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On the basis of our previous field survey, we postulate that the pattern and degree of zinc (Zn) isotope fractionation in the Zn hyperaccumulator Noccaea caerulescens (J. & C. Presl) F. K. Mey may reflect a relationship between Zn bioavailability and plant uptake strategies. Here, we investigated Zn isotope discrimination during Zn uptake and translocation in N. caerulescens and in a nonaccumulator Thlaspi arvense L. with a contrasting Zn accumulation ability in response to low (Zn-L) and high (Zn-H) Zn supplies. The average isotope fractionations of the N. caerulescens plant as a whole, relative to solution (Δ(66)Znplant-solution), were -0.06 and -0.12‰ at Zn-L-C and Zn-H-C, respectively, indicative of the predominance of a high-affinity (e.g., ZIP transporter proteins) transport across the root cell membrane. For T. arvense, plants were more enriched in light isotopes under Zn-H-A (Δ(66)Znplant-solution = -0.26‰) than under Zn-L-A and N. caerulescens plants, implying that a low-affinity (e.g., ion channel) transport might begin to function in the nonaccumulating plants when external Zn supply increases. Within the root tissues of both species, the apoplast fractions retained up to 30% of Zn mass under Zn-H. Moreover, the highest δ(66)Zn (0.75‰-0.86‰) was found in tightly bound apoplastic Zn, pointing to the strong sequestration in roots (e.g., binding to high-affinity ligands/precipitation with phosphate) when plants suffer from high Zn stress. During translocation, the magnitude of isotope fractionation was significantly greater at Zn-H (Δ(66)Znroot-shoot = 0.79‰) than at Zn-L, indicating that fractionation mechanisms associated with root-shoot translocation might be identical to the two plant species. Hence, we clearly demonstrated that Zn isotope fractionation could provide insight into the internal sequestration mechanisms of roots when plants respond to low and high Zn supplies.

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Flexoelectricity, representing the coupling between electrical polarizations and strain gradients, should be taken into account in the analysis of electromechanical responses of nanostructures where large strain gradients are expected. In this paper, we will explore the influence of flexoelectricity on the electromechanical coupling behavior of a simply supported piezoelectric nanoplate by using the Kirchhoff plate theory. The governing equations and corresponding boundary conditions are deduced from Hamilton's principle, and the analytical solutions are obtained for the deflection and natural frequency. The results indicate that the deflections predicted by the present model are smaller than those calculated by the classical one which only considers piezoelectricity, while the frequencies exhibit the opposite trend. In addition, the flexoelectric effect is more prominent for thinner plates; the differences of the deflections or frequencies between the two models are gradually diminishing with an increase in the plate thickness. The current work may contribute to the understanding of the higher-order electromechanical coupling mechanism. Moreover, the modified plate model can be utilized to accurately design novel piezoelectric nanoplate-based sensors in nanoelectromechanical systems.

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