Information on the partial molar entropy, entropy and heat capacity of the film is derived from the isosteres. Nm is the number of atoms required to fill all the sites and b is related to the adsorption energy. However, it is generally used to get a rough idea of a system's behavior and especially to arrive at a
Since ~ and A behave analogously to P and V, we can write for the energy of the film. Vie makes the assumption that the "volume" of the film for sub-monolayer coverages is proportional to the coverage.
J NRT
CHAPTER II
The basic measurements in the current study were performed with helium adsorbed on the copper sponge. Secondly, it is believed that the pre-plating will help smooth out any irregularities in the bare copper. However, the first step was to determine the monolayer capacity of the bare sponge for nitrogen at 77°K.
An isotherm on bare copper was then taken for each of the four gases and fitted to the BET equation to determine the monolayer capacity. As previously mentioned, these systems at submonolayer coverages were completely unexplored at the beginning of this research; and it was not known whether certain regions would prove to be of special interest.
ZOVEN~ W~TH COLD
A spiral groove was made in the wall of the sponge shell, which was then coated. The spectrometer makes it possible to measure the partial pressure of the helium alone. All helium isotherms were performed at temperatures below 4.2°K and relied on a bath of pumped liquid helium for cooling.
Figure (2-6) shows the usable liquid range (i.e. between N.B.P. and T.P.) of the various practical liquid coolants available in between. 150 K and OK, as well as the temperature ranges within which it is possible to perform an isotherm on each of the noble gases. In the case of neon, the bulk vapor pressure had to be kept below ~100 Torr due to the large effective dead volume at these temperatures.
Such high pressures in such a large effective volume would have meant that almost all of the gas admitted into the system would have remained in the gas phase rather than adsorbing. The total internal volume of the vacuum is approximately 2000 cm3. During normal operation. In fact, however, much of the argon would remain in the gas phase in the volume at room temperature due to the high vapor pressure (~20 Torr) of an argon monolayer at 77°K.
For each of the four rare gases and for nitrogen, an adsorption isotherm was taken at the most appropriate temperature on bare copper. Since adsorption measurements concern only that part of the gas that is adsorbed, the gas phase correction must be subtracted. The reason for this, as well as our meaning of the term monolayer in this.
The dotted portion shows the change that would result from using the preliminary results of reference (70) instead of the Weber-Schmidt results in the data reduction. The isosteres and related quantities discussed in the preceding section form the bulk of the numerical data of this work; however, there were
P (Torr)
We have already mentioned in Chapter II that one of the limits placed on this experiment was that of a background partial pressure of helium. The pores of the sponge are of the order of microns in size and therefore it may take a long time for the gas to be distributed evenly throughout the sponge. If, however, the helium atoms have lateral mobility over the substrate; then this can complement gas diffusion and bring about faster equilibrium.
Figure (J-29) shows the rate of approach to equilibrium for a variety of coating-helium coverage combinations. The two lower swings were actually followed for more than ten days. 260 hours) each and still falling; the final observed values are shown on the far left side of the figure (J-28) as the upper limits of the pressures. These curves represent extreme cases of waiting for equilibrium; generally data attempted. at 4.2 K were discontinued if they took more than two or three days to reach equilibrium.
Rate of approach to pressure equilibrium for various combinations of helium. one lifetime of the bath) due to the increased disturbances caused by the transfer of fresh liquid helium to the bath which is already below the normal boiling point. The consequences of the rapid approach to equilibrium of the two curves will not be discussed in the next chapter; however, from a strictly experimental point of view, this made it possible to obtain Ne data down to extremely low coverages than. The isotherm is still non-linear even at 0.05 layers and indeed does not appear to follow any simple relationship.
Isosteric heat of adsorption, qst/R, of helium on Ar 1.0 over a wide range of coverage. The vertical dashed line indicates the coverage where the number of helium atoms equals the number of argon atoms. This curve shows why many early studies obtained incorrect results for the capacity of monolayer adsorbed helium: an uncritical application of BET theory essentially assigns monolayer status.
CHAPTER IV CONCLUSIONS
The most important phenomena that the five systems have in common are: The heat of adsorption at 4°K is significantly greater than at 3°K except at the highest coverages and has approximately the same value for each substrate at typical temperatures and coverages;. the oS/oNR curves each show an inverted region where the amount is less at 4°K than it is at This process and the fact that it occurs for all substrates constitutes one of the most important observations resulting from the research and will be discussed subsequently; currently. Simple two-dimensional Debye behavior would require the entropy and heat capacity of the film to be monotonically increasing coverage functions and indeed both reference (JO) and (Jl) found.
Stewart and Dash did not publish an analysis of the magnitude of the term linear in T in their data, if any; however, they found that the coexistence of two different Debye solids must be assumed. We would like to investigate the consequences of assuming that He adsorption on the surface takes place in the form of clusters or patches. Squeezing the base with the helium atom brings the neighboring atom closer to the underlying copper atom. From their data, they estimated this bond to be "' 8°K.
In view of the construction of the sponge (chapter II), it follows that pressure-driven diffusion provides a lower limit on the rate of mass transport. This figure also shows that any of the pre-coatings significantly increase the pressure over that on bare copper. This has the effect of severely limiting what we can say about those theories that are primarily concerned with the temperature-dependent properties of the film - quantum mechanics.
Furthermore, Dash (J4 . ) has stated that tunneling effects should not be apparent in thermal measurements when kT is much larger than the peak of the tunneling band Dash apparently does not provide an explanation for this statement, but what he probably means is that, for example, 15 0 K is a low enough temperature that very few atoms will be excited into the thermal band, but it is also a high enough temperature for the tunnel band to be populated at uniform way. Our data have shown that there can be significant differences in film mobility for different substrates, but the question remains: How does the mobility quantitatively depend on the substrate. This can be answered by systematic measurements of diffusion rates in different substrates.
APPENDIX I
A sponge similar to the one used in this research but without such a large central hole would be useful. in the range of 1 Torr upwards. To operate in the region below ~ 10 -6 Torr, the problems of background pressure and diffusion time must be met. But at extremely low pressure, the only problem is making sure the heat conductivity is good enough to make the same sponge useful for heat capacity.
Of course, if the microscopic structure of copper affects the properties of the film, . then using continuous foil instead of powder may add additional complications.). First of all, more direct contact between the sponge and the meter would increase the effective pumping speed of the bath, this can be accomplished as shown in Figure (A-1). Second, eliminating borosilicate glass from the high vacuum system would be highly desirable.
If one does not wish to use an all-metal system, it may be possible to substitute an aluminosilicate glass, such as Corning #1723, which has the low expansion coefficient and high operating temperature of borosilicate glass, as well as the low helium diffusion constant of soda-lime glass (??.7 8. There may also be ways to reduce the problems associated with changes in liquid helium levels and helium retransfer. If the filler tube were made with a vacuum-jacketed construction, the experiment would be impervious to changes in the level of the liquid helium bath.
The innermost Dewar would contain the experiment and be pumped and regulated in the usual way. Cold liquid helium can then be transferred from the outer liquid helium dewar to the inner dewar at operating temperature, see figure (A-J). It is possible that the problem of the thermo-molecular effect can be completely bypassed at least at the highest pressures (~ 10-3 Torr).
APPENDIX II
For a summary of saturated film properties see: J.Wilks, The Properties of Liquid. The work done on physical adsorption between the 1930s and 1960s is summarized and critically discussed by: D.M.Young and A.D.Crowell, Physical Adsorption of Gases (Butterworths, London, 1962). This paper shows theoretically that helium atoms are adsorbed on the ~oo] surface of a LiF crystal will.
The material in this section is largely summarized from Young and Crowell, op. G.A.Cook, Argon, Helium and the Rare Gases, I, ed. It is not certain that these were actually Ohmite resistors; they were selected from department stock on the basis of a favorable resistance ratio, R4 • 2/R 300 •. Insulating and dipping varnish #56.
