Ind. Eng. Chem. R e s . 1987,26, 1227-1232 u = local axial fluid velocity, v ( r ) / ( v ) ,dimensionless
U = Graetz function, dimensionless v = local axial fluid velocity, m/s ( v ) = mean axial fluid velocity, m/s X = fluid-phase concentration,(c - c r ) / ( c r r c’), - dimensionless Xw= fluid-phase concentration at channel wall, dimensionless X = mixing-cup concentration, dimensionless ( X ) = mean fluid-phase concentration, dimensionless Y = absorbed-phase concentration, (r - I”)/(I”’ - I”), dimensionless z = axial coordinate, m z1 = axial coordinate, zD/(( v ) r w 2 ) ,dimensionless Greek Symbols p = Freundlich isotherm parameter, dimensionless y = Euler’s constant (0.5772) r = adsorbed-phase concentration, mol/m2 { = coordinate defined by eq 8, dimensionless X = eigenvalue of Graetz function, dimensionless A = partition ratio, (2/rw)(I”’- I ” ) / ( c ” - c’), dimensionless E = radial coordinate, r/rw, dimensionless = psi (digamma) function
+
Superscripts
’ = presaturated ”
value
1227
Literature Cited Abramowitz, M.; Stegun, I. A., Eds. Handbook of Mathematical Functiotw; National Bureau of Standards: Washington, DC, 1964. Coppola, A. P.; LeVan, M. D. Chem. Eng. Sci. 1981,36,967. Drew, T. B. Trans. Am. Inst. Chem. Eng. 1931,26, 26. Fedkiw, P.; Newman, J. AIChE J . 1979,25, 1077. Fedkiw, P.; Newman, J. Int. J. Heat Mass Transfer 1982,25, 935. Jakob, M. Heat Transfer; Wiley: New York, 1949; Vol. 1, pp 451-459. LeVan, M. D.; Vermeulen, T. AIChE Symp. Ser. 1984,80(233),34. Newman, J. “The Graetz Problem”; UCRL-18646, Lawrence Radiation Laboratory, University of California, Berkeley, 1969. Rohsenow, W. M.; Choi, H. Y. Heat, Mass, and Momentum Transfer; Prentice-Hall: Englewood Cliffs, NJ, 1961; pp 139-142. Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984; pp 261-268. Sartory, W. K. Ind. Eng. Chem. Fundam. 1978, 17, 97. Schlunder, E. U. Chem. Eng. Sci. 1977, 32, 845. Schweich, D. AIChE J . 1983,29,935. Vermeulen, T.; LeVan, M. D.; Hiester, N. K.; Klein, G. In Perry’s Chemical Engineers’ Handbook, 6th Ed.; McGraw-Hill: New York, 1984; Section 16. Zwietering, T. N. Chem. Eng. Sci. 1959, 1 1 , 1.
Received f o r review December 5, 1985 Accepted March 16, 1987
= feed value
Knudsen Diffusion in Bidisperse Mixtures of Uniform Spheres Tremitchell Wright,+ Douglas M. Smith,* and D o r o t h y L. Stermer U N M Powders and Granular Materials Laboratory, Department of Chemical and Nuclear Engineering, Uniuersity of New Mexico, Albuquerque, N e w Mexico 87131
Knudsen diffusion of a nonadsorbing gas in model unconsolidated porous media is considered. Monodisperse silica microspheres in the size range 130-400 nm with size standard deviation of 3-4% of the diameter have been fabricated. Porous media has been fabricated by pelleting either a single sphere size or a mixture of known weight fraction and sphere size. Nitrogen effective diffusivities are obtained a t 303 K and 13 kF’a by using a gas permeation experiment. Mean pore radius definitions based upon mercury porosimetry or twice the ratio of pore volume t o surface area were inadequate. Instead, a mean pore radius definition obtained from a version of the parallel pore model described Knudsen diffusion in both monodisperse and bidisperse packings of spheres. A single tortuosity factor of 1.48 was sufficient for all diffusion measurements. This 7 value agrees favorably with previously reported values of 1.47 (experimental) and 1.40 (Monte Carlo simulations) obtained for monodisperse packings. For Knudsen transport in porous media, the transport rate is described by an effective diffusivity which relates the Knudsen diffusion coefficient for a capillary, sample porosity, and tortuosity: De = D k € / T (1) The diffusion coefficient for a straight long capillary of radius r is given by (Knudsen, 1928)
If the pore network of a solid consists of a series of nonintersecting cylindrical pores of a single radius, the application of eq 1 and 2 to describe transport is straightforward. However, if the pores are not uniform, a mean *Author to whom correspondence should be addressed. Present address: Proctor and Gamble, Miami Valley Laboratory, Cincinnati, OH 45247.
0888-5885/87/2626-1227$01.50/0
pore radius, P, must be used in place of the capillary radius, r, in eq 2. This implies that the tortuosity factor, r , is a function of how P is defined for a given solid. In addition to the question of how to define a mean pore radius from a given pore size distribution (PSD), what experimental technique is used to actually measure the PSD will also effect the magnitude of T . For example, the common pore size measurement techniques of mercury porosimetry and analysis of nitrogen desorption isotherms measure the size of the smallest constriction in a pore and not the hydraulic radius (Lowell, 1979). For a value of T for a particular solid to be meaningful, the techniques used to measure the PSD and to calculate r from the PSD must be specified. Many porous solids of engineering interest resemble unconsolidated assemblages of particles. Examples of this type of solid include metal oxide catalyst supports/adsorbents fabricated from sol synthesis techniques and geologic formations such as sandstones. Since the number of dead-end pores is quite small in this type of material and the pores are highly cross-linked and isotropic (Dul0 1987 American Chemical Society
1228 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987
lien, 1979), one would expect that given the proper definition of the mean pore radius, the tortuosity factor should be independent of the pore size distribution. For simple model solids such as random packings of uniform spheres and random packings of bidisperse mixtures of spheres, we address this question of the proper choice of F to minimize the variation of T for transport in the Knudsen diffusion regime.
Background Hoogschagen (1955) has measured tortuosity factors for both monodisperse and bidisperse packings of uniform spheres in the bulk diffusion regime. For a monodisperse packing with c equal to 0.43, T was found to be 1.42. For bidisperse mixtures of spheres with size ratio (R) equal to 0 . 3 , ~increased to 1.52 for a weight fraction of large spheres ( W) equal to 0.5 and to 1.62 W equal to 0.8. Currie (1960) reports measurements of De and T in the bulk diffusion regime for various glass sphere and sand mixtures. For monodisperse packings, T was =1.48 for the glass spheres and -1.60 for the sand particles. For a variety of glass sphere bidisperse packings with unspecified size/weight distributions, T was found to vary between 1.48 and 1.81 for a c range of 0.355 to 0.183. For sand particle bidisperse packings, T was found to vary between 1.67 and 2.17 for a e range of 0.346 to 0.197. Since transport was in the bulk diffusion regime, the pore size of the solids was not important. Although Knudsen diffusion in bidisperse mixtures of spheres has not been experimentally investigated previously, Monte Carlo simulations of Knudsen diffusion in sphere packings have been reported (Abbasi et al., 1983). For a variety of different model porous solids formed by combining sphere packings, in a mathematical sense, the tortuosity was found to vary between 2.5 and 5.0 for c in the region of 0.4. However, the question of how the average pore radius should be obtained for the model porous media was not addressed. The tortuosity factor for Knudsen diffusion in monodisperse packings of uniform spheres has been calculated by using Monte Carlo techniques by Smith and Huizenga (1984). T was calculated to be 1.40 for c equal to 0.386 and 1.72 when the porosity was 0.438 if the characteristic pore size was taken to be twice the ratio of pore volume to surface area:
More recently, Huizenga and Smith (1986) have fabricated random packings of uniform monodisperse spheres with small enough particle size (100-600 nm) that the gas mean free path was sufficiently greater than the pore size and Knudsen diffusion-dominated transport. For a mean pore radius defined by eq 3, the tortuosity factor was found to be 1.47. In order for Knudsen diffusion to dominate, monodisperse microspheres must be fabricated such that the pore space between the spheres is much smaller than the mean free path of the diffusing gas. Strober and Fink (1968) report a technique for the synthesis of monodisperse silica spheres with mean diameter on the order of 1 pm. Tetraalkyl silicates are reacted with water and ammonium hydroxide in a low molecular weight alcohol cosolvent. The silica ester is first hydrolized, and the resulting silicic acid condenses to form spherical amorphous silica particles with a narrow size distribution. The sphere si72 depends on the ester molecular weight, alcohol molecular weight, and the water and ammonia concentrations. The ammonia serves as both a catalyst for the hydrolysis and to control the degree of agglomeration by changing the double layer
c
I
e
1
Figure 1. TEM micrograph o f 229-nm-diameter spheres (X97.50).
thickness around the growing particles. Huizenga and Smith (1986) have studied the TEOS-H,O-NH,OH-EtOH system and produced silica spheres in the size range of 100-600 nm with a typical size standard deviation of 743%.
Experimental Section The silica sphere growth scheme reported by Huizenga and Smith (1986) has been changed to produce narrower size distributions. Modifications to the growth scheme include the use of higher quality reagents, lower TEOS concentration, and more control of reactant mixing. Tetraethyl orthosilicate (technical grade, Aldrich Chemical Co.) was distilled and combined with approximately onehalf of the solvent (reagent-grade ethanol). The desired quantities of water (distilled) and ammonium hydroxide (14.5 M reagent grade, Fisher) were combined with the remaining ethanol. A 250-mL Erlenmeyer flask containing the water, ammonium hydroxide, and ethanol was placed on a Eberbach platform shaker operating a t 60 Hz. After premixing, the ethanol/TEOS mixture was rapidly added tr, the reaction mass. After the invisible formation of silicic acid, the onset of condensation was indicated by an increased opalescence of the mixture starting 1-3 min after the EtOH/TEOS addition. After this initial transition, a turbid white suspension appears within several more minutes. Complete details concerning the sphere growth scheme are given elsewhere (Wright, 1985). After 24 h, a sample of the sphere slurry was analyzed with a Hitachi 600 transmission electron microscope. The mean size and size standard deviation were determined from analysis of TEM micrographs containing several hundred spheres. Figure 1 is a micrograph of 229-nmdiameter spheres with a standard deviation of *11.6 nm. The high degree of size and shape uniformity is readily apparent. Particles which appear to be not spherical are actually several overlapping spheres. The sphere slurry was dried by using a Ruchi Rotovapor R110 rotary vacuum
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1229 Table I. Sphere Reaction Conditions and Physical Properties ammonia, M
water, M
diameter, nm
m2/g
He density, g/cm3
TEM area,
TEOS,M
BET area,
m2/g
b
0.108 0.280 0.280
1.o 0.55 2.0
2.4 12.0 4.8
182 f 4.2 800 f 11.4 402 f 17.8
3 1.56 22.14 14.19
2.06 2.09 2.1 1
20.7 9.1 6.05
1.53 2.42 2.11
I. 0.50
-
0.m-
om ! 0
0.1
0.1
0.3
0.4
0.5
0.8
0.7
0.8
0.S
1I
W
Figure 3. Variation of porosity for bidisperse sphere mixtures.
Figure 2. T K \ l micrograph
of
a single sphere (X325000).
system operated at 357 K. The surface area of the silica powder was determined by using nitrogen adsorption at 77 K (Quantasorb flow surface area analyzer) and BET theory (Lowell, 1979). The true density was determined from helium displacement measurements made by using a Quantachrome micropycnometer. The reaction conditions and physical properties of the three different sphere sizes used in this work are summarized in Table I. Although numerous combinations of ammonia and water concentration will result in the same sphere size, the standard deviation of size and surface morphology will be different. Values presented in Table I were selected from the results of many sphere growth experiments with the intention of minimizing size deviation. We should note that the relative variation in size for all spheres used in this work (-3-4%) is less than the spheres illustrated in Figure 1. Surface areas, as measured via BET analysis, are significantly greater than what is. expected based on the TEM diameter. The magnitude of the difference between the BET and TEM surface areas does not appear to be a function of sphere size (see Table I). In order to determine if this increased area is a result of internal porosity or roughness on the sphere external surface, a high-resolution TEM study was conducted. The surfaces of single spheres on a carbon film were studied by using a JEOL JEM-2000FX 200-kV TEM. Figure 2 is a micrograph of a single sphere a t a magnification of 5000o0. Surface roughness is readily apparent on a very small scale (“2 nm). Also, no internal porosity is apparent. The helium densities that we measure and report
in Table I are very close to those reported for amorphous silica (2.1-2.2 g/cm3) (ner, 1979). In order to produce model porous media for diffusion measurements, mixtures of two monodisperse sphere sizes were added to an agitated flask in the desired weight proportions. After 30-min agitation via a magnetic stirrer, the powder mixture is formed into pellets (0.457-cm 0.d. X 1.27-cm length). Pellet pressing was undertaken a t 70 MPa (loo00 psia) by using a hand press and stainless steel die. Earlier work using a single sphere size demonstrated that the pellet porosity is effectively independent of pelleting pressure over the pressure range 7-70 MPa (Huizenga, 1984). T o minimize possible problems with axial porosity variation, powder was added stepwise to the die between pressings. Typically, 20-35 presses per pellet were used. Following pellet formation, the pellet porosity was determined from the pellet volume, weight, and powder true density. For selected samples, mercury porosimetery was conducted over the pressure range 0-210 MPa by using a Quantachrome Autoscan-33 continuous scanning p o r e simeter. The contact angle for our silica spheres and mercury is 138.7O as measured by the Quantachrome Corp. Bidisperse mixtures of uniform spheres should exhibit lower porosity because the relatively small spheres tend to fill voids inaccessible to larger spheres. Figure 3 is a plot of porosity (e) as a function of the weight fraction ( W) of larger spheres in the mixture for both sphere size ratios that we use (R = 0.44 and R = 0.33). As expected, a minimum in porosity occurs a t intermediate W values. For monodisperse packings, c is in the range 0.35-0.4, as is commonly observed for random packings of large spheres (Haughey and Beveridge, 1969). In addition to our experimental c values, theoretical predictions of t vs. W are calculated by using the model of Ouchiyama and Tanaka (1981). This model requires that the value for the porosity of a monodisperse packing be fixed. T o compare theory and experiment, we assume that this monodisperse packing porosity is the average of the observed porosity for W equal to 0 and 1 for that particular R value. For a R value of 0.44,agreement between theory and experiment is excellent. This would seem to indicate that complete mixing of the two sphere sizes occurs before pelleting. For R equal
1230 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Table 11. Reproducibility Experiments and BidisDerse Random Packings W , wt W , wt sphere Dele, cm2/s fract fract size. nm 0.2 1.0 132 0.067 0.2 0.067 1.0 132 0.184 0.4 1.0 402 0.4 0.181 1.0 402 ~
for Monodisperse sphere size, nm 132/300 132/300 132/300 132/300
Dele,
cm2/s 0.107 0.111 0.099 0.121
to 0.33, agreement with theory is quite poor. This may be attributed to the larger difference between the monodisperse porosities at W equal to 0 and 1 as compared to the 0.44 mixtures. The Ouchiyama and Tanaka model requires that the end-point porosities be equal. Nitrogen effective diffusivities have been measured at 303 K by using a flow permeation experiment. Pellets were sealed into a tube, and a pressure gradient was imposed across the sample such that the upstream pressure was -13 kPa and the downstream pressure was less than 13 Pa. From the pressure drop, volumetric flow rate, pellet length, and pellet cross-sectional area, De was calculated. Complete details of the effective diffusivity measurement scheme are given by Wright (1985). Past work with monodisperse sphere packings and a range of gases/ pressures has shown that Knudsen diffusion is dominant and no measurable surface transport exists a t this combination of temperature, pressure, diffusing gas, and pore size (Huizenga and Smith, 1986). Results In order to assess the reproducibility of our pellet fabrication and effective diffusivity measurement schemes, a series of duplication experiments have been conducted. In each experiment, several pellets were fabricated from the same silica powder, or powder mixtures, and De was measured. The results of these experiments are presented in Table 11. With the exception of the W = 0.4 pellets, agreement is within 3%. As given by eq 1 and 2, a plot of DeIC vs. the mean pore radius should be linear with slope inversely proportional to r if the value of r is constant for the various solids studied. In addition, extrapolation of the data should pass through the origin. For a bidisperse mixture of spheres, the ratio of twice the pore volume to surface area is given by 2 t rl r- = -3 (1 - t ) (1 - W + W R )
20
0
60
40
80
100
0
MEAN PORE RADIUS nm
Figure 4. Effective diffusivity vs. mean pore radius when i; is calculated by using eq 4.
9
0.25-
2rE-w2E
0.200.15-
I
//
a
! W
E W
e/‘,
0.10-
e/
45 /A?
I:
/
Pr*r.nl
Work, bldlsp.rra
Prasenl Work. monod1sp.r..
0.05-
0 H u h n p a , monodlspwsa
0.00 1
Figure 5. Effective diffusivity vs. mean pore radius as measured with mercury porosimetry.
bidisperse pellets. The mean pore radius was calculated from the pore volume distribution by using (Smith 1970) P=
s,”
r/V, dV
(5)
(4)
For porous solids fabricated from monodisperse powders (i.e., W = 0 or W = l),eq 4 reduces to eq 3. Figure 4 is a plot of our measured D e / t vs. P as calculated by using eq 4. In addition to the monodisperse and bidisperse ( R = 0.33 and R = 0.44) data from this work, the nitrogen diffusion results of Huizenga and Smith (1986) for monodisperse packings are presented. Dele vs. p is well represented by a straight line for monodisperse packings. In addition, extrapolation of a “best-fit’’ line for the monodisperse data passes very near the origin. The tortuosity factor of 1.53 calculated from the slope of the best-fit line agrees quite well with the r value of 1.47 reported by Huizenga and Smith (1986) for a wide range of gases. In contrast, the bidisperse packing results deviate considerably from both straight line behavior and the monodisperse packing results. Bidisperse packing results are consistently above the monodisperse results, indicating that the role of the smaller pores associated with the small spheres is overemphasized in eq 4. Pore size distributions were obtained from mercury porosimetry for a limited number of monodisperse and
Effective diffusivities are plotted in Figure 5 vs. r determined from eq 5. The monodisperse packing is well represented by a straight line which passes very near the origin. A tortuosity factor was calculated to be 1.34 which is significantly less than using eq 4. However, this discrepancy was expected since porosimetry measures the size of the pore constrictions and not the “true” average pore size. For consolidated porous materials with more complex pore networks, one would expect this difference between mercury porosimetry and twice the ratio of pore volume to surface area to be even greater. For the limited number of bidisperse packing data points, the data are adequately described by a straight line, but analysis of the line’s slope indicates a r of 1.08. A tortuosity factor this low is not satisfactory for a solid, with t in the range 0.3-0.4, since this implies that the pores are almost all aligned in the direction of diffusion. Scanning electron microscope observations and physical insight both indicate that this is not possible. The low 7 is instead the result of the fact that the pore size is underpredicted when using mercury porosimetry and the “over-weighting”of the smaller pores in eq 5. This overweighting occurs because toroidal filling
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1231 n
10
I I
0 1
’1
/
P
f
0.15-
2
Y e_
0
w
6 5
0.10-
0 ,
4// 0.01//
0.00
If the extension of our work to unconsolidated materials with more particle sizes, wider particle size range, and other porosities is justified, then eq 7 may be used to predict the mean pore size from a particle size distribution and the tortuosity factor may be taken to be 1.44-1.50.
Conclusions The study of the Knudsen diffusion of nonadsorbing gases in model unconsolidated porous solids has been extended to bidisperse mixtures of uniform microspheres. Mean pore radius definitions based on mercury porosimetry and twice the ratio of pore volume to surface area were found to be inadequate. When the mean pore radius was obtained from a version of the parallel pore model, effective diffusivities from this work for both monodisperse and bidisperse packings, as well as previously published monodisperse packing results, were well correlated. A single tortuosity factor value of 1.48 described all results satisfactorily from this mean pore radius definition. This T value agrees with previously reported values of 1.47 (experimental) and 1.40 (Monte Carlo simulations) obtained for monodisperse packings.
M 40
80
60
100
120
MEAN PORE RADIUS nm
Figure 6. Effective diffusivity vs. mean pore radius when P is calculated by using eq 6.
effects appear as small pores and the presence of large pores are masked by network/percolation effects. The parallel path or parallel pore model is often used to describe the pore network in porous solids (Satterfield, 1970). The basic assumption is that the solid contains a network of parallel, nonintersecting cylindrical pores with a size distribution which matches the observed PSD. Although this is certainly not how the actual pore structure in unconsolidated random packings of spheres appears, we have calculated an average pore radius expression by using this concept. However, the measured PSD is not used. We assume that Knudsen diffusion occurs through a network of cylindrical pores of radius P. The total flux through this equivalent pore is equal to the sum of the fluxes through pores of radius calculated by using r1 and r2 in eq 3. By requiring that the total volume and total cross-sectional area of our equivalent pores be equal to the total of the small and large pores, we obtain
We should note that r calculated from eq 6 is not equal to twice the ratio of pore volume to surface area except in the limit of W equal to 0 or 1. Measured values of De/€ are plotted vs. f calculated by using eq 6 in Figure 6. It is quite apparent that agreement between all monodisperse and bidisperse data and a single straight line is satisfactory. The tortuosity factor calculated from the slope of the line in Figure 6 is 1.48 which is in agreement with the value of 1.47 given for monodisperse sphere packings by Huizenga and Smith (1986). The excellent agreement between eq 6 and the measured effective diffusivities is remarkable since no parameters other than the measured porosity and particle size distributions are used. The reasons why a parallel pore model, which assumes no connection between pores, works so well for a porous solid with a high degree of pore interconnections are not clear. SEM examination and pellet porosities both indicate that complete mixing of the small and large spheres has been obtained. The model used to develop eq 6 and described Knudsen diffusion in unconsolidated materials can be generalized to
C Wiri3 E
3 (1 - t)
i=l
N i=l
(7) Wiri2
We thank Dave Seltzer of the Quantachrome Corp. for providing mercury contact angle measurements and Dr. A. K. Datye for the high-resolution TEM analysis. Support for T. Wright has been provided by a GEM fellowship. Additional funding was provided by the University of New Mexico’s Research Allocations Committee.
Nomenclature De = effective diffusivity Dk = Knudsen diffusivity f = sticking coefficient M = molecular weight r = capillary radius F = mean pore radius rs = sphere radius rl = radius of small spheres r2 = radius of large spheres ri = radius of the ith particle component R = sphere size ratio, r 1 / r 2 R = gas constant ?= temperature V = pore volume Vt = total pore volume W = weight fraction of large spheres Wi = weight fraction of the ith particle component Greek Symbols 6 = ratio of BET surface area to geometric (TEM) surface area t = porosity T = tortuosity
Literature Cited Abbasi, M. H.; Evans, J. W.; Abramson, I. S. AIChE J . 1983,29,617. Currie, J. A. Br. J . Appl. Phys. 1960, 11, 318. Dullien, F. A. L. Porous Media, Fluid Transport and Pore Structure; Academic: New York, 1979. Haughey, D. T.; Beveridge, G. S. G. Can. J . Chem. 1969, 47, 130. Hoogschagen, J. Ind. Eng. Chem. 1955, 47, 906. Huizenga, D. G. M.S. Thesis, Montana State University, Bozeman, 1984.
Huizenga, D. G.; Smith, D. M. AIChE J. 1986, 32, 1. Iler, R. K. The Chemistry of Silica; Wiley-Interscience: New York,
N
2 r=---
Acknowledgment
1979.
Knudsen, M. Ann. Phys. 1928,28, 73. Lowell, S. Introduction to Powder Surface Area; Wiley-Interscience: New York, 1979.
1232
I n d . Eng. Chem. Res. 1987, 26, 1232-1234
Ouchiyama, N.; Tanaka, T. Ind. Eng. Chem. Fundam. 1981,20,67. Satterfield, C. N. Mass Transfer in Heterogeneous Catalysis; MIT Press: Cambridge, MA, 1970. Smith, J. M. Chemical Engineering Kinetics, 2nd ed.;McGraw-Hill: New York, 1970. Smith, D. M.; Huizenga, D. G. Proceedings of the 10th IASTED Symposium on Applied Modelling and Simulation; ACTA Press:
New York, 1984; p 13. Strober, W.; Fink, A. J . Colloid Inter. Sci. 1968, 26, 62. Wright, T. M.S. Thesis, University of New Mexico, Albuquerque, 1985.
Receiued for reuiew March 25, 1986 Accepted March 19, 1987
Stoichiometry of Ferrous Nitrosyl Complexes David Littlejohn and S. G. Chang* Lawrence Berkeley Laboratory, MIS 7O-llOA, Applied Science Division, University of California at Berkeley, Berkeley, California 94720
T h e ferrous ion t o nitric oxide ratio has been determined for the class of compounds Fe"(L),(NO),, where L = H20, citrate, IDA, NTA, and EDTA. All compounds studied were found to have a maximum ferrous ion to nitric oxide ratio of 1:l. In addition, the equilibrium constant for the binding of nitric oxide to Fe"(H,O), was determined to be 470 M-l a t pH 3 and 25 O C . A number of ferrous chelates rapidly and reversibly react with nitric oxide in aqueous solutions (Littlejohn and Chang, 1982) and have been proposed as agents to aid in the removal of nitric oxide from power plant flue gas streams (Chang et al., 1982). The strength of the ferrous ion-nitric oxide bond is highly dependent on the chelate used in the complex (Griffiths and Chang, 1986). There has been some discrepancy in the literature about the stoichiometry of a number of ferrous nitrosyl complexes. McDonald et al. (1965) studied several ferrous nitrosyl complexes by electron spin resonance and found both mono- and dinitrosyl complexes, depending on the ligand involved. Hishinuma et al. (1979) measured the absorption of a diluted nitric oxide gas stream passed through a solution containing Fe"(EDTA), where EDTA = ethylenediaminetetraacetate, and found a mononitrosyl complex. Pearsall and Bonner (1982) report evidence for a dinitrosyl complex, as well as mononitrosyl complex, in ferrous ion solutions with an acetate buffer. Ogura and Ishikawa (1983) and Ogura and Watanabe (1982) investigated the complexation of nitric oxide with Fe"-aminocarboxylic acid complexes by electrochemical and spectroscopic means and found Fen-to-NO stoichiometries of 1:2 for the EDTA complex, 1:2 and 1:l for NTA (nitrilotriacetate) and IDA (iminodiacetate) complexes, and 1:l for EDDA (ethylenediaminediacetate) and glycine. Because of the conflicts about the stoichiometry in the literature, we decided to study a number of ferrous nitrosyl complexes that have potential for use in flue gas scrubbing systems. We have investigated the stoichiometry of the binding of nitric oxide to Fer1(H20),,Fe"(cit) (where cit = citrate), Fe"(IDA), Fe"(NTA), and Fe"(EDTA) by measuring the absorption of nitric oxide by solutions of these compounds. Experimental Section Nitric oxide (Matheson, C.P.) was purified by three trap-to-trap distillations in which the first and last portions were discarded each time. The purified nitric oxide was stored a t liquid nitrogen temperature until use. Reagent-grade chelates and ferrous ammonium sulfate were used to prepare the ferrous chelate solutions. We believe the ammonium and sulfate ions do not appreciably influence the chemistry of this system. Prior to addition of the ferrous salt, the chelate solutions were thoroughly degassed on a vacuum line by repeated evacuation and cavitation. The bulb containing the solution was filled with argon, and 0888-58S5/87/2626-1232$01.50/0
the ferrous salt was added. After addition of the ferrous salt, the solutions were treated with concentrated HC1 or NaOH to obtain the desired pH under an atmosphere of Ar. The solutions were then degassed once more. An evacuated bulb of known volume was filled to the desired pressure of nitric oxide and then expanded into the evacuated bulb containing the ferrous chelate solution. Once the pressure had stabilized and was recorded (approximately 20 s), the solution was vigorously stirred. The pressure was monitored until it stabilized again, generally about 15 min. All pressure determinations were made with a Model 270 Baratron pressure gauge. After correcting for the water vapor pressure, the observed pressure drop was used to calculate the amount of nitric oxide absorbed by the solution. The solubility of nitric oxide in aqueous solutions (Armor, 1974) (1.95 X M/atm for pure water) was taken into account to determine the amount bound to the ferrous chelates. All work was done at 25 "C. Results and Discussion Reference experiments were done with nitric oxide expansions into water and sodium sulfate solutions to determine the accuracy of the method. These experiments yielded nitric oxide solubilities that were in good agreement with values given by Armor (1974). Buffers were not used for pH control because of the possibility of interference with the ferrous chelate complex. Fe"(H,O), + NO. The ferrous ion concentration used ranged from 1.15 X to 5.0 x M, corresponding to ionic strengths of = 0.08-0.20. The solution pH was 3.3 in all runs. At a nitric oxide pressure of 1 atm, the hydrated ferrous ion did not completely bind with nitric oxide, due to the relatively small equilibrium constant for binding (Chang et al., 1982; Kustin et al., 1966). After correcting the solubility of nitric oxide, the amount of nitric oxide absorbed was used to calculate the equilibrium constant, assuming 1:1Fe-to-NO stoichiometry. For K,, = [Fen(H20)5NO]/[Fe"(HZO),][NO,], we obtained a value of 470 f 20 M-l, in excellent agreement with earlier results (Chang et al., 1982; Kustin et al., 1966). It does not appear that Fe11(H20)6forms a dinitrosyl under these conditions, since the temperature jump experiments showed no evidence of a two-step decomposition (Chang et al., 1982; Kustin et al., 1966). Fe"(EDTA) + NO. All work was done with a ferrous ion concentration of 2.0 X M and an EDTA concen0 1987 American Chemical Society
