Force between molecules

Before we come to a discussion of the liquid and solid states, where interactions between molecules are of the utmost importance, it is useful to discuss briefly the interactions between molecules in the vapour phase. These interactions can usually be thought of as occurring between pairs of molecules, with occasional three-body interactions being treated as a special and uncommon case, and for many purposes it also suffices to treat cases where the molecules involved are not extremely close together. Neither of these simplifications can be made for molecules in a condensed phase. 

Whilst the interaction forces between two molecules cannot rigorously be split up into contributions arising from diflferent effects, it is often a help to make some such separation and we shall do it here. If we deal only with simple, closed-shell diamagnetic molecules, of which the water molecule is one, then the interaction energy between two such molecules can be considered as arising from four causes (i) electrostatic interaction between the permanent multipole moments of the two molecules (ii) electrostatic interaction between the permanent multipole moments of one molecule and the moments which these induce in the other molecule because of its finite polarizability (iii) an interaction of quantum origin between the instantaneous fluctuating dipole moments of the two molecules (dispersion forces) (iv) an inter- 

All these interactions are taken into account automatically in a proper quantum-mechanical treatment (Buckingham, 1965) but it is instructive to examine them separately. 

The interaction between permanent multipole moments is quite straightforward to calculate. Using the definitions of the multipole moments given in (1.6) and choosing sjrmmetry axes as in fig. 1.2, the electrostatic potential due to an isolated molecule can be written (Coulson Eisenberg, 1966 a) as 

Since the molecule is uncharged there is no r term, the dipole term falls off as r and the quadrupole terms as r . Another similar molecule at the point (r, 6, j ) and with an orientation specified by new s)nnmetry axes x, y, z will have an energy determined by the interaction of its dipole moment p, with the field component —8VI8z and of its quadrupole moments with the field gradients — 8WI8idj. If the s -axis of this molecule, which is also the axis of its dipole moment, has polar angles O, j ) in the co-ordinate system of the first molecule, then the dipole-dipole interaction energy between these two fixed molecules Uj](0, j) O, ) = —cos [3 cos 0 — i] 

In Chapter 7, we saw that the formation of chemical bonds is always governed by minimization of the energy of the atoms involved. As we turn our attention to the structures of solids, we ll see that the same principle still holds. The structure of any solid, whether crystalline or amorphous, is determined by the balance of attractive and repulsive forces between the atoms or molecules involved. In this section, we will consider the nature of intermolecular forces—the forces between molecules. 

Intermolecular forces are also critically important in biochemical molecules such as proteins and DNA. Biomedical engneers need to consider this type of interaction at least as often as materials engneers. 

Dispersion forces, sometimes called London forces, are common to all molecules. They are also referred to as instantaneous dipole-induced dipole forces. This rather awkward sounding term points us to the origin of these forces, so let s consider each part of the name separately. To begin with, recall that a dipole exists whenever we have two oppositely charged points or objects separated by some distance. 

The quantum mechanical picture of the atom, and hence our pictures of various orbitals, arises from ideas of probability and average position. To understand the notion of an instantaneous dipole, though, we ll need to step away ftom that viewpoint. Instead, we ll need to consider electron positions or distributions at a single instant. For an electron in an s orbital, for example, the ideas presented in 

Now we combine the ideas of the instantaneous and induced dipoles. Consider two molecules that are separated by a small distance. One molecule experiences a fluctuation in its electron density, creating an instantaneous dipole. The second molecule will then experience that dipole as an external electric field, creating an induced dipole in the second molecule. This combination is the instantaneous 

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The equation of state for an ideal gas, that is a gas in which the volume of the gas molecules is insignificant, attractive and repulsive forces between molecules are ignored, and molecules maintain their energy when they collide with each other. 

The capillary effect is apparent whenever two non-miscible fluids are in contact, and is a result of the interaction of attractive forces between molecules in the two liquids (surface tension effects), and between the fluids and the solid surface (wettability effects). 

The next point of interest has to do with the question of how deep the surface region or region of appreciably unbalanced forces is. This depends primarily on the range of intermolecular forces and, except where ions are involved, the principal force between molecules is of the so-called van der Waals type (see Section VI-1). This type of force decreases with about the seventh power of the intermolecular distance and, consequently, it is only the first shell or two of nearest neighbors whose interaction with a given molecule is of importance. In other words, a molecule experiences essentially symmetrical forces once it is a few molecular diameters away from the surface, and the thickness of the surface region is of this order of magnitude (see Ref. 23, for example). (Certain aspects of this conclusion need modification and are discussed in Sections X-6C and XVII-5.)... 

McLachlan A D 1963 Retarded dispersion forces between molecules Proc. R. Soc. A 271 387... 

It has long been known from statistical mechanical theory that a Bose-Einstein ideal gas, which at low temperatures would show condensation of molecules into die ground translational state (a condensation in momentum space rather than in position space), should show a third-order phase transition at the temperature at which this condensation starts. Nonnal helium ( He) is a Bose-Einstein substance, but is far from ideal at low temperatures, and the very real forces between molecules make the >L-transition to He II very different from that predicted for a Bose-Einstein gas. 

Fig. 4, 33 The Drude model for dispersive interactions. (Figure adapted from Rigby M, E B Smith, W A Wakeham and G C Maitland 1986. The Forces Between Molecules. Oxford, Clarendon Press.)...

A substance exists as a liquid rather than a gas because attractive forces between molecules (mtermolecular attractive forces) are greater m the liquid than m the gas phase Attractive forces between neutral species (atoms or molecules but not ions) are referred to as van der Waals forces and may be of three types... 

In general aldehydes and ketones have higher boiling points than alkenes because they are more polar and the dipole-dipole attractive forces between molecules are stronger But they have lower boiling points than alcohols because unlike alcohols two carbonyl groups can t form hydrogen bonds to each other... 

Until surface contact, the force between molecules is always one of attraction, although this attraction has different origins in different systems. London forces, dipole-dipole attractions, acid-base interactions, and hydrogen bonds are some of the types of attraction we have in mind. In the foregoing list, London forces are universal and also the weakest of the attractions listed. The interactions increase in strength and also in specificity in the order listed. 

The classical kinetic theoty of gases treats a system of non-interacting particles, but in real gases there is a short-range interaction which has an effect on the physical properties of gases. The most simple description of this interaction uses the Lennard-Jones potential which postulates a central force between molecules, giving an energy of interaction as a function of the inter-nuclear distance, r. 

The molecules of liquids are separated by relatively small distances so the attractive forces between molecules tend to hold firm within a definite volume at fixed temperature. Molecular forces also result in tlie phenomenon of interfacial tension. The repulsive forces between molecules exert a sufficiently powerful influence that volume changes caused by pressure changes can be neglected i.e. liquids are incompressible. 

In the case of an associating fluid with the repulsive-attractive reference system potential, the attractive van der Waals forces between molecules may also be considered in a perturbational manner [114]. The Helmholtz free energy can be written as a sum of three terms... 

The mechanism by which analytes are transported in a non-discriminate manner (i.e. via bulk flow) in an electrophoresis capillary is termed electroosmosis. Eigure 9.1 depicts the inside of a fused silica capillary and illustrates the source that supports electroosmotic flow. Adjacent to the negatively charged capillary wall are specifically adsorbed counterions, which make up the fairly immobile Stern layer. The excess ions just outside the Stern layer form the diffuse layer, which is mobile under the influence of an electric field. The substantial frictional forces between molecules in solution allow for the movement of the diffuse layer to pull the bulk... 

The generally low melting and boiling points of molecular substances reflect the fact that the forces between molecules (intermolecular forces) are weak. To melt or boil a molecular... 

Hydrogen bond An attractive force between molecules found when a hydrogen atom is bonded to N, O, or F, 238-240, 616... 

The forces between molecules are strongly affected by the presence of molecular dipoles. Two molecules that possess molecular dipoles tend to attract each other more strongly than do molecules without dipoles. One of the most important results of this is found in solvent properties. Table 17-IV shows some solubility data of... 

The temperature-independent van der Waals parameters a and b are unique for each gas and are determined experimentally (Table 4.5). Parameter a represents the role of attractions so it is relatively large for molecules that attract each other strongly and for large molecules with many electrons. Parameter b represents the role of repulsions it can be thought of as representing the volume of an individual molecule (more precisely, the volume per mole of molecules), because it is the repulsive forces between molecules that prevent one molecule from occupying the space already occupied by another molecule. 

Molecules am act one another. Fiuni that simple fact spring fundamentally important consequences. Rivers, lakes, and oceans exist because water molecules attract one another and form a liquid. Without that liquid, there would be no life. Without forces between molecules, our flesh would drip off our bones and the oceans would be gas. Less dramatically, the forces between molecules govern the physical properties of bulk matter and help to account for the differences in the substances around us. They explain why carbon dioxide is a gas that we exhale, why wood is a solid that we can stand on, and why ice floats on water. At very close range, molecules also repel one another. When pressed together, molecules resist further compression. 

We have to refine our atomic and molecular model of matter to see how bulk properties can be interpreted in terms of the properties of individual molecules, such as their size, shape, and polarity. We begin by exploring intermolecular forces, the forces between molecules, as distinct from the forces responsible for the formation of chemical bonds between atoms. Then we consider how intermolecular forces determine the physical properties of liquids and the structures and physical properties of solids. 

A gas will obey the ideal gas equation whenever it meets the conditions that define the ideal gas. Molecular sizes must be negligible compared to the volume of the container, and the energies generated by forces between molecules must be negligible compared to molecular kinetic energies. The behavior of any real gas departs somewhat from ideality because real molecules occupy volume and exert forces on one another. Nevertheless, departures from ideality are small enough to neglect under many circumstances. We consider departures from ideal gas behavior in Chapter if. 

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