Glassy water

Assuming that for water AGd is 7 kcal/mol, calculate the rate of nucleation for ice nuclei for several temperatures and locate the temperature of maximum rate. Discuss in terms of this result why glassy water might be difficult to obtain. 

Amorphous water (also called glassy water or amorphous ice) can form when the temperature is decreased extremely rapidly below the glass transition temperature (Tg) of water (about 130 K at 0.1 MPa) (Mishima and Stanley, 1998). There are three types of amorphous ice low-density amorphous ice (LDA), high-density amorphous ice (HDA), and very high-density amorphous ice (VHDA), with VHDA being discovered most recently (Finney et al., 2002). 

Mishima, O. and Stanley, H.E. 1998. The relationship between liquid, supercooled and glassy water. Nature 396, 329-335. 

The more recently developed cryo-TEM technique has started to be used with increasing frequency for block copolymer micelle characterization in aqueous solution, as illustrated by the reports of Esselink and coworkers [49], Lam et al. [50], and Talmon et al. [51]. It has the advantage that it allows for direct observation of micelles in a glassy water phase and accordingly determines the characteristic dimensions of both the core and swollen corona provided that a sufficient electronic contrast is observed between these two domains. Very recent studies on core-shell structure in block copolymer micelles as visualized by the cryo-TEM technique have been reported by Talmon et al. [52] and Forster and coworkers [53]. In a very recent investigation, cryo-TEM was used to characterize aqueous micelles from metallosupramolecular copolymers (see Sect. 7.5 for further details) containing PS and PEO blocks. The results were compared to the covalent PS-PEO counterpart [54]. Figure 5 shows a typical cryo-TEM picture of both types of micelles. 

Sugisaki, M., Suga, H., and Seki, S. (1968). Calorimetric study of the glassy state. 4. Heat capacities of glassy water and cubic ic ull. Chem. Soc. Jap., 41 2591-2599. 

F. W. Starr, M.-C. Bellissent-Funel and H. E. Stanley, Structural evidence for the continuity of liquid and glassy water, arXiv condensed matter, 9811118, (vl), 1998, 1. 

Debenedetti, P. G., Supercooled and glassy water. J. Phys. Condensed Matter 15, R1669-R1726 (2003). 

Debenedetti PG. Supercooled and glassy water. J. Phys. Cond. 

The structural correlations are strongly enhanced in the under-cooled state as the temperature is reduced towaids the metastable limit of -40°C (to D2O) and various thermoph ical properties exhibit diverged behaviour [8]. The exact nature of this anomaly is still the subject of some controversy. However, the difiraction pattern indicates that the stmcture is evolving towards that of amorphous ice which is characterised as a continuous random networit of tetrahedral hydrogen-bonds [9]. Recent neutron measurements on amorphous ice [10] have re-infor the earlier conjectures tuid shown that the structure is similar to that of hyper-quenched glassy water produced by rapid cooling of micron-sized water droplets. It can now be realised that the CRN mo l for the disordered phase of ice is effectively the limiting stmcture of water at low temperatures. 

Section II provides a summary of Local Random Matrix Theory (LRMT) and its use in locating the quantum ergodicity transition, how this transition is approached, rates of energy transfer above the transition, and how we use this information to estimate rates of unimolecular reactions. As an illustration, we use LRMT to correct RRKM results for the rate of cyclohexane ring inversion in gas and liquid phases. Section III addresses thermal transport in clusters of water molecules and proteins. We present calculations of the coefficient of thermal conductivity and thermal diffusivity as a function of temperature for a cluster of glassy water and for the protein myoglobin. For the calculation of thermal transport coefficients in proteins, we build on and develop further the theory for thermal conduction in fractal objects of Alexander, Orbach, and coworkers [36,37] mentioned above. Part IV presents a summary. 

The normalized density of states is p(o>), N is the total number of vibrational modes, T is temperature, kB is Boltzmann s constant, and Vis the volume of the macromolecule or cluster. In what follows we address first thermal transport in a glassy water cluster, then turn to proteins. 

Before carrying out the energy diffusion calculations on the water cluster, it is useful to determine the speed of sound in glassy water, which we compute from the dispersion relation for the water cluster. To compute a dispersion relation, we need to assign a wave number, k, to a normal mode of frequency, go. We have obtained dispersion relations for proteins [111] via computation of the correlation function for the direction of atomic displacements as a function of distance for individual normal modes of the protein, a function that was studied in earlier work by Nishikawa and Go [112], Computation of the correlation function allows us to match a wave number of a plane wave to a normal mode... 

A fit through the points in the plot gives a slope of 14 A ps-1, which is a reasonable value for the speed of sound in glassy water, consistent with a value of about 15 A ps-1 in water [113]. 

Therefore, experiments are performed on immobilized liquids , or in other words on amorphous water (also called vitreous water or glassy water). Currently, three structurally distinct amorphous states of water are known low- (LDA) , high- (HDA) and very high- (VHDA) density amorphous ice We emphasize that HDA is not a well defined state but rather comprises a number of substates. It has been suggested to use the nomenclature uHDA ( unrelaxed HDA ) ", eHDA ( expanded HDA ) " and/or rHDA ( relaxed HDA ) to account for this. Even though no signs of micro-crystallinity have been found in neutron or X-ray diffraction studies, it is unclear whether... 

ACp could be made arbitrarily steep so as to very closely simulate the experimental glass transition. In the above expression, AHi refers to the maximum value of this enthalpy (at 0 K) Tr and D are adjustable temperatures. The idea of cooperativity used here is unconventional. It is understandable, however, that as temperature increases, a few secondary bonds get broken (such as hydrogen bonds in glassy water), the strains in... 

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