Investigating the Lapse in Third Sound Signal from Superfluid 4He Adsorbed on Carbon Nanotubes

Two theoretical models are developed and tested to understand a particular mode of superfluid vibration called third sound. In particular we are trying to explain a brief lapse in third sound in early 4He film development on a carbon nanotube substrate. We use a resonant cavity of nanotubes at 1.3 K and introduce 4He gas. Using a variable-frequency heat pulse and a thermometer, we utilize the temperature waves generated by the superfluid oscillations in order to detect third sound. The experimental data consists of resonant peaks, representing superfluid oscillation, at various film thicknesses. There are two goals within the theoretical work: accurate calculation of film thickness from 4He gas pressure readings, and mathematical models for two qualitative explanations. These two hypotheses—quasi-solidification and nanotube filling—are compared against experiment. We have found that quasisolidification is a good predictor of the lapse in third sound. More data is needed to more firmly support this conclusion, and several experimental and theoretical improvements are proposed. If further evidence points towards the quasi-solidification model, it could become part of the explanation of superfluid behavior in thin films. Introduction The intrinsic properties of superfluid 4He lead to several novel sound modes, some of which have well-formulated theories that are experimentally confirmed. The following research was conducted to more clearly understand a particular mode called third sound. In particular, this work aims to experimentally confirm and theoretically explain a brief lapse in third sound as thin films of 4He build up on a carbon nanotube substrate. The third sound phenomenon is based on several physical facts: • According to Landau’s two-fluid model, the superfluid phase consists of two components, a normal fluid and a superfluid, which act independently. • A superfluid has zero viscosity. • A superfluid acts as a thermal superconductor. It flows frictionlessly to eliminate temperature gradients. • Temperature moves through a superfluid as a wave. (In a normal fluid, it spreads diffusively.) [1] Third sound occurs on very thin films of liquid helium. These films are created by the van der Waals potential, which is strong at close range. The vdW force is the dipole-dipole electric attraction that forms between 4He gas and a solid surface (called the substrate). Third sound occurs when this film is formed at a temperature below 2.18 K, and is disturbed by a temperature gradient. A thermal pulse will cause the superfluid component to propagate towards the heat source, while the normal fluid remains viscously clamped to the surface. This surge will lead to peaks of the superfluid component. These cold, superfluid-dense peaks will be restored through the vdW attraction, and through the nature of the superfluid which now flows towards the warmer troughs. [1] The resulting thickness and temperature waves—third sound—can be measured using a thermometer. Third sound has been studied and theorized on flat substrates, but there is not yet a comprehensive understanding of this behavior on cylindrical geometry. We are working towards a complete theoretical model for very thin 4He films adsorbed on carbon nanotubes. There are two goals in this theoretical work: 1. Accurately calculate film thickness based on experimental cell gas pressure as 4He film builds on the nanotube substrate. 2. Explain the loss and re-entrant behavior of the superfluid third sound signal found experimentally (Figure 1). Figure 1. A lapse in third sound signal in early layers of superfluid film In fact, achieving the first goal is the key to achieving the second goal, as will be explained later in the paper.