NOTES checked using a Zeiss interferometer. When all conditions had reached equilibrium, taps A12 and B12 were opened, and ammonia and hydrogen chloride were allowed to counterdiffuse into the reaction tube. Measuremente of the rate of ring formation and ring separation were recorded. At the end of each experiment the reaction tube was carefully removed from the apparatus and was sectioned, and the ammonium chloride from a section was carefully transferred onto a microscope slide for examination. Photomicrographs were taken of each sample a t a total magnification of 1000. Particle size analyses of the product over a range of reactant compositions 1-5% at two temperatures, 25 and 30’, were obtained. Examples of the distribution of sizes of the particles as a percentage frequency vs. size in microns are shown in Figures 2-5. The majority of particles were between 0.25-2.5 p mean diameter. Comparison of the sample populations obtained from experiments over the full range of concentrations studied showed no significant difference at the 5% level. Furthermore, (comparing samples between rings formed after 5 and 601min showed again no significant difference at the 5% level, suggesting that subsequent agglomeration of the particles does not take place. Above the critical moisture content for ring formation, we conclude that the concentration of the reactants does not effect the particle size distribution of the product formed and that no significant agglomeration of the particles takes place after nucleation and growth.
Possible Error in the Calibration of Knudsen Cells by Mercury Effusion’
by David A. Northrop Sandia Laboratory, Albuquerque, N e w Mexico (Received M a y 2, 1968)
The purpose of this note is to illustrate a possible experimental error in the calibration of Knudsen cells by mercury effusion. This error is particularly insidious in that it results in effective orifice areas that are quite different from the expected Clausing-corrected orifice areas but which produce coincident vapor pressure curves when applied to rate-temperature data obtained from different cells. This error does not affect the linearity or the slope of the usual log P ws. 1/T plot. It does affect the consistency and magnitude of the derived vapor pressures. This effect was encountered in the course of an investigation of vaporization in telluride systems where graphite is a convenient cell material. This graphite was porous and this porosity is the direct cause of the
4323
1.’
I
I
I
I
,001
.002
,003
.OM
I
*
I
005
-
CLAUSINC CORRECTEDAREA kin2)
Figure 1. Comparison of the Clausing-corrected orifice areas and effective orifice areas determined by mercury (0)and lead ( 0 )effusion.
crossover and nonzero intercept in Figure 1 and the separate but parallel lines of set A, Figure 2. Similar effects could be noted for other types of nonorifice losses. As no further attempts were made to illustrate the error, the cell porosity is an unfortunate but necessary parameter. The error to be described is independent of cell material and is not limited to porous graphite cells. Four graphite cells were calibrated at the same time by mercury effusion. The cells were contained in a flask attached to a liquid nitrogen trapped vacuum system. The flask was immersed in a water bath maintained at 25.00 0.05’. Effusion times and weight loss were sufficiently great to make the temperature uncertainty the largest source of error in the calibration procedure. The vapor pressure of mercury was taken as 1.998 X t ~ r r . ~Four ! ~ separate calibrations were reproducible to better than 1%. The orifice areas were also measured from photomicrographs of the orifices and corrected for channel length by conventional Clausing correction^.^ The effective orifice areas determined by mercury effusion and the measured Clausing-corrected areas are compared in Figure 1 ; the dashed line represents agreement between the two methods.
*
(1) This work was supported by the U. S. Atomic Energy Commission. (2) K. D. Carlson, P. W. Gilles, and R. J. Thorn, J . Chem. Phys., 38, 2725 (1963). (3) R. H. Busey and W. F. Giauque, J . Amer. Chem. Soe., 75, 806 (1953). (4) S. Dushman, “Scientific Foundations of Vacuum Techniques,” John Wiley & Sons, Inc., New York, N. Y., 1962, p 95.
Volume 72, Number 12 November 1968
4324
NOTES -2.0
c
1
-2.0
O 0 o
-3.i
e o
o CELL II e CELL I l l
SET A 0
e
o
e
\
e
Oo
e
0
0
e
-41
e
OO
e
-2.0
o e
-e -
0
e
0
* e
0
a
e
0 e 0
-5.0
e
m
2
0
e
-3. 0 0
-
e
0
-4.0
00
e
e
e
SET B 0
QO
4
Oa
%
5 5
b
b
0
e * e
0
e
e
-6.0
e 1
I
1
-6.0
e
SET C
-5.0
0
0
L
n
-3.0
-6.0
I
lMH)/TK Figure 2. Vapor pressures calculated with different area values from the same rate-temperature experimental data: set A, Clausing-corrected areas; set B, effective orifice areas determined by mercury effusion; set C, effective orifice areas determined by lead effusion.
Vapor pressures calculated via the Knudsen equation for rate-temperature telluride data from cells I1 and I11 are shown in Figure 2. The customary use of Clausingcorrected areas results in the parallel pressure curves of set A, while the application of the effective areas derived by mercury effusion results in the vapor pressures of set B. (Note the offset pressure axis.) This apparent discrepancy was resolved when it was discovered that the mercury vapor was not effectively removed from the cell region during the calibration runs. The room temperature walls of the vacuum system and the distant liquid nitrogen cold trap did not form an adequate sink for the effusing molecules. The high precision of the calibrated areas was the result of the same total flux from the four cells in each calibration. Thus the ratio of the observed rate of mercury effusion (or calibrated area) to the maximum rate (or area) expected for ideal effusion conditions was the same for each cell, resulting in the coincident vapor pressure calculations. A change in the total flux due to The Journal of Physical Chemistry
different temperatures, orifices, or number of cells would be reflected in different calibrated areas. Calibration of the same cells with leads at 600-900" resulted in the effective areas shown by the solid circles in Figure 1. I n this calibration, the temperature of the vacuum system walls adjacent to the furnace was less than 300" and thus served as an adequate trap, since the lead partial pressures are less than torr. These lead-calibrated areas appear to be the most reliable as they are consistent with a Clausing-corrected orifice loss plus a contribution to the weight loss due to permeation through the cell wall. (The effective thickness of a cell lid decreased slightly with increasing area, and this produced the small differences in the permeation contribution seen in Figure 1.) When these latest values are applied to the same rate-temperature (6) R. Hultgren, R. L. Orr, P. D. Anderson, and K. K. Kelley, March 1966 Supplement to "Selected Values of Thermodynamic Properties of Metals and Alloys," John Wiley & Sons, Inc., New York, N. Y . , 1963.
4325
NOTES data, they produce the coincident pressures shown in Figure 2, set IC. These calculated pressures are lower than those in set B by a factor of 2.5. The Clausing-corrected areas were incorrect and inconsistent for these telluride studies with porous cells. The mercury-calibrated areas werc incorrect, but they were internally consistent; these areas reduced the experimental data to coincident vapor pressure curves. A third-law AH298 or a AXT from the intercept would show that these calibrated areas were in error if reliable thermodynamic data were available. However, in many cases, such as these telluride materials, the thermodynamic properties have not been measured directly and can only be evaluated from the data for isomorphous compounds or by other estimation methods. These values may not be accurate enough for a definitive judgment of error in the experimental data. An experimenter would tend to have confidence in the coincident sets of pressures obtained with the erroneous mercury-calibrated areas. These results emphasize the necessity of an effective sink or trap for the vaporizing molecules during all vaporization studies. The vapor pressures of most materials investigated by these methods are low enough at ambient temperatures to efficiently remove the effusing molecules by condensation. This is not true for mercury, and thus special care must be taken when this material is used for the calibration of Ihudsen cells. The error in the calibrations may be completely masked by the self-consistency of subsequent data obtained with the cells.
A New Method for Studying Ion Adsorption by Ying-Chech Chiu and
AI. A. Genshaw
The Electroehemirrtry Laboratory, The University of Pennsylvania, Philadelphia, Pennsylvania 19104 (Received M a y IS, 1068)
Ellip~ometry~l-~ an experimental technique involving the analysis of the phase change (A) and the change in amplitude ratio (tan $) of polarized light reflected from a surface, has often been used in the study of very thin films. This technique is now applied to the determination of the adsorption from solution of ions at a mercury surface. The ellipsometer used was made by 0. C. Rudolph & Sons, Inc. (i\lodel 437-2003) and used a zirconium arc as the light source (filtered at X 5460 A). A rectangular cell made of quartz was employed. In order to minimize the effect of mechanical vibration, a thin layer of mercury on gold foil was used as the reflecting surface. The surface was first reduced at -1.0 V (us. sce) while nitrogen was bubbling through the solution and then the potential was changed to -0.7 V
by the use of a Wenking potentiostat. In the bromide experiments, it was found that the data are more reproducible if the surface was treated by a potential sweep in the potential range used in the experiment for three or four cycles before the actual recording was taken. The angle of incidence of light was 68.2" to the reflecting surface and the quarter-wave plate was fixed at 45". An extinction setting of the optical components was first found by the swing m e t h ~ d . ~ The method of determining A, the relative phase change, was to set the polarizer about 4" from the extinction setting. Small changes in A then cause changes in the intensity of the light. These changes are linear in A under the experimental condition and may be calibrated by determining the relation between the polarizer position and the intensity. To ensure that the changes in intensity were due to changes in A and not artifacts such as might result from a movement of the surface due to electrocapillary effects, measurements were made on each side of the null (on one side an intensity decrease is observed, while an increase is observed on the other) and some points were checked by the swing method. Also, measurements were made in 0.64 M NaF. In the fluoride solution the change in A between -0.700 and -0.200 V was less than that corresponding to 0.05 in e for Br-. This supports the interpretation that the changes in A in Br-- and SCN--containing solutions are due to adsorption, as the calculations indicate that the refractive index of sodium fluoride is very close to that of water and thus it will not be detected. The adsorption study was made with sodium thiocyanate (Baker Analyzed reagent) solution and potassium bromide (Baker Analyzed reagent) solution. The calculations of A and $ from the polarizer and analyzer reading were made using standard techniques.1-3 From these the optical constants of mercury at -0.7 V us. sce in 0.64 N NaF were found to be 1.45-5.31 i. Other values reported are 2.O-5.17ij6 1.485-4.55i16and 1.602-4.73i.I In order to analyze the experimental data, a model must be made of the layer of adsorbed ions. The model taken is to assume that a layer of ions and water molecules of a thickness equal to the length of the ion is always present at the surface (the length of SCN(1) K. H. Zaininger and A. G. Revesz, R C A Review, 25, 85 (1964) (2) "Ellipsometry in the Measurement of Surfaces and Thin Films, Symposium Proceedings, Washington, 1963, U. 5. Department of Commerce," National Bureau of Standards, Miscellaneous Publication 256, U. 5. Government Printing Office, Washington, D. C., 1964. (3) F. L. McCrackin, E. Passaglia, R. R. Stromberg, and H. L. Steinberg, J . Res. N a t . B u r . Stand., Part A , 6 7 , 363 (1963). (4) H. J. Rudolph, J . Opt. SOC.Amer., 4 5 , 50 (1955). ( 6 ) J. O ' M . Bockris, M.A. V. Devanathan, and A. K. N. Reddy, Proc. R o y . SOC.,279, 327 (1964). (6) L. E. Smith and R. R. Stromberg, J . Opt. SOC.Amer., 5 6 , 1539 (1966). (7) T. Smith, ibid., 57, 1207 (1967).
Volume 79, Number 12 November 1968
