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Langmuir 2002, 18, 932-940

Molecular Modeling of Interactions of Diphosphonic Acid Based Surfactants with Calcium Minerals

Pradip,* Beena Rai, and T. K. Rao

Tata Research Development and Design Centre, 54B, Hadapsar Industrial Estate, Pune 411013, India

Shailaja Krishnamurthy and R. Vetrivel

National Chemical Laboratory, Dr. Homi Bhabha Road, Pune 411008, India

J. Mielczarski and J. M. Cases

Laboratoire Environnement et Mineralurgie, 15, Av. du Charmois, BP 40, F-54501 Vandoeuvre Les Nancy Cedex, France Received April 30, 2001. In Final Form: September 6, 2001

The interactions of two diphosphonic acid based surfactants, namely alkylimino-bis-methylenediphosphonic acid (IMPA-8) and 1-hydroxy-alkylidene-1,1-diphosphonic acid (Flotol-8), with three calcium minerals, fluorite, calcite, and fluorapatite, were quanitfied on the basis of molecular modeling computations. Both force field (UFF) and semiempirical quantum mechanical (MNDO) methods were employed for this purpose. The results of theoretical calculations in terms of the prediction of the order of response of these three minerals to flotation with diphosphonic acid reagents were found to match remarkably well with the experimental microflotation test results. The utility and power of this approach in the design/screening of surfactant molecules for flotation separation are demonstrated, and its tremendous implications for the industry are discussed.

Introduction The design of highly selective surfactants for specific industrial applications is a challenging task. Most of the commercial specialty/performance chemicals currently being used in the industry were discovered largely through a trial and error methodology. A critical review of the literature on this topic1-7 indicates that there does not yet exist a theoretical framework that can provide practicing engineers and chemists a scientific and rational basis to select and or/design new surfactants for a specified application. Two important issues need to be addressed for the rational design of surfactants, namely (a) the selection of the appropriate functional group/groups which provide interaction specificity to the particular surface and (b) the design of an appropriate molecular architecture optimized for its end use. Pradip et al.1-3,8,9 have elucidated the various components of a novel and still evolving paradigm of surfactants' design based on identifying the

* To whom correspondence may be addressed. E-mail: [email protected] pune.tcs.co.in. Phone: 91-20-6871058. Fax: 91-20-6810921.

(1) Pradip. In Proceedings of Symposium on Reagents for Better Metallurgy; Mulukutla, P. S., Ed.; SME-AIME: 1994; Chapter 24, p 245. (2) Pradip. Trans. Ind. Inst. Met. 1997, 50 (6), 48. (3) Pradip. Met., Mater. Process. 1998, 10 (1), 41. (4) Somasundaran, P., Moudgil, B. M., Eds. Reagents in Mineral Technology; Marcel Dekker Pub.: New York, 1988; p 755. (5) Pradip. Miner. Metall. Process. 1988, 5 (3), 114. (6) Jones, M. J., Oblatt, R., Eds. Reagents in the Mineral Industry; IMM Pub.: London, U.K., 1984; p 294. (7) Fuerstenau, D. W.; Herrera-Urbina, R. In Advances in Coal and Mineral Processing; Chander, S., Klimpel, R., Eds.; SME-AIME Pub.: 1989; Chapter 1, p 3. (8) Pradip. Curr. Sci. 1992, 63 (4), 180. (9) Pradip; Rai, B.; Rao, T. K.; Krishnamurthy, S.; Vetrivel, R.; Mielczarski, J.; Cases, J. M. J. Colloid Interface Sci., in press.

molecular recognition mechanisms underlying selective adsorption/interactions and employing molecular modeling tools to screen/identify promising molecular architectures. While there is a large body of empirical knowledge available on the kind of functional groups/molecular architecture needed for a particular application, it is not being utilized effectively in current designs of surfactants. This is due to the lack of a scientifically sound, quantitative yet theoretical methodology which can indicate the relative efficacy of a set of surfactant structures in order to screen/ identify the most promising ones only, for subsequent synthesis, characterization, and testing. If we are in a position to theoretically, a priori, and quantitatively assess and predict the relative order of performance of different surfactant structures, it would certainly lead to significant savings in time, cost, and efforts in the development of surfactants. It is in this context that we have been exploring the utility of available molecular modeling tools for this purpose. We present in this paper our work on the interaction of diphosphonic acid based surfactants with calcium mineral surfaces in order to illustrate the utility of molecular modeling tools in the design of tailor-made surfactants for industrial applications. The separation of sparingly soluble calcium minerals such as fluorite [CaF2], calcite [CaCO3], fluorapatite [Ca10(PO4)6F2], dolomite [(Ca,Mg)CO3], and scheelite [CaWO4] from each other remains a challenging problem without a satisfactory solution to date. The difficulty arises out of their similar surface properties and solubilities, the same chelating cation in their structure, and similar responses to various known families of flotation collectors such as fatty acids. It is however well established that fluorite is invariably found to be the most flotable and that calcite is the least responsive to oleate flotation. Many possible

10.1021/la010625q CCC: $22.00 © 2002 American Chemical Society Published on Web 01/10/2002

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Table 1. Chemical Names and Structures of Diphosphonic Acid Reagents

hypotheses have also been suggested in the literature to explain this observation.10-14 Pradip and co-workers have on the other hand proposed that one ought to utilize the information on the crystal structure differences among the mineral surfaces to understand the differences in response of certain surfactants to minerals containing the same cation.8,9 Significant template effects (that is, depending on the crystal structure, there is a definite distribution of adsorption sites on the surface) are responsible for the observed differences in the nature of surfactant adsorption, aggregation, and/ or self-assembly (also known as molecular recognition) occurring at mineral/water interfaces. This valuable information about the molecular recognition phenomena must be employed in the design of industrial surfactants such as flotation collectors. On the basis of a critical review of the past literature, Pradip1 had earlier proposed that the reagents having two or more functional groups, appropriately spaced so as to enhance their stereochemical/structural compatibility with the surface, were likely to be more selective than conventional monofunctional reagents. The known family of surfactants based on diphosphonic acids' functionality were therefore selected for detailed exploration in this work as selective flotation collectors for difficult to accomplish separation among calcium minerals. Diphosphonates are well-known corrosion inhibitors. Excellent work reported by Black et al.15 and Davey et al.16,17on the design of diphosphonate reagents based on structural compatibility with the barite [BaSO4] surface illustrated the possibility of rational design of reagents. More recently, Coveney and Humphries18 reported the molecular modeling computations on diphosphonates as cement retarders. Earlier efforts toward quantifying the interaction of surfactants with mineral surfaces using a molecular modeling approach include those of Aliaga and Somasundaran,19 Mann and co-workers,20-22 Takahashi et al.,23-25 Grases et al.,26 Arad et al.,14 de Leeuw et al.,27 Berhouet and Toulhoat,28 and Frank et al.29 Collins et al.30 conducted extensive investigations with alkyl imino-bis-methylene diphosphonic acids as flotation

(10) Sorensen, E. J. Colloid Interface Sci. 1973, 45 (3), 601. (11) Pugh, R.; Stenius, P. Int. J. Miner. Process. 1985, 15, 193. (12) Khosla, N. K.; Biswas, A. K. Trans.-Inst. Min. Metall. 1985, 94, C4. (13) Finkelstein, N. P. Trans.-Inst. Min. Metall. 1989, 98, C157. (14) Arad, D.; Kraftory, M. A.; Zolotoy, B. N.; Finkelstein, P.; Weissman, A. Langmuir 1993, 9, 1446. (15) Black, S. N.; Bromley, L. A.; Cottier, D.; Davey, R. J.; Dobbs B.; Rout, J. E. J. Chem. Soc., Faraday Trans. 1991, 87 (20), 3409. (16) Davey, R. J.; Black, S. N.; Bromley, L. A.; Cottier, D.; Dobbs, B.; Rout, J. E. Nature 1991, 353, 549. (17) Davey, R. J.; Rohl, A. L.; Gay, D. H.; Catlow, C. R. A. J. Am. Chem. Soc. 1996, 118, 642. (18) Coveney, P. V.; Humphries, W. J. Chem. Soc., Faraday Trans. 1996, 92 (5), 831. (19) Aliga, W.; Somasundaran, P. Langmuir 1987, 3, 1103. (20) Mann, S. Nature 1988, 332, 119. (21) Mann, S.; Didymus, J. M.; Sanderson, N. P.; Heywood, B. R. J. Chem. Soc., Faraday Trans. 1990, 86 (10), 1873. (22) Reeves, N. J.; Mann, S. J. Chem. Soc., Faraday Trans. 1991, 87 (24), 3875. (23) Takahashi, K. Proceedings of XVII IMPC; Dresden, 1991; Vol. 2, p 393. (24) Numata, Y.; Takahashi, K.; Liang, R.; Wakamatser, J. Proceedings of the XX International Mineral Processing Congress, Aachen, Germany; Hoberg, H. H., Blottnitz, H. GMDB, Eds.; 1997; Vol. 3, p 367. (25) Numata, Y.; Takahashi, K.; Liang, R.; Wakamatser, J. Int. J. Miner. Process. 1998, 53, 75. (26) Grases, F.; Gracia-Raso, A.; Palou, J.; Costa-Bauza, A.; March, J. G. Colloids Surf. 1991, 54, 313. (27) de Leeuw, N. H.; Parker, S. C.; Hanumantha, R. K. Langmuir 1998, 14, 5900. (28) Berhouet, S.; Toulhoat, H. Langmuir 1994, 10, 1832. (29) Frank, I.; Marx, D.; Parrinello, M. J. Chem. Phys. 1996, 104 (20), 8143.

collectors for a wide variety of minerals including calcium minerals. Kotlyarevsky et al.31 reported on the development and characterization of diphosphonic acid collectors with a different structure (as shown in Table 1). These reagents, also known as Flotol reagents, were tested for a wide variety of ores containing phosphate, tungsten, tin, fluorite, and oxidized sulfide minerals in the former USSR. The commercial reagent Flotol-7,9, containing 1-hydroxyalkylidene-1,1-diphosphonic acid, is reported to be a commercial collector.31 Pradip and co-workers32,33 also reported on their successful results on wolframite [(Fe,Mn)WO4] flotation using diphosphonic acids having a variety of different structures. Zhu and Xiao34 found tetradecyl imino-bis-methylene phosphonic acid to be an excellent flotation collector for wolframite flotation. Alkyl phosphonic acids and styrene phosphonic acids are also known to be effective flotation collectors, for example, for tin, titanium, and tungsten ores.31-37 We present in the following section our flotation results on three calcium minerals using two kinds of diphosphonic acid reagents synthesized in our own laboratory along with the corresponding theoretical molecular modeling calculations. The objective of this communication is to validate our proposed methodology of predicting the relative strength/order of interaction of a particular reagent with different mineral surfaces on the basis of molecular modeling computations. Molecular Modeling of Mineral-Reagent Interactions While all the calcium minerals do form chelate bonds with these reagents on the surface, their interaction is remarkably different with each mineral. We have carried out molecular modeling calculations (quantum mechanical and force field) to quantify the relative strength of mineral-reagent interactions for the three mineral surfaces, namely, fluorite, calcite, and fluorapatite, with two diphosphonic acid reagents whose chemical names and structures are given in Table 1. As discussed in the

(30) Collins, D. N.; Wright, R.; Watson, D. In Reagents in the Mineral Industry; Jones, M. J., Oblatt, R., Eds.; IIM Pub.: London, 1984; p 1. (31) Kotlyarevsky, I. L.; Alferiev, I. S.; Krasnukhina, A. V.; Pomazov, V. D.; Egorov, N. V. In Reagents in the Mineral Industry; Jones, M. J., Oblatt, R., Eds.; IIM Pub.: London, 1984; p 173. (32) Pradip. Bull. Mater. Sci. 1996, 19 (2), 267. (33) Pradip; Chaudhari, N. C. Trans. Ind. Inst. Met. 1997, 50 (5), 383. (34) Zhu, Y.; Xiao, Y. Xiyou Jinshu 1989, 8, 18 [CA: 112: 60132k]. (35) Sreenivas, T.; Manohar, C. Miner. Process. Extr. Metall. Rev. 1999, 19, 461. (36) Zhang, X. P.; Misra, M.; Smith, R. N.; Qiao, J. K. Miner. Eng. 1996, 9 (3), 331. (37) Liu, Q.; Peng, Y. Miner. Eng. 1999, 12 (12), 1419.

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Figure 2. Optimized structure of Flotol-8 with partial Mulliken charges on the constituent atoms (color code for atoms: C, cyan; H, black; O, red; P, yellow).

Figure 1. Optimized structure of IMPA-8 with partial Mulliken charges on the constituent atoms (color code for atoms: C, cyan; H, black; N, blue; O, red; P, yellow).

following section, the relative magnitudes of interaction energies computed on the basis of theoretical considerations alone compare very well with the flotation response observed in practice. Quantum Chemical Method. We have used semiempirical level MNDO (MOPAC 6.0)38 calculations to model the interactions of reagents with the mineral surfaces. Reagent Molecules. The geometry of the phosphonic acid reagent was optimized using the BFGS (BroydenFletcher-Goldfarb-Shanno) technique.39 The optimization was considered to be converged when a gradient of 0.1 kcal/mol is reached. The SCF (self-consistent field) convergence criterion was set as 10-5 eV during the computations. The optimized structures of IMPA-8 and Flotol-8 with partial Mulliken charges on the constituent atoms are shown in Figures 1 and 2. For the IMPA-8 molecule, the negative charges on both the phosphonic groups are different, but in the Flotol-8 molecule, both the phosphonic acid groups carry equal negative charge. For both reagents the negative charges on phosphonic groups are compensated by the overall positive charge on the alkyl chain. The negative charge on the nitrogen atom in IMPA-8 is compensated by a total positive charge on the two methylene groups. On the basis of a comparison of their dipole moments, the IMPA-8 molecule (µ ) 4.1 D) was found to be more polar than Flotol-8 (µ ) 3.1 D). It is worth remarking that both phosphonic acid reagents bear alternating positive and negative charges in their functional groups.

(38) MOPAC, Version 6.0; Manual available from QCPE, Indiana University, Bloomington, IN 47405.

The diphosphonic acid group has four acidic protons. Though the pKa's for the octyl diphosphonic acids used in this investigation are not available, the pKa values for ethyl imino-bis-methylenediphosphonic acid belonging to the same family of reagents are reported to be 12.42, 5.92, 4.7, and <2.0, respectively.40 Mineral Surfaces. Cluster models of minerals were generated to represent the basal planes, namely [100], [110], and [111]. The atom positions were taken from the structural reports of fluorite,41 calcite,42 and fluorapatite43 based on X-ray studies. The cluster models of the surfaces were two to three layers thick, containing nearly 45 atoms. Such a large cluster was essential to represent the complete electronic interactions with the approaching reagent molecule. Care was taken to make the cluster model totally neutral. The cluster models generated on the basis of the above criteria have the molecular formulas Ca16F32 for fluorite, Ca10(CO3)10 for calcite, and Ca10(PO4)6F2 for fluorapatite. Since the semiempirical parameters for the element Ca are not available in MOPAC 6.0, the Ca was uniformly treated as a point charge with two positive charges and as a 100% ionic alkaline earth metal for all the three minerals considered in this study. The molecular graphics pictures of fluorite {111}, calcite {110}, and fluorapatite {100} surfaces, at the planes considered to be cleavage planes for respective minerals, are shown in Figure 3. The fluorite surface has an alternating layer of Ca2+ and F- ions with cubic symmetry. Calcite also has an alternating layer of Ca2+ and (CO3)2(39) Shanno, D. F. J. Optim. Theory 1985, 46, 87. (40) Carter, R. P.; Carroll, R. L.; Irani, R. R. Inorg. Chem. 1967, 6 (5), 939. (41) Cheetham, A. K.; Fender, B. E. F.; Cooper, M. J. J. Phys. 1971, 4, 3107. (42) Elliot, N. J. Am. Chem. Soc. 1937, 59, 1380. (43) Sundarsan, K.; Mackie, P. E.; Young, R. A. Mater. Res. Bull. 1972, 7, 1331.

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Figure 5. Optimization of the adsorption angle of IMPA-8 on the fluorite {100} surface.

Figure 3. Cluster models of (a) fluorite {111}, (b) calcite {110}, and (c) apatite {100} surfaces (see annotations for directions and atoms exposed on the surface) (color code for atoms: C, cyan; Ca, green; F, violet; O, red; P, yellow).

Figure 6. Optimization of the adsorption distance of IMPA-8 on the fluorite {100} surface.

Table 2. Comparison of UFF Optimized Crystal Structures with Experimentally Obtained Structures of Calcium Minerals lattice parameters (in deg and Å) mineral fluorite calcite apatite UFF optimized R ) ) ) 90, a ) 5.464 R ) ) 90, ) 120 a ) 4.99, c ) 17.064 R ) ) 90, ) 120 a ) 9.368, c ) 6.884 exp (from refs 48 and 49) R ) ) ) 90, a ) 5.130 R ) ) 90, ) 120 a ) 4.92, c ) 15.5 R ) ) 90, ) 120 a ) 9.22, c ) 6.52

Figure 4. Schematic representation of the mineral-reagent adsorption complex.

ions with rhombohedral symmetry. Fluorapatite has a complex structure with hexagonal symmetry. Ca2+ and F- ions are in near planar arrangement, surrounded by a (PO4)3- tetrahedron. Mineral-Reagent Complexes. Initially an adsorption complex was generated between reagent and the mineral surfaces using the molecular graphics method. The criterion was that the interaction between positive centers on the mineral surfaces and negative centers on the molecule should be maximum, while the functional group of the molecule lies over the mineral surface. The complex thus created was further optimized by varying r and as shown in Figure 4, where r is the shortest distance between the mineral surface and the reagent molecule and is the angel between the mineral surface plane and the norm of the alkyl chain in the reagent molecule. To keep the reference point the same, we have defined r (see Figure 6) as the distance of the methyl carbon of the octyl chain in the IMPA-8 molecule, which is the farthest atom from the surface. was varied from 30° to 150° in steps of 15°. The calculated values of total energies for different values of

were computed in order to determine the opt, corresponding to the lowest energy conformation (Figure 5). Similarly r was varied from 2 to 5 Å in steps of 0.5 Å to obtain ropt (Figure 6). The optimized conformation thus corresponds to the one with ropt and opt. Force Field Method. The MSI program CERIUS2 (version 4.0)44 was used to model the mineral-reagent interactions by the force field approach (universal force field, UFF). Though there are many well-parametrized force fields (DriedingII, MM2, Pcff) available to model organic and polymer molecules, very few can handle inorganic materials such as minerals. We chose to use the UFF, as it offers a versatile, although approximate, parametrization for a wide range of atoms including calcium, atoms of particular interest to this study. Coveney and Humphries18 have reported their results on UFF computations for the interactions of diphosphonate ad(44) CERIUS2, Version 4.0; available from Molecular Simulations Inc., 9685 Scranton Road, San Diego, CA 92121-3752.

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Figure 7. Optimized complexes of IMPA-8 on (a) fluorite {111}, (b) calcite {110}, and (c) apatite {100} surfaces (see annotations for atoms exposed on the surface) (color code for atoms: C, cyan; Ca, green; F, violet; H, black; N, blue; O, red; P, yellow).

ditives with a cement (ettringite) surface. More recently, Sieval et al.45 have used the UFF to model the adsorption of alkyl monolayers on the silica (111) surface. The UFF is a purely diagonal and harmonic force field in which bond stretching is described by a harmonic term, angle bending by a three-term Fourier cosine expansion, and torsion and inversion by cosine-Fourier expansion terms. The van der Waals interactions are described by the Lennard-Jones potential, and electrostatic interactions are termed as atomic monopoles and a screened (distancedependent) Coulombic term.46-48 To check the validity of the UFF for modeling calcium minerals, we minimized the crystal structures of fluorite, calcite, and fluorapatite with the UFF. The results are

(45) Sieval, A. B.; van den Hout, B.; Zuilhof, H.; Sudholter, E. J. R. ¨ Langmuir 2000, 16 (7), 2987.

summarized in Table 2. The UFF predicted values (lattice parameters) are comparable to experimental measurements.49,50 Computational Details. The molecular modeling methodology followed for the force field approach was similar to the one described by Oliver et al.51 A surface cell was

(46) Rappe`, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024. (47) (a) Casewit, C. J.; Colwell, K. S.; Rappe`, A. K. J. Am. Chem. Soc. 1992, 114, 10035. (b) Casewit, C. J.; Colwell, K. S.; Rappe`, A. K. J. Am. Chem. Soc 1992, 114, 10046. (48) Rappe`, A. K.; Colwell, K. S.; Casewit, C. J. J. Inorg. Chem. 1993, 32, 3438. (49) Dana, E. S., Ford, W. F., Eds. Textbook of Mineralogy, with an extended treatise on crystallography and physical mineralogy, 4th ed.; Wiley Eastern Pub.: New Delhi, 1949. (50) Blackburn, W. H., Dennen, W. H., Eds. Principles of Mineralogy; Wm C Brown Pub.: Dubuque, 1988.

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Figure 8. Optimized complexes of Flotol-8 on (a) fluorite {111}, (b) calcite {110}, and apatite {100} surfaces (see annotations for atoms exposed on the surface) (color code for atoms: C, cyan; Ca, green; F, violet; H, black; O, red; P, yellow).

created from the unit cell of a mineral at a given Miller plane ([100], [110], and [111]). The surface cell was then extended to a periodic super lattice of approximately 25 × 25 Å2. The top two layers of the surface cluster were relaxed with respect to energy, and the bottom two layers were kept fixed. Several initial surface cells (pertaining to the cleavage of each Miller plane at different locations) were created, and the cluster obtained from each surface cell was minimized with respect to energy. The most stable surface cluster with the highest negative energy was chosen for further computations. The optimized reagent molecule was docked on this surface cluster and allowed to relax completely. Several initial conformations (20) for the reagent on the surface were considered so as to locate the minimum energy conformation of the complex. Calculation of Interaction Energy (E). The mineral-reagent interaction energy (E), for both force field and quantum chemical methods, was computed using the following equation:

reagent complex, and Emolecule and Esurface are the total energies of the reagent and the mineral surface, respectively. It is worth noting that the more negative magnitude of the interaction energy (E) indicates more favorable interactions between the mineral surface and the reagent. Modeling the Effect of Water. To simulate the aqueous environment in force field calculations, one can employ an empirical dimensionless scaling factor to mediate or dampen the long-range electrostatic interactions. However, this is not the actual D (dielectric constant) of the solvent but a scaling factor, which approximates the effective dielectric permittivity of the medium. We have used a value of 4.0 in UFF calculations for a reasonable approximation of the water environment.52-54 Alternatively, one can compute the adsorption energy of a water molecule on the mineral surfaces and compare it with the interaction energy of the flotation reagent on the surface, that is, to confirm whether the reagent will indeed replace water on the surface. We have computed

(51) Oliver, P. M.; Watson, G. W.; Kelsey, E. T.; Parker, S. C. J. Mater. Chem. 1997, 7, 563. (52) Harvey, S. C. Proteins: Struct., Funct., Genet. 1989, 5, 78. (53) Guenot, J.; Kollman, P. A. Protein Sci. 1992, 1, 1185. (54) Guenot, J.; Kollman, P. A. J. Comput. Chem. 1993, 14, 295.

E ) Ecomplex - (Esurface + Emolecule)

Ecomplex is the total energy of the optimized mineral-

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Table 7. UFF Interaction Energies (kcal mol-1, at E ) 1.0) of IMPA-8 on Calcium Minerals (the Interaction Energies for Water Are Shown in Parentheses) mineral ropt 4.8 5.9 5.0 fluorite calcite apatite {100} -285.2 (-47.6) -145.2 (-58.9) -87.9 (-43.0) {110} -141.9 (-47.2) -100.5 (-32.2) -87.2 (-44.0) {111} -191.4 (-23.6) -93.5 (-31.0) -79.0 (-27.0)

Table 3. MNDO Optimized Structures [opt (in deg) and ropt (in Å)] for IMPA-8 Adsorption on Calcium Mineral Surfaces {100} mineral fluorite calcite apatite opt 109.7 104.5 111.4 ropt 4.8 4.6 5.1 {110} opt 92.0 95.6 128.1 ropt 5.2 4.8 5.4 {111} opt 127.8 107.3 99.5

Table 4. MNDO Optimized Structures [opt (in deg) and ropt (in Å)] for Flotol-8 Adsorption on Calcium Mineral Surfaces {100} mineral fluorite calcite apatite opt 79.9 99.9 108.2 ropt 4.6 6.0 6.2 {110} opt 95.4 138.4 115.9 ropt 6.1 5.0 6.1 {111} opt 95.0 107.3 142.4 ropt 5.1 5.4 4.5

Table 8. UFF Interaction Energies (kcal mol-1, at E ) 1.0) of Flotol-8 on Calcium Minerals (the Interaction Energies for Water Are Shown in Parentheses) mineral fluorite calcite apatite {100} -251.8 (-47.6) -137.4 (-58.9) -120.7 (-43.0) {110} -181.0 (-47.2) -128.5 (-32.2) -85.0 (-44.0) {111} -198.2 (-23.6) -135.7 (-31.0) -116.7 (-27.0)

Table 5. MNDO Interaction Energies (kcal mol-1) of IMPA-8 on Calcium Mineral Surfaces as Compared to Water (the Values in Parentheses Are for Water) mineral fluorite calcite apatite {100} -571.6 (-191.4) 18.9 (20.8) 618.0 (30.0) {110} -322.8 (456.6) 97.8 (6.9) 76.1 (20.8) {111} -141.6 (286.0) 76.1 (90.0) -0.1 (25.4)

Table 9. UFF Interaction Energies (kcal mol-1) of IMPA-8 on Calcium Minerals (the Interaction Energies for Water Are Shown in Parentheses) fluorite {111} in a vacuum ( )1.0) in water ( )4.0) -191.4 (-23.6) -46.5 (-4.4) calcite {110} -100.5 (-32.2) -34.4 (-6.5) fluorapatite {100} -87.9 (-43.0) -33.5 (-16.4)

Table 6. MNDO Interaction Energies (kcal mol-1) of Flotol-8 on Calcium Mineral Surfaces as Compared to Water (the Values in Parentheses Are for Water) mineral fluorite calcite apatite {100} -638.8 (-191.4) -1.6 (20.8) 0.7 (30.0) {110} -346.1 (456.6) -66.6 (6.9) -5.5 (20.8) {111} -149.7 (286.0) 25.1 (90.0) 9.2 (25.4)

Table 10. UFF Interaction Energies (kcal mol-1) of Flotol-8 on Calcium Minerals (the Interaction Energies for Water Are Shown in Parentheses) fluorite {111} in a vacuum ( )1.0) in water ( )4.0) -198.2 (-23.6) -34.5 (-4.4) calcite {110} -128.5 (-32.2) -30.0 (-6.5) fluorapatite {100} -120.7 (-43.0) -24.5 (-16.4)

the interaction energy for water, by both MNDO and UFF methods, on all the mineral surfaces studied and compared with those for reagent molecules. Results and Discussion MNDO Computations. The MNDO optimized structures of mineral-reagent complexes are shown in Figures 7 and 8 for IMPA-8 and Flotol-8 for the three calcium minerals at their cleavage planes, respectively. However, all three basal crystal planes, namely [100], [110], and [111], were considered for these computations, and the ropt and opt values obtained for the optimized complexes are summarized in Tables 3 and 4 (for IMPA-8 and Flotol8, respectively). The computed interaction energies for IMPA-8 and Flotol-8 are summarized in Tables 5 and 6, respectively. Considering that the cleavage planes for fluorite, calcite, and fluorapatite are [111], [110], and [100], respectively, on the basis of the theoretically computed values of the corresponding interaction energies, one can predict that the relative order of the flotation response of IMPA-8 and Flotol-8 reagents for the three minerals should be

fluorite > calcite > fluorapatite

The above prediction is based on the assumption that the flotability of these minerals is strongly dependent on the mineral-reagent interactions. UFF Computations. Force field computation results for IMPA-8 and Flotol-8 are summarized in Tables 7 and 8, respectively. The interaction energies were found to be in the order

fluorite > calcite > fluorapatite

Effect of Aqueous Environment. Since flotation systems are aqueous, we have also attempted to simulate the aqueous environment/effect of the water medium on mineral-reagent interactions. We also computed the interaction energy of water with all three calcium mineral surfaces and for all three planes. The results of MNDO computations for Flotol-8 are presented in Table 6 in parentheses. It is clear from the magnitude of these values that water will be substituted by Flotol-8 on all the surfaces. Similarly, UFF calculations were carried out for water interactions with calcium minerals. The energy values thus obtained are compared with those obtained for the reagents in Tables 7 and 8. The magnitude of the interaction energy is higher for the reagents, and hence reagent adsorption is favored, as observed in practice. The MNDO computation results with IMPA-8, however, need some discussion. The interaction energies for IMPA-8 with fluorite are certainly more favorable than those for water, but the same is not the case for calcite and fluorapatite (Table 5). From the relative magnitude of the interaction energy values, it would seem that water should be preferred over IMPA-8 on the surfaces of calcite and fluorapatite. The reasons for this discrepancy are not clear, since IMPA-8 does adsorb on calcite and fluorapatite from aqueous solution even though very minimally. A similar observation with respect to the interaction of methanoic acid as compared to water was made by de Leeuw et al.27 recently. We have also computed interaction energies using the force field approach by varying the effective permittivity of the medium. A value of ) 4.0 was used to simulate the effect of an aqueous environment. The results are summarized in Tables 9 and 10 for IMPA-8 and Flotol-8, respectively, at the cleavage planes of respective mineral

Diphosphonic Acid Based Surfactants

Langmuir, Vol. 18, No. 3, 2002 939

Figure 9. (a, top) Recovery of fluorite, calcite, and apatite as a function of molar concentration of IMPA-8. (b, center) MNDO and (c, bottom) UFF interaction energies of IMPA-8 on fluorite {111}, calcite {110}, and apatite {100} surfaces.

Figure 10. (a, top) Recovery of fluorite, calcite, and apatite as a function of molar concentration of Flotol-8. (b, center) MNDO and (c, bottom) UFF interaction energies of Flotol-8 on fluorite {111}, calcite {110}, and apatite {100} surfaces.

Microflotation experiments were conducted with 1 g of mineral in a modified Hallimond tube setup.33 Stock solutions of reagents were first prepared and then further diluted to make 100 mL solutions of the required concentrations in volumetric flasks. The pH of the solutions (solution pH) was adjusted using HNO3 and NaOH solutions of suitable concentrations. The mineral was added to the solution in the flask. Conditioning of the mineral in the reagent solution was done in a rotary shaker for 20 min. The contents of the flask were transferred to the Hallimond tube, and a further conditioning was done for 1.5 min. The mineral particles were maintained in a state of suspension by moderate stirring with the help of a magnetic stirrer. The equilibrium pH of the solution was measured just before the commencement of the flotation process. The same pH conditions prevailed till the end of flotation, except in the case of calcite. With calcite, there was a gradual tendency toward increased pH, particularly maintained at lower pH conditions. The nitrogen gas flow rate was 40 mL/min. At the end of 1 min of flotation, the float and tail fractions were collected separately, dried, and weighed, and the percentage recovery was determined. The pH values referred to in all the figures are the equilibrium pH values only. The concentrations of the reagent in solution are presented in terms of its molar concentration (mol/L or M). Microflotation results on three calcium minerals, namely fluorite, calcite, and fluorapatite, using IMPA-8 and Flotol-8 are presented in Figures 9a, and 10a, respectively. The order of the

surfaces. A decrease in the interaction energy values is observed, though disproportionately higher for fluorite as a consequence of taking into account the presence of the water medium during adsorption. The relative order of interaction however remains unchanged. These findings thus suggest that to a first approximation one can use the molecular modeling calculations in a vacuum, so far as the relative strength of mineral-reagent interactions is concerned. We are exploring other methods also to incorporate solvent effects in our theoretical computations. Experimental Section

High purity mineral samples of fluorite, calcite, and fluorapatite were procured from Geologist Syndicate, Calcutta, India, Alminrock Indscr, Bangalore, India, and Florida, respectively. The samples were hand crushed and stage ground in a laboratory planetary mill to obtain the desired size fraction, -48 +65 mesh, for microflotation studies. The powders were analyzed by X-ray diffraction and chemical analysis and found to be pure minerals. The diphosphonic acid reagents used in this investigation were synthesized and characterized in our laboratory as per standard procedures.55,56

(55) Moedritzer, K.; Irani, R. R. J. Org. Chem. 1966, 31, 1603. (56) Nichelson, D. A.; Vaughn, H. J. Org. Chem. 1971, 36, 3843.

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Pradip et al.

flotation response of both the reagents for these minerals was observed as

Concluding Remarks It is thus established, for the first time to our knowledge, that the order of the flotation response of different minerals for a flotation reagent of a given structure can be predicted with a high degree of confidence using molecular modeling techniques. It is worth noting that the theoretical computations carried out in this work do not require any experimental data. The knowledge of the structure of the reagent molecule, as well as the surface with which it is interacting, is sufficient to predict the relative affinity of the particular molecule with different surfaces and/or the relative strength of different reagent molecules for a given surface. The promising implications of such a methodology in the design of highly selective flotation reagents in particular and tailormade surfactants in general are thus demonstrated in this work. Acknowledgment. Financial support from IndoFrench Centre for Promotion of Advanced Research (IFCPAR) for this work is gratefully acknowledged.

LA010625Q

fluorite > calcite > fluorapatite

Comparison of Theoretical Predictions with Experimental Observations Considering that the cleavage planes for fluorite, calcite, and fluorapatite are considered to be [111], [110], and [100], respectively, the corresponding interaction energies (computed by both MNDO and UFF methods) for the adsorption of IMPA-8 and Flotol-8 molecules on the three mineral surfaces are compared with the experimentally observed order of flotation in Figures 9 and 10, respectively. It is indeed interesting to note that the relative affinity of the reagents with fluorite, calcite, and fluorapatite as predicted, on the basis of totally theoretical considerations, is the same as observed during flotation of these minerals using these reagents. It is thus concluded on the basis of this work that molecular modeling computations can indeed be employed to assess the relative strengths of interaction of various molecules with mineral surfaces.

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