Ethylene Mixtures by

2148

Langmuir 2009, 25, 2148-2152

Selective Paraffin Removal from Ethane/Ethylene Mixtures by Adsorption into Aluminum Methylphosphonate-r: A Molecular Simulation Study Maaike C. Kroon†,‡ and Lourdes F. Vega*,‡,§ Process Equipment, Department of Process and Energy, Faculty of Mechanical, Maritime and Materials Engineering, Delft UniVersity of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands, MATGAS Research Center, Carburos Meta´licos/Air Products-CSIC-UAB, Campus de la UAB, Bellaterra, 08193 Barcelona, Spain, and Institut de Cie`ncia de Materials de Barcelona, Consejo Superior de InVestigaciones Cientı´ficas, ICMAB-CSIC, Campus de la UAB, Bellaterra, 08193 Barcelona, Spain ReceiVed September 16, 2008. ReVised Manuscript ReceiVed NoVember 5, 2008 Most adsorbent materials used for olefin/paraffin separation show preferential adsorption of the olefin. Recently, the material aluminum methylphosphonate polymorph alpha (AlMePO-R) was found to be able to selectively adsorb the paraffin instead of the olefin, from an ethyl chloride/vinyl chloride mixture (Herdes, C.; Valente, A.; Lin, Z.; Rocha, J.; Coutinho, J. A. P.; Medina, F.; Vega, L. F. Langmuir 2007, 23, 7299). However, several questions remain still open regarding the reasons for this selective paraffin adsorption, as well as the suitability of AlMePO-R as adsorbent for other olefin/paraffin separations. In this work, the adsorption of ethane/ethylene mixtures by AlMePO-R is investigated using grand canonical Monte Carlo simulations in order to determine the effect of molecular interactions, size, and shape on the selective adsorption. For this purpose three different force fields have been used for the fluids, investigating the effect of the molecular details of the fluid on the adsorption behavior. All three force fields gave the same qualitative behavior. It was found that AlMePO-R is also able to selectively adsorb the paraffin from ethane/ethylene mixtures. Moreover, ethane molecules arrange exactly in the same way in the adsorbent material as ethyl chloride, with the methyl groups directed toward each other, although ethane has much smaller dynamic diameter compared to ethyl chloride. Therefore, a key factor determining the selectivity is found to be the molecular interaction between the methyl group of AlMePO-R and the methyl group of the paraffin.

I. Introduction The separation of olefins and paraffins is an important industrial process. Olefins are the building blocks of many common polymers. The olefins need to be sufficiently pure in order to produce plastics. However, in the industrial synthesis of olefins (i.e., ethylene, propylene, vinyl chloride), the corresponding paraffin (i.e., ethane, propane, ethyl chloride) is also present in the effluent. These paraffins need to be separated from the olefins for a cost-effective and low volatile organic compound (VOC) emission polymer production. Unfortunately, this purification step is not easy to achieve, especially in the later stages of the process, mainly due to the similarity in their molecular properties. Currently, high-pressure distillation is used as the standard purification method, which is energy-intensive and expensive. Single-tray efficiencies are low because the difference in boiling point is very small (∼5 K), resulting in large reflux ratios (15-25) and large columns (>200 theoretical stages, height of 75-90 m, diameter 2-6 m). The olefin/paraffin separation is the most energy intensive separation carried out in the petrochemical industry.1 A cheaper, more efficient, less energy-intensive and cleaner method for separating olefins from paraffins would be very desirable. Measures are taken by several companies and researchers to improve this separation, either by trying to improve the distillation, such as using multiple downcomer distillation trays, or a heat * To whom correspondence should be addressed. Phone: +34-935929950. Fax: +34-935929951. E-mail: [email protected]. † Delft University of Technology. ‡ MATGAS Research Center. § Consejo Superior de Investigaciones Cientı´ficas. (1) Moulijn, J. A.; Makkee, M.; Van Diepen, A. E.; Chemical Process Technology; John Wiley and Sons Ltd.: Chichester, 2001.

pump compressor system as both reboiler and condenser or by investigating alternative separation methods. One of these alternative separation methods is adsorption, which is still in the research phase. Several inorganic materials, such as activated carbon, activated alumina, silica gel, and zeolites, can be used to adsorb organic gases. Commonly, these materials are incorporated with transition metal ions (copper or silver) when used for olefin/paraffin separation, resulting in the preferential adsorption of the olefin.2-8 This selective adsorption is due to the strong interaction between the unsaturated bond in the olefin and the metal ion in the surface, forming a π-complexation. Examples of this preferential olefin adsorption include the ethane/ ethylene separation using activated alumina with CuCl2,3 as adsorbent; the selective olefin adsorption of propane/propylene on Cu/SBA-15 mesoporous silica4,5 or Ag/SBA-15 mesoporous silica6 and the selective adsorption of propylene on zeolites (carbon molecular sieves 4A).7,8 Because the olefin is preferably adsorbed by these inorganic materials, it is the paraffin that is easily obtained in its pure form. The olefin has to be removed first from the absorbent before it can be obtained, where a high separation factor is difficult to achieve, because it is difficult to prevent paraffins from physically adhere to the adsorbent too. Unfortunately, in several industrial processes the desired product is the olefin (raw material for (2) Yang, R. T.; Kikkinides, E. S. AIChE J. 1995, 41, 509. (3) Blas, F. J.; Vega, L. F.; Gubbins, K. E. Fluid Phase Equilib. 1998, 150-151, 117. (4) Basaldella, E. I.; Tara, J. C.; Aguilar Armenta, G.; Patı˜no-Iglesias, M. E.; Rodrı´guez Castell´; on, E. J. Sol-Gel Sci. Technol. 2006, 37, 141.. (5) Grande, C. A.; Araujo, J. D. P.; Cavenati, S.; Firpo, N.; Basaldella, E.; Rodrigues, A. E. Langmuir 2004, 20, 5291. (6) Jiang, D. E.; Sumpter, B. G.; Dai, S. Langmuir 2006, 22, 5716. (7) Grande, C. A.; Rodrigues, A. E. Ind. Eng. Chem. Res. 2004, 43, 8057. (8) Giannakopoulos, I. G.; Nikolakis, V. Ind. Eng. Chem. Res. 2005, 44, 226.

10.1021/la803042z CCC: $40.75  2009 American Chemical Society Published on Web 01/07/2009

Paraffin RemoVal from Ethane/Ethylene Mixtures

polymers) and not the paraffin. Therefore, adsorption is not an option to replace the current distillation columns (yet). However, when it is the paraffin that is selectively adsorbed, the olefin can be easily obtained in its pure form, which would make the adsorption process a very attractive alternative. Recently, for the first time, an adsorption material was found that was able to selectively adsorb the paraffin instead of the olefin. This research involved the selective absorption of ethyl chloridecomparedtovinylchlorideusingthehybridinorganic-organic material aluminum methylphosphonate polymorph alpha (AlMePO-R).9 This material with composition Al2(PO3CH3)3 was first reported in 1995 by Maeda et al.,10 after which the structure was thoroughly studied.11-13 It was found that small differences in the adsorbent structure and adsorbent-adsorbate interactions have a strong effect on the adsorption behavior, thus creating opportunities for highly selective adsorptive separations.14,15 However, it is still unclear why AlMePO-R selectively adsorbs the ethyl chloride compared to the vinyl chloride and whether this material is also suited for other olefin/paraffin separations. As AlMePO-R was clearly more selective to ethyl chloride than AlPO14, it was proposed that a key factor determining the specific adsorption is the specific interaction between the methyl groups on the surface and the ethyl chloride molecule.9 However, some other competing effects may also lead to this behavior, such as steric effects due to the rigidity of the vinyl chloride compared to the ethyl chloride molecule. Further investigations with different olefin/paraffin mixtures and/or modified adsorbent materials and pore sizes will help elucidate these key factors. In this work we investigate, based on the molecular structure of the fluids and the adsorbent, why AlMePO-R selectively adsorbs the paraffin instead of the olefin and whether this material is also suited for other olefin/paraffin separations. For this purpose we use grand canonical Monte Carlo (GCMC) simulations with different fluid force fields in order to gain insight in the adsorptive behavior of AlMePO-R. A previously developed molecular model for AlMePO-R is used,16,17 which was validated by an excellent prediction of the adsorption of pure nitrogen and water,17 and the adsorption of pure ethyl chloride and vinyl chloride9 in this material. More specifically, we study the adsorption of pure ethane and ethylene and their mixtures in AlMePO-R as an example of a different olefin/paraffin separation, and to see the effect of molecular interaction and size on the selective adsorption by AlMePO-R. The final goal of this work is to quantify the selective adsorption of ethane versus ethylene in this adsorbent material in the search for paraffin-selective materials. The rest of the paper is organized as follows. The next section is devoted to the methodology, describing the molecular models used for the fluids and the adsorbent, as well as the GCMC simulation details. Results and discussion are presented next. Finally, some concluding remarks are provided in the last section. (9) Herdes, C.; Valente, A.; Lin, Z.; Rocha, J.; Coutinho, J. A. P.; Medina, F.; Vega, L. F. Langmuir 2007, 23, 7299. (10) Maeda, K.; Akimoto, J.; Kiyozumi, Y.; Mizukami, F. Angew. Chem., Int. Ed. Engl. 1995, 34, 1199. (11) Edgar, M.; Carter, V. J.; Tunstall, D. P.; Grewal, P.; Favre-Nicolin, V.; Cox, P. A.; Lightfood, P.; Wright, P. A. Chem. Commun. 2002, 8, 808. (12) Brown, S. P.; Ashbrook, S. E.; Wimperis, S. J. Phys. Chem. B 1999, 103, 812. (13) Li, N.; Xiang, S. J. Mater. Chem. 2002, 12, 1397. (14) Maeda, K.; Kiyozumi, Y.; Mizukami, F. J. Phys. Chem. B 1997, 101, 4402. (15) Maeda, K. Microporous Mesoporous Mater. 2004, 73, 47. (16) Schumacher, C.; Gonzalez, J.; Wright, P. A.; Seaton, N. A. Phys. Chem. Chem. Phys. 2005, 7, 2351. (17) Herdes, C.; Lin, Z.; Valente, A.; Coutinho, J. A. P.; Vega, L. F. Langmuir 2006, 22, 3097.

Langmuir, Vol. 25, No. 4, 2009 2149 Table 1. LJ Parameters of AlMePO-r Used in the Simulations16,17 site

σ (nm)

ε/kB (K)

Al P O CH3

0.2655 0.3500

128.13 120.15

II. Methodology 1. Molecular Models. The AlMePO-R material was modeled as consisting of single Lennard-Jones (LJ) spheres for the individual atoms, where the LJ parameters of the Al, P, and O atoms were taken from Schumacher et al.16 and the methyl groups are represented as single LJ sites located at the positions of the C atom, with parameters from Herdes et al.17 The LJ parameters of AlMePO-R used in this work are given in Table 1 for completeness. The AlMePO-R model structure was created from crystallographic data as previously described.17 The crystallographic elementary cell of AlMePO-R is a trigonal space group P13c with a ) 1.39949 nm and c ) 0.85311 nm.10 The structure consisted of a three-dimensional net in which aluminates and methylphosphonates alternate. The most remarkable feature of AlMePO-R is the existence of unidimensional channels running parallel to the c axis, where all the methyl groups point toward the centers of the channels.11-13 The simulation cell used in this work consisted of 96 aluminum atoms, 144 phosphorus atoms, 432 oxygen atoms, and 144 methyl groups. In order to investigate the influence of the molecular details on the adsorption behavior, both ethane and ethylene were modeled using three different force fields: two united-atom molecular models, i.e., the OPLS-UA model18 and the TraPPE model,19 and a two-center LJ force field with point quadrupole potential, i.e., the 2CLJQ model.20,21 The first two models only use the LJ intermolecular potential for the nonbonded interactions. The 2CLJQ model describes the total fluid-fluid potential as a sum of the LJ interactions and the quadrupolar interactions (φQQ), where the quadrupole moment of the fluid (Q) is an additional model parameter located at the geometric center of the molecule:

φQQ )

3 Q2 [1 - 5(ci2 + cj2) - 15ci2cj2 + 2(c - 5cicj)2] 4 (4πε )r5 0

ab

(1) with

ci ) cos θi

(2)

cj ) cos θj

(3)

c ) cos θi cos θj + sin θi sin θj cos φij

(4)

where rab is the center-to-center distance among the molecules, θi and θj are the polar angles of the molecular axis with respect to a line joining the molecular centers, φij is the difference in azimuthal angles, and ε0 is the vacuum permittivity. The LJ parameters for the CH3 groups of ethane and the CH2 groups of ethylene for the three different models and the quadrupole moment for the 2CLJQ model are provided in Table 2. (18) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Am. Chem. Soc. 1984, 106, 6638. (19) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1998, 102, 2569. (20) Curbelo, S.; Mu¨ller, E. A. Ads. Sci. Technol. 2005, 23, 855. (21) Vrabec, J.; Stoll, J.; Hasse, H. J. Phys. Chem. B 2001, 105, 12126.

2150 Langmuir, Vol. 25, No. 4, 2009

Kroon and Vega

Table 2. Force Fields and Parameters for Ethane and Ethylene Used in the Simulations18-21 parameters component ethane ethylene

force field

ε/kB (K)

σ (Å)

L0 (Å)

Q (B)

OPLS-UA TraPPE 2CLJQ OPLS-UA TraPPE 2CLJQ

104.1 98.0 136.99 70.44 85.0 76.95

3.775 3.75 3.4896 3.850 3.675 3.7607

1.53 1.54 2.3762 1.34 1.33 1.2695

0.8277 4.331

ethane ethylene

T (K)

P (kPa)

F (mol/L)

ξ (Å-3)

273.15 298.15 323.15 273.15 298.15 323.15

2390.73 4201.45 6906.72 4101.03 6957.74 11152.44

1.5550 3.5906 6.9481 3.5787 7.5649 8.7048

0.0264 0.0362 0.0498 0.0423 0.0618 0.0808

2. Simulation Details. The adsorption isotherms were obtained using GCMC simulations.22 GCMC simulations yield the average number of molecules adsorbed in the model adsorbent with known pore volume, V, which is in equilibrium with a reservoir of the adsorptive gas at a given temperature, T, and chemical potential, µ. For convenience, the activity ξ instead of the chemical potential is used as input

ξ)

exp(µ ⁄ kBT) Λ3

(5)

where Λ is the de Broglie wavelength and kB is the Boltzmann constant. Usually, adsorption data are represented as the amount of fluid (ethane/ethylene) adsorbed in the adsorbent (AlMePO-R) versus the relative pressure p/p0 in the bulk phase. In order to convert the activity into pressure, the virial equation of state in terms of activity is used23 2 2 p 2ξξ0 + (F0 - ξ0)ξ ) p0 (F + ξ )ξ2 0

0

Fexc )

〈N〉 - Fbulk V

(7)

where 〈N〉 is the mean number of molecules inside the pore, and Fbulk is the bulk density under the same conditions, calculated using bulk simulations.

III. Results and Discussion

Table 3. State Points of Ethane and Ethylene at Different Temperatures component

ethane/ethylene molecules adsorbed was converted to the amount of ethane/ethylene adsorbed on AlMePO-R in excess to what is present in the bulk:

(6)

0

where ξ0 and F0 are the activity and density of the saturation state point of pure ethane or ethylene at the needed temperature. The state points were calculated from bulk simulations and can be found in Table 3. The positions of the atoms of the adsorbent material were fixed during the simulations. This implies that the solid-solid interactions do not affect the calculations, as they cancel out when energetically comparing simulated configurations. Hence, only solid-fluid and fluid-fluid interactions were calculated. The Lorentz-Berthelot mixing rules were used to calculate the LJ parameters between sites of different types. The simulations required 5 × 107 configurations to reach the equilibrium. Average properties were calculated over blocks with 5 × 105 configurations once the equilibrium was reached. The fluid-fluid potential was cut at rc ) 6 σff as recommended by Duque and Vega.24 In order to compare with previous experimental and simulation data on ethyl chloride/vinyl chloride adsorption, the number of (22) Frenkel, D.; Smit, B. Understanding Molecular Simulation; Academic Press: London, 1996. (23) Hansen, J.-P.; McDonald, I. R.; Theory of Simple Liquids, 2nd ed.; Academic Press: London, 1986. (24) Duque, D.; Vega, L. F. J. Chem. Phys. 2004, 121, 8611.

The isotherms for pure ethane and pure ethylene in AlMePO-R were simulated using GCMC simulations. The simulated isotherms for pure ethane with the three different models (OPLSUA, TraPPE, 2CLJQ) at three different temperatures, 273.15, 298.15, and 323.15 K, are depicted in Figure 1. These temperature values were chosen because they are the experimental conditions used for ethane/ethylene separations. The error bars are small and they fall within the symbols representing the data points. It can be seen that the three models give similar results, indicating the suitability of all three models for describing pure ethane. This also indicates that, at these conditions, the details of the three models are not that relevant. This was expected because the quadrupole moment of ethane is very small. Therefore, taking the quadrupole moment of ethane explicitly into account in the 2CLJQ model will not lead to large differences compared to the OPLS-UA model and the TraPPE model, which do not take the quadrupole moment of ethane explicitly into account. Figure 2 shows the simulated isotherms for pure ethylene with the three different models at 273.15, 298.15, and 323.15 K. Again, the three models give similar results, although it can be noticed that the TraPPE model predicts slightly higher ethylene adsorption than the OPLS-UA model and the 2CLJQ model. Because ethylene has a large quadrupole moment, it is expected that the 2CLJQ model with explicit quadrupole moment interactions gives the best results. The OPLS-UA model results are in good agreement with those obtained with the 2CLJQ and are expected to be better than the TraPPE model results. The reason is that the OPLS-UA parameters were fitted to unsaturated hydrocarbon data at standard conditions close to the conditions used in this work, whereas TraPPE parameters were fitted to unsaturated hydrocarbon data over a wider range of conditions and with a minimum number of different pseudoatoms needed, losing some of the accuracy. When comparing Figures 1 and 2, it can be noticed that the adsorption of pure ethane is always higher than the adsorption of pure ethylene, so preferential adsorption of the paraffin by AlMePO-R is also observed for ethane/ethylene mixtures. Figure 3 compares the adsorption of pure ethane and pure ethylene at 273.15, 298.15, and 323.15 K using the OPLS-UA model. It can be noticed that the adsorption of both ethane and ethylene is higher at lower temperatures, whereas the selectivity to ethane adsorption seems to be higher at higher temperatures (larger difference between pure ethane and pure ethylene adsorption). The optimal separation temperature should therefore be a tradeoff between a higher overall adsorption at lower temperatures and a higher selectivity at higher temperatures. The obtained isotherms for ethane and ethylene were also compared to the isotherms determined previously for ethyl chloride and vinyl chloride.9 Here, the adsorption of pure ethyl chloride compared to pure vinyl chloride was also higher at all temperatures, and this difference was increasing with increasing temperature. The difference in adsorption between ethyl chloride and vinyl chloride is larger than the difference in adsorption

Paraffin RemoVal from Ethane/Ethylene Mixtures

Langmuir, Vol. 25, No. 4, 2009 2151

Figure 1. Adsorption isotherms of pure ethane in AlMePO-R at 273.15, 298.15, and 323.15 K using the OPLS-UA model (diamonds), the TraPPE model (squares), and the 2CLJQ model (triangles)

Figure 2. Adsorption isotherms of pure ethylene in AlMePO-R at 273.15, 298.15, and 323.15 K using the OPLS-UA model (diamonds), the TraPPE model (squares), and the 2CLJQ model (triangles)

Figure 3. Adsorption isotherms of pure ethane (diamonds) and ethylene (squares) in AlMePO-R at 273.15, 298.15, and 323.15 K using the OPLS-UA model

between ethane and ethylene, indicating that AlMePO-R is more selective for ethyl chloride/vinyl chloride separation. However, the maximum amount of both ethyl chloride (1.05 mmol/g) and vinyl chloride (0.90 mmol/g) adsorbed is lower than the maximum amount of both ethane (1.4 mmol/g) and ethylene (1.25 mmol/g) adsorbed. Thus, the adsorbed amount of both ethane and ethylene in AlMePO-R is higher than that of ethyl chloride and vinyl chloride, essentially due to their smaller size. Interestingly, although the dynamic diameter of both ethyl chloride and vinyl chloride (4.9 Å)25 is much larger than the dynamic diameter of both ethane and ethylene (4.4 Å), all four molecules fit in the triangular channels of AlMePO-R (with side length of around 7.0 Å),10 in the same arrangement, at the center of the channel, contrary to the adsorption of nitrogen, which adsorbed at the three locations.17 Moreover, the snapshots at maximum loading depicted in Figure 4 show that ethane and ethylene molecules arrange exactly in the same way in AlMePO-R as ethyl chloride,9 for which a snapshot at maximum loading is (25) Rimmer, D.; McIntosh, R Can. J. Chem. 1974, 52, 3699.

also shown for comparison purposes. The methyl groups of ethane are directed toward the methyl groups of AlMePO-R, again indicating that molecular interaction between the methyl groups is a key factor determining selectivity. GCMC simulations were also used to study the adsorption behavior of mixtures of ethane and ethylene on AlMePO-R in order to find the optimal conditions for separation. Because ethylene is the desired product, the concentration of ethylene is generally higher than the concentration of ethane. Therefore, the possibility of selectively removing the minority compound (ethane) by adsorption is investigated. This selectivity (S) of ethane over ethylene is defined as the ratio of the mole fractions (xi) in the pore divided by the ratio of the mole fractions in the bulk:

S)

(xethane ⁄ xethylene)pore (xethane ⁄ xethylene)bulk

(8)

Figure 5 shows the selectivity of AlMePO-R for ethane over ethylene as a function of pressure at 273.15, 298.15, and 323.15

2152 Langmuir, Vol. 25, No. 4, 2009

Kroon and Vega

Figure 4. Snapshots at maximum loading for ethane (left), ethylene (middle), and ethyl chloride (right) in AlMePO-R. Both ethane and ethylene are represented in gray, whereas the Cl atoms of ethyl chloride are represented in green. A ball-and-stick representation of the material is used for visual clarity.

Figure 5. Selectivity of AlMePO-R for ethane over ethylene as a function of pressure at 273.15, 298.15, and 323.15 K using the OPLS-UA model for a fixed bulk composition of ethane/ethylene ) 1:9. The dashed lines are guides for the eye.

K using the OPLS-UA model for a fixed bulk composition of ethane/ethylene ) 1:9. This selectivity sharply increases with pressure to a maximum at around 10 kPa, after which the selectivity decreases with increasing pressure. In contrast to the adsorption results obtained for the pure compounds, it can be noted that the selectivity for ethane over ethylene is actually highest at the lowest temperature considered instead of the other way around. AlMePO-R is selective for ethane over ethylene for all three temperatures, with a maximum in selectivity of S ) 7.8 at 273.15 K, S ) 5.2 at 298.15 K, and S ) 3.8 at 323.15 K at the same pressure (∼10 kPa). Although this pressure is too low for practical applications, the selectivity at more reasonable pressures (between 0.1 and 1.0 MPa) is still high enough for separation by adsorption. A maximum in selectivity at low pressures was also previously observed for ethyl chloride/vinyl chloride mixtures,7 an additional proof of similarity between selective ethane adsorption and selective ethyl chloride adsorption by AlMePO-R; this further reinforces the same conclusion that the molecular interactions are a key factor determining the selectivity of AlMePO-R for the paraffins, and not the steric effects.

IV. Conclusions On the basis of molecular simulations, it is demonstrated that the material AlMePO-R, which is able to selectively adsorb the paraffin (ethyl chloride) from ethyl chloride/vinyl chloride (26) Gupta, V.; Nivarthi, S. S.; McCormick, A. V.; Davies, H. T. Chem. Phys. Lett. 1995, 247, 596.

mixtures, can also be used to selectively adsorb the paraffin (ethane) from ethane/ethylene mixtures. Ethane and ethylene adsorb in a similar manner and with the same arrangement as the ethyl chloride molecules, in spite of their differences in size and geometry. The methyl groups of ethane are directed toward the methyl groups of AlMePO-R. Therefore, a key factor determining the selectivity of AlMePO-R is found to be the molecular interaction between the methyl group of this material and the methyl group of the paraffin. Further investigations should be performed in order to find new materials with even better selective adsorption behavior. An additional conclusion from this work is that GCMC simulations can be a powerful tool for predicting and clarifying adsorptive behavior and for the design of new adsorbents before synthesizing or performing adsorption measurements, provided accurate force fields are available. Acknowledgment. The authors are indebted to Carmelo Herdes for his outstanding contribution to this work. We are also grateful to Cor Peters, Geert-Jan Witkamp, Joa˜o A.P. Coutinho, and A. Valente for helpful discussions and their constructive comments. Financial support from Delft University of Technology is gratefully acknowledged. Additional financial support for this work has been provided by the Spanish government under Projects No. CTQ2005-00286/PPQ and CTQ2008-05370/PPQ and the Catalan government (2005SGR-00288). LA803042Z