96
PROPERTIES OF INDIVIDUAL NANOPARTICLES
6
5
1
0
0
0.5
1
1.5
2
2.5
TEMPERATURE (K)
Figure 4.23. Specific heat versus temperature for liquid helium (solid line) and a liquid
consisting of clusters of 64 helium atoms (dark circles). The peak corresponds to the transition
to the superfluid state. [Adapted from P. Sindzingre, Pbys. Rev. Lett. 63, 1601 (1989).]
When boson condensation occurs in liquid He4 at the temperature 2.2 K, called
the lambda point (A 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 1 K. 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 the 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 the 0-H stretch of the water molecule in
the liquid phase at 3200-3600cm-’ 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 the
oxygen atom of another. Figure 4.24 shows the structure of one such water cluster.
At ambient conditions 80% of water molecules are bonded into clusters, and as the
PROPERTIES OF INDIVIDUAL NANOPARTICLES
6
5
1
0
0
0.5
1
1.5
2
2.5
TEMPERATURE (K)
Figure 4.23. Specific heat versus temperature for liquid helium (solid line) and a liquid
consisting of clusters of 64 helium atoms (dark circles). The peak corresponds to the transition
to the superfluid state. [Adapted from P. Sindzingre, Pbys. Rev. Lett. 63, 1601 (1989).]
When boson condensation occurs in liquid He4 at the temperature 2.2 K, called
the lambda point (A 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 1 K. 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 the 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 the 0-H stretch of the water molecule in
the liquid phase at 3200-3600cm-’ 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 the
oxygen atom of another. Figure 4.24 shows the structure of one such water cluster.
At ambient conditions 80% of water molecules are bonded into clusters, and as the