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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...
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Related Experiment Video

Updated: Aug 30, 2025

Two-way Valorization of Blast Furnace Slag: Synthesis of Precipitated Calcium Carbonate and Zeolitic Heavy Metal Adsorbent
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Adsorbate-adsorbent potential energy function from second virial coefficient data: a non-linear Hopfield Neural

Felipe Silva Carvalho1, João Pedro Braga2, Márcio Oliveira Alves3

  • 1Departamento de Química - ICEx, Universidade Federal de Minas Gerais, 31270-901, Belo Horizonte, MG, Brazil.

Journal of Molecular Modeling
|September 2, 2022
PubMed
Summary
This summary is machine-generated.

The Hopfield Neural Network effectively retrieves potential energy parameters from adsorption data. This robust method accurately fits experimental results, even with noisy datasets.

Keywords:
AdsorptionHopfield neural networkIll-posed inverse problemsSecond virial coefficient

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Area of Science:

  • Physical Chemistry
  • Computational Chemistry
  • Materials Science

Background:

  • Hopfield Neural Networks (HNN) are adept at solving ill-posed inverse problems.
  • Potential energy functions are crucial for understanding adsorbate-adsorbent interactions.
  • Adsorption data relates to the second virial coefficient and potential energy via integral equations.

Purpose of the Study:

  • To apply a non-linear Hopfield Neural Network approach for empirical potential energy function parameter retrieval.
  • To determine parameters governing adsorbate-adsorbent interactions from experimental adsorption data.

Main Methods:

  • Utilizing a non-linear Hopfield Neural Network to solve the inverse problem.
  • Relating adsorption data to the second virial coefficient and potential energy function through integral equations.
  • Validating the method with simulated datasets, including those with added noise.

Main Results:

  • The Hopfield Neural Network successfully retrieved empirical parameters for the potential energy function.
  • The method demonstrated robustness and accuracy when applied to simulated data with and without noise.
  • Experimental adsorption data for propionitrile on activated carbon was effectively analyzed.

Conclusions:

  • The non-linear Hopfield Neural Network is a robust and effective tool for determining potential energy parameters from adsorption data.
  • This computational approach offers a reliable method for analyzing experimental adsorption phenomena.
  • The study validates the HNN's capability in addressing complex inverse problems in physical chemistry.