Anomalous effective dimensionality of quantum gas adsorption near nanopores

Abstract

Three problems involving quasi-one-dimensional (1D) ideal gases are discussed. The simplest problem involves quantum particles localized within the 'groove', a quasi-1D region created by two adjacent, identical and parallel nanotubes. At low temperature (T), the transverse motion of the adsorbed gas, in the plane perpendicular to the axes of the tubes, is frozen out. Then, the low T heat capacity C(T) of N particles is that of a 1D classical gas: C(*)(T) = C(T)/(Nk(B)) --> 1/2. The dimensionless heat capacity C(*) increases when T ≥ 0.1T(x, y) (transverse excitation temperatures), asymptoting at C(*) = 2.5. The second problem involves a gas localized between two nearly parallel, co-planar nanotubes, with small divergence half-angle γ. In this case, too, the transverse motion does not contribute to C(T) at low T, leaving a problem of a gas of particles in a 1D harmonic potential (along the z axis, midway between the tubes). Setting ω(z) as the angular frequency of this motion, for T ≥ τ(z) ≡ ω(z)ħ/k(B), the behavior approaches that of a 2D classical gas, C(*) = 1; one might have expected instead C(*) = 1/2, as in the groove problem, since the limit γ ≡ 0 is 1D. For T << τ(z), the thermal behavior is exponentially activated, C(*) ∼ (τ(z)/T)(2)e(-τ(z)/T). At higher T (T ≈ ε(y)/k(B) ≡ τ(y) >> τ(z)), motion is excited in the y direction, perpendicular to the plane of nanotubes, resulting in thermal behavior (C(*) = 7/4) corresponding to a gas in 7/2 dimensions, while at very high T (T > ħω(x)/k(B) ≡ τ(x) >> τ(y)), the behavior becomes that of a D = 11/2 system. The third problem is that of a gas of particles, e.g. (4)He, confined in the interstitial region between four square parallel pores. The low T behavior found in this case is again surprising--that of a 5D gas.

Quasi-One Dimensional Fluids That Exhibit Higher Dimensional Behavior

“…The adsorbed gas then exhibits Q1D behavior at low N. However, one can also inquire about the case when the tubes are not quite parallel, but instead diverge, leaving a particularly attractive region between them, with a minimum potential energy (V 0 ) located at equilibrium position r 0 . In a forthcoming study, [1] we will report remarkable results for this geometry, as exemplified in Fig. 3.…”

“…[1] For example, chemists, materials scientists and physicists have created and explored numerous physical systems in which atoms and molecules are confined within quasi-one dimensional (Q1D) environments. The variety of these systems is remarkable, such as the peapod geometry, i.e., a line of buckyballs within a carbon nanotube, [2,3] fluids within artificial materials created by templating [4,5] and Q1D optical lattices created by laser fields.…”

The heat capacity of nitrogen chain in grooves of single-walled carbon nanotube bundles

“…One or several layers of molecules (atoms) adsorbed at the outer surface of the c-SWNT bundle form quasi-two-dimensional (2D) or quasithree-dimensional (3D) systems. The 1D, 2D and 3D systems have different properties at low temperatures [6,[33][34][35][36][37][38][39].…”

Quasi-One Dimensional Fluids That Exhibit Higher Dimensional Behavior

“…One of the most interesting topics within modern condensed matter physics is that of phenomena in reduced dimensionality, resulting from some degree of spatial localization of the particles comprising a system. [1] For example, chemists, materials scientists and physicists have created and explored numerous physical systems in which atoms and molecules are confined within quasi-one dimensional (Q1D) environments. The variety of these systems is remarkable, such as the peapod geometry, i.e., a line of buckyballs within a carbon nanotube, [2,3] fluids within artificial materials created by templating [4,5] and Q1D optical lattices created by laser fields.…”