CAPÍTULO 2. DESCONSIDERACIÓN MORAL Y JURÍDICA DE LOS ANIMALES
2. Argumento de las capacidades
The structural differences between [Al2(0 3PC2H4P0 3)(H2 0)2F2] H2O and [Al2(0 3PC3H6P0 3)(H2 0)2F2]*H2 0 originate from the different orientation o f the corrugated inorganic sheets. The arrangement of these sheets depends upon the number of carbon atoms in the diphosphonate species and dictates the size and shape o f the pores formed, and hence the resultant properties.
In order to rationalise the topologically different structures formed with the ethylenediphosphonate and propylenediphosphonates the relative energies o f the materials were probed using computational methods. Hypothetical structures were generated for the ‘unaligned’ aluminium ethylenediphosphonate and the ‘aligned’ aluminium propylenediphosphonates and the energetic stability o f these materials were compared to the observed structures in both bases. Conclusions were then drawn about the structural determining effects of the alkyldiphosphonate.
Calculations based upon density functional theory (DFT) were selected to calculate the energy of the structures in each case, using a plane wave model. This method was selected as it can accurately describe both the organic and inorganic portions o f the aluminium alkylenediphosphonate system. A full description of Density Functional Theory is given in reference 65. All calculations were completed using the CASTEP code by Dr. Ben Slater.^^
Structures were generated for the observed and hypothetical structures for each alkylendiphosphonate, these structures were then relaxed, or minimised, in order to calculate their relative energy. The initial structures to be relaxed were generated from the observed crystal structures, i.e. the aligned [Al2(0 3PC2H4?0 3)(H2 0)2F2] H2O and the unaligned [Al2(0 3PC3H6P0 3)(H2 0)2F2]*H2 0 structure. In each case the extra framework waters were removed, since the binding energies of these species are small and our considerations are solely o f the framework stabilities, and the symmetry o f the structures was reduced to PI whilst preserving the original lattice parameters. The hypothetical structures were generated from the observed structures by translating one of the inorganic layers (half of the non carbon atoms) by half a unit cell along the b
direction in the ethylene case to form the ‘unaligned’ structure and by half a unit cell along the a direction in the propylene case to form the ‘aligned’ structure. The carbon atoms, which form the diphosphonate chains were assigned an appropriate starting position and their positions were subsequently optimised using a molecular dynamics package, whilst fixing the framework atomic positions, to provide a configuration at a low energy minima in order to minimise the computational expense of the DFT calculation. The axially coordinated oxygen atoms and the carbon atoms were geometrically assigned hydrogen atoms so as to ensure the oxygen and carbon atoms had a reliable starting electronic configuration. All the structures produced were relaxed through the DFT approach described in order to determine the total lattice energy for each structure. The calculations progress as a series o f steps, each successive step is required to be o f lower energy than the previous. Convergence criteria for the calculations were threefold; the minimum tolerance for root-mean-squared atomic displacement must be less than 10*^ Â, the minimum tolerance for the residual root-
Chapter 4; Structural Studies of Aluminium and Gallium Ethylene Diphosphonates
mean-squared force is 0.05 eV A'% and the minimum tolerance for the energy is 2*10'^ eV.
The final relaxed structures are shown in Figure 4.15 and the absolute and relative lattice energies for the ethylene and propylene; ‘aligned’ and ‘unaligned’ structures are given in Table 4.10. Evidence for the reliability o f these calculations arises from a comparison o f the generated relaxed structures o f the ‘aligned’ ethylenediphosphonate and the ‘unaligned’ propylene diphosphonates with the experimentally observed crystal structures. In both cases the structures are very similar, with comparable bond angles and lengths observed.
r (d)
Figure 4.15 Relaxed structures o f (a) the observed aligned aluminium
ethylenediphosphonate, (b) the hypothetical unaligned aluminium
ethylenediphosphonate, (c) the hypothetical aligned aluminium
propylenediphosphonate and (d) the observed unaligned aluminium
propylenediphosphonate
The organic portions of structures, a-d (nomenclature from Figure 4.15), were
removed from their frameworks and the terminal carbon atoms capped with hydrogens
in order to yield fragments with accurate electronic configurations. The carbon and
hydrogen positions, excluding the capping hydrogens, were fixed. The carbon
Chapter 4: Structural Studies o f A lum inium and Gallium Ethylene D iphosphonates
associated with the organic components of the relaxed structures was determined. The
structure o f the organic frameworks (i-iv) are shown in Figure 4.16 The resultant
energy differences, between the ‘aligned’ and ‘unaligned’ organics o f similar chain
length are summarised in Table 4.10 and the bond distances and angles o f the fragments
i-iv are given in Table 4.5 of the appendix.
Figure 4.16 Configurations of the organic components from the relaxed structures of
aligned aluminium ethylenediphosphonate (i), hypothetical unaligned aluminium ethylenediphosphonate (ii), hypothetical aligned aluminium propylenediphosphonate (iii), observed unaligned aluminium propylenediphosphonate (iv)
Table 4.10 Summary of the absolute and relative energies of structures a-d, and fragments i-iv as described in Figures 4.15 and 4.16
Description Lattice Energies (kJ mol^)
a-b (Figure 4.15) -111.483
Organic fragments, i-ii (Figure 4.16) -93.9
d-c (Figure 4.15) -76.227
Organic fragments, iv-iii (Figure 4.16) -93.62
The energetically most favourable structure is that which is observed for both
the aluminium ethylene and propylene materials. For the aluminium
ethylenediphosphonate the energy differences between the observed (aligned, a) and the hypothetical (unaligned, b) structures is -111.685 kJ mol*’. This energy difference can be rationalised by considering the differences in energy between the ‘aligned’ (i) and ‘unaligned’ (ii) organic ethylene fragments o f -94.25 kJ m o l'\ This value accounts for the majority of the total energy difference, the remainder can be attributed to the energy differences o f the inorganic layers. The observed ‘unaligned’ propylene structure is more stable than the hypothetical ‘aligned’ structure by -76.6 kJ m o l'\ An explanation of this result on the basis of different conformational energies o f the organic fragments is more difficult since the unaligned (iii) and aligned (iv) fragments are similar in energy. The major contribution to the energy difference appears to originate from differences with the orientation of the inorganic sheets. An inspection of the bond lengths and angles for the organic fragments (Appendix 4.5) reveals that in each case
Chapter 4; Structural Studies o f Aluminium and Gallium Ethylene Diphosphonates
the organic fragments o f higher energy, contain unfavourable C-C bond distances and C/H-C-C/H angles.
4.7 Discussion
The aluminium propylene diphosphonate, [Al2(0 3PC3H6?0 3)(H2 0)2F2] H2O, is structurally similar to the isostructural materials [Al2(0 3PC2H4P0 3)(H2 0)2p2] H2O and a-[Ga2(0 3PC2H4P0 3)(H2 0)2p2] H2O. All are formed from identical inorganic sheets,
with the sheets linked together in an ‘unaligned’ fashion for
[Al2(0 3PC3H6?0 3)(H2 0)2F2] H2O, as opposed to an ‘aligned’ fashion as for the ethylene diphosphonates.
Calculations performed on the ‘aligned’ and the ‘unaligned’ aluminium ethylene and propylenediphosphonates reveal that the observed structures are energetically more stable in each case. Additional calculations of the energies bound up within the organic components o f these structures show that the differences in energy resulting from the different configuration of the organic units can, to a certain extent, account for the differences in energy of the framework structures. The length o f the alkyl group o f the diphosphonic acid is seen to determine the structure o f the resultant framework. We have not managed to synthesise the aluminium methylenediphosphonate member of this series, instead structurally dissimilar phases results as described in Chapter 8.
A
r
Figure 4.17 The structures of the lanthanide series, Ln"*H[0 3P(CH2)nPÛ3] for w - 1 (a), 2 (b), 3 (c)
The series of lanthanide diphosphonate materials Ln”'H[0 3P(CH2)nPÛ3] where = 1, 2, 3 for methylene, ethylene and propylene diphosphonates, was synthesised
using a range of the lanthanide elements by Serpaggi et al? The structure o f this series
Chapter 4: Structural Studies of Aluminium and Gallium Ethylene Diphosphonates
organic pillars. However, the lanthanide inorganic layers have a different composition and topology to the aluminium diphosphonates. The inorganic layers are composed of edge sharing, LnOg, dodecahedra to form linear chains which are linked together through phosphonate groups to form buckled sheets. Unlike the aluminium diphosphonates, the topology of the layers in the lanthanide diphosphonates dictates that the pore width sizes are consistent throughout each material. The buckling of these sheets results in ‘aligned’ sheets for the lanthanide ethylenediphosphonate and ‘unaligned’ structures for the lanthanide methylene and propylenediphosphonates. The general observation can be made for both the aluminium and lanthanide diphosphonate pillared materials that structures formed with even numbers of carbon atoms in the alkyldiphosphonate form ‘aligned’ structures and those with odd numbers o f carbon atoms form ‘unaligned’ structures’. Thus providing possible implications for the rational design of structures in these systems.
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