Attractive-forces

There is a fundamental difference between the rheological behaviour of hard sphere or repulsive particle suspensions and attractive particle suspensions due to the attractive bond between particles. The bonds between particles must be broken in order to pull the particles apart to allow flow to occur. The result of the attractive bonds between particles is that an attractive particle network is formed when the suspension is at rest. The attractive bonding produces material behaviour that is characterized by viscoelasticity, a yield stress (minimum stress required for flow) and shear thinning behaviour. 

The shear thinning of an attractive particle network is more pronounced than for hard sphere suspensions of the same particles at the same volume fraction 

It has been pointed out in the previous section that the rheological behaviour of hard sphere suspensions (non-interacting particles) was not influenced by the size of the particles. This is not true of attractive particle networks. When the particles in a suspension are attractive, smaller particle size results in increased rheological properties such as 5deld stress, viscosity and elastic modulus (described next). The influence of particle size can be determined by considering that the rheological properties of attractive particle networks depend upon the strength of the bond between particles and the number of bonds per unit volume that need to be broken. For example, consider the shear yield stress  

The strength of the bond of an attractive particle network increases linearly with particle size as indicated by Equations (5.8) and (5.11). 

This would make one think that the larger size particles result in suspensions with greater yield stress, viscosity and elastic modulus. It is the influence of the number of bonds per unit volume that produces the opposite result. The number of bonds that need to be broken per unit volume depends upon the structure of the particle network and the size of the particles. In the first instance we assume that the structure of the particle network does not vary with particle size. (Details of the aggregate and particle network structure are beyond the scope of the present text.) Then the number of bonds per unit volume simply varies with the inverse cube of the particle size  

FIGURE 3.1 Interacting semi-infinite slabs A and B with a separating medium C. 

It is convenient to integrate first with respect to r. The result is 

Equation 3.3 applies for a unit volume in region A. If we integrate this result over all of region A (i.e., between Zj = 0 and h o°) we obtain the total interaction energy between the two semi-infinite regions. Acmally it is convenient to calculate the energy cPab per unit area  

Here the Hamaker constant, A, is given by It is a key parameter charac- 

It should be noted that the attractive interaction between two large bodies decreases much more slowly as they are separated than does the interaction between two molecules. According to Equations 3.1 and 3.5, the interaction is proportional to the inverse square of the separation distanee in the former case and the inverse sixth power in the latter ease. For eolloidal particles, London-van der Waals interaetions are signifieant for separation distanees h up to about 100 nm (1000 A). 

Their origin lies with electrostatic interactions between opposite charges. But, if molecules are electrically neutral, how can there be positive and negative charges  

As a result, water ends up with a net negative charge of (-c), whose center lies close to the center of the oxygen atom and with a net positive diarge of (+e), whose center lies in the middle of the distance between the two hydrogen atoms. We refer to such a molecule as a dipole, with a dipole moment  

All asymmetric nonhydrocarbon molecules (ketones, alcohols, ethers, etc.) are dipoles since the centers of the positive and negative charges. 

On the basis of the strength of the attractive forces among molecules it is convenient to classify them, somewhat arbitrarily, into two main types  

In the second group the interaction is so strong that physical aggregates are formed. The most typical example is hydrogen bonding where, in the case of acetic acid for example, dimers are formed. 

Electrostatic interactions between molecules can result from the net charges of ions and also from permanent charge separation in neutral species. In this section, we will examine the nature of these interactions. 

Recall from basic physics that the force between point charges is inversely proportional to the square of the distance between the charges, that is  

This equation is written for CCS units and is known as Coulombs law. See Appendix D for the SI units equivalent of Coulomb s law. The potential energy between species i andj is found by rearranging Equation (4.4), and using the expression for force given by Coulombs law  

Point charges exert strong forces and fall off relatively slowly with distance. It is uncommon for an isolated net charge to exist in nature since it will typically find an oppositely charged species and combine. However, some molecular examples exist, including the following  

Electrolytes (e.g., 18M H2SO4) Net charges exist in the liquid phase in electrolyte solutions and molten salts. In an H2SO4 acid bath, for example, H+ and SO4 exist in the liquid and exert Coulombic forces. The polar structure ofwater allows charged species to be stable. The water forms an electrostatic cloud that shields the ions from one another. The electrostatic interactions of the charged species within the electrolyte solution form a key component in the behavior of electrochemical systems.  

---

The virial equation is appropriate for describing deviations from ideality in those systems where moderate attractive forces yield fugacity coefficients not far removed from unity. The systems shown in Figures 2, 3, and 4 are of this type. However, in systems containing carboxylic acids, there prevails an entirely different physical situation since two acid molecules tend to form a pair of stable hydrogen bonds, large negative... 

These surface active agents have weaker intermoiecular attractive forces than the solvent, and therefore tend to concentrate in the surface at the expense of the water molecules. The accumulation of adsorbed surface active agent is related to the change in surface tension according to the Gibbs adsorption equation... 

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). 

Figure 5.29 Water droplet with attractive forces...

The method seirsibility depeird essentially on the poles force attraction which exists at the position of the defect. This attraction force depend on the value of the leakage field, so of the magnetic exciting field which has created them. 

The long-range van der Waals interaction provides a cohesive pressure for a thin film that is equal to the mutual attractive force per square centimeter of two slabs of the same material as the film and separated by a thickness equal to that of the film. Consider a long column of the material of unit cross section. Let it be cut in the middle and the two halves separated by d, the film thickness. Then, from one outside end of one of each half, slice off a layer of thickness d insert one of these into the gap. The system now differs from the starting point by the presence of an isolated thin layer. Show by suitable analysis of this sequence that the opening statement is correct. Note About the only assumptions needed are that interactions are superimposable and that they are finite in range. 

If attractive forces are present, then according to an equation by Frenkel (see Ref. 2), the average time of stay t of the molecule on the surface will be... 

Van der Waals Equations of State. A logical step to take next is to consider equations of state that contain both a covolume term and an attractive force term, such as the van der Waals equation. De Boer [4] and Ross and Olivier [55] have given this type of equation much emphasis. 

Such attractive forces are relatively weak in comparison to chemisorption energies, and it appears that in chemisorption, repulsion effects may be more important. These can be of two kinds. First, there may be a short-range repulsion affecting nearest-neighbor molecules only, as if the spacing between sites is uncomfortably small for the adsorbate species. A repulsion between the electron clouds of adjacent adsorbed molecules would then give rise to a short-range repulsion, usually represented by an exponential term of the type employed... 

The existence of intennolecular interactions is apparent from elementary experimental observations. There must be attractive forces because otherwise condensed phases would not fomi, gases would not liquefy, and liquids would not solidify. There must be short-range repulsive interactions because otherwise solids and liquids could be compressed to much smaller volumes with ease. The kernel of these notions was fomuilated in the late eighteenth century, and Clausius made a clear statement along the lines of this paragraph as early as 1857 [1]. 

In 1873, van der Waals [2] first used these ideas to account for the deviation of real gases from the ideal gas law P V= RT in which P, Tand T are the pressure, molar volume and temperature of the gas and R is the gas constant. Fie argried that the incompressible molecules occupied a volume b leaving only the volume V- b free for the molecules to move in. Fie further argried that the attractive forces between the molecules reduced the pressure they exerted on the container by a/V thus the pressure appropriate for the gas law isP + a/V rather than P. These ideas led him to the van der Waals equation of state ... 

Adsorbates can physisorb onto a surface into a shallow potential well, typically 0.25 eV or less [25]. In physisorption, or physical adsorption, the electronic structure of the system is barely perturbed by the interaction, and the physisorbed species are held onto a surface by weak van der Waals forces. This attractive force is due to charge fiuctuations in the surface and adsorbed molecules, such as mutually induced dipole moments. Because of the weak nature of this interaction, the equilibrium distance at which physisorbed molecules reside above a surface is relatively large, of the order of 3 A or so. Physisorbed species can be induced to remain adsorbed for a long period of time if the sample temperature is held sufficiently low. Thus, most studies of physisorption are carried out with the sample cooled by liquid nitrogen or helium. 

When an atom or molecule approaches a surface, it feels an attractive force. The interaction potential between the atom or molecule and the surface, which depends on the distance between the molecule and the surface and on the lateral position above the surface, detemiines the strength of this force. The incoming molecule feels this potential, and upon adsorption becomes trapped near the minimum m the well. Often the molecule has to overcome an activation barrier, before adsorption can occur. 

Weeks J D, Selinger R L B and Broughton J Q 1995 Self consistent treatment of attractive forces in... 

Weeks J D, Katsov K and Vollmayr K 1998 Roles of repulsive and attractive forces in determining the structure of non uniform liquids generalized mean field theory Phys. Rev. Lett. 81 4400... 

Muller L J, Vanden Bout D and Berg M 1993 Broadening of vibrational lines by attractive forces ultrafast Raman echo experiments in a CH2l CDCl2 mixture J. Chem. Phys. 99 810-19... 

Van der Waals complexes can be observed spectroscopically by a variety of different teclmiques, including microwave, infrared and ultraviolet/visible spectroscopy. Their existence is perhaps the simplest and most direct demonstration that there are attractive forces between stable molecules. Indeed the spectroscopic properties of Van der Waals complexes provide one of the most detailed sources of infonnation available on intennolecular forces, especially in the region around the potential minimum. The measured rotational constants of Van der Waals complexes provide infonnation on intennolecular distances and orientations, and the frequencies of bending and stretching vibrations provide infonnation on how easily the complex can be distorted from its equilibrium confonnation. In favourable cases, the whole of the potential well can be mapped out from spectroscopic data. 

Figure 2.5 shows the boiling points of the hydrides in elements of Groups IV. V, VI and VII. Clearly there is an attractive force between the molecules of the hydrides of fluorine, oxygen and nitrogen... 

The attractive force is called hydrogen bonding and is normally represented by a dotted line, for example A—H A—H it is this... 

This term describes the repulsive forces keeping two nonbonded atoms apart at close range and the attractive force drawing them together at long range. 

The hydrogen atom is a three-dimensional problem in which the attractive force of the nucleus has spherical symmetr7. Therefore, it is advantageous to set up and solve the problem in spherical polar coordinates r, 0, and three parts, one a function of r only, one a function of 0 only, and one a function of [Pg.171]

We assume that the nuclei are so slow moving relative to electrons that we may regard them as fixed masses. This amounts to separation of the Schroedinger equation into two parts, one for nuclei and one for electrons. We then drop the nuclear kinetic energy operator, but we retain the intemuclear repulsion terms, which we know from the nuclear charges and the intemuclear distances. We retain all terms that involve electrons, including the potential energy terms due to attractive forces between nuclei and electrons and those due to repulsive forces... 

Atoms combine with one another to give compounds having properties different from the atoms they contain The attractive force between atoms m a compound is a chemical bond One type of chemical bond called an ionic bond, is the force of attraction between oppositely charged species (ions) (Figure 1 4) Ions that are positively charged are referred to as cations, those that are negatively charged are anions... 

Were we to simply add the ionization energy of sodium (496 kJ/mol) and the electron affin ity of chlorine (—349 kJ/mol) we would conclude that the overall process is endothermic with AH° = +147 kJ/mol The energy liberated by adding an electron to chlorine is msuf ficient to override the energy required to remove an electron from sodium This analysis however fails to consider the force of attraction between the oppositely charged ions Na" and Cl which exceeds 500 kJ/mol and is more than sufficient to make the overall process exothermic Attractive forces between oppositely charged particles are termed electrostatic, or coulombic, attractions and are what we mean by an ionic bond between two atoms... 

The H—O—H angle m water (105°) and the H—N—H angles m ammonia (107°) are slightly smaller than the tetrahedral angle These bond angle contractions are easily accommodated by VSEPR by reasoning that electron pairs m bonds take up less space than an unshared pair The electron pair m a covalent bond feels the attractive force of... 

---