Forces repulsive

Repulsive forces would arise if a hydrophilic group such as an ammo function was too close to a hydrophobic group such as an aromatic ring. Alternatively, two charged groups of identical charge would be repelled. 

Based on the strengths of the four types of bonds above, we might expect the relative importance of the bonding forces to follow the same order as their strengths, that is, 

First of all, in most proteins there are far more van der Waals and hydrogen bonding interactions possible, compared to covalent or ionic bonding. We only need to consider the number and types of amino acids in any typical globular protein to see why. The only covalent bond which can contribute to tertiary structure is a disulfide bond. Only one amino acid out of our list can form such a bond—cysteine. However, there are eight amino acids which can interact with each other through van der Waals bonding Gly, Ala, Val, Leu, lie, Phe, Pro and Met. 

There are examples of proteins with a large number of disulfide bridges, where the relative importance of the covalent link to tertiary structure is more significant. Disulfide links are also more significant in small polypeptides such as the peptide hormones vasopressin (Fig. 3.12) and oxytocin (Fig. 3.13). However, in the majority of proteins, disulfide links play a minor role in controlling tertiary structure. 

As far as ionic bonding is concerned, only four amino acids (Asp, Glu, Lys, Arg) are involved, whereas eight amino acids can interact through hydrogen bonding (Ser, Thr, Cys, Asn, Gin, His, Tyr, Trp). Clearly, the number of possible ionic and covalent bonds is greatly outnumbered by the number of hydrogen bonds or van der Waals interactions. 

Both attractive and repulsive interactions occur among different regions of polypeptide chains and are responsible for most secondary and tertiary structure. 

Covalent bonds involve the equal sharing of an electron pair by two atoms. Examples of important covalent bonds are peptide (amide) and disulfide bonds between amino acids, and C-C, C-O, and C-N bonds within amino acids. 

Coordinate covalent bonds involve the unequal sharing of an electron pair by two atoms, with both electrons (originally) coming from the same atom. The electron pair donor is the ligand, or Lewis base, whereas the acceptor is the central atom (because it frequently can accept more than one pair of electrons), or Lewis acid. These bonds are important in all interactions between transition metals and organic ligands (e.g., Fe + in hemoglobin and the cytochromes). 

Ionic interactions arise from electrostatic attraction between two groups of opposite charge. These bonds are formed between positively charged (o -ammonium, -ammonium, guanidinium, and imidazolium) side chains and negatively charged (ionized forms of a-carboxyl, j6-carboxyl, y-carboxyl, phosphate, and sulfate) groups. 

Van der Waals attractive forces are due to a fixed dipole in one molecule that induces rapidly oscillating dipoles in another molecule through distortion of the electron cloud. The positive end of a fixed dipole will pull an electron cloud toward it the negative end will push it away. The strength of these interactions is strongly dependent on distance, varying as 1/r where r is the interatomic separation. The Van der Waals forces are particularly important in the nonpolar interior structure of proteins, where they provide attractive forces between nonpolar side chains. 

In addition to the attractive forces, there are also repulsive forces from the inner electrons and the atomic nuclei, which prevent the collapse of the crystal lattice. The superposition of the repulsion and the attraction yields the equilibrium distance ro between the molecules, cf. Fig. 2.5. 

The repulsive forces are based on Coulomb repulsion and, according to the Pauli principle, on the interdiction for additional electrons to be found in a region of space where all the fully-occupied orbitals overlap. These effects become important only at very small distances and increase very rapidly with further decreasing distance. Their exact calculation is very difficult and laborious. They are generally treated using readily-applicable approximations. 

The simplest approximation is that of a rectangular potential with the assumption 

A value n = 12 is often used, yielding for the sum of repulsion and attraction the so called Lennard-Jones potential 

Compare also Fig. 2.5. The equilibrium distance where dV/dr = 0 will be denoted 

Particles that interact with long range repulsive forces behave much like hard spheres when the distance between the particles is larger than the range of the repulsive force. This is usually the case when the volume fraction is low (average 

Even dilute suspensions of repulsive particles will have slightly greater viscosity than hard spheres because of the additional viscous dissipation related to the flow of fluid through the repulsive region around the particle. For particles with EDL repulsion this is known as the primary electro-viscous effect (Hunter, 2001). The total drag on the particle and the double layer is greater than the drag on a hard sphere. The increase in viscosity due to the primary electro-viscous effect is typically minimal. 

Concentrated suspensions can have significantly elevated viscosities (relative to hard spheres at the same volume fraction) due to the interaction between overlapping EDLs. For particles to push past each other the double layer must be distorted. This effect is known as the secondary electro-viscous effect (Hunter, 2001). Similar effects occur when the repulsion is by steric mechanism. 

The influence of repulsive forces on suspension viscosity is usually handled by considering the effective volume fraction of the particles. The effective volume fraction is the volume fraction of the particles plus the fraction of volume occupied by the repulsive region around the particle. 

In the simplest example of colloid stability, suspension partides would be stabilized entirely by the repulsive forces created when two charged surfaces approach each other and their electric double layers overlap. The repulsive energy VR for spherical particles, or rigid droplets, is given approximately as  

In practice the situation may be more complicated. The shear plane may actually lie about 20 nm further away from the surface than the Stern plane, closer to the Gouy plane [271]. Also, if particle surfaces are covered by long chain molecules (physically or chemically bonded to the surface) then steric repulsion between particles may be significant. This repulsion is due to an osmotic effect caused by the high concentration of chains that are forced to overlap when particles closely approach, and also due to the volume restriction, or entropy decrease, that occurs when the chains lose possible conformations due to overlapping. 

If the distance r between two molecules i and j becomes very small, their electron clouds start to overlap leading to strong repulsive forces. Such forces are not well understood and, while theoretical considerations suggest that the repulsive potential should be an exponential function of the intermolecular distance (Reed and Gubbins, 1973), the following expression is typically used as more convenient  

We will discuss next the physical attractive forces, and the resulting intermolecular potentials, and then consider the chemical ones. 

In this discussion of colloid stability, the reasons why colloidal dispersions can have different degrees of kinetic stability are explored and how these are influenced, and can therefore be modified, by solution and surface properties. Encounters between species in a dispersion can occur frequently due to any of Brownian motion, sedimentation or stirring. The stability of the dispersion depends on how the species interact when this happens. The main cause of repulsive forces is the electrostatic repulsion between like-charged objects. The main cause of attractive forces is the van der Waals forces between objects. 

There also exist dispersion or London-van der Waals forces that molecules exert towards each other. These forces are usually attractive in nature and result from the orientation of dipoles, whether dipole-dipole (Keesom dispersion forces), dipole-induced dipole (Debye dispersion forces) or induced dipole-induced dipole (London dispersion forces). Except for quite polar materials, the London dispersion forces are the most significant of the three. For molecules the force varies inversely with the sixth power of the inter-molecular distance. For particles and droplets, the force varies approximately inversely with inter-particle distance. 

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Madeluag constant For an ionic crystal composed of cations and anions of respective change z + and z, the la ttice energy Vq may be derived as the balance between the coulombic attractive and repulsive forces. This approach yields the Born-Lande equation,... 

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. 

Fig. V-5. The repulsive force between crossed cylinders of radius R (1 cm) covered with mica and immersed in propylene carbonate solutions of tetraethylammonium bromide at the indicated concentrations. The dotted lines are from double-layer theory (From Ref. 51).

Weeks J, Chandler D and Anderson H C 1971 Role of repulsive forces in determining the equilibrium structure of simple liquids J. Chem. Phys. 54 5237... 

Figure A3.1.1. Typical pair potentials. Illustrated here are the Lennard-Jones potential, and the Weeks-Chandler- Anderson potential, which gives the same repulsive force as the Leimard-Jones potential.

The van der Waals attraction arises from tlie interaction between instantaneous charge fluctuations m the molecule and surface. The molecule interacts with the surface as a whole. In contrast the repulsive forces are more short-range, localized to just a few surface atoms. The repulsion is, therefore, not homogeneous but depends on the point of impact in the surface plane, that is, the surface is corrugated. 

As the tip is brought towards the surface, there are several forces acting on it. Firstly, there is the spring force due to die cantilever, F, which is given by = -Icz. Secondly, there are the sample forces, which, in the case of AFM, may comprise any number of interactions including (generally attractive) van der Waals forces, chemical bonding interactions, meniscus forces or Bom ( hard-sphere ) repulsion forces. The total force... 

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 electrostatic potential at a point is the force acting on a unit positive charge placed at that point. The nuclei give rise to a positive (i.e. repulsive) force, whereas the electrons give rise to a negative potential. The electrostatic potential is an observable quantity that can be determined from a wavefunction using Equations (2.222) and (2.223) ... 

The urigin uf van der Waals repulsive forces is mutual interaction of electrons in atttrn 1 and those in atom 4. 

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... 

On August 29,1982, physicists at the Heavy Ion Research Laboratory, Darmstadt, West Germany made and identified element 109 by bombing a target of Bi-209 with accelerated nuclei of Fe-58. If the combined energy of two nuclei is sufficiently high, the repulsive forces between the nuclei can be overcome. 

The small differences m stability between branched and unbranched alkanes result from an interplay between attractive and repulsive forces within a molecule (intramo lecular forces) These forces are nucleus-nucleus repulsions electron-electron repul sions and nucleus-electron attractions the same set of fundamental forces we met when... 

Nonbonded interactions are the forces be tween atoms that aren t bonded to one another they may be either attractive or repulsive It often happens that the shape of a molecule may cause two atoms to be close in space even though they are sep arated from each other by many bonds Induced dipole/induced dipole interactions make van der Waals forces in alkanes weakly attractive at most distances but when two atoms are closer to each other than the sum of their van der Waals radii nuclear-nuclear and electron-electron repulsive forces between them dominate the fvan derwaais term The resulting destabilization is called van der Waals strain... 

Diaxial repulsion (Section 3 10) Repulsive forces between axial substituents on the same side of a cyclohexane nng... 

Van der Waals radius (Section 2 17) A measure of the effec tive size of an atom or a group The repulsive force between two atoms increases rapidly when they approach each other at distances less than the sum of their van der Waals radii Van der Waals strain (Section 3 2) Destabilization that results when two atoms or groups approach each other too closely Also known as van der Waals repulsion Vicinal (Section 6 14) Describing two atoms or groups at tached to adjacent atoms... 

The above potential is referred to as a Lennard-Jones or 6-12 potential and is summed over all nonbonded pairs of atoms ij. The first positive term is the short range repulsion and the second negative term is the long range attraction. The parameters of the interaction are Aj and B... The convenient analytical form of the 6-12 potential means that it is often used, although an exponential repulsion term is usually considered to be a more accurate representation of the repulsive forces (as used in MM-t). 

The forces which bring about adsorption always include dispersion forces, which are attractive, together with short-range repulsive forces. In addition, there will be electrostatic (coulombic) forces if either the solid or the gas is polar in nature. Dispersion forces derive their name from the close connection between their origin and the cause of optical dispersion. First... 

An expression for the short-range repulsive force (which arises from the interpenetration of the electron clouds of the two atoms) can also be derived from quantum-mechanical considerations" as... 

The effect of polarity in enhancing the energy of interaction has been discussed by Kiselev and his associates who distinguish between non-specific adsorption, where only dispersion and repulsive forces are involved 4>d and and specific adsorption, where coulombic contributions (some or all of (p, [Pg.11]

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