The most common products obtained in the synthesis of zirconium-based metal−organic frameworks (ZrMOFs) are fine powders. The particle size of a typical ZrMOF UiO-66 was first reported to be around 200 nm, so the original crystal structure was only solved by powder XRD coupled with Rietveld refinement due to the incapability of single crystal XRD to solve such small crystals with poor crystallinity. One may ask the reason why the particle size of UiO-66 is so small compared to that of other common MOFs and what the key factor terminating the growth of UiO-66 is. In this work, we try to answer this question by proposing a hypothesis that the partially deprotonated ligand caused by the accumulated protons in the reaction solution is the key factor preventing the continuous growth of the UiO-66 crystal. The hypothesis is verified by growth reactivation with the addition of a deprotonating agent in an in situ biphase solvothermal reaction. As long as the protons were sufficiently coordinated by the deprotonating agent, the continuous growth of UiO-66 is guaranteed. Moreover, the modulation effect can impact the coordination equilibrium and nucleation so that an oriented attachment growth of UiO-66 film was achieved in membrane structures.

Dynamical systems are frequently used to model biological systems. When these models are fit to data, it is necessary to ascertain the uncertainty in the model fit. Here, we present prediction deviation, a metric of uncertainty that determines the extent to which observed data have constrained the model's predictions. This is accomplished by solving an optimization problem that searches for a pair of models that each provides a good fit for the observed data, yet has maximally different predictions. We develop a method for estimating a priori the impact that additional experiments would have on the prediction deviation, allowing the experimenter to design a set of experiments that would most reduce uncertainty. We use prediction deviation to assess uncertainty in a model of interferon-alpha inhibition of viral infection, and to select a sequence of experiments that reduces this uncertainty. Finally, we prove a theoretical result which shows that prediction deviation provides bounds on the trajectories of the underlying true model. These results show that prediction deviation is a meaningful metric of uncertainty that can be used for optimal experimental design.

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