
The average rate at which a nanoparticle loses mass over time.Mass loss rate is the average speed at which a nanoparticle sheds its material, typically measured in atoms per second or grams per second. In the context of the provided research, this concept is central to understanding how gold nanoparticles on a hot substrate gradually shrink — a process that affects their optical and electronic properties. The rate depends on temperature, particle size, and the surrounding environment, and it is a key parameter in nanofabrication and sensor design.
The systematic study of nanoparticle mass loss dates back to the mid-20th century with the development of thermogravimetric analysis, but the specific application to gold nanoparticles on substrates gained prominence in the 1990s with advances in in-situ electron microscopy.
At elevated temperatures, surface atoms gain enough energy to overcome the binding forces that hold them in the nanoparticle lattice. These atoms then evaporate or diffuse away, reducing the particle's mass over time. The rate is governed by an Arrhenius-type relationship, where the activation energy for desorption and the temperature exponentially influence how quickly mass is lost. For gold on a hot substrate, the process can be accelerated by surface diffusion and interactions with the substrate material.
This concept is used to predict the stability of nanoparticles in high-temperature catalytic converters and to design nanoscale sensors that must maintain their size over time.
A single gold nanoparticle can lose thousands of atoms per second at temperatures just a few hundred degrees Celsius, yet remain visible under an electron microscope for hours.
| M | variable | Mass of the donor star — mass kilogram |
| M_dot | variable | Time derivative of the donor mass — mass loss rate kilogram per second |
| J | variable | Orbital angular momentum of the binary — angular momentum kilogram square metre per second |
| J_dot | variable | Time derivative of the orbital angular momentum — angular momentum loss rate kilogram square metre per second squared |
| zeta | variable | Mass-radius exponent of the donor star — mass radius exponent |
| zeta_L | variable | Mass-radius exponent of the Roche lobe — roche lobe mass radius exponent |
| \dot{M} | variable | Mass loss rate of the planet — mass loss rate kilogram per second |
| \eta | variable | Heating efficiency (fraction of incident energy used for escape) |
| R_{\text{XUV}} | variable | Radius at which the planet absorbs XUV radiation — radius metre |
| F_{\text{XUV}} | variable | Incident XUV flux at the planet — irradiance watt per square metre |
| M_p | variable | Planet mass — mass kilogram |
| R_p | variable | Planet radius — radius metre |
| G | constant | Newtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| \dot{M} | variable | Mass loss rate of the planet — mass loss rate kilogram per second |
| R_p | variable | Planet radius — radius metre |
| F_{XUV} | variable | Incident XUV flux at the planet — energy flux watt per metre squared |
| M_p | variable | Planet mass — mass kilogram |
| K | variable | Efficiency factor (dimensionless, often ~0.1-1) |
| G | constant | Newtonian gravitational constant — gravitational constant = 6.67430e-11 metre cubed per kilogram per second squared |


