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Microporous Vanadium Pentaoxide. 1. Vanadyl Isopropoxide in Microemulsions Sameer D. Desai and E. L. Cussler* Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 Received April 22, 1996. In Final Form: December 20, 1996X Vanadium pentaoxide nanoparticles can be made by adding vanadyl isopropoxide to water contained in a reverse microemulsion of Aerosol OT in toluene. First-order rate constants of this process are on the order of 40 s-1, as measured using a stopped flow reactor. These rate constants are directly proportional to the water concentration and inversely related to the surfactant concentration. While this behavior is inconsistent with earlier theories for reactions in dilute detergent solutions, it is consistent with a reaction limited by alkoxide transport across a thick surfactant layer surrounding the micelles’ water core.
Introduction In this laboratory, we are developing a variety of ways to make microporous vanadium oxides. Because these oxides have surface areas exceeding 100 m2/g, they are of interest in catalysis and electrochemistry. Our specific interest is in using these materials as intercalation cathodes for high-performance lithium batteries. Combined with lithium’s low molecular weight, these materials lead to batteries with unusually high specific energy densities, up to 1140 W h/kg.1 However, because of the slow transport mechanisms, the highest energies can only be achieved at an average specific power, ∼100 W/kg. By making the cathodes microporous, we hope to dramatically increase this specific power. Previous efforts to make microporous vanadium penatoxide have centered on hydrogels, which have the required microstructure. When these hydrogels are air-dried, the structure collapses as a result of capillary forces. To avoid this, earlier workers used supercritical drying and sometimes successfully captured the microstructure.2-4 However, supercritical drying has proved difficult to practice at the industrial scales required to manufacture highperformance batteries. We are currently studying three new ways to make these microporous materials without supercritical drying. First, we can make the materials by phase inversion of vanadium pentaoxide hydrogels. This method, a parallel of the phase inversion used to make reverse osmosis membranes, proceeds by spinodal decomposition. It is accomplished by immersing the hydrogel in a suitable nonsolvent such as acetone. The second method uses detergent-directed self-assembly to make hexagonal and lamellar structures. It finds precedent in the microporous silicas like MCM41, which have been made by workers at Mobil Oil.5 We describe a third method for making microporous vanadium pentaoxide in this paper and its companion. This third method proceeds via the polymerization of vanadyl isopropoxide in a reverse microemulsion formed with the surfactant sodium dioctyl sulfosuccinate (Aerosol OT). A reverse microemulsion is a thermodynamically X Abstract published in Advance ACS Abstracts, February 15, 1997.
(1) Park, H. K.; Smyrl, W. H. J. Electrochem. Soc. 1994, L25-L26. (2) Chaput, F.; Dunn, B.; Fuqua, P.; Salloux, K. J. Non-Cryst. Solids 1995, 188, 11-18. (3) Le, D. B.; Passerini, S.; Tipton, A. L.; Owens, B. B.; Smyrl, W. H. J. Electrochem. Soc. 1995, L102-L103. (4) Salloux, K.; Chaput, F.; Wong, H. P.; Dunn, B.; Breiter, M. W. J. Electrochem. Soc. 1995, L191-L192. (5) Kresge, C. T.; Leonowicz, M. E.; Roth, W. J.; Vartuli, J. C.; Beck, J. S. Nature 1992, 359, 710-712.
S0743-7463(96)00390-3 CCC: $14.00
stable, three-phase system containing water droplets on the order of 5 nm, protected by a surfactant coating and dispersed in a continuous oil medium. We pursued polymerization in this medium to regulate the high reactivity of the alkoxide with water, a result of rapid hydrolysis and condensation. By isolating the polymerization in microdroplets, we hoped to achieve better control of the reaction rate, leading to smaller sizes and higher surface areas. This has already been accomplished with other inorganic oxides, such as silica and titania. The kinetics in this third method can be separated into three steps that occur at very different speeds. The first is the reaction of alkoxide and water in the microemulsion droplets to produce polyions. It takes about 40 ms. The second step, the conversion of these polyions into polymer ribbons, takes about 10 min. The final step, which involves making large clusters from the ribbons, is the slowest step, taking an hour or more. Controlling the properties of the final, microporous product requires analyzing the chemical kinetics of all these steps. In this paper, we analyze only the kinetics of the initial reaction between the alkoxide and the water in the microemulsion. In the alkoxide-microemulsion reaction, we find behavior which is the antithesis of past theoretical predictions for reactions observed in microemulsions. We explore the differences between past theories and the behavior expected here in the next section of the paper. In later sections, we describe our experiments and then test the results against the old and new theories. The results on these initial kinetics supply the starting point for kinetic studies of later steps, given in the companion paper. Theory In this section, we want to predict how the rate of reaction between the vanadyl isopropoxide and the microemulsion varies with process conditions and detergent concentrations. We develop these predictions in three stages. First, we review Smoluchowski kinetics as they apply to our system. Second, we discuss the conventional case of low-detergent concentration, a system which has been investigated in earlier studies. Third, we explore the case of high-detergent concentration, which has not been deeply explored. To begin, we write a mass balance on the alkoxide in a volume containing one micelle. This volume equals n-1, where n is the number concentration of micelles. The amount of alkoxide consumed is related to the flux j1 of alkoxide diffusing to the micelle’s surface © 1997 American Chemical Society
Microporous Vanadium Pentaoxide
dc1
(n1) dt ) -πd j
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2
1
) -πd2k(c1 - 0)
(1)
where c1 is the average alkoxide concentration in the surrounding bulk solution; d is the micelle diameter, and k is an overall mass transfer coefficient for transferring the alkoxide from the solution into the micelle’s interior, where it quickly reacts. Rearranging this equation, we see that the alkoxide disappears by first-order kinetics:
dc1/dt ) -κc1
(2)
where κ is the rate constant
κ ) πd2nk
(3)
This is one of the results called Smoluchowski kinetics. To use it, we must estimate d, n, and k. As a second step, we estimate κ for the case of a microemulsion containing only a small amount of detergent. In this case, we expect inverted micelles to form, with basically all the detergent assembled at the micelle surface (Figure 1a). We expect that the volume fraction φ of the micelles’ water core, which is proportional to the concentration of water per volume microemulsion c2, is given by
(π6)d
φ)n
3
∝ c2
(4)
This implies that essentially all the water is in the micelles. It also implies that the water core has a diameter almost equal to the diameter of the micelle; including this difference does not change the conclusions.6 We also expect that the micelle area per volume a is proportional to the detergent concentration c3, so that
a ) n(πd2) ∝ c3
(5)
This implies that essentially all the surfactant is in the surfaces of the micelles. Equations 4 and 5 are easily combined to give, for example
d ) 6φ/a
(6)
Thus when more water is added to a system with a small, constant detergent concentration, the micelle size d goes up while the micelle concentration n goes down, and the area per volume a remains the same. This behavior has been verified by a variety of equilibrium measurements on dilute detergent solutions.7,8 Our estimates of the kinetics of this dilute detergent case depend on what controls the mass transfer coefficient k. These estimates assume that the chemical kinetics are very fast, so that the overall rates are controlled by diffusion. In the most common limit, k is controlled by diffusion of alkoxide from the bulk solution to the micelle surface. In this case, we may show that k equals (2D/d), where D is the alkoxide diffusion coefficient in the bulk oil.9 As a result, eqs 3, 5, and 6 can be combined to give (6) Desai, S. D. Microemulsion Guided Synthesis of Microporous Vanadium Pentoxide. Ph.D. Thesis, University of Minnesota, 1996. (7) Day, R. A.; Robinson, B. H.; Clarke, J. H. R.; Doherty, J. V. J. Chem. Soc., Faraday Trans. 1 1979, 75, 132-139. (8) Pileni, M.-P.; Zemb, T.; Petit, C. Chem. Phys. Lett. 1985, 118, 414-420. (9) Cussler, E. L. Diffusion; Cambridge University Press: Cambridge, 1984; p 44.
Figure 1. Two types of micelles. In both cases, the micelle core contains essentially all of the system’s water. 2
2Da2 c3 κ) ∝ 6φ c2
(7)
The rate would increase with the square of detergent concentration but decrease with increasing water concentration. In another important limit of dilute detergent, k is controlled not by diffusion in the bulk solution but by permeation across the surfactant clustered at the micelle’s wall. If we assume the micelle shape is constant, then k is a constant, unaffected by micelle size. Now, eqs 3 and 5 lead to
κ ) ak ∝ c3
(8)
The rate varies linearly with detergent concentration but is independent of water concentration. Equations 7 and 8 will each be checked by the experiments described below. We now turn to the third stage in our analysis, the estimation of κ for the case of high detergent concentration. We suspect this may be the case in our experiments, where the volume fraction of detergent is at least six times greater than the volume fraction of water. In this case, we again assume that the chemical kinetics are fast, so that the overall rates are controlled by diffusion. Our basic picture of the solution is also unchanged: we imagine that the micelles still have an aqueous core surrounded by a surface of detergent headgroups. However, because there is so much detergent, not all of it can fit around the micelles. Some is excluded. We postulate that much of this excluded surfactant assembles outside of the micelles, forming a vesicular structure like that shown in Figure 1b. This type of structure, requiring excess surfactant, is very different than the picture of the conventional micelle shown in Figure 1a. The assumption of this alternative structure finds some support in the different structures observed under some microemulsion compositions with Aerosol OT. One example may be the percolation behavior of ionic conductivity seen when the volume fraction of water is increased.10 Since this effect is observed at volume fractions around 7% and is not observed with water self-diffusion, it is believed that droplet clusters form, rather than an open network of channels. In addition, when these microemulsions have equal volumes of water and oil, an ordered (10) Maitra, A.; Mathew, C.; Varshney, M. J. Phys. Chem. 1990, 94, 5290-5292.
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cubic structure of droplets can form, with excess surfactant layered between the water rich regions.11,12 Our estimates of κ in the concentrated limit in Figure 1b differ sharply from those in the dilute case in Figure 1a. First, the volume fraction of water is now assumed to be proportional to the number of micelles
(π6)d
φ)n
3
∝ c2
(9)
where d is a constant. In this concentrated case, adding water to increase c2 and φ makes more micelles; in the dilute case in eq 4, adding water makes a smaller number of larger micelles. In this concentrated case, adding still more surfactant changes neither the number nor the size of the micelles but does increase the thickness l of the surfactant layer around the micelles. If alkoxide diffusion across this wall layer limits growth, then
k)
P 1 ∝ l c3
Figure 2. Results for vanadium isopropoxide oxide reactions. The measurements give the absorption vs wavelength and time.
(10)
where P is this layer’s permeability. By combining eqs 3, 9, and 10, we find
κ)
6φP c2 ∝ dl c3
(11)
This prediction for the concentrated case is the antithesis of eqs 7 and 8 for the dilute case. It too will be checked by the experiments described below. Experimental Section Sodium dioctyl sulfosuccinate (Aerosol OT, Sigma, 99%) was chosen for three reasons: it forms a reverse microemulsion over a wide range of concentrations without a cosurfactant; it is has been well studied; and it does not react with the vanadium precursor. Toluene (EM Science) was filtered through a 0.45 µm filter. Vanadyl isopropoxide (Gelest) was distilled once. The kinetic studies were performed on a Tritech Dynamic Instruments Model SR1A stopped flow apparatus using a quartz tungsten halogen lamp and a Tracor-Northern TN-6500 rapidscan spectrometer. The mixing flow cell was a four-jet tangential mixer with an optical path length of 1.12 cm. For studies below 25 °C, the stopped flow reactor was cooled. Two reagent solutions were prepared for each experiment. The first solution, the colorless reverse microemulsion, contained toluene, water, and the surfactant. After being stirred for 10 min, the solution was filtered through a 0.45 µm filter. The second solution was prepared by combining 200 µL of vanadyl isopropoxide with 22.56 g of toluene in a nitrogen-filled glovebox. This solution also appeared colorless. Before the experiments were begun, both solutions were degassed for 15 min. Equal volumes of the two solutions were mixed in the stopped flow reactor using a 15 psi pressure on the feed. The reaction mixtures had a limited range of compositions. The highest surfactant concentration (20%) was limited by the mixing rate, i.e., by the viscosity. The lower concentration limits of surfactant (10%) and of water (2.6%) were controlled by the phase diagram for the single-phase microemulsion. The upper concentration of water (5%) reflects the fastest times that could be measured accurately. Alkoxide concentrations greater than 0.4% also resulted in reactions too fast to measure, while lower concentrations resulted in unstable microemulsions.
Results and Discussion In this section, we give examples of the data obtained and summarize the kinetic constants observed for the reaction of vanadyl isopropoxide with water in the Aerosol OT microemulsion. We also discuss the variation of these (11) Kotlarchyk, M. Physica 1986, 136B, 274-280. (12) Jahn, W.; Strey, R. J. Phys. Chem. 1988, 92, 2294-2301.
Figure 3. Absorbance showing first-order kinetics. The slope on the figure is the rate constant κ.
kinetic constants in terms of the theory developed above and the aqueous chemistry of vanadium. As detailed in the previous section, our experiments mixed a toluene solution of vanadyl isopropoxide with a microemulsion of water in toluene, stabilized by AOT. The resulting clear solution typically contained 0.4% alkoxide, 3% water, 19% surfactant, and the remainder toluene. The absorbance of this solution was measured every 5 ms at wavelengths from 200 to 900 nm, as shown in Figure 2. We chose to measure the average absorbance between 500 and 520 nm as an indication of the kinetics of the process. This absorbence varies with time as exemplified by the data in the inset of Figure 3. Plots of the absorbance produce straight lines like that in Figure 3, implying a first-order decay of the alkoxide to form hydrolyzed vandium polyions. The slope on this figure is the first-order rate constant, κ, and was reproducible to better than (10%. We measured rate constants at the seven solution concentrations shown in Table 1. Experiments were at least in triplicate. The rate constants observed are fast, implying halflives around 40 ms. Such rapid processes are frequently diffusion controlled. The rate constant varies with the 1.1 power of water concentration, as shown by the solid line in Figure 4. This variation is close to that suggested by eq 11, which is based on the assumption that adding more water makes more micelles of a constant size. This in turn implies that the detergent is present in excess, so that the surrounding solution contains extra surfactant with which to coat the new micelles. The results in Figure 4 seem inconsistent with more established theories of microemulsion structure. These theories suggest that the size of micelle droplets is
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Table 1. Rate Constants for Forming Colloidal Vanadium Polyionsa solution
water
surfactant
alkoxide
κ
A B C D E F G (pH ) 7)
5.01 3.851 3.126 2.63 2.86 3.133 5.01
18.2 18.7 19 19.2 15.6 11.4 18.2
0.428 0.428 0.428 0.428 0.433 0.44 0.428
39 32 24 19 22 29 12
a All concentrations are in weight percent, with the remainder of the solution toluene. The pH was initially 6.2, except in G where it was buffered at pH ) 7. The units of κ are s-1.
Figure 6. Absorbance vs time of the reaction of vanadium isopropoxide with water in a reverse microemulsion at long times. These data show the presence of other chemical changes that occur after the completion of the initial reaction studied examined here.
Figure 4. Rate constant vs water concentration. These data are consistent with the number of micelles increasing with added water.
Figure 5. Rate constant vs surfactant concentration A decreasing rate constant with increasing surfactant concentration is consistent with an increase in thickness of the surfactant layer around the microemulsion droplets. The activation energy of 25 kJ/mol obtained from the data in the inset also suggests a diffusion-limited reaction.
controlled by the ratio of water to surfactant: adding water increases the micelle size and decreases the micelle concentration. If this were true, the rate constant should vary with the reciprocal of the water concentration, as suggested by eq 7 and shown by the dotted line in Figure 4. This does not fit the results. Similarly, our data do not support eq 8, based on a similar picture of micelles but with a different rate-controlling step. The rate constant varies with the -0.9 power of the detergent concentration, as shown in Figure 5. This is close to the inverse proportionality given by eq 11 and, thus, supports the assumption that κ is limited by diffusion across a detergent layer, as suggested by Figure 1b. These rate constants do not support the more conventional
prediction that rate should vary with the first or second power of detergent concentration, suggested by eqs 8 and 7, respectively. These predictions are based on the assumption that adding more detergent produces more micelles. This is the case for dilute detergent solutions but apparently not for the concentrated microemulsions used here. The rate constant shows an Arrhenius temperature dependence, as shown in the inset of Figure 5. The activation energy is 25 kJ/mol, lower than the 50-100 kJ/mol that one would expect for a chemically controlled kinetic process.6 This result supports our view that the reaction between the microemulsion and the alkoxide is controlled by diffusion of the alkoxide through the surfactant film. The experiments in this paper give no direct information on the actual chemical changes occurring. Unfortunately, there is little earlier work on the reaction of vanadium alkoxides and water: what limited work is available has been more concerned with the properties of the gel produced that with the kinetics.13,14 We can, however, speculate on the chemical changes by drawing parallels with the acidification of the orthovanadate ion.15 In so doing, we are implying that each micelle is essentially a small volume of aqueous solution whose properties approximate that of the bulk. On this basis, we assume that our studies involve two sequential chemical steps. The first step is hydrolysis:
VO(OC3H7)3 + 3H2O f VO(OH)3
(12)
This step is presumably fast, faster than the 40 ms measured above. To support this, we note that the exchange rate of ethanol with protonated orthovanadate ions in bulk water at a pH of 7.5 has a characteristic time around 1 ms.16 As a result, we infer that hydrolysis is not the rate-controlling step in our experiments. We assume the second key reaction in our microemulsion is the formation of decavanadate: (13) Hirashima, H.; Tsukimi, K.; Muratake, R. Formation of V2O5 Gels from Vanadyl Alkoxides. In Ultrastructure Processing of Advanced Materials; Uhlmann, D. R., Ulrich, D. R., Eds.; John Wiley & Sons, Inc.: New York, 1992; pp 285-289. (14) Nabavi, M.; Sanchez, C.; Livage, J. Eur. J. Solid State Inorg. Chem. 1991, 28, 1137-1192. (15) Livage, J. Chem. Mater. 1991, 3, 578-593. (16) Gresser, M. J.; Tracey, A. S. J. Am. Chem. Soc. 1985, 107, 42154220.
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10VO(OH)3 f H2V10O284- + 4H+ + 12H2O (13) This species is found after acidification of orthovanadate, typically at vanadium concentrations greater than 10-4 M.15 It has been detected by 51V NMR in gels created by hydrolysis of vanadium alkoxides in excess water.16 Since within the micelles of our system, the water to alkoxide ratio is 100:1 and the vanadium concentration (based on water phase) is 1 × 10-2 M, we suspect the decavanadate ion has also formed. This belief is further supported by a stopped flow study of decavanadate formation, which also showed fast kinetics.17 Thus we believe that the chemical changes in our microemulsion closely parallel those in bulk solution. However, while our kinetics are fast, they are probably controlled by alkoxide diffusion, and not by chemical reactions. We should mention the presence of two other reactions following the one discussed in this paper. One of these reactions has a half-life of a few minutes, while the other one is on the order of an hour. As seen in Figure 6, they are hard to separate using the stopped flow reactor. We (17) Clare, B. W.; Kepert, D. L.; Watts, D. W. J. Chem. Soc., Dalton Trans. 1973, 23, 2476-2478.
Desai and Cussler
detail investigations of these reactions via other experimental methods in the companion paper. Conclusions We have measured the kinetics of vanadyl isopropoxide reacting with water in a reverse microemulsion. The firstorder rate constant is directly proportional to the water concentration and inversely proportional to the surfactant concentration. These results are consistent with the diffusion of alkoxide across the walls of microemulsion droplets surrounded by surfactant. After the alkoxide penetrates into the water core, it rapidly hydrolyzes to form VO(OH)3 and decavanadate ions. These species then react further as described in the companion paper. Acknowledgment. The authors benefited from discussions with M. G. Kulkarni, Ryan Gordon, and Kent Mann. The work was primarily supported by the Defense Advanced Research Projects Agency (Grant 92-05112). Other support came from the National Science Foundation (Grant CTS 96-27361) and from the Department of Defense (Grant DAA 404-95-1-0094). LA960390W
