Figure 4.22. Illustration of how fermions and bosons distribute over the energy levels of a system at high and low temperature.

Figure 4.23. Specific heat versus temperature for liquid helium (solid line) and a liquid consisting of clusters erf 64 heSurff atoms (dark circles). The peak corresponds to the transition to the superflu id state. [Adapted from P. Sindzmgre, Phys. Rev. Lett. 63,1601 (1989).]

When boson condensation occurs in liquid He4 at the temperature 2.2 K, called the lambda point (Z point), the liquid helium becomes a superfluid, and its viscosity drops to zero. Normally when a liquid is forced though a small thin tube, it moves slowly because of friction with the walls, and increasing the pressure at one end increases the velocity. In the superfluid state the liquid moves quickly through the tube, and increasing the pressure at one end does not change the velocity. The transition to the superfluid state at 2.2 K is marked by a discontinuity in the specific heat known as the lambda transition. The specific heat is the amount of heat energy necessary to raise the temperature of one gram of the material by 1K. Figure 4.23 shows a plot of the specific heat versus temperature for bulk liquid helium, and for a helium cluster of 64 atoms, showing that clusters become superfluid at a lower temperature than die bulk liquid of He atoms.

4.4.3. Molecular Clusters

Individual molecules can form clusters. One of the most common examples of this is the water molecule. It has been known since the early 1970s, long before the invention of the word nanoparticle, that water does not consist of isolated H20 molecules. The broad Raman spectra of die O—H stretch of the water molecule in the liquid phase at 3200-3600 cm-1 has been shown to be due to a number of overlapping peaks arising from both isolated water molecules and water molecules hydrogen-bonded into clusters. The H atom of one molecule forms a bond with die oxygen atom of another. Figure 4.24 shows the structure of one siich water cluster. At ambient conditions 80% of water molecules are bonded into clusters, and as the

Figure 4.24. A hydrogen-bonded duster of five water molecules. The large spheres are oxygen, and the small spheres are hydrogen atoms.

temperature is raised, the clusters dissociate into isolated H20 molecules. In the complex shown in Fig. 4.24 die H atom is not equidistant between the two oxygens. Interestingly, it has been predicted that under 9 GPa of shock loading pressure a new form of water might exist called symmetrically hydrogen-bonded water, where the H atom is equally shared between both oxygens. It is possible that such water could have properties different from those of normal water. There are other examples of molecular clusters such as (NH3)n+, (COj)^ and (QHS)30

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