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Research spanning nearly a century has found that math plays an important role in the learning of chemistry. Here, we use a large dataset of student interactions with online courseware to investigate the details of this link between math and chemistry. The activities in the courseware are labeled against a list of knowledge components (KCs) covered by the content, and student interactions are tracked over a full semester of general chemistry at a range of institutions. Logistic regression is used to model student performance as a function of the number of opportunities a student has taken to engage with a particular KC. This regression analysis generates estimates of both the initial knowledge and the learning rate for each student and each KC. Consistent with results from other domains, the initial knowledge varies substantially across students, but the learning rate is nearly the same for all students. The role of math is investigated by labeling each KC with the level of math involved. The overwhelming result from regressions based on these labels is that only the initial knowledge varies strongly across students and across the level of math involved in a particular topic. The student learning rate is nearly independent of both the level of math involved in a KC and the prior mathematical preparation of an individual student. The observation that the primary challenge for students lies in initial knowledge, rather than learning rate, may have implications for course and curriculum design. 

Abstract As the heat generation at device footprint continuously increases in modern high-tech electronics, there is an urgent need to develop new cooling devices that balance the increasing power demands. To meet this need, cutting-edge cooling devices often utilize microscale structures that facilitate two-phase heat transfer. However, it has been difficult to understand how microstructures enhance evaporation performances through traditional experimental methods due to low spatial resolution. The previous methods can only provide coarse interpretations on how physical properties such as permeability, thermal conduction, and effective surface areas interact at the microscale to effectively dissipate heat. This motivates researchers to develop new methods to observe and analyze local evaporation phenomena at the microscale. Herein, we present techniques to characterize submicron to macroscale evaporative phenomena of microscale structures by using microlaser-induced fluorescence (μLIF). We corroborate the use of unsealed temperature-sensitive dyes by systematically investigating the effects of temperature, concentration, and liquid thickness on the fluorescence intensity. Considering these factors, we analyze the evaporative performances of microstructures using two approaches. The first approach characterizes the overall and local evaporation rates by measuring the solution drying time. The second approach employs an intensity-to-temperature calibration curve to convert temperature-sensitive fluorescence signals to surface temperatures, which calculates the submicron-level evaporation rates. Using these methods, we reveal that the local evaporation rate between microstructures is high but is balanced with a large capillary-feeding. This study will enable engineers to decompose the key thermofluidic parameters contributing to the evaporative performance of microscale structures. 

Abstract As modern electronics continuously exceed their performance limits, there is an urgent need to develop new cooling devices that balance the increasing power demands. To meet this need, cutting-edge cooling devices often utilize microscale structures that facilitate two-phase heat transfer. However, it has been difficult to understand how microstructures trigger enhanced evaporation performances through traditional experimental methods due to low spatial resolution. The previous methods can only provide coarse interpretations on how physical properties such as permeability, thermal conduction, and effective surface areas interact at the microscale to effectively dissipate heat. This motivates researchers to develop new methods to observe and analyze local evaporation phenomena at the microscale. Herein, we present techniques to characterize submicron to macroscale evaporative phenomena of microscale structures using micro laser induced fluorescence (μLIF). We corroborate the use of unsealed temperature-sensitive dyes by systematically investigating their effects on temperature, concentration, and liquid thickness on the fluorescence intensity. Considering these factors, we analyze the evaporative performances of microstructures using two approaches. The first approach characterizes local or overall evaporation rates by measuring the solution drying time. The second method employs an intensity-to-temperature calibration curve to convert temperature-sensitive fluorescence signals to surface temperatures. Then, submicron-level evaporation rates are calculated by employing a species transport equation for vapor at the liquid-vapor interface. Using these methods, we reveal that capillary-assisted liquid feeding dominates evaporation phenomena on microstructured surfaces. This study will enable engineers to decompose the key thermofluidic parameters contributing to the evaporative performance of microscale structures. 

Interlayer exciton diffusion in transition metal dichalcogenide heterostructures is controlled by the moiré potential.