Physica B 194-196 (1994) 895-896 North-Holland
FREE EXPANSION OF HYDROGEN IN HELIUM AT LOW TEMPERATURES. Dan A. Scardino, Hsi-Lung Tsou, and T.E. Huber, Polytechnic University, Brooklyn, NY 11201. In order to understand the formation of clusters of molecular hydrogen in helium we evaluated isentropic-expansion paths on the pressure-temperature phase diagrams. The optimal initial conditions are derived. The prospect of detecting the resulting clusters using infrared absorption spectroscopy and light scattedng optical is discussed, the ultimate goal being that of observing supercooled liquid hydrogen. Preliminary results will be discussed. The triple point of para-hydrogen is 13.81 K. Quantitative estimates of the extent to which it is possible to supercool liquid H2, including quantum tunneling, were published by Marls, Seidel, and Huber 1. Marls, Seidel, and Williams did experimental work of near-millimeter size droplets levitated in dense helium. 2 They were able to supercool to 10.6 K for a few seconds indicating the need to supercool smaller droplets more rapidly to achieve lower temperatures. E. L. Knuth, P. Schilling, and J. P. Toennies did preliminary experiments on supercooling hydrogen in a supersonic beam. 3 The lowest deduced cluster temperatures were 6 K. They were realized for expansion along isentropes passing slightly to the liquid side of the critical point. We are studying a cooling method based on expanding a mixture of hydrogen mixing with helium. The method is similar to the method used by Wilson in his "cloud chamber". Here we present computer simulations which were performed to find the temperature as a function of volume in an adiabatic expansion. We assume that helium and hydrogen are ideal gases. In equilibrium, when the vapor pressure of hydrogen becomes less than the partial pressure of hydrogen, the hydrogen condenses in clusters. Some representative results are shown in Fig. 1. For monatomic ideal gases (in the absence of condensation) T = T~8~6r. 8 is the expansion parameter given by the fraction of final volume to initial volume. For intermediate
expansion parameters the temperature dependence differs from a power law indicating condensation. For large expansion parameter, hydrogen is condensed and its specific heat is small in comparison to that of helium gas. The integrated absorbance is Iv= Ioglo(Io/I), where I and I0 are the transmitted and incident intensities, respectively. Iv = A L (NN) F R / 8, where L is the pathlength and A is a coefficient. A = 10"21 cm 2 for the roto-vibrational line S 1(0).4 F is the fraction of particles that are hydrogen and R is the fraction of hydrogen that is condensed in clusters. The resulting surface induced dipole is another source of infrared absorption, particularly in the pure vibrational line Q1.2 This effect is not considered. To understand these effects we use the variable • = (N/V) F R/8 or optical density. Figure 2 shows the final temperature of the clusters as a function of the optical density. Since absorbance changes below 1% are not readily detectable, for pathlengths of 10 cm the minimum optical density detectable is 1018/cm3. In this simulations we have assumed that the gases are ideal because we believe that this does not introduce significant errors. To check this we calculated T~ as a function of the expansion parameter from experimental thermodynamic data for pure helium. 6 Our results do not deviate significantly from those obtained for ideal gases.
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1 0 z°
........ I ........ 100 1000
Ratio ( V / V i )
Fig. 1. Temperature of the gas mixture after expansion. The initial temperature is 28 K. Initial pressure and helium density are 1.275 MPa and 3.3x1021 cm 3, respectively.
Fig. 2. Temperature as a function of optical density. The initial conditions are the same as in Fig. 1.
The simulations reported in this paper show that for such densities temperatures on the order of 3 K are achievable and suggest that experiments of this type may provide the first direct proof of their state. This work was supported in part by NSF through Grant DMR9013127.
H.J. Marls, G.M. Seidel, and T.E. Huber, J. Low Temp. Phys. 51,471 (1983). H.J. Marls, G.M. Seidel, F.I.B. Williams, and J.G. Lardon, Phys. Rev. Lett.56, 2380 (1986). E. L. Knuth, B. Schilling, and J. P. Toennies, 17th International Symposium on Rarefied Gas Dynamics, Aachen 1990.
H.P. Gush, W.F.G. Hare, E.J. Allin, and H.L. Welsh. Can. J. Phys. 38, 176 (1960) T.E. Huber and C.A. Huber, Phys. Rev. Lett. 5__9,1120 (1987). R.D. Carty, U.S. Department of Commerce, Technical Notes, NBS-631.