Microscopic theory of phase transitions in hydrogen-bonded phenol-amine adducts

Abstract

Second-order reversible ferroelastic phase transitions in a recently discovered class of hydrogen-bonded phenol-amine adducts has already been analyzed by Landau theory. The analysis is however phenomenological and does not directly indicate the microscopic origin of this phase transition. In this paper, a microscopic theory is presented. It is proposed that the main mechanism responsible for the phase transition is the interaction of hydrogen bonds with the lattice vibrations or phonons of the crystal. These interactions with the phonons induce long range cooperative interactions between the hydrogen bonds, which causes the phase transition behavior at the critical temperature. Critical exponents for unit cell parameters and heat capacity are derived with a variational meanfield approach, and shown to be consistent with the prediction of Landau's theory.

Mean field statistical mechanics of model Hamiltonian for hydrogen bonded phase transitions

“…It is important to note that an explicit effective spin Hamiltonian does not appear at any stage of the calculations in Ref. [1]. This is an important difference between the two calculations.…”

“…Recently, a microscopic model was proposed [1] to explain structural phase transitions in a class of hydrogen bonded organic crystals called phenolamine adducts. The phenol-amine adducts [2,3] are simpler in structure than much more complicated biological systems and we believe that the proposal of a prototype microscopic model of phase transitions caused by hydrogen bond interactions has a wide fundamental interest since it is known that hydrogen bonds are important in a large class of organic materials in molecular biology and chemistry [4].…”

“…Acceptor κ interacts via a hydrogen atom H between donor σ 1 or σ 2 to form or break a hydrogen bond (see Ref. [1]). With mirror symmetry, both hydrogen bonds are formed or broken with equal probability.…”

“…A variational mean field type of calculation is done on the effective spin Hamiltonian. It is important to note that the earlier variational calculation [1] was applied to the total model Hamiltonian containing spin-phonon interaction terms. No explicit effective spin Hamiltonian was obtained at any stage of the calculations and the mathematical steps of the statistical mechanical calculations were different from the present ones since there were four variational parameters instead of just two here.…”

“…The variational method used in Ref. [1] is generally applied to spin-phonon systems where exact separation of spin and phonon operators is not possible because of noncommutation properties of the spin components. However, in the model Hamiltonian discussed, the spin variables commute with one another.…”