ABSTRACT
Gold nanoparticles (AuNPs) are employed in numerous applications, including optics, biosensing and catalysis. Here, we demonstrate the stabilizer-free electrochemical synthesis of AuNPs inside nanoliter-sized reactors. Droplets encapsulating a gold precursor are formed on a microfluidic device and exposed to an electrical current by guiding them through a pair of electrodes. We exploit the naturally occurring recirculation flows inside confined droplets (moving in rectangular microchannels) to prevent the aggregation of nanoparticles after nucleation. Therefore, AuNPs with sizes in the range of 30 to 100â nm were produced without the need of additional capping agents. The average particle size is defined by the precursor concentration and droplet velocity, while the charge dose given by the electric field strength has a minor effect. This method opens the way to fine-tune the electrochemical production of gold nanoparticles, and we believe it is a versatile method for the formation of other metal nanoparticles.
ABSTRACT
The Repayment Policy for Multiple Loans is about a given set of loans and a monthly incoming cash flow: what is the best way to allocate the monthly income to repay such loans? In this article, we close the almost 20-year-old open question about how to model the repayment policy for multiple loans problem together with its computational complexity. Thus, we propose a mixed integer linear programming model that establishes an optimal repayment schedule by minimizing the total amount of cash required to repay the loans. We prove that the most employed repayment strategies, such as the highest interest debt and the debt snowball methods, are not optimal. Experimental results on simulated cases based on real data show that our methodology obtains on average more than 4% of savings, that is, the debtor pays approximately 4% less to the bank or loaner, which is a considerable amount in finances. In certain cases, the debtor can save up to 40%.
