Hydration Numbers from Diffraction Studies

The interference of radiation, x-rays or neutrons, scattered from correlated atoms yields eventually experimental values of the pair correlation function g,s(r). The diffraction methods yield the intensity / of the beam of the radiation at a fixed wavelength X diffracted at various angles 0 for the defined variable k  

Structure factors, S. ik), for scattering from two correlated atoms i and j in the 

Here 1(9) is the intensity of the scattered radiation at the angle 0, normalized to the instrumentation employed and to the total number of atoms in the system exposed to the radiation, c. is the concentration of the jth atom species, and is the coherent scattering amplimde from this species, and the summation extends over all the atomic species present. There are as many linear relationships between the structure factors and the intensity 1(0) as there are pairs of correlated atoms in the system and special means have to be employed to extract from than the desired information, namely the partial structure fartors S (k). 

Once the partial structure factors are available from the diffraction experiments, they are submitted to Fourier transformation to yield the partial pair correlation functions  

Then the solvent-coordination number of the ion in the solution, h, is obtained by the integration according to Equation 4.32. Second hydration shells have been definitely ascribed to divalent and trivalent cations from x-ray diffraction measurements. The coordination number h for water molecules in this second shell is generally assumed to be 12, the number then being corroborated by the diffraction data. 

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In recent years, X-ray diffraction studies of aqueous solutions have established primary hydration numbers for several fast-exchange cations 45,187-190 the timescale of X-ray diffraction is very much shorter than that of NMR spectroscopy. Octahedral hydration shells have been indicated for Tl3+,191 Cd2+, Ca2+, Na and K+, for example. For the lanthanides, [Ln(OH2)9]3+ is indicated for La, Pr and Nd, but [Ln(OH2)8]3 for the smaller Tb to Lu.192,193 Sometimes there are difficulties and uncertainties in extracting primary hydration numbers from X-ray data. Thus hydration numbers of eight and of six have been suggested for Na+ and for K+,194 and for Ca2+,195 and 8 and 9 for La3+, 196 In some cases rates of water exchange between primary and secondary hydration shells are so fast as to raise philosophical questions in relation to specific definitions of hydration numbers.197... 

Case study theophylline anhydrate and monohydrate The type of structural information that can be obtained from the study of the x-ray diffraction of single crystals will be illustrated through an exposition of studies conducted on the anhydrate and hydrate phases of theophylline (3,7-dihydro-l,3-dimethyl-LH-purine-2,6-dione). The unit cell parameters defining the two phases are fisted in Table 7.2, while the structure of this compound and a suitable atomic numbering system is located in Fig. 7.3. 

With the exception of studies using NMR technique ) or Taube s isotopic dilution method or also X-ray diffraction techniqueof concentrated electrolyte solutions, the hydration numbers are not always integral numbers which quite often represent deviations of experimental data from results of a theoretical description of an equilibrium property. Therefore, these hydration numbers depend on the solution property studied. 

Aqueous Solvation.—A review, covering the 1968—1972 publications, deals with physical properties, thermodynamics, and structures of non-aqueous and aqueous-non-aqueous solutions of electrolytes, and complete hydration limits. Thermodynamic aspects of ionic hydration also reviewed include the thermodynamic theory of solvation the molecular interpretation of ionic hydration hydration of gaseous ions (AG s, H s, and AA s) thermodynamic properties of ions at infinite dilution in water, solvent isotope effect in hydration reference solvents and ionic hydration and excess properties. A third review on the hydration of ions emphasizes the structure of water in the gaseous, liquid, and solid states the size of ions and the hydration numbers of ions and the structure of the hydrated shell from measurements of mobility, compressibility, activity, and from n.m.r. spectra. Pure water and aqueous LiCl at concentrations up to saturation have been examined by neutron and X-ray diffraction. For the neutron studies LiCl and D2O are employed. The data are consistent with a simple model involving only... 

Tables 2.5a,b provide a comprehensive list of guest molecules forming simple si and sll clathrate hydrates. The type of structure formed and the measured lattice parameter, a, obtained from x-ray or neutron diffraction are listed. Unless indicated by a reference number, the cell dimension is the 0°C value given by von Stackelberg and Jahns (1954). Where no x-ray data exists, assignment of structure I or II is based on composition studies and/or the size of the guest molecule. Tables 2.5a,b also indicate the year the hydrate former was first reported, the temperature (°C) for the stable hydrate structure at 1 atm, and the temperatures (°C) and pressures (atm) of the invariant points (Qi and Q2). Both cyclopropane and trimethylene oxide can form si or sll hydrates. Much of the contents of these tables have been extracted from the excellent review article by Davidson (1973), with updated information from more recent sources (as indicated in the tables).

A number of studies on photochemistry of the nucleic acid bases in aqueous solutions demonstrated that while uracil undergoes reversible hydration under exposure to UV irradiation, the other bases (thymine, adenine, and guanine) were stable [41,42], However, the sensitivity of dissolved thymine to UV irradiation can be significantly increased if the solution is rapidly frozen [43]. In 1960 the thymine photoproduct was isolated from irradiated frozen aqueous solution of thymine. Elemental analysis, molecular weight measurements, powder X-ray diffraction, NMR and IR spectroscopy confirmed that the most likely photoproduct is a thymine dimer [20]. Similar photoproduct was obtained by hydrolysis of irradiated DNA. Its formation was attributed to reaction between two adjacent thymine groups on the same DNA chain [44], Independently an identical compound was isolated from DNA of UV-irradiated bacteria [45]. 

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