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Abstract We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H$$_2$$ O and D$$_2$$ O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density$$\rho (T)$$ , isothermal compressibility$$\kappa _T(T)$$ , and self-diffusion coefficientsD(T) of H$$_2$$ O and D$$_2$$ O are in excellent agreement with available experimental data; the isobaric heat capacity$$C_P(T)$$ obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H$$_2$$ O and D$$_2$$ O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H$$_2$$ O and D$$_2$$ O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H$$_2$$ O, from PIMD simulations, is located at$$P_c = 167 \pm 9$$ MPa,$$T_c = 159 \pm 6$$ K, and$$\rho _c = 1.02 \pm 0.01$$ g/cm$$^3$$ . Isotope substitution effects are important; the LLCP location in q-TIP4P/F D$$_2$$ O is estimated to be$$P_c = 176 \pm 4$$ MPa,$$T_c = 177 \pm 2$$ K, and$$\rho _c = 1.13 \pm 0.01$$ g/cm$$^3$$ . Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water,$$P_c = 203 \pm 4$$ MPa,$$T_c = 175 \pm 2$$ K, and$$\rho _c = 1.03 \pm 0.01$$ g/cm$$^3$$ ). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of$$T_c$$ for D$$_2$$ O and, particularly, H$$_2$$ O suggest that improved water models are needed for the study of supercooled water.
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Thermodynamic basis for the demarcation of Arctic and alpine treelines
Abstract At the edge of alpine and Arctic ecosystems all over the world, a transition zone exists beyond which it is either infeasible or unfavorable for trees to exist, colloquially identified as the treeline. We explore the possibility of a thermodynamic basis behind this demarcation in vegetation by considering ecosystems as open systems driven by thermodynamic advantage—defined by vegetation’s ability to dissipate heat from the earth’s surface to the air above the canopy. To deduce whether forests would be more thermodynamically advantageous than existing ecosystems beyond treelines, we construct and examine counterfactual scenarios in which trees exist beyond a treeline instead of the existing alpine meadow or Arctic tundra. Meteorological data from the Italian Alps, United States Rocky Mountains, and Western Canadian Taiga-Tundra are used as forcing for model computation of ecosystem work and temperature gradients at sites on both sides of each treeline with and without trees. Model results indicate that the alpine sites do not support trees beyond the treeline, as their presence would result in excessive CO$$_2$$ loss and extended periods of snowpack due to temperature inversions (i.e., positive temperature gradient from the earth surface to the atmosphere). Further, both Arctic and alpine sites exhibit negative work resulting in positive feedback between vegetation heat dissipation and temperature gradient, thereby extending the duration of temperature inversions. These conditions demonstrate thermodynamic infeasibility associated with the counterfactual scenario of trees existing beyond a treeline. Thus, we conclude that, in addition to resource constraints, a treeline is an outcome of an ecosystem’s ability to self-organize towards the most advantageous vegetation structure facilitated by thermodynamic feasibility.
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- Award ID(s):
- 2012850
- PAR ID:
- 10381824
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Scientific Reports
- Volume:
- 12
- Issue:
- 1
- ISSN:
- 2045-2322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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