Hydrogen-bonded molecules dielectric relaxation

This bimodal dynamics of hydration water is intriguing. A model based on dynamic equilibrium between quasi-bound and free water molecules on the surface of biomolecules (or self-assembly) predicts that the orientational relaxation at a macromolecular surface should indeed be biexponential, with a fast time component (few ps) nearly equal to that of the free water while the long time component is equal to the inverse of the rate of bound to free transition [4], In order to gain an in depth understanding of hydration dynamics, we have carried out detailed atomistic molecular dynamics (MD) simulation studies of water dynamics at the surface of an anionic micelle of cesium perfluorooctanoate (CsPFO), a cationic micelle of cetyl trimethy-lainmonium bromide (CTAB), and also at the surface of a small protein (enterotoxin) using classical, non-polarizable force fields. In particular we have studied the hydrogen bond lifetime dynamics, rotational and dielectric relaxation, translational diffusion and vibrational dynamics of the surface water molecules. In this article we discuss the water dynamics at the surface of CsPFO and of enterotoxin. 

Thus, specific interactions directly determine the spectroscopic features due to hydrogen bonding of the water molecules, while unspecific interactions arise in all or many polar liquids and are not directly related to the H-bonds. Now it became clear that the basis of four different processes (terms) used in Ref. [17] and mentioned above could rationally be explained on a molecular basis. One may say that specific interactions are more or less cooperative in their nature. They reveal some features of a solid state, while unspecific interactions could be understood in terms of a liquid state of matter, if we consider chaotic gas-like motions of a single polar molecule, namely, rotational motions of a dipole in a dense surroundings of other molecules. The modem aspect of the spectroscopic studies leads us to a conclusion that both gas-like and solid-state-like effects are the characteristic features of water. In this section we will first distinguish between the following two mechanisms of dielectric relaxation ... 

The effective correlation times for an approximately isotropic motion, tr, ranged from 40.3 ps in methanol to 100.7 ps in acetic acid for 5a, and from 61.6 ps to 180.1 ps for 5b in the same solvents. Neither solvent viscosity nor dielectric constant bore any direct relationship to the correlation times found from the overall motion, and attempts to correlate relaxation data with parameters (other than dielectric constant) that reflect solvent polarity, such as Kosover Z-values, Win-stein y-values, and the like, were unsuccessful.90 Based on the maximum allowed error of 13% in the tr values derived from the propagation of the experimental error in the measured T, values, the rate of the overall motion for either 5a or 5b in these solvents followed the order methanol N,N-dimethylformamide d2o < pyridine < dimethyl sulfoxide. This sequence appears to reflect both the solvent viscosity and the molecular weight of the solvated species. On this basis, and assuming that each hydroxyl group is hydrogen-bonded to two molecules of the solvent,137 the molecular weights of the solvated species are as follows in methanol 256, N,N-dimethylformamide 364, water 144, pyridine 496, and dimethyl sulfoxide 312. 

The dielectric relaxation of water (Hasted, 1973) can be characterized by a relaxation time m = 9-3 X 10-12 s at 293 K with activation energy 20 kj mol-1. The spread of relaxation times is remarkably small for such a complicated liquid. The data are interpreted in terms of rotation by water molecules having two hydrogen bonds, the spread of relaxation times showing that symmetrically hydrogen bonded and asymmetrically hydrogen bonded water molecules have slightly different relaxation times. 

It is well known [54,270] that the macroscopic dielectric relaxation time of bulk water (8.27 ps at 25°C) is about 10 times greater than the microscopic relaxation time of a single water molecule, which is about one hydrogen bond lifetime [206,272-274] (about 0.7 ps). This fact follows from the associative structure of bulk water where the macroscopic relaxation time reflects the cooperative relaxation process in a cluster of water molecules. 

The quantitative interpretation of the dielectric relaxation times is still not on a satisfactory basis. The earliest attempt in this direction was made on the basis of an ion-oriented hydration sheath, for the formation of which a calculated number of hydrogen-bonds must be broken. This breakage changes the equilibrium of species in the liquid, and statistical relationships connect the proportion of bonds broken, the equilibrium populations, and the relaxation time. From the observed shift of relaxation time one can calculate the number of molecules in the sheath, and show that for temperatures between 276 and 298 K it is approximately the same as the number calculated from the depression of the static permittivity (comparison in Figure 4 of ref. 54). This treatment is open to criticism on the following grounds ... 

To explain the bimodal dielectric relaxation in aqueous protein solutions, Nandi and Bagchi proposed a similar dynamic exchange between the bound and the free water molecules [21]. The bound water molecules are those that are attached to the biomolecule by a strong hydrogen bond. Their rotation is coupled with that of the biomolecule. The water molecules, beyond the solvation shell of the proteins, behave as free water molecules. The free water molecules rotate freely and contribute to the dielectric relaxation process, whereas the rotation of the doubly hydrogen-bonded bound water molecules is coupled with that of the biomolecule and hence is much slower. The free and bound water molecules are in a process of constant dynamic exchange. The associated equilibrium constant, K, can be written as... 

A dimer, involved in the VIB state and formed by H20 or D20 molecules, is specified as compared with the variant 3b. The dimer represents a rough structure of the hydrogen bond. Dielectric relaxation arises, first, due to... 

The first mechanism (a) refers to dielectric relaxation pertinent to a permanent dipole influenced by a rather narrow hat intermolecular potential the next two (b, c) refer to the complex permittivity generated by two elastically vibrating hydrogen-bonded (HB) molecules. The last mechanism (d) refers to a nonrigid dipole vibrating in direction perpendicular to that of the undisturbed H-bond. 

Based on the dielectric and dynamic mechanical data, it appears that water and small polar molecules contribute to three dispersions in this poly(amide-imide). One is the low temperature relaxation between -100 and 0°C. This may be a hydrogen bonded relaxation since the activation enthalpy was 30 kJ/mol. This occurs at concentrations of water ranging between 0 to 4 weight percent. Two, the dielectric relaxation between 0 and 70 C can probably be attributed to conductive contaminants whose mobility is dependent upon a minimum amount of water. Three, at high water concentrations, greater than 2 weight percent, the water/NMP contributes to the beta relaxations observed between 50 and 150 C. 

Dielectric relaxation measurements by Buchner, Wachter et al. (Buchner et al. 1994,2002, Buchner and Hefter 2009 Chen et al. 2003 Tromans et al. 2004 Wachter et al. 2005, 2006, 2007) made mainly for studying ion association in aqueous solutions, yielded also the reorientation times of the water molecules. The cooperative reorientation time of bulk water, ree, decreases with increasing salt concentration, reflecting the weakening of the hydrogen bonded stmcture of the water. These measurements were made at salt concentrations, ce < 1M and yielded the coefficient b ofEq. (3.7) ... 

---