Van der Waals Forces

12 Key excerpts on "Van der Waals Forces"

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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 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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  Physics of Matter

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

    (Publisher)

  The figure also shows the positions of the two interacting atoms at the equilibrium separation. Taking the diameter of the atoms to be a, we see that the two atoms are nearly touching when they are at the equilibrium separation. 50 Physics of Matter 2.3 Types of interatomic bonding The forces that act between atoms result in four principal types of bonding. These are: van der Waals, ionic, covalent, and metallic bonding. Here we describe these four types of bonding and how they arise from inter- atomic forces. 2.3.1 van der Waals bonding Perhaps surprisingly, even atoms (and molecules) that are electrically neutral bind together. We know, for example, that inert-gas atoms such as neon first condense and then solidify at a low temperature and atmos- pheric pressure; the notable exception being helium, which does not. Similarly, nitrogen molecules condense to produce liquid nitrogen at low temperatures. The attractive forces that bind neutral atoms and molecules are called Van der Waals Forces, named after Johannes van der Waals. The most important of these forces is the dispersive van der Waals force. As we will see, this force arises from distortions that are induced in the electron charge distribution of the interacting atoms when they approach closely together. van der Waals bonding occurs in all atoms and molecules although as we shall see, its relatively low strength can be over- shadowed when much stronger forces come into play. As usual, short-range repulsive forces ensure that the atoms or molecules do not coalesce. To illustrate the origin of the van der Waals attractive force, we consider the interaction between two neon atoms. We recall from Section 1.3.4 that all the electronic shells of neon are full, which makes it an inert gas. Averaged over time, the electron charge distribution of the atom is spherically symmetric, i.e. the centre of the distribution coincides with the nucleus, as illustrated pictorially in Figure 2.8a.

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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)

  From Table 7.3 ,vander WaalsforcesincludeKeesom(dipole-dipole),Debye (dipole- induced dipole), and London dispersive interactions(induceddipole-induceddipole).These short-range forces(n = 6)canallbeexpressedas: U r C r ( ) = -6 (7.19) The most important component of the van der Waals force, as seen earlier, is the London term. T ABLE 7.5 Intermolecular Energy Dependence on Distance for Various Types of Interactions Type of Interaction Model Example Dependence of Energy on Distance (a) Charge-charge Longest-range force; nondirectional + – NH 3 O O C + -1/r (b) Charge-dipole (fixed) Depends on orientation of dipole q – q + + q + q – NH 3 H H O + 1/r 2 (c) Dipole-dipole Depends on mutual orientation of dipole q – q + q – q + q + q – H H O q + q – H H O 1/r 3 (d) Charge-induced dipole Depends on polarizability of molecule in which dipole is induced q – q + + q – NH 3 + q + 1/r 4 (e) Dipole-induced dipole Depends on polarizability of molecule in which dipole is induced q – q + q – q + q + q – H H O q – q + 1/r 6 (f) Dispersion-London forces Involves mutual synchronization of fluctuating charges q – q – q + q – q – q + q – q + 1/r 6 (g) Fermi repulsion Occurs when outer electron orbitals overlap – – 1/r 12 (h) Hydrogen bond Charge attraction + partial covalent bond q + q – H N O C Length of bond fixed Electrochemical and Optical Analytical Techniques 529 Regardless of other interactions found within a complex system of atoms and molecules, there willalmostalwaysbeacontributionfromvander Waals forces. Taking into account both repulsive andattractiveinteractions,agoodapproximation tothetotalpotentialenergyofinteractionbetween twoneutralatomsorpolarmoleculesisgivenby theLennard-Jonespotential: U r B r C r ( ) = + -12 6 (7.20) The C / r 6 termistheattractivevanderWaalsterm, also known as the dispersive term (Equation 7.19).

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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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  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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  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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  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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  The Hydrogen Bond and the Water Molecule

  The Physics and Chemistry of Water, Aqueous and Bio-Media

  • Yves Marechal(Author)
  • 2006(Publication Date)
  • Elsevier Science

    (Publisher)

  Compared to enthalpies of covalent bonds, this energy is weak and temperature has consequently almost no influence on the structure of molecules as long as it is not much higher than 300 K. When two identical molecules come in close proximity they, nevertheless, suffer residual electrostatic inter-actions called Van der Waals interactions. These are at the origin of the condensations of gases into liquids when temperature decreases, with the notable exception, however, of liquid water where these interactions are negligible and condensation is almost entirely due to another interaction that we shall consider throughout this book and define below: the hydrogen bond. Energies of Van der Waals interactions are typically of the order of about 0.01 eV for small molecules, which is at least two orders of magnitude smaller than the energies of covalent bonds. Their origin is electric dipole–dipole interactions, also called Keesom interaction, or induction (called Debye interaction in solids), which is at the origin of a dipole moment induced in an apolar molecule that interacts with the per-manent dipole moment of a polar molecule, or dispersion interaction (also called London 4 1. The Hydrogen Bond: Formation, Thermodynamic Properties, Classification interaction), which is at the origin of phase correlations between electronic displace-ments. If R labels some average distance of the two molecules, then this interaction is represented by a potential well with a minimum for some value of R . At larger R it is attrac-tive and varies as R n with n 6, which indicates that such an interaction most rapidly falls off with distance. At smaller values of R , on the other side of the well, it is strongly repulsive, meaning that it hinders molecules from coming into close contact. It allows all atoms to take on a “Van der Waals radius”, which is the effective (approximate) size this atom occupies when it is part of any molecule.

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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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  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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  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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