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Abstract Metabolic scaling theory has been pivotal in formalizing the expected energy expenditures across populations as a function of body size. Coexistence theory has provided a mathematization of the environmental conditions compatible with multispecies coexistence. Yet, it has been challenging to explain how observed community‐wide patterns, such as the inverse relationship between population abundance density and body size, can be unified under both theories. Here, we provide the foundation for a tractable, scalable, and extendable framework to study the coexistence of resource‐mediated competing populations as a function of their body size. For a given thermal domain and response, this integration reveals that the metabolically predicted 1/4 power dependence of carrying capacity of biomass density on body size can be understood as the average distribution of carrying capacities across feasible environmental conditions, especially for large communities. In line with empirical observations, our integration predicts that such average distribution leads to communities in which population biomass densities at equilibrium are independent from body size, and consequently, population abundance densities are inversely related to body size. This integration opens new opportunities to increase our understanding of how metabolic scaling relationships at the population level can shape processes at the community level under changing environments.
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Size-dependent shape distributions of platinum nanoparticles
While it is well established that nanoparticle shape can depend on equilibrium thermodynamics or growth kinetics, recent computational work has suggested the importance of thermal energy in controlling the distribution of shapes in populations of nanoparticles. Here, we used transmission electron microscopy to characterize the shapes of bare platinum nanoparticles and observed a strong dependence of shape distribution on particle size. Specifically, the smallest nanoparticles (<2.5 nm) had a truncated octahedral shape, bound by 〈111〉 and 〈100〉 facets, as predicted by lowest-energy thermodynamics. However, as particle size increased, the higher-energy 〈110〉 facets became increasingly common, leading to a large population of non-equilibrium truncated cuboctahedra. The observed trends were explained by combining atomistic simulations (both molecular dynamics and an empirical square-root bond-cutting model) with Boltzmann statistics. Overall, this study demonstrates experimentally how thermal energy leads to shape variation in populations of metal nanoparticles, and reveals the dependence of shape distributions on particle size. The prevalence of non-equilibrium facets has implications for metal nanoparticles applications from catalysis to solar energy.
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- Award ID(s):
- 1652694
- PAR ID:
- 10407999
- Date Published:
- Journal Name:
- Nanoscale Advances
- Volume:
- 4
- Issue:
- 18
- ISSN:
- 2516-0230
- Page Range / eLocation ID:
- 3978 to 3986
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/D2NA00326K
