Correlation Effects in Kinetics of One‐Dimensional Atomic Systems

Abstract

The paper is devoted to the analysis of the correlation effects and manifestations of general properties of 1D systems (such as spatial heterogeneity that is associated with strong density fluctuations, the lack of phase transitions, the presence of frozen disorder, confinement, and blocked movement of nuclear particle by its neighbours) in nonequilibrium phenomena by considering the four examples. The anomalous transport in zeolite channels is considered. The mechanism of the transport may appear in carbon nanotubes and MOF structures, relaxation, mechanical properties, and stability of nonequilibrium states of free chains of metal atoms, non-Einstein atomic mobility in 1D atomic systems. Also we discuss atomic transport and separation of two-component mixture of atoms in a 1D system—a zeolite membrane with subnanometer channels. We discuss the atomic transport and separation of two-component mixture of atoms in a 1D system—zeolite membrane with subnanometer channels. These phenomena are described by the response function method for nonequilibrium systems of arbitrary density that allows us to calculate the dynamic response function and the spectrum of relaxation of density fluctuations 1D atomic system.

Emerging quasi-0D states at vanishing total entropy of the 1D hard sphere system: A coarse-grained similarity to the car parking problem

“…Consequently, we have a range of volume fraction φ s as the onset densities of a solidlike behavior: 0.7 < φ s < 0.83 [26]. First, it is to be noted that a theoretical approach to the formation of high-and low-density 1D clusters has demonstrated the existence of a second maximum for the compressibility of an attractive 1D system at φ = 0.71, which is close to the aforementioned lower bound of φ s , and is also consistent with a large interatomic distance in monoatomic Au chains experimentally observed [19,20]. The upper bound of φ s (the volume fraction of 0.83) is determined by the vanishing residual multi-particle entropy of the 1D HS system [26][27][28], which also agrees with a jamming density of the square lattice model driven by strong external fields [29][30][31].…”

“…The upper bound of φ s (the volume fraction of 0.83) is determined by the vanishing residual multi-particle entropy of the 1D HS system [26][27][28], which also agrees with a jamming density of the square lattice model driven by strong external fields [29][30][31]. Yet the bases of these coincidences are tentative not merely because the decrease of attractive potential strength has been found to smear the extremal compressibility around the lower bound [19,20], but also beacause there remain some controversies over the aforementioned criterion for the upper bound using the residual entropy [26][27][28].…”

“…While it has been demonstrated that eq. ( 31) with a truncation of ĉ ≈ C 0 is relevant to describing density fluctuations of a finite cluster formed in dense 1D HS system [18][19][20] and can be extended to two-component systems [51], no dynamical crossover has been detected prior to close packing. Our thermodynamic view, however, suggests the possibility that the interfacial fluctuations of 1D clusters would compete with the free energetic gain of the quasi-0D state when φ ≥ φ c = 0.731 • • • , which has not been taken into ac-count by eq.…”

“…The comparison between the blue and red broken lines demonstrates the equivalence of eqs. (10) and (20). The downward green arrow indicates that the slopes of fco(φ; 0.5, φ1) and f het (φ; 0, φ1) approach each other as φ1 → φc and merge at φ1 = φc = 0.731 • • • .…”

“…Theoretically, the appearance of self-generated pinning by geometrically localized particles is to be explained in terms of collective particle dynamics. The dynamical density functional theory [17], however, has found no signatures of the temporary freezing in the 1D HS system [17][18][19][20], other than the dynamical crossover from the single-file diffusion to the Goldstone-type dynamics which can be reproduced with the help of the response function method using the frequency spectrum of relaxational dynamics in the 1D HS system [12,20]. From thermodynamic aspect, the exact free energy of the uniform 1D HS system has also predicted no anomaly without close packing as [21][22][23][24][25]; nevertheless, there exists a variety of theoretical criteria for a crossover phenomenon from the conventional liquid to a pseudo-crystalline state in the 1D HS system [26].…”