How lithium-ion batteries work conceptually: thermodynamics of Li bonding in idealized electrodes.

A good explanation of lithium-ion batteries (LIBs) needs to convincingly account for the spontaneous, energy-releasing movement of lithium ions and electrons out of the negative and into the positive electrode, the defining characteristic of working LIBs. We analyze a discharging battery with a two-phase LiFePO4/FePO4 positive electrode (cathode) from a thermodynamic perspective and show that, compared to loosely-bound lithium in the negative electrode (anode), lithium in the ionic positive electrode is more strongly bonded, moves there in an energetically downhill irreversible process, and ends up trapped in the positive electrode. Only a sufficiently high charging voltage can drive it back to the other electrode. Since the stronger bonding in the positive electrode lowers the energy by ∼320 kJ mol-1, a lot of energy is released. This explanation is quantitatively supported by an analysis of cohesive-energy differences of the electrode materials. Since electrons are only intermediates in the discharge reaction and the chemical potential of the electron cannot be measured, electrons do not need to be assigned a distinct energetic role. The incorporation of Li+ and an electron into the cathode is accompanied by the reduction of another ion or atom, usually a transition metal such as Fe or Co. The metal's ionization energy in the corresponding oxidation step correlates with the cell voltage, based on a decomposition of cohesive energy into electronic and ionic components. We relate the differences in cohesive energies to the chemical potential of lithium atoms, which is quantified, for instance for a two-phase electrode. The analysis is extended to a single-phase LixCoO2 cathode, whose average voltage can be calculated from the cohesive-energy difference between LiCoO2 and CoO2.

Treatment times for delivering adjuvant breast radiotherapy at a cancer centre in Ontario, Canada.

BACKGROUND: Time is a valuable commodity that impacts hospital flow, patient experience and economic resources. This study aims to identify factors that affect daily treatment time over a course of radiation therapy (RT) in patients who underwent adjuvant breast RT. METHODS: In all adjuvant breast/chestwall RT patients treated from October 2017 to May 2018, daily set-up, beam delivery time, and overall treatment times were collected. A multivariable linear regression analysis was conducted to identify significant predictive factors related to treatment time. A general linear regression model was used to determine whether there was a learning curve effect throughout the course of treatment that decreased treatment time as patient and staff familiarity with the treatment procedure increased. RESULTS: A total of 567 patients were included with a median age of 61 years. The average overall treatment time for 2-field and 4-field RT was 8.3 (SD 2.4) and 13.1 (SD 5.6) minutes, respectively. Factors that significantly increased overall treatment times in patients prescribed 2-field RT were: bilateral techniques, breath-hold (BH) techniques, prone techniques (PR), reverse decubitus techniques (RD), wide tangents techniques, the use of bolus and number of segments delivered. (p < 0.05). Factors that significantly increased overall treatment times in patients who received 3-field and 4-field RT were: wide tangents volumes, a higher number of monitor units (MUs), bilateral techniques and BH techniques (p < 0.05). Older patients (≥60) who underwent 3-field and 4-field RT demonstrated a statistically significant increase in set-up time (p < 0.0001). Overall treatment time decreased from 10.0 to 9.3 min over the course of treatment, suggesting a minor learning curve (p = 0.009). CONCLUSION: The use of bilateral RT, BH, PR, RD, wide tangents, bolus, increasing treatment volumes, and increasing plan complexity were associated with increased treatment times. Future research should quantify the impact of other factors (BMI, mobility, patient care assessments, and imaging protocols) and utility of technological tools (time-predicting models, machine learning tools, and operations research models) on treatment time to optimize RT scheduling and improve resource management.