Microscopic theory of phase transitions in hydrogen-bonded phenol-amine adducts Pye Ton How, Beck Sim Lee, Hoong-Kun Fun,* Ibrahim Abdul Razak, and Suchada Chantrapromma † School of Physics, Universiti Sains Malaysia, 11800 USM Penang, Malaysia Received 11 March 2004; revised manuscript received 1 December 2004; published 23 May 2005 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 interac- tion 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. DOI: 10.1103/PhysRevB.71.174109 PACS numbers: 63.70.+h, 63.20.Ls, 61.50.Ks I. INTRODUCTION Crystalline solids containing phenol-amine adducts are widely used to study hydrogen bonds. Phenol-amine adducts are produced by the interaction of phenols, compounds hav- ing at least one hydroxyl group, and amines, compounds having at least one amino group. The phenols and amines in the solid state are generally linked by intermolecular O–H ¯ O, O–H ¯ N or N–H ¯ O types of hydrogen bonds which are among the most robust and versatile synthons in crystal engineering. Studies on the hydrogen bondings in these phenol-amine adducts can be used as a model for the more complicated hydrogen bonding in biological systems in which hydrogen bondings play a crucial and an important role. Owing to our interests in hydrogen bondings in such systems, we have investigated systematically in single crys- tal forms a class of phenol-amine adducts and their crystal structures were reported. 1–8 Some of these single crystals of phenol amine adducts undergo a reversible phase transition with variation in temperature. For these samples, a hydrogen atom is transferred from the phenol which then becomes an anion to the amine which then becomes a cation. Hydro- gen bonds are then established between the donor/amine/ cation and the acceptor/phenol/anion. As a result, these crys- tals undergo a temperature-dependent structural phase transition, which is second-order ferroelastic in its nature. These are the first reported cases of structural phase transi- tion induced by hydrogen bonding interactions. The phase transition that has been observed are classified into two categories 1 orthorhombic-to-monoclinic transi- tion, and 2 monoclinic-to-triclinic transition. In both these categories, the phase transitions are a result of the breaking of a mirror-plane symmetry when the temperature is lowered through the critical temperature, T c ; the lower symmetric phase being the low-temperature phase. In this paper, a microscopic theory for the reversible ferroelastic-type structural phase transitions observed in a re- cently discovered class of hydrogen-bonded organic cystals is presented. It is proposed that the main mechanism respon- sible for the phase transition is the interaction of hydrogen bonds with the lattice vibrations or phonons of the crystal. The hydrogen bonds are modelled as two-level systems, and described by pseudo spin variables. For a comprehensive overview of hydrogen bonding, see the book by Jeffrey 9 and references therein. The spin-phonon coupling then induces long range cooperative interactions between pseudo spins, and results in a second-order phase transition at the critical temperature. The steps involved in the calculation can be summarized as follows: 1 The hydrogen bonding interaction is modelled as a two- level system, and cast into the form of a spin-phonon Hamil- tonian. 2 A variational principle involving a trial Hamiltonian is employed. The trial Hamiltonian is chosen such that spin and phonon are decoupled in a mean-field sense. The resulting variational free energy is thus a mean-field approximation. 3 Thermodynamics of the model is obtained from the mean-field free energy. A critical point is found, and various critical exponents calculated. We believe this microscopic analysis of phase transitions caused by hydrogen bonds could have wide implications since hydrogen bonds occur in a large class of materials and the hydrogen bond plays an important and pivotal role in molecular biology and chemistry. This is also the latest addition to the class of indirect cooperative phase transitions, which though being highly im- portant, currently consist of relatively few cases. Well known examples of phonon mediated indirect cooperative transi- tions include superconductivity and Jahn-Teller transitions. II. MODEL HAMILTONIAN We assume that, if the additional hydrogen bond interac- tions can be “switched off,” all the remaining inter- and in- tramolecular interactions can be approximated by a harmonic potential. This leads to harmonic phonon modes. The Hamil- tonian of the crystal is then split into the sum of two parts: PHYSICAL REVIEW B 71, 174109 2005 1098-0121/2005/7117/17410913/$23.00 ©2005 The American Physical Society 174109-1