Van der Waals interaction (also known as London dispersion
Van der Waals (VDW) interactions are probably the most basic type of interaction imaginable Any two molecules experience Van der Waals interactions Even macroscopic surfaces experience VDW interactions, but more of this later The physical process that leads to Van der Waals interactions is clear, but it is difficult to
The van der Waals interaction - University of Cambridge
DEvdW;2d1E2~R52 e2x 1 2a E 4pR6, ~14 which is the van der Waals interaction What makes this work, then, is the point that one can use the instantaneous position of one atom to provide an action at a distance cor-relation with a second atom in the vicinity Finally, we note that the electric polarizability itself can be
Interaction between atoms and molecules I The long range van
The interaction turns out to be attractive and is, for example, responsible for the condensation of rare gases into liquids and solids It is present in the interaction of all atoms and molecules and is referred to as the van der Waals interaction or the dispersion interaction Consider two hydrogen atoms as an example
Suppression and enhancement of van der Waals interactions
van der Waals interaction between two neutral polarizable molecules can be significantly altered by the existence of the dielectric surface compared to that of the free space He showed that the van der Waals interaction potential of a pair of molecules in the vicinity of a dielectric surface depends on the detailed geometry
Chapitre 14 : Exercices
A Interaction de van der Waals B Liaison hydrogène C Interaction électrostatique Données : Electronégativités : 2,2 ; 3,4 ; 2,7 Schémas de Lewis : Le sulfate de cuivre est composé d’ions cuivre (II) et d’ions sulfate
First-Principles Models for van der Waals Interactions in
ABSTRACT: Noncovalent van der Waals (vdW) or dispersion forces are ubiquitous in nature and influence the structure, stability, dynamics, and function of molecules and materials throughout chemistry, biology, physics, and materials science These forces are quantum mechanical in origin and arise from electrostatic interactions between
seminar Van der Waals forces 04052007 - IJS
Van der Waals forces are relatively strong compared to thermal energy The rule of thumb is, that Hamaker constant is within 1k BTroom to 100k BTroom for most materials interacting across vacuum and lower for non-vacuum intermediate media An interesting estimation for strength of van der Waals forces is the case of fly on the ceiling Fly with
[PDF] force de debye
[PDF] nombres complexes terminale s annales
[PDF] liaison intermoléculaire définition
[PDF] force dipole dipole
[PDF] interaction intermoléculaire definition
[PDF] force de debye exemple
[PDF] formule du champ magnétique
[PDF] exercice corrigé magnetisme
[PDF] induction magnétique formule
[PDF] clavier packard bell bloqué
[PDF] touche clavier packard bell ne fonctionne plus
[PDF] mémoire sur la satisfaction client pdf
[PDF] défi de fanfaron 7 lettres
[PDF] suivre le ramadan en 6 lettres
The van der Waals interaction
Barry R. Holstein
a) Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003 and Institute for Nuclear Theory, Department of Physics, University of Washington, Seattle, Washington 98195 ~Received 14 August 2000; accepted 17 October 2000! The interaction between two neutral but polarizable systems at separationR, usually called the van der Waals force, is discussed from different points of view. The change in character from 1/R 6 to 1/R 7 due to retardation is explained. ©2001 American Association of Physics Teachers. @DOI: 10.1119/1.1341251#I. INTRODUCTION
The interaction between charged particles via the Cou- lomb interaction is one of the most important features in physics and is familiar to any student of the subject. The way in which electrons and protons bind to form the hydrogen atom is also well known and is a staple of any quantum mechanics course. 1However, less familiar is the interaction
between such bound systems at separationR, which is the so-called van der Waals force and is of a completely differ- ent character from its Coulombic analog. 2That this must be
the case is clear from the fact that the hydrogen atom is neutral, so that to lowest order there is no interaction. On the other hand the system is polarizable, and thus can interact with the other polarizable system, leading to a short-ranged attraction which varies as 1/R6 , and this feature is discussed by a number of quantum mechanical references. 3,4Somewhat
less well known is the fact that at larger distances the char- acter of the interaction changes and varies as 1/R 7 Ðdiscussion of this feature can be found, e.g., in the quantum ®eld theory book by Itzykson and Zuber. 5It is clear
that the origin of this change is retardation, i.e., the ®nite propagation time of signals connecting the two systems, but the precise way in which this modi®cation comes about is not so easy to calculate and is not generally presented. The nature of the van der Waals force is quite topical at present due to the possible importance of such effects for the interactions of small color dipoles such as charmonium or bottomonium, 6 so it is useful to examine the physics of this effect. In the next section, then, we review the usual textbook discussion leading to the London;1/R 6 interaction. 7 Then in Sec. III, we show how retardation effects modify the char- acter of the force and change its asymptotic dependence to the Casimir±Polder form;1/R7 8In a brief concluding sec-
tion we summarize our ®ndings and discuss the relevance to modern particle and nuclear physics.II. STANDARD VAN DER WAALS INTERACTION
The basic physics of the van der Waals force can be un- derstood from a simple one-dimensional model of the atom which consists of electrons bound by harmonic oscillator forces to heavy protons at ®xed separationRin addition toCoulomb interactions between the four charges
9 H5H 0 1H 1 with~see Fig. 1!H 0 512mp 12 11 2m v 02 x 1 2 11 2mp 22
11 2mv 02 x 2 2 ~1! H 1 5e 2 4p S 1
R11R1x
1 2x 2 21R1x 1 21
R2x 2 D Assuming that the atomic separation is large compared to the size of the atom (R@x 1 ,x 2 ), we can approximate H 1 '22e 2 x 1 x 2 4pR 3 ~2! and the system can be diagonalized in terms of coordinates x6 5(x 1 6x 2 )/&, yielding H5p 12 2m112 S mv 02 22e
2 4pR 3D x 12 1p 22
2m 1 1 2 S mv 02 12e 2 4pR 3D x 22
,~3! i.e., in terms of independent harmonic oscillators with shifted frequencies v 6 5 Av 02 72e
2 4pmR 3 .v 0 7e 2 4pmv 0 R 3 2e 4 32p
2 m 2 v 03 R 6
1¯.~4!
The van der Waals potential is simply the shift in the ground state~zero point!energy due to the Coulomb interaction and is found to be V ~R!51 2 v 1 11 2 v 2 22S 12 v 0D .2e 4 32p
2 m 2 v 03 R 6 .~5! We can write this result in a more familiar form by noting that when an external electric ®eld is applied to this system, the leading order Hamiltonian becomes H5H 0 ~x 1 ,x 2 !1eE 0 x 1 1eE 0 x 2 5H 0 ~z 1 ,z 2 !2e 2 E 02 mv 0 2 ~6! withz i5x i 1eE 0 /mv 02 , and corresponds to an induced elec- tric dipole moment d52 dH dE 0 52e
2 E 0 mv 02 .~7!