Heavy water model

Why is the boiling point of heavy water greater than that of ordinary water (a) Propose a model that allows you to estimate the difference or, from the known difference, to estimate any unknown parameters in the model, (b) Use your model to estimate the boiling point of extraheavy water, ... 

Fig. 2.9.3 Proton spin density diffusometry in a two-dimensional percolation model object [31]. The object was initially filled with heavy water and then brought into contact with an H2O gel reservoir, (a) Schematic drawing ofthe experimental set-up. The pore space is represented in white, (b) Maps ofthe proton spin density that were recorded after diffusion times t varying from 1.5 to 116 h. Projections of the...

A number of researchers [15, 38 40, 43, 113, 124 126, 128, 146] have used mixed quantum/classical models, mostly as described in Section III.A, to calculate vibrational line shapes for this system, and several are in fair agreement with experiment. Here we describe our latest work involving approaches discussed in Section III.C. Our theoretical line shapes are calculated as briefly described in previous sections and in published work [98]. From an MD simulation of SPC/E heavy water, we determine the electric field on each putative H atom. We then use electric field maps to determine the transition frequency and dipole derivative. The orientational contribution to mp(t) we... 

A second important application of CMD has been to study the dynamics of the hydrated proton. This study involved extensive CMD simulations to determine the proton transport rate in on our Multi-State Empirical Valence Bond (MS-EVB) model for the hydrated proton. = Shown in Fig. 4 are results for the population correlation function, (n(t)n(O)), for the Eigen cation, HsO, in liquid water. Also shown is the correlation function for D3O+ in heavy water. It should be noted that the population correlation function is expected to decay exponentially at long times, the rate of which reflects the excess proton transport rate. The straight line fits (dotted lines) to the semi-log plots of the correlation functions give this rate. For the normal water case, the CMD simulation using the MS-EVB model yields excellent agreement with the experimental proton hopping... 

The latter is determined by the oscillation frequency, decaying coefficient, and vibration lifetime. This nonrigid dipole moment stipulates a Lorentz-like addition to the correlation function. As a result, the form of the calculated R-band substantially changes, if to compare it with this band described in terms of the pure hat-curved model. Application to ordinary and heavy water of the so-corrected hat-curved model is shown to improve description (given in terms of a simple analytical theory) of the far-infra red spectrum comprising superposition of the R- and librational bands. 

Section VI will present a first step for description (again in terms of the hat-curved model) of the collective (cooperative) effects in water due to the H bonds (i.e., following Walrafen [16]), resulting from the specific interactions. The dielectric spectra of ordinary and heavy water will be calculated in this section. For this purpose we shall apply (with some changes) recent investigation [6, 8] based on the concept of a nonrigid dipole. Other applications of the hat-curved model to water will be described in Sections VII, IX, and X. 

D. Quite another approach, as compared with Refs. 7 and 12b was proposed in Refs. 6 and 8 in terms of a semiphenomenological molecular model capable of describing the wideband dielectric and far-infrared spectra of ordinary and heavy water. In the model the total dipole-moment vector was presented as a sum of two components. The absolute value p of the first component is set constant in time the second component, p(f), changes with time harmonically. Such rather formal presentation of a total dipole moment ptot is possibly a simplest step in taking account of the collective effects, since a time-varying dipole moment p(f) arises due to cooperative motion of nearby polar water molecules. 

Both HC-HO and HC-CS models yield very good description of the wideband spectra in ordinary and heavy water, but interpretation of these compsite model differs. 

The main advantage of the hat-curved potential is that it is possible to narrow the width Avor of the librational absorption band by decreasing the form factor /. Indeed, Avor attains its maximum value when/ = 1. Note that / = 1 is just the case of the hat flat or its simplified variant, the hybrid model, both of which were described in Section IV. The latter was often applied before (VIG) and is characterized by a rather wide absorption band, especially in the case of heavy water. In another extreme case, / — 0, the linewidth Avor becomes very low. When / = 0, we have the case of the parabolic potential well, whose dielectric response was described, for example, in GT and VIG. Thus, when the form factor/of the hat-curved well decreases from 1 to 0, the width Avor decreases from its maximum to some minimum value. 

Figure 35. Frequency dependence in the submillimeter wavelength region of the real (a, b) and imaginary (c, d) parts of the complex permittivity. Solid lines Calculation for the composite HC-HO model. Dashed lines Experimental data [51]. Dashed-and-dotted lines show the contributions to the calculated quantities due to stretching vibrations of an effective non-rigid dipole. The vertical lines are pertinent to the estimated frequency v b of the second stochastic process. Parts (a) and (c) refer to ordinary water, and parts (b) and (d) refer to heavy water. Temperature 22.2°C.

In Figs. 66 and 68 the calculated absorption and loss spectra are depicted for ordinary water at the temperatures 22.2°C and 27°C and for heavy water at 27°C. The solid curves refer to the composite model, and the dashed curves refer to the experimental spectra [42, 51]. For comparison of our theory with experiment at low frequencies, in the case of H20 we use the empirical formula [17] comprising double Debye-double Lorentz frequency dependences. In the case of D20 we use empirical relationship [54] aided by approximate formulae given in Appendix 3 of Section V. The employed molecular constants were presented in previous sections, and the fitted/estimated parameters are given in Table XXIV. The parameters of the composite model are chosen so that the calculated absorption-peak frequencies ilb and vR come close to the... 

Fig. 36. Proposed model for heavy water/epoxy interactions heavy water molecules may form aggregates in the free volume of the polymer or disrupt the hydrogen bonds in the resin...

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