Anomalous effective dimensionality of quantum gas adsorption near nanopores

Abstract

Three problems involving quasi-one-dimensional (1D) ideal gases are discussed. Thesimplest problem involves quantum particles localized within the ‘groove’, a quasi-1Dregion created by two adjacent, identical and parallel nanotubes. At low temperature (T), the transverse motion of the adsorbed gas, in the planeperpendicular to the axes of the tubes, is frozen out. Then, the lowT heatcapacity C(T) of N particles is that of a 1D classical gas: . The dimensionless heat capacityC* increaseswhen T ≥ 0.1Tx, y (transverse excitation temperatures), asymptoting atC* = 2.5. The second problem involves a gas localized between two nearlyparallel, co-planar nanotubes, with small divergence half-angleγ. In this case, too, the transverse motion does not contribute toC(T) atlow T, leaving a problem of a gas of particles in a 1D harmonic potential (along thez axis, midway betweenthe tubes). Setting ωz as the angular frequency of this motion, for , the behavior approaches that of a 2D classical gas,C* = 1; one might haveexpected instead C* = 1/2, as in the groove problem, since the limit is 1D. For , the thermal behavior is exponentially activated,C* ∼ (τz/T)2e − τz/T. Athigher T (), motion is excited in the y direction, perpendicular to the plane of nanotubes, resulting in thermal behavior (C* = 7/4) corresponding to agas in 7/2 dimensions,while at very high T (), the behavior becomes that of aD = 11/2 system. The third problem is that of a gas of particles, e.g. 4He, confined in the interstitial region between four square parallel pores. The lowT behavior found in this case is again surprising—that of a 5D gas.