# TRANSPORT IN NONLINEAR CHAINS AND ACROSS SEVERAL CONDENSED MATTER INTERFACES

Open Access

- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- July 20, 2011
- Committee Members:
- Gerald Dennis Mahan, Dissertation Advisor
- Gerald Dennis Mahan, Committee Chair
- Jorge Osvaldo Sofo, Committee Member
- Jun Zhu, Committee Member
- John V Badding, Committee Member

- Keywords:
- Solitons
- one-dimensional lattice
- pair distribution function
- Kapitza resistance at interfaces

- Abstract:
- The characteristic length scales of the materials synthesized, are becoming increasingly small with the advances in experimental techniques. Many of these microscopic structures found their places in important commercial applications, while research is going on toward finding materials with even smaller length scales. The thermal loads imposed on these devices and structures create a major obstacle toward their applicability. This challenge is driving a renewed interest among researchers from various disciplines, toward the topic of thermal management. The interest in the topic of thermal transport served as the motivation for the work performed in the dissertation. More specifically, the following topics were investigated: egin{itemize} item {f Transport in One-Dimensional Nonlinear Systems:} Thermal transport in materials can be explained in terms of the motion of the heat carriers at the microscopic level, with the heat carriers typically being electrons, phonons, atoms, or molecules. However, an important and surprising situation emerges in some low dimensional model systems; the thermal conductivity diverges with system size. It was shown (Toda, 1979) that nonlinearity has an important effect in the heat transport in low dimensional systems. We investigate the transport of energy in a nonlinear one-dimensional chain. We show the spontaneous generation of solitons with the application of forcing functions at the end of the chain and study the different properties of the solitons generated in the chain. item {f Transport in FLuids extemdash Study of Pair Distribution Function:} Thermal transport in fluids is also diffusive in nature. The transport of heat depends on the distribution of particles in the fluid. It is well known that the two-particle distribution function can describe most of the thermodynamic properties for classical fluids in thermal equilibrium. We review the approximate integral equation theories (Percus-Yevick, Hypernetted chain approximation) to obtain the pair distribution function of classical fluids. We find that these methods are highly dependent on the choice of the thermodynamic parameters of the fluid. We solve several Lennard-Jones fluid systems with different density and temperature values and prepare a density-temperature compressibility diagram. This diagram shows the region of applicability of these theories and helps us obtain the pair distribution function for a Lennard-Jones fluid with known thermodynamic parameters. We also suggest a modification of the integral-equation theories to obtain the pair distribution functions of quantum fluids. We show how the knowledge of pair distribution function can be used to obtain various thermodynamic properties of the quantum fluid helium-4. item {f Thermal Transport Across Interfaces:} When thermal energy is transported from one material to another, there is a discontinuity in temperature at the interface between them. This thermal boundary resistance is known as Kapitza resistance. The scattering of phonons at interfaces is one of the main reasons behind the presence of thermal boundary resistance. We explore the scattering of acoustic waves at several solid-solid interfaces using lattice dynamical methods. We consider the interfaces formed between two similar lattices with different lattice parameters. The different lattices considered are given by: one-dimensional harmonic chain, two-dimensional rhombic lattice, two-dimensional square-lattice and three-dimensional FCC lattice, respectively. We derive matrix equations to obtain the reflection and transmission coefficients for an acoustic wave incident on the interface. These coefficients can reproduce the familiar expressions in the continuum limit and are consistent with the conservation relations. We discuss a method to obtain the thermal boundary resistance for neutral solid-fluid interfaces. The acoustic mismatch theory works poorly for solid-fluid interfaces. One reason is that this theory only includes the long wavelength acoustic phonons. Transverse sound waves are shown to exist in fluids, although the waves are highly damped and totally diffusive at long wavelength. These damped waves can diffuse through interfaces and they can carry heat away from the interface. Hence the transverse sound waves can still play a role in the thermal boundary resistance. Our theory includes all the phonon modes in the solid and all the sound modes in the fluid, in the calculation of the thermal boundary resistance. We provide an application of the method to obtain the thermal boundary resistance at the interface between solid Argon and liquid Neon. Our method yields the value for Kapitza conductance for solid Argon-fluid Neon interface to be $0.0374$GW/Km$^2$. end{itemize}