LT 21 Proceedings of the 21st International Conference on Low Temperature Physics Prague, August 8-14, 1996

Part S1 - Quantum Fluids and Solids: Helium films

Mass transport in thin superfluid 4He films in porous media

Minoru Kubota, Tatsuya Yano, Takeshi Iida, Goh Ueno, \rladimir Kovacik: Maxim K. Zalalutdinov t

Institute for Solid State Physics, Tokyo University, 7-22-1 Roppongi, Minato-ku, 106 Tokyo, Japan

Possibility to utilize thernml conductivity to study superfluid thin 4He films on porous glass has been exanfined in temperature range T=(0.6-1.1)K. The detailed measurements performed for the fihn in normal state can be qualitatively described by the ideal gas conductance. In the superfluid state at T~0.6K a sharp increase of the temperature gradient along the sample at a critical heating power has been observed below T~. This feature is sinfilax to that at T~IK, where thermal conductivity technique is supposed to be applicable,

1. I N T R O D U C T I O N

Superfluid (SF) thin I-Ie films on porous sub- strates provide unique possibility to study effects of intermediate dimensionality. The fihn, two dimen- sional (2D) itself, is multiply (3D) connected. This, together with the quantization of circulation should lead to formation of vortices with nontrivial topol- og3" and finite critical velocity Vc [1] above which su- pcrflow become dissipative~ Thermal transport tech- nique is one of few methods to study properties of SF 4He fihns [2]. It reflects directly the SF dynam- ics, because heat flux to the system (~ produces flow of the SF component with velocity v, and no entropy to the heater, while counterflow of the gas carries out the entropy and provides cooling. The applicability of the method at low T is believed to be questionable because of insufficient cooling due to low evaporation rate and gas pressure p. All known experiments had been carried out for T > I K [3]. This, however, lim- its the possibility to study submonolayer films with critical temperatures Tc <IK, the subject of our in- terest. The aim of the present work is to examine, whether the method could be used for such systems.

2 . R E S U L T S

Fig.1 shows thermal conductance K v.s. cover- age n curves for sample cell with normal 4 He fihn on porous glass (pore size d=lltm) at different temper- atures. Above critical coverage nc, SF state appears at corresponding temperature. At low n, K does not depend on the amount of He and corresponds to t h e

glass substrate conductance h'0. As n increases, dras- tic increase of K more thaal four orders of magnitude has been observed. Further increase of n leads to saturation of K. The temperature gradient AT(Q)

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Next, fig.2 shows the (~ v.s. AT curves in the SF state for n~30/~mole/m ~ (Tc=630 inK) at dif- ferent T. While at T=Tc we observed linear depen- dence with the slope corresponding to the normal

* On leave from Institute of Physics, Prague, Czech Repub- lic. Supported by .]apaneese Society for Promotion of Science.

f On leave from Luklns Institute of Physical Problems, Moscow, Russia. Supported by Monbusho.

Czechoslovak Journal o( Physics, Vol. 46 (1996), Suppl. $1 43"7

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AT (inK) state conductance, records at lower T reveal a juml) at critical value (~, ~ lOp.W from high conductance, at tr ibuted to the SF behavior, to normal state con- ductance. This is consistent with tile behavior of fihns with Tc ~ l . 2 K [41 and (~ of the same order of magnitude. However, the steplike feature is sharper, and destruction of SF state obviously occurs at the llot end after exceeding (~c. Data in fig.2 correspond to thernlall3.' stabilized state, except for the nearest vicinity of Q,, where the behavior is unstable.

3. DISCUSSION

Observed K(T,n) dependences in tile normal state may be qualitatively explained by the conduc- tance of ideal gas Kig = nigS, l//lcy/, where S~f/ and lefy are corresponding effective cross section and distance from the hot end to the cold walls, obtained by averaging of the cell geometry, and ideal gas con-

1 ductivity ~ig = ~pgcvvA, where A is mean free path, .~ average 4 He atom velocity, cv specific heat at con- stant volume and Pa the gas densit3: The geometry factor, however, might be the major source of er- rors. Utilizing the ideal gas theory, 4He saturated vapor pressure p0(T) curve [5], coverage dependence of tile pressure ln(po/p)=a/Th a [2] (cr is tile van der Vqaals constant and h fihn thickness in atonlic lay- ers) and empirical formula for A of 4He[5], we cal-

eulate Ko(T,n ). Adding measured h'0 we will get solid curves in fig.1 (a=3OK and completion of tile flint layer at nl=17.31mlole/m2). In this model, the sharp increase ill g occurs, when 11 is large enough and Kig >> h'0. Hmvever, I) is still so snlall, that A >> leyy, and, therefore Kig depends on p, which increa.ses drastically with increase of n. When p in- creases so, that A << le/$, Kig I)ecomes pressure and therefore coverage independent.

For our SF state measurements, the difference fi'om the T > I K case is, that A >> icH and the gas flow is bMlistic, while at higher T diffusive. We can argue so because K(n) does not reach the saturation, when SF occurs at nc for 600inK. Nevertheless, the feature at Qc is consistent with the observations at. T , ~1.2K [4]. This supports the applicability of the method for Te < IK . However, the problem is rather complex and one has to take iuto account changes of other parameters as the gas pressure and fihn thick- ness h, latter might occur due to reduced evaporation rate at this T and resulting increase of h at the hot end [2]. The fact, that the jump in AT at Q, oc- curs, when T of the hot end is surely below Te .(AT is low enough), supports the interpretation of Q, as the exceeding of a critical velocity vc [4]. Then, the He flow to the hot end is limited by v~, which leads to overheating and destruction of the SF state there.

4. C O N C L U S I O N S

We have studied thermal conductivity of the sys- tem of 4He fihn on porous substrate and gas for nor- real and SF state at temperatures T=(0.6-1.1)K. All features of tile thermal conductivity in tile normal state can be qualitatively interpreted by that of ideal gas and empty cell conductance. In the SF state, the low T measurements reveal qualitatively the same features, as those at T,~I.2K, despite the different mass transport regime. However, further study is necerssary for complete understanding of tile trans- port processes in tile superfluid fihn - vapor system.

REFERENCES [1] T. Minoguchi, Y.Nagaoka, Prog. Theor. Phys.

80 (1988) 397. {2] S.Teitel, J. Low Temp. Phys. 46 (1982) 77. [3] See for example G.Agnolet et al., Phys. Rev.

Left. 47 (1981) 1537. [4] M.Kubota et ai., d. Low Temp. Phys. 101

(1995} 265. [5] W.H.Keesom, Helium, Elsevier, Amsterdam

(1942).

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