Van der Waals Attraction

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  Electrolytes

  Supramolecular Interactions and Non-Equilibrium Phenomena in Concentrated Solutions

  • Georgii Georgievich Aseyev(Author)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  135 4 Supermolecular Interactions 4.1 VAN DER WAALS COMPONENTS OF ATTRACTION POTENTIAL The electromagnetic interaction in the system of many particles in water appears in the form of exchange, multipole, fluctuation, and other interaction forces. Among such interaction forces, one can distinguish those that deplete at large distances as a power function. Such forces are frequently called long-range forces in contrast to short-range forces that deplete rapidly (usually exponentially) with the increase of distance. The short-range forces-distance type of dependence is not most often uni-versal and can be determined by a certain structure of electron shells of atoms. The distinctive feature of long-range forces is, on the contrary, known versatility of their behavior at long distances. At that, if the average charge density and average dipole moment density are equal to zero in an equilibrium medium, then the main long-range forces, in general, are the forces of fluctuation origin that are frequently called the van der Waals forces. They can be calculated by the quantum mechanical approach, but meanwhile accurate values are provided by experimental measurements. Describing the van der Waals interaction among particles, the specific nature of macroscopic condensed media can be fully estimated by using their dielectric permit-tivities in the solution or polarizabilities. Fruitfulness of using dielectric formalism in the theory of van der Waals forces is connected with the aforementioned versatil-ity of their dependence from distance among particles. Results of the theory of van der Waals forces, in which only dielectric permittivities or particle polarizabilities are used in formulation, are often called macroscopic. The aggregate of such results is sometimes called the macroscopic approach in the theory of van der Waals forces or the macroscopic theory of van der Waals forces.

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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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  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)

  For example, the atoms in solid argon and the molecules in solid polyethylene are held together only by van der Waals forces. Van der Waals forces also play an important role in the interactions between colloid particles, in the forces across interfaces (surface and interfacial tension) and in thin films and membranes. At short range, below about 4 Á, exchange or chemical binding forces take over as the electron clouds of interacting atoms begin to overlap, and there is now a strong repulsive force term. This is the second term in the Lennard-Jones 6-12 potential U = -Ald 6 + B/d 12 (6) This equation is widely used because of its simplicity, but there is no theoretical basis for the twelfth power repulsive term. On the other hand, an exponential repulsive term (6-exp potential) has stronger theoretical justification and is also commonly used. The behavior at short range is not well understood, however, and in what follows we shall concentrate more on the study of van der Waals forces when there is no overlap, i.e., for separations greater t h a n ~ 4 Á. I I . V A N D E R W A A L S DISPERSION FORCES B E T W E E N A T O M S , MOLECULES, A N D S M A L L P A R T I C L E S Theories of dispersion forces are described as microscopic or macro-scopic according to the method of approach. In microscopic theories the force between atoms or molecules or small particles is obtained in terms of their microscopic properties, for example, their atomic or VAN DER WAALS FORCES: THEORY AND EXPERIMENT 5 molecular polarizabilities. In macroscopic theories one obtains the force between large bodies in terms of their macroscopic properties, such as their dielectric constant. Historically, the microscopic theories preceded the more complicated macroscopic theories, and we shall consider them in that order, starting with miscroscopic theories.

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  Physics of Matter

  • George C. King(Author)
  • 2023(Publication Date)
  • Wiley

    (Publisher)

  Although relatively weak, van der Waals forces play a dominant role in the bonding of a wide variety of atomic and molecular systems including, for example, organic molecules, colloidal systems, and pharmaceu- tical drugs. And, interestingly, it is thought that it is the van der Waals force that enables geckos to stick to smooth surfaces such as glass. We also saw, in Section 1.2, that atomic force microscopy exploits van der Waals forces between a surface and the AFM tip to image the surface. 2.3.4 Ionic bonding In the case of van der Waals bonding, we saw that the electric dipole field of an atom distorts the charge distribution of a neighbouring atom. And this results in an attraction between the two atoms. By contrast, in ionic bonding, it is the transfer of an electron from one atom to another that produces the attraction. Consider the example of sodium chloride, (NaCl). An atom of sodium has a total of 11 electrons with the electron configuration 1s 2 2s 2 2p 6 3s. It has one electron, the 3s electron, outside the closed-shell config- uration of neon: 1s 2 2s 2 2p 6 . On the other hand, a chlorine atom has a total of 17 electrons and the electron configuration 1s 2 2s 2 2p 6 3s 2 3p 5 , which means that it is short of one electron compared to the closed-shell con- figuration of argon, which has a complete 3p 6 shell. We recall from Section 1.3.4 that electronic configura- tions having full shells of electrons are particularly stable. Hence, by transferring an electron from a sodium atom to a chlorine atom, we obtain a combination of two particularly stable configurations. This results in a positively charged sodium ion, Na + and a negatively charged chlorine ion, Cl . These attract each other through the Coulomb force and form the molecule NaCl. The potential energy between the sodium ion and the chlorine ion can be written as V r A r p B r 6 e 2 4πε 0 r , (2.14) The forces that bind atoms together 55 where A and B are constants and p has a value close to 9.

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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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  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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  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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  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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  Physical Chemistry

  Understanding our Chemical World

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

    (Publisher)

  (Note how we pronounce ‘Waals’ as ‘vahls’.) interactions’, or ‘van der Waals forces’ after the Dutch physicist Johannes Diderik van der Waals (1837–1923) who first postulated their existence. A van der Waals force operates over a relatively 44 INTRODUCING INTERACTIONS AND BONDS O H H d + d + d − Figure 2.3 The water molecule has a ‘V’ shape. Experiments show that gaseous water has an O–H length of 0.957 18 ˚ A; the H–O–H angle is 104.474 ◦ . Water is polar because the central oxygen is electronega- tive and the two hydrogen atoms are electropositive. The vertical arrow indicates the resultant dipole, with its head pointing toward the more negative end of the molecule H O H O O H H H H H O H H H O O H O O H O H H H H H H Figure 2.4 Water would be a gas rather than a liquid at room temperature if no van der Waals forces were present to ‘glue’ them together, as indicated with dotted lines in this two-dimensional representation. In fact, water coalesces as a direct consequence of this three-dimensional network of dipole–dipole interactions. Note how all the O–H · · · O bonds are linear short distance because the influence of a dipole is not large. In practice, we find that the oxygen atoms can interact with hydrogen atoms on an adjacent molecule of water, but no further. The interactions between the two molecules helps to ‘glue’ them together. It is a sobering thought that water would be a gas rather than a liquid if hydrogen bonds (which are merely a particularly strong form of van der Waals forces) did not promote the coalescence of water. The Earth would be uninhabitable without them. Figure 2.4 shows the way that liquid water possesses a three-dimensional network, held together with van der Waals interactions. Each H 2 O molecule in liquid water undergoes at least one interaction with another molecule of H 2 O (sometimes two). Nevertheless, the interactions are not particularly strong – perhaps as much as 20 kJ mol −1 .

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  Solid-State Physics, Fluidics, and Analytical Techniques in Micro- and Nanotechnology

  • Marc J. Madou(Author)
  • 2011(Publication Date)
  • CRC Press

    (Publisher)

  540 Solid-State Physics, Fluidics, and Analytical Techniques in Micro- and Nanotechnology integratedattractiveforcesbetweencolloidparticles arereferredtoas long-range van der Waals forces (see Figure 7.26a ). They are generally important when ordinary colloid particles are within 100 nm of eachotherandbecomelargeastheparticlesurfaces approachoneanother.Theresultisthatcolloidpar-ticlesaggregatequicklyasexternaleffects,suchas Brownian motion and/or bulk fluid motion (e.g., by stirring), bring them within range. In aqueous media,oneeffectthatcanslowdowntheaggrega-tionprocessisthepresenceofelectricchargeonthe surfaces of the particles as shown in Figure 7.26b . Solid surfacesincontactwithwatergenerallyacquire achargebyoneoracombinationofthemechanisms weillustratedearlierin Figure7.23 (e.g.,oxidepar-ticlesacquirechargeviathepH-dependentioniza-tionoftheirsuperficial–OHgroups).Thesecharged solid surfaces attract a cloud of ions of opposite charge(counterions)totheirvicinity.Astheparti-clesapproach,thesecloudsoflikechargebeginto overlap,settinguprepulsion. Whenthiselectrostaticrepulsionisputtogether with the long-range Van der Waals Attraction, a totalinteractioncurveofthetypeshownin Figure 7.27 results. This adding of these forces was first carried out by Derjaguin and Landau in Russia andVerweyandOverbeekintheNetherlandsin the 1940s in the so-called the DLVO theory . The curve that results when combining these forces has an energy barrier, and approaching particles mustpossesssufficientkineticenergytoovercome thatbarrieriftheyaretoaggregate.Ifthebarrieris largerelativeto kT ,theprobabilityofaggregating (thestickingprobability)duringacollisionislow.

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