Van der Waals Forces

10 Key excerpts on "Van der Waals Forces"

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  eBook - ePub

  Intermolecular and Surface Forces

  • Jacob N. Israelachvili(Author)
  • 2010(Publication Date)
  • Academic Press

    (Publisher)

  6 Van der Waals Forces

  6.1 Origin of the Van der Waals-dispersion Force between Neutral Molecules: the London Equation

  The various types of physical forces described so far are fairly easy to understand, since they arise from straightforward electrostatic interactions involving charged or dipolar molecules. But there is a another type of force that like the gravitational force—acts between all atoms and molecules, even totally neutral ones such as helium, carbon dioxide, and hydrocarbons. These forces have been variously known as dispersion forces, London forces, charge-fluctuation forces, electrodynamic forces, and induced-dipole-induced-dipole forces. We shall refer to them as dispersion forces, since it is by this name that they are most widely known. The origin of this name has to do with their relation to the dispersion of light in the visible and UV regions of the spectrum, as we shall see. The literature on this subject is quite voluminous, and the reader is referred to books and reviews by1 London (1937), Hirschfelder et al., (1954), Moelwyn-Hughes (1961), Margenau and Kestner (1971), Israelachvili (1974), Mahanty and Ninham (1976), and Parsegian (2006).

  Dispersion forces make up the third and perhaps most important contribution to the total van der Waals force between atoms and molecules, and because they are always present (in contrast to the other types of forces that may or may not be present, depending on the properties of the molecules), they play a role in a host of important phenomena such as adhesion; surface tension; physical adsorption; wetting; the properties of gases, liquids, and thin films; the strengths of solids; the flocculation of particles in liquids; and the structures of condensed macromolecules such as proteins and polymers. Their main features may be summarized as follows:

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  Polymer Interface and Adhesion

  • Souheng Wu(Author)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  2 Molecular Interpretations

  Van der Waals recognized the existence of intermolecular force in 1879, and introduced an attractive energy term and an excluded volume term into the ideal gas law. Subsequent workers have found that there are various types of intermolecular forces, including dispersion (nonpolar) force, dipole (dipole-dipole) force, induction (dipole-induced dipole) force, and hydrogen bonding. These intermolecular forces are commonly known as the Van der Waals Forces . The van der Waals force between two molecules is a short-range force, varying with r−7 , where r is the intermolecular distance. On the other hand, the van der Waals force between two macroscopic bodies is a long-range force, varying with z−3 , where z is the distance between two flat plates. It should be noted here that the variation of van der Waals force between two macroscopic bodies depends on the shapes of the bodies. For instance, it varies with z−2 between two spheres (see Section 2.5.5 ). Various molecular forces are discussed and used to analyze the interfacial energies in this chapter. Several reviews of intermolecular forces are available elsewhere [1 –8 ].

  2.1 Microscopic Theories of Van der Waals Forces

  2.1.1 Dispersion (Nonpolar) Energy

  Dispersion force exists between any pair of molecules. Its magnitude depends on the electronic frequency of the molecule, which is measurable from the dispersion of refractive index, hence the name dispersion force. However, the term nonpolar force should be preferrable. In 1927, Wang [9 ] showed that neutral and nonpolar molecules attract each other. In 1930, London [10 ] made the first quantum mechanical treatment; hence the force is also known as the London dispersion force or London force. London’s treatment has since been refined [8 ,10 –19 ].

  A molecule, with or without a permanent dipole moment, has an instantaneous dipole moment as its electrons fluctuate. This instantaneous dipole will induce a dipole in another molecule. The interaction between these two dipoles averaged over all instantaneous electronic configurations is the dispersion force. Note that the interaction between instantaneous dipoles of two molecules averaged over all electronic configurations is small compared with the interaction between an instantaneous dipole and its induced dipole, because two instantaneous dipoles in two molecules lack synchronization.

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  Applications of Biophotonics and Nanobiomaterials in Biomedical Engineering

  • Mohammad E. Khosroshahi(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  12 (r) which gives rise to the dispersive van der Waals force between molecules 1 and 2 can be defined as:

  (4.15)

  V 12

  ( r )

  = -

  A 12

  r 6

  where A12 is the Hamaker constant whose value depends on the type of molecule considered and the distance r. The cohesive forces are sometimes called dispersion interaction, because the same parameters determine both of the optical properties of the molecules, i.e., the dispersion of light and the forces between them. The Van der Waals Forces are long range and can be effective at large distances (> 10 nm) down to interatomic spacing (< 0.1 nm). In molecular dynamics, the energy of interactions E(r) between biomolecules is normally shown by the Lennard-Jons potential,

  (4.16)

  E

  ( r )

  =

  E c

  [

  (

  r 0

  r

  )

  12

  - 2

  (

  r 0

  r

  )

  6

  ]

  where Ec is the characteristic energetic constant. The attractive (negative) term corresponds to the van der Waals force for a point particle and the repulsive (positive) term is the hard sphere force. The Van der Waals Forces exist between all atoms and molecules, whatever other forces may also be involved. We may divide Van der Waals Forces into three groups: (i) Dipole–dipole forces, (ii) Dipole-induced dipole forces and (ii) Dispersion forces.

  4.2.2 Hydrogen bonding

  This is an important effect in a wide range of hydrogenated polar molecules and determines their different molecular shapes. Hydrogen bonds are typically stronger than Van der Waals Forces and have energies in the range of 10–40 kmol–1

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  Physics and Chemistry of Interfaces

  • Hans-Jürgen Butt, Karlheinz Graf, Michael Kappl(Authors)
  • 2023(Publication Date)
  • Wiley-VCH

    (Publisher)

  Introductions to surface forces include [ 7, 174, 175 ]. Van der Waals Forces are discussed comprehensively in [ 176 ]. 5.1 Van der Waals Forces Between Molecules Forces between macroscopic objects result from a complex interplay of the interaction between molecules in the two objects and the medium separating them. The basis for an understanding of intermolecular forces is the Coulomb 1 force. The Coulomb force is the electrostatic force between two charges and : (5.1) If the two charges are in a medium, the permittivity is higher than one, and the electrostatic force is reduced accordingly. The potential energy between two electrical charges that are a distance apart is (5.2) For charges with opposite signs, the potential energy is negative. They reduce their energy when they get closer. Example 5.1 The potential energy between and, being 1 nm apart, in a vacuum is This is 56 times higher than the thermal energy at room temperature. Most molecules are not charged. Still, the electric charge is often not distributed evenly. A molecule can have a more negative side and a more positive side. In carbon monoxide, for example, the oxygen is more negative than the carbon atom. To first order, the electric properties of such molecules are described by the so‐called “dipole moment”. For the simple case of two opposite charges and that are a distance apart, the dipole moment is given by. It is given in units of Coulomb meters. Often, the old unit Debye is used. One Debye is equal to a positive unit charge and a negative unit charge that are 0.21 apart; it is denoted by C m. The dipole moment is a vector that points from minus to plus. If we have more than two charges, we must integrate the charge density over the whole volume of the molecule, which leads to the general definition of the dipole moment: (5.3) Let us now return to intermolecular interactions

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  Applied Colloid and Surface Chemistry

  • Richard M. Pashley, Marilyn E. Karaman(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  It is interesting to note that molecular interaction forces vary with the inverse distance to a power greater than 3. This means that these forces are short‐ranged within a material, unlike gravitational forces, and only molecules within 10 or so diameters effectively contribute to the cohesive or surface energy of a material. This is quite unlike gravity, which has a slower distance dependence and so has to be summed over the entire body or region of space. Interestingly, this difference was not appreciated by Einstein in some of his early work.

  Because the dispersion force acts between neutral molecules, it is ubiquitous (compare the gravitational force); however, between polar molecules there are also other forces. Thus, there may be permanent dipole‐dipole and dipole‐induced dipole interactions, and of course, between ionic species there is the Coulomb interaction. The total force between polar and non‐polar (but not ionic) molecules is called the van der Waals force. Each component can be described by an equation of the form V = C/d

  n

  , where for the dipole‐dipole case n = 6 and C is a function of the dipole moments. Clearly, it is easy to give a reasonable distance dependence to an interaction; however, the real difficulty arises in determining the value of C.

  Common types of interactions between atoms, ions and molecules in vacuum are given in the table below. In the table, V(r) is the interaction free energy (in J); Q is the electric charge (in C); u the electric dipole moment (C m); α the electric polarisibility (C2 m2 J−1 ) and r is the distance between interacting atoms or molecules (m). ν, is the electronic absorption (ionization) frequency (s−1 ). The corresponding interaction force is, in each case, obtained by differentiating the energy V(r) with respect to distance r

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  Chemical Principles of Nanoengineering

  • Andrea R. Tao(Author)
  • 2023(Publication Date)
  • Wiley-VCH

    (Publisher)

  Intermolecular forces are responsible for these “weak” or secondary bonds that occur between molecules, particles, and surfaces. The bonds that result from intermolecular forces lack specificity, stoichiometry, and directionality. These forces can also result in interactions that occur over long distances – much longer than interatomic bond lengths.

  As we will see throughout Chapter 1 , intermolecular forces play an important role in dictating materials and molecular behavior at the nanoscale. We will cover five different types of intermolecular forces: electrostatic, hydrogen bonding, van der Waals (vdW ), hydrophobic, and steric forces. For each of these, we will derive and discuss their universal force laws. We will also discuss the differences between these forces for molecules versus nanoscale objects. Finally, we will develop an understanding of how potential energy diagrams can be used to predict the overall intermolecular interactions between two objects as a function of separation distance. This knowledge will be applied toward understanding the behavior of nanosystems ranging from atoms and molecules (e.g. DNA and polymers) to particles and other nanomaterials (e.g. liposomes, metal nanoparticles, C60 ).

  1.1 The Pairwise Potential

  Intermolecular forces can lead to attraction or repulsion between atoms, molecules, particles, and surfaces, and contribute significantly to how nanoscale materials and systems behave. These forces are classified as conservative forces, meaning that they satisfy the relationship:

  (1.1)

  where F is the force, V(r) is the potential energy of the object, and r is distance. Because of this relationship, potential energy can be used as a descriptor of whether the force between two objects is attractive or repulsive.

  We often consider pairwise potentials that describe V(r) as a function of separation distance to determine attraction or repulsion. For example, two possible pairwise potentials between two spherical particles of radius R

  s

  are depicted in Figure 1.2

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  Forces of the Quantum Vacuum:An Introduction to Casimir Physics

  • William M R Simpson, Ulf Leonhardt(Authors)
  • 2015(Publication Date)
  • WSPC

    (Publisher)

  1 ]. The question is then, what is the origin of the long-range attractive force suggested by van der Waals?

  Keesom calculated the interaction potential between two molecules with a permanent dipole moment. At a finite temperature T , the molecules are randomly rotating and there exists a non-vanishing average potential scaling as U ∝ −T /r 6 , where r is the distance between the molecules [2 ]. A similar result may be obtained when the dipole of one molecule is induced by that of the other molecule, whose dipole is in turn induced by thermal fluctuations, rather than being permanent. Namely, classical physics considerations showed that an attractive 1/r 6 potential may exist between any pair of particles, so long as they are polarisable – in other words, that their dipoles can be induced by an electric field. The potential is driven by thermal fluctuations, and hence grows linearly with T . This result, whilst providing a physical mechanism for an attractive force between a large class of neutral particles, was nevertheless inconsistent with experimental evidence, which showed that at very low temperatures the force seemed to diminish very slowly with temperature and even reach a constant value, rather than decreasing linearly with temperature T [2 , 3 ].

  This calls quantum physics into play, and in 1930 London [2 ] used lowest order quantum mechanical perturbation theory, combined with electrostatic considerations, to obtain an attraction varying as 1/r 6 between polarisable molecules at zero temperature. London interpreted this interaction, now widely known as the dispersion force, as originating from the zero-point motion of the molecular degrees of freedom, which is a strictly quantum mechanical effect. London’s remarkable result did not end the story however, since experimental results in the late 1940s led to a suggestion made by Overbeek, that at long distances r the intermolecular potential decreases more rapidly with r than the 1/r 6 scaling, possibly due to retardation [4 ]. Indeed, using an analysis based on quantum electrodynamics, Casimir and Polder (1948) [4 ] were able to obtain an interaction potential at zero temperature that falls off as 1/r 7

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  Principles of Colloid and Surface Chemistry, Revised and Expanded

  • Paul C. Hiemenz, Raj Rajagopalan, Paul C. Hiemenz, Raj Rajagopalan(Authors)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  ■ * * *

  In this section we have examined the three major contributions to what is generally called the van der Waals attraction between molecules. All three originate in dipole-dipole interactions of one sort or another. There are two consequences of this: (a) all show the same functional dependence on the intermolecular separation, and (b) all depend on the same family of molecular parameters, especially dipole moment and polarizability, which are fairly readily available for many simple substances. Many of the materials we encounter in colloid science are not simple, however. Hence we must be on the lookout for other measurable quantities that depend on van der Waals interactions. Example 10.2 introduces one such possibility. We see in Section 10.7 that some other difficulties arise with condensed systems that do not apply to gases.

  In the next section we take a preliminary look at the way van der Waals attractions scale up for macroscopic (i.e., colloidal) bodies. This will leave us in a better position to look for other measurements from which to estimate the van der Waals parameters.

  10.5  Van der Waals Forces BETWEEN LARGE PARTICLES AND OVER LARGE DISTANCES

  The interaction between individual molecules obviously plays an important role in determining, for example, the nonideality of gas, as illustrated in Example 10.2 . It is less clear how to apply this insight to dispersed particles in the colloidal size range. If atomic interactions are assumed to be additive, however, then the extension to macroscopic particles is not particularly difficult. Moreover, when dealing with objects larger than atomic dimensions, we also have to consider interactions over appropriately large distances. In the case of the London attraction, forces over large distances show a more rapid decay than indicated by the inverse sixth-power equations derived in Section 10.4 . This is known as (electromagnetic) retardation. We discuss these two important issues in this section before developing the equations for interactions between macroscopic bodies in Section 10.6

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  Wettability

  • Erle C. Donaldson, Waqi Alam(Authors)
  • 2013(Publication Date)
  • Gulf Publishing Company

    (Publisher)

  Stone, 1996 ).

  2.5.2 London Dispersion Forces

  London forces are long-range interactions that refer to those where the energy of separation (U r ) exhibits a characteristic pair potential behavior which is some inverse power of the radius of separation:

  (2.21)

  The important long-range forces with respect to wettability are:(1) electrostatic, originating from Coulombic forces between static charges and permanent dipoles (they can be attractive or repulsive);(2)dipole moments, induced in molecules by electric fields of adjacent molecules (these are always attractive); and (3) dispersion forces that develop from charge distributions of molecules. The long-range forces are constantly fluctuating in response to the movements of the electrons as the molecules approach each other where the motions of the electron clouds become coordinated, favoring lower energy configurations that become stronger as the molecular separations decrease.

  Dispersion forces act between all interactions of particles (atoms and molecules). The London dispersion forces contribute up to a third of the total interactive forces that are known as the van der Waals force. The London forces are effective at relatively long-range (0.2 to 10 nm).

  The attractive interaction of nonpolar compounds is unusual because they do not have permanent dipoles or electrostatic properties, thus the time average dipole moment of nonpolar molecules is zero; yet they exert an attractive force toward each other. The origin of this attractive force is quantum mechanical. The simplest model of a nonpolar molecule can serve to explain the source of the dispersion forces. Consider an electron distribution around the nucleus of a spherical molecule. The time average distribution of the electron’s positions is a spherical electron cloud. The molecule, however, is composed of positive and negative charges with the negative charges oscillating about the positive with an angular frequency. Therefore, at any given instant the molecule experiences a separation of charges that corresponds to an instantaneous dipole moment.

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  Some Electrical and Optical Aspects of Molecular Behaviour

  The Commonwealth and International Library: Chemistry Division

  • Mansel Davies, Robert Robinson, H. M. N. H. Irving, L. A. K. Staveley(Authors)
  • 2014(Publication Date)
  • Pergamon

    (Publisher)

  YSTEM will be at equilibrium when the forces in it are balanced, that is, when no net force is present. This is one of the major physical laws which, in its simple form, is not graced with a name. It applies equally well to the interactions of molecules as it does to astronomical systems. The fact that molecules may have net electric charges—when they form ions—that many of them have significant permanent electric moments, and that they each and all have finite polarizabilities ensures that forces of an electric character will come into play when any two molecules approach one another.

  We shall first assume that such molecules are saturated valencywise and are chemically stable. What is then observed on their approach to one another is the residual interaction which causes molecules to condense from the gas phase to the liquid and to freeze to the solid. The same forces are responsible for many other interactions such as the Van der Waals Forces in the gaseous state, the formation of molecular complexes (including hydrates and solvates), the viscous forces in liquids, and many solubility relations.

  The aim in this chapter will be to consider the form and order of magnitude of such interaction energies and to refer to some typical examples of their occurrence. A warning is, however, necessary. Whilst these forces are often most readily represented as of an electrostatic character it is also possible to treat them quantum-mechanically. When that is done other features also become apparent—the exchange forces (or resonance energy) becoming significant at very close approach of the atoms.

  Accordingly, whilst the electrostatic types of forces will often predominate at large distances, they do not necessarily provide the whole story of the interaction between even supposedly saturated molecules. As is indicated later, the general attractions (dispersion forces) and repulsions between non-polar molecules are of a quantum mechanical nature.*

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