THE SURFACE TENSION OF LIQUID HELIUM

1953 ◽  
Vol 31 (7) ◽  
pp. 1165-1169 ◽  
Author(s):  
K. R. Atkins
Keyword(s):  
Surface Tension ◽  
Free Energy ◽  
Surface Energy ◽  
Liquid Helium ◽  
Normal Modes ◽  
Zero Point ◽  
Total Surface Energy ◽  
Helium Surface ◽  
Point Energy ◽  
Helium Ii

Following a suggestion due to Frenkel, the normal modes of a liquid helium surface are taken to be surface tension waves. The free energy associated with these modes is estimated and is found to give a major contribution to the temperature dependence of the surface tension of liquid helium II. The zero-point energy of the modes is shown to be an appreciable fraction of the total surface energy at 0°K.

Zero Point Diffusion in Liquid Helium II

Nature ◽  
1946 ◽  
Vol 157 (3999) ◽  
pp. 839-840 ◽  
Author(s):  
J. G. DAUNT ◽  
K. MENDELSSOHN
Keyword(s):  
Liquid Helium ◽  
Zero Point ◽  
Helium Ii

The Calculation of Zero-Point Energies of Molecules by Perturbation Methods

1963 ◽  
Vol 18 (2) ◽  
pp. 216-224 ◽  
Author(s):  
Max Wolfsberg
Keyword(s):  
Perturbation Methods ◽  
Secular Equation ◽  
Isotope Effects ◽  
Normal Modes ◽  
Zero Point ◽  
Perturbation Series ◽  
Quantum Mechanical ◽  
Perturbation Scheme ◽  
Point Energy ◽  
The Mean

Two methods are proposed for calculating zero-point energies of molecules. The first makes use of the fact that one can easily write down the quantum mechanical HAMILTONian for a vibrating system. The zero-point energy can then be obtained by a perturbation scheme without solving the secular equation. The second method requires a knowledge of the normal modes and frequencies of a reference molecule, but then enables one to calculate isotope effects by a perturbation scheme. The methods are applied to some examples and the convergence of the perturbation series is investigated. The approximate validity of the law of the mean for the isotope effect on zero-point energies is explored within the framework of the methods.

SOME COMMENTS ON HELIUM FILMS

1954 ◽  
Vol 32 (5) ◽  
pp. 347-355 ◽  
Author(s):  
K. R. Atkins
Keyword(s):  
Zero Point ◽  
Heat Radiation ◽  
Helium Film ◽  
Zero Point Energy ◽  
Helium Films ◽  
Point Energy ◽  
Solid Portion ◽  
Helium Ii ◽  
Qualitative Understanding ◽  
Λ Point

The Polanyi potential theory is applied to the helium film and leads to a qualitative understanding of the high density of the first few layers and the differential entropy. Between 1.75°K. and the λ-point the film may consist of an inner solid portion, an intermediate portion of helium I, and an outer portion of helium II. For thick films the variation of zero-point energy with thickness must be considered. The zero-point energy of the Debye waves is shown to be important at film thicknesses of the order of 4 × 10−6 cm. The effect of heat radiation incident upon the film is considered.

On the Surface Tension of Liquid Helium II

1967 ◽  
Vol 163 (1) ◽  
pp. 200-205 ◽  
Author(s):  
W. Brouwer ◽  
R. K. Pathria
Keyword(s):  
Surface Tension ◽  
Liquid Helium ◽  
Helium Ii

Localization of Positronium in Polymers

2010 ◽  
Vol 666 ◽  
pp. 67-70
Author(s):  
Yoshinori Kobayashi ◽  
T. Ichikawa
Keyword(s):  
Surface Tension ◽  
Driving Force ◽  
Zero Point ◽  
Light Particle ◽  
Quantum Mechanical ◽  
Molecular Liquids ◽  
Zero Point Energy ◽  
Point Energy ◽  
Hole Expansion ◽  
Large Quantum

A good correlation is found between ortho-positronium (o-Ps) pick-off annihilation lifetimes and surface tensions of molecular liquids and polymers. Systematic shortening of the o-Ps lifetime with increasing surface tension suggests that the hole for Ps localization in polymers may be that subjected to considerable expansion as in liquids. The driving force of this hole expansion is the large quantum mechanical zero-point energy of a light particle confined in an angstrom size space. The hole expansion is insignificant in a larger nm scale pore, where the zero-point energy is much lowered.

scholarly journals Does glycosyl transfer involve an oxacarbenium intermediate? Computational simulation of the lifetime of the methoxymethyl cation in water

2011 ◽  
Vol 83 (8) ◽  
pp. 1507-1514 ◽  
Author(s):  
Ian H. Williams ◽  
J. Javier Ruiz Pernía ◽  
Iñaki Tuñón
Keyword(s):  
Free Energy ◽  
Computational Simulation ◽  
Zero Point ◽  
Md Simulations ◽  
Quantum Corrections ◽  
Water Molecules ◽  
Point Energy ◽  
Classical Estimate ◽  
High Level ◽  
Energy Surfaces

2D free-energy surfaces for transfer of the methoxymethyl cation between two water molecules are constructed from molecular dynamics (MD) simulations in which these atoms are treated quantum-mechanically within a box of 1030 classical solvent water molecules at 300 K. This provides a simple model for glycosyl transfer in water. The AM1/TIP3P surfaces with 2D-spline corrections at either MPWB1K/6-31+G(d,p) or MP2/6-31+G(d,p) contain a shallow free-energy well corresponding to an oxacarbenium ion intermediate in a DN*AN mechanism. MD analysis at three temperatures leads to a classical estimate of the lifetime of the methoxymethyl cation in water; when quantum corrections for vibrational zero-point energy are included, the lifetime is estimated to be about 1 ps, in agreement with the best experimental estimate. This suggests that computational simulation, with appropriate high-level correction, is a reliable tool to obtain detailed and reliable mechanistic descriptions for glycosidases. In view of the importance of developing improved anti-influenza drugs, simulations of sialidases that considered both sialyl oxacarbenium ion and covalent sialyl-enzyme as possible intermediates could provide particular insight.

The nucleation of cavities at grain boundaries

1987 ◽  
Vol 45 ◽  
pp. 288-291
Author(s):  
P. J. Goodhew
Keyword(s):  
Surface Tension ◽  
Surface Energy ◽  
Grain Boundaries ◽  
Radiation Damage ◽  
Impurity Concentration ◽  
Driving Force ◽  
Nucleation And Growth ◽  
Phase Boundaries ◽  
Cavity Nucleation ◽  
Spherical Bubble

Cavity nucleation and growth at grain and phase boundaries is of concern because it can lead to failure during creep and can lead to embrittlement as a result of radiation damage. Two major types of cavity are usually distinguished: The term bubble is applied to a cavity which contains gas at a pressure which is at least sufficient to support the surface tension (2g/r for a spherical bubble of radius r and surface energy g). The term void is generally applied to any cavity which contains less gas than this, but is not necessarily empty of gas. A void would therefore tend to shrink in the absence of any imposed driving force for growth, whereas a bubble would be stable or would tend to grow. It is widely considered that cavity nucleation always requires the presence of one or more gas atoms. However since it is extremely difficult to prepare experimental materials with a gas impurity concentration lower than their eventual cavity concentration there is little to be gained by debating this point.

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