MASSSPECTROMETRIC STUDY OF CUPROUS BROMIDE
327 1
roughness that was used in this experiment. This is because the change in surface area of the solid by roughening it tames a change in surface energy of the soiid and in interface energy of the solid-liquid interface and brings about a new energy balance in the ‘Young-Dupr6 equation.
Putting the obtained parameters into eq 2, x 2 for differing degrees of roughness was calculated and compared with the observed x2. The agreement between them was very good, showing that the model was acceptable, and conversely, Wenzel’s theory was shown to be reasonable. Specimens of the third group were prepared in a different way from the other groups. I n this group, Wenzel’s relation was also well explained by the proposed model. Thus, Wenael’s relation was verified experimentally, and it can be concluded that the contact angle should be decided in terms of surface energy of the soiid, the liquid, and the solid-liquid interface at least in the range of roughness in this experiment.
Conclusion From the observed surface profiles and electron micrographs, a simplified model was proposed. Then ’Wenzel’s relatiion between contact angle and roughness was applied to the observed contact angle and the calculated roughness. For the second group, the contact angles were constant regardless of hal,. This could be explained reasonably by the pmposed model and Wenzel’s relation. For the first group, from the experimental relation of :c2 and cos 0, the parameters a, p, and y of the model were determined. On the other hand, from some experimental values of ha, and x, a and n were estimated.
Acknowledgment. We should like to express our gratitude to Professor Takanashi and Dr. Sato, Research Institute for Scientific Measurements, Tohoku University, who kindly facilitated our using the profilometes.
Mass Spectrometric Study of the Vaporization of Cuprous Bromide
by D. W. Schaaf and N. W. Gregory* Department of Chemistry, University of Washington, Seattle, Washington 98196
(Received April 7, 1972)
Publication costs assisted by the National Science Foundation
An effusion-mass spectrometric study of cuprous bromide indicates that in the vicinity of 700°K the trimer i s the dominant molecular species in the saturated vapor, along with substantial amounts of tetramer. Heats of vaporization for these two species are derived.
Vaporization characteristics of cuprous bromide have recently been studied by spectrophotometric1 and effusion methods.’ We now report results of a mass spectrometric study in which intensities of mass peaks, generated by ionization of molecules in a beam issuing from a Knudsen effusion cell containing a condensed sample of cuprous bromide, were observed as a function of the temperature of the cell. Heats of vaporization for Cu3Br3 and C:u4Bri have been derived and re,mlts compared with the earlier studies on the bromide 3s well as with recently reported mass spectrometric m ork on cuprous chlor~de.~
with a ltnife-edged orifice ca. 1 “‘in diameter. The cell was heated by a quartz-lined nichrome element mounted in a stainless steel vacuum chamber. Most of the effusate was trapped immediately above the cell on a copper plate, cooled with liquid nitrogen. An orifice in this plate permitted a beam of molecules to move without interference through two additional collimating orifices (1 mm diameter), inserted in the portals of a gate valve, into the ionizer of a Spectrosean 750 mass’analyzer probe. Temperatures of the cell at the top, side, and bottom were measured with calibrated
~
(1) D. I,. Hilden and N. W. Gregory, J . Phys. Chem., 76, 1632 (1972).
x ~ ~~ ~ ~c t i oi r ~~ e ~ t ~ ~ Cuprous bromide was prepared by reaction of copper and br0mine.I Samples were placed in a cylindrical glass effusion cell ca. 30 mm long and 25 mm in diameter
(2) R. A. J. Shelton, Trans. Faraday Soc., 57, 2113 (1961). (3) M. Guido, G. Balducci, G. Gigli, and M . Spoliti, J . Chem. Phys., 55, 4566 (1971).
The Journal of Physical Chemistry, Vo2. 76, N o . 2 g 3 297%’
D. W. SCHAAP AND N. W. GREGORY
3272 chromel-alumel thermocouples and were controlled within k 1-2' by independent heating elements. Background pressures in the probe chamber were in the Torr range; those in the effusion chamber were in the range of Torr.
3.00
Results
2.50
Pons observed and their relative intensities, as indicated by the ion current for the most abundant isotope, %reshown in Table 1. While the instrument is capable of unit mass resolution in the range of interest, the signal intensity was low relative to background and all peaks were not fully resolved into isotopic components. Ion identification was made on the basis of mass range (instrument calibrated with perfluorokerosene) and in the cases where resolution was sufficient (Cu3Br3+, Cu+) by isotopic distribution. Correction for background was made by subtracting the ion current measured with a shutter intercepting the beam. The relati -\.e intensities shown were measured with the effusion sample at '700°K and the ionization voltage at 70. Appearance potentials, also measured with the sample source at 700"K, were derived by extrapolation of the ion current plotted as a function of ionization voltage, with the latter varied by 2-V intervals up to 40 V. Voltage readings were calibrated by observation of appearance potentials for Nz+, HzO', and Oz+ in the background s p e ~ t r u m . ~ Appearance potentials ;or the cuprous bromide ions are similar t o those reported for corresponding ions in the cuprous chloride system3 and indicate that Cu4Br4+and Cu3Br3+are the only simple parent ions produced in significant quantities. Thus we assume that the effusion beam consists principally of Cur, r4 and @u3Br3,with smaller ions resulting from fragmentation of these molecules.
Table I : Mass Spectral Data for CuBr Vapor Ionic species
Re1 intensities
4.4 5.9 100 '54 8.4
32 21 25
AP, eV
- R d ( l n I+T)/ d(l/T), kcal/mol
9.2 10.4 9.7 12.4 16.8 15.0 17.1 16.7
33.3 36.1 28.5 28.9 32.2 30.8 30.9 31.2
A plot of I T T (log scale) vs. 1 / T , where T is the absolute temperature of the Knudsen cell containing the vapor in equilibrium with CuBr(p) and I + is the ion current, is shown for each of the ions in Figure 1. Transitions in solid CuBr, y (zincblend) -+ p (hexagonal) at 385' and for ,L? to a! (body centered cubic) at 470" have been reported;j the p -+ 01 transition temperThe Journal of Physical Chemistry, Vol. 76, .Vo. 99,1979
? +H Y
-g 2.00
1.50
I .oo 1.36 1.38 1.40 1.42 1.44 1.46 1.40 1.5C
IOOO/T
(OK-')
Figure 1. Plot of I+T (log scale) us. 1/T for various ions generated from a molecular beam of cuprous bromide vapor. Ion currents (A x 107, after subtraction of the background current) represent values for the most abundant isotopic species.
ature appears slightly above the upper limit of the molecular flow range for the vapor pressure.2 The range of our study has been confined to the region of stability of the 0 phase as, in general, a good quantitative measure of ion intensity was not practical over a significant temperature range for the y phase, Linear least-squares lines are shown for each ion in Figure I and the corresponding slopes listed in Table I. Several independently prepared samples were studied with concordant results. If ionization eficiencies and instrumental constants are assumed independent of the temperature of the sample source, values of -R d(ln I+T)/d(l/T) for ions which arise from zi single neutral molecule may be taken as a measure of the heat of sublimation of that species, Since masses higher than the parent ion of the tetramer were not observed, slopes for Cu4Brq+ and Cu4Br3+may be associated with the heat of sublimation of Cu4Br4 (from CuBr(6)); the average value for these two ions is 35.7 kcal mol-'. From the relative ion currents and estimated fragmentation ratios (discussed below) it, appears that Cu3Br3 is the dominant species in the effusion beam. Hence this species is believed t o be the major source of Cu3Br3+; the temperature dependence of the intensity of the mass peak of this species gives an apparent heat of sublimation of 28.5 kea1 mol-' for Cu3Rr3, slightly larger than (4) R. W. Kiser, "Introduction to Mass Spectrometry and Its Applications," Prentice-Hall, Englewood Cliffs, N. J., 1965. (5) S. Hoshino, J. Phys. Sac. Jap., 7, 560 (1932).
MASSSPECTROME~TBIC STUDYOF CUPROUS BROMIDE the value based on spectrophotometric measurements (27.8 kcal),' and somewhat less than the apparent heat hased on Sheiton's total rate of effusion (30.9 kcal).2 The heat predicted by the slope in Figure 1 is expected to be slightly larger than the true value if Cu4Br4contributes significantly to the formation of Cu3Bra+;however, the difference between the mass spectral and spectrophotometric values is probably not beyond the combined experimental errors. The conclusion that the smaller ions arise principally from fragmentation of the trimer and tetramer receives further support from the observation that the slopes observed (Figure 1 and Table I) for these species are intermediate between those for Cu3Brl+ and CudBr4+. If two m m e molecules contribute to the formation of a gnver~ion, the line (Figure 1) should not be strictly h e a r , though the deviation from linearity over f,he small temperature interval of the experiment is expected to be small; curvature cannot be detected within experjmental error. Hence the linear least-squares slopes have been used t o make a rough cistimate of the fractional contribution from Cu4Br4 and Cu3Br3, respectively, in each case, assuming the fragmentation ratios t o be independent of temperature. Each ion current was corrected by the appropriate isoiopic distribution factor; however, no allowance could be made for possible differences in detection efficiencies for the various ions or ionization efficiencies for the parent molecules This treatment indicates that the CuaBr~:Cu1~Br4 ratio in the original beam is roughly 5:1, a value considerably greater than found in the chloride bystem (1.4:1)e3 These comparative values are generally consistent with conclusions based on the spectrometric study, uhere absorbance attributed t o the tetramer in the vapor of the chloride was clearly evident, but a similar effect in the bromide system was not detected.'
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An independent estimate of P(trimer)/P(tetramer) in the equilibrium vapor of the bromide can be made by comparison of the temperature dependence of the total rate of effusion measured by Shelton2with the temperature dependence of the parent ion currents found in the present work. This gives a pressure ratio of 3.6 at 686"K, which together with Shelton's effusion rate indicates standard entropies of vaporization of 36 and 28 cal mol-' deg-' for tetramer and trimer, respectively. The calculation neglects contribution of tetramer to the trimer parent ion peak; the concentration ratio Is determined by a ratio of differences of similar slopes, with attendant large uncertainty. When compared with the relative ion currents, the derived coneentration ratio suggests that in ionization the fraction of tetramer converted t o Gu4Br4+ is much smaller than the fraction of trimer converted to Cu3jRra6. If one assumes that the standard entropy change at 700°K €or the reaction
is the same for the bromide and the chloride, respectively, then the values of AH" derived, -2.3 rtr 1 kcal for the bromide and - 10.3 f 1.8 kcal for the ~ h l o r i d e , ~ may be used to estimate the ratio of the equilibrium constants in the two cases. The experimental uncertainty in the heats is large. This calculation, together with vapor pressure d a t ~ t ,predicts ~ , ~ that only between 0.1 and 2.5% (the range based on the indicated uncertainties in the heats) of the molecules in saturated cuprous bromide vapor at 700°K are tetramer, This estimate appears low in comparison with the relative intensities shown in Table I.
Acknowledgment. This work was carried out with financial support from the National Science Foundation, Grant No. 6608X, which is acknowledged with thanks.
The Journal of Physical Chemistry, Vol. 76,No. 88, 1072
