Nucleation mechanisms of gibbsite as suggested by computational molecular modelling

Terri J. Soar and Andrea R. Gerson

Ian Wark Research Institute,
University of South Australia,
Mawson Lakes, S.A. 5095,
AUSTRALIA

ABSTRACT

An extensive study of the possible mechanisms of gibbsite nucleation under caustic conditions has been carried out using semi-empirical quantum mechanical molecular modelling. The entropy, enthalpy, Gibbs free energy and species transformation activation energies have been calculated for a wide range of OH- and H2O coordinated Al-containing monomers, dimers, trimers and tetramers while in a solution environment. From these calculations we have found that the Al(OH)4- (Moolenaar et al., 1970) monomer is the most likely monomer to form while [(OH)3Al-(O)-Al(OH)3]2- (Moolenaar et al., 1970) is the most likely dimer to form. In addition it was found that due to the stability of the Al(OH)4- monomer that no dimerisation reaction involving this species was possible to give an energetically favourable dimer (i.e. D G° r was always greater than zero). We have therefore proposed a mechanism by which the dimer is formed through reaction of two unstable monomers (possibly Al(OH)52- or Al(OH)63-) which may be present in very small concentrations. The reaction of minor monomeric species to forms dimers and subsequently oligomers may be the rate determining step in the nucleation process. Polymerisation occurs through further addition of these species. Formation of the double -OH- bridging found between neighbouring Al atoms in gibbsite occurs by dissociative addition of H2O to the already existing -O- bridge.

key words:

gibbsite, nucleation, crystallisation, computational molecular modelling, Gibbs free energy

Nucleation mechanisms of gibbsite as suggested by computational molecular modelling

Terri J. Soar and Andrea R. Gerson

1.0 INTRODUCTION

Although the Bayer process has existed for over 100 years, the fundamental chemistry involved in this process remains unknown. The crystallisation of gibbsite from the highly concentrated caustic aluminate solution typically takes 2 to 3 days to reach economically viable yields. The rate determining step is not understood and as it occurs during the crystallisation of gibbsite, the chemistry of the reaction mechanisms involved must first be determined in order to be able to make the Bayer process more efficient.

Many investigations have been undertaken which have attempted to identify solution species and/or define the earliest steps in nucleation and growth of gibbsite particles. The Al speciation under conditions of low to moderate pH is in contrast to that observed at high pH. It is the high pH speciation that is the focus of this study. Several Raman and infra-red spectroscopic investigations have also been carried out on dilute caustic aluminate solutions ([Al] < 1 M) where most studies have interpreted the spectra obtained as being due solely to the tetrahedrally coordinated aluminate ion (Kopylova et al., 1974; Lippincott et al., 1952; Moolenaar et al., 1970; and Porotnikova et al., 1973). Conductance, acid-titration and freezing-point measurements have been used to show that the aluminate ion is a mono-valent ion (Sakamoto, 1963). Polymer structures have also been detected in dilute aluminium containing solutions. Raman, infra-red and 27Al NMR spectroscopic studies on concentrated caustic aluminate solutions ([Al] > 1 M) have concluded that the tetrahedral Al(OH)4- is the predominant Al-containing solution species (Moolenaar et al., 1970). Additional Raman and infra-red bands were also observed at these higher concentrations and pH ranges. Interpretation of the extra bands was made by the direct comparison of their frequencies with the spectra of the K2[(HO)3AlOAl(OH)3] crystalline structure (Johansson, 1966) and its deuterated analogue. It was concluded that the additional bands were likely to be due to the (OH)3AlOAl(OH)32- species. The results of a number of experiments carried out on concentrated caustic aluminate liquors have concluded that the aluminate ion has a tendency to polymerise and that the formation of aluminium-containing polymers in solution occurs by the release of bound H2O during the period before the visual detection of any crystals (Zambo, 1986). No observation, that the authors are aware of, of Keggin ion (Bottero et al., 1980) formation in concentrated caustic aluminate liquors has been made. There have been no additional reliable observations of vibrational absorptions that increase on aging of solutions other than those already attributed to Al(OH)4- and [(OH)3Al-O-Al(OH)3]2- thus the bonding within any polymeric species that form must be indistinguishable from the monomeric and dimeric species that have been identified.

It has been shown that the rate determining step in nucleation of Al(OH)3 under caustic conditions is not the coordination transformation required to go from Al(OH)4- in solution to octahedrally coordinated Al in gibbsite (May et al., 1997). In addition it is known that water has a peculiar effect on supersaturation in caustic aluminate solutions with dilution often increasing supersaturation (Misra and White, 1970). In an effort to better understand the nucleation mechanism(s) and predict the rate determining step of gibbsite formation from highly caustic aluminate solutions, a computational molecular modelling speciation study has been undertaken.

2.0 METHODOLOGY

Molecular modelling provides a means to discriminate between particular reaction pathways on the basis of the relative energetics of the participating and resulting species (Gerson et al., 1996). Moreover, the process of species optimisation to obtain energy minimisation results in an optimised species geometry. In all calculations described in this text all atomic positions were allowed to refine. Final species geometries are described as unstable where one or more Al to O distances are greater than 2 Å. A four-fold coordinated Al-O bond length as found from optimisation of an Al(OH)4- species is 1.76 Å. In gibbsite, where the Al is 6-fold coordinated to –OH, the average Al-O bond length is 1.90 Å (Saalfeld and Wedde, 1974).

The calculations described herein employed the restricted Hartree-Fock method with self consistent field calculations using AM1 (Dewar et al., 1985). This methodology is supplied in the software program MOPAC93 (Stewart, 1993). Electrostatic repulsion and exchange stabilisation integrals are evaluated by approximate means, a restricted basis set of one s and three p Slater-type orbitals per atom is used, and overlap integrals S are ignored in the secular equation

  (1)

Molecular orbitals and s and p bond strengths are generated from overlap integrals.

AM1 parameters for Al were optimised by Dewar and Holder (1990). AM1 is parameterised to reproduce experimental heat of formation values at 298 K hence the standard heat of formation, D Hf°, is calculated. A comprehensive comparison of experimental and calculated D Hf° values has been performed by Stewart (1993) and is reviewed by Gerson et al. (1996).

Solvent effects are modelled using COSMO - Conductor-like Screening Model (Klamt and Shüürmann, 1993). COSMO belongs to the class of dielectric continuum models. In these models, the solute molecule is embedded in a dielectric continuum of permittivity ?, i.e. the solute molecule forms a cavity within the dielectric. From electrostatics, it is known that the response of a homogeneous dielectric continuum to any charge distribution of solute consists of a surface charge distribution on the interface arising from polarisation of the dielectric medium.

The relative permittivity or dielectric constant for concentrated sodium aluminate solutions is difficult to measure experimentally. Experimental dielectric constants have been reported for lower electrolyte concentrations by Rao and Premaswarup (1966). NaOH solutions of 0.25 M and 2.00 M (at 298 K) produced dielectric constants of 73 (± 2) and 59.5, respectively. Similarly, the electrolyte MgCl2 at concentrations 1 M, 3 M and 4 M (at 298 K) gave dielectric constants of 57.1, 44.3 and 42.0, respectively. From these experimental results, it is apparent that the dielectric constant decreases with increasing electrolyte concentration. In addition, electrolyte double-layer theories reported in literature utilise various dielectric constant values (MacDonald and Barlow, 1965). These range from 1 through to 20 where the average is approximately 10. Therefore to model the low dielectric conditions expected within the solution double layers or solvation shells of a caustic aluminate liquor, a dielectric constant of 10.0 was selected for these computational investigations.

To properly assess the relative stability of species it is necessary to calculate heats of reaction (D Hr°). The heat of reaction can be calculated from the D Hf° of the reactants (A and B) in isolation from each other, and the D Hf° of the products (A+B):

  (2)

The more negative the reaction energy, the more favourable the reaction. This methodology has been successfully applied to a limited study aimed at defining the initial polymerisation reaction steps, in caustic aluminate liquors, involved in the formation of Al(OH)3 (Gerson et al., 1996). These calculations, in contrast to the majority of those presented here were carried out in a vacuum environment. A comparison of the effect of the vacuum and dielectric continuum environments on stability and reaction energy is made in section 3.1.

It is possible to calculate the entropy of a given species taking into account vibration, rotational and transformational contributions. It is not possible to calculate the conformational contribution to the entropy using this methodology, however for small species this can safely be assumed to be a relatively minor constituent. Given the entropy and enthalpy it is then possible to calculate Gibbs free energy of formation (D Gf°) by:

D G° f = D H° f – T(D S° f). (3)

where D H° f is the heat of formation in kJ mol-1, T is the temperature in Kelvin (298 K) and D S° f is the entropic contribution in kJ mol-1. Gibbs free energy of reaction (D Gr°) can be calculated using the same methodology as for the calculation of D Hr°. Selection of the most energetically stable species and most likely reactions are based on Gibbs free energy values. It is possible, however, that even though the D Gr° for a particular reaction is favourable in actuality the reaction will not readily take place. This may be due to exceptionally high activation energies.

Transition states, and hence activation energies (Ea), may be calculated. This involves locating and following the reaction coordinate connecting the two stable systems, reactants and products, on a (3n-6)-dimensional geometry surface (Dewar et al., 1984, and Stewart, 1993). The transition state is associated with the highest energy point located along this reaction coordinate. Energy of activation is defined as the difference in energy between the transition and reactant compounds.

3.0 RESULTS AND DISCUSSION

3.1 Monomers

All possible negatively or neutrally charged Al monomers with 4-, 5- and 6-fold Al coordination to all possible stoichiometries and geometries of water and/or OH- were investigated. Only negatively charged and neutral species were assessed as it was felt that there was no possibility of a positively charged species existing in a solution containing a high concentration of OH-. The D Hf° and D Gf° values for the eight most stable species are shown in Table 1 for a dielectric continuum environment. The species values for a vacuum environment are also given. Al(OH)4- is not the most stable species based on D H° f and D G° f criteria. In the vacuum environment the neutral species tend to have greater stability. In the dielectric continuum environment where the charge can be partially stabilised by the local polarisability of the dielectric continuum the charged species are stabilised relative to the vacuum environment.

 

Table 1

Monomeric Al-containing species D H° f and D G° f (kJ mol-1). n.s. indicates the Al-containing species became sterically unstable on optimisation

Monomer

D H° f

(kJ mol-1)

D G° f

(kJ mol-1)

 

Vacuum

Dielectric constant = 10.0

Vacuum

Dielectric constant = 10.0

Al(OH)63-

-397

-2355

-518

-2473

Al(OH)4(H2O)2-

n.s.

-2062

n.s.

-2189

Al(OH)52-

-1131

-2073

-1242

-2184

Al(OH)4(H2O)-

n.s.

-1838

n.s.

-1954

Al(OH)3(H2O)3

-1639

-1771

-1760

-1901

Al(OH)4-

-1308

-1613

-1419

-1720

Al(OH)3(H2O)2

-1408

-1528

-1523

-1645

Al(OH)3(H2O)

-1142

-1246

-1248

-1350

To evaluate the energetics of reaction of species the D H° r and D G° r required to convert one monomeric species to another have been calculated. In order to do this stoichiometric (and charge) balanced equations must be defined and the D H° f and D G° f of all the species involved in the reaction (including OH- and H2O) must be calculated. It was found on carrying out this process, that Al(OH)4- gives rise to the most stable system in both the vacuum and dielectric continuum environment. D H° r and D G° r energies for the conversion of the 8 most stable species (listed in Table 1) to Al(OH)4- are given in Table 2. The more negative the energy the more favourable the forward reaction, i.e. the more likely the reaction is to give rise to an Al(OH)4- product. It is apparent from Table 2 that all the reactions listed are favourable. This confirms the experimental result that Al(OH)4- is the most stable and hence most abundant monomer in caustic aluminate solutions.

Table 2

D H° r and D G° r (kJ mol-1) for monomeric species to form Al(OH)4-. n.s. indicates the Al-containing species was sterically unstable.

Monomer

D H° r

(kJ mol-1)

D G° r

(kJ mol-1)

 

Vacuum

Dielectric constant = 10.0

Vacuum

Dielectric constant = 10.0

Al(OH)63-

-1029

-276

-1121

-367

Al(OH)3(H2O)3

-354

-176

-461

-270

Al(OH)4(H2O)2-

n.s.

-113

n.s.

-205

Al(OH)3(H2O)2

-337

-138

-394

-189

Al(OH)3(H2O)

-355

-139

-365

-147

Al(OH)4(H2O)-

n.s.

-56

n.s.

-103

Al(OH)52-

-236

-49

-287

-96

Al(OH)4-

0

0

0

0

Unfortunately software limitations currently restrict the calculation of species involving Na+ or K+ in a dielectric continuum environment. D H° r energies for the conversion of ion paired species to ion paired Al(OH)4- indicate that in a vacuum environment ion paired Al(OH)4- does not give rise to the most stable system. Therefore for our purposes non-ion paired models in a dielectric continuum environment give rise to more realistic results than ion paired species in a vacuum environment. Hence it is the non-ion paired species in the dielectric continuum environment that we focus on in this text.

In order to be able to critically assess the likelihood of exchange between different monomeric species it is necessary to calculate the activation energy (Ea) required for conversion of one species to another. The Ea for a range of reactant monomers going to Al(OH)4- are given in Table 3. The negative Ea figures given in Table 3 effectively mean that the reaction occurs spontaneously and requires no energy input.

The reverse reaction activation energies (column 3 Table 3) from the Al(OH)4- monomer to give another monomeric species are all positive. However, some of these are sufficiently small that it is possible that, at any one time in solution a very small concentration of these other monomers exist even though they are less energetically favourable than Al(OH)4-.

In order to calculate the concentrations of these species in solution the equilibrium constant for the reactions of interest must first be calculated. Assuming a reaction

A+B ® C +D (4)

the following equilibrium constant, K, can be defined

K=[(a)C (a)D]/[(a)A (a)B] (5)

where a = g m and g is the activity coefficient and m is the species molality (mol kg-1). The equilibrium constant may be calculated from

D G° r = -RTln(K) (6)

where R is the gas constant (8.3145 J K-1 mol-1) and T is the temperature in Kelvin (298.0 K). Hence by assuming an activity coefficient of 1 and some idealised concentrations, [Al(OH)4-] = 2.7 M, [OH-] = 1.1 M and [H2O] = 30 M, concentrations of the minor monomeric species can be calculated. These are given in Table 3, column 4. The most major Al-containing monomeric species after Al(OH)4- is calculated to be Al(OH)5 2- at a concentration of 9.5 ´ 10-14 mol kg-1. It should be noted that all monomeric species, other than Al(OH)4- are predicted to be present in insufficient concentrations to be detectable by spectroscopic techniques.

Table 3

Energies of activation (kJ mol-1) for monomeric species transforming to Al(OH)4- in a dielectric continuum environment using dielectric constant of 10.0 and the calculated reactant monomer concentration (mol kg-1) resulting from the reaction

Monomer

Ea to give Al(OH)4-

(kJ mol-1)

Ea from Al(OH)4-

(kJ mol-1)

Molality

(mol kg-1)

Al(OH)4(H2O)2-

-52

61

3.8 x 10-34

Al(OH)4(H2O)-

-49

7

2.8 x 10-18

Al(OH)3(H2O)3

-21

155

2.5 x 10-38

Al(OH)63-

11

287

3.4 x 10-44

Al(OH)3(H2O)2

26

164

4.0 x 10-26

Al(OH)52-

43

92

9.5 x 10-14

Al(OH)3(H2O)

52

191

3.4 x 10-19

3.2 Dimers

In order to test the relative stability of various dimers a range of molecular models were developed. A number of assumptions were made regarding the structure of these models to limit the enormous range of possibilities. All dimers modelled were assumed to be symmetrical, i.e. each Al had identical coordination. In addition only OH- coordination was considered. However, bridging groups could be either –O– or –OH– with either one or two bridges being present. The coordination of the Al atoms in the dimer was varied from 3 to 6-fold. Table 4 shows the 11 dimers with the most stable (negative) D G° f.

Table 4

D G° f and D G° r (kJ mol-1) for the dimeric species listed below reacting to form [(OH)3Al-O-Al(OH)3]2- in an environment of dielectric constant of 10.0. These are listed in order of the most likely to least likely reaction

Dimer

D G° f

(kJ mol-1)

D G° r

(kJ mol-1)

[(OH)4Al-O2-Al(OH)4]6-

-3453

-1462

[(OH)4Al-(OH)2-Al(OH)4]4-

-3948

-521

[(OH)3Al-O2-Al(OH)3]4-

-3324

-471

[(OH)4Al-O-Al(OH)4]4-

-3724

-408

(OH)2Al-O-Al(OH)2

-1676

-216

[(OH)4Al-(OH)-Al(OH)4]3-

-3725

-184

(OH)2Al-(OH)2-Al(OH)2

-2102

-128

[(OH)3Al-(OH)-Al(OH)3]-

-2669

-120

[(OH)3Al-(OH)2-Al(OH)3]2-

-3286

-63

[(OH)2Al-(O)2-Al(OH)2]2-

-2642

-33

[(OH)3Al-O-Al(OH)3]2-

-3012

0

It was found on calculation of D G° r for transformations between dimers that it is the dimer [(OH)3Al-(OH)2-Al(OH)3]2- that gives rise to the most stable system. This dimer is the structure suggested in Moolenaar’s spectroscopic study (Moolenaar et al., 1970). In Table 4 D G° r with respect to (i.e. as the product) [(OH)3Al-O-Al(OH)3]2- are also given. In all cases the D G° r is negative indicating the reaction is favourable. The second most favourable dimer is [(OH)2Al-(O)2-Al(OH)2]2- with a Gibbs free energy of reaction to give ‘Moolenaar’s’ dimer of only –33 kJ mol-1.

The four most energetically favourable dimers are predicted to be:

[(OH)3Al-O-Al(OH)3]2-

[(OH)2Al-(O)2-Al(OH)2]2-

[(OH)3Al-(OH)2-Al(OH)3]2-

[(OH)3Al-(OH)-Al(OH)3]-

in order of decreasing stability. These dimers show the full range of possible bridging structures, one and two –O– bridges and one and two –OH– bridges.

It is generally agreed that Al(OH)4- is the predominant monomeric solution species under caustic conditions. This monomer has a theoretical point group of S4, however its IR and Raman vibrations are assigned successfully with the point group Td. This implies that the hydrogens are sufficiently diffuse to be effectively ignored. Absorption frequencies very similar to those attributed to –O– have been observed in hydroxyaluminate compounds which are known to contain no oxygen bridging, e.g. gibbsite 585, 559 and 532 cm-1 (Olphen and Fripiat, 1979) and bayerite, approximately 540 cm-1 (Bradley et al., 1993). Hence, this implies that it may not be possible to distinguish –O– and –OH– bridging groups particularly where rapid proton exchange may be occurring.

3.3 The Dimerisation Reaction

Calculations of D G° r to form dimers has indicated that two Al(OH)4- monomers will not react to form any dimer, i.e. the Gibbs free energy of reaction is always positive. On analysis this is not a surprising finding given that the nucleation process to form solid Al(OH)3 is very slow. However, the concentration of Al(OH)4- is very high. The Ea for the growth of gibbsite has been measured to be relatively low; 54 kJ mol-1 (Mordini and Cristol, 1982), 79 kJ mol-1 (King, 1973). If the dominant monomeric species reacted to form a dimer it would be expected that this process, and possibly subsequent polymerisation reactions would occur quite rapidly particularly if the activation energy is as low as that indicated by experiment.

The D H° r and D G° r of all possible combinations of all possible monomeric reactants to give all the dimers modelled in this study have been calculated. However, for this discussion, the descriptions are limited to the reactions between the four most energetically favourable monomers (Al(OH)4-, Al(OH)52-, Al(OH)4(H2O)-, Al(OH)3(H2O)) to give the most energetically favourable dimer ([(OH)3Al-O-Al(OH)3]2-) which give rise to a negative Gibbs free energy of reaction on formation of a dimer (Table 5).

Table 5

D H° r and D G° r for monomer + monomer ® dimer reactions between the four most energetically favourable monomers to give the most energetically favourable dimer. Only the favourable, i.e. negative, D G° r values are given. All calculations have been carried out using a dielectric continuum environment with a dielectric constant of 10.0

Monomer reactant

Monomer reactant

Dimer product

D H° r

(kJ mol-1)

D G° r

(kJ mol-1)

Al(OH)4-

Al(OH)52-

[(OH)3Al-O-Al(OH)3]2-

19

-5

Al(OH)4-

Al(OH)4(H2O)-

[(OH)3Al-O-Al(OH)3]2-

12

-12

Al(OH)4-

Al(OH)3(H2O)

[(OH)3Al-O-Al(OH)3]2-

-71

-56

Al(OH)52-

Al(OH)52-

[(OH)3Al-O-Al(OH)3]2-

-30

-101

Al(OH)52-

Al(OH)4(H2O)-

[(OH)3Al-O-Al(OH)3]2-

-37

-108

Al(OH)52-

Al(OH)3(H2O)

[(OH)3Al-O-Al(OH)3]2-

-120

-152

Al(OH)4(H2O)-

Al(OH)4(H2O)-

[(OH)3Al-O-Al(OH)3]2-

-44

-115

Al(OH)4(H2O)-

Al(OH)3(H2O)

[(OH)3Al-O-Al(OH)3]2-

-127

-159

Al(OH)3(H2O)

Al(OH)3(H2O)

[(OH)3Al-O-Al(OH)3]2-

-210

-203

It can be seen in Table 5 that the least energetically favourable monomer, Al(OH)3(H2O), is the most likely to react to form a dimer. However, the least energetically favourable monomer while being the most reactive will also be present in smaller concentration than the three more stable monomers (Table 3). It is likely that the dimerisation reaction may follow many paths and proceed through both unstable monomers and unstable dimers before reaching the most stable dimer. The proposed reaction scheme is shown schematically in Figure 1. This reaction scheme is shown to include the dimer [(OH)3Al-(OH)2-Al(OH)3]2-. In order to build up a Al(OH)3 structure, which possess 6-fold octahedral –OH– coordination with pairs of Al atoms being bridged by pairs of –OH– bridges, it is necessary at some stage of the nucleation process for –OH– bridges to form between Al atoms. This –OH– bridged dimer is shown at this stage of the nucleation mechanism to indicate that these bridges may viably form during the dimerisation process even though it would be expected that this dimer would be present in smaller concentrations than [(OH)3Al-O-Al(OH)3]2-.

3.4 Trimers and Tetramers

It is not within the scope of this study to model large polymeric systems. However, by analysing the thermodynamics of some small oligomers a greater level of understanding may be gained into the formation of larger species. The oligomers chosen to model were trimer and tetramer Al-containing species. These species were all symmetric, were either neutral or negatively charged, contained aluminium atoms with 4, 5 or 6-fold OH coordination and contained Al pairs bridged by two –OH– groups. In addition, tetramers considered were either linear or branched. OH coordination was assumed due to the necessity to render the model more gibbsite-like on increase in oligomeric size. The D G° f of the trimer species is given in Table 6 and the tetramer species in Table 7.

Table 6

D G° f and D G° r of each trimer to form [(3)Al-(2)-Al(1)-(2)-Al(3)]2-. The number in ( ) indicate the number of attached OH group or –( )– bridging hydroxyl groups. All calculations are carried out in a dielectric continuum environment with a dielectric constant of 10.0

Trimer

Al coordination and charge

D G° f

(kJ mol-1)

D G° r

(kJ mol-1)

[(4)Al-(2)-Al(2)-(2)-Al(4)]5-

[6-6-6]5-

-5834

-639

[(4)Al-(2)-Al(1)-(2)-Al(4)]4-

[6-5-6]4-

-5065

-398

[(3)Al-(2)-Al(2)-(2)-Al(3)]3-

[5-6-5]3-

-4758

-145

[(3)Al-(2)-Al(1)-(2)-Al(3)]2-

[5-5-5]2-

-4343

0

[(3)Al-(2)-Al-(2)-Al(3)]-

[5-4-5]-

-3685

-98

[(2)Al-(2)-Al(1)-(2)-Al(2)]

4-5-4

-3127

-96

Table 7

D G° f and D G° r of each tetramer to form [(3)Al-(2)-Al(2)-(2)-Al(2)-(2)-Al(3)]4-. The number in ( ) indicate the number of attached OH groups or –( )– bridging hydroxyl groups. All calculations are carried out in a dielectric continuum environment with a dielectric constant of 10.0

Tetramer

Al coordination and charge

D G° f

(kJ mol-1)

D G° r

(kJ mol-1)

[(4)Al-(2)-Al(2)-(2)-Al(2)-(2)-Al(4)]6-

[6-6-6-6]6-

-6787

-1234

[(4)Al-(2)-Al-(2)-Al(4)]6-

|

(2)

|

Al(4)

[6-6-6]6-

|

6

-6739

-1282

[(2)Al-(2)-Al(2)-(2)-Al(2)-(2)-Al(2)]2-

[4-6-6-4]2-

-5257

-524

(2)Al-(2)-Al(2)-(2)-Al(2)

|

(2)

|

Al(2)

[4-6-4]0

|

4

-4161

-500

[(3)Al-(2)-Al-(2)-Al(3)]3-

|

(2)

|

Al(3)

[5-6-5]3-

|

5

-5856

-485

(2)Al-(2)-Al(1)-(2)-Al(1)-(2)-Al(2)

[4-5-5-4]0

-4198

-463

[(3)Al-(2)-Al(1)-(2)-Al(1)-(2)-Al(3)]2-

[5-5-5-5]2-

-5380

-401

[(3)Al-(2)-Al(2)-(2)-Al(2)-(2)-Al(3)]4-

[5-6-6-5]4-

-6227

0

The most energetically favourable trimer is [(3)Al-(2)-Al(1)-(2)-Al(3)]2- where the number in ( ) indicates the number of OH- groups. The D G° r of each trimer transformation to give this trimer are shown in Table 6. The most energetically favourable tetramer of those modelled is [(3)Al-(2)-Al(2)-(2)-Al(2)-(2)-Al(3)]4- as indicated in Table 7 by the negative D G° r for other tetramers to form this tetramer. Although a range of species with –O– bridges have not been examined there is no reason apparent to the authors why trimers and larger species could not exist with –O– bridging structures. This assumption is particularly likely to be correct in light of the calculations that have indicated that [(OH)3Al-O-Al(OH)3]2- is the most stable dimer formed.

The combinations of monomeric and dimeric reactants which will give rise to an energetically favourable reaction to form the most stable trimer, [(3)Al-(2)-Al(1)-(2)-Al(3)]2-, are limited. As indicated in Table 8, there are no favourable combinations of the most energetically favourable dimer with the four most favourable monomers to give the most stable trimer using D G° r. It is apparent from Table 8 that the more unstable the reacting monomer and/or dimer, and hence the more minor the concentration of this species in solution, the more likely the trimerisation reaction will occur. Consequently it appears that, as for the dimerisation reaction, the trimerisation reaction will primarily occur through the reaction of minor solution constituents. The schematic mechanism for the formation of trimer from a dimer is shown in Figure 1. Both trimers shown in Figure 1 are symmetrical. There is no reason for this except that symmetrical trimers have been modelled. It is entirely possible that trimer or larger species may exist with a mixture of 1 or 2 –OH– or –O– bridging structures. The trimer [(3)Al-O-Al(1)-O-Al(3)]2- has been included in the proposed mechanism in Figure 1 as it is a structural relation to the Moolenaar dimer with single –O– groups bridging the Al atoms. Calculations to indicate the thermodynamic viability for the transformation of this trimer to [(3)Al-(2)-Al(1)-(2)-Al(3)]2- revealed a negative heat of reaction (-57 kJ mol-1) and a positive Gibbs free energy of reaction (55 kJ mol-1). Hence, the Moolenaar-type trimer may also be associated with a dimer to trimer step of the overall reaction mechanism.

Table 8

Favourable D G° r of the four most stable monomers with the four most stable dimers to give [(3)Al-(2)-Al(1)-(2)-Al(3)]2-. All calculations are carried out in a dielectric continuum environment with a dielectric constant of 10.0

Monomer

Dimer

D G° r (kJ mol-1)

Al(OH)3(H2O)

[(OH)2Al-(O)2-Al(OH)2]2-

-14

Al(OH)3(H2O)

[(OH)3Al-(OH)2-Al(OH)3]2-

-44

Al(OH)52-

[(OH)3Al-(OH)-Al(OH)3]-

-50

Al(OH)4(H2O)-

[(OH)3Al-(OH)-Al(OH)3]-

-57

Al(OH)3(H2O)

[(OH)3Al-(OH)-Al(OH)3]-

-101

Solution species containing four or more Al atoms are of particular significance as the possible formation of branched structures may start to resemble that of gibbsite. However, the most energetically favourable tetramer of those modelled is not branched. Although this tetramer is linear, it does contain Al-coordinations of 5 (at either end) and 6 (in the middle). This at least begins to resemble gibbsite. Figure 1 includes schematics of reactions from the most energetically favourable trimer to the most energetically favourable tetramer by the addition of Al(OH)52-. However, calculation of the associated D G° r (i.e. 300 kJ mol-1) indicates an unfavourable reaction. As for trimerisation, the involvement of minor solution species may again play a primary role in the formation of tetramers.

Also shown in Figure 1 is the branched tetramer

[(3)Al-(2)-Al-(2)-Al(3)]3-

|

(2)

|

Al(3)

which contains a central Al with 6-fold coordination to 3 pairs of bridging hydroxyl groups. This structure is analogous to the coordination of Al found in gibbsite but its involvement is only speculated. Longer linear polymers containing Al may exist in solution. These polymer chains may continue to grow in the one dimension until becoming entropically unstable so that further Al additions give rise to branching. Another possibility is that many of these long linear chains undergo cross-linking and thereby creating a "framework" of polymers. The gradual filling in and ordering of branched polymers would explain the observations of aging concentrated caustic aluminate solutions using cryo-TEM, SAXS, SANS and DLS (Gerson et al., 1998). The mechanism to form branched polymers is currently under investigation.

Figure 1

Schematic of the proposed reaction mechanism from the most energetically favourable monomer to the most energetically favourable tetramer (second to last species). The species shown within grey shaded boxes are those which are proposed on the basis of both experimental and theoretical evidence. The thickness of the arrows indicates the extent of the reaction in that direction.

4.0 CONCLUSIONS

An extensive study of the possible Al-containing solution species present in highly caustic aluminate solutions has been carried out using computational molecular modelling incorporating solvent effects. From these calculations it was found that the most energetically stable species include Al(OH)4- and [(OH)3Al-(OH)2-Al(OH)3]2- which confirm the experimental findings in caustic aluminate solutions. Larger most energetically stable Al-containing species were found to be [(3)Al-(2)-Al(1)-(2)-Al(3)]2- and [(3)Al-(2)-Al(2)-(2)-Al(2)-(2)-Al(3)]4-. Other monomer species may exist at very low concentrations.

Calculations of the most energetically favourable dimers show no trends of favoured bridging groups. Bridging species –O– and –OH–, either singular or double, are all energetically possible. In highly caustic aluminate solutions, rapid proton exchange may be occurring which would make distinguishing the existing bridges experimentally particularly difficult.

Dimerisation of Al(OH)4- to form any dimer was found to be energetically unfavourable. The calculation suggest that the formation of dimers and trimers will primarily occur through the reaction of minor constituents. The rate determining step of gibbsite nucleation may therefore involve the reaction of these minor species. The reaction mechanism may follow many paths proceeding through different unstable Al-containing species.

The experimental effect of water in highly caustic aluminate solutions may be explained on the basis of the mechanism proposed in Figure 1. The unusual solubility plot of gibbsite suggests that two factors may effect the solubility. The addition of water dilutes the solution and reduces the collision frequency between the reacting species. On the other hand the addition of water is required to form –OH– bridges in oligomeric species – precursors to gibbsite.

acknowledgments

Financial support for the project is acknowledged from the Australian Research Council’s SPIRT grants program and the alumina industry (Alcoa of Australia, Billiton, Comalco, Nabalco, Queensland Alumina and Worsley Alumina) through the Australian Minerals Industries Research Association (project P380B).

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