Thermodynamic measurements of the first layer of Ne adsorbed on closed-end single-walled carbon nanotube bundles

We report the results of thermodynamic measurements done on Ne films adsorbed on HiPCo™ single-walled, closed-end, purified carbon nanotube bundles. The heat capacity was measured for 17 coverages between 0.015 and 1.14 single atomic layers for $1.8\mathrm{K}<T<19\mathrm{K}$. A few complementary adsorption isotherms were measured on the same cell over a similar range of coverages for $18.1\mathrm{K}<T<29.5\mathrm{K}$. Our results indicate that Ne deposits, in order, in high binding energy sites, the grooves on the outside of the bundles, the surface of the outer nanotubes, and after compressing the full monolayer, on a second layer. All of the films show solidlike behavior in the range studied. For the lowest coverage films, we compare our results to theoretical estimates and calculate the one-dimensional Debye temperature. For the higher coverage films, we calculate two-dimensional Debye temperatures and compare to results obtained on Ne adsorbed on flat graphite (Grafoil™). We estimate the two-dimensional (2D) compressibility of the films near monolayer completion from the vapor pressure isotherms. Agreement is found between the monolayer completion coverage inferred from heat-capacity isotherms and a minimum in the compressibility. In spite of the solidlike behavior and similarities to Ne/graphite, we do not observe any phase transition in the range of temperatures and coverages studied, which overlaps with the sublimation, melting, and vaporization transitions of 2D Ne.

Figure 1

Pressure isotherm for Ne adsorbed on SWNTB. Point B is indicated in bold.

Figure 2

Background heat capacity (filled squared) and background plus $1.99\mathrm{scc}$ STP Ne adsorbed (open circles) vs $T$. Inset shows the lowest $T$ data in an expanded scale.

Figure 3

$C$ vs $T$ of Ne films at several low coverages where the film is expected to be 1D. Each curve is offset by $0.0075\mathrm{J}∕\mathrm{K}$ for clarity.

Figure 4

$C$ vs $T$ of Ne films at few coverages within the single-line phase and into the three-line phase. Each curve is offset from the one below by $0.015\mathrm{J}∕\mathrm{K}$.

Figure 5

$C$ vs $T$ at several Ne coverages from filling of the grooves into the second layer. Each curve is offset by $0.03\mathrm{J}∕\mathrm{K}$.

Figure 6

Heat-capacity isotherms at select temperatures for Ne film on SWNTB. The upward arrow marked M shows monolayer completion. Downward arrow points to a feature close to three-line phase completion.

Figure 7

Specific heat isotherm for different coverages of Ne adsorbed on SWNTB. Arrows are shown pointing to coverage corresponding to (H) heterogeneous sites completion, (3L) three-line completion, and (M) monolayer completion.

Figure 8

(Color online) Specific heat isotherm up to $34.6\mathrm{scc}$ of Ne adsorbed on SWNTB. Estimated vertical error bars are shown for some of the data points.

Figure 9

Isosteric heat calculated from pressure isotherm data for Ne adsorbed on SWNTB (filled squares). Monolayer is indicated with an arrow marked M. Open circles are the isosteric heat of first layer Ne adsorbed on Grafoil (Ref. 19) scaled as described in the text. The broken line at $255\mathrm{K}$ is the latent heat of sublimation for bulk Ne at its triple point, and the solid line at $378\mathrm{K}$ is the depth of the laterally averaged potential (Ref. 39) for Ne adsorbed on graphite.

Figure 10

Log-log plot of measured specific heat for $3.98\mathrm{scc}$ Ne film vs temperature (solid circles). Also shown are results for the model of Kostov et al. with $3.08\mathrm{\AA }$ (dashed line) and $2.92\mathrm{\AA }$ (dotted line) Ne-Ne separations and for a 3D Einstein model (solid line) with characteristic temperature of $28\mathrm{K}$, see text.

Figure 11

Log-log plot of the difference specific heat between $23.8\mathrm{scc}$ film and a $5.98\mathrm{scc}$ film of Ne (solid circles). Also shown are results from the model of Kostov et al. with 3.08 and $2.92\mathrm{\AA }$ Ne-Ne separations.

Figure 12

2D Debye temperature of adsorbed Ne films at several coverages. Coverages of Huff and Dash are altered to overlap the presently studied range of coverage (see text).

Figure 13

Measured specific heat plotted as a function of reduced temperature for 23.8 and $133.8\mathrm{scc}$ Ne. The log-log plot also shows the specific heat calculated by solving the integrals numerically for a 2D and 3D Debye solid.

Figure 14

2D Debye temperatures for Ne on Grafoil $(1–10\mathrm{K})$ and on carbon nanotube bundles $(2–8\mathrm{K})$.

Figure 15

Isothermal compressibility of the 2D Ne film in ${\mathrm{m}}^2∕\mathrm{J}$ at $19.2\mathrm{K}$ around monolayer coverage. Monolayer completion (marked M) is indicated by an arrow.

Figure 16

Log-log plot of difference specific heat for films in the second layer in terms of number of atoms in excess of a coverage $\left(133.8\mathrm{scc}\right)$ closest to monolayer $(\approx 135\mathrm{scc})$ vs $T$ in the $3–20\mathrm{K}$ range. (a) $153.6–133.8\mathrm{scc}$ and (b) $143.7–133.8\mathrm{scc}$. One negative difference data point from (a) and four from (b) were deleted when plotted in log scale. Log-log plot exaggerates scatter at the smallest specific heat.

Figure 17

Heat capacity between 5 and $8\mathrm{K}$ showing a feature in the heat capacity at around $6.5\mathrm{K}$. Heat capacity for (a) $29.7\mathrm{scc}$, (b) $46.6\mathrm{scc}$, and (c) $94.2\mathrm{scc}$ Ne films. Error bars are shown for the film heat capacity.

Figure 18

Difference heat capacity (as explained in the text) between 4 and $10\mathrm{K}$ showing a feature in the heat capacity at around $6.5\mathrm{K}$. Also shown on the same plot is the difference between background heat-capacity data and a smooth fit to the background.