© Copyright 2004 American Chemical Society
MAY 25, 2004 VOLUME 20, NUMBER 11
Letters Molecular Dynamics Study of Temperature Dehydration of a C12E6 Spherical Micelle Fabio Sterpone,† Carlo Pierleoni,*,‡ Giuseppe Briganti,§ and Massimo Marchi† Commissariat a` l’Energie Atomique, DSV-DBJC-SBFM, Centre d’E Ä tudes, Saclay, 91191 Gif-sur-Yvette Cedex, France, INFM and Dipartimento di Fisica, Universita` di l’Aquila, Via Vetoio, 67100 Coppito L’Aquila, Italy, and INFM and Dipartimento di Fisica, Universita` di Roma “La Sapienza”, P.A.Moro 2, 00185 Roma, Italy Received October 22, 2003. In Final Form: March 17, 2004 Hydration of a spherical micelles of C12E6 in solution is studied by molecular dynamics simulation. The interface is found to be separated in an inner part composed of water and hydrophobic and hydrophilic moieties and an outer part with hydrophilic moiety and water only. Hydration numbers in the inner and in the outer parts are in excellent agreement with experimental data from various different methods. Temperature dehydration occurs in the inner region only and is related to the presence of water molecules directly in contact with the hydrophobic core at low temperature.
Aggregation states, sizes, and phase transitions of the oligooxyethylene glycol CiEj family of nonionic surfactant are the result of a delicate balance between inter- and intraaggregate interactions,1 the strength of which can be related to the hydration state of the hydrophilic part of the aggregates. A variety of experimental techniques have been devised to estimate the amount of water in the interfacial region of a micelle. Most of these methods, such as light scattering, dielectric and ultrasonic relaxation, small-angle neutron scattering, aggregate and heavy water diffusion by NMR, and 17O magnetic relaxation, extract the hydration number from bulk measurements through the application of suitable models of water-solute interactions. Depending on the member of the CiEj family, the concentration of the surfactant, the temperature, and the experimental method, estimates of the hydration number ranging from 1 to 9 have been reported in the † Commissariat a ` l’Energie Atomique, DSV-DBJC-SBFM, Centre d’E Ä tudes. ‡ INFM and Dipartimento di Fisica, Universita ` di l’Aquila. § INFM and Dipartimento di Fisica, Universita ` di Roma “La Sapienza”.
(1) Carlstrom, G.; Halle, B. J. Chem. Soc., Faraday Trans. 1 1989, 85, 1049.
literature (see ref 2 for a collection of data and references). Jonstro¨mer et al.3 first recognized that hydration, defined as the number of water molecules per oxyethylene (EO) units, is not uniform in the interface of a spherical aggregate but depends on the distance from the oil core. By a cell-diffusion model analysis of the D2O diffusion in a low concentration C12E8/D2O solution (e35% surfactant), they reported values of 2.8 and 14 for the hydration of the inner layer and the outer layer, respectively, at T ) 5 °C. They also reported dehydration with temperature in the inner layer (the hydration number decreases to 1 at T ) 66 °C) but not in the outer one. More recently, Romsted and Yao2,4 introduced a new experimental approach, known as the chemical trapping method, which exploits the reactivity of a chemical probe to water and OH group and is able to provide a direct measure of the local hydration number, i.e., near the detector molecule itself. The probe, attached to a long hydrophobic tail, is integrated in the micelle and can react with water at the micellar interface. The technique has been applied to (2) Romsted, L. S.; Yao, J. Langmuir 1996, 12, 2425-2432. (3) Jonstromer, M.; Jonsson, B.; Lindman, B. J. Phys. Chem. 1991, 95, 3293-3300. (4) Romsted, L. S.; Yao, J. Langmuir 1999, 15, 326-336.
10.1021/la035964t CCC: $27.50 © 2004 American Chemical Society Published on Web 04/27/2004
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holomicelles (C12E6)2 and mixed micelles of the CiEj family4 at different temperatures and surfactant concentrations. For C12E6/H2O at 1% molar concentration of surfactant, they observed a linear decrease of hydration with temperature from 4.2 at T ) 20 °C to 2.8 at T ) 60 °C.2 This behavior is steady across the cloud point of the solution which occurs at about T ) 50 °C.5,6 Comparing these results with the cell-diffusion model analysis mentioned above they concluded that the chemical probe was preferentially sampling the interfacial region near the oil core. Despite these efforts the understanding of the hydration process in nonionic micelles is still very partial and a number of unanswered questions remain: Is the watermicelle interface separated in two regions in which hydration occurs with two distinct mechanisms? Or is the change of hydration more gradual through the interface? What is the origin of the observed temperature dehydration which seems to occur near the micellar core only? To deal with these questions, molecular dynamic (MD) simulation can be fruitful since it provides a molecular resolution of the process. We have performed MD simulations of a C12E6 spherical micelle in water solution at a mole fraction concentration less than 1%, at atmospheric pressure and at two temperatures, namely, T ) 10 °C and T ) 45 °C. Our simulations show that the interfacial region is naturally separated in two subregions, the inner layer filled with a mixture of hydrophobic moiety, hydrophilic moiety, and water, and an outer layer in which only hydrophilic chains and water are present. In striking agreement with the experimental estimates from the chemical trapping method,2 our simulations find a hydration number of the inner interface of 4.25 at T ) 10 °C and 3.44 at T ) 45 °C. Our results also indicate that temperature dehydration at constant shape occurs mainly in the first shell of the interface (to be defined below) close to the oil core, in qualitative agreement with the cell-diffusion model analysis.3 Water molecules directly exposed to the rough surface of the hydrophobic core, which is not uniformly screened by the hydrophilic chains, are found largely responsible for this effect. Finally by extrapolating our data for the hydration number of the outer interfacial region (see below), we infer an average hydration number of 13.8 for a C12E8 spherical micelle in good agreement with the cell-model analysis.3 C12E6/water solutions below 5% mole faction of solute and below 15 °C forms aggregates with spherical shape of about 45 monomers.7 Increasing the temperature the optimal shape of the aggregates gradually changes to elongated cylinders up to the cloud point at 50 °C above which the solution separates in two subsolutions with different surfactant concentrations.8-11 To mimic the low concentration micellar solution, our simulations were performed in a box containing 45 C12E6 monomers associated in a spherical micelle and 8448 water molecules. The force field used to model the system has been discussed in detail in a previous work.12 Here, we just mention that the parameters for the EO-EO and the EO-water interactions are taken from the work of Tasaky on a single poly(ethylene oxide) (PEO) chain in water,13 represented (5) Mitchell, D. J.; Tiddy, G.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 975. (6) Brown, W.; Johnsen, R.; Stilbs, P.; Lindman, B. J. Phys. Chem 1983, 87, 4548. (7) Puvvada, S.; Blankschtein, D. J. Phys. Chem. 1990, 92, 3710. (8) Corti, M.; Degiorgio, V. J. Phys. Chem. 1981, 85, 1442. (9) Kato, T.; Seimiya, T.; Seimiya, T. J. Phys. Chem. 1986, 90, 3159. (10) Strey, R. Ber. Bunsen-Ges. 1996, 100, 182. (11) Missel, P. J.; Mazer, N. A.; Benedek, G. B.; Young, C. Y.; Carey, M. C. J. Phys. Chem. 1980, 84, 1044. (12) Sterpone, F.; Briganti, G.; Pierleoni, C. Langmuir 2001, 17, 5103. (13) Tasaky, K. J. Am. Chem. Soc. 1996, 118, 8459.
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Figure 1. Density profiles as function of the distance from the center of mass of the micelle: (A) hydrophobic moiety and water; (B) hydrophilic moiety.
by the SPC model.14 The force field for the hydrocarbon tail is extracted from the work of Tobias et al.15 Our simulations were run for 1.2 and 2 ns after equilibration at T ) 10 °C and T ) 45 °C, respectively. More details will be given in a forthcoming publication. The reliability of the present model potential can be evaluated by comparing our estimates of the apparent molar volume of the solute (443.9 cm3/M at T ) 10 °C and 456.9 cm3/M at T ) 45 °C) with experimental data (443 m3/M at T ) 10 °C and 460 cm3/M at T ) 45 °C).16 The simulations are performed at constant pressure (P ) 1 atm) and constant aggregation number. The chosen concentration is within the range where the change of shape with temperature is experimentally observed and at T ) 45 °C elongated cylinders are most probable. The fixed number of surfactant chains and the “short” integration in time prevent the direct observation of the shape transition in our MD experiments. The aggregate shape, monitored through the eigenvalues of the inertia tensor, is quite insensible to temperature. Indeed we obtained ratios of the principal moments of inertia of 1.33(2): 1.18(2):1 at T ) 10 °C and 1.27(3):1.15(3):1 at T ) 45 °C. The above-mentioned agreement between simulation and experiments for the hydration of the inner shells of the interface suggests that it is quite insensitive to the overall shape of the aggregate as was already inferred from experimental data at various concentrations and for various phases.2 In Figure 1 we report, for the two temperatures studied, the mass density profiles of the hydrophobic moiety and water (A) and of the hydrophilic moiety (B) as a function of the distance from the micellar center of mass. The interfacial region extends from 11 Å (distance below which water is absent) to 33 Å (limit above which hydrophilic moiety is absent). It is naturally divided in two distinct regions: the inner region from 11 to 20 Å where the three components coexist; and the outer region beyond 20 Å where only the hydrophilic moiety and water are found. The water density profile at T ) 45 °C is always slightly below the profile at T ) 10 °C. However taking into account the overall density variation of the system with temperature, the two profiles differ in the inner interfacial region only. In the same region, the density of the hydrophilic moiety increases with temperature and the density of the (14) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Hermans, J. In Intermolecular Forces; Pullman, B., Ed.; Reider: Dordrecht, 1981. (15) Tobias, D. J.; Tu, K.; Klein, M. L. J. Chem. Phys. 1997, 94, 1492. (16) Maccarini, M.; Briganti, G. J. Phys. Chem. A 2000, 104, 11451.
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Figure 2. Number of water molecules per EO unit versus the shell edge. Experimental data, extrapolated from Figure 4 of ref 2, are reported as horizontal dashed lines. The thick curve is a quadratic fit to data at both temperatures in the four outer shells: Nw ) a + b(R - c)2, a ) 5.53, b ) 0.24, c ) 22.23.
hydrophobic moiety is largely unchanged. Therefore temperature dehydration at constant shape is due to the relative distribution of water and EO units. To make theoretical estimates of the hydration number per EO unit, we define six shells by integrating the EO density profile (multiplied by the spherical volume element) and computing the distance at which multiples of the aggregation number, 45, are found. In this way each shell contains one EO unit per chain on average. The number of water molecules in each shell is the integral of the water density profile over the shell. The average hydration number for the shell can be identified with the ratio between the number of water molecules in the shell and the aggregation number. The results for the two investigated temperatures are presented in Figure 2 and compared with estimates from the chemical trapping method. In this figure we report on the horizontal axis the edges of the shells and on the vertical axis the amount of water per EO unit (Nw) in the given shell. The data in Figure 2 unequivocally show that temperature dehydration occurs mainly in the first shell, whereas the outer shells exhibit only small effects. For the first layer we get Nw ) 4.25 at 10 °C and Nw ) 2.4 at 45 °C, in good agreement with the experiment (4.5 at T ) 10 °C and 3.35 at T ) 45 °C2). The agreement becomes even more striking if we average the hydration number over the first two shells, i.e., the inner part of the interface. We then get Nw ) 4.25 at T ) 10 °C and Nw ) 3.44 at T ) 45 °C. This finding suggests that the chemical probe in Romsted’s method remains within the two inner shells of the interface. In the outer shells the degree of hydration increases with distance from 6 to 15, giving an average hydration number of 8.86 at T ) 10 °C and of 8.83 at T ) 45 °C. Hydration of the outer part of the interface in spherical aggregates of C12E8, as inferred from water diffusion data, is reported to be 14 and to be independent of temperature.3 To compare this estimate with our findings, we have fitted our results for the four outer shells, combining together data at the two temperatures, with a quadratic function (thick curve in Figure 2). Assuming a shell thickness of 2 Å, we can extrapolate this curve to a C12E8 spherical aggregate (by adding two more shells). In doing so we obtain an average hydration of 13.8 for the outer part of the interface, in good agreement with the experimental estimate. To further investigate the dehydration phenomenon, we performed additional calculations on our MD trajectories. We obtained an estimate of the number of nearest neighbor solute-solvent contacts by modeling the excluded
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Figure 3. Probability distribution of EO units in an angular sector.
volume of each molecule through its Voronoi polyhedron.17 We found that the number of water molecules in contact with the hydrophobic part of the aggregate decreases from 226 at T ) 10 °C to 209 at T ) 45 °C (∼8%). On the other hand, the number of water molecules in contact with the hydrophilic part of the aggregate decreases from 1070 at T ) 10 °C to 1062 at T ) 45 °C (∼0.8%), indicating that dehydration concerns mainly that part of the oil core surface directly exposed to water. Its extent can be inferred from the radial distribution of the hydrophilic part of the chains. Since we are dealing with a spherical aggregate of 45 chains, we have divided the solid angle around the center of the aggregate in 45 sectors of equal angular amplitude and counted the number of EO units in each sector.12 The histograms for the two temperatures are shown in Figure 3. At both temperatures more than 20 sectors do not contain EO units, indicating that almost half of the surface of the oil core is not screened by the hydrophilic terminations. The inset in Figure 3 shows that at T ) 10 °C the distribution is more structured with a first maximum around 6 and a second small peak around 9. This structure disappears with increasing temperature. Water molecules exposed to the solute in the interface region thus experiences two different environments. Part of the water molecules are directly in contact with the oil core interface, thus weakly bounded to the solute and with a high degree of rotational freedom.18 The remaining water molecules are trapped in the hydrogen bond network around the hydrophilic chains. In our simulations, these waters form single hydrogen bonds with EO units but are also involved in several hydrogen bond bridges, of one and/or two water molecules, between different EO units. The hydration number as defined above considers all water molecules within a given shell according to the aggregate symmetry. A more “local” definition of hydration is given by the number of water molecules within a sphere of 3 Å radius centered at the oxygen atom of each EO unit of the chains. The choice of a 3 Å cutoff is based on the ether oxygen-water oxygen, g(R), which shows a first minimum near that distance.12 Results averaged over chains are reported in Figure 4 for the two temperatures. Hydration number within this definition exhibits a slow variation with the EO index along the chain (unit 1 is the innermost EO unit bonded to the hydrophobic moiety) with a maximum at 4 which is related to a peculiar structural properties of the hydrophilic chains. Indeed, polyoxyethylene glycol polymers in water solution form helixes with four units per turn.13 The helix is stabilized (17) Neighboring atoms are defined when their polyhedra share a facet. (18) Walrafen, G. E.; Che, Y.-C. Chem. Phys. 2000, 258, 427.
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Figure 4. Number of waters per EO unit vs the EO index in the hydrophilic fragment. Water molecules are counted inside a sphere of 3 Å centered on the oxygen atom of the unit.
by water molecules forming hydrogen bond bridges between the oxygen of EOn and EOn+2 units.13 For a EO6 chain in the helical conformation only the oxygen of the two central EO units, units 3 and 4, participate to two such hydrogen bonded water bridges (bridging units 1-3, 3-5 and 2-4, 4-6, respectively). In our system, the EO terminations show a partially folded structure with only the fourth unit being hydrogen-bonded forward (4-6) and backward (2-4) along the chain. Similar H-bonded structures have been observed in C12E2 self-aggregate systems.19,20 The hydrogen bond analysis confirms this picture: oxygen of unit 4 has a higher probability to be bridged by a water molecule to another EO oxygen of the same chain. On the other hand the 1-3 bridge is disfavored from the presence of the hydrophobic core. This explains the observed maximum at 4 in Figure 4. Temperature dehydration according to Figure 4 is small and almost constant along the chains with a maximum of 0.16 for the first EO units. An exception occurs for the third EO units where no effect is present. Direct comparison between (19) Bandyopadhyay S.; Tarek M.; Lynch M. L.; Klein M. L. Langmuir 2000, 16, 942. (20) Allen R.; Bandyopadhyay S.; Klein M. L. Langmuir 2000, 16, 10547.
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Figure 2 and Figure 4 shows that in the innermost shell of the interface all water molecules are in contact with the EO unit at the higher temperature while at T ) 10 °C one water molecule over four is in contact with the hydrophobic core only. In conclusion, our study provides a molecular view of the dependence of hydration with temperature for a spherical micelle of C12E6, and reconcile apparent discrepancies between different experimental results. We find that the micellar interface is unequivocally divided in an inner and an outer part. A fraction of water molecules in the inner region is directly in contact with the hydrophobic moiety and mainly contribute the temperature dehydration. In the same region the density of the hydrophilic moiety increases with temperature providing a slightly better screening of the oil core. Estimates of the hydration number based on the observed density profiles are in excellent agreement with experimental data at both temperatures2 despite our aggregate remaining spherical at the higher temperature. This finding suggests that the hydration of the inner region of the interface is largely independent of the aggregate shape. In the outer region, hydration numbers defined through the density profiles increase rapidly with the distance. Also, the average hydration number for an hypothetical C12E8 spherical micelle, obtained by extrapolating our data, is in good agreement with estimates inferred from experimental data of water diffusion.3 Within this definition hydration number behavior in the outer part of the interface should reflect the geometrical shape of the aggregate, though not in a trivial way. However the reported temperature independence in C12E8 micelle across the shape transition3 would imply a considerable variation with temperature of the density profiles in the outer region, a point which deserves further investigation. Acknowledgment. We thank Simone Melchionna for useful discussion. We acknowledge the European Science Foundation support through the SIMU program. This work has been supported by the INFM Parallel Computing Initiative. LA035964T
