Relaxation in Liquid Water

Water is not only the most abundant of all liquids on this planet but also one of the most complex (see Section 2.4). The dielectric constant (permittivity) at frequencies below about lO is about 78 at room temperature, and this is about one whole order of magnitude higher than the dielectric constant of simple liquids such as carbon tetrachloride. Kirkwood was the first to develop a model to explain why the dielectric constant of water is so high. He pictured groups of HjO s coupled together by means of H bonding. His idea was that the dielectric constant of water consists of three parts. 

there would be the part based on the distortion of the electronic shells of the atoms making up water molecules. Because their inertia is so small, electrons have no difficulty in keeping up with an applied field as its frequency increases. Such a contribution is part of the permittivity of any liquid. 

The second part can be viewed as the distortion of the nuclei of the atoms making up water—how much the applied field disturbs the positions of the nuclei in the 0 and H atoms of molecular water. This part is also present in all liquids. 

The third contribution involves the dipole moment of the individual molecules. In water and associated liquids, the dipoles should be taken in groups as a result of the intermolecular H bonding (Fig. 4.98). It is this coupling of the molecules that provides the huge permittivity of water. 

Were water a simple unassociated dipolar liquid, the effect of an applied field would be simply to orient it, to inhibit its random libration and bend the average 

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With local information given by INM analysis in mind, we next see the character of rotational relaxation in liquid water. The most familiar way to see this, not only for numerical simulations [76-78] but for laboratory experiments, is to measure dielectric relaxation, by means of which total or individual dipole moments can be probed [79,80]. Figure 10 gives power spectra of the total dipole moment fluctuation of liquid water, together with the case of water cluster, (H20)io8- The spectral profile for liquid water is nearly fitted to the Lorentzian, which is consistent with a direct calculation of the correlation function of rotational motions. The exponential decaying behavior of dielectric relaxation was actually verified in laboratory experiments [79,80]. On the other hand, the profile for water cluster deviates from the Lorentzian function. As stated in Section III, the dynamics of finite systems may be more difficult to be understood. 

C R0nne, L Thrane, P-O Astrand, A Wallqvist, KV Mikkelsen, SR Keiding. Investigation of the temperature dependence of dielectric relaxation in liquid water by THz reflection spectroscopy and molecular dynamics simulation. J Chem Phys 107 5319-5331, 1997. 

Neutral hydrogen in the magnetic fields in interstellar space may have excited state life times that is measured in years—in contrast hydrogen in liquid water at room temperature display excited state lifetimes of 3 seconds. Why is this How come that the liquid water can lead to a more efficient relaxation of the proton... 

The frequencies of rotational transitions are much smaller than vibrational frequencies, which means that the rotational motion is slower than the vibrational one. For a free molecule, the period of rotational motion is within 10 12-10 9 s. In condensed media the rotational motion is even slower, its period being respectively greater. At this stage it is more correct to speak of the relaxation time of the molecules. The latter essentially depends on the phase state of the medium. For example, in liquid water the relaxation time of molecular dipoles in an external electric field is about 10 11 s, whereas in ice (at 0°C) it is — 1 () 5 s. 

Fits to single (one floating parameter) and double (three floating parameters) exponential decay laws are always poorer as judged by the x2 and residual traces. In the case where we assume that there is some type of excited-state process (e.g., solvent relaxation) we find that the spectral relaxation time is > 20 ns. This is much, much greater than any reasonable solvent relaxation process in supercritical CF3H. For example, in liquid water, the solvent relaxation times are near 1 ps (56). 

The existence of the solvated electron is well authenticated, then, in the radiolysis of polar liquids. The fate of the corresponding positive ions is less clear. Lea54 suggested that in liquid water the ion H20 + would decompose within the relaxation time of water (10-11 sec) on becoming hydrated... 

Figure 41. The scheme pertaining to the composite hat-curved—harmonic oscillator model the contributions of various mechanisms of dielectric relaxation to broadband spectra arising in liquid water. Frequency v is given in cm-1.

The hydrogen bonds in liquid water have an average lifetime of less than 10"10 second as measured by dielectric relaxation times (4). But the hydrogen bonds between water and a polymer could exist for longer than 10"7 seconds. Such a structure would appear permanent at the frequencies used in the ultrasonic impedometer (107 cycles/sec. range), and should demonstrate a measurable shear stiffness at these frequencies. 

Ohmine I, Tanaka H. Fluctuation, relaxations, and hydration in liquid water - hydrogen-bond rearrangement dynamics. Chem. Rev. 1993 93 2545-2566. 

Since the reduced spectrum x"( ) clearly shows the low-ftequency Raman modes, we introduced a simple model to analyze the spectral profile of x"(.v) for obtaining the quantitative information. The model is composed of two damped harmonic oscillator modes and one Debye type relaxation mode (liquid water) or one Cole-Cole type relaxation mode (aqueous solution). Cole-Cole type relaxation is usually adopted in analyzing the dielectric relaxation. The formula of Cole-Cole type relaxation is represented as ... 

Three types of surface are in use for water simulations. The first consists of simple empirical models based on the LJ-C potential. There seems to be no purpose in continuing to develop and use such models as they give little, if any, new information. A second group attempts to improve the accuracy of the potential using semiempirical methods based on a comprehensive set of experimental data. These models allow for physical phenomena such as intramolecular relaxation, electrostatic induced terms, and many-body interactions, all of which are difficult to incorporate correctly in liquid water theories. There is room for much more work in these areas. The third group makes use of the most advanced ab initio methods to develop accurate potentials from first principles. Such calculations are now converging with parameterized surfaces based on accurate semiempirical models. Over the next few years it seems very likely that the continued application of the second and third approaches will result in a potential energy surface that achieves quantitative accuracy for water in the condensed phase. 

Zawodzinski et al. [64] have reported self-diffusion coefficients of water in Nafion 117 (EW 1100), Membrane C (EW 900), and Dow membranes (EW 800) equilibrated with water vapor at 303 K, and obtained results summarized in Fig. 36. The self-diffusion coefficients were deterinined by pulsed field gradient NMR methods. These studies probe water motion over a distance scale on the order of microns. The general conclusion was the PFSA membranes with similar water contents. A, had similar water self-diffusion coefficients. The measured self-diffusion coefficients in Nafion 117 equilibrated with water vapor decreased by more than an order of magnitude, from roughly 8 x 10 cm /s down to 5 x 10 cm /s as water content in the membrane decreased from A = 14 to A = 2. For a Nafion membrane equilibrated with water vapor at unit activity, the water self-diffusion coefficient drops to a level roughly four times lower than that in bulk liquid water whereas a difference of only a factor of two in local mobility is deduced from NMR relaxation measurements. This is reasonably ascribed to the additional effect of tortuosity of the diffusion path on the value of the macrodiffusion coefficient. For immersed Nafion membranes, NMR diffusion imaging studies showed that water diffusion coefficients similar to those measured in liquid water (2.2 x 10 cm /s) could be attained in a highly hydrated membrane (1.7 x 10 cm /s) [69]. 

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