J . Phys. Chem. 1993,97, 2800-2801
2800
Comment on Porosities of Ice Films Used To Simulate Stratospheric Cloud Surfaces Leon F. Keyser,' Ming-Taun Leu, and Steven B. Moore Earth and Space Sciences Division, Jet Propulsion Luboratory, California institute of Technology, Pasadena, California 91 109 Received: August 10, 1992;
In Final Form: December 18, 1992
In a recent article Hanson and Ravishankara (HR) obtained data for the reaction probabilities (7s) of N205 and ClONO2 on ice films of varying thickness.' They interpreted the observed change in y as evidence that no corrections for internal diffusion were needed and, thus, by implication that their films were effectively nonporous. H R also calculated y vs thickness by using the theory of surface reaction and pore diffusion2 and obtained results that did not agree with their experimental data. The purpose of this comment is to point out the following: (1) the strong evidence that vapor deposited ice films can be highly porous; (2) that porous films do not always show a large increase in reactivity or uptake capacity with thickness; (3) that H R made assumptions that resulted in the poor fit of their data; and (4) the need for characterization of the ice films used. (1) Ice films formed by deposition from the vapor phase have been widely used to simulate stratospheric cloud surfaces for laboratory measurements of reaction and uptake rates. To obtain intrinsic surface reaction probabilities that can be used in atmospheric models, we need to know the area of the film surface that actually takes part in the reaction. If the films are smooth and nonporous, the geometric area can be used, as was done in all of the early work using these ice films. However, studies of the morphology of films deposited under conditions (temperature, pressure, deposition rate, sample size, film thickness, substrate) similar to those used for the rate measurements show that the films have temperature-sensitive surface areas much larger than the geometric area3 and that they are composed of loosely consolidated granules with diameters of a few micrometers or le~s.3.~ The large internal areas of such films consist of the surface areas of the individual ice granules. The loose packing of the granules makes these films highly porous and allows rapid gasphase diffusion into the interior of the film. For porous films, the observed rates are affected by the internal surface area, and corrections, which account for the interaction of surface reaction and pore diffusion, are required in order to extract intrinsic Y S . ~ The magnitude of these corrections is less than a factor of 3 for an observed y > 0.1. However, for y < 0.1, the corrections become larger and the use of geometric areas for porous films results in ys that are upper limits to the true values. (2) An increase in reactivity with thickness implies that a film is porous, but the converse is not always true. That is, a porous film can show little or no change in reactivity with increased thickness depending on its morphology. This can be seen by considering a simple model based on our studies of these films using optical and electron microscopy and gas adsorption (BET) In this approximation, the film comprises spherical granules stacked in layers. For a porous film, the relation between the observed probability, y(obs), which is calculated by using the geometric area, and the true value, yl, is given by2 r(obs) = + TJSJ (1) where S,and S,are, respectively, the external and internal surface areas of the film per unit geometric area and TJ is an effectiveness factor defined below. If eq 1 is written in terms of the bulk
density, Pb, and the specific surface area, s,,we have (2) ~(obs= ) YtP$g(he + Vhi) where he and hi are, respectively, the external and internal thickness of the film; the total thickness, h, is h, h,. The specific surface area can be written
+
s, = 6/P,d
(3) wherept is the truedensity of the ice and d is the granule diameter. If we take the external surface to be the upper half of the top layer of spherical granules, he = d / 2 For simple cubic packing (SCP), Pb
(4)
= (*/6)P,
(5)
where N L is the number of granule layers. Substituting eqs 3-6 into eq 2 gives r ( W = r,(*/2)[1 + TJW, - 1)1 (7) The effectiveness factor, TJ,is the fraction of the film surface that participates in the reaction; it is determined by the relative rates of surface reaction to pore diffusion and is given by2 TJ
= $-' tanh 4
(8)
4 = (h,/4[3Pb/2(P, - Pb)1(3TYt)'/2
(9)
where is a tortuosity factor and cylindrical pores are assumed (see ref 2 for details). In the layer model, the packing and, hence, the bulk density and tortuosity are independent of film thickness. Thus, eqs 6-9 show that the observed film reactivity dependsonly on the number of layers, NL. If the film morphology is such that the granule size remains approximately constant, N Lincreases with thickness and a large change in reactivity can be observed. However, if the granule size increases proportionately with the thickness, N L remains constant and no variation in reactivity will be observed even though the film is highly porous. Between these two extreme cases, the granule size could increase less rapidly than thickness and a moderate change in reactivity would be observed. The ratio of bulk to true density calculated from eq 5 is 0.52; this is the value measured for HNO3.3Hz0 (NAT).3 However, for H 2 0 ice, the measured density ratio is 0.68,3 which is close to the value of 0.74 predicted from a layer model comprising hexagonal close-packed (HCP) spheres, eq 10 below. To model NAT ice, SCP can be used; however, for H20 ice, HCP is a better approximation and will be used in the remainder of this discussion. For HCP, eqs 5-7 become5
hi = d [ ( N L- 1)(2/3)''2 y(obs) = 3-'i2yt*(1
+ (1/2)1
+ 7[2(NL - 1) + (3/2)''2]}
(1 1) (12)
Electron micrographs of ice films show that granule sizes are of the order of micrometers and that they increase with deposition times and, thus, with thickness. In these experiments, we examined thin films (less than about 20 r m ) formed in situ by vapor dep~sition.~ By combining these results with eqs 8-12, we have calculated Y(obs) vs h for granule sizes that increase from
0022-3654/93/2097-2800S04.00/0 0 1993 American Chemical Society
The Journal of Physical Chemistry. Vol. 97, No. 11, 1993 2801
Comments 10-1k
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4
10-2
Y
10-41 1
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10 THICKNESS, Frn
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100
Figure 1. Plot of observed reaction probability, r(obs), vs film thickness. Curves are calculated from q s 8-12 by using parameters for H20 ice from refs 2 and 3: Pb = 0.63 g cm-', p, = 0.925 g cm-), 7 = 4. The same granule-size distribution is used to calculate both curves: sizes from about 0.6 to 6 wm [or thicknesses from 1 to 100 wm with number of granule layers from 2 to 20; the relation between number of layers and film thickness can be approximated by N L = 2 9 loglo h, where h is in micrometers. Data points are from ref 1 with thickness corrected by the factor 1.0/0.63 since HR used Pb = 1.0 g cm-'. (m) N205 on HNO3treated H20 ice: effectiveness factors are between 1.0 and 0.75; best fit (0) N ~ O on J H20 ice: effectiveness factors occurs at 7,= 1.9 X are between 0.82 and 0.10; best fit occurs at y, = 1.8 X IO-'.
+
about 0.6 to 6 pm for thicknesses between 1 and 100 gm. The granule size distribution and y, were varied to obtain the best fit. The results are shown in Figure 1 along with the experimental data of HR. The filled boxes are for N205 on HN03-treated H20ice, which is called NAT by HR and may actually consist of a thin layer of NAT on the surface of H20 ice granules. There is good agreement between the experimental data and the theory with the best fit occurring for y, = 1.9 X 10-5. This value is a factor of 30 lower than the experimental average. By using the same granule-size distribution as that used for N2O5 on NAT, y(obs) vs h was calculated for N2O5 on untreated H2O ice; the results are given in Figure 1. Again the agreement is good; the best fit occurs for y, = 1.8 X 10-3, which is 9 times lower than the experimental average. A similar analysis can be made of saturation experiments, in which the amount of ClONOz and HCl taken up increased by a factor of 2 as the film thickness increased from 3 to 30 pm.l The uptakecapacity should be proportional to the total film surface area per unit geometric area, which for HCP is given by 3 - 1 / 2 ~ [ 2 N ~ - 1 (3/2)]/2]. The same granule-size distribution used above predicts a factor of 2.5 increase in uptake capacity over the range of film thicknesses used. Considering the simplicityof the model, this is in reasonably good agreement with experiment. The model results imply that the ys observed by HR are significantly affected by porosity; however, it is not possible to state quantitatively the magnitude of this effect since they did not characterize their films. The results alsoshow that the absence of a large increase in reactivity or uptake capacity with thickness is not a reliable indication that the films are nonporous. (3) In applying the theory to their data, HR implicitly assumed that r(obs) = y,at a film thickness near 1 pm, which is equivalent
+
to saying that thin films are nonporous; this is inconsistent with the morphology shown in electron micrographs of such films.3.4 In their calculation, HR set S, = 1.0 m2 g-l, which corresponds to a granule diameter of 6.5 gm (eq 3); for this S,, the results can be applied only to films thicker than 6.5 gm since NLcannot be less than 1. They also assumed that the effectiveness factors are independent of thickness, which is true only in the unlikely case of constant NL. Thus, the theoretical curves, calculated by HR and shown by them in their Figure 1, are not a valid comparison of the pore diffusion theory with experiment. H R suggested that the BET surface areas measured by using N2 and Ar may be invalid because these adsorbates diffused through the ice matrix itself. Several observations disprove this. Measurements of dead space (adsorptioncell volume- ice volume) were carried out with He; the ice densities obtained agree within 10%with theliteraturevaluesand show that there is no significant diffusion of He into the ice m a t r i ~ .Thus, ~ if He is excluded from the matrix, the larger N2 and Ar will be as well. Moreover, surface areas measured with N2, Ar, and Kr agree among themselves and with areas calculated from granule sizes observed in the electron microscopy experiment^.^^^ The surfaces sampled by the adsorbates are the same as those available to reactant species, such as ClONOz and HCl, because the granule sizes and, hence, the pore sizes are of the order of micrometers. This is much larger than the dimensions of any reactant or adsorbate used and means that they cannot be excluded from the pores because of size. (4) BET adsorption measurements and studies of the cubicto-hexagonal phase transition show that ice films can have large surface areas that are very sensitive to deposition and annealing temperatures.3.6 Electron microscopy experiments confirm this and show that even thin films (
