodriguez Patino, J. M. Ind. Eng. Chem. Res. 1996, 35, 4449. (18) Rodriguez Nino, M. R.; Wilde, P. J.; Clark, D. C.; Rodriguez Patino, J. M. Langmuir 1998, 14, 2160. (19) Brooks, C. F.; Fuller, G. G.; Frank, C. W.; Robertson, C. R. Langmuir 1999, 15, 2450. (20) Wustneck, R.; Moser, B.; Muschiolik, G. Colloids Surf., B 1999, 15, 263.
10.1021/la020623l CCC: $22.00 © 2002 American Chemical Society Published on Web 12/02/2002
Lysozyme and PEG2000 Rheological Study
tions for which they are evaluated; in particular, G′ and G′′ (and the corresponding parameters) are frequency dependent. In this way, it is difficult to compare all the experimental results rarely obtained in similar experimental conditions. In this paper, we propose to compare ramp type and sinusoidal rheological approaches by applying a same mechanical model which corresponds to a viscoelastic body and which has been already successfully applied to many kinds of interfacial systems in the past.1,5,21,22 In this model, three physical constants are determined: an interfacial conservative elasticity Ee related to a long range organization of the interfacial monolayer and consequently to the interactions between the interfacial molecules; an interfacial dissipative elasticity Ene related to molecular reorganization like expulsion of molecular chains upon compression and interactions of molecules with the adjacent liquid-phase molecules; and a relaxation time τ representing the necessary time for the interface to reach a new equilibrium energetic state after the perturbation. A film of dipalmitoyphosphatidylcholine (DPPC), a very well-known phospholipid, was previously studied by our group5 at the dichloromethane (DCM)-water interface by using a pendant drop tensiometer. It was shown that if the rheological approach was based either on ramp type compression or on sinusoidal area variation, similar constants values were obtained by using the mechanical model based on the Maxwell theory. Nevertheless, one can wonder if it would be the same with more complex systems such as polymer or protein. To answer this question, rheological behaviors of poly(ethylene glycol) (PEG2000) and hen egg-white lysozyme (HEWL) were investigated respectively at DCM-water and air-water interfaces by using the continuous or sinusoidal perturbation approaches. The three physical interfacial constants were determined in both cases and compared. Materials and Methods Materials. R-Methoxy, ω-hydroxy-PEG2000 and HEWL (product code L6876, dialyzed and lyophilized, containing buffer salts as sodium acetate and sodium chloride (3 × crystallized) protein, approximately 95%) were purchased from Sigma Chemical Co. (L’Isle d’Abeau, France) and were used without further purification. Analytical grade dichloromethane (DCM) was from Prolabo (Paris, France). Ultrapure water was obtained from a Millipore system (Milli-Q Plus 185, Molsheim, France). Pendant Drop Tensiometer. Adsorption kinetics and rheological measurements were carried out at air-water and DCM-water interfaces by means of a pendant drop method (Tracker, ITConcept, Longessaigne, France).23 A drop was formed with an Exmire microsyringe (Prolabo, Paris, France) into an optical glass bowl (Hellma, France) containing the other phase. The axial symmetric shape (Laplacian profile) of the drop was analyzed by use of a video camera connected to a microcomputer. From the analysis of the numerical image with the Laplace equation integrating the points of the drop profile, the interfacial tension, surface area, and volume of the drop were recorded in real time (five measurements per second).5,14,23,24 The 0.001 mg/mL PEG2000 in DCM and 5 mg/mL HEWL in (21) Boury, F.; Ivanova, T.; Panaiotov, I.; Proust, J. E.; Bois, A.; Richou, J. J. Colloid Interface Sci. 1995, 169, 380. (22) Malzert, A.; Boury, F.; Saulnier, P.; Ivanova, T.; Panaiotov, I.; Benoit, J. P.; Proust, J. E. J. Colloid Interface Sci. Submitted for publication. (23) Grimaldi, M.; Bois, A.; Nury, S.; Rivie`re, C.; Verger, R.; Richou, J. OPTO 1991, 104.
Langmuir, Vol. 18, No. 26, 2002 10249
Figure 1. (a) Schematic ramp type surface area variation of a drop of a surface film. (s) Fast compression when 0 < t < tf. For t > tf, the surface area is maintained constant. (‚‚‚) Slow compression when 0 < t < ts. For t > ts, the surface area is maintained constant. (b) Schematic related surface pressure change (∆π ) γ0 - γ) versus time: (s) Fast compression; (‚‚‚) Slow compression; (c) Mechanical model of the monolayer.
water concentrations were chosen in order to rapidly reach an equilibrium surface tension. All the measurements were performed at controlled room temperature (20 ( 1 °C). Ramp Type Perturbation Approach. Theoretical Aspects. Because of the friction of the monolayer on the liquid substrate, the propagation is not instantaneous. This friction is accompanied by a counterflow in the subphase related to the Marangoni effect. So, in a general pattern, the rheological analysis simultaneously involves relaxation processes with characteristic relaxation time τ and a propagation process along the length of the monolayer with a characteristic time τM. But, when the reequilibration of the surface pressure gradients along the monolayer is faster than the surface relaxation time, i.e., τ is much larger than τM, one can consider the dynamic response as a whole, neglecting the Marangoni effect. Moreover, as reported in a previous paper,5 dynamic phenomena on the interface related to Marangoni rearrangements can be neglected in the studied conditions. Figure 1parts a and b presents theoretical results that could be related to fast compressions (during the time tf) and slow compressions (during the time ts) of a monolayer at an interface. Figure 1a and Figure 1b correspond to the relative area variation and surface pressure variations versus time, respectively. For both compressions, it is important to note that the relaxation occurs not only for t > tf or ts but also during the compression (for t < tf or (24) Labourdenne, S.; Gaudry-Rolland, N.; Letellier, S.; Lin, M.; Cagna, A.; Esposito, G.; Verger, R.; Rivie`re, C. Chem. Phys. Lipids 1994, 71, 163.
10250
Langmuir, Vol. 18, No. 26, 2002
Malzert et al.
ts). However, this effect is usually observed only at slow compression rate considering the nonlinear variations of the surface pressure for 0 < t < ts. One can remark in Figure 1b that the surface pressure does not reach its initial value at the end of the relaxation. In such a case, it can be assumed that only a certain part of the interfacial energy has been lost during the experiment and the other part is conserved. That is why we assume that, during the relaxation, the total surface pressure change,
∆π ) π(t) - πi,
(1)
can be represented as a sum of one equilibrium ∆πe and one nonequilibrium ∆πne contribution:
∆π ) ∆πe + ∆πne
(2)
The related theoretical approach was intensely developed in previous papers, 1,14 considering the mechanical model represented in Figure 1c. τ was deduced from the experimental results related to the fast compression for t > tf with the following equation:
ln
π(t) - π∞ t )π0 - π∞ τ
(3)
In the same way, we have shown that the addition of strains for the two parallel branches was represented by
τ ∆π A ) Ee + Ene (1 - e-(t)/(τ)) Ut i t
(4)
Experimental Protocol. For the determination of Ee, Ene, and τ, one has to successively perform the following: (i) Fast (d/dt ∆A(t)/Ai) ) U/Ai typically higher than 0.01 s-1 compression (with ∆πmax typically lower than 2 mN/ m) in order to determine more precisely the relaxation (t > tf, see Figure 1b). Using eq 3, the relaxation time τ is deduced. (ii) Slow (d/dt ∆A(t)/Ai) ) U/Ai typically lower than 0.004 s-1) monolayer compression (with ∆πmax < 2 mN/m) in order to determine the compression relaxation part (t < ts, see Figure 1b). The values of τ and eq 4 are used to determine Ee and Ene. Sinusoidal Perturbation Approach. Theoretical Aspects. The aim of this method is to interpret the response of the interfacial tension to several harmonic variations (characterized by their pulsation ω) of the interfacial area A (Figure 2a). For each pulsation, the relative variation of the interface area versus time is considered as the “input” of the system defined by the drop in its environment. In the same way, the variation of the interfacial surface pressure (π) versus time is considered as the output. We obtained the following situation: For each pulsation ω, and at every time t, an adequate harmonic analysis of these two signals allows the calculation of a complex transfer function (or complex elasticity) given by
G h (ω) ) E h (ω) ) A h
dπ dA h
(5)
We have verified that this complex function is independent of t when the surface pressure π has reached its equilibrium value. This transfer function can be transformed in the expression
G h (ω) ) G′(ω) + iG′′(ω)
(6)
where G′(ω) and G′′(ω) correspond to the real part and the imaginary part of the transfer function, respectively. So
Figure 2. (a) Schematic sinusoidal surface area variation (s) and surface tension variation (‚‚‚) versus time. (b) Theoretical variations versus pulsation ω of G′ (eq 8) (]) and G′′/ω (eq 9) (b) where G′ and G′′ are the real and the imaginary parts of the transfer function G h (ω) ) A h dπ/dA h , respectively; the extrapolations allowing the determination of Ee, Ene, and τ are presented.
the graphs G′(ω) and G′′(ω) are characteristic of the rheological behavior of the interfacial layer. The dephasage angle φ is also given by
tg(φ) )
G′(ω) G′′(ω)
(7)
Considering that the interface follows a mechanical model (Maxwell theory) previously described (see Figure 1c), the conservative part of the transfer function (G′(ω)) is theoretically represented by the following equations:5
G′(ω) ) Ee + Ene
ω2τ2 1 + ω2τ2
(8)
Similarly, the imaginary part of the transfer function is written
G′′(ω) 1 ) Eneτ ω 1 + ω2τ2
(9)
The characteristic theoretical graphs of these functions (presented in Figure 2b) were drawn considering eqs 8 and 9 with Ee ) 6 mN/m, Ene ) 18 mN/m, and τ ) 10 s. Experimental Protocol. (i) The relative area variation of the drop was chosen at 2.5% (for a drop of 20 mm2) corresponding to the linear regime. We have verified that nonlinear phenomena appear when relative variations are larger than 10%. (ii) The range of pulsation is 0.05 < ω < 7 rad/s corresponding to the apparatus limitations. (iii) After the stabilization of the surface pressure, three sinusoids are performed for each pulsation.
Lysozyme and PEG2000 Rheological Study
Langmuir, Vol. 18, No. 26, 2002 10251
Figure 3. Adsorption kinetics of (a) PEG2000 from DCM (Cbulk ) 0.001 mg/mL) at the DCM-water interface. (b) HEWL (Cbulk ) 5 mg/mL) at the air-water interface.
(iv) An adequate Fourier analysis allows for each pulsation the determination of G, G′, and G′′. (v) The validity of the mechanical model (Figure 1c) is verified, considering the shape of the experimental graphs G′ and G′′/ω versus ω. (vi) The physical constants Ee, Ene, and τ are extrapolated considering the following equations:
limG′(ω) ) Ee
(10)
lim G′(ω) ) Ene + Ee
(11)
Figure 4. (a) Typical results of the graphical determination of the characteristic time, experimental values (points) and theoretical values (solid line). The measurements were recorded during the fast compression of the PEG2000 monolayer adsorbed at the DCM-water interface from DCM with a velocity of 0.32 s-1. (b) Typical results of the graphical determination of Ee, the equilibrium part of the elasticity, and Ene, the nonequilibrium part of the elasticity. The measurements were recorded during the slow compression of the PEG2000 monolayer adsorbed at the DCM-water interface from DCM with a velocity of 0.004 s-1.
limG(ω) ) Ea
(13)
G(ω) ) (G′(ω) + G′′(ω))1/2
(14)
at the interface.25 The very low decrease in γ observed after 300 s would correspond to the reorganization of polymer segments at the interface.25 The equilibrium surface tension γeq was 21.9 mN/m. Interfacial dilatational rheological properties were studied after adsorption kinetics reached an equilibrium state (after ≈1000 s). Ramp Type Measurements. The development of the relaxation phenomena at the end of the fast compression (for t > tf) corresponds to the characteristic time necessary for the layer to reach a new equilibrium state. As a slow compression rate of the interfacial layer favors the layer relaxation still during the compression,5 the relaxation time (τ) was determined considering an important related rate of compression (0.32 s-1). Applying eq 3 to the data for which t > tf (Figure 4a), we obtain an average value
(15)
τ ) 10 ( 2 s
ωf0
ωf+∞
lim ωf0
G′′(ω) ) Eneτ ω
(12)
One can also note that the apparent dilatational elasticity, Ea, usually found on true π-A isotherms, can be extrapolated with ωf0
where
Ea ) -A
dπ dA
Results and Discussion I. PEG2000. Adsorption Kinetics at the DCMWater Interface. Figure 3a shows the experimental surface tension variations versus time of PEG2000 dissolved in DCM at the DCM-water interface. To link the surface tension variations only to the adsorption of PEG2000 at the DCM-water interface, the area of the drop was maintained constant. The rapid decrease of the surface tension (γ) for the first 300 s from 28 mN/m, the γ of the pure DCM-water interface, to 22.5 mN/m would correspond to diffusion and adsorption of PEG segments
Ee and Ene were determined considering slow compression rate (0.004 s-1). Thus, the two physical constants are determined in static conditions independently on the experimental conditions. Considering the τ value and eq 4, we plotted the evolution of (∆π)/(Ut)Ai versus τ/t(1 - e-(t)/(τ)). Upon extrapolation to the Y-axis, Ee can be deduced. From the slope of the straight line, Ene can be estimated (Figure 4b). We obtain (25) Beverung, C. J.; Radke, C. J.; Blanch, H. W. Biophys. Chem. 1999, 81, 59.
10252
Langmuir, Vol. 18, No. 26, 2002
Malzert et al.
Ee ) 1 ( 1 mN/m, Ene ) 4 ( 1 mN/m Sinusoidal Measurements. Figure 5a shows sinusoidal type experiments for PEG2000 for an ω ) 2.09 rad/s pulsation, which correspond to the simultaneous variations versus time of the surface tension and area. One can observe only a small dephasing angle between the area variations and the surface tension. The area variations do not strictly follow typical sinusoids at the top and bottom of the sinusoids, in relation with a little length of stroke of the syringe piston. These artifacts still exist for lower pulsation (results not shown) and cannot be attributed to nonlinear phenomena. It is important to note that these artifacts are significant only in the fourth harmonic of the related Fourier development (results not shown) and do not significantly influence the values of G′ and G′′. The experimental variation of G′ (dotted line with diamonds) and G′′/$ (full line with circles) versus ω are presented in Figure 5b. Values of the three physical constants were deduced from extrapolations of the experimental curve to static conditions (see eqs 10, 11, and 12) and were estimated to
Ee ) 1 ( 1 mN/m Ene ) 5.5 ( 1 mN/m and
τ ) 10 ( 2 s No significant difference can be observed between values of Ee, Ene, and τ obtained by both approaches. Discussion. The energetic constant Ee corresponds to a conservative elastic response of the monolayer induced by the rheological perturbation. It is related to the intrinsic monolayer cohesion, describing all the lateral interactions (hydrophobic as well as hydrophilic) between all the amphiphilic polymer segments in the interfacial zone, taking the role of the so-called Hooke constant in 3D mechanical fields.5 The low Ee value determined for PEG2000 would indicate only few interactions or condensations of polymer segments in the plane of the DCM-water interface upon compression. This high flexibility could be explained by the ability of polymer chains to penetrate into both phases at the DCM-water interface.26,27 Ene characterizes the dissipation of the rheological perturbation energy related to polymer chains reorganization and interactions between the interfacial polymer molecules and the bulk phase ones (DCM and water).5,21 In this way, Ene strongly depends on the solubility values. Finally, τ represents the necessary time for the interface to reach a new equilibrium energetic state.5 Low τ and Ene values indicate a fast reorganization and a low energetic dissipation, i.e., expulsion of only few segments upon compression. PEG2000 is a peculiar polymer which is soluble in both organic solvents and water.28 Here, PEG2000 was initially dissolved in the organic phase. When adsorbed at the liquid-liquid interface, the polymer chains can penetrate in the both phases. It is known that two to three water molecules can link each PEG segment by hydrogen bonds.28,29 From that, (26) Noskov, B. A.; Akentiev, A. V.; Loglio, G.; Miller, R. J. Phys. Chem. B 2000, 104, 7923. (27) Xu, Z.; Holland, N. B.; Marchant, R. E. Langmuir 2001, 17, 377. (28) Harris, J. M. In Poly(Ethylene Glycol) Chemistry; Harris, J. M., Ed.; Plenum Press: New York, 1992; p 1.
Figure 5. (a) Sinusoidal type rheological measurements. Surface area and surface tension sinusoidal variations (ω ) 2.09 rad/s) versus time of a PEG2000 monolayer adsorbed at the DCM-water interface from DCM (Cbulk ) 0.001 mg/mL). (b) Experimental variations of G′ (]) and G′′/ω (b) versus ω for a PEG2000 monolayer adsorbed at the DCM-water interface from DCM (Cbulk ) 0.001 mg/mL). Extrapolation of the curve G′′/ω ) f(ω) to ω ) 0 was also plotted (‚‚‚).
although PEG2000 exhibits a greater affinity for DCM than for water,30 reorganization of the PEG2000 film occurring upon compression of the interfacial layer would imply expulsion of some polymer segments toward water and, more particularly, expulsion of tails corresponding to ω-hydroxy ends, i.e., the most hydrophilic PEG segments. II. HEWL. Adsorption Kinetics at the Air-Water Interface. Note that the study of interfacial properties of HEWL was carried out at the air-water interface because an elastic behavior of the protein was observed at the DCM-water interface. When interfacial films exhibit a pure elastic behavior, the viscoelastic mechanical model is not required to assess the apparent elasticity of the film (Ea), describing the global equilibrium and nonequilibrium properties of the film,31 since in this case, Ea is directly deduced from eq 15. A value of 7.5 ( 0.3 mN/m was determined for the HEWL interfacial film at the DCM-water interface from both the ramp and the sinusoidal compression types. Figure 3b shows the experimental surface tension variations versus time of HEWL at the air-water interface. As in the case of PEG2000, the area of the drop was maintained constant. In the studied conditions, no induction time32 was observed, but a decrease in γ was shown as soon as the drop was formed. The equilibrium (29) Ide, M.; Yoshikawa, D.; Maeda, Y.; Kitano, H. Langmuir 1999, 15, 926. (30) Tomaszewski, K.; Szymanski, A.; Lukaszewski, Z. Talanta 1999, 50, 299. (31) Boury, F.; Ivanova, T.; Panaiotov, I.; Proust, J. E. Langmuir 1995, 11, 599. (32) Miller, R.; Fainerman, V. B. F.; Makievski, A. V.; Kra¨gel, J.; Grigoriev, D. O.; Kazakov, V. N.; Sinyachenko, O. V. Adv. Colloid Interface Sci. 2000, 86, 39.
Lysozyme and PEG2000 Rheological Study
Langmuir, Vol. 18, No. 26, 2002 10253
Figure 7. Experimental variations of G′ (]) and G′′/ω (b) versus ω for a HEWL layer adsorbed at the air-water interface (Cbulk ) 5 mg/mL). Extrapolation of the curve G′′/ω ) f(ω) to ω ) 0 was also plotted (‚‚‚).
and
τ ) 15 ( 5 s Figure 6. (a) Typical results of the graphical determination of the characteristic time, experimental values (points) and theoretical values (solid line). The measurements were recorded during the fast compression of the HEWL layer adsorbed at the air-water interface with a velocity of 0.24 s-1. (b) Typical results of the graphical determination of Ee, the equilibrium part of the elasticity, and Ene, the nonequilibrium part of the elasticity. The measurements were recorded during the slow compression of the HEWL layer adsorbed at the air-water interface with a velocity of 0.0001 s-1.
part of the adsorption kinetics was reached after about 1000 s, and the equilibrium surface tension γeq was 54.8 mN/m. This value is in accordance with those previously reported in the literature.33 Interfacial dilatational rheological properties were studied after adsorption kinetics reached an equilibrium state (after ≈1500 s), because during the equilibration process, elasticity moduli are time dependent.12 Ramp Type Measurements. The relaxation time τ was determined after a fast compression (rate of compression of 0.24 s-1) of the drop applying eq 3 to the data. We obtain (Figure 6a)
τ)9(2s Ee and Ene were determined after a slow compression (rate of compression of 0.0001 s-1) of the drop, considering the τ value, and eq 4 illustrated by Figure 6b, which shows the evolution of (∆π)/(Ut)Ai versus τ/t(1 - e-(t)/(τ)):
Ee ) 89 ( 5 mN/m,
Ene ) 18 ( 5 mN/m
Sinusoidal Measurements. The experimental variation of G′ (dotted line with diamonds) and G′′/$ (full line with circles) versus ω are presented in Figure 7. Values of the three physical constants were deduced from extrapolations of the experimental curve to static conditions (see eqs 10, 11, and 12) and were estimated to the following:
Ee ) 80 ( 10 mN/m Ene ) 20 ( 5 mN/m
No significant difference can be observed between both approaches, since similar values of Ee, Ene, and τ are obtained. Discussion. It is established from many studies (i.e., X-ray reflectivity, circular dichroism and infrared spectroscopy studies) that adsorption of HEWL at the airwater interface leads to some unfolding of the protein molecules accompanied with conformational rearrangements (i.e., an increase of antiparallel β-sheets to the detriment of R-helixes and intermolecular associations).34-37 The high value of Ee determined for HEWL adsorbed at the air-water interface can be explained by a strong internal cohesion of the protein interfacial film, related to strong interactions between adsorbed polypeptide chains through hydrogen bonding, hydrophobic, or hydrophilic bonding.38,39 It is reported that at aqueous protein concentrations higher than 10-2 mg/mL, HEWL molecules adsorbed at the air-water interface form multilayers.33,40 Fainerman and Miller41 also speculated that in the concentrated adsorption layer of protein at the equilibrium, twodimensional (2D) aggregation occurs, making the assumption of multilayer adsorption redundant. Furthermore, according to McRitchie, interfacial properties of proteins are governed more by segments of molecules than by whole molecules.42 (33) Jiang, Q.; Chiew, Y. C. Colloids Surf., B 2001, 20, 303. (34) Prins, A.; Bos, M. A.; Boerboom, F. J. G.; van Kalsbeek, H. K. A. I. In Proteins at Liquid Interfaces; Mo¨bius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1998; p 221. (35) Tripp, B. C.; Magda, J. J.; Andrade, J. D. J. Colloid Interface Sci. 1995, 173, 16. (36) Green, R. J.; Hopkinson, I.; Jones, R. A. L. Langmuir 1999, 15, 5102 (37) Postel, C. Structure et cine´tique d’adsorption d’une prote´ine mode`le a` l’interface eau-air. Thesis of University of Paris VI, 2000. (38) Murray, B. S. In Proteins at Liquid Interfaces; Mo¨bius, D., Miller, R., Eds.; Elsevier Science: Amsterdam, 1998; p 179. (39) Izmailova, V. N.; Yampolskaya, G. P. In Proteins at Liquid Interfaces; Mo¨bius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1998; p 103. (40) Hunter, J. R.; Kilpatrick, P. K.; Carbonell, R. G. J. Colloid Interface Sci. 1990, 137, 462. (41) Fainerman, V. B. F.; Miller, R. Langmuir 1999, 15, 1812. (42) McRitchie, F. In Proteins at Liquid Interfaces; Mo¨bius, D., Miller, R., Eds.; Elsevier: Amsterdam, 1998; p 149.
10254
Langmuir, Vol. 18, No. 26, 2002
The high value of Ene is significant of high energetic dissipation, indicating an important reorganization of the adsorbed polypeptide chains. Nevertheless, from the low value of τ showing that a new equilibrium energetic state of the protein film is rapidly reached after compression, one can think that the expulsion of segments of HEWL molecules from the interfacial film toward water is damped by protein molecules, sublayers, or protein aggregates. One can also note that as multilayers provide a reservoir of protein close to the interface, the protein molecules in it should be able to readily interchange with the interface as the area is varied.12 This assumption is well supported by high Ene value. Nevertheless, as the protein molecules in the first layer would be irreversibly adsorbed,40,43 and as same physical constants values are obtained by both rheological approaches, this would more indicate reversible expulsion of molecular segments in the first layer rather than protein molecules desorption and simultaneous adsorption of protein molecules from the sublayers. Conclusion In this paper, we performed two 2D rheological approaches (ramp type compression and sinusoidal area
Malzert et al.
variation) for two given interfacial films (PEG2000 at the DCM-water interface, and HEWL at the air-water interface) to determine three physical constants: equilibrium elasticity Ee, nonequilibrium elasticity Ene, and relaxation time τ, which are calculated under a mechanical model based on the Maxwell theory. For both PEG2000 and HEWL, Ee, Ene, and τ characterize not only the interfacial layer but also its interactions with the adjacent phases. It was shown that both approaches give the same results in both studied cases. In conclusion, even for complex interfacial systems such as proteins or polymers, ramp type or sinusoidal type rheological experiments seem adequate to better understand the interfacial molecular organization. One can note, nevertheless, that in comparison with the sinusoidal area variation approach, the ramp type compression approach is simpler and more rapid to use and, for these reasons, can be recommended to determine rheological properties of interfacial films. LA020623L (43) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 415.
