Hierarchically-structured materials and surface-based microfluidic systems exhibit diverse properties that are inherently multi-scale in origin. In particular, different molecular, mesoscopic, and micron-scale properties and processes are often correlated and collectively account for many properties of interest, such as bulk catalytic activities or electrokinetic flow rates. However, such properties and processes often exhibit complex relationships over the different length scales that are not well understood, and consequently, difficult to control. Establishing correlations between them has been challenging, in part due to the difficulty of rigorously characterizing complex, heterogeneous materials and surface-based microfluidic experiments over multiple length scales, particularly at the molecular and mesoscopic levels.

Herein, new multi-scale understanding and correlations have been established for different hierarchically-structured organic-inorganic solids or surface-based microfluidic systems, enabling control of material or device properties over discrete length scales. The molecular-level compositions, structures, interactions, and dynamics have been measured in diverse hierarchically-structured materials, such as mesostructured zeolites, mesostructured organosilicas, and organosiloxane foams, and subsequently correlated with their meso- and macroscopic material structures and properties. The results reveal new insights on the molecular-level interactions that govern their syntheses, the resulting local compositions and material structures, and the relationships among material properties over multiple characteristic length scales. Multi-dimensional solid-state nuclear magnetic resonance (NMR) spectroscopy is a cornerstone of these investigations, which enables correlative measurements in multiple frequency dimensions of the through-space or through-bond interactions between the constituent nuclei within the different materials.

Other multi-scale relationships have been elucidated theoretically in microfluidic systems that rely on transport near the microchannel surfaces, including devices that use electrokinetic flows or embedded surface sensors. The local ion or analyte concentrations, fluxes, and fluid velocities have been computed in model microfluidic systems, establishing quantitatively the effects of mesoscale surface roughness on micron-scale electro-osmotic flow rates or qualitatively distinct sensing regimes on analyte binding curves. Physically-motivated scaling relations and finite element computations are the foundations of this research, enabling quantitative and intuitive relationships to be derived between quantities such as forces, fluxes, and flow rates.

The results are expected to guide rational design strategies aimed at synthesizing novel hierarchically-structured and self-assembled materials with different molecular compositions and framework structures, or similarly, fabricating microfluidic devices with controllable electrokinetic properties or enhanced sensing capabilities. Collectively, the multi-scale approach and molecular-level emphasis, the different materials and microfluidic systems, and new insights contained within this dissertation are expected to be of broad interest to researchers in chemical engineering, materials science, physics, and chemistry.