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Related Concept Videos

Gibbs Free Energy02:39

Gibbs Free Energy

One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
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The free energy change for a reaction that occurs under the standard conditions of 1 bar pressure and at 298 K is called the standard free energy change. Since free energy is a state function, its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the...
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How can we compare the energy that releases from one reaction to that of another reaction? We use a measurement of free energy to quantitate these energy transfers. Scientists call this free energy Gibbs free energy (abbreviated with the letter G) after Josiah Willard Gibbs, the scientist who developed the measurement. According to the second law of thermodynamics, all energy transfers involve losing some energy in an unusable form such as heat, resulting in entropy. Gibbs free energy...
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The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).
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Free Energy and Equilibrium00:55

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Realistic Membrane Modeling Using Complex Lipid Mixtures in Simulation Studies
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Free energy evaluation in field-theoretic polymer simulations.

Erin M Lennon1, Kirill Katsov, Glenn H Fredrickson

  • 1Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA.

Physical Review Letters
|October 15, 2008
PubMed
Summary

We developed a new thermodynamic integration method for free energy calculations in polymer simulations. This approach accurately models phase transitions, like the one observed in diblock copolymer melts.

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Area of Science:

  • Computational physics
  • Polymer science
  • Statistical mechanics

Background:

  • Field-theoretic simulations are crucial for understanding polymer behavior.
  • Accurate free energy calculations are essential for predicting phase transitions.
  • Existing methods face challenges with the sign problem in polymer field theories.

Purpose of the Study:

  • To present a novel thermodynamic integration method for free energy evaluation.
  • To apply this method to field-theoretic simulations of classical fluids and polymers.
  • To address the sign problem in polymer field theories.

Main Methods:

  • Thermodynamic integration using an Einstein crystal reference state.
  • Complex Langevin sampling for computing thermodynamic averages.
  • Application to a diblock copolymer melt system.

Main Results:

  • The method is applicable to both ordered and disordered phases.
  • Complex Langevin sampling effectively overcomes the sign problem.
  • The method successfully demonstrates the transition between cubic gyroid and disordered phases in a diblock copolymer melt.

Conclusions:

  • The presented method offers a robust approach for free energy calculations in polymer field-theoretic simulations.
  • This technique facilitates the study of experimentally observed phase transitions.
  • The method is a valuable tool for advancing the understanding of polymer self-assembly.