Related Experiment Video
Updated: May 7, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Fluctuation-stabilized marginal networks and anomalous entropic elasticity
M Dennison1, M Sheinman, C Storm
1Department of Physics and Astronomy, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands.
Physical Review Letters
|September 17, 2013
Summary
Thermal networks of Hookean springs show unexpected rigidity below the isostatic point. This shear modulus is temperature-dependent, driven by entropic forces, revealing novel elastic properties.
Area of Science:
- Physics
- Materials Science
- Network Theory
Background:
- Mechanical systems with Hookean springs typically lose rigidity below a critical isostatic connectivity.
- Understanding the interplay between thermal fluctuations and mechanical properties is crucial for designing robust materials.
Purpose of the Study:
- To investigate the elastic properties of thermal networks of Hookean springs.
- To determine the shear modulus (G) and its temperature dependence (T) in these networks, particularly below the isostatic point.
Main Methods:
- Theoretical analysis of thermal networks composed of Hookean springs.
- Calculation of shear modulus (G) as a function of temperature (T).
- Comparison of behavior at and below the isostatic point.
Main Results:
- Thermal networks exhibit a non-zero shear modulus (G) even below the isostatic point.
- The shear modulus shows an anomalous, sublinear dependence on temperature (G ∝ T^α, with α ≈ 0.8) below the isostatic point.
- At the isostatic point, the shear modulus scales with the square root of temperature (G ∝ √T).
Conclusions:
- The observed anomalous temperature dependence of the shear modulus is entropic in origin.
- Thermal fluctuations introduce rigidity in networks that would be mechanically fragile.
- This finding has implications for the design and understanding of materials with tunable elastic properties.
More Related Videos
Related Concept Videos
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.
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...
01:21Entropy 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...
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...
01:22Elastic Strain Energy for Normal Stresses
Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
If...
If...