| Using classical statistical-mechanical methods, I studied two systems: the dissociation of a weakly bound pair of molecules in solution and the uncoiling transition of a helical poly-ion (charged polymer) in solution. Because of the relatively weak energies, which are comparable to the temperature, {dollar}ksb{lcub}B{rcub}T,{dollar} the stability of these systems depends on properties of the solution. The vibrational spectrum during the dissociation process is calculated as a function of temperature and ionic concentration. An example of a weak bond is a hydrogen bond, in which the potential energy is comparable to {dollar}ksb{lcub}B{rcub}T.{dollar} The thermal motions of a weakly bound pair of molecules cannot be treated using the normal modes of small amplitude vibrations, i.e., the harmonic approximation is not valid. To study the anharmonic affects which become more important as the temperature increases, I used the self-consistent phonon approximation. This approximation gives the restoring forces of a solid body for cases in which the atoms have a large amplitude motion, as occurs when the solid melts. The resultant effective force constants are in terms of a thermal statistical average of the second derivative of the potential energy over the possible displacements of the pair of molecules. The potential energy is calculated using the potential of mean force (PMF) for a pair of ions, which is the free energy of the two ions fixed at a certain distance apart. The PMF includes the screening Coulomb forces and the spatial correlation due to the hard-cores. The second system, mentioned above, involves the uncoiling transition of a DNA double helix. A result of this investigation is that coiling of the helix is a function of the dielectric constant of the solvent, the counter-ion radius, the counter-ion concentration, and the temperature. The change in the free energy between coiled and uncoiled conformations was calculated by applying the PMF to pairs of charges on a model poly-ion, formed from two infinite chain of charges wound into a double helix. The distribution of counter-ions was calculated by solving the Poisson-Boltzmann equation of a uniformly charged cylinder with counter-ions. |
