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摘要
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 gamma. 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 omega(z) as the angular frequency of this motion, for T >= tau(z) equivalent to omega(z)(h) over bar /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 gamma equivalent to 0 is 1D. For T << tau(z), the thermal behavior is exponentially activated, C* similar to (tau(z)/T)(2)e-(tau z/T). At higher T (T approximate to is an element of(y)/k(B) equivalent to tau(y) >> tau(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 > (h) over bar omega(x)/k(B) equivalent to tau(x) >> tau(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.
- 出版日期2010-8-25
