ABSTRACT
We report an evaluation of a semi-empirical quantum chemical method PM7 from the perspective of uncertainty quantification. Specifically, we apply Bound-to-Bound Data Collaboration, an uncertainty quantification framework, to characterize (a) variability of PM7 model parameter values consistent with the uncertainty in the training data and (b) uncertainty propagation from the training data to the model predictions. Experimental heats of formation of a homologous series of linear alkanes are used as the property of interest. The training data are chemically accurate, i.e., they have very low uncertainty by the standards of computational chemistry. The analysis does not find evidence of PM7 consistency with the entire data set considered as no single set of parameter values is found that captures the experimental uncertainties of all training data. A set of parameter values for PM7 was able to capture the training data within ±1 kcal/mol, but not to the smaller level of uncertainty in the reported data. Nevertheless, PM7 was found to be consistent for subsets of the training data. In such cases, uncertainty propagation from the chemically accurate training data to the predicted values preserves error within bounds of chemical accuracy if predictions are made for the molecules of comparable size. Otherwise, the error grows linearly with the relative size of the molecules.
ABSTRACT
Driven by its importance in nature and technology, droplet impact on solid surfaces has been studied for decades. To date, research on control of droplet impact outcome has focused on optimizing pre-impact parameters, e.g., droplet size and velocity. Here we follow a different, post-impact, surface engineering approach yielding controlled vectoring and morphing of droplets during and after impact. Surfaces with patterned domains of extreme wettability (high or low) are fabricated and implemented for controlling the impact process during and even after rebound--a previously neglected aspect of impact studies on non-wetting surfaces. For non-rebound cases, droplets can be morphed from spheres to complex shapes--without unwanted loss of liquid. The procedure relies on competition between surface tension and fluid inertial forces, and harnesses the naturally occurring contact-line pinning mechanisms at sharp wettability changes to create viable dry regions in the spread liquid volume. Utilizing the same forces central to morphing, we demonstrate the ability to rebound orthogonally-impacting droplets with an additional non-orthogonal velocity component. We theoretically analyze this capability and derive a We(-.25) dependence of the lateral restitution coefficient. This study offers wettability-engineered surfaces as a new approach to manipulate impacting droplet microvolumes, with ramifications for surface microfluidics and fluid-assisted templating applications.
