Broken H-bonds

Third, the success of the composite HC-SD model described in Section IX implies the idea that liquid water presents as if a solution of two components. The main one comprises 95% of molecules (librators), which reorient rather freely in a deep potential well and are characterized by a broken H-bond. The second component comprises 5% of molecules, which are H-bonded and perform fast vibration. Molecules of the first group live much longer than those of the second group. Thus a physical sense of the HC model is clarified in Section X as that describing dielectric response of dipoles with broken H-bonds. 

The two oxides require no correction for CFSE, and the Me-O bondings are predominantly ionic. A linear relationship between PZC + 1/2 log (2 - v/v) and (v/L) confirms the plausibility of the Eqs. 25 and 26 for predicting PZC s in a series of oxides. A certain deviation behaviour of hydrogen-bonded hydroxides and oxyhydroxides from the linear relationship is explained by the fact that structure-forming OH- have a specific affinity toward the broken H-bonds on the surface layer and may be classified as non-dissocia-tive adsorption . 

Simple computer experiments (which employ 6-8 million water molecules) in which various fractions of H-bonds in ordinary ice are allowed to break are presented (6.1-6.2). The results of our calculations show that the small fraction of broken H-bonds (13-20%), which is usually considered enough for melting, is not sufficient to break up the network of H-bonds into separate clusters. Consequently, liquid water can be considered to be a deformed network with some ruptured H-bonds. The cooperative effect, first suggested by Frank and Wen, was examined by combining an ab initio quantum mechanical method with a combinatorial one (6.2). In agreement with the results obtained in (6.1), it is shown that 62-63% of H bonds must be broken in order to disintegrate a piece of ice (containing 8 million water molecules) into disconnected clusters. 

By considering that the main difference between liquid water and ice consists of the percentage of hydrogen bonds (H-bonds) of the latter being broken, we determined, by suitable computer experiments, the fractions of water molecules which are present as clusters and as a continuous network as a function of the percentage of broken H-bonds. The calculations have been carried out for both bulk and multilayer ice. 

Other as a strong donor. This means that at room temperature in liquid water there are more than 80% broken H-bonds than in ice (Ih). This opinion has been critically discussed in the hterature. ... 

By comparing the heats of melting and sublimation one finds that only 13% of H-bonds in ice are broken upon melting A similar result (19%) was recently suggested on the basis of a heuristic density-functional method. Many other estimates of the percentage of broken H-bonds are available in the literature. " These estimates, based both on experimental results obtained by various techniques and on theoretical models, provided values ranging from 2 to 72%, " which are dependent on the definition used for an H-bond in liquid water. 

Figure 2. Percentage of molecules in small clusters (compared to the total of 6 X 10 molecules of water) as a function of percentage of broken H-bonds.

Figure 3. Percentages of water molecules having 4, 3, 2, 1, and 0 H-bonds as functions of the percentage of broken H-bonds.

TABLE 1 Average Size of Clusters as a Function of Percentage of Broken H-bonds... 

Figure 5. Fraction of broken H-bonds (f) required for full fragmentation in clusters of several layers of ice. The solid line represents the fraction of broken H-bond (0.61) required for full fragmentation of the bulk ice (a cubic piece).

The calculations regarding several layers of ice have shown that the percentage of broken H-bonds needed for full fragmentation of layers increases with an increasing number of layers and reaches the value for bulk ice at 5—8 layers. 

Thin films of ice and water are of interest in the nanosciences. " Usually these films are considered to be confined between two solid surfaces (walls). It was found that films thicker than 20— 30 A have properties close to those of the bulk. These observations are consistent with our results that the percentage of broken H-bonds required for full fragmentation of layers reaches the bulk value for 5—8 layers. 

Relation between the Number of Broken Bonds and Structure. Percolation Threshold. Figure 2 presents the fraction of water molecules in small clusters as a function of the fractions of broken H bonds. The calculations show that the small amount of 13—20% of broken H bonds, usually considered to occur in melting, is not sufficient to disintegrate the network of H bonds into separate clusters and that the overwhelming majority of water molecules (>99%) belongs to a new distorted but unbroken network. This result was also obtained by us before when we assumed equal probability of rupture of H bonds and also by others a long time ago. It may be used as a test for any models of the water structure. For instance, the so-called cluster or mixture models are not consistent with the above conclusion. 

Figure 4. The contributions (%) from various types of broken H bonds to the total number of broken H bonds. (A) six H-bonded neighbors, (B) five H-bonded neighbors, (C) four H-bonded neighbors, (D) three H-bonded neighbors, and (E) two H-bonded neighbors (see also the caption to Figure 1).

TABLE 3 Average Size of Clusters versus the Percentage of Broken H Bonds... 

In liquid ethanol, the yield of quenchable triplets is <0.03 (benzophenone 1.00) for HB, 4-methoxy HB and 2,2 dlhydroxybenzo-phenone (8). The yield of Isoprene dimers relative to benzophenone (50% isoprene) is found to be 0.03 in cyclohexane and 0.15 in ethanol if HB is used as sensitizer. The lack of plperylene sensitization even in ethanol Indicates a very short lifetime of T of HB even in its broken H-bond form (8). 

We may wonder what happens at molecular level when ice, a crystal, melts and becomes a liquid, hi most hquids the correlations of positions and orientations of constituent molecules rapidly fall off when the distance between them increases. Furthermore, correlations between nearby molecules display rapid fluctuations that make the hquid a fluid. Most of these hquids, however, consist of molecules that mainly interact via weak Van der Waals forces, which are, at room temperature, much less directional than H-bonds, the only molecular interactions established by H2O molecules in liquid water. The fnst idea that usually comes to mind is then that a relatively great proportion of H-bonds are broken in liquid water, so that HjO molecules may gain some independence, making these correlations fall off rapidly with distance. Experiments teU us that the proportion of broken H-bonds is much too small in hquid water to be at the origin of its fluidity. We rapidly examine the fnst type of such experiments, thermodynamics, and describe in more detail a more informative type of experiment IR spectroscopy, from which will emerge an image of the H-bond network of hquid water... 

Supposing that the concentration of broken H-bonds (or free 0-H groups) in liquid water is C, and that H-bonds have same energy in water and ice, we write ... 

As already seen in Ch. 4, IR spectroscopy is by far the most precise method to provide information on H-bonds. It is therefore interesting to examine this particular point of the existence of free O H groups, or of broken H-bonds in liquid water. This is the object of Figure 9.1 where the IR absorption spectrum of a 1 jim thick film of liquid water is displayed together... 

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