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Langmuir 2006, 22, 6814-6817
Micellar Spheres in a High Frequency Oscillatory Field Antonis Kelarakis,*,† Je´roˆme J. Crassous, and Matthias Ballauff Physikalishe Chemie I, UniVersita¨t Bayreuth, UniVersita¨tsstrasse 30, 95440 Bayreuth, Germany
Zhuo Yang and Colin Booth Department of Chemistry, UniVersity of Manchester, Manchester M13 9PL, United Kingdom ReceiVed March 23, 2006. In Final Form: May 30, 2006 The viscoelasticity of aqueous micellar solutions of two oxyethylene/oxybutylene block copolymers (E92B18 and B20E510) has been investigated using a torsional resonator operated at 26 kHz. For both systems considered, values of the dynamic viscosity (η′∞) point to partial draining of the micellar corona induced by the high-frequency oscillatory field. At low effective volume fractions, values of the elastic modulus (G′∞) indicate that the repulsive interactions between micelles can be modeled by a power law function u(r) ∝ 1/rν with exponents close to 13 and 6 for copolymers E92B18 and B20E510 respectively. At a critical copolymer concentration (c*) plots of log(G′∞) against log(c) deviate from the straight lines established at low concentrations, implying that the systems undergo ergodic/nonergodic transitions.
1. Introduction Dilute micellar solutions and concentrated mesophases of block copoly(oxyalkylene)s are a subject of intense study due to their major academic and industrial interest.1 The work described in this paper concerns EmBn copolymers, where E denotes an oxyethylene unit, OCH2CH2, and B denotes an oxybutylene unit, OCH2CH(C2H5), and m and n denote number-average block lengths in repeat units. The structure and dynamics of E/B micelles and micellar gels have been extensively characterized by scattering techniques, such as static and dynamic light scattering (SLS and DLS)2 and small-angle X-ray and neutron scattering (SAXS and SANS).3,4 The results of this systematic investigation now allow the preparation of micellar solutions with a wide variety of welldefined tailored properties. In that sense, aqueous solutions of diblock copolymers can be viewed as model systems for understanding the behavior of spherical particles that interact via short-range repulsive forces. The parameter that dictates the micellar behavior in these systems is the effective interaction potential between micelles,5,6 u(r), which greatly depends on the relative size of core and corona, which in turn is determined by the copolymer composition, i.e., the m/n ratio. It has been demonstrated7 that the ratio rt/rh (with rt being the thermodynamic radius obtained from SLS and rh the hydrodynamic radius obtained from DLS) can be used as a criterion for evaluating the hardness of spherical polymer coils, with rt/rh f 1 indicating ideal hard sphere behavior and lower values showing a soft sphere potential. Differences in the effective * To whom correspondence should be addressed. E-mail: ak385@ cornell.edu. † Current address: Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853. (1) Nace, V. M. In Nonionic Surfactants: Polyalkylene block copolymers; Marcel Dekker: New York, 1996; Vol. 60. (2) Booth, C.; Atwood, D. Macromol. Rapid Commun. 2000, 21, 501. (3) Kelarakis, A.; Havredaki, V.; Derici, L.; Yu, G.-E.; Booth, C.; Hamley, I. W. J. Chem. Soc., Faraday Trans. 1998, 94, 3639. (4) Castelletto, V.; Hamley, I. W.; Pederson, J. S. Langmuir 2004, 20, 2992. (5) McConnell, G. A.; Gast, A. P.; Huang, J. S.; Smith, S. D. Phys. ReV. Lett. 1993, 71, 2102. (6) Hamley, I. W.; Daniel, C.; Mingvanish, W.; Mai, S.-M.; Booth, C.; Messe, L.; Ryan, A. J. Langmuir 2000, 16, 2508. (7) Selser, J. In Light Scattering: Principles and DeVelopment; Brown, W., Ed.; Clarendon Press: Oxford, U.K., 1996; Chapter 7.
interaction potential between spherical micelles lead to the possibility of ordering in body-centered cubic (bcc) or facecentered cubic (fcc) symmetries.8 Micelles with compact E-block coronas (small values of m/n) at low concentration act as hard spheres and pack into fcc arrays. bcc packing is favored for micelles with expanded E-corona (large values of m/n), which exhibit softer potential. The complex viscoelastic nature of aqueous micellar solutions and gels of block copolymers has also been systematically investigated. However, the rheological behavior of micellar systems in the limit of high frequency has been reported only rarely.9-11 Recent theoretical approaches12-15 and corresponding experimental investigations of, for example, suspensions of charge-stabilized and sterically stabilized colloidal spheres16-24 underline the fact that high-frequency rheology is a powerful technique for studying the interactions between colloidal particles. In particular, it has been shown that the elastic modulus, G′∞, can be used to probe the magnitude of the short-range interaction potential between the particles, whereas the viscous modulus, (8) Hamley, I. W.; Mai, S.-M.; Ryan, A. J.; Fairclough, J. P. A.; Booth, C. Phys. Chem. Chem. Phys. 2001, 3, 2972. (9) Buitenhuis, J.; Fo¨rster, S. J. Chem. Phys. 1997, 107, 262. (10) Constantin, D.; Freyssingeas, E.; Palierne, J.-F.; Oswald, P. Langmuir 2003, 19, 2554. (11) Constantin, D.; Palierne, J.-F.; Freyssingeas, E.; Oswald, P. Europhys. Lett. 2002, 58, 236. (12) Wagner, N. J. J. Colloid Interface Sci. 1993, 161, 169. (13) Lionberger, R. A.; Russel, W. B. J. Rheol. 1994, 38, 1885. (14) Lionberger, R. A.; Russel, W. B. J. Rheol. 1997, 41, 399. (15) Elliot, S. L.; Russel, W. B. J. Rheol. 1998, 42, 361. (16) Bergenholtz, J.; Horn, F. M.; Richtering, W.; Willenbacher, N.; Wagner, J. Phys. ReV. E 1998, 58, 4088. (17) van der Werff, J. C.; de Kruif; C. G.; Blom, C.; Mellema, J. Phys. ReV. A 1989, 39, 795. (18) Shikata, T.; Pearson, D. S. J. Rheol. 1994, 38, 601. (19) Bergenholtz, J.; Willenbacher, N.; Wagner, N. J.; Morrison, B.; Ende, D.; Mellema, J. J. Colloid Interface Sci. 1998, 202, 430. (20) Weiss, A.; Ballauff, M.; Willenbacher, N. J. Colloid Interface Sci. 1999, 216, 185. (21) Deike, I.; Ballauff, M.; Willenbacher, N.; Weiss, A. J. Rheol. 2001, 45, 709. (22) Fritz, G.; Maranzano, B. J.; Wagner, N. J.; Willenbacher, N. J. NonNewtonian Fluid Mech. 2002, 102, 149. (23) Horn, F. M.; Richtering, W.; Bergenholtz, J.; Willenbacher, N.; Wagner, N. J. J. Colloid Interface Sci. 2000, 225, 166. (24) Crassous, J. J.; Regisser, R.; Ballauff, M.; Willenbacher, N. J. Rheol. 2005, 49, 851.
10.1021/la0607860 CCC: $33.50 © 2006 American Chemical Society Published on Web 06/30/2006
Micellar Spheres in a High Frequency Oscillatory Field
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Table 1. Molecular Characteristics of the Copolymers and Micellar Properties in Aqueous Solution at 25 °Ca copolymer
Mn/103g mol-1 (NMR)
wt %, E (NMR)
Mw/Mn (GPC)
Nw
c*/wt %
δt
rt/nm
δh
rh/nm
E92B18 B20E510
5.7 23.9
76.5 94.0
1.06 1.06
163 62
8.3 3.3
9.5 22.7
14.8 23.2
10.1 36.9
15.5 27.9
a M ) number-average molar mass of the copolymer. M /M ) ratio of weight-average to number-average molar mass of the copolymer. N n w n w ) weight-average association number of the micelles. c* ) critical gelation concentration. δt and rt ) thermodynamic expansion factor and radius of the micelles. δh and rh ) hydrodynamic expansion factor and radius of the micelles.
G′′∞, can provide information regarding the effective volume fraction of the suspended particles. In this report, we present the results of a study of the rheology of aqueous micellar solutions of E/B block copolymers using a torsional resonator that is operated at 26 kHz. Rheological data collected under this oscillatory field can provide a close approximation for the high-frequency behavior of the micellar systems. We consider two copolymers, namely E92B18 and B20E510, both of which have lengthy B blocks, thus ensuring complete micellization in dilute solution at 25 °C. The critical micelle concentration (cmc) of copolymer EmB16 has been estimated3 to be close to 4 mg/dm3, and even lower values might be expected for copolymers E92B18 and B20E510, given that, within a given block architecture, the logarithm of cmc (molar values) decreases linearly with increase in B-block length and is only weakly dependent on E-block length.2 Reversing the polymerization sequence (as in the case of B20E510) induces only a minor effect on the cmc.2 The association properties of the copolymers studied here, the structure and dynamics of the resulting micellar solutions, and the flow behavior of the concentrated gels have been well reported.25-29 Based on the relative lengths of E and B blocks and the rt/rh ratio, the micelles of E92B18 are considered as hard spheres and their concentrated solutions pack in fcc structures, whereas the micelles of B20E510 have softer interactions and form bcc gels. Here we report for first time the viscoelasticity of aqueous solutions of copolymers of this type under an extreme oscillatory field.
26 kHz. The theoretical background and the principles of measurement by torsional resonators have been presented in detail elsewhere.18-21,30 We emphasize that the oscillatory wave can travel within the bulk phase of the samples inducing a deformation well within the linear viscoelastic region. Analytical calculations30 performed on the basis of the operational characteristics of a very similar piece of equipment support the conclusion that the deformation amplitude of the surrounding fluid does not exceed 1%.
3. Results and Discussion 3.1. Effect of Frequency on the Effective Volume Fraction of the Micelles. In a dilute micellar solution, the correlation functions obtained from dynamic light scattering measurements, when analyzed by a suitable mathematical model (e.g., constrained regularized CONTIN method31), can reveal the distribution of decay rate (Γ), hence the distribution of apparent mutual diffusion coefficient Dapp
Dapp ) Γ/q2
(1)
where q is the scattering vector. Extrapolation of average values of Dapp to zero concentration yield the average intrinsic diffusion coefficient D. The average hydrodynamic radius rh, which is defined as the radius of the hydrodynamically equivalent hard sphere corresponding to D, can then be derived via the StokesEinstein equation
rh ) kT/(6πηsD)
(2)
2. Experimental Section A. Materials. Copolymer E92B18 was prepared by sequential anionic polymerization of ethylene oxide (EO) followed by 1,2butylene oxide (BO) in a repeat synthesis of E96B18, a copolymer prepared and used in a previous work.25 The preparation of copolymer B20E510 was by sequential anionic polymerization of BO followed by EO as described previously.27 We denote the polymer so produced as B20E510 to signify the change in the copolymerization route, as this results in a copolymer with methoxy-terminated B-blocks compared with the hydroxyl-terminated B blocks of copolymer E92B18. Gel permeation chromatography (GPC) was used to confirm narrow chain length distributions (Mw/Mn), and 13C NMR spectroscopy was used to obtain absolute values of number-average molar mass (Mn) and to confirm the diblock architecture. The molecular characteristics of the copolymers are summarized in Table 1. Selected micellar properties of the two copolymers in aqueous solution, obtained from static and dynamic light scattering and the tube inversion method (presented in refs 25 and 27), are also listed in Table 1. B. Methods. Torsional Resonator. The cylindrical torsional resonator used in this study was constructed in the Institut fu¨r Dynamische Materialpru¨fung, Ulm, Germany, and was operated at (25) Mingvanish, W.; Mai, S.-M.; Heatley, F.; Booth, C.; Attwood, D. J. Phys. Chem. 1999, 103, 11269. (26) Kelarakis, A.; Mingvanish, W.; Daniel, C.; Li, H.; Havredaki, V.; Booth, C.; Hamley, I. W.; Ryan, A. J. Phys. Chem. Chem. Phys. 2000, 2, 2755. (27) Kelarakis, A.; Havredaki, V.; Viras, K.; Mingvanish, W.; Heatley, F.; Booth, C.; Mai, S.-M. J. Phys. Chem. B 2001, 105, 7384. (28) Castelletto, V.; Hamley, I. W.; Yang, Z.; Haeussler, W. J. Chem. Phys. 2003, 119, 8158. (29) Castelletto, V.; Hamley, I. W.; Waigh, T. A. J. Chem. Phys. 2004, 121, 11474.
where k is the Boltzmann constant and ηs is the viscosity of the solvent at temperature T. The hydrodynamic volume fraction of the micelles φ can be determined by the relationship
φ ) cδh/1000Fa
(3)
where c is the copolymer concentration (in g dm-3), Fa is the density of the anhydrous liquid copolymer,32 and δh is the hydrodynamic expansion factor, defined as
δh ) Vh/Va
(4)
where Vh is the hydrodynamic volume of the micelle and Va is the volume of the anhydrous micelle. The values of rh and Vh determined from DLS experiments are measures of the micellar dimensions under condition of almost zero frequency. On the basis of the values reported in Table 1, it is apparent that the copolymer B20E510 (which has very long hydrophilic blocks) forms micelles with δh ) 36.9, which is far higher than δh ) 10.1 measured for copolymer E92B18. In the vicinity of zero frequency, therefore, the micelles of B20E510 are highly swollen, i.e., a large number of water molecules are present in the micellar corona. (30) Fritz, G.; Pechhold, W.; Willenbacher, N.; Wagner, N. J. J. Rheol. 2003, 47, 303. (31) Provencher, S. W. Makromol. Chem. 1979, 180, 201. (32) Mai, S.-M.; Booth, C.; Nace, V. M. Eur. Polym. J. 1997, 33, 991.
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Kelarakis et al. Table 2. Micellar Properties in Aqueous Solution at 25 °C with and without HF Oscillatory Fielda copolymer
rh/nm
rHF/nm
VE/nm3
VEHF/nm3
nwater
nwater,HF
E92B18 B20E510
15.5 27.9
14.1 21.5
1.04 2.87
0.78 1.31
35 96
26 44
a r and r h HF ) hydrodynamic radii of the micelles in the limit of low and high frequency. VE and VEHF ) volume of each water- swollen E unit of the micelles in the limit of low and high frequency. nwater and nwarter,HF ) number of water molecules per E-unit in the micellar corona in the limit of low and high frequency.
Figure 1. Relative high-frequency viscosities of aqueous solutions of block copolymers E92B18 (Figure 1a) and B20E510 (Figure 1b) at 25 °C as a function of polymer concentration. The solid lines display the functions defined from eq 5 with δ ) δh and δ ) 1, and the dashed lines display the best fits of eq 5 to the experimental data obtained in the HF limit.
In the limit of high frequency, the apparent hydrodynamic radius of the micelles (rHF) can be estimated from the relative viscosity η′∞/ηs. Figure 1, panels a and b, presents values of η′∞/ηs measured at 25 °C for aqueous solutions of block copolymers E92B18 and B20E510, respectively, plotted as a function of concentration. The two data sets are fitted with the semiempirical equation proposed by Lionberger and Russel13 for hard sphere suspensions
η′∞ 1 + 1.5φeff(1 + φeff - 0.189φeff2) ) ηs 1 - φ (1 + φ - 0.189φ 2) eff
eff
(5)
eff
with φeff ∝ δHFc (in analogy with eq 3), and where φeff and δHF are respectively the effective volume fraction and the hydrodynamic expansion factor that correspond to the high-frequency limit. The best fits of the two data sets give δHF ) 7.7 and 17.1 for copolymers E92B18 and B20E510, respectively. These values are considerably lower than the corresponding δh values (in the vicinity of zero frequency). In particular, δHF/δh ) 0.76 for E92B18 and δHF/δh ) 0.46 for B20E510. Thus it is seen that, within the high frequency regime, the hydrophilic micellar corona exhibits a degree of drainage, which is most pronounced for the highly solvent-swollen micelles of B20E510. Similar behavior has been observed20,21 for sterically stabilized colloidal spheres, and has been attributed to changes in the mobility of the water molecules, so that they “escape” from the hydration layer of the particles. It is of interest to note that the shrinkage of the micellar volume, demonstrated above, is only partial, not total; that is, a large number of water molecules still remain within the micellar corona. This is immediately obvious in Figure 1, panels a and b, where the bottom solid lines correspond to the curves obtained from eq 5 for δ ) 1 and the upper solid lines display the curves obtained for δ ) δh. In both cases, the experimental data fall within these two extreme limits, consistent with the concept of frequency-induced partial drainage of the micelles.
There is experimental evidence33,34 that water can enter the cores of the micelles of the copolymer E92B18, associated with the OH ends of its B blocks, but not the cores of micelles of copolymer B20E510, the B blocks of which are methoxy terminated. However, the effect on micelle properties is small, and this difference between the two copolymers can be ignored for present purposes. Accordingly, within the assumption that micelles have a spherical structure with a liquidlike core35,36 free of solvent molecules, we can further evaluate the extent of drainage of the micellar corona, as described below. The average core volume (vc) and core radius (rc) can be estimated from the equation
Vc ) (4/3)πrc3 ) nVBNw
(6)
where Nw is the weight-average association number of the micelles (determined by SLS and listed in Table 1) and VB is the volume of a B unit
VB ) MwB/FBNA
(7)
with MwB ) 72 g mol-1 and FB ) 1.0 g cm-3 being the molar mass of a B unit and the density of liquid poly(oxybutylene)32 respectively. Obviously, the hydrodynamic radii (rh and rHF) reduced by rc provide the thickness of the micellar corona (〈L〉 h and 〈L〉 HF) and, hence, the volume of each water swollen E unit VE and VEHF can be determined by the relations
(4/3)π(rh3 - rc3) ) mNwVE ) 〈L〉h
(8)
(4/3)π(rHF3 - rc3) ) mNwVEHF ) 〈L〉HF
(9)
Values of VE and VEHF thus obtained are listed in Table 2. Taking into account that the volume of an unswollen liquid E unit is 0.073 nm3 and that the volume of one water molecule is close to 0.030 nm3, the number of water molecules associated with each E-unit can be estimated. The values for the copolymers E92B18 and B20E510 of respectively 35 and 96 water molecules per E unit in the zero frequency limit are reduced to 26 and 44 water molecules in the high-frequency limit. These results indicate that, despite the significant extent of frequency-induced micellar drainage, a large number of water molecules remain in the corona. Raman spectroscopy has been used to show that there are six water molecules in the hydration shell of an E unit: two H-bonded directly to the ether oxygen and four involved in hydrophobic hydration of the hydrophobic part of the unit.37 The rest will be essentially bulk water, restricted to the corona to an extent, which (33) Derici, L.; Ledger, S.; Mai, S.-M.; Booth, C.; Hamley, I. W.; Pedersen, J. S. Phys. Chem. Chem. Phys. 1999, 1, 2773. (34) Kelarakis, A.; Mai, S.-M.; Havredaki, V.; Nace, V. M.; Booth, C. Phys. Chem. Chem. Phys. 2001, 3, 4037. (35) Chu, B.; Zhou, Z.-K. J. Colloid Interface Sci. 1988, 126, 171. (36) Luo, Y.-Z.; Nicholas, C. V.; Attwood, D.; Collett, J. H.; Price, C.; Booth, C.; Chu, B.; Zhou, Z.-K. J. Chem. Soc. Faraday Trans. 1993, 89, 539. (37) Goutev, N.; Nickolov, Z. S.; Georgiev, G.; Matsuura, H. J. Chem. Soc., Faraday Trans. 1997, 93, 3167.
Micellar Spheres in a High Frequency Oscillatory Field
Langmuir, Vol. 22, No. 16, 2006 6817
is determined by the balance of osmotic and dynamic forces in a given situation. It should be emphasized that the micelles of copolymer B20E510 although they exhibit a pronounced degree of shrinkage in the HF regime still have more water molecules per E-unit compared to those of E92B18, a fact which indicates that B20E510 micelles have the softer interaction potential even at the HF limit. This is discussed in some detail in the following section. 3.2. Interaction Potential and Structural Rearrangements of Micellar Spheres. The relation between the HF elastic modulus and the micellar interaction potential can be described by the equation suggested by Zwanzig and Mountain38
G′∞ ) FkT +
∫0∞g(r) ∂r∂
2π 2 F 15
[
]
∂u(r) dr ∂r
r4
(10)
where F is the particle number density, k is the Boltzmann constant, g(r) is the radial distribution function with r as the center-center separation, and u(r) the pair interaction potential. Assuming a lattice-like microstructure, G′∞ can be related to the second derivative of u(r):39,40
G′∞(r) ) bFm(r)
[ ] ∂2u(r) ∂r2
(11)
where Fm(r) ) κφeff,max/r depends on the type of the structure (for fcc κ ) 12 and φeff,max ) 0.74, for bcc κ ) 8 and φeff,max ) 0.68) and b is a number estimated as b ) (5π)-1. The intermicellar distance can be related to φeff,max at close packing.41
φeff,max φeff
r 3 ) d3
(12)
where d is the sphere diameter d ) 2rHF. From eqs 11 and 12 and taking into account that the interaction potential of repulsive spheres can be modeled42 as u(r)∝ r-v, the power law dependence of G′∞ on volume fraction can be written
G′∞ ∝ (φeff)µ
(13)
where µ ) 1+ ν/3, which for the present system (through eq 3) implies
G′∞ ∝ cµ
(14)
Figure 2 presents log(G′∞) values for aqueous solutions of the two copolymers plotted as a function of log(c). A common feature for both copolymers is that the data obtained in the dilute region can be fitted by straight lines revealing µ ) 5.3 (ν ) 12.9) for E92B18 and µ ) 3.1 (ν ) 6.3) for B20E510. This observation clearly indicates that the partially drained micelles of E92B18 preserve a harder potential in the HF regime compared to B20E510 (38) Zwanzig, R.; Mountain, R. D. J. Chem. Phys. 1965, 43, 4464. (39) Mewis, J.; D’Haene, P. Makromol. Chem., Macromol. Symp. 1993, 68, 213. (40) Buscall, R.; Goodwin, J. W.; Hawkins, R. H.; Ottewill, R. H. J. Chem. Soc. Faraday Trans. 1 1982, 78, 2889. (41) Paulin, S. E.; Ackerson, B. J.; Wolfe, M. S. J. Colloid Interface Sci. 1996, 178, 251. (42) Hoover, W. G.; Young, D. A.; Grover, R. J. Chem. Phys. 1972, 56, 2207.
Figure 2. High-frequency storage modulus G′∞ as a function of polymer concentration for aqueous solutions of block copolymers E92B18 (filled circles) and B20E510 (open circles) at 25 °C.
micelles, despite the fact that the latter undergo a more pronounced degree of shrinkage. The obtained values can be compared with µ ) 4, determined by a similar process for aqueous suspensions of polystyrene/poly(N-isopropylacrylamide) core/shell particles21 and µ ) 7.7 for poly(methyl methacrylate) spheres suspended in benzyl alcohol.41 Another common feature of the data sets presented in Figure 2 is that at high concentrations the data points clearly deviate from the straight lines established at low concentrations. This behavior relates to the micellar packing (gelation) that takes place in concentrated solutions. As the concentration of micellar spheres increases, micelles are increasingly caged by their neighbors and the system undergoes an ergodic/nonergodic transition29,43-46 at φeff,max. On the basis of the concept of structural arrest, in nonergodic systems, long-range interactions are eliminated and only short-range interactions can take place. Several theoretical analyses and experimental techniques have been developed to predict and explain the order-disorder phase diagram of hard and soft spheres. Besides conventional rheology, a variety of scattering techniques have been used to capture the sol-gel transition in polymeric systems, the most prominent being diffusing wave spectroscopy (DWS), which is based on the determination of the field correlation function g(1)(t). It has been shown29,46 that in dilute solutions the dynamics can be described by a single relaxation time that corresponds to the diffusion of the micelles. At higher volume fractions, a second much slower mode appears (eventually becomes dominant) that is attributed to the presence of micellar clusters. We demonstrate here that the dramatic changes in the interparticle dynamics that occur at the transition point from a diffusive to a subdiffusive relaxation pattern (as monitored from DLS) are also reflected in the abrupt break points in the G′∞(c) curves. Due to the finite size of micelles, related phenomena such as compression of the spheres should also be considered at high concentrations, and are expected to become more prominent in densely packed systems. In that sense, the high concentration regions of the G′∞(c) curves do not immediately reflect only the interparticle repulsions, but rather express a complex behavior arising from both repulsive and compressive forces experienced by the micelles. LA0607860 (43) Pusey, P. N.; van Megen, W. Phys. ReV. Lett. 1987, 59, 2083. (44) Chen, S.-H.; Chen, W.-R.; Mallamace, F. Science 2003, 30, 619. (45) Grandjean, J.; Mourchid, A. Europhys. Lett. 2004, 65, 712. (46) Romer, S.; Sceffold, F.; Schurtenberger, P. Phys. ReV. Lett. 2000, 85, 4980.
