Related Experiment Video
Updated: Aug 3, 2026
16:24
Controlling the Size, Shape and Stability of Supramolecular Polymers in Water
Published on: August 2, 2012
Entropic effects on the size dependence of cluster structure
1University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
Physical Review Letters
|May 1, 2001
Summary
Vibrational entropy significantly influences cluster structures. Structural phase diagrams reveal how cluster shape changes with size and temperature in rare gas and metal clusters.
Area of Science:
- Physical Chemistry
- Materials Science
- Computational Chemistry
Background:
- The equilibrium structure of atomic and molecular clusters is fundamental to understanding their properties.
- Traditional studies often focus on energy minimization, potentially overlooking entropic effects.
Purpose of the Study:
- To investigate the role of vibrational entropy in determining the equilibrium structures of atomic clusters.
- To construct comprehensive structural phase diagrams for clusters.
Main Methods:
- Development and application of computational methods to calculate vibrational properties.
- Construction of structural phase diagrams based on size and temperature.
- Analysis of rare gas and metal cluster systems.
Main Results:
- Vibrational entropy is shown to be a critical factor in dictating cluster equilibrium structures.
- Structural phase diagrams illustrate clear dependencies of cluster geometry on size and temperature.
- The findings are validated for representative rare gas and metal clusters.
Conclusions:
- Entropic contributions are essential for accurate predictions of cluster structures.
- Structural phase diagrams provide valuable insights into cluster behavior across different conditions.
- This work advances the understanding of cluster thermodynamics and structural evolution.
Related Concept Videos
02:54Trends in Lattice Energy: Ion Size and Charge
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
02:39Entropy
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
01:10Entropy Change in Reversible Processes
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
01:20Entropy and the Second Law of Thermodynamics
The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
01:26Entropy and the Second Law of Thermodynamics
Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
01:21Entropy Changes Accompanying Specific Processes
Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...