Erratum: Fermi Statistics of Two-Dimensional Free-Electron Systems [Am. J. Phys. 32, 749 (1959)]

1965 ◽  
Vol 33 (2) ◽  
pp. 172-172
Author(s):  
J. P. McKelvey ◽  
E. F. Pulver
Keyword(s):  
Free Electron ◽  
Two Dimensional ◽  
Electron Systems ◽  
Fermi Statistics

Fermi Statistics of Two-Dimensional Free-Electron Systems

1964 ◽  
Vol 32 (10) ◽  
pp. 749-761 ◽  
Author(s):  
J. P. McKelvey ◽  
E. F. Pulver
Keyword(s):  
Free Electron ◽  
Two Dimensional ◽  
Electron Systems ◽  
Fermi Statistics

Pathway Complexity in the Stacking of Imine-linked Macrocycles Related to Two-Dimensional Covalent Organic Frameworks

2019 ◽  
Author(s):  
Shiwei Wang ◽  
Anton Chavez ◽  
Simil Thomas ◽  
Hong Li ◽  
Nathan C. Flanders ◽  
...  
Keyword(s):  
Temperature Dependence ◽  
Structural Similarity ◽  
Discrete Models ◽  
Side Chains ◽  
Two Dimensional ◽  
Assembly Process ◽  
Covalent Organic Frameworks ◽  
Electron Systems ◽  
Monomer Structure ◽  
Kinetic Traps

This work reports on the assembly of imine-linked macrocycles that serve as models of two-dimensional covalent organic frameworks (2D COFs). Interlayer interactions play an important role in the formation of 2D COFs, yet the effect of monomer structure on COF formation, crystallinity, and susceptibility to exfoliation are not well understood. For example, monomers with both electron-rich and electron-poor π-electron systems have been proposed to strengthen interlayer inter-actions and improve crystallinity. Here we probe these effects by studying the stacking behavior of imine-linked macrocycles that represent discrete models of 2D COFs. <div><br></div><div>Specifically, macrocycles based on terephthaldehyde (PDA) or 2,5-dimethoxyterephthaldehyde (DMPDA) stack upon cooling molecularly dissolved solutions. Both macrocycles assemble cooperatively with similar ΔHe values of -97 kJ/mol and -101 kJ/mol, respectively, although the DMPDA macrocycle assembly process showed a more straightforward temperature dependence. Circular dichroism spectroscopy performed on macrocycles bearing chiral side chains revealed a helix reversion process for the PDA macrocycles that was not observed for the DMPDA macrocycles. <br></div><div><br></div><div>Given the structural similarity of these monomers, these findings demonstrate that the stacking processes associated with nanotubes derived from these macrocycles, as well as for the corresponding COFs, are complex and susceptible to kinetic traps, casting doubt on the relevance of thermodynamic arguments for improving materials quality. <br></div>

Two-dimensional electron systems and interfacial coupling in LaCrO3/KTaO3 heterostructures

2021 ◽  
Vol 118 (19) ◽  
pp. 192905
Author(s):  
Athby H. Al-Tawhid ◽  
Divine P. Kumah ◽  
Kaveh Ahadi
Keyword(s):  
Two Dimensional ◽  
Electron Systems ◽  
Dimensional Electron ◽  
Interfacial Coupling ◽  
Two Dimensional Electron Systems
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