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Gibbs Free Energy

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...

Free Energy

Free Energy

Free energy—abbreviated as G for the scientist Gibbs who discovered it—is a measurement of useful energy that can be extracted from a reaction to do work. It is the energy in a chemical reaction that is available after entropy is accounted for. Reactions that take in energy are considered endergonic and reactions that release energy are exergonic. Plants carry out endergonic reactions by taking in sunlight and carbon dioxide to produce glucose and oxygen. Animals, in turn, break down the...

Gibbs Free Energy and Thermodynamic Favorability

Gibbs Free Energy and Thermodynamic Favorability

The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:

Free Energy Changes for Nonstandard States

Free Energy Changes for Nonstandard States

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:

Coupled Reactions

Coupled Reactions

Cellular processes such as building and breaking down complex molecules occur through stepwise chemical reactions. Some of these chemical reactions are spontaneous and release energy, whereas others require energy to proceed. Cells often couple the energy-releasing reaction with the energy-requiring one to carry out important cell functions.
Energy in adenosine triphosphate or ATP molecules is easily accessible to do work. ATP powers the majority of energy-requiring cellular reactions. Cells...

An Introduction to Free Energy

An Introduction to Free Energy

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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Studying DNA Looping by Single-Molecule FRET

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Free energy of multiple overlapping chains.

Katherine Klymko¹, Angelo Cacciuto

¹Department of Chemistry, Columbia University, New York, New York 10027, USA.

Physical Review Letters

|January 17, 2012

Summary

Pair additivity is often inaccurate for soft polymer nanoparticles. Simulations reveal its inadequacy increases with chain density, necessitating a revised scaling theory for complex polymer interactions.

Area of Science:

Polymer physics
Soft matter science
Nanoparticle interactions

Background:

Pair additivity is a common approximation for describing interactions in complex systems.
Its accuracy for soft polymer-based nanoparticles, especially under high density, is not well understood.

Purpose of the Study:

To quantitatively assess the accuracy of pair additivity in describing interactions between soft polymer-based nanoparticles.
To investigate the influence of chain number and length on the effectiveness of pair additivity.
To develop a more accurate theoretical framework for these interactions.

Main Methods:

Numerical simulations were employed to compute the free energy cost of overlapping polymer chains.
The study analyzed the deviation from pair additivity as a function of chain density.

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A crossover phenomenon from isotropic to star-polymer behavior was identified and characterized.

Main Results:

Pair additivity becomes increasingly inadequate as the density of polymer chains in the overlapping region rises.
Existing scaling theories based on polymer confinement offer only partial explanations.
A novel isotropic to star-polymer crossover was observed for a large number of chains.

Conclusions:

Pair additivity is a limited approximation for soft polymer nanoparticle interactions under dense conditions.
A revised scaling theory is proposed to better describe the complex physics, including the observed crossover.
Understanding these interactions is crucial for designing and predicting the behavior of soft nanomaterials.