Structural Biochemistry/Chemical Bonding/Strength of Interactions

The following interactions; ion-ion, ion-dipole, dipole-dipole, dispersion, and Van Der Waals with respect to the strength of the interaction vary in terms of strength levels. The strength of the interaction rests largely on the distance on which they can act on each other.

Ion-Ion Interactions
Coulomb’s law delivers that the electric force acting on a point charge q1 as a result of the presence of a second point charge q2. The potential energy, U(r), is given by the equation: U(r)= (q1q2)/(4*π*E0)*(1/r). In which potential energy arises from the forces between species. Where q1 and q2 are the two charges, separated by a distance “r” in the vacuum. E0 is the permittivity of a vacuum and 1/(4*π*E0) represents Coulombs’ constant. This equation is characteristic of the relationship between two charges. The ion-ion interactions act over a large distance. Or it can be said that the two charges interact with each other via U~1/r.

Dipole-Dipole
For dipole-dipole interactions assume two polar molecules A and B having permanent dipole moments L1 and L2. The force one molecule exerting on another will depend on L1 and L2, the distance r, and the relative orientation. The dipole moments of two molecules tend to align with the positive end of one dipole near the negative end of the other, so that the forces of attraction between them are maximized. The potential energy of the interaction can be simplified to U= -2L1L2/ (4*π* E0*r^3) for a horizontal orientation and U= -2L1L2/ (4*π* E0*r^3) for a vertical orientation. The negative sign indicates that the interaction is attractive. For dipole-dipole interactions the two dipoles interact with each other via U~1/r^3.

Ion-Dipole
For ion-dipole interactions the interaction between an ion and polar molecule is given by: U=-(qL)/( 4*π* E0*r^2) where q=ion charge and L again represents the dipole. Note: The equation is valid when the ion and dipole lie along the same axis. For ion-dipole interactions the cation and negatively charged end of the dipole interact with each other via U~1/r^2.

Ion-Induced Dipole
For ion-induced dipoles the interaction is dependent on the orientation of the dipole and for dipole-induced-dipole interactions is dependent on the polarizability of the molecule in which the dipole is induced. Ion-induced dipoles interact with each other via U~1/r^2 and dipole-induced-dipole interactions interact with each other via U~1/r^5.

Dispersion & Van Der Waals Interactions
Dispersion interactions otherwise known as London interactions interact with each other via U~1/r^6. Van der Waals Repulsion repels at an even shorter distance and is based upon the Pauli exclusion principle. One can calculate the interaction utilizing quantum mechanics. These interactions are dependent on the inverse of the 12th power of the distance, U~1/r^12. John Edward Lennard accounted for the repulsive and attraction interactions in nonionic systems: U=-A/r^6+B/r^12 where A and B are constants for two interacting molecules which gives the general form of the equation: U=4*E*[(H/r)^12-(H/r)^6] for a given pair of molecules where E is the depth of the potential  well and H is the separation at which U=0. Therefore Van Der Waals interactions are dependent upon U~1/r^12.

The ranking of the above interactions in descending order are as follows: Ion-ion, ion-dipole, ion-induced dipole, dipole-induced-dipole, dispersion forces, and Van Der Waals interactions.

Again, the strength of the interaction rests largely on the distance on which they can act on each other.