Developing Calorimeters for Thermal Transport and Biological Measurements with Picowatt Resolution

Abstract

Calorimetry, a heat measuring process, has opened a way to quantify generated heat, both in physical and in biological systems. The resolution of a typical calorimeter (Q ̇=G_Th× ∆T) can be improved in three ways, either by improving temperature resolution (∆T) or by reducing thermal conductance (G_Th) or both. With intensive efforts to improve thermal resolution, microcalorimeters can now be widely used for measuring minute heat generation and transport in the micro/nanoscale. Still, there are several topics that remain insufficiently explored due to sensitivity limitations. One unanswered question in nanoscale thermal science is of thermal transport in single-atomic or single-molecular junctions. Similar to electrical conductance, many theoretical studies suggest that thermal conductance is also quantized. While quantized electric conductance (2e2/h or 1/12.9 kΩ-1) was measured in the late 20th century, quantized thermal conductance measurements at room temperature (π2 kB2T/3h or 300 pW/K) have been challenging due to insufficient calorimeter resolution and technical obstacles in creating stable atomic junctions. A second elusive measurement is metabolic rates in small model organisms. This research is fueled by accrued evidence that human diseases, such as cancer and obesity, and aging are correlated to abnormal metabolic states. Recent advances in calorimetry have benefitted from both operations in a vacuum where parasitic heat conduction can be attenuated and the use of microfabrication tools which significantly decrease thermal conductance and increase temperature resolution. However, such approaches cannot be simply adopted for biological systems so that none of the currently available bio-calorimetric tools are capable of the sub-nW resolution that is necessary for resolving C. elegans metabolic heat output. Biocalorimetery has to be performed in a liquid environment to keep organisms alive, and the size of calorimeters cannot be smaller than that of the micro-sized biological organisms. Moreover, integration of optical imaging is challenging as this naturally couples environmental temperature fluctuations into the system. This dissertation presents two types of calorimeters. The first calorimeter is to measure thermal conductance at atomic scale, especially in single atomic or single-molecular junctions. It features a high stiffness (10 N/m) for stably holding atomic and molecular junctions at room temperature. Further, we achieved both a high temperature resolution (0.6 mK in a 10 Hz bandwidth) and a low thermal conductance (800 nW/K) of thermal bridge to resolve quantized thermal conductance (300 pW/K) in atomic junctions and length independent thermal conductance (25 pW/K) in molecular junctions. The second calorimeter is employed to measure metabolic heat outputs from C. elegans. Specifically, we achieved unprecedented heat resolution of 270 pW for biological systems, which represents a 500-fold improvement over calorimeters employed for past C. elegans studies and a 10-fold improvement compared to the state-of-the-art bio-calorimeters. This advance was realized by 1) achieving a low thermal conductance of 27 µW/K by operating in a high vacuum environment and attenuating the radiative conductance via gold coating, 2) achieving temperature stability of ±5 µK over a day using three nested shields with independent temperature control for each shield. Using this calorimeter, we demonstrate for the first time, time-resolved metabolic measurements of single C. elegans from ~4 nW for the L1 stage to ~100 nW for the adult stage. These demonstrations clearly highlight the broad potential of this tool for studying the role of metabolism in disease, development and aging of small model organisms and single cells.