Lattice Energies, Charge Distributions and Thermochemical Data for Salts containing Complex Ions
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In this work, we report the electric-field effects on ionic hydration of Cl–, Na+, and Pb2+ using molecular dynamics simulations. It is found that the effect of weak fields on ionic hydration can be neglected. Strong fields greatly disturb the water orientation in the hydration shells of ions, though ion coordination number remains almost unchanged. Under strong fields, the first hydration shell of ions is significantly weakened and the ion–water interaction energy is dramatically reduced; surprisingly, the second hydration shells of Cl– and Na+ are slightly structured because of the optimal water orientation; moreover, ionic hydration structures become asymmetrical along the field direction because of the uniformly aligned water dipoles. Compared with Na+ and Pb2+, the hydration of Cl– is less disturbed by external fields, probably ascribed to the different water reorientation around anions and cations as well as the different structure-maker/breaker nature of the ions. Additionally, strong fields significantly enhance ion mobility and remarkably shorten the water residence time in the hydration shell. This work demonstrates that applying strong fields is an effective way to weaken ion hydration.
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The difficulty of modelling ion channels in membranes due to the low electrostatic energy of small ions in aqueous solution is discussed. Models based upon ordered water cage structures are shown to provide suitable low energy binding sites that are selective for both unhydrated ionic size and valence. The barriers for motion of ions within these channels are shown to be low.
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An empirical method based on chemical bond theory for the estimation of the lattice energy for ionic crystals has been proposed. The lattice energy contributions have been partitioned into bond dependent terms. For an individual bond, the lattice energy contribution made by it has been separated into ionic and covalent parts. Our calculated values of lattice energies agree well with available experimental and theoretical values for diverse ionic crystals. This method, which requires detailed crystallographic information and elaborate computation, might be extended and possibly yield further insights with respect to bond properties of materials.
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Lattice energies for ionic materials which separate into independent gaseous ions can be calculated by standard Born-Haber-Fajans thermochemical cycle procedures, based on the energies of formation of those ions. However, if complex ions (such as sulfates) occur in the material, then a sophisticated calculation procedure must be invoked which requires allocation of the total ion charge among the atom components of the complex ion and evaluation of the attractive and repulsive energy terms. If, instead, the total ion charge is allocated to the central atom of the complex ion (with zero charge on the coordinated atoms), to create a "condensed charge ion" (having zero self-energy), then a straightforward calculation of the electrostatic (Madelung) energy, E(M)', correlates well with published lattice energies: U(POT)/kJ mol(-1) = 0.963E(M)', with a correlation coefficient, R(2) = 0.976. E(M)' is here termed the "condensed charge" electrostatic (Madelung) energy. Thus, using the condensed charge ion model, we observe that a roughly constant proportion (∼96%) of the corresponding lattice energy arises from the electrostatic interaction terms. The above equation permits ready evaluation of lattice energies for ionic crystal structures containing complex ions, without the necessity to estimate any of the problematic nonelectrostatic interaction terms. A commentary by Prof. H. D. B. Jenkins substantiating this analysis is appended.
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The Born-Lande equation has been used to calculate the lattice energy and bulk modulus of twenty one ionic crystals. These computations were carried out by means of a FORTRAN code, whose basic inputs are the name of crystal, the Born exponent, the number of charges and the lattice constant The lattice energies obtained are in close agreement with both the theoretical and the experimental reported values. It has been found that as the ionic radii of either the cations or anions increases the lattice energy decreases. Simalarly, ionic crystals consisting of divalent ions have much larger lattice energies than those with monovalent ions .
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