London Dispersion Forces

12 Key excerpts on "London Dispersion 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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  Chemical Physics & Physical Chemistry

  • (Author)
  • 2014(Publication Date)
  • Library Press

    (Publisher)

  ________________________ WORLD TECHNOLOGIES ________________________ Chapter- 5 Intermolecular Force Intermolecular forces are relatively weak forces between molecules or between different chemical groups of the same large molecule which act at the distances of Van der Waals radii or larger. This is in contrast to chemical bonds which are stronger, act at the shorter distances, and are formed between different atoms of the same molecule. London Dispersion Forces Interaction energy of argon dimer. The long-range part is due to London Dispersion Forces London Dispersion Forces (LDF, also known as dispersion forces , London forces , induced dipole–induced dipole forces ) is a type of force acting between atoms and ________________________ WORLD TECHNOLOGIES ________________________ molecules. They are part of the van der Waals forces. The LDF is named after the German-American physicist Fritz London. The LDF is a weak intermolecular force arising from quantum induced instantaneous polarization multipoles in molecules. They can therefore act between molecules without permanent multipole moments. London forces are exhibited by nonpolar molecules because of the correlated movements of the electrons in interacting molecules. Because the electrons from different molecules start feeling and avoiding each other, Electron density in a molecule becomes redis-tributed in proximity to another molecule. This is frequently described as formation of instantaneous dipoles that attract each other. London forces are present between all chemical groups and usually represent main part of the total interaction force in condensed matter, even though they are generally weaker than ionic bonds and hydrogen bonds. This is the only attractive intermolecular force present between neutral atoms (e.g., a noble gas). Without London forces, there would be no attractive force between noble gas atoms, and they wouldn't exist in liquid form.

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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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  Progress in Surface and Membrane Science

  Volume 7

  • J. F. Danielli, M. D. Rosenberg, D. A. Cadenhead, J. F. Danielli, M. D. Rosenberg, D. A. Cadenhead(Authors)
  • 2013(Publication Date)
  • Academic Press

    (Publisher)

  The energy of interaction between two such atoms is U = -(u 1 2 * 2 + u 2 2 oc 1 )ld 6 (4) where a x and

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  The Chemical Bond

  Chemical Bonding Across the Periodic Table

  • Gernot Frenking, Sason Shaik(Authors)
  • 2014(Publication Date)
  • Wiley-VCH

    (Publisher)

  16 Dispersion Interaction and Chemical Bonding

  Stefan Grimme

  16.1 Introduction

  From the various types of chemical bonding discussed in this book, the dispersion bonds are usually considered as being the weakest and therefore the least important for chemistry. This clearly holds true for the strength of a typical atom-pair-wise interaction, which is on the order of 0.5 kcal mol−1 or less for molecules composed of light elements ( ). The closed-shell rare gas dimers with dissociation energies ( ) of 0.08, 0.28, and 0.40 kcal mol−1 for , , and , respectively, are classical examples. Dispersion interactions can be heuristically defined as the long-range attractive part of the van der Waals (vdW)-type interaction potential between nonpolar atoms and molecules that are not covalently bonded to each other, although the terms “dispersion” and “vdW” are often used synonymously [1]. Because the term “dispersion” has a wide variety of meanings in natural sciences, it is recommended to clearly distinguish it from other, partly related phenomena by using “London dispersion” in honor of F. London, who provided the first theory for this interaction [2]. For a detailed discussion of London dispersion (we use from now on the short form) and its relation to noncovalent interactions (NCIs) excellent monographs and review papers are available, for example, Refs. [3–5].

  Despite its weakness, the dispersion interaction is extremely important for the formation and structure of many types of condensed matter and the special properties and function of biochemical systems [6–9]. The main reason for this fact is that the dispersion is ubiquitous, always attractive (bonding) and that the interactions are to a good approximation (errors <5–10%) additive. Hence, they add up already in medium-sized molecular systems to values that approach and easily surpass typical covalent and ionic interactions (which are on the order of per pair interaction). The view that not only rare gas aggregates, liquids or molecular crystals are strongly influenced by dispersion but also chemical bonding and the thermochemistry of common reactions is just emerging [10] (although this idea scatteredly has been proposed much earlier; see, e.g., Ref. [11]; for a related review about closed-shell interactions see Ref. [12]). That dispersion effects are not weak at all can be shown by a simple paper and pencil treatment of model systems (see Figure 16.1

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  Formulations

  In Cosmetic and Personal Care

  • Tharwat F. Tadros(Author)
  • 2016(Publication Date)
  • De Gruyter

    (Publisher)

  5 Interaction forces between particles or droplets in cosmetic formulations and their combination Three main interaction forces can be distinguished: (i) van der Waals attraction; (ii) double Layer repulsion; (iii) steric interaction. These interaction forces and their combination are summarized below. 5.1 Van der Waals attraction As is well known, atoms or molecules always attract each other at short distances of separation. The attractive forces are of three different types: dipole–dipole inter-action (Keesom), dipole-induced dipole interaction (Debye) and London dispersion force. The London dispersion force is the most important, since it occurs for polar and nonpolar molecules. It arises from fluctuations in the electron density distribution. At small distances of separation r in vacuum, the attractive energy between two atoms or molecules is given by, G aa = − β 11 r 6 . (5.1) β 11 is the London dispersion constant. For particles or emulsion droplets which are made of atom or molecular assem-blies, the attractive energies have to be compounded. In this process, only the London interactions have to be considered, since large assemblies have neither a net dipole moment nor a net polarization. The result relies on the assumption that the interaction energies between all molecules in one particle with all others are simply additive [1]. For the interaction between two identical spheres in vacuum the result is, G A = − A 11 6 ( 2 s 2 − 4 + 2 s 2 + ln s 2 − 4 s 2 ) . (5.2) A 11 is known as the Hamaker constant and is defined by [1], A 11 = π 2 q 2 11 β ii . (5.3) q 11 is the number of atoms or molecules of type 1 per unit volume, and s = ( 2R + h )/ R. Equation (5.2) shows that A 11 has the dimension of energy. For very short distances (h ≪ R), equation (5.2) may be approximated by, G A = − A 11 R 12h . (5.4) When the droplets are dispersed in a liquid medium, the van der Waals attraction has to be modified to take into account the medium effect.

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  Chemistry

  The Molecular Nature of Matter

  • Neil D. Jespersen, Alison Hyslop(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  Because of the way the dipoles are formed, the positive end of one is always near the negative end of the other, so there is an intermolecular attraction between the molecules. It is a very short-lived attrac- tion, however, because the electrons keep moving; the dipoles vanish as quickly as they form. In another moment, however, the dipoles will reappear in a different orientation and there will be another brief dipole–dipole attraction. In this way the short-lived dipoles cause momentary tugs between the particles. When averaged over a period of time, there is a net overall attraction. It tends to be relatively weak, however, because the attractive forces are only “turned on” part of the time. The momentary dipole–dipole attractions that we’ve just discussed are called instan- taneous dipole-induced dipole attractions. They are also called London dispersion forces (or simply London forces or dispersion forces ). London forces exist between all molecules and ions. Although they are the only kind of attraction possible between nonpolar molecules, London forces even occur between oppo- sitely charged ions, but their effects are relatively weak compared to ionic attractions. The Strengths of London Forces We can use boiling points to compare the strengths of intermolecular attractions. As we will explain in more detail later in this chapter, the higher the boiling point, the stronger the attractions between molecules in the liquid. The strengths of London forces depend chiefly on three factors. One is the polarizabil- ity of the electron cloud of a particle. This is a measure of how easily the electron cloud can be distorted, and the ease of forming instantaneous and induced dipoles. In general, as the volume of the electron cloud increases, its polarizability also increases. When an electron cloud is large, the outer electrons are generally not held very tightly by the nucleus (or nuclei, if the particle is a molecule).

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  Physical Chemistry

  Understanding our Chemical World

  • Paul M. S. Monk(Author)
  • 2005(Publication Date)
  • Wiley

    (Publisher)

  The tighter binding precludes the ready formation of an induced dipole. For this reason, larger (and therefore heavier) atoms and molecules generally exhibit stronger dispersion forces than those that are smaller and lighter. 48 INTRODUCING INTERACTIONS AND BONDS Atomic nucleus Electrons d − d − d + d + Figure 2.6 Schematic diagram to show how an induced dipole forms when polarizable electrons move within their orbitals and cause a localized imbalance of charge (an ‘induced dipole’ in which the negative electrons on one atom attract the positive nucleus on another). The dotted line represents the electrostatic dipole interaction Aside The existence of an attractive force between non-polar molecules was first recognized by van der Waals, who published his classic work in 1873. The origin of these forces was not understood until 1930 when Fritz London (1900–1954) published his quantum- mechanical discussion of the interaction between fluctuating dipoles. He showed how these temporary dipoles arose from the motions of the outer electrons on the two molecules. We often use the term ‘dispersion force’ to describe these attractions. Some texts prefer the term ‘London–van der Waals’ forces. Polarizability The electrons in a molecule’s outer orbitals are relatively free to The ease with which the electron distribu- tion around an atom or molecule can be distorted is called its ‘polarizability’. move. If we could compare ‘snapshots’ of the molecule at two different instants in time then we would see slight differences in the charge distributions, reflecting the changing positions of the electrons in their orbitals. The ease with which the electrons can move with time depends on the molecule’s polarizability, which itself measures how easily the electrons can move within their orbitals. In general, polarizability increases as the orbital increases in size: The weakest of all the intermolecular forces in nature are always Lon- don dispersion forces.

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  Applied Colloid and Surface Chemistry

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

    (Publisher)

  9 Van Der Waals Forces and Colloid Stability

  Historical development of van der Waals forces. The Lennard‐Jones potential. Intermolecular forces. Van der Waals forces between surfaces and colloids. The Hamaker constant. The DLVO theory of colloidal stability.

  HISTORICAL DEVELOPMENT OF VAN DER WAALS FORCES AND THE LENNARD‐JONES POTENTIAL

  In 1873 van der Waals pointed out that real gases do not obey the ideal gas equation PV = RT and suggested that two ‘correction’ terms should be included to give a more accurate representation, of the form (P + a/v

  2

  )(V − b) = RT. The term a/v

  2

  corrects for the fact that there will be an attractive force between all gas molecules (both polar and non‐polar) and hence the observed pressure must be increased to that of an ideal, non‐interacting gas. The second term (b) corrects for the fact that the molecules are finite in size and act like hard spheres on collision; the actual free volume must then be less than the total measured volume of the gas. These correction terms are clearly to do with the interaction energy between molecules in the gas phase.

  In 1903 Mie proposed a general equation to account for the interaction energy (V) between molecules:

  (9.1)

  of which the most usual and mathematically convenient form is the Lennard‐Jones 6‐12 potential:

  (9.2)

  where the first term represents the attraction and the second the repulsion between two molecules separated by distance d. This equation quite successfully describes the interaction between non‐polar molecules, where the attraction is due to so‐called dispersion forces, and the very short‐range second term is the Born repulsion, caused by the overlap of molecular orbitals.

  From our observation of real gases, it is clear that attractive dispersion forces exist between all neutral, non‐polar molecules. These forces are also referred to as London forces after the explanation given by him in about 1930. At any given instant, a neutral molecule will have a dipole moment because of fluctuations in the electron distribution in the molecule. This dipole will create an electric field which will polarize a nearby neutral molecule, inducing a correlated dipole moment. The interaction between these dipoles leads to an attractive energy of the form V = −C/d

  6

  . The time‐averaged dipole moment of each molecule is, of course, zero, but the time‐averaged interaction energy is finite, because of this correlation between interacting temporary diploes. It is mainly this force which holds molecular solids and liquids, such as hydrocarbons and liquefied gases, together. The L‐J interaction potential V

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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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  Understanding Chemistry through Cars

  • Geoffrey M. Bowers, Ruth A. Bowers(Authors)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  Then one more person sits down in the row. Clearly, there is not enough space for that person’s shoulders, so they turn slightly to one side. This leaves you with two choices: you can continue to face directly forward and put up with the squeezing caused by the lack of space, or you can turn you shoulders in the same direction to reduce the squeezing force. Atoms and molecules do the same thing with their electron distri-butions: When the number of electrons in a space gets too crowded, the molecules adjust their distribution of electrons to make everything more comfortable, leading to lower energy in the system and our attractive dis-persion force. 93 Chapter four: Intermolecular forces Intermolecular forces are responsible for several important properties of fluids used in a car. Viscosity, surface tension, boiling points, and melting points are all direct results of the types and strengths of intermolecular forces present in a chemical system. They also influence the solubility of materials. We discuss these topics in the remainder of this chapter. Figure 4.1 Dispersion interactions. The black spheres represent the nuclei, and the gray spheres denote electrons circulating about each nucleus. In the second image, the nonsymmetric arrangement of electrons on atom #1 causes a brief attraction between the nucleus of atom #1 and the electrons of atom #2. 94 Understanding chemistry through cars 4.2 Solubility Chemistry Concepts : solution chemistry, solubility, intermolecular forces Expected Learning Outcomes : • Explain the concept of solubility and solubility limits • Use intermolecular forces to explain the relative solubility of various materials In the previous section, we briefly mentioned saltwater as an example of a system involving ion–dipole forces. Saltwater is a simple mixture of salt and water. If you take table salt and put it in water, you will see the salt crystals vanish as saltwater forms.

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  Intermolecular Forces, Volume 12

  • Joseph O. Hirschfelder(Author)
  • 2009(Publication Date)
  • Wiley-Interscience

    (Publisher)

  It is surprising to many field theorists that one of the trickiest and the first nontrivial calculation of a complicated fourth-order process in quantum electrodynamics was initiated by investigations of the stability of lyophobic colloids (like quartz suspension or a gold sol). This stability problem has been the subject of considerable investigation by Overbeek in Holland and by VERY LONG-RANGE INTERMOLECULAR FORCES 177 Deryagin in Russia. The stability is due to the competition between electrostatic forces of repulsion-mostly in the form of double layers on relatively “ flat ” molecules-and the van der Waals attraction. Some sols or gels are thixotropic and there is a very weak minimum in the potential-energy curve so that the stability of the gel can be broken fairly easily. Detailed investigation (see Verwey and O ~ e r b e e k ~ ~ ) showed that the minimum was too large and that a Iiieaker van der Waals attraction is required in the range -200 A or so. Overbeek suggested that the retardation of the basic interactions into electronic ones would cause a reduction in the potential energy between the two mol- ecules. He states24 “The London-forces being of an electrical nature need a certain time for their propagation. In the theory of London this time is completely neglected as it uses the nonrelativistic Schrodinger equation. If we picture the London-van der Waals forces as an attraction between the temporary dipole of one atom and the dipole induced by it on the second atom the finite velocity of propagation of electro- magnetic actions causes the induced dipole to be retarded against the inducing one by a time equal to Rnlc (n is the refractive index of the medium at the frequency coupled with the temporary dipole). The reaction of the induced dipole on the first one again is retarded by the same time and if in this time lag of 2Rnlc the direction of the first dipole is altered by 90”, the force exerted is exactly nullified .

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