London – van der Waals forces and torques exerted on an ellipsoidal particle by a nearby semi-infinite slab

1981 ◽  
Vol 59 (13) ◽  
pp. 2004-2018 ◽  
Author(s):  
Howard Brenner ◽  
Lawrence J. Gajdos
Keyword(s):  
Potential Energy Function ◽  
Intermolecular Forces ◽  
Separation Distance ◽  
Intermolecular Potential ◽  
Integration Scheme ◽  
Intermolecular Potentials ◽  
Ellipsoidal Particle ◽  
Principal Axes ◽  
Infinite Slab ◽  
Centrally Symmetric

A Hamaker-type integration of the pairwise en vacuo intermolecular forces is performed for a homogeneous triaxial ellipsoidal particle in proximity to a homogeneous semi-infinite slab bounded by a plane wall. The orientation of the ellipsoid relative to the plane is taken to be arbitrary, as too is its distance from the plane. The integrated potential energy function of the ellipsoid with respect to the slab is found to possess nonadditive positional and orientational contributions. This macroscopic potential is employed to compute the force and torque on the ellipsoid as functions of both its position and orientation relative to the plane.The novel integration scheme pertains to centrally-symmetric pairwise intermolecular potentials of arbitrary functional form. Specific results are derived for classical inverse-power intermolecular potentials possessing both attractive (r−n) and repulsive (−r−m) additive components (with n > m). In stable equilibrium the ellipsoid aligns itself with the shortest of its three principal axes perpendicular to the bounding wall, and at a separation distance comparable to the length scale of the intermolecular potential itself.

VIBRATIONAL FREQUENCY PERTURBATIONS IN THE RAMAN SPECTRUM OF COMPRESSED GASEOUS HYDROGEN

1964 ◽  
Vol 42 (6) ◽  
pp. 1058-1069 ◽  
Author(s):  
A. D. May ◽  
G. Varghese ◽  
J. C. Stryland ◽  
H. L. Welsh
Keyword(s):  
Raman Band ◽  
Intermolecular Forces ◽  
Hydrogen Gas ◽  
High Spectral Resolution ◽  
Intermolecular Potential ◽  
Dispersion Forces ◽  
Frequency Shifts ◽  
Linear Coefficient ◽  
Relative Population ◽  
Good Agreement

The frequencies of the Q(J) lines of the fundamental Raman band of compressed hydrogen gas were measured with high spectral resolution for a series of densities from 25 to 400 Amagat units at 300 °K and 85 °K. The frequency shifts are expressed as a power series in the gas density. The linear coefficient at a given temperature has the form aJ = ai + ae(nJ/n), where ai, constant for all the Q lines, can be interpreted in terms of isotropic intermolecular forces, and ae(nJ/n), proportional to the relative population of the initial J level, arises from the inphase coupled oscillation of pairs of molecules. The temperature variation of ai is analyzed on the basis of the Lennard-Jones intermolecular potential and the molecular pair distribution function. The repulsive overlap forces and the attractive dispersion forces give, respectively, positive and negative contributions to ai, which can be characterized by the empirical parameters Krep and Katt. The values of Katt and ae are in good agreement with calculations based on the polarizability model of the dispersion forces. The relation of the results to the Raman frequency shifts in solid hydrogen is discussed.

Intermolecular forces and properties of fluid. I. The automatic calculation of higher virial coefficients and some values of the fourth coefficient for the Lennard-Jones potential

1960 ◽  
Vol 254 (1279) ◽  
pp. 487-498 ◽  
Keyword(s):  
Virial Coefficient ◽  
Mathematical Problem ◽  
Virial Coefficients ◽  
Intermolecular Forces ◽  
Lennard Jones Potential ◽  
Intermolecular Potentials ◽  
Jones Potential ◽  
Lennard Jones ◽  
Experimental Values ◽  
First Time

The prediction of the virial coefficients for particular intermolecular potentials is generally regarded as a difficult mathematical problem. Methods have only been available for the second and third coefficient and in fact only few calculations have been made for the latter. Here a new method of successive approximation is introduced which has enabled the fourth virial coefficient to be evaluated for the first time for the Lennard-Jones potential. It is particularly suitable for automatic computation and the values reported here have been obtained by the use of the EDSAC I. The method is applicable to other potentials and some values for these will be reported subsequently. The values obtained cannot yet be compared with any experimental results since these have not been measured, but they can be used in the meantime to obtain more accurate experimental values of the lower coefficients.

CALCULATION OF THE SELF-BROADENING OF RAMAN LINES DUE TO DIPOLAR AND QUADRUPOLAR FORCES

1963 ◽  
Vol 41 (3) ◽  
pp. 433-449 ◽  
Author(s):  
J. Van Kranendonk
Keyword(s):  
Phase Shift ◽  
Cross Sections ◽  
Scattered Light ◽  
Rotational Quantum Number ◽  
Intermolecular Forces ◽  
Intermolecular Potential ◽  
Radiation Process ◽  
Impact Theory ◽  
Order Of Magnitude ◽  
The Impact

The impact theory of Raman line broadening due to anisotropic intermolecular forces, developed previously, is applied to the broadening due to dipolar and quadrupolar forces. The optical cross sections are calculated assuming the isotropic intermolecular potential to be a hard-sphere potential, and neglecting the spread in velocities. Explicit expressions are derived for the phase-shift contribution to the width of the isotropic (j = 0) and anisotropic (j = 2) Raman scattered light as a function of the rotational quantum number J. For j = 2 scattering the phase shifts produced in the radiation do not vanish when the initial and final states of the radiation process are identical, and the phase-shift contribution to the width of the anisotropic components of the Q lines is of the same order of magnitude as for the S lines. In all cases the phase-shift contribution tends to zero when J becomes large compared with j. The contribution to the width of the inelastic collisions also tends to zero for large J, but this is characteristic of the long-range interactions considered here and results from the correspondingly short range of the resonance factors. The theory is compared with the available experimental data on H2 and N2. It is pointed out that quite generally an observation of the broadening of the isotropic and anisotropic Raman lines allows a determination of the lifetimes of the rotational levels and of the phase-shift contributions to the width of the anisotropic lines.

Molecular Dynamic Simulation of Surface Roughness Effects on Nanoscale Flows

2009 ◽  
Author(s):  
Ali Kharazmi ◽  
Reza Kamali
Keyword(s):  
Surface Roughness ◽  
Solid Wall ◽  
Intermolecular Forces ◽  
Intermolecular Potential ◽  
Roughness Effects ◽  
Time Step ◽  
Restoring Force ◽  
Rapid Sampling ◽  
Micro Channels ◽  
Fifth Order

In the present study, a molecular based scheme has been developed for simulating flows in nano- and micro-channels with roughness. In micro channel flow, there is some difference on the flow friction between roughness and cavitations which is not well studied. The presented approach is based on the molecular dynamics (namely MD) in which different ensemble has been used. For modeling the simulation the classical Newtonian particles are allowed to obey Newtonian mechanics and intermolecular forces are founded by integrating intermolecular potential. Lennard-Jones potential is used to model the interactions between particles. Particles equation of motion is integrated using fifth order Gear predictor-corrector. To ensure rapid sampling of phase space, the time step is made as large as possible. Periodic boundary condition is implemented via minimum image convention. Each atom of the solid wall is anchored at its lattice site by a harmonic restoring force and its temperature has been controlled by utilizing Nose-Hoover thermostat. The roughness is implemented on the lower channel wall. To make a comparison between the effect of roughness and cavitation, the same dimension is used for both for different aspect ratio. To allow comparison with previous results the same fluid density has been used. The effects of surface roughness and cavitation on velocity distribution of hydrophobic and hydrophilic wall undergoing Poiseuille flow are presented.

scholarly journals Intermolecular Lennard-Jones (22-11)Potential Energy Surface in Dimer of N8 Cubane Cluster

2017 ◽  
Vol 59 (2) ◽  
Author(s):  
Jamshid Najafpour
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Density Functional ◽  
Energy Surface ◽  
Separation Distance ◽  
Basis Set ◽  
Intermolecular Potential ◽  
Basis Set Superposition Error ◽  
Lennard Jones

<p>We have calculated the intermolecular potential energy surface (IPES) of the dimer of cubic N8 cluster using <em>ab initio </em>and the density functional theory (DFT) calculations. The <em>ab initio </em>(HF/3- 21G(d)) and DFT (B3LYP/6-31G(d) and aug-cc-pVDZ) calculations were performed for two relative orientations of N8-N8 system as a function of separation distance between the centers of cubic N8 clusters. In this research, the IPES, <em>U</em>(<em>r</em>), of the N8-N8 system is studied, where the edge of N8 approaches to face or edge of the other considered N8. Then, the Lennard-Jones (12-6) and (22-11) adjustable parameters are fitted to the computed interaction energies for edge-face and edge-edge orientations. In this research for the first time, the IPESs proportionated to the Lennard-Jones (22-11) potential are derived that are compatible with the computed IPES curves. Assuming a set of Lennard-Jones parameters, the second virial coefficients are obtained for the N8-N8 complex at a temperature range of 298 to 1000 K. Both the corrected and uncorrected basis set superposition error (BSSE) results are presented confirming the significance of including BSSE corrections.</p>

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