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Related Concept Videos

Entropy02:39

Entropy

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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...
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Entropy01:18

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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
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Entropy and Solvation02:05

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The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
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Entropy and the Second Law of Thermodynamics01:20

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

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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...
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Third Law of Thermodynamics02:38

Third Law of Thermodynamics

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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Understanding shape entropy through local dense packing.

Greg van Anders1, Daphne Klotsa1, N Khalid Ahmed1

  • 1Departments of Chemical Engineering and.

Proceedings of the National Academy of Sciences of the United States of America
|October 26, 2014
PubMed
Summary
This summary is machine-generated.

Shape-driven ordering in particle systems arises from directional entropic forces (DEFs). These forces, quantified here, are crucial for understanding self-assembly and phase behavior in anisotropic particle suspensions.

Keywords:
colloidsentropynanoparticlesself-assemblyshape

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Area of Science:

  • Colloid and materials science
  • Statistical mechanics
  • Soft matter physics

Background:

  • Entropy governs colloidal phase behavior, including ordering of anisotropic particles into complex structures.
  • Directional entropic forces (DEFs) are proposed to drive this ordering but lack rigorous definition and quantification.
  • Existing models often focus on specific interactions, leaving a unified understanding incomplete.

Purpose of the Study:

  • To quantitatively define and compute Directional Entropic Forces (DEFs) in generic anisotropic particle systems.
  • To demonstrate that DEFs are a primary driver of entropy-driven phase behavior upon particle crowding.
  • To unify the understanding of entropy-driven self-assembly and packing behavior across various particle shapes.

Main Methods:

  • Development of a quantitative definition for DEFs in generic hard particle systems.
  • Computation of DEFs for several hard particle systems using simulations.
  • Analysis of experimental systems to provide evidence for the contribution of shape-induced entropic effects to self-assembly.

Main Results:

  • DEFs were quantitatively defined and computed, found to be on the order of a few times thermal energy at ordering onset.
  • DEFs were shown to be comparable in magnitude to traditional interactions like depletion and van der Waals forces.
  • Direct quantitative evidence was provided for the role of shape-induced entropic effects in experimental self-assembly.

Conclusions:

  • Shape-driven phase behavior in anisotropic particle systems is quantitatively explained by DEFs.
  • DEFs arise from entropy maximization through optimized local particle packing, a mechanism applicable to diverse systems.
  • This work provides a unified framework for understanding entropy-driven phase behavior of arbitrary shapes, integrating classical theories.