Avalanches and Hysteresis: Helium in a Porous Geometry
Hysteresis and Avalanches
Several years ago we engaged in a study of the capillary condensation and avalanche
properties of helium in the porous substrate Nuclepore. Nuclepore is a polycarbonate
sheet 10 microns thick, perporated by nearly straight holes which intersect. The
pore size we most often utilize is 2000 Angstroms, although we have studied
pores as small as 300 Angstroms. We measured the amount of helium
in the Nuclepore by means of direct capacitance measurements with capacitance
electrodes evaporated directly onto the Nuclepore surface. The Nuclepore was sealed
in an experimental chamber and helium could be added or subtracted through a capillary
fill line. Also in the chamber was a substrate on which we could measure the time of flight of
third sound pulses
which gave an in situ measure of the chemical potential when the helium film is
in the superfluid state.
Figure 1: An example of a global hysteresis loop for the filling and draining of
Nuclepore. As helium is added to the sample cell, the the third sound time of
flight grows (the helium film on the third sound substrate grows in thickness) and
the capacitance increases as the pores begin to fill with helium, first as a film,
then as filled pores. For relatively large chemical potential, the pores have
completely filled with helium and the capacitance becomes independent of the third
sound time of flight. Withdrawal of the helium results in a draining of the pores.
The draining is initially dramatic over a narrow range of chemical potential values.
Our interest was in the hysteresis properties of the Nuclepore as a model porous
system - one which is not too complicated for analysis, but is not trivial either.
Measurements have demonstrated return point memory, and the near congruence of
hysteresis subloops taken between common chemical potential end points [1,2].
Figure 2: An illustration of the property of return point memory (the return of the
capacitance to the starting value following a hysteresis sub-loop), and the near
congruence of hysteresis subloops taken between common chemical potential values. Helium is admitted to the sample cell and then
withdrawn, added again, etc., in a sequence of steps. Note that the various
subloops have nearly identical shapes. If the material were composed of pores which
did not interact, the Preisach model for independent domains (taken from the
literature of magnetic phenomena) would predict perfect congruence. The lack of perfect congruence indicates that the pores interact.
Here the main filling and draining curves have
been offset for clarity.
Measurements taken as helium is withdrawn from the capillary condensed material
reveal avalanches (Figure 3, below) as relatively large numbers of
pores drain in a correlated
manner [1,2,5]. The presence of avalanches has not been observed for fluids
in other porous systems, presumably due to the fact that our working fluid
is superfluid helium, rather than an ordinary viscous fluid such as argon or water.
Figure 3: An example of the capacitance of a (different) Nuclepore sample during the
slow withdrawal of helium from the sample cell. Shown in the left figure is the
capacitance as a function of time. The much higher resolution view of the right shows
that the capacitance of the sample is reduced in a series of steps during which the
pores drain via avalanches which involve large numbers of pores draining (on the resoultion
of the measurement) nearly simultaneoulsy. The largest avalanches seen involve several
Our experiments  have shown that the avalanches are
highly correlated across the samples. Two separate capacitors on a single
sample show avalanches which
are highly correlated in time and in amplitude. The avalanches are due to pores
distributed widely (and dilutely) across the substrate. The interaction between the pores
has been shown to be enabled by the presence of the superfluid. Pore to pore connections
interior to the samples have
some importance in determining avalance size, but the presence of the superfluid film
provides essential coupling. This has been determined by measuring the correlation for
avalanches seen on two separate samples of Nuclepore (and finding none) and then measuring
the correlations for two separate samples connected by a non-porous bridge which creates a film
connection, but no porous conncetion. Our most recent publications document substantial details
of our work [6,7,8]
 M.P. Lilly, P.T. Finley and R.B. Hallock, Phys. Rev. Lett. 71, 4186 (1993).
 M.P. Lilly and R.B. Hallock, Physica B 194-196, 691 (1994).
 M.P. Lilly and R.B. Hallock, Mat. Res. Soc. Symposium Proceedings,
vol. 366, ed. J.M. Drake et al., 1995, p. 241.
 M.P. Lilly and R.B. Hallock, J. Low Temp. Phys. 101, 385 (1995).
 M.P. Lilly, A.H. Wootters and R.B. Hallock, Phys. Rev. Lett. 77, 4222 (1996).
 M.P. Lilly and R.B. Hallock, "Probing the Internal Structure of Nuclepore with Hysteretic Capillary Condensation", (with M.P.
Lilly), Phys. Rev. B 63, 174503 (2001).
 M.P. Lilly and R.B. Hallock, "Avalanche Behavior in the Draining of Superfluid Helium from the
Porous Material Nuclepore" (with M.P. Lilly), Phys. Rev. B 64, 024516 (2001).
 M.P. Lilly, A.H. Wootters and R.B. Hallock, "Avalanches in the Draining of Nanoporous Nuclepore
Mediated by the Superfluid Helium Film" (with M.P. Lilly and A.H. Wootters),
Phys. Rev. B 65, 104503 (2002).