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A Study of the Relation between Bicontinuous Microemulsions and Oil/Water Nano-emulsion Formation D. Morales,†,‡ J. M. Gutie´rrez,‡ M. J. Garcı´a-Celma,†,§ and Y. C. Solans*,† Departament Tecnologia de Tensioactius, IIQAB-CSIC, Jordi Girona 18-26, 08034 Barcelona, Spain, Departament Enginyeria Quı´mica i Metallu´ rgia, Universitat de Barcelona, Martı´ i Franque´ s 2, 08028 Barcelona, Spain, and Departament Farma` cia i Tecnologia Farmace` utica, Universitat de Barcelona, Avgda Joan XXIII s/n, 08028 Barcelona, Spain Received February 24, 2003. In Final Form: May 22, 2003 Oil/water (O/W) nano-emulsions have been formed in the system water/C16E6/mineral oil by the phase inversion temperature (PIT) method. The relation between the phase equilibria observed at the hydrophiliclipophilic balance (HLB) temperature or the PIT (i.e., the nature, number, and relative volume fractions of the involved phases), the droplet sizes, and polydispersities of the resulting emulsions have been determined. Milky white emulsions were obtained when, at the HLB temperature, a three-phase equilibrium formed by water (W), shear-birefringent microemulsion (D), and oil (O) was observed. However, bluish transparent O/W nano-emulsions with droplet sizes as low as 40 nm were formed in a narrow range of oil-to-surfactant ratios in which a D or W + D phases were the initial equilibrium phases. In the W + D equilibria, droplet sizes were independent from the water content, indicating that nanodroplet formation is mainly controlled by the structure of the D phase. These results suggest that the main requirement for bluish transparent O/W nano-emulsion formation is the complete solubilization of the oil component in a bicontinuous microemulsion, independent of whether the initial phase equilibrium is single or multiphase.
Introduction Nano-emulsions, also referred to in the literature as miniemulsions,1-5 ultrafine emulsions,6,7 emulsoids,8-10 unstable microemulsions,6,11 submicrometer emulsions,12,13 etc., are a class of emulsions with droplet sizes in the nanometric scale, typically in the range between 50 and 500 nm. By a suitable selection of the system components and preparation method, kinetically stable and optically transparent nano-emulsions can be produced. The simi* To whom correspondence should be addressed: Telephone: +34-93-4006159. Fax: +34-93-2045904. E-mail: csmqci@iiqab. csic.es. † IIQAB-CSIC. ‡ Departament Enginyeria Quı´mica i Metallu ´ rgia, Universitat de Barcelona. § Departament Farma ` cia i Tecnologia Farmace`utica, Universitat de Barcelona. (1) Ugelstad, J.; El-Aasser, M. S.; Vanderhoff, J. W. J. Polym. Sci., Polym. Lett. Ed. 1973, 11, 503-513. (2) El-Aasser, M.; et al. Colloids Surf. 1984, 12, 79-97. (3) El-Aasser, M. S.; Lack, C. D.; Vanderhoff, J. W.; Fowkes, F. Colloids Surf. 1988, 29, 103-118. (4) El-Aasser, M. S.; Miller, C. M. In Polymeric Dispersions: Principles and Applications; Asua, J. M., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1997; pp 109-126. (5) Sudol, E. D.; El-Aasser, M. S. In Emulsion Polymerization and Emulsion Polymers; Lovell, P. A., El-Aasser, M. S., Eds.; John Wiley & Sons, Ltd.: Chichester, U.K., 1997; pp 700-722. (6) Nakajima, H. In Industrial Applications of Microemulsions, Solans, C., Kunieda, H., Eds.; Marcel Dekker: New York, 1997; Vol. 66, pp 175-197. (7) Nakajima, H.; Tomomasa, S.; Okabe, M. Premier Congres Mondial De l’E Ä mulsion, Paris, France, 1993, Paper No. 1-11-162. (8) Lachampt, F.; Vila, R. M. Am. Perfum. Cosmet. 1967, 82, 29-36. (9) Lachampt, F.; Vila, R. M. Parfum., Cosmet., Savons 1967, 10, 372-382. (10) Lachampt, F.; Vila, R. M. Parfum. Cosmet. Savons 1969, 12, 239-251. (11) Rosano, H. L.; Lan, T.; Weiss, A.; Whittam, J. H.; Gerbacia, W. E. F. J. Phys. Chem. 1981, 85, 468-473. (12) Benita, S. In Submicron Emulsions in Drug Targeting and Delivery, Florence, A. T., Gregoriadis, G., Eds.; Harwood Academic Publishers: Amsterdam, 1998; Vol. 9. (13) Benita, S.; Levy, M. J. Pharm. Sci. 1993, 82, 1069-1079.
larities between these kinds of emulsions and microemulsions have been the origin of misinterpretations; some of the earlier reported microemulsions were not true thermodynamically but kinetically stable systems.11,14-16 A direct consequence of the thermodynamic instability of nano-emulsions is the dependence of their properties on the preparation method. The formation of highly stable bluish transparent dispersions at the water-rich region of pseudoternary water/ethoxylated surfactant/oil systems was described long ago.8-10 These dipersions, termed “emulsoids”, were formed generally in a range of oil-tosurfactant ratios between 0.3 and 0.8, being limited by micellar solutions and milky white emulsions, respectively. The method used for preparing the samples was identical to the phase inversion temperature (PIT) method. According to this method, introduced by Shinoda,17 samples are prepared at their hydrophilic-lipophilic balance (HLB) temperature (where surfactant affinities for water and oil are balanced) and quickly heated or cooled in order to obtain water/oil (W/O) or oil/water (O/W) emulsions, respectively. Three-phase equilibrium consisting of water, bicontinuous microemulsion, and oil phases, ultralow interfacial tensions, and maximum solubilization properties occur at the HLB temperature,18 enabling the emulsification of oil and water in very small droplets. Winsor19 predicted the phase behavior of water/surfactant/oil systems on the basis of the R-theory; the R parameter being defined as an interaction energy balance between the amphiphile(14) Prince, L. M. In Microemulsions: Theory and Practice;. Academic Press: New York, 1977. (15) Assih, T.; Delord, P.; Larche´, F. C. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; Vol. 3, pp 1821-1828. (16) Podzimek, M.; Friberg, S. J. Dispersion Sci. Technol. 1980, 1, 341-359. (17) Shinoda, K.; Saito, H. J. Colloid Interface Sci. 1968, 26, 70. (18) Shinoda, K.; Friberg, S. E. Adv. Colloid Interface Sci. 1975, 4, 281-300. (19) Winsor, P. A. Trans Faraday Soc. 1948, 44, 376.
10.1021/la0300737 CCC: $25.00 © 2003 American Chemical Society Published on Web 07/24/2003
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oil and amphiphile-water phases. Shinoda17 showed that temperature could dramatically affect this parameter in nonionic surfactant systems. Thus, at low temperatures R < 1 (Winsor I systems) and the corresponding equilibrium phases are O/W microemulsion with excess oil. However, at high temperatures, R > 1 (Winsor II systems) and the phase equilibrium corresponds to W/O microemulsion with excess water. At intermediate temperatures, R ) 1, and the system is balanced. In this situation, Winsor III (consisting of water, microemulsion, and oil phases in equilibrium) or Winsor IV systems (single-phase microemulsion) occur. Therefore, phase inversion from O/W to W/O or vice versa should be produced through Winsor III or Winsor IV systems. Indeed, several studies on emulsion formation by the PIT method from Winsor III and Winsor IV equilibria have been reported.20-22 The spontaneous emulsification produced within the microemulsion phase when heating/cooling the system was found to be the main reason to obtain small and uniform emulsion droplets. A decrease in droplet size was observed when microemulsion volume fractions increased. The PIT method has been used in industrial applications to produce fine emulsions with low energy consumption. Best results were produced when either a bicontinuous microemulsion or lamellar liquid crystalline phases were present during phase inversion.6,7,23-26 A systematic study on O/W nano-emulsion formation by the PIT method in pseudoternary water/ethoxylated surfactant/aliphatic hydrocarbon oil systems has been reported recently.27,28 Nano-emulsion droplet sizes were found to increase by decreasing surfactant/water ratios at fixed oil or by increasing oil/water ratios at constant surfactant. These results were related to the corresponding increase in the HLB temperatures and in the equilibrium oil/water interfacial tensions. A phase inversion in a way similar to that by changing temperature has been reported at a constant temperature by slow addition of water to an oilsurfactant mixture.29-32 The lowest droplet sizes of the resulting O/W nano-emulsions were obtained for certain range of oil-to-surfactant ratios, where a bicontinuous D phase was crossed during the emulsification process. Apart from the above-mentioned W + D + O, D and LR equilibria, a rich variety of phase equilibria W + D, D + O, W + LR + D, D + LR + O, etc., also occur at the HLB temperature in water/nonionic surfactant/oil systems.33 The phase behavior of these systems at the HLB temperature has been schematized in Figure 1. The present work has focused on studying the relation between the (20) Friberg, S.; Solans, C. J. Colloid Interface Sci. 1978, 66, 367368. (21) Solans, C.; Garcia-Dominguez, J. J.; Friberg, S. E. Proc. Jornadas CED 1981, XII, 509-525. (22) Min˜ana-Pe´rez, M.; Gutron, C.; Zundel, C.; Anderez, J. M.; Salager, J. L. J. Dispersion Sc. Technol. 1999, 20, 893-905. (23) Wadle, A.; Fo¨rster, T.; Rybinski, W. v. Colloids Surf., A 1993, 76, 51-57. (24) Fo¨rster, T.; Rybinski, W.; Wadle, A. Adv. Colloid Interface Sci. 1995, 58, 119-149. (25) Fo¨rster, T. In Surfactants in Cosmetics, Rieger, M., Rhein, L. D., Eds.; Marcel Dekker: New York, 1997; Vol. 68, pp 105-125. (26) Nakajima, H.; Tomomasa, S.; Kochi, M. J. Soc. Cosmet. Chem. Jpn. 1983, 34, 335. (27) Izquierdo, P.; et al. Langmuir 2002, 18, 26-30. (28) Izquierdo, P. Ph.D Thesis, University of Barcelona, 2002. (29) Forgiarini, A.; Esquena, J.; Gonzalez, C.; Solans, C. Prog. Colloid Polym. Sci. 2000, 115, 36-40. (30) Forgiarini, A.; Esquena, J.; Gonza´lez, C.; Solans, C. Langmuir 2001, 17, 2076-2083. (31) Forgiarini, A.; Esquena, J.; Gonza´lez, C.; Solans, C. Prog. Colloid Polym. Sci. 2001, 118, 184-189. (32) Forgiarini, A. Ph.D Thesis, Universitat de Barcelona, 2001. (33) Kunieda, H.; Shinoda, K. J. Dispersion Sci. Technol. 1982, 3, 233-244.
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Figure 1. Schematic phase behavior of ternary water/poly(oxyethylenated) nonionic surfactant/aliphatic hydrocarbon oil systems at the HLB temperature: I, single-phase region; II, two-phase region; III, three-phase region; W, water; D, surfactant phase; LR, lamellar liquid crystal; Om, oil microemulsion; O, oil.
phase equilibria observed at the HLB temperature, either W + D + O, W + LR + D, W + D, or D phases, and the properties of the resulting O/W emulsions prepared by the PIT method. Experimental Section Materials. Mineral oil (d(20°C) ) 0.85 g/mL; η(40°C) ) 33 cSt) was purchased from Merck. A technical grade hexaethylene glycol monohexadecyl ether surfactant (abbreviated as C16E6) was provided by Huntsman Surface Science. Both products were used as received. Water was deionized and Milli-Q filtered. Methods. Phase Diagrams. Samples were weighed, sealed in glass ampules, and thoroughly homogenized at 70 °C by means of a vibromixer. Samples were then frozen at -18 °C during a minimum of 8 h, placed into thermostated baths, and gently homogenized, and they were allowed to stand until equilibrium. Anisotropic phases were identified under polarized light, visually and by optical video-microscopy (Reichert Polyvar 2). Electrical Conductivity. The specific conductivity of samples was determined by means of a Crison-525 conductimeter with a Pt/platinized electrode. No additional electrolyte was added to water because of the use of technical grade surfactant.23 Hydrophilic-Lipophilic Balance Temperature Determination. HLB temperatures were measured by conductimetry and phase diagram determinations. No additional electrolyte was added to water. Temperature was gradually raised until a conductivity jump was produced. Samples with high water content (e.g. 95 wt %) did not show a conductivity jump when heated, and the corresponding phase inversion temperatures were determined by cooling the samples prepared at 80 °C by slow addition of water to a surfactant/oil mixture with gentle stirring. When this method failed, HLB temperatures were obtained by visual observation of phase separation (i.e., by determining the lowest temperature at which a fast separation of the oil phase took place). Emulsification by the Phase Inversion Temperature Method. O/W nano-emulsions were prepared according to the method described by Shinoda,17 consisting of cooling samples from their respective HLB temperatures to a lower temperature. In this work samples were cooled to 40 °C by immersion in a thermostated water bath with gentle stirring. Droplet Size Determination. Mean droplet size and polydispersity indexes were determined by photon correlation spectroscopy (PCS) using a Malvern 4700 photon correlation spectrophotometer (Malvern Instruments, Malvern U.K.). An argon laser (λ ) 488 nm) with variable intensity was used to cover the size range involved. Measurements were always carried out at a scattering angle of 90° and at 40 °C.
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Figure 2. Phase behavior of the water/C16E6/mineral oil system as a function of temperature and surfactant content. The oilto-water weight ratio (Row) is fixed at 0.2. A single-phase shearbirefringent (D) microemulsion and a three-phase region of water (W), D, and oil (O) are shown. The surrounding regions of the diagram consist of multiphase equilibria.
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Figure 3. Phase equilibria for samples with a fixed oil-towater weight ratio (Row) equal to 0.2 and different surfactant concentrations at the corresponding HLB temperatures.
Results and Discussion Nano-emulsion Formation at a Fixed Row. The phase diagram of the water/C16E6/mineral oil system, as a function of temperature and surfactant concentration for a fixed oil/(water + oil) weight ratio (Row) equal to 0.2 (Figure 2) shows a typical fish-like shape. The observed phase behavior is expected for water/ethoxylated surfactant/aliphatic hydrocarbon systems.34,35 A three-phase equilibrium formed by water, a shear-birefringent microemulsion, and oil was obtained at surfactant concentrations between 1 and 4 wt % in the temperature range between 60 and 100 ˚C. This three-phase region is shifted to higher temperatures as surfactant concentration decreases. This behavior has been described in systems with technical grade surfactants being related to the partition of surfactant homologues between water and oil.34,36 A single-phase region consisting of a shear-birefringent microemulsion was found between 4 and 11 wt % surfactant. This microemulsion region is divided into two branches located around 48 and 60 °C. The microstructure of these two regions is different as suggested by conductometric measurements: whereas a sample with 9 wt % surfactant showed an specific conductivity of 225 µS/cm at 60 °C, the specific conductivity of the same sample at 48 °C was 575 µS/cm. The microstructure of D microemulsion at 60 °C is thought to be bicontinuous and similar to the previously reported,37 whereas a water continuous structure is suggested at 48 °C. Samples with surfactant concentrations between 1 and 9 wt % selected from the phase diagram of Figure 2 were used to carry out emulsification studies by the PIT method. Volume-phase determinations at the HLB temperature (Figure 3) showed that between 1 and 3 wt % surfactant, the volume percentage of the D phase increases from 9 to 77%, whereas the oil phase volume percentage decreases from 18 to 4%. The HLB temperatures and the corresponding phase equilibria for all the studied samples are shown in Table 1. Nano-emulsion formation was carried out, as described in the Experimental Section, by lowering the temperature from the corresponding HLB temperature (34) Kunieda, H.; Shinoda, K. J. Colloid Interface Sci. 1985, 107, 107-121. (35) Kahlweit, M.; et al. Langmuir 1988, 4, 499-511. (36) Kunieda, H.; Ishikawa, N. J. Colloid Interface Sci. 1985, 107, 122-128. (37) Strey, R.; Schomacker, R.; Roux, D.; Nallet, F.; Olsson, U. J. Chem. Soc., Faraday Trans. 1990, 86, 2253-2261.
Figure 4. Droplet size, at 40 °C, as a function of surfactant concentration for samples with an oil-to-water weight ratio (Row) fixed at 0.2, after emulsification by the PIT method. Table 1. HLB Temperatures and Corresponding Phase Equilibria for Compositions of the Water/C16E6/Mineral Oil System with a Fixed Oil-to-Water Weight Ratio (Row) of 0.2 and Different Surfactant Concentrations C16E6 (wt %)
HLB temp (°C)
obsd phase equilibria at the HLB temp
1 2 3 4 5 6 7 8 9
97 76 66 62 60 59 58 57 56
W+D+O W+D+O W+D+O D D D D D D
to 40 °C. The droplet sizes of the resulting emulsions are plotted in Figure 4 as a function of the surfactant concentration. Droplet size decreases as the surfactant concentration increases. The decrease is sharp, from 2 µm to 80 nm, for 1 wt % and 4 wt % surfactant, respectively. Highly polydisperse emulsions, characterized by polydispersity indexes of 0.3, were obtained below 2 wt % surfactant. In contrast the polydispersities of nanoemulsions above this surfactant concentration were lower than 0.2. The visual appearance of the samples changes from milky white (1 wt %) to translucent (4 wt %). Nanoemulsion droplet sizes show lower dependence with surfactant content at surfactant concentrations between 5 and 9 wt %, decreasing from 60 to 40 nm, respectively. These O/W nano-emulsions are bluish and transparent dispersions which can be infinitely diluted with water. These results illustrate the relation between the phase behavior at the HLB temperature and the resulting droplet sizes and polydispersities. As shown in Figure 3, the lower the percentage of microemulsion phase volume, the higher droplet sizes and polydispersities. These results agree with
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Figure 5. Phase equilibria for samples with 95 wt % water and different oil-to-surfactant weight ratios (Ros) at the corresponding HLB temperatures. Figure 7. Phase behavior of the water/C16E6/mineral oil system as a function of temperature and water content. The oil-tosurfactant weight ratio (Ros) is fixed to 0.67. The boundaries of isotropic liquid (L); shear-birefringent microemulsion (D); and lamellar liquid crystal (LR) are shown. The sourrounding regions of the diagram consist of multiphase equilibria not determined.
Figure 6. Droplet size, at 40 °C, as a function of oil-tosurfactant weight ratio (Ros) for samples with 95 wt % water, after emulsification by the PIT method.
those reported earlier20,21 in a similar system. It was concluded that emulsification is optimum when a singlephase D microemulsion (Winsor IV microemulsion) is the starting point as a result of spontaneous emulsification taking place in the microemulsion phase when the temperature is lowered from the HLB temperature. Nano-emulsion Formation at Constant Water Concentration. According to the literature,33 phase equilibria such as W + D, W + D + LR, and W + LR + O are also expected to occur at the HLB temperature near the water-rich region, as shown in Figure 1. The effect of such phase equilibria on the emulsion properties was studied as a function of oil/(oil + surfactant) weight ratio (Ros) at 95 wt % water. Figure 5 shows the HLB temperatures and the corresponding phase equilibria observed for selected samples. W + D + LR equilibria are observed at Ros ) 0.4 and 0.5, W + D equilibria at Ros ) 0.6 and 0.7, and W + D + O equilibria at Ros ) 0.8 and 0.9. The droplet sizes obtained after emulsification of the samples by the PIT method are plotted in Figure 6. A U-shape curve showing a minimum droplet size (40 nm) at Ros ) 0.67 is obtained. Droplet sizes increase from the minimum value, 40 nm (Rso ) 0.67), to 75 nm as Rso decreases to 0.4, and to 800 nm as Ros increases to 0.9. Equivalent results were reported by Forgiarini32 after emulsification at constant temperature, which can be attributed to similar phase transitions. Polydispersity indexes also show low values, of the order of 0.1, at Ros between 0.6 and 0.7. Comparing the results of Figures 5 and 6, it can be observed that the lowest droplet sizes are obtained when the initial phase equilibria was W + D. Increasing Ros causes the separation of an excess oil phase resulting in higher droplet sizes. On the other hand, a decrease of the Ros produced the separation of a lamellar liquid crystalline phase which also resulted in higher droplet sizes. Thus, a complete solubilization of the oil
Figure 8. Phase equilibria for samples with an oil-to-surfactant weight ratio (Ros) equal to 0.67 and different water concentrations at the corresponding HLB temperature.
phase into a bicontinuous microemulsion at the HLB temperature seems to be the requirement for the formation of bluish transparent O/W nano-emulsions by the PIT method. The existence of a single-phase (D) or a two-phase (D + W) equilibria at the initial emulsification temperature seems to be irrelevant for the final droplet size. Nano-emulsion Formation at Constant Ros. It was also considered of interest to study nano-emulsion formation at the Rso values where the minimum droplet sizes were attained. The phase diagram at an Ros fixed to 0.67 as a function of temperature and water concentration is plotted in Figure 7. A solubility region extends in a wide temperature range between 30 and 90 °C up to 10 wt % water, which narrows (56-60 °C) at higher water concentrations, solubilizing up to 80 wt % water. An inverse microemulsion region (L), between 0 and 30 wt % water, gradually transforms to a shear-birefringent D phase as water concentration increases. If more than 80 wt % water is added to the D phase at 56 °C, a water excess phase is quickly separated and a W + D equilibrium is observed. The phase diagram also shows another D region around 48 °C between 42 and 80 wt % water and two regions corresponding to a lamellar phase (LR) formed around 40-48 and 56 °C at water concentrations between 24 and 56 wt %. Figure 8 shows the HLB temperatures and the corresponding phase equilibria of the samples selected to carry out the emulsification studies. A single-phase D microemulsion was observed at 75 and 80 wt % water concentrations, whereas a W + D equilibrium was found in samples in the range of 85-95 wt % water. The phase volume percentage of the D phase decreases from 91 to 9% as the water content increases from 85 to 95 wt %, respectively. Bluish transparent O/W nano-emulsions
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Figure 9. Droplet size, at 40 °C, as a function of water content for samples with an oil-to-surfactant weight ratio (Ros) fixed at 0.67 after emulsification by the PIT method.
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that droplet sizes are mainly controlled by the structure of the D sponge phase, independently from the volume of excess water in equilibrium. From these results it could be inferred that excess water acts only as a dilution medium. However, the oil droplet concentration is different depending on the composition, being proportional to the volume percentage of the D phase. Moreover, bluish transparent O/W nano-emulsions were obtained because no excess oil was separated at the HLB temperature at this Ros. The mechanism for bluish transparent O/W nanoemulsion formation suggested by these results is the thermal disruption of a D sponge phase. The hydration of the ethoxylated groups is dramatically increased by reducing the temperature,38 promoting a curvature change of the surfactant monolayer and consequently the oil droplet formation. A schematic view of the proposed emulsification mechanism from a single-phase D and from two phases W + D is plotted in Figure 10. In A, a D phase collapses giving nanodroplets. In B, emulsification takes place in the D phase and the excess water acts as a dilution medium for the droplets. This mechanism will be confirmed by studying the phase changes during the emulsification process. Conclusions
Figure 10. Schematic representation of a possible mechanism for O/W nano-emulsion formation by the PIT method. The curvature of the surfactant interfacial film is changed by cooling, and the D bicontinuous phase is disrupted, forming nanodroplets. (A) An oil-swollen D microemulsion phase is the initial equilibrium phase; (B) two phases, W + D, are the initial equilibrium, and the water excess is not participating in nanodroplet formation but as a dilution medium.
were formed by PIT emulsification of samples between 75 and 95 wt % water. The resulting droplet sizes (Figure 9) were of the order of 40 nm, independent of the water content, and polydispersity indexes were lower than 0.2, indicating narrow size distributions. It can be interpreted (38) Karlstro¨m, G. J. J. Phys. Chem. 1985, 89, 4962.
O/W nano-emulsions with droplet sizes as low as 40 nm have been formed in the water/C16E6/mineral oil system by using the PIT method either from a single-phase D or a two-phase W + D equilibria. The W + D equilibrium has been found in a narrow range of oil-to-surfactant ratios (Ros) at the HLB temperature. At this Ros range, droplet sizes are independent from the water concentration, indicating that droplet formation is mainly controlled by the structure of the D phase and that the excess water acts as a dilution medium for the droplets. These results suggest that the main requirement for the formation of bluish transparent O/W nano-emulsions is to achieve a complete solubilization of the oil phase in a bicontinuous microemulsion, independently of whether the initial phase equilibria is single or multiphase. Acknowledgment. Financial support from MCYT (Grant PPQ2002-04514-CO3), and from the Generalitat de Catalunya DURSI (Grant 2001SGR-00357) is gratefully acknowledged. D.M. also acknowledges the Ph.D. grant from the University of Barcelona. LA0300737
