Time scales hydration

Li TP, Hassanali AAP, Kao YT, Zhong DP, Singer SJ (2007) Hydration dynamics and time scales of coupled water-protein fluctuations. J Am Chem Soc 129(11) 3376-3382... 

The first subnanosecond experiments on the eh yield were performed at Toronto (Hunt et al., 1973 Wolff et al., 1973). These were followed by the subnanosecond work of Jonah et al. (1976) and the subpicosecond works of Migus et al. (1987) and of Lu et al. (1989). Summarizing, we may note the following (1) the initial (-100 ps) yield of the hydrated electron is 4.6 0.2, which, together with the yield of 0.8 for dry neutralization, gives the total ionization yield in liquid water as 5.4 (2) there is -17% decay of the eh yield at 3 ns, of which about half occurs at 700 ps and (3) there is a relatively fast decay of the yield between 1 and 10 ns. Of these, items (1) and (3) are consistent with the Schwarz form of the diffusion model, but item (2) is not. In the time scale of 0.1-10 ns, the experimental yield is consistently greater than the calculated value. The subpicosecond experiments corroborated this finding and determined the evolution of the absorption spectrum of the trapped electron as well. 

The general picture is such that the majority of excess protons are located in the central part of the hydrated hydrophilic nanochannels. In this region, the water is bulklike (for not too low degrees of hydration) with local proton transport properties similar to those described for water in Section 3.1.1.1.1. Therefore, the transport properties are indeed a function of the considered length and time scales,22 225 activation enthalpies of both... 

O2 consumption rate becomes smaller under 0.7 V, the O2 concentration at the reaction surface recovers, thus leading to an increase in the cell current density. The current rise time corresponds well with the characteristic time scale of gas phase transport as analyzed above. The rise in the cell current, however, experiences an overshoot because the polymer membrane still maintains a higher water content corresponding to 0.6 V. It then takes about 15 s for the membrane to adjust its water content at the steady state corresponding to 0.7 V. This numerical example clearly illustrates the profound impact of water management on transient dynamics of low humidity PEFC engines where the polymer membrane relies on reaction water for hydration or dehydration. 

Shortly after the discovery of the hydrated electron. Hart and Boag [7] developed the method of pulse radiolysis, which enabled them to make the first direct observation of this species by optical spectroscopy. In the 1960s, pulse radiolysis facilities became quite widely available and attention was focussed on the measurement of the rate constants of reactions that were expected to take place in the spurs. Armed with this information, Schwarz [8] reported in 1969 the first detailed spur-diffusion model for water to make the link between the yields of the products in reaction (7) at ca. 10 sec and those present initially in the spurs at ca. 10 sec. This time scale was then only partially accessible experimentally, down to ca. 10 ° sec, by using high concentrations of scavengers (up to ca. 1 mol dm ) to capture the radicals in the spurs. From then on, advancements were made in the time resolution of pulse radiolysis equipment from microseconds (10 sec) to picoseconds (10 sec), which permitted spur processes to be measured by direct observation. Simultaneously, the increase in computational power has enabled more sophisticated models of the radiation chemistry of water to be developed and tested against the experimental data. 

For example, the rate constant for dissociation of hydrated S02, kl2, is 3.4 X 10r s l so that the half-life for dissociation of the hydrated S02 is only 0.2 yu,s. Similarly, the second ionization, reaction (13), occurs on time scales of less than a millisecond (Schwartz and Freiberg, 1981). Thus, regardless of which of the three species, S02 H20, HSO, or SO3-, is the actual reactant in any particular oxidation, the equilibria will be reestablished relatively rapidly under laboratory conditions, and likely under atmospheric conditions as well. The latter is complicated by such factors as the size of the droplet, the efficiency with which gaseous S02 striking a droplet surface is absorbed, the chemical nature of the aerosol surface, and so on for example, the presence of an organic surface film on the droplet could hinder the absorption of S02 from the gas phase. 

For example, for formaldehyde (R = H) at neutral pH, the pseudo-first-order rate constant for the hydration reaction (forward reaction), k =k [H20], is about 10 s 1 and the first-order rate constant for dehydration, k2, is about 5x 10-3 s-1. In Chapter 20 we will use this example to show that the reactivity of compounds can influence the kinetics of air/water exchange if both processes (reaction and exchange) occur on similar time scales. 

Fig. 7. Hydration of DNA, and with a drug recognized in the minor groove. Time scales are indicated for bulk water, dynamically ordered water, configurational changes and structured water...

In sharp contrast to the large number of experimental and computer simulation studies reported in literature, there have been relatively few analytical or model dependent studies on the dynamics of protein hydration layer. A simple phenomenological model, proposed earlier by Nandi and Bagchi [4] explains the observed slow relaxation in the hydration layer in terms of a dynamic equilibrium between the bound and the free states of water molecules within the layer. The slow time scale is the inverse of the rate of bound to free transition. In this model, the transition between the free and bound states occurs by rotation. Recently Mukherjee and Bagchi [14] have numerically solved the space dependent reaction-diffusion model to obtain the probability distribution and the time dependent mean-square displacement (MSD). The model predicts a transition from sub-diffusive to super-diffusive translational behaviour, before it attains a diffusive nature in the long time. However, a microscopic theory of hydration layer dynamics is yet to be fully developed. 

CSMPlug can predict the total dissociation time by two-sided depressurisation, and by evenly applied radial heat input to an accuracy of 10%, provided accurate plug properties are known. Predictions from the one-sided depressurisation module are less accurate than those of the other modules, but are within an order of magnitude of those observed dissociation times for laboratory scale hydrates are typically over predicted but industrial hydrates are under predicted. 

Because of the complexity of hydrated PEMs, a full atomistic modeling of proton transport is impractical. The generic problem is a disparity of time and space scales. While elementary molecular dynamics events occur on a femtosecond time scale, the time interval between consecutive transfer events is usually 3 orders of magnitude greater. The smallest pore may be a few tenth of nanometer while the largest may be a few tens of nanometers. The molecular dynamics events that protons transfer between the water filled pores may have a timescale of 100-1000 ns. This combination of time and spatial scales are far out of the domain for AIMD but in the domain of MD and KMC as shown in Fig. 2. Because of this difficulty, in the models the complexity of the systems is restricted. In fact in many models the dynamics of excess protons in liquid water is considered as an approximation for proton conduction in a hydrated Nation membrane. The conformations and energetics of proton dissociation in acid/water clusters were also evaluated as approximations for those in a Nation membrane.16,19 20 22 24 25... 

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