Negative-to-Positive Thermal Conductivity Temperature Coefficient Transition Induced by Dynamic Fluctuations of the Alkyl Chains in the Layered Complex (C₄H₉NH₃)₂CuCl₄

A negative-to-positive transition of the temperature coefficients of thermal conductivity was found in the two-dimensional organic–inorganic layered complex (C₄H₉NH₃)₂CuCl₄ (C4CuCl4) over the three structural phase transitions in the range 176–218 K. The coefficients of the low-temperature phases (85–200 K, α and β phases) were negative, as is typical for insulating crystals, whereas those of the high-temperature phases (200–300 K, γ and δ phases) were positive, as is typical for glasses and liquids. Single-crystal X-ray structure analyses revealed that the tilted C₄H₉NH₃ ⁺ chains in the α and β phases were fully outstretched in the δ phase, and the interlayer distances between the CuCl₄ ²⁻ planes increased significantly. The γ phase was an intermediate phase that crystallized with an incommensurate structure, in which the CuCl₄ ²⁻ sheets formed wave-like structures consisting of connected alternating regions of β-like and δ-like moieties. In the γ and δ phases, thermal fluctuations of the C₄H₉NH₃ ⁺ chains were found in the electron density maps; however, powder X-ray diffraction (PXRD) data indicated that the thermal expansion of the C₄H₉NH₃ ⁺ layers was restricted by the rigid CuCl₄ ²⁻ layers. This situation was considered to induce glass-like thermal conducting properties in the material, such as a positive temperature coefficient. The mean free path of the phonons estimated by using the thermal conductivities and heat capacities was a function of T⁻¹ in the range 85–200 K, as would be expected for crystals, whereas it was approximately constant in the range 200–300 K, which is typical of glasses. In addition, the existence of soft vibration modes in the two-dimensional perovskite CuCl₄ ²⁻ sheets was revealed by analysis of the incommensurate crystal structure of the γ phase. These low-energy vibration modes were believed to induce the cooperative phase transitions, along with the thermal fluctuations and van der Waals interactions in the C₄H₉NH₃ ⁺ layers.