scholarly journals Vibrations of Finite Linear Chains of Molecules

1978 ◽  
Vol 31 (4) ◽  
pp. 313
Author(s):  
J Mahany ◽  
BB Deo
Keyword(s):  
Infinite Chain ◽  
Chain Molecule ◽  
Vibration Frequencies ◽  
Finite Chain ◽  
Linear Chains ◽  
Matrix Partitioning ◽  
Finite Linear ◽  
Long Chain ◽  
Partitioning Technique ◽  
Secular Determinant

Szigeti's (1961) method for obtaining the vibration frequencies of a finite chain (representing a long-chain molecule) from those of an associated infinite chain is analysed by a matrix partitioning technique. It is shown that this method has the advantage of reducing the dimensionality of the secular determinant. The approach is illustrated by an example.

scholarly journals Reaction Kinetics of a Long Chain Molecule

1965 ◽  
Vol 5 (5) ◽  
pp. 245-255
Author(s):  
Masahiro TANAKA ◽  
Nanako INOUE ◽  
Ei TERAMOTO
Keyword(s):  
Reaction Kinetics ◽  
Chain Molecule ◽  
Kinetics Of ◽  
Long Chain

Effects of Long-chain Molecule Additives in Water on Vortex Streets

Nature ◽  
1966 ◽  
Vol 211 (5045) ◽  
pp. 169-170 ◽  
Author(s):  
G. E. GADD
Keyword(s):  
Chain Molecule ◽  
Vortex Streets ◽  
Long Chain

Good-and bad-solvent effect on the rotational statistics of a long chain molecule

1998 ◽  
Vol 8 (1-2) ◽  
pp. 209-218 ◽  
Author(s):  
Giuseppe Allegra ◽  
Fabio Ganazzoli ◽  
Sergio Bontempelli
Keyword(s):  
Solvent Effect ◽  
Chain Molecule ◽  
Long Chain

scholarly journals The torsional flexibility of aliphatic chain molecules

1940 ◽  
Vol 174 (956) ◽  
pp. 137-144 ◽  
Keyword(s):  
Room Temperature ◽  
Threshold Energy ◽  
Chain Molecule ◽  
Aliphatic Chain ◽  
Chain Molecules ◽  
Distortion Effect ◽  
A Chain ◽  
Single Bonds ◽  
Long Chain ◽  
Made In

The rotation of the CH 3 groups round the single C—C bond in ethane is associated with a threshold energy of about 3000 gcal./gmol. or 2 x 10 -13 erg/mol. (Schäfer 1938; Kistiakowsky, Lacher and Strutt 1939). In an aliphatic CH 2 chain where the carbon atoms are linked together by single bonds the corresponding energy must be of the same order and is most likely rather smaller. Supposing we consider any particular C—C bond in the chain and treat the two parts at each side of this bond as rigid rotators, then their kinetic energy would be 2 x 1/2 kT which at room temperature amounts to about one-fifth of the threshold energy. It seems very likely under these circumstances that a chain molecule of say ten to twenty carbon atoms should already at room temperature show signs of distortion due to internal rotation. If this is true, then the previously observed increase of the crystal symmetry at the melting-point of paraffins (Müller 1930, 1932) and the corresponding changes of the polarization of long-chain ketones (Müller 1937, 1938) can no longer be ascribed entirely to a rotation of the molecule in the field of the surrounding molecules but must at least partly be due to this internal distortion. It is clear that a distortion of this type tends to destroy the anisotropy of the molecule and to give an apparent isotropy to the crystal. The present experiments were made in order to obtain an estimate of the magnitude of the distortion effect. It is found to be surprisingly large.

The use of electron gas modification in the evaluation of the vibration frequencies and the specific heat of lithium

1960 ◽  
Vol 259 (1298) ◽  
pp. 361-369 ◽  
Keyword(s):  
Experimental Data ◽  
Phase Transformation ◽  
Electron Gas ◽  
Vibration Frequencies ◽  
Specific Heats ◽  
Air Temperatures ◽  
Set Up ◽  
Good Agreement ◽  
Secular Determinant

A secular determinant for the determination of vibration frequencies of lithium has been set up by Launay’s method which takes the electron gas into account. Theoretical elastic constants have been used in the calculation of the force constants. Frequencies have been calculated for 47 points of the first Brillouin zone which gives the value of 3 x 1000 = 3000 frequencies by symmetry. Specific heats have been calculated by numerical computation in the range 300 to 6°K and show good agreement with the experimental data. The agreement below liquid-air temperatures is surprising in view of the known phase transformation of lithium.

Finite linear chains of potassium: A dft calculation of their interatomic distances and average electrical polarizabilities

2019 ◽  
Vol 114 ◽  
pp. 113588
Author(s):  
F. Félix-López ◽  
R.E. Félix-Medina ◽  
F.C. Delgado-Nieblas ◽  
J.J. Molina-Duarte ◽  
J.G. Ibarra-Armenta ◽  
...  
Keyword(s):  
Dft Calculation ◽  
Interatomic Distances ◽  
Linear Chains ◽  
Finite Linear

Reversible multi-coloring reaction of spironaphtooxazine controlled by long-chain molecule

2010 ◽  
Vol 213 (2-3) ◽  
pp. 189-193 ◽  
Author(s):  
Kenji Kinashi ◽  
Takashi Horiguchi ◽  
Kyoji Tsutsui ◽  
Kenji Ishida ◽  
Yasukiyo Ueda
Keyword(s):  
Chain Molecule ◽  
Long Chain
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