Diffusion crystal hydrates

Ionic radii in the figure are measured by X-ray diffraction of ions in crystals. Hydrated radii are estimated from diffusion coefficients of ions in solution and from the mobilities of aqueous ions in an electric field.3-4 Smaller, more highly charged ions bind more water molecules and behave as larger species in solution. The activity of aqueous ions, which we study in this chapter, is related to the size of the hydrated species. 

Order arising through nucleation occurs both in equilibrium and nonequilibrium systems. In such a process the order that appears is not always the most stable one there are often competing processes that will lead to different structures, and the structure that appears is the one that nucleates first. For instance, in the analysis of the different possible structures in diffusion-reaction systems17-20 one can show, by analyzing the bifurcation equations, that there are several possible structures and some of them require a finite amplitude to become stable if this finite amplitude is realized through fluctuation, this structure will appear. In the formation of crystals (hydrates) the situation is similar the structure that is formed depends, according to the Ostwald rule, on the kinetics of nucleation and not on the relative stability. 

Steinhoff et al. (1989) measured the temperature and hydration dependence of the ESR spectra of hemoglobin spin-labeled at cysteine )8-93. They observed the critical temperature near 200 K, as described above, and the sensitivity of the spectrum to hydration level. Spectrum simulations suggested that there were two types of motion in the dry protein, a fast vibration of the label within a limited motion cone upon the addition of water, a hydration-dependent motion assigned to the fluctuations of the protein, of correlation time 10 sec in samples of high hydration and at 300 K. The temperature dependence of the motional properties of a spin probe (TEMPONE), diffused into hydrated single crystals, closely paralleled the motional properties of the label. This was taken to be evidence for coupling between the dynamical properties of the protein and the adjacent solvent. 

Crystal packing diagram for raffinose pentahydrate. Three of the water molecules are located in a channel (Wl, W2, and W4) and two are located outside of the channel (W3 and W5). For clarity, only the oxygen molecules of the water are shown at 50% of the van der Waals radii. (Source Reproduced from Ahlqvist, M.U.A. and Taylor, L.S. Water diffusion in hydrated crystalline and amorphous sugars monitored using H/D exchange, /. Pharm. Sci., 91, 690-698, 2002. With permission of the copyright owner.)... 

The moisture-solid interaction is an inevitable aspect of pharmaceutical development. Elucidation of moisture-induced physical alterations in amorphous pharmaceuticals is crucial, especially for ASD. Gravimetric measurement on the rate and extent of moisture gain (sorption) by or loss (desorption) from amorphous samples as a function of RH or as a function of time at a constant RH (isohumic condition) can provide a wealth of information of ASD. The key structural properties of ASD measureable by moisture sorption/desorption are drug-polymer interactions, moisture-induced glass transition, crystallization, hydrate formation/dehydration, etc. while that associated with particulate or bulk properties are hygroscopicity, diffusivity, pore size, surface area, etc. (Burnett et al. 2009). 

At low and medium supersaturations the number of particles formed depends on the number of heterogeneous nuclei and usually does not exceed 10 cm (Fig. 1). Once formed, crystals enlarge by deposition of solute ions at the surface, surface diffusion to a suitable site, and incorporation into the crystal lattice (see also Sections II.A and II.B). Under these conditions strongly hydrated cations are likely to form different crystal hydrates with different solubilities. Crystals thus formed are coarser and contain less—primarily crystalline—water than... 

Hydrated bilayers containing one or more lipid components are commonly employed as models for biological membranes. These model systems exhibit a multiplicity of structural phases that are not observed in biological membranes. In the state that is analogous to fluid biological membranes, the liquid crystal or La bilayer phase present above the main bilayer phase transition temperature, Ta, the lipid hydrocarbon chains are conforma-tionally disordered and fluid ( melted ), and the lipids diffuse in the plane of the bilayer. At temperatures well below Ta, hydrated bilayers exist in the gel, or Lp, state in which the mostly all-trans chains are collectively tilted and pack in a regular two-dimensional... 

The values of hj for different ions are between 0 and 15 (see Table 7.2). As a rule it is found that the solvation number will be larger the smaller the true (crystal) radius of the ion. Hence, the overall (effective) sizes of different hydrated ions tend to become similar. This is why different ions in solution have similar values of mobilities or diffusion coefficients. The solvation numbers of cations (which are relatively small) are usually higher than those of anions. Yet for large cations, of the type of N(C4H9)4, the hydration number is zero. 

The ionic mobility and diffusion coefficient are also affected by the ion hydration. The particle dimensions calculated from these values by using Stokes law (Eq. 2.6.2) do not correspond to the ionic dimensions found, for example, from the crystal structure, and hydration numbers can be calculated from them. In the absence of further assumptions, diffusion measurements again yield only the sum of the hydration numbers of the cation and the anion. 

To summarize, the hydration status of the drug molecule and other components of a pharmaceutical formulation can affect mass transport. Solubility of drug crystals in an aqueous or nonaqueous solvent may depend on the presence or absence of moisture associated with the drug. Hydration may also determine the hydrodynamic radii of molecules. This may affect the frictional resistance and therefore the diffusion coefficient of the drug molecules. Diffusion of drugs in polymeric systems may also be influenced by the percent hydration of the polymers. This is especially tme for hydrogel polymers. Finally, hydration of... 

The utilization of IR spectroscopy is very important in the characterization of pseudopolymorphic systems, especially hydrates. It has been used to study the pseudopolymorphic systems SQ-33600 [36], mefloquine hydrochloride [37], ranitidine HC1 [38], carbovir [39], and paroxetine hydrochloride [40]. In the case of SQ-33600 [36], humidity-dependent changes in the crystal properties of the disodium salt of this new HMG-CoA reductase inhibitor were characterized by a combination of physical analytical techniques. Three crystalline solid hydrates were identified, each having a definite stability over a range of humidity. Diffuse reflectance IR spectra were acquired on SQ-33600 material exposed to different relative humidity (RH) conditions. A sharp absorption band at 3640 cm-1 was indicative of the OH stretching mode associated with either strongly bound or crystalline water (Fig. 5A). The sharpness of the band is evidence of a bound species even at the lowest levels of moisture content. The bound nature of this water contained in low-moisture samples was confirmed by variable-temperature (VT) diffuse reflectance studies. As shown in Fig. 5B, the 3640 cm-1 peak progressively decreased in intensity upon thermal... 

Solvates and hydrates can be unstable when removed from solution, and are not usually desired as the solid form of the final API. The water or solvent molecules often lie along a crystal axis and can diffuse out of the crystal along these channels to achieve equilibrium with the surrounding vapour phase. In some instances this weakens the crystal structure and may cause fragmentation. 

Table 2.3 gives the self-diffusion coefficients of some important ions in submerged soils and Figure 2.2 shows the values for the elemental ions plotted against ionic potential ( z /r where z is the absolute ionic charge and r the crystal ionic radius). As the ionic potential increases the hydration layer of water molecules around the ion increases, and therefore the mobility tends to decrease. Also, at the same ionic potential, cations diffuse faster than anions. The mobilities... 

Terrace Ion-Transfer Mechanism, In the terrace siteion-transfer mechanism a metal ion is transferred from the solution (OHP) to the flat face of the terrace region (Fig. 6.15). At this position the metal ion is in the adion (adsorbed-like) state, having most of its water of hydration. It is weakly bound to the crystal lattice. From this position it diffuses on the surface, seeking a position of lower energy. The final position is a kink site. 

Polymer crystals grown from silica gel at room temperature contain 1-D chains of [Er(TMA)(H20)5]n,[4] The use of a highly controlled layer diffusion method gives 2-D [ErfTMA)(H20)3]n. In this material loss of two ancillary aqua groups allows pendant carboxylates of adjacent 1-D polymer strands to connect and create a sheet. Finally the use of hydrothermal conditions (180°C, autogenous pressure. 3 days) allows formation of anhydrous [Er(TMA)]n. This has a 3-D network with no simple topological relationship to the hydrated forms.[5]... 

Proton NMR spectroscopy and dielectic constant measurements provide evidence about the motion of the water molecules in crystal structures, as reviewed by Davidson and Ripmeester (1984). At very low temperatures (<50 K) molecular motion is frozen in so that hydrate lattices become rigid. The hydrate proton NMR analysis suggests that the first-order contribution to motion is due to reorientation of water molecules in the structure the second-order contribution is due to translational diffusion at these low temperatures. 

This is one distinguishing feature between hydrates and ice water molecules diffuse two orders of magnitude slower in hydrates than in ice. As shown in Table 2.8, ice water molecules diffuse almost an order of magnitude faster than they reorient about a fixed position in the crystal structure. In direct contrast, hydrate water molecules reorient 20 times faster than they diffuse. As for all... 

---