Determination of Phonon Density of States from Constant-Pressure Heat Capacity Data of Soft Organic Materials in the Glassy and Crystalline States by Using the Real-Coded Genetic Algorithm

A method was proposed to derive the phonon density [g(ω)] of states of materials from their heat capacity data by using Real-Coded Genetic Algorithm (RCGA) with Just Generation Gap + Real-Coded Ensemble Crossover. The performance of the method was confirmed by testing whether or not the RCGA reproduces a reasonable g(ω) by analyzing the set of heat capacity data evaluated from an initially assumed model g0(ω) composed of Debye and optical modes. As an example, constant-pressure heat capacities (CPs) were measured for soft molecular materials, diphenyl phosphate (DPP) and diphenylphosphinic acid, in the condensed state, and their g(ω)s were determined from the CP data by applying the RCGA. The unusual behavior that the CP value of glass was smaller than the one of the crystal in the temperature range from 10 to 70 K was observed in DPP; the behavior is contrary to that expected ordinarily for the glass as compared with the crystal. The g(ω)s determined by the RCGA demonstrated that the unusual behavior was attributed to the blue shift in g(ω) of ω = 30-240 K in the glass compared with the crystal. The blue shift and other effects were discussed reasonably as originating from the competitive concurrence of strong and weak intermolecular hydrogen bonds in DPP, with the help of determination of their intramolecular vibrations for the isolated molecule by the density functional theory calculation. It was concluded that the method using the RCGA is of value for obtaining the microscopic information of g(ω) from the precise heat capacity data and for investigating any difference between the details of g(ω)s in different phases of materials.