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Generation of small unsupported hydrogen clusters
Physb=21190=Reddy=Venkatachala=BG
Physica B 284}288 (2000) 383}384
Generation of small unsupported hydrogen clusters T.E. Huber*, P. Constant Howard University, 500 College St. N.W., Washington, D.C. 20059, USA
Abstract Molecular hydrogen is a composite boson that is lighter than He and He, and a super#uid phase has been predicted for ¹ (5 K. Since hydrogen freezes at 14 K the challenge is to supercool the liquid at low enough temperature for # super#uidity to occur. Much progress has been made towards this end, using one of the two approaches: the material is dispersed in a nanoporous host and/or it is made into unsupported microparticles. We discuss an approach based on a cryogenic `Wilson chambera. 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: Bose}Einstein condensation; Hydrogen; Super#uidity
1. Introduction It has long been speculated that, due to the low mass of the hydrogen molecule, liquid H might be a super#uid at low temperatures. The temperature for Bose}Einstein condensation ¹ of para-hydrogen (J"0) in the ideal # gas approximation is 6.6 K, ¹ of ortho-hydrogen # (J"1) is 1.5 K. Since H has a triple point for freezing of 13.8 K, the challenge is to supercool the liquid to low enough temperatures. Quantitative estimates of the extent to which it is possible to supercool liquid H , includ ing quantum tunneling, were published by Maris et al. [1]. One way to depress the triple point is to restrict the dimensions of the sample. The lowest temperature at which the freezing was observed is 8.5 K for a 2.5 nm pore diameter porous Vycor glass (PVG) [2]. Knuth, Schilling, and Toennies supercooled hydrogen in a supersonic beam [3]. The lowest cluster temperatures deduced were around 6 K. Although this method is very interesting, diagnostic techniques for such short lived clusters are di$cult to develop. A method is needed that generates more material and with a longer residence time in the scattering apparatus. One way is to generate micropar-
* Corresponding author. Fax: #1-202-806-5475. E-mail address: [email protected] (T.E. Huber)
ticles by the relatively `slowa expansion of a mixture of p-H and helium by a method analogous to the Simon refrigerator. The nucleation of microparticles in a supersaturated gas can be homogeneous or heterogeneous. In the absence of dust and ions, the supersaturated vapor will condense in small droplets as a result of #uctuations (homogeneous nucleation). A theory of this process was "rst given by Volmer and Weber see Ref. [4]. Their classical approach allows for a calculation of nucleation rates that stand well to experimental tests. One case that is particularly relevant here is the nucleation rate of supersaturated helium gas at low temperatures in a cloud chamber [5]. If these rates were found to be slow, the clusters would not have time to grow during the expansion. However, the nucleation rates are found to be very high, with homogeneous nucleation proceeding readily. Here we report "rst time measurement of the critical supersaturation of molecular H . We have employed a low-temperature cell (volume"10 cm) with windows that allow optical access. In this study we have used a near-infrared absorption apparatus with fast response (0.3 ms). The experimental method consists in admitting gas at pressure P slightly less than the condensation pressure P . Then the gas is expanded adiabatically, over a time of about 0.1 s, by opening a valve to an under-pressurized
0921-4526/00/$ - see front matter 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 7 7 4 - X
Physb=21190=SNR=VVC=BG
384
T.E. Huber, P. Constant / Physica B 284}288 (2000) 383}384
Following the classical nucleation theory [5], the nucleation rate of hydrogen is
Fig. 1. The expansion of pure hydrogen gas as indicated in the text. The dashed line is the equilibrium vapor pressure [6].
container, thereby controlling the "nal pressure of the expansion. As a result, the gas in the cell becomes colder and, for large expansions, saturated. In Fig. 1, we show several series of expansions for three initial temperatures which are ¹ "28.5, 29, and 32 K and are represented by circles, squares and hexagons, respectively. The initial state is the state with the highest temperature for each series. The empty symbols represent expansions that did not exhibit optical beam attenuation at a wavelength of 2 lm. The full symbols represent cases where we observed substantial optical beam attenuation. The degree of supersaturation is obtained for the full symbols and is S"P /P "1.10$0.05 for ¹ "29 K.
S "exp[0.557v (p /¹)/2], (1) ! *% where v is the molar volume and p is the surface *% tension of liquid hydrogen in contact with the vapor. Using typical parameters for hydrogen, v "35 cm/mol, p "10\ J/cm and ¹"27 K [6], we "nd that *% S "1.14. This indicates that the nucleation pro! cess in e!ect in our cryogenic microparticle generator is homogeneous. At lower temperatures condensation by dust and ions will likely be more important and we plan to study this aspect of our experiment more. Also interesting is the study of the dependence of critical supersaturation upon the optical wavelength in order to obtain the microparticle size distribution.
References [1] H.J. Maris, G.M. Seidel, T.E. Huber, J. Low Temp. Phys. 51 (1983) 471. [2] R.H. Torii, H.J. Maris, G.M. Seidel, Phys. Rev. B 41 (1990) 7167. [3] E.L. Knuth, P. Schilling, J.P. Toennies, in: A.E. Beylich (Ed.), Proceedings of the 17th International Symposium on Rare"ed Gas Dynamics, 1990, Aachen, Germany, VCH Weinheim, New York, 1991, p. 1035. [4] L. Farkas, Z. Phys. Chem. (Leipzig) A 125 (1927) 236. [5] M.H. Edwards et al., Can. J. Phys. 38 (1960) 335. [6] R.B. Scott, Cryogenic Engineering, Van Nostrand, New York, 1959, p. 298.
Physica B 284}288 (2000) 383}384
Generation of small unsupported hydrogen clusters T.E. Huber*, P. Constant Howard University, 500 College St. N.W., Washington, D.C. 20059, USA
Abstract Molecular hydrogen is a composite boson that is lighter than He and He, and a super#uid phase has been predicted for ¹ (5 K. Since hydrogen freezes at 14 K the challenge is to supercool the liquid at low enough temperature for # super#uidity to occur. Much progress has been made towards this end, using one of the two approaches: the material is dispersed in a nanoporous host and/or it is made into unsupported microparticles. We discuss an approach based on a cryogenic `Wilson chambera. 2000 Published by Elsevier Science B.V. All rights reserved. Keywords: Bose}Einstein condensation; Hydrogen; Super#uidity
1. Introduction It has long been speculated that, due to the low mass of the hydrogen molecule, liquid H might be a super#uid at low temperatures. The temperature for Bose}Einstein condensation ¹ of para-hydrogen (J"0) in the ideal # gas approximation is 6.6 K, ¹ of ortho-hydrogen # (J"1) is 1.5 K. Since H has a triple point for freezing of 13.8 K, the challenge is to supercool the liquid to low enough temperatures. Quantitative estimates of the extent to which it is possible to supercool liquid H , includ ing quantum tunneling, were published by Maris et al. [1]. One way to depress the triple point is to restrict the dimensions of the sample. The lowest temperature at which the freezing was observed is 8.5 K for a 2.5 nm pore diameter porous Vycor glass (PVG) [2]. Knuth, Schilling, and Toennies supercooled hydrogen in a supersonic beam [3]. The lowest cluster temperatures deduced were around 6 K. Although this method is very interesting, diagnostic techniques for such short lived clusters are di$cult to develop. A method is needed that generates more material and with a longer residence time in the scattering apparatus. One way is to generate micropar-
* Corresponding author. Fax: #1-202-806-5475. E-mail address: [email protected] (T.E. Huber)
ticles by the relatively `slowa expansion of a mixture of p-H and helium by a method analogous to the Simon refrigerator. The nucleation of microparticles in a supersaturated gas can be homogeneous or heterogeneous. In the absence of dust and ions, the supersaturated vapor will condense in small droplets as a result of #uctuations (homogeneous nucleation). A theory of this process was "rst given by Volmer and Weber see Ref. [4]. Their classical approach allows for a calculation of nucleation rates that stand well to experimental tests. One case that is particularly relevant here is the nucleation rate of supersaturated helium gas at low temperatures in a cloud chamber [5]. If these rates were found to be slow, the clusters would not have time to grow during the expansion. However, the nucleation rates are found to be very high, with homogeneous nucleation proceeding readily. Here we report "rst time measurement of the critical supersaturation of molecular H . We have employed a low-temperature cell (volume"10 cm) with windows that allow optical access. In this study we have used a near-infrared absorption apparatus with fast response (0.3 ms). The experimental method consists in admitting gas at pressure P slightly less than the condensation pressure P . Then the gas is expanded adiabatically, over a time of about 0.1 s, by opening a valve to an under-pressurized
0921-4526/00/$ - see front matter 2000 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 7 7 4 - X
Physb=21190=SNR=VVC=BG
384
T.E. Huber, P. Constant / Physica B 284}288 (2000) 383}384
Following the classical nucleation theory [5], the nucleation rate of hydrogen is
Fig. 1. The expansion of pure hydrogen gas as indicated in the text. The dashed line is the equilibrium vapor pressure [6].
container, thereby controlling the "nal pressure of the expansion. As a result, the gas in the cell becomes colder and, for large expansions, saturated. In Fig. 1, we show several series of expansions for three initial temperatures which are ¹ "28.5, 29, and 32 K and are represented by circles, squares and hexagons, respectively. The initial state is the state with the highest temperature for each series. The empty symbols represent expansions that did not exhibit optical beam attenuation at a wavelength of 2 lm. The full symbols represent cases where we observed substantial optical beam attenuation. The degree of supersaturation is obtained for the full symbols and is S"P /P "1.10$0.05 for ¹ "29 K.
S "exp[0.557v (p /¹)/2], (1) ! *% where v is the molar volume and p is the surface *% tension of liquid hydrogen in contact with the vapor. Using typical parameters for hydrogen, v "35 cm/mol, p "10\ J/cm and ¹"27 K [6], we "nd that *% S "1.14. This indicates that the nucleation pro! cess in e!ect in our cryogenic microparticle generator is homogeneous. At lower temperatures condensation by dust and ions will likely be more important and we plan to study this aspect of our experiment more. Also interesting is the study of the dependence of critical supersaturation upon the optical wavelength in order to obtain the microparticle size distribution.
References [1] H.J. Maris, G.M. Seidel, T.E. Huber, J. Low Temp. Phys. 51 (1983) 471. [2] R.H. Torii, H.J. Maris, G.M. Seidel, Phys. Rev. B 41 (1990) 7167. [3] E.L. Knuth, P. Schilling, J.P. Toennies, in: A.E. Beylich (Ed.), Proceedings of the 17th International Symposium on Rare"ed Gas Dynamics, 1990, Aachen, Germany, VCH Weinheim, New York, 1991, p. 1035. [4] L. Farkas, Z. Phys. Chem. (Leipzig) A 125 (1927) 236. [5] M.H. Edwards et al., Can. J. Phys. 38 (1960) 335. [6] R.B. Scott, Cryogenic Engineering, Van Nostrand, New York, 1959, p. 298.