SURFACE DIFFUSION OF CARBON DIOXIDE ON ALUMINA J
.
B
.
R I V A R 0 L A' A N
D J
.
M
.
SM I T
H , Uniaersity of California, D a w , Calif.
To study the significance of surface diffusion on a solid catalyst, the diffusion of carbon dioxide through boehmite (A1203.HZO) pellets was measured at 25" C. and 1 atm. The surface contribution was separated from the observed total diffusion rate b y evaluating the pore volume contribution from a random pore model. This model was also used to develop a relationship among the surface diffusion rate, the diffusivity, D, and the geometrical properties of the porous media. The results indicate that surface diffusion increases with pellet density, and for high-density pellets i s as important as pore volume diffusion b y Knudsen and bulk processes. The value of D, for carbon dioxide on boehmite was found to b e about 0.5 to 0.9 X 1 OP4 sq. cm. per second.
HE transport of mass in porous media occurs in many Tenginerring problems. In one area, solid catalytic reactions, the surface area of the porous catalyst is comparatively large with respect to the pore volume. For such systems the migration of adsorbed molecules on the pore \valls may be significant. If this is the case, surface diffusion should be considered along with volume diffusion (bulk and Knudsen types) in the pores when evaluating the total transport rate. There have recently appeared several papers on experimental volume diffusion in the pores of catalytic materials--~ for example, the measurements of \Veisz and Sch\vartz ( 7 7 ) on a variety of catalyst samples and those of \Vakao and Smith (70) on a model for volume diffusion in alumina pellets. Similar information is not available for surface diffusion on common catalyst supports. The work of Flood and Tomlinson ( 6 ) and Carman and Raal (4) established the existence of surface flow. Barrer and colleagues (7-3) have presented theory and data for the surface diffusivity of several gases. T o calculate surface diffusivities from such data it is necessary to know the pore structure or use a representative model of the porous solid. Barrer ( 7 ) devised a transient method Xvhich is applicable for Knudsen volume diffusion and for a porous solid which can be described by a parallel pore model. ,4t room temperature and for Vycor glass (a material of low porosity and very small pores), the surface contribution was comparable to volume diffusion for many gases. In the present work it was desired to study surface diffusion on a commonly used solid catalyst or carrier. T h e diffusion of carbon dioxide on alumina (boehmite?A1203.H20, was used) a t 25' C. was chosen. \Vith pellets made from boehmite powder the bidisperse pore size range results in both Knudsen and bulk types of volume diffusion. Also it has been shown (70) that alumina cannot be represented by a parallel, capillary concept; instead, a random pore model predicts well volume diffusion rates. Hence, Barrer's method was not employed in the present work. Instead, steady-state diffusion rates were measured for both components of the carbon dioxidehydrogen system at 25' C. and 1-atm. pressure. Then the random pore model was used to evaluate the surface diffusivity from the data. Alumina powder has the advantage that pellets of different densities, and hence different surface areapore volume ratios, can be prepared. Data were measured for pellets of three different densities to see if the theory would
1
Present address. Faculty of Science, University of Cuyo, Sail
Luis, Argentina. 308
I&EC
FUNDAMENTALS
account for the increase in surface diffusion expected for the higher density pellets. Measurements were also made with the same pellets to determine the diffusion rates of hydrogen and nitrogen. T h e data indicated that surface diffusion was not measurable in this system. Hence these results could be used to check the applicability of the random pore model-that is, volume diffusion rates were computed from the theory (70) and compared with the data. T h e random pore model contains no unknown parameters, so that predicted and observed data can be directly compared. This cannot be done for the parallel pore model, because the tortuosity factor is involved, and this must be evaluated experimentally Apparatus
Figure 1 is a schematic drawing of the equipment, which consisted of a conventional constant-pressure, countercurrent diffusion apparatus [similar to that employed by LYakao (70)]. T h e pellet was macie by compressing boehmite powder into a stainless steel ring (0.d. 15 mm., i.d. 9.53 mm., height 6.35 mm.) as shown in the inset figure. The gases leaving the diffusion cell, DC? were analyzed with a Cow-Mac, eightfilament (30-S geometry), thermal conductivity cell, TCC. Pure gases from cylinder 1 or 2 were used as reference substances. Flow rates leaving the system were measured with soap film meters, S F M l and SFM2. T h e third meter, SFM3, \vas used for calibration. T h e cell was calibrated after each run by closing valves V9, V70, and V6 to bypass the cell. Valve V5 is opened to supply the desired flow rate of hydrogen and valves VI7 and V72 are used to regulate the rate of gas (either carbon dioxide or nitrogen) to give a flow corresponding to the previously measured diffusion rate through the pellet. The cell \\as immersed in a constant temperature bath, maintained a t 25' C., and operated at constant current (110 to 150 amperes). T h e arrangement of the apparatus was such that only the diffusion rate of gas 2 into gas 1 could be measured at one time. T o obtain counterdiffusion data. the lines connecting the cylinders were interchanged. By using but one thermal conductivity cell and operating in this fashion, it was possible to maintain the mole fraction of gas 2 on the face of the pellet close to unity. Electrolytic grade hydrogen was passed first through Deoxo, 3. and silica gel, 4. units to remove oxygen and water. T h e carbon dioxide and nitrogen had quoted, minimum purities of 99.5 and 99.6%. respectively. Prior to a run the pellet, in place in the apparatus, was degassed from both sides by evacuation for one hour. Following this a slow rate of n;trogen was passed through the pellet for a second hour. Finally, the pellet was again evacuated from both sides for 3 hours. .4 longer degassing sequence showed no change in diffusion rates.
Table I?
-0
-0
Figure 1.
Properties of Boehmite Powder Particle Size Distribution Microns 70h e r
U. S.std. sieve 100 200 325
194 74 44
87 48 35
Data from Sorptometer (Pretreatment: Heating for 8 hours at 350" C. in Stream of Helium) Surface area. S , = 324 sq. m./g. Pore volume. V q = 0.38 c c . / g . .4verage pore radius. 2V,/S, = 23 A.
Schematic flow diagram of apparatus
1 . Hydrogen cylinder 2. Carbon dioxide or nitrogen cylinder 3. Deoxo unit 4. Silica gel CFM I , CFMZ. Capillary flowmeters DC. Diffusion cell M. Manometer SFMI, SFMZ, SFM3. Soap fllm meters T I , T2. Liquid traps TCC. Thermal conductivity cell VI-V12. Regulator valves
1 a.
Diagram of diffusion cell
Table II.
Pore Geometry of Boehmite Pellets
Boehmite, A1203.H20.
Pellet No. 0
1 2
Pellet diameter 3 / 8 inch; thickness 1 / 4 inch; volume 0.452 cc.
Macropores Au. Pellet Void pore Density, fraction, radius, PB co ea,A .
0.79 1 00 1 15
0.33 0 20 0 12
1710 575 348
Particle Density, pp
1.18 1 25 1 31
~ Micropores _ _ Au. Void pore fraction, radtus, t i t , A.
0.292 0 37 0 426
18.2 18 2 18 2
I.
Inlet gas 0. Outlet gas P. Pellet T. Teflon tube
Properties of Pellets
Boehmite Powder. T h e alumina powder was a spraydried. precipitated alumina. from the American Cyanamid Co., of the monohy-drate (boehmite) form. Its properties are given in Table I . The data on particle size distribution were supplied by the -4merican Cyanamid Co. and the Sorptometer data were measured with a Perkin-Elmer Sorptometer by adsorbing nitrogen from a helium stream at liquid nitrogen temperature. For the diffusion measurements the only pretreatment of the pellets was the degassing procedure described in the previous section. Prior to the Sorptometer measurements the powder \vas degassed by passing a slow stream of helium over the polvder at 350' C. for 8 hours.
The desorption curve from the Sorptometer measurements gave data for volume adsorbed as a function of partial pressure of nitrogen in the helium stream. From these data the pore volume distribution as a function of pore size was calculated using a modified form of the Kelvin equation, as described by Pierce (8). The results, shown by the solid line on the left side of Figure 2, indicate a micropore distribution peak a t about 20 A . T h e Wheeler average pore radius, 2 V 0 / S 0 , given in Table I is 23 A . ? in good agreement with the pore volume distribution curve. Pellets. Two pellets were prepared a t each density level and diffusion measurements were carried out on both pellets. As indicated in Table IV. the densities were closely reproducible. Average values are given in the second column of Table 11. T h e two pellets of each density level were broken,
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309
_
mixed, and heated a t 350” C. in helium for 8 hours and their macropore properties were determined in a mercury porosimeter. T h e maximum pressure of the apparatus (5000 p.s.i.a.) limited mercury penetration to pores of equivalent cylindrical radii greater than about 150 A . The third column of Table I1 gives the void fraction of the sample in pores larger than 150 A. -that is, the macropore void fraction. T h e average macropore radii were calculated from the expression
Table 111. Pellet ‘Yo.
0-a
0-b
T h e data needed to use this equation are the macropore volume-pore size distribution. This information was calculated from the porosimeter measurements and the resultant distributions are shown by the three curves on the right side of Figure 2. T h e curves on this figure show good coincidence between the micropore and macro branches. Previous work (9) has shown that the pelleting process affects the micropore structure of the powder only at the higher pellet densities, and then only to a small extent. This is shown in another way by considering the density of the particles in the pellets. This quantity is equal to the density of the pellet. p B . divided by 1 - e, (fifth column of Table 11). T h e small increase with density is probably due to a slight crushing of the particles in preparing the pellet. Such small changes in density may, however, have an appreciable effect on diffusion rates. T h e micropore void fraction, ei. is equal to the volume of the micropores, 0.38 cc. per gram (Table I ) , multiplied by the density of the pellet. p B . T h e average pore radius of the micropores is given in the last column of Table 11. It was calculated from the micropore size distribution given in Figure 2 and the equation 1 “1 dC = adVi (2)
VI
1
T h e result, 18.2 A , , is not much different from the Wheeler average radius. 23 A. The averages defined by Equations 1 and 2 have been shown (9) to be the correct values for evaluating mean Knudsen diffusivities in macro- and micropores. This information is necessary in the application of the random pore model (Equations 8 and 15). Results
Counterdiffusion rates were measured a t three flow rates for each pellet. Typical results are illustrated in Table 111. In Table I V all the data are summarized in the form of ratios of diffusion rates, LVH2/.t-s2and .VH2/’.V~oz.which were obtained by averaging the three values, each a t a different flow rate. If the diffusion occurs only in the volume of the pores. by either bulk or Knudsen mechanisms, the ratio of the constant pressure-counterdiffusion rates is equal to the inverse ratio of the square root of the molecular Lveights of the two gases. These so-called, theoretical diffusion ratios are also tabulated for each system in Table I\’. T h e experimental H2-Ne results agree \cell with the theoretical ratio 3.73. This agreement lends confidence to the experimental apparatus and shoxvs that surface diffusion does not occur for this system. In contrast: the experimental ratio .VH2/.V~o, is significantly less than the theoretical value. This shows that the total tracsport rate for carbon dioxide is increased because of surface diffusion. T h e experimental ratio would be expected to vary with pellet density, because of variation in the ratio of surface to pore volume. T h e observations show a relative increase in carbon dioxide diffusion rate (decrease in ratio) as the density increases. 310
l&EC
FUNDAMENTALS
a
Typical Diffusion Data
Pellet Densit).
System A+B
G./Cc.
0.789
0.792
Hz
Nz
NB
Hz
HB
iY2
Hz
c02
1-b
0.993
HP
Nz
1-b
1.008
COz
Hz
Cc./sec. at
0-a 0-b
1-a 1-b 2-a 2-b (.V,,lS,,),,,,,
Dzffusion Ratea of A X IO2.
Cc./Sec.
Cc. ISec.
3.47 3.94 5.19 3.28 2.61 1.13 5.38 4.60 3.82 6.21 5.10 4.18 3,61 4.62 5.65 1 08 1.84 2.87
10 10 10 2 2 2 9
9 9 9 9 9
3 3 3 0 0 0
4 3 4 74 72 75 91 95 88 72 81 70 16 11 19 79 88 78
25’ C. and 7 atm.
Table IV. Pellet .Yo.
Floz~ Ratea of R,
Summary of Diffusion Rate Data
Pellet Density,
‘VH,/.YX2
G./Cc.
Exptl.
0.789 0.792 0.993 1.008 1.14 1.17
3.80 3.85 3.59 3.58 3.70 3.43
=
(”)‘* 2.076
3.73 3.73 3.73 3.73 3.73 3.73 =
4.28 4.23 3.61 3.58 3.28 3.14
4.67 4.67 4.67 4.67 4.67 4.67
3.73
Volume and Surface Diffusion Rates
The experimental data demonstrate the existence of surface diffusion of carbon dioxide in boehmite pellets. The next step is to separate the surface contribution from the total and use these results to calculate surface diffusivities. Accurate evaluation of D, is difficult because the separation of the surface contribution imrolves subtracting two large numbers. However, approximate values can be obtained by the procedure described in the following paragraphs. T h e total diffusion flow. at a plane in the porous media perpendicular to the direction of diffusion. Y, may be expressed as the sum of the volume and surface contributions.
(3) This expression applies to a binary system a t constant pressure and gives the flux (moles,’sec. sq. cm. of area of pellet) of component -4 in terms of the volume and surface coefficients aV and as. These coefficients depend upon the diffusivities and the geometry of the porous media. A s Barrer ( 7 ) has pointed out, if equilibrium exists beaveen the molecules in the gas phase and those on the surface of the pore walls. the concentration on the surface is given by CAa
=
KsCA
(4)
where Ks is the absorption equilibrium constant and C4 the usual concentration in the gas phase. Since diffusion rates are slow with respect to rates of adsorption and desorption, this
is a satisfactory assumption. Combining Equations 4 and 3, and assuming k',?independent of concentration, gives
Table V.
Volume Diffusion Rates, Hz-Nz System
(Cc./sec. X 10' IIydrogen __ Calcd. ExPtI. (4.8 )
Pellet .\-0.
25' C.)
at
i-\.
trogen
_ _ _ _ _._ - .
Calcd. (Eq. 8)
Ex@.
where
and Surface Diffusion of Carbon Dioxide on Boehmite at 25' C.
Table VI.
Dijuusron Rate, Cc./Sec. X 102
~
This equation, after integration. gives an expression for both volume and surface contributions from the known gas phase concentrations a t the ends of the pellet. Equation 5 will be used to obtain the surface diffusion confor carbon dioxide on boehmite. First tribution, (.\;.02)s. the volume contribution, ( . V C ~ * ) ~is , calculated from the random pore model and then subtracted from the measured total diffusion rate. However, prior to this, the suitability of the random pore approach can be tested by calculating \,olume diffusion contributions for the N.:-H? system. T h e coefficient @+is a fqnction of composition as well as diffusivities when both Knudsen a n d bulk diffusion occur, as is the case Liith alumina pellefs. T h e integrated form of Equation 6 has been developed earlier (70) and may be written:
(.YA)"R Z'LCYA ~
= t,2
In 1 ~~~~
~
CYAYA~ f
~
1-
DAB
CUAYA,
~
~
~~
p-01.
Pellet
contr.
.Yo.
Total
Q
2 29
(Eq. 8) 2 21
1 2
0 83 0 48
0 620 0 220
(.vc.ot)s x 70'. D , x
Surf.
G. .lfole/
contr.
Sec. Cc.
0 08 0 21 0 26
0 46 1 2 1 5
+
704, Sq. Cm. ISec.
0 56 0 93 0 92
DAB','PD~~
+D
~ ~ ~ / P D ~ ~
DIRECTION Ea(I
- 8q)
€a ( l - € a )
DIFFUSION OF
L-4-4 €a l-6a ocA(YAl
~~~~~
1 -
YAl CYA ~
+ 2
-
YA2) ~
YA2
+
DAB0jDkiP __ 1 €**/(I - €,)2
(8)
+
Equation 8 was used to calculate diffusion r a t x for hydrogen and nitrogen at the conditions of the experimental measurements. 'The average Knudsen diffusivities. Dko and Dki, were evaluated from the average pore radii given in Table 11, kihich also includcs the necessary void fractions. T h e bulk diffusivity. D A B o ,for the N2-H2 system \vas determined from the Chapman-Enskog equation (7) to be 0.760 sq. cm. per second a t 25' C.? and 1-atm. pressure. All other quantities were knoLvn from the experimental measurements: or could be calculated. For example. CY is defined as
(9) For nitrogen in the Nn-Ha system, = -2.73 and for hydrogen aFTY = 0.731. T h e results. converted to the diffusion rate in cubic centimeters per w o n d through the pellet. are given in Table V along lvith the average experimental measurements for each pellet density. 'The agreempnt is excellent for the pellet of lowvst density. T h e deviations increase as the density increases aiid are due perhaps to difficulties in measuring accurately very low diffusion rates. and a slight crushing of the boehrnitr poLvder in the pelleting process. Even a small amount of crushiqg may create cracks in the poivder which \vould incrrase the diffusion rate. Ecluation 8 \vas next used to calculate the volume diffusion contribution for carbon dioxide. For this case acO2 = -3.67. T h e results are given in the third column of Table VI.
Figure 3. materials
Diffusion mechanisms in bidisperse porous
Surface Diffusivify of Carbon Dioxide
I'he observed. total diffusion rates for carbon dioxide, averaged for each pellet density. are given in the second column of Table V I . T h e fourth and fifth columns give the surface contribution, obtained from Equation 5,
T h e surface diffusion is seen to increase with pellet density, a n d hence, surface area per pellet. For the most dense pellet the surface contribution is greater than the volume value. T o evaluate Ds> we must determine and integrate Equation 7. T h e random pore model is shown in Figure 3 and described in detail elsewhere ( 7 0 ) . 'The dotted squares depict the particles of alumina Lvhich contain micropores, and the spaces betlveen particles represent the macropore region. 'I'he pellet is supposed to be a n assembly of identical particles which have a diffusion path length A.Y. Briefly, the diffusion rate per unit cross-sectional area of pellet is the sum of the contributions in three parallel paths: a macropore region of effective cross-sectional area ea2, the micropore region of area E?\ and a region containing macro- and micropores in series with a n effective area 2 ~ , ( 1- E , ) . In the series path the micropore part will contain nearly all of the pore surface because the micropores are small w i t h respect to the macropores (Table 11). Hence. the macropore path of length I t / 2 will control surface diffusion in the series path. \l'ith these concepts, the surface diffusion rate per unit area across a n element of pellet of length I r is "01.
3
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311
AcA (.YA)s= - [n,2ad, 4- ni2rdi 4-2(n82rd,)] DsKs AX
(11)
Table VII.
where the n values refer to the number of pores per unit crosssectional area of pellet in each of the three paths. For the macropore region. the volume of the cylindrical pores is given by eQ2Axand also by n,aciQ2Ax. Equating these two expressions gives a
Equilibrium Adsorption of Carbon Dioxide on Boehmite Powder at 25' C. Vol. Val. PTeSSUTe, Adsorbed," Pressure, Adsorbed, Atm. Cc./G. Atm. Cc./G. 0,081 7.78 0.466 13.3 0.171 8.65 0.338 14.0 0 246 10 3 0 628 15 2 0 285 11 0 0 705 16 6 0 398 12 9 0 875 16 6 Volume at S T P , 0" C., 7 atm.
Similarly, for the micropore and series paths ni =
n,
=
ei2 -
ad 12
2eQ(1 -
Ea)
r&2
Substituting the n values in Equation 11 gives
or
Equation 15 is the desired expression relating the surface diffusivity and the properties of the porous media to the surface diffusion rate. If the diffusion process occurs in the linear section of the equilibrium adsorption curve, K s will be a constant across the pellet of length L. Then Equation 15 in integrated form is
T h e (.Yco2)s data given in Table V I , the measured mole ~ : fractions at the ends'of the pellet, ( y c o n ) > and ( y c ~ ) the porosity, and average pore radius information about the pellets are sufficient to evaluate DsKs from Equation 17. In this case the micropore radius, fit, is so much less than the macropore radii that the micropore term predominates in Equation 17. Physically this means that most of the surface is in the micropores. The adsorption equilibrium for carbon dioxide on the boehmite powder was measured at 25' C . using the Sorptometer-i.e., by adsorbing carbon dioxide from a He-COZ stream. The results are shown in Table V I I . While the relation between volume adsorbed and pressure is approximately linear, this linearity does not extend down to zero pressure. Thus the pressures are too high for the data to to follow Equation 4. Values of Ks vary from 0.64 X 3.2 x 10-5 cm. This variation with pressure is not unexpected, since the fraction of the solid surface covered with adsorbed carbon dioxide also varies Tvith pressure. From the volume adsorbed, and the estimated area occupied by one carbon dioxide molecule, the surface covered at different pressures can be calculated. Comparison with the total surface (324 sq. meters per gram) indicates that the fraction of a monomolecular layer on the surface varied from about 10% a t p = 0.081 a t m . to 30%, at p = 0.875 a t m . If a n average value of 1.2 X 10-5 cm. is taken for K s , the diffusivity may be estimated from the product D S K s , as obtained from Equation 17. The results are given in the last column of Table V I . These diffusivities must be regarded as approximate values. For one thing D S is a function of the fraction of the surface 312
18EC FUNDAMENTALS
covered (5). In the present experiments this fraction changes with position in the pellet because the partial pressure of carbon dioxide in the gas phase changes. Further, K s is not constant over the concentration range across the pellet. Judging from the results in Table V for the N2-HZ system. the predicted volume diffusion rates for the higher density pellets may be somewhat low. If this is so. the (.Vco2)s given in Table V I for pellets 1 and 2 may be too high. This could explain the higher values of Ds for these two pellet densities. T o test the magnitude of the computed D,, another procedure can be used to evaluate the surface diffusion rate, (,YA)s. In this alternative approach, the observed data for nitrogen in the S2-HZ system are employed first to calculate (.Yco2)v. For volume diffusion. the rates are related to the molecular weights as follows :
where .Ynz is the experimental nitrogen diffusion rate in the Nz-H:! system. After (.Yco2)v is obtained, the same procedure is used as before-that is, obtain (,Vco2)S from Equation 10 and D, using Equation 17. T h e diffusivities determined by sq. cm. per second. this method range from 0.56 to 0.95 x These results are the same in magnitude as those given in Table V I but show significant percentage deviations. T h e comparison illustrates the level of accuracy expected in calculations of surface diffusivities. No information was found for surface diffusivities of carbon dioxide on alumina. Barrer and Barrie ( 2 ) give 2.6 X IOp4 and 5.0 X sq. cm. per second for Ds for ethane and krypton on Vycor porous glass at 19' C . under conditions of sq. cm. per low surface coverage. \.slues of about 0.5 x second have been reported for argon-silica at low temperatures (5). Data for other systems at coverages of fractions of a monomolecular layer are of this same order of magnitude (5) when compared a t the same temperature with respect to the boiling point-Le., same T/Tb ratio. Thus the data for carbon dioxide on alumina given in Table V I are similar to those for other surface diffusivities. Conclusions
A method (Equation 15) of evaluating surface diffusivities for porous media has been developed using the random pore model. This approach requires porosity and pore size distribution data but includes no parameters that must be evaluated from other rate data. Experimental diffusion data for carbon dioxide on alumina at 25' C. indicate that for high-surface pellets the surface contributio:i is as important as the volume diffusion rate. The surface diffusivity for the C02-boehmite system at 2.5' C . was found to be 0.5 to 0.9 X sq. cm. per second at conditions where the mo- olayer coverage of the surface varied from about 10 to 307,. Additional data are needed to assess the significance of surface diffusion in heterogeneous catalysis-for example, to
determine the influence upon effectiveness factors in gas-solid catalytic systems. Mrasurements for reactants a t the temperature and pressure of the reaction ivould br preferable.
= = = = = =
pore radius. cm. average radius for diffusion in macropores, cm. radius of micropores. cm. concentration of A in gas phase, gram moles,' cc. concentration of A on pore surface? gram moles,'(sq. cm.) bulk diffusivity in binar>-gas A-B, sq. cm.;sec. bulk diffusivitv at atmospheric pressure. sq. cm.,'sec. average Knudsen diffusivity of gas A in macropores, sq. cm., sec. average Knudsen diffusivity of gas A in micropores. sq. cm., sec. surface diffusivity, sq. cm. sec. adsorption equilibrium constant, defined by Equation 4. cm. length of porous pellet. cm. molecular weight. grams,'mole total diffusion rate of gas A in x direction, gram moles, (sec.) (sq. cm. of pellet cross section j volume and surface diffusion rates. gram moles,'(sec.)(sq. cm.) number of equivalent circular pores per unit cross-sectional area of pellet total pressure = 1 a t m . gas constant temperature, O K. surface area. sq. meters,'gram pore volume per gram of porous solid, cc./ gram total pore volume, cc.,'gram
\,olume in micropores, cc. 'gram rnacropore volume. cc., gram distance in direction of diffusion, cm. mole fraction of gas A side of pellet to which gas A is supplied side of pellet to which gas B is supplied
+ + .vA/.yB
= 1 dYB'.YA = 1 = void fraction = = =
pellet density, g./cc. particle density, g./cc. coefficients of volume and surface diffusion, defined by Equations 6 and 7, sq. cm./sec.. and cm.,.'sec.. respectively
literature Cited (1) Barrer, R. M., J . Phys. Chem. 57, 35 (1953). (2) Barrer, K. M., Barrie, J. A . , Proc. Roy. Soc. (London) A213,
250 (1952). (3) Barrer, R. M., Grove, D. M., Trans. Faraday Soc. 47, 837 (1951). (4) Carman, P., Kaal, F. A,, Proc. Roy. Soc. (London) A209, 38 (1951) ; Trans. Faraday Sac. 50, 842 (1954). (5) Everett, D. H.. Stone, F. S., eds., "Structure and Properties of Porous Materials," Colston Papers, Proc. 10th Symp. Colton Research Soc., C n i v . of Bristol. pp. 170-82, Butterworths, London, 1958. (6) Flood, A . E , Tomlinson, R. H., Can J . RPS.B26, 38 (1948). (~, 7 ) Hirschfelder. J . O., Curtiss, C. F.. Bird, K. B.. "Molecular Theory of Gases and 'Liquids," p. 539, \Viley, New York, 1954. (8) Pierce: C., J . Phys. Chem. 57, 149 (1953). (9) Robertson, J . K . ? Smith, J. M.. A.I.Ch.E. J . 9, 342 (1963). (10) \Vakao, Noriaki. Smith, J. M., Chem. Eng. Sci. 17, 825 (1962). (11) \Veisz: P. B., Schwartz, .4.B.. J . Catalysis 1, 399 (1962). RECEIVED for review December 16, 19 63 ACCEPTED June 15, 19 64
Study sponsored by the United States Army Research Office (Durham) through Grant DA-ARO(D)-31-124-G191. The financial assistance provided is gratefully acknowledged. The alumina was provided by the American Cyanamid Co.
SECONDARY NUCLEATION FROM AQUEOUS SOLUTION T. P. M E L I A ' AND W.
P.
M O F F I T T
Alkali Dioision, Imperial Chemical Industries, Ltd., Winnington, Northwtch, Cheshire, England
When a solute crystallizes from a supersaturated aqueous solution two types of nucleation may occur. Primary nucleation invariably occurs heterogeneously on foreign, solid bodies present in the solution as a result of atmospheric (or other) contamination. The primary nuclei develop in the supersaturated environment and give birth to large numbers of fresh nuclei; this i s termed secondary nucleation. The primary nucleus from which the secondary nuclei originate i s called the parent nucleus or crystal. The rate of secondary nucleation is dependent on the degree of agitation of the solution, the rate of cooling, the degree of supercooling of the solution, and the type of crystal which i s formed when the small nuclei develop, but i s independent of the number, size, surface characteristics, and chemical nature of the parent crystal. Two possib l e mechanisms for the production of secondary nuclei are discussed.
over-all process of crystallization from solution can be represented by the equation nA A,, give a crystal A,, with a n acin \,.hich molecules of solute companying change n l x in the thermodynamic function x-e,g,, entrap)., enthalpy, or free energy, From the standpoint of THE
-
Present address, Department of Chemistry and Applied Chemistry, The Royal College of .4dvanced Technology, Salford 5, Lancashire, England.
mechanism crystallization is regarded as a two-stage process: nucleation and growth. Results obtained previously 1.3) indicate that t\vo types of nucleation, primary and secondary. occur in the crystallization of inorganic salts from supcrsaturated aqueous solutions. In the present paper \ce are primarily concerned with the secondary nucleation procrss. T h e primary nucleation stage of the.crystal1ization process the 'Ormation Of Ordered aggregates by the bimolecular addition of molecules according to the schemc IS) VOL. 3
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