Approaching Liquid Water

The difficulties in predicting and understanding the structure of liquid water are well known.As noted by Stillinger and Weber in 1983, At pres- 

Mode Lewerenz and Watts Bernu et al. Lewerenz and Watts Bernu et al. Experiment 

In related experiments and calculations, Gregory et al. investigated dipole moments in small water clusters and found an enhancement of the dipole moment of a water molecule due to the electric field of surrounding monomers. This provides an explanation and description for one of the peculiar properties of water in the condensed form. 

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One important class of integral equation theories is based on the reference interaction site model (RISM) proposed by Chandler [77]. These RISM theories have been used to smdy the confonnation of small peptides in liquid water [78-80]. However, the approach is not appropriate for large molecular solutes such as proteins and nucleic acids. Because RISM is based on a reduction to site-site, solute-solvent radially symmetrical distribution functions, there is a loss of infonnation about the tliree-dimensional spatial organization of the solvent density around a macromolecular solute of irregular shape. To circumvent this limitation, extensions of RISM-like theories for tliree-dimensional space (3d-RISM) have been proposed [81,82],... 

In this section, rather than give a detailed account of theories of the liquid state, a more qualitative approach is adopted. What follows includes first a description of the structure of ice then from that starting-point, ideas concerning the structure of liquid water are explained. 

A recent breakthrough in molecular theory of hydrophobic effects was achieved by modeling the distribution of occupancy probabilities, the pn depicted in Figure 4, rather than applying a more difficult, direct theory of po for cavity statistics for liquid water (Pohorille and Pratt, 1990). This information theory (IT) approach (Hummer et al., 1996) focuses on the set of probabilities pn of finding n water centers inside the observation volume, with po being just one of the probabilities. Accurate estimates of the pn, and po in particular, are obtained using experimentally available information as constraints on the pn. The moments of the fluctuations in the number of water centers within the observation volume provide such constraints. 

Tunon et al.194 studied the water molecule in liquid water. The sample of conformations by the microscopic environment (water in this case) was obtained using Monte Carlo technique. The energy was calculated as in the approach of Stanton et al.189 i.e., using Eqs. 4.25 and 4.26. The solvent induced increase of the dipole moment amounted to 0.61 Debye in line with the results by Wei and Salahub and close to the experimental value of 0.75 Debye. The solvation enthalpy amounted —12.6 kcal/mol, while the value calculated by Salahub and Wei and the experimental ones were —10.4 kcal/mol and —9.9 kcal/mol, respectively. 

We have described our most recent efforts to calculate vibrational line shapes for liquid water and its isotopic variants under ambient conditions, as well as to calculate ultrafast observables capable of shedding light on spectral diffusion dynamics, and we have endeavored to interpret line shapes and spectral diffusion in terms of hydrogen bonding in the liquid. Our approach uses conventional classical effective two-body simulation potentials, coupled with more sophisticated quantum chemistry-based techniques for obtaining transition frequencies, transition dipoles and polarizabilities, and intramolecular and intermolecular couplings. In addition, we have used the recently developed time-averaging approximation to calculate Raman and IR line shapes for H20 (which involves... 

In 2000 and 2001, fuel-cell models were produced by the dozens. These models were typically more complex and focused on such effects as two-phase flow ° where liquid-water transport was incorporated. The work of Wang and co-workers was at the forefront of those models treating two-phase flow comprehensively. The liquid-water flow was shown to be important in describing the overall transport in fuel cells. Other models in this time frame focused on multidimensional, transient, and more microscopic effects.The microscopic effects again focused on using an agglomerate approach in the fuel cell as well as how to model the membrane appropriately. 

The membrane and diffusion-media modeling equations apply to the same variables in the same phase in the catalyst layer. The rate of evaporation or condensation, eq 39, relates the water concentration in the gas and liquid phases. For the water content and chemical potential in the membrane, various approaches can be used, as discussed in section 4.2. If liquid water exists, a supersaturated isotherm can be used, or the liquid pressure can be assumed to be either continuous or related through a mass-transfer coefficient. If there is only water vapor, an isotherm is used. To relate the reactant and product concentrations, potentials, and currents in the phases within the catalyst layer, kinetic expressions (eqs 12 and 13) are used along with zero values for the divergence of the total current (eq 27). 

The general results of the 3-D models are more-or-less a superposition of the 2-D models discussed above. Furthermore, most of the 3-D models do not show significant changes in the 1-D sandwich in a local region. In other words, a pseudo-3-D approach would be valid in which the 1-D model is run at points in a 2-D mesh wherein both the channel and rib effects can easily be incorporated. Another pseudo-3-D approach is where the 2-D rib models are used and then moved along the channel, similar to the cases of the pseudo-2-D models described above. This latter approach is similar to that by Baker and Darling. In their model, they uncouple the different directions such that there is a 1-D model in the gas channel and multiple 2-D rib models. However, they neither treat the membrane nor have liquid water. In all, the use of CFD means that it is not significantly more complicated to run a complete 3-D model in all domains. 

The more rigorous approach to liquid water transport is a true two-phase model in which the two phases travel at different velocities. At the same time, the interfacial tension effect and GDL wettability, essential for successful PEEC operation, are fully accounted for. The work of Wang et al., Nguyen et ai 69 71 You and Liu, Mazumder and Cole, Bern-ing and Djilali, and Pasaogullari and Wang falls into this category. These two-phase models are reviewed in section 3.7. 

The single-phase model described herein considers the total water amount without distinguishing liquid water from water vapor. This approach is valid under the condition that liquid saturation within the gas... 

Jenkins et al. developed a capillary electrophoresis system for the measurement of iohexol as a marker of the glomerular filtration rate (GFR) with a run time of 5.25 min and a coefficient of variation (CV) of 4.3% at 80 mg L" [121]. The GFR, calculated from the plasma clearance, had a reproducibility of 5.47 %. A similar approach (liquid chromatography-mass spectrometry with positive electrospray ionization after enrichment by solid phase extraction) was applied by Putschew et al. for the determination of iodinated contrast agents in treatment plant effluents and surface waters [118]. 

Horita and Wesolowski (1994) have summarized experimental results for the hydrogen isotope fractionation between liquid water and water vapor in the temperature range 0-350°C (see Eig. 2.3). Hydrogen isotope fractionations decrease rapidly with increasing temperatures and become zero at 220-230°C. Above the crossover temperature, water vapor is more enriched in deuterium than liquid water. Fractionations again approach zero at the critical temperature of water (Fig. 2.3). 

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