Hydration shell definition

Remarkable data on primary hydration shells are obtained in non-aqueous solvents containing a definite amount of water. Thus, nitrobenzene saturated with water contains about 0.2 m H20. Because of much higher dipole moment of water than of nitrobenzene, the ions will be preferentially solvated by water. Under these conditions the following values of hydration numbers were obtained Li+ 6.5, H+ 5.5, Ag+ 4.4, Na+ 3.9, K+ 1.5, Tl+ 1.0, Rb+ 0.8, Cs+0.5, tetraethylammonium ion 0.0, CIO4 0.4, NO3 1.4 and tetraphenylborate anion 0.0 (assumption). 

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... 

A somewhat intermediate view has also been adopted by Horne and Birkett (SO), who also propose a multilayer model of hydration where both the firmly bonded, first hydration layer and the disordered zone of the Frank-Wen model are accepted. However, they suggest the existence of a second layer of water molecules (separating the primary hydration shell and the disordered zone) around the ion, consisting of rarified or extended clusters of water molecules with density less than waters but definitely not of Ice-I like structure. We return to this aspect later. In this connection, compare also our discussion of the studies by Vaslow (150), Griffith and Scheraga (67), and Luz and Yagil (103). 

However, from pulse radiolysis studies of aqueous solutions definite evidence for processes such as 5 has been obtained recently (2), and the rate constant for the reaction with C03-2 has been shown to be 2 X 108 M 1 sec. 1. Thus, Reaction 5 or 5a can be justifiably assumed to occur between the anions S04 2, HP04 2, P04-3, and C03-2 and the OH radicals formed according to Equation 1 in the hydration shell of these ions. 

These diagrams indicate the limit of the hydration shell in the gas-phase ion as the first minimum in the radial distribution function. It is well pronounced for K, which has 8 molecules as the calculated coordination number on the cluster curiously, the sharpness of the definition for Na" is less atAl= 6 (and sometimes 7). The influence... 

Figure 7.7 The radial distribution function ko( ) for oxygen atoms about a K+ ion in liquid water. See Rempe et al. (2004). The dashed curve is the contribution to Ko(r) from the nearest four oxygen atoms, and the dashed-dot curve is the contribution from the 5 and 6 nearest oxygen atoms. Notice the lack of definition obtained from the Ko(r) solely because a minimum separating a from a 2 mean hydration shell is indistinct.

With this picture the terms hydration shell and bound water are understood to mean the water at the hydration end point. With this definition several questions should be addressed. 

Biological systems are, by definition, multicomponent systems. One should keep in mind the difficulties of constructing molecular level pictures that satisfactorily describe systems such as a protein in a reverse micelle or a protein in a concentrated aqueous salt solution, which are certainly much simpler than anhydrobiotic organisms, for example. It is not clear to what extent the water of the hydration shell can be replaced by a third component (e.g., lipid) or what effect such replacement has on protein or enzyme properties. 

The most inclnsive definition of hydration shell describes it as consisting of all thermodynamically altered water molecnles in the vicinity of a solnte. From a thermodynamic standpoint, hydration can be viewed as binding of water molecnles to the hydration sites of a solnte. The energetics of this association is modulated by the type of solute-solvent interactions (electrostatic, hydrogen bonding, van der Waals) and by solnte-indnced solvent reorganization. The latter occnrs even in the absence of appreciable solute-solvent interactions becanse the eqnUib-rium distribution of hydrogen-bonded water networks of the bulk becomes disrupted at the solute surface. 

As an example of the type of information that can be obtained, the composition and anisotropy of the hydration shells in the vicinity of the mercury surface is analyzed. Figure 27 shows the average coordination number of the ions as a function of position (the mercury surface is located at z = 0 A). Here, the coordination number is defined as the number of water molecules the ion-oxygen distance of which is smaller than 2.5 A, 3.2A, 3.9 A, and 4.2A for Li+, F , Cl , and I, respectively. This definition is based on the positions of the first minima of the ion-oxygen pair correlation functions. 

Water residence times on the protein surface are not directly measurable experimentally, bnt can be defined as the relaxation time of time correlation functions of the popnlation of the hydration shell [5], Due to differences in the definition from one investigation to another, the values reported in the literature exhibit considerable variability. Nonetheless, heterogeneity in water dynamics near the protein surface is clearly manifested in distributions of water residence times. The distribution we have constrncted for the N state of HocLA in solution from the residence time of water next to each residue is plotted up to lOOps in Figure 16.1d. The distribution is very broad, ranging from 2.6 to 241 ps, but highly skewed toward shorter residence times. The mean residence time of 23 ps is about 2.5 times longer than the rotational correlation time for hydration water. 

Information accumulated thus far on the hydration of mineral ions has been critically analyzed in the recent review by Marcus [163] entitled Effect of ions on the structure of water Structure making and breaking. It is important that definite changes have been noted in the water structure and in the structure of diffuse hydration shells with electrolyte concentrations. Neutron diffraction of CaCl2 and Ca(N03)2 solutions in D2O has shown [164] a decrease of Ca hydration number from 10 to 6 when the salt concentration increased from 1 to 4.5 M. 

The same water model, SPC/E at 25 °C was used by other authors too. Chowd-huri and Chandra (2001) employed 256 water molecules per ion, as well as lower ratios at increasing concentrations, and reported the average residence times of water molecules near ions in ps Na+ 18.5, K+ 7.9, and Cl 10.0. Guardia et al. (2006) also reported residence times in ps of the water molecules in the first hydration shells of ions Li+ 101, Na+ 25.0, K+ 8.2, Cs+ 6.9, F 35.5, Cl 14.0, and I 8.5, compared with 10 1 for water molecules in the bulk. These values, resulting from detailed considerations of the hydrogen bond dynamics in water and near the ions, can be compared with experimental values derived from NMR. According to Bakker (2008) these are Li+ 39, Na+ 27, K+ 15, Cl 15 (by definition the same as for K+), Br 10, and 5 ps, and for water molecules in the bulk 17 ps, calculated from the self diffusion coefficient. 

At the surface of the micelle we have the associated counterions, which in number amount to 50-80% of the surfactant ions, which as noted above is a number quite invariant to the conditions. Simple inorganic counterions are very loosely associated with the micelle. The counterions are very mobile and there is no specific complex formed with a definite counterion-head-group distance. Rather, the counterions are associated by long-range electrostatic interactions to the micelle as a whole. They remain hydrated to a great extent, and especially cations tend to keep their hydration shells. 

Cations in aqueous solution have the water molecules oriented toward them, and for small multivalent cations such as Mg " " and transition metal cations, this results in a coordinate bond in the first hydration shell. These water molecules form hydrogen bonds with molecules in a second hydration shell. Other cations, such as Ca " " and the alkali metal ones, do not have a definite number of coordinated water molecules but a distribution with a fi actional average number. 

Thus different parts of the molecule may carry hydration shells that have significantly different properties. This leads to mutually destructive intramolecular overlap of water shells and the resulting overall hydration characteristics will definitely represent these complexities. This makes it difficult to define hydrophobic parameters for organic functional groups because they will depend on their position in the molecule. Only long alkyl functionalities do not suffer from these overlap effects. Recent kinetic studies have demonstrated these effects and rough estimates have been made of the extent of the overlap region in the total hydration shell vide supra). 

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. 

The RMRT of water molecnles in the second hydration shell of cations (the first for univalent ones) are compared in Table 5.4. with log(A /s), the (logarithm of the) experimental (mainly from NMR measurements) rate constant of the first-order reaction of water molecules leaving the hydration shells of cations in exchange for incoming molecnles. The larger the RMRT of the water molecules, the slower is the exchange as measnred by log(A /s), but a definite proportionality or linear dependence could not be established. 

Two interrelated topics that bear most directly on the description of the hydration shell—i.e., the bound water layer(s)—are the definition of the shell and its thickness. The problem of how the bound water can be sufficiently precisely defined is discussed elsewhere [11,37,51] and we shall not pursue it further here. It is clear, however, that the extent to which water is affected by a nearby surface is a function of the distance between them, namely the thickness of the hydration shell. Second-layer water (and, obviously, multilayer water) is much less perturbed than the water adjacent to the surface. We have used several methods to evaluate the thickness of the interphasal water layer in system A (as revealed by the low-temperatme behavior of water) [2,11] and found it to be about 0.5 nm. Virtually the same value has been assessed for the thickness of the bound water layer on many organic and inorganic substrates [37,52-57]. As 0.5-0.6 nm is the thickness of two water molecules [45], we may envisage two monolayers of interphasal (or boimd) water that are loosely associated with the substrate. We have shown that Aw/eo = 3 for system A at a total water content of 30 wt%. 

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