Ind. Eng. Chem. Res. 1997, 36, 675-681
675
A Rapid Method for the Determination of Growth Rate Kinetic Constants: Application to the Precipitation of Aluminum Trihydroxide Herve´ Muhr, Jean-Pierre Leclerc, and Edouard Plasari* Laboratoire des Sciences du Ge´ nie Chimique, CNRS-ENSIC/INPL, BP 451, 54 001 Nancy Cedex, France
Fre´ de´ ric Novel-Cattin Renault Direction de la Recherche, 9-11 avenue du 18 Juin 1940, 92 500 Rueil Malmaison, France
The growth rate kinetics of crystallization of aluminum trihydroxide from caustic aluminate solutions of aluminum-air batteries are studied in a laboratory batch isothermal precipitator. A method using high seed charges varying from 200 to 800 kg of Al(OH)3 per m3 of aluminate solutions is developed for the rapid determination of kinetic constants of the crystal growth rate expression. Thus, it is shown that growth rate increases with the square of the supersaturation, and the temperature effect on the growth rate follows an Arrhenius relation with an activation energy term of E/R ) 8164 K. It is also shown that the growth rate of aluminum trihydroxide is very sensitive to impurities in the aluminum electrodes and to additives in the electrolytic solution. This method can be extended to other precipitation reactions characterized by very low crystal growth rates. Introduction This study is linked to the development of an aluminum-air battery, where the aluminum is attacked by a solution of NaOH or KOH. Aluminum is then solubilized in solution in the form of aluminates. The regeneration of the electrolytic solution containing aluminates is necessary to prevent precipitation in the cell and for economic considerations: the precipitate has to be recycled. Thus, it is necessary to build a regenerator outside the cell, in which the electrolytic solution can be regenerated by precipitation of aluminates on seed particles in the form of aluminum trihydroxide (Gibbons and Gregg, 1992; Niksa and Wheeler, 1988). Because of the significance of the industrial Bayer process, many authors already studied the kinetics of precipitation of aluminum trihydroxide (Misra and White, 1970; Halfon and Kaliaguine, 1976; White and Bateman, 1988; Van Straten et al., 1984; Veesler and Boistelle, 1993). Many papers are also devoted to a specific aspect such as solubility (Misra, 1970), caustic concentration (White and Bateman, 1988), or agglomeration (Brown, 1988; Ilievki and White, 1994; Veesler et al., 1994). In our specific case, the growth rate of aluminum trihydroxide was the most significant parameter conditioning the regenerator size. For this reason, a detailed study was necessary in order to obtain growth rate kinetic data peculiar to the aluminum-air battery system. Many series of experiments were required to elucidate the influence of several factors such as temperature, electrolyte composition, and impurities provided by aluminum electrodes on growth rate of aluminum trihydroxide. Actual methods for the measuring of this growth rate are too time consuming (residence times in the batch crystallizer being of the order of 30100 h (Misra and White, 1970; Halfon and Kaliaguine, 1976; White and Bateman, 1988a) due to its very low * To whom correspondence should be addressed. Phone: (33) 3 83 17 50 99. Fax: (33) 3 83 32 73 08. E-mail:
[email protected]. S0888-5885(96)00401-0 CCC: $14.00
values. For this reason, a rapid method characterized by residence times of 2-3 h was elaborated in order to obtain the crystal growth rate expression for the development of the regeneration process within a short time. Principle of the Method The stability of supersaturated caustic aluminate solutions is shown by the prolonged induction periods up to several weeks for precipitation from unseeded solutions. Since spontaneous nucleation is practically impossible, the presence of seed is necessary to promote the precipitation. Moderate seed charges in relation to the quantity of alumina in the aluminate solutions were used by many authors to study the precipitation of this compound (Misra and White, 1970; Halfon and Kaliaguine, 1976; White and Bateman, 1988). In these cases, 30 to more than 100 h are needed to carry out one experiment due to very low crystal growth rate and moderate seed charge. Solution composition and crystal size distribution of the solid phase were measured at several intervals of time in order to obtain growth rate kinetic expressions. Generally, for long residence time runs, undesirable phenomena such as secondary nucleation, agglomeration, and breakdown become important and can disturb the determination of the growth rate. For this reason, we proposed the use of high seed charges of aluminum trihydroxide having several experimental advantages: (1) the residence time in the crystallizer to carry out one experiment is short; thus, the influence of the phenomena cited above can be neglected; (2) the surface area of the precipitation of aluminum trihydroxide on the seed charge remains practically unchanged due to the small quantity of precipitated alumina with respect to the mass of seed; (3) only the time dependence of alumina concentration in the aluminate solution and the initial seed particle size distribution are sufficient to obtain the crystal growth rate expression; (4) the mathematical treatment of the experimental data is simple, and the numerical differentiation is avoided. © 1997 American Chemical Society
676 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997
The precipitation of aluminum trihydroxide corresponds to the reaction (Veesler and Boistelle, 1993) Al(OH)4 f Al(OH)3 + OH
(1)
Under seeding conditions and assuming zero nucleation rate, independent growth rate on particle size, no agglomeration, and no breakdown, the population balance relation in the case of a well-agitated batch crystallizer (Randolph and Larson, 1988) can be simplified yielding
G(t)
∂ψ(L,t) ∂ψ(L,t) + )0 ∂L ∂t
In all previous studies, the growth rate of aluminum trihydroxide is considered to be surface-reaction controlled because of the very low growth rate (a few micrometers per hour), the high activation energy, and the negligible effect of agitation on growth rate (Misra and White, 1970; Halfon and Kaliaguine, 1976; White and Bateman, 1988). In this case Cc(t) ) C(t). For high seeding ratio and short experimentation time, the precipitation surface area can be considered unchanged, i.e. m2 ≈ m20, where m20 is the second-order moment of initial seed population density. In these conditions, the substitution of eq 5 in eq 8 yields
(2) -
with ψ(L,t)0) ) ψ0(L) where ψ(L,t) and ψ0(L) represent population density at time t and population density of the seed charge, respectively; G(t) is the crystal growth rate varying as a function of time. The kth moment of the population density is defined by
mk )
∫0∞Lkψ(L,t) dL
(3)
dC(t) 3φvFc MAl2O3 ) m k [C(t) - Ce]g dt φ 2MAl(OH)3 20 g
Integration of eq 9 gives
1 1 ) (g - 1)Kt [C(t) - Ce]g-1 [C0 - Ce]g-1
K) (4)
(10)
where
From eq 2, it is easily obtained
dmk ) kG(t)mk-1 (k ) 1, 2, ...) dt
(9)
3φvFc MAl2O3 m k φ 2MAl(OH)3 20 g
(11)
The seed charge is generally characterized by its mass particle size distribution g(L). Knowing that
In most cases, growth rate of aluminum trihydroxide can be represented as a power law (Misra and White, 1970; Halfon and Kaliaguine, 1976; Veesler and Boistelle, 1993)
Cs0 g(L) φvFc L3
ψ0(L) )
(12)
it follows that
G(t) ) kg[Cc(t) - Ce]g ) kgσg
(5)
where σ is the supersaturation, while Cc(t) and Ce are the concentrations of alumina on the crystal surface as kg of Al2O3 per m3 of the aluminate solution at time t and at equilibrium, respectively. The concentration of the solid phase as kg of Al(OH)3 per m3 of suspension is given by the expression
∫0∞L3ψ(L,t) dL ) φvFcm3
Cs(t) ) φvFc
(6)
where Fc and φv are the density and the volumetric shape factor of aluminum trihydroxide particles. The mass balance for alumina (Al2O3) at time t can be represented by the following expression
VL[C0 - C(t)] ) Vs [C (t) - Cs0] 2MAl(OH)3 s (7)
where VL and Vs are the volume of the liquid phase (aluminate solution) and the volume of the suspension, respectively. Derivation of eq 7 and substitution of eq 4 yield
-
dC(t) 3φvFc MAl2O3 ) G(t) m2 dt φ 2MAl(OH)3
where φ is the ratio VL/Vs.
Cs0
(8)
∫0∞
φvFc
g(L) dL L
(13)
and
K)
3Cs0 MAl2O3 φ 2MAl(OH)3
∫0∞
kg
g(L) dL L
(14)
where Cs0 is the initial concentration of seed as kilograms of aluminum trihydroxide per cubic meter of suspension. The ratio Cs0/φ can be represented as
C s0 φ
MAl2O3
MAl2O3 [m - m30] ) φvFcVs 2MAl(OH)3 3
m20 )
)
ms VL
(15)
where ms is the mass of the seed charge used for each experiment. Equations 10 and 14 provide the growth rate kinetic constants kg and g from the experimental data of alumina concentration as a function of time. Especially, eq 14 shows that in the case of high seed charges, the shape factor value is not necessary for the determination of the growth rate kinetic expression. Experimental Setup and Procedure The laboratory batch crystallizer was a flask of 1.5 L capacity agitated by a Rushton turbine at a constant speed of 350 rpm. The crystallizer was immersed in a constant-temperature bath, and all runs were carried out isothermally. Caustic aluminum solutions were
Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 677
Figure 1. Particle size distribution of the bulk seed charge (L in µm).
Figure 2. N (at current time t) to N (at initial time) versus time for different seed charges (L in µm).
Table 1. Range of the Operating Parameter Conditions parameters initial alumina concentration: C0 (kg of Al2O3/m3 of aluminate solution) temperature (°C) NaOH concentration (mol/m3) initial supersaturation: C0 - Ce (kg of Al2O3/m3) initial supersaturation ratio: C0/Ce seed charge (kg of Al(OH)3/m3 of aluminate solution)
range of conditions 117 40-70 4000 52 (70 °C) to 83 (40 °C) 1.8 (70 °C) to 3.4 (40 °C) 200-800
prepared by dissolving aluminum (minimum 99.5% purity) in analytical grade NaOH solutions. One liter of this solution was carefully filtered and added to the crystallizer just prior to the start of a crystallizer run. The crystallizer was allowed to reach the desired temperature and a known amount of suitably sized aluminum trihydroxide seed crystals, preheated to this temperature, was then added to begin the run. Small amounts of suspension were sampled out without modifying the course of the precipitation. Samples were filtered, and the solution was analyzed to access the aluminum concentration. Runs were performed for a period of approximately 150 min. Mass particle size distribution of seeds was determined by the laser diffraction analyzer Malvern Mastersizer, giving the mass fraction of crystals in classes increasing in geometrical progression. The evolution of the precipitation was followed by back-titration of aluminum using EDTA and ZnSO4 solutions. The choice of operating conditions was fixed by the running of the aluminum-air battery. Table 1 illustrates the conditions used in this study. Seeds used in all experiments were composed of aluminum trihydroxide of RECTAPUR quality commercialized by PROLABO. Figure 1 shows the bulk particle size distribution of seed charge. In many experiments, seeds of several narrow size distributions obtained from the bulk by sieving were also used. Results and Discussion Preliminary experiments were carried out in order to find out the effects of secondary nucleation, agglomeration, and breakdown. Figure 2 shows the evolution of the particle number concentration versus time (determined by integration of eq 12) for three kinds of seeds. A slight decreasing of the particle number concentration can be observed for seeds from bulk aluminum trihydroxide and seeds from the fraction lower than 32 µm.
Figure 3. Evolution of the integral I ) ∫∞0 g(L)/L dL versus time for different seed charges (L in µm).
The unchanged particle number concentration of the seed charge from the fraction 20-50 µm proves that the slight decrease of the particle number concentration for other seed charges was due to an agglomeration phenomenon of very fine particles. According to eq 13, the integral I ) ∫∞0 g(L)/L dL is directly proportional to the precipitation surface area of aluminum trihydroxide. Figure 3 shows that the evolution of this integral versus time is similar to the evolution of particle number concentration. Nevertheless, in all cases the variations of the particle number concentration and of the integral with time are too small, and the effects of the undesirable phenomena cited above can be neglected. Thus, eqs 10 and 14 can be used to determine the kinetic constants of the crystal growth rate expression, especially with seeds not containing fractions of very fine particles. Previous studies have shown that the growth rate of aluminum trihydroxide has a square law dependence on supersaturation (Misra and White, 1970; Halfon and Kaliaguine, 1976; White and Bateman, 1988; King, 1973). Adopting g ) 2, eq 10 gives
1 1 1 1 - ) Kt ) Kt or σ σ0 C(t) - Ce C0 - Ce
(16)
In Figure 4, 1/σ - 1/σ0 is plotted as a function of time at 40, 50, 60, and 70 °C for different bulk seed charges. Straight lines confirm the second-order law and allow determination of the kinetic constant K by a list square procedure. Reproductibility of the results was investigated by carrying out the same experiment three times (seed concentration 800 kg/m3, temperature 50 °C). The
678 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997
Figure 5. Effect of seeding ratio on overall kinetic constant.
Figure 6. 1/σ - 1/σ0 plotted as a function of time for different seed size distributions (L in µm). Table 2. Particle Characterization of Different Seed Charges distribution no.
range size diameter (µm)
average diameter (µm)
1 2 2 bis 3 4 5
L < 32 20 < L < 50 32 < L < 50 50 < L < 71 71 < L < 112 bulk
18 33 41 60 85.8 52.7
solubilities were obtained from the correlation given by Misra (1970)
Ce 2486.7 1.0875 + CNa2O ) exp 6.2106 CNa2O T T
[
Figure 4. 1/σ - 1/σ0 plotted as a function of time: (a) 40, (b) 50, (c) 60, and (d) 70 °C.
kinetic constant K was obtained with a deviation less than 10%, which is a fairly good result. For all experiments, the initial alumina concentrations C0 were determined by sampling after 2 min of seed addition into the aluminate solution, while the equilibrium
]
(17)
Effect of Solid Concentration. Kinetic constant K obtained from the experiments of Figure 4 is plotted in Figure 5 against seed charge for different temperatures: 40, 50, 60, and 70 °C. The resulting straight lines prove the validity of eqs 14 and 15. Effect of Crystal Size Distribution. The effect of crystal size distribution was studied determining the kinetic constant K for seeds of different particle size distribution at temperature T ) 60 °C and seed charge ms/VL ) 400 kg/m3. Table 2 illustrates the distributions used. In Figure 6, 1/σ - 1/σ0 is plotted against time for different distributions. Once again, straight lines are obtained, which allow determination of the kinetic constant K. In Figure 7, K is plotted against I ) ∫∞0 g(L)/L dL. The straight line shows that the model is valid and can be used for the obtaining of the full kinetic law.
Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 679
Figure 7. Effect of the integral I ) ∫∞0 g(L)/L dL on overall kinetic constant.
Figure 9. Plot of predicted alumina concentration values against measured values. Table 4. Concentration of Impurities in Different Kinds of Aluminum
Figure 8. Arrhenius plot of kinetic constant data. Table 3. Reported Activation Energies for the Growth Rate Constant of Al(OH)3 refs (White and Bateman, 1988)
E/R (K)
Misra and White (1970) King (1973) Low (1975) Oberley and Scott (1978) Mordini and Cristol (1982) White and Bateman (1989)
7200 6400 7500 10000 9500 8500
Effect of Temperature. Previous workers showed that the effect of temperature on growth rate follows an Arrhenius relationship. Figure 8 shows the Arrhenius plot, where values of kg are plotted against 1/T for temperatures varying from 40 to 80 °C. The distribution of particle size is the same for all runs and centered on 52.7 µm. The straight line represented in Figure 8 corresponds to the activation energy term E/R. The average value leads to E/R ) 8164 K. This result is in good agreement with different literature values, which are scattered between 6400 and 10 000 K as shown in Table 3. From the straight line of Figure 8, the variation of the kinetic constant kg against temperature can be obtained
kg ) 9.9 × 10-3 exp(-8164/T)
(18)
For temperatures varying from 40 to 80 °C, this relation gives values of the kinetic constant kg in very good agreement with those resulting from the relation proposed by Misra and White (1970). Now, the alumina concentration in the aluminate solution can be estimated as a function of all parameters
impurity (ppm)
Alu 0
Alu 1
Alu 2
Alu 3
Si Fe Cu Mn Mg Cr Ni Zn Sn Ti total
2500 1930 8 0 0 280 0 120 2500 300 7638
1050 3110 23 18 10 3 33 56 2 57 4362
17 10 29 0.5 0.41 0.17 0.26 2.6 0.1 0.5 61
0.88 0.98 0.27 0.05 0.4 0.075 0.26 0.4 0.08 0.19 3.6
(seed charge ratio, seed particle size distribution, temperature, and time) by eqs 14-16. It is then possible to compare the theoretical value of alumina concentration obtained by these equations with experimental values for all experiments. Figure 9 shows that good agreement is obtained with a relative error less than 15%. This is a reasonable limit in view of the experimental errors. Practical Use of the Method. All previous experimental tests show that the precipitation model presented above is verified and the proposed method can give accurate results in a short time. For practical purposes, 300-600 g of seed (of known mass particle size distribution) per liter of aluminate solution can be generally used. The variation of alumina concentration against time is obtained by sampling at equal time intervals over 2-3 h, and the overall kinetic constant K is easily determined by a least-squares technique (one free parameter) according to eq 16. After that, the kinetic constant of crystal growth rate kg is calculated from eqs 14 and 15. Effect of Impurities. Effect of impurities on precipitation is generally accepted in the industry and has been discussed by Halfon and Kaliaguine (1976) and Brown (1988a,b). In this study, the effect of impurities was demonstrated determining the kinetic constant using different qualities of aluminum for the preparation of aluminate electrolytic solutions. Impurities were of inorganic origin. In our case, the main additive in the electrolyte was sodium stannate, which may be present to the extend of 0.5% by weight. The experiments were performed with 400 kg/m3 of seed, a distribution of particle size centered on 52.7 µm (distribution no. 5) and a temperature of 60 °C. Four kinds of aluminum noted Alu 0, Alu 1, Alu 2, and Alu 3 were tested. Impurity content is precised in Table 4. All values are indicated in parts per million.
680 Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 Table 5. Kinetic Constant Values for Different Kinds of Aluminium (T ) 60 °C) kind of aluminium
kinetic constant kg (m7/(kg2 s))
Alu 0 Alu 1 Alu 2 Alu 3 Alu 1 + stannate in solution Alu 3 + stannate in solution
1.1 × 10-13 1.7 × 10-13 2.9 × 10-13 3.2 × 10-13 1.4 × 10-13 2.2 × 10-13
The results in Table 5 are obtained for different qualities of aluminum. Four examples presented in Tables 4 and 5 show that the impurities in the aluminum electrodes and the presence of additives in the electrolytic solution noticeably affect the crystal growth rate of aluminum trihydroxide. The highest impurity content gives the lowest crystal growth rate. Thus, attention must be paid to the choice of aluminum electrode quality, from which the size of the electrolyte regenerator device depends. Conclusions The precipitation of aluminum trihydroxide from aluminate solutions is characterized by very low crystal growth rates. For this reason, a method using high seed charges is developed in order to determine the growth rate kinetic constants in a short time (2-3 h instead of 30-100 h required in the case of classical methods). Under high seed charge conditions, the effects of secondary nucleation, agglomeration, and breakdown can be neglected allowing the obtaining of a simple precipitation model verified by the experiments. Only experimental alumina concentration versus time and the initial mass particle size distribution of the seed charge are required to validate the growth rate law by the model. Especially, the shape factor of seed particles is not required, which constitutes another advantage of this method. The growth rate of aluminum trihydroxide from electrolytic aluminate solutions of an aluminum-air battery has a square law dependence on supersaturation, and the influence of the temperature follows an Arrhenius relation with a high activation energy term E/R of the order of 8164 K. Thus, the results obtained here are in general agreement with those published by many authors (Misra and White, 1970; Halfon and Kaliaguine, 1976; White and Bateman, 1988; King, 1973). Precipitation tests of aluminum trihydroxide in aluminate solutions produced by the dissolution of aluminum electrodes of different qualities in caustic solutions containing or not sodium stannate as additive show that the impurities noticeably decrease the growth rate. Consequently, published values of the kinetic constant kg need to be supported by an accurate description of the impurities contained in the solution. The values of parameters used in this study are of the order of those encountered in the industrial Bayer process. Thus, this method represents an useful and rapid way for the obtaining of growth rate data in different specific situations of the Bayer process. In addition, the method can be applied for other substances characterized by low crystal growth rates. Acknowledgment The authors gratefully acknowledge Renault for financial support during this work.
Nomenclature C(t) ) alumina concentration in the aluminate solution at current time t, kg of Al2O3/m3 Cc(t) ) solution alumina concentration on the crystal surface at current time t, kg of Al2O3/m3 Ce ) alumina solubility, kg of Al2O3/m3 CNa2O ) sodium oxide concentration in the aluminate solution, kg of Na2O/m3 Cs(t) ) seed concentration at current time t, kg of solid Al(OH)3 per m3 of suspension Cs0 ) seed concentration at initial time, kg of solid Al(OH)3 per m3 of suspension C0 ) alumina concentration in the aluminate solution at initial time, kg of Al2O3/m3 E ) activation energy in Arrhenius equation, J/mol g ) exponent in growth rate expression g(L) ) mass particle size distribution of seed charge, 1/m or 1/µm G(t) ) linear crystal growth rate, m/s I ) integral ∫∞0 g(L)/L dL, 1/m k ) index and exponent kg ) kinetic constant in growth rate expression, (m/s)(m3/ kg)g in general and m7/(kg2 s) for g ) 2 K ) overall kinetic constant, (kg/(m3 s))(m3/kg)g in general and m3/(kg s) for g ) 2 L ) particle size, m or µm mk ) kth order moment of the population density ms ) mass of seed, kg MAl(OH)3 ) molecular weight of seed, kg/mol MAl2O3 ) molecular weight of Al2O3, kg/mol N(t) ) total number of particles at current time t R ) gas constant, J/(mol K) T ) temperature, K or °C t ) time, s or min VL ) liquid volume, m3 Vs ) suspension volume (liquid + seed), m3 Fc ) crystal density, kg/m3 σ ) supersaturation, kg of Al2O3/m3 σ0 ) initial supersaturation, kg of Al2O3/m3 φ ) term defined in relation 8 φv ) volumetric shape factor ψ(L,t) ) population density function at current time t, 1/m4 ψ0(L) ) population density function of seed charge, 1/m4
Literature Cited Brown, N. Effect of calcium ions on agglomeration of Bayer aluminium trihydroxide. J. Cryst. Growth 1988a, 92, 26-32. Brown, N. Effect of copper ions on the crystallization of Bayer aluminium trihydroxide. J. Cryst. Growth 1988b, 87, 281-286. Gibbons, D. W.; Gregg, K. J. Closed cycle Aluminium-Oxygen fuel cell with increased mission duration. IEEE 1992, 38-41. Halfon, A.; Kaliaguine, S. Secondary nucleation and growth rate kinetics. Can. J. Chem. Eng. 1976, 54, 160-167. Ilievki, D.; White, E. T. Agglomeration during precipitation: agglomeration mechanism identification for Al(OH)3 crystals in stirred caustic aluminate solutions. Chem. Eng. Sci. 1994, 49, 3227-3239. King, W. R. Some studies of alumina trihydrate precipitation kinetics. Light Met. 1973, 551-556. Misra, C. Solubility of aluminium trihydroxide (hydrargillite) in sodium hydroxide solution. Chem. Ind. 1970, 619-623. Misra, C.; White, E. T. Kinetics of crystallization of aluminium trihydroxide from seeded caustic aluminate solutions; Chemical Engineering Progress Symposium Series 110; New York, 1970; Vol. 67, pp 53-65. Niksa, M. J.; Wheeler, D. J. Aluminium-Oxygen batteries for space applications. J. Power Sources 1988, 22, 261-267.
Ind. Eng. Chem. Res., Vol. 36, No. 3, 1997 681 Randolph, A. D.; Larson, M. A. Theory of particulate processes; Academic Press: New York, 1988. Van Straten, H. A.; Holtkamp, B. T. W.; de Bruyn, P. L. Precipitation from supersaturated aluminate solutions. J. Colloid Interface Sci. 1984, 98 (2), 342-362. Veesler, S.; Boistelle, R. About supersaturation and growth rates of hydrargillite Al(OH)3 in alumina caustic solutions. J. Cryst. Growth 1993, 130, 411-415. Veesler, S.; Roure, S.; Boistelle, R. General concepts of hydrargillite Al(OH)3 agglomeration. J. Cryst. Growth 1994, 135, 505-512. White, E. T.; Bateman, S. H. Effect of caustic concentration on
the growth rate of Al(OH)3 particles. Light Met. 1988, 157163.
Received for review July 12, 1996 Revised manuscript received December 17, 1996 Accepted December 17, 1996X IE960401G
X Abstract published in Advance ACS Abstracts, February 1, 1997.
