No abstract

Simple and economical ferric ion detection is necessary in many industries. An europium-based metal organic framework has selective sensing properties for solutions containing ferric ions and shows promise as a key component in a new sensor. We study an idealised sensor that consists of metal organic framework (MOF) crystals placed on a polymer surface. A two-dimensional diffusion model is used to predict the movement of ferric ions through the solution and polymer, and the ferric ion association to a MOF crystal at the boundary between the different media. A simplified one-dimensional model identifies the choice of appropriate values for the dimensionless parameters required to optimise the time for a MOF crystal to reach steady state. The model predicts that a large non-dimensional diffusion coefficient and an effective association with a small effective flux will reduce the time to steady-state. The effective dissociation is the most significant parameter to aid the estimation of the ferric ion concentration. This paper provides some theoretical insight for material scientists to optimise the design of a new ferric ion sensor.

Using the Lennard–Jones potential, we determine analytical expressions for van der Waals interaction energies between a point and a rectangular prism-shaped pore, writing them in terms of standard elementary functions. The parameter values for a new ferric ion sensor are used to compare these calculations with the cylindrical pore approximation for the interactions between an ion and a metal organic framework (MOF) pore. The results using the prismatic pore approximation predict the same qualitative outcomes as a cylindrical pore approximation. However, the prismatic approximation predicts lower magnitudes for both the interaction potential energy minimum and the force maximum, since the average distance from the centre-line to the surface of the prism is greater. We suggest that in some circumstances it is sufficient to use the simpler cylindrical approximation, provided that the cylinder radius is chosen so that the cross-sectional area is equal to the area of the prism pore opening. However, atoms at the nodes should remain approximated by semi-infinite lines. We also determine the interaction between a second ferric ion and a blocked MOF pore; as expected, the second ferric ion experiences a force away from the pore, implying that approaching ferric ions can only occupy vacant MOF pores.