Topics in equilibrium and nonequilibrium thermodynamics: computing crystalline free energies and engineering Maxwell’s demon.

This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of $10^{-5}k_BT$ per particle. In developing the numerical method, we find several scaling properties of crystalline solids in the thermodynamic limit. Using these scaling properties, we derive an explicit asymptotic formula for the free energy per particle in the thermodynamic limit. In addition, we describe several changes of coordinates that can be used to separate internal degrees of freedom from external, translational degrees of freedom. The second part of the dissertation focuses on engineering idealized physical devices that work as Maxwell's demon. We describe two autonomous mechanical devices that extract energy from a single heat bath and convert it into work, while writing information onto memory registers. Additionally, both devices can operate as Landauer's eraser, namely they can erase information from a memory register, while energy is dissipated into the heat bath. The phase diagrams and the efficiencies of the two models are solved and analyzed. These two models provide concrete physical illustrations of the thermodynamic consequences of information processing.

Applications of Photoinduced Electron Transfer Chemistry: Photoremovable Protecting Groups and Carbon Dioxide Conversion

Traditional organic chemistry has long been dominated by ground state thermal reactions. The alternative to this is excited state chemistry, which uses light to drive chemical transformations. There is considerable interest in using this clean renewable energy source due to concerns surrounding the combustion byproducts associated with the consumption of fossil fuels. The work presented in this text will focus on the use of light (both ultraviolet and visible) for the following quantitative chemical transformations: (1) the release of compounds containing carboxylic acid and alcohol functional groups and (2) the conversion of carbon dioxide into other useable chemicals. Chapters 1-3 will introduce and explore the use of photoremovable protecting groups (PPGs) for the spatiotemporal control of molecular concentrations. Two new PPGs are discussed, the 2,2,2-tribromoethoxy group for the protection of carboxylic acids and the 9-phenyl-9-tritylone group for the protection of alcohols. Fundamental interest in the factors that affect C–X bond breaking has driven the work presented in this text for the release of carboxylic acid substrates. Product analysis from the UV photolysis of 2,2,2-tribromoethyl-(2′-phenylacetate) in various solvents results in the formation of H–atom abstraction products as well as the release of phenylacetic acid. The deprotection of alcohols is realized through the use of UV or visible light photolysis of 9-phenyl-9-tritylone ethers. Central to this study is the use of photoinduced electron transfer chemistry for the generation of ion diradicals capable of undergoing bond-breaking chemistry leading to the release of the alcohol substrates. Chapters 4 and 5 will explore the use of N-heterocyclic carbenes (NHCs) as a catalyst for the photochemical reduction of carbon dioxide. Previous experiments have demonstrated that NHCs can add to CO2 to form stable zwitterionic species known as N-heterocylic-2-carboxylates (NHC–CO2). Work presented in this text illustrate that the stability of these species is highly dependent on solvent polarity, consistent with a lengthening of the imidazolium to carbon dioxide bond (CNHC–CCO2). Furthermore, these adducts interact with excited state electron donors resulting in the generation of ion diradicals capable of converting carbon dioxide into formic acid.