Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Maxwell's Thermodynamic Relations01:23

Maxwell's Thermodynamic Relations

4.7K
Maxwell's thermodynamic relations are very useful in solving problems in thermodynamics. Each of Maxwell's relations relates a partial differential between quantities that can be hard to measure experimentally to a partial differential between quantities that can be easily measured. These relations are a set of equations derivable from the symmetry of the second derivatives and the thermodynamic potentials.
All thermodynamic potentials are exact differentials. Therefore, their second-order...
4.7K
Third Law of Thermodynamics02:38

Third Law of Thermodynamics

22.2K
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.
22.2K
Statements of the Second Law of Thermodynamics01:15

Statements of the Second Law of Thermodynamics

5.1K
The second law of thermodynamics can be stated in several different ways, and all of them can be shown to imply the others. The Clausius’ statement of the second law of thermodynamics is based on the irreversibility of spontaneous heat flow. It states that heat will not flow from the colder body to the hotter body unless some other process is involved. Additionally, as per the Kelvin’s statement, it is impossible to convert the heat from a single source into work without any other...
5.1K
Thermodynamic Potentials01:26

Thermodynamic Potentials

1.7K
Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
1.7K
The Carnot Cycle01:30

The Carnot Cycle

4.3K
Converting work to heat is an irreversible process, and the purpose of a heat engine is to reverse the effect partially. Heat engines aim to increase the efficiency of the reversal, that is, maximize the work retrieved from heat. If the efficiency of a heat engine were 100%, it would imply reversing the process completely without introducing any other effect. Thus, it would violate the second law of thermodynamics.
What could be the theoretical limit to the efficiency of a heat engine? The...
4.3K
Toughness and Hardness of Aggregate01:22

Toughness and Hardness of Aggregate

677
Toughness and hardness are critical properties of aggregate materials used in concrete, particularly on pavement surfaces and industrial flooring subjected to heavy loads. Toughness is defined as the aggregate's resistance to failure by impact and is measured by the aggregate impact value (AIV). For this, the aggregate impact value test is performed, wherein the impact is delivered by a standard hammer, which falls freely under its own weight onto the aggregates. The aggregates fragment in...
677

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Constrained Multipole Moment Density Functional Theory for the Frozen Contribution in Non-Covalent Complexes.

Journal of chemical theory and computation·2026
Same author

Molecular interactions of cinnamyl and quinoxaline derivatives with Bcl-2 antiapoptotic proteins: a computational study.

Organic & biomolecular chemistry·2026
Same author

The interlocking process in molecular machines explained by a combined approach: the nudged elastic band method and machine learning potential.

Chemical science·2026
Same author

Impact of N-terminal acetylation on Cu(I) coordination by alpha synuclein protein.

Journal of inorganic biochemistry·2026
Same author

Benchmarking CuₙO (n = 1, 2) complexes via ab initio methods: structural, electronic, and thermodynamic insights with biochemical relevance.

Journal of molecular modeling·2025
Same author

Computationally Efficient Yet Quantitatively Accurate Scaled MP2 Protocols for the Prediction of Weak Interaction Energies in Complex Biological Systems.

ACS omega·2025

Related Experiment Video

Updated: Feb 24, 2026

Quantitative Hardness Measurement by Instrumented AFM-indentation
08:21

Quantitative Hardness Measurement by Instrumented AFM-indentation

Published on: November 22, 2016

10.3K

Thermodynamic hardness and the maximum hardness principle.

Marco Franco-Pérez1, José L Gázquez1, Paul W Ayers2

  • 1Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Ciudad de México 09340, Mexico.

The Journal of Chemical Physics
|August 24, 2017
PubMed
Summary

A new thermodynamic hardness definition measures charge transfer propensity. This temperature-dependent model, proportional to T⁻¹(I-A) at zero fractional charge, avoids Dirac delta functions and links to minimum softness principles.

More Related Videos

Author Spotlight: Establishing an Accurate Microhardness Testing Protocol for Craniofacial Tissues
06:16

Author Spotlight: Establishing an Accurate Microhardness Testing Protocol for Craniofacial Tissues

Published on: April 26, 2024

1.3K
Author Spotlight: Advanced Techniques for Characterizing Tissue Mineralization in Bone Regeneration Research
07:29

Author Spotlight: Advanced Techniques for Characterizing Tissue Mineralization in Bone Regeneration Research

Published on: September 27, 2024

1.3K

Related Experiment Videos

Last Updated: Feb 24, 2026

Quantitative Hardness Measurement by Instrumented AFM-indentation
08:21

Quantitative Hardness Measurement by Instrumented AFM-indentation

Published on: November 22, 2016

10.3K
Author Spotlight: Establishing an Accurate Microhardness Testing Protocol for Craniofacial Tissues
06:16

Author Spotlight: Establishing an Accurate Microhardness Testing Protocol for Craniofacial Tissues

Published on: April 26, 2024

1.3K
Author Spotlight: Advanced Techniques for Characterizing Tissue Mineralization in Bone Regeneration Research
07:29

Author Spotlight: Advanced Techniques for Characterizing Tissue Mineralization in Bone Regeneration Research

Published on: September 27, 2024

1.3K

Area of Science:

  • Quantum Chemistry
  • Chemical Physics
  • Materials Science

Background:

  • The concept of chemical hardness is crucial for understanding chemical reactivity and stability.
  • Existing definitions of hardness often involve approximations or discontinuities, particularly for fractional electron numbers.

Purpose of the Study:

  • To propose an alternative definition of thermodynamic hardness within the grand canonical ensemble formalism.
  • To investigate the temperature dependence and implications of this new hardness definition.
  • To establish a link between thermodynamic hardness, fractional charge, and chemical stability principles.

Main Methods:

  • Derivation of thermodynamic hardness using the grand canonical ensemble formalism.
  • Analysis of the partial derivative of electronic chemical potential with respect to the thermodynamic chemical potential.
  • Application of the three-state ensemble model to analyze temperature-dependent hardness.

Main Results:

  • The proposed thermodynamic hardness is temperature-dependent and measures charge transfer propensity.
  • At zero fractional charge and low temperatures, hardness is proportional to T⁻¹(I-A), where I is ionization potential and A is electron affinity.
  • The new definition avoids the Dirac delta function, yielding near-zero hardness for non-zero fractional charges.

Conclusions:

  • The thermodynamic hardness provides meaningful insights into the hardness properties of chemical species with integer or fractional electron numbers.
  • This definition establishes a connection between maximum hardness and the minimum softness principle.
  • Both principles are fundamentally related to conditions of minimum fractional charge and maximum system stability.