Related Experiment Video
Updated: May 13, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Hill's small systems nanothermodynamics: a simple macromolecular partition problem with a statistical perspective
1Department of Applied Mathematics, University of Washington, Seattle, WA 98195-2420 USA.
Journal of Biological Physics
|March 2, 2013
Summary
This study clarifies nanothermodynamics for small systems by linking chemical potentials to system size. It shows differences arise from equilibrium re-partitioning and system fluctuations, enhancing understanding of statistical mechanics.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Biophysics
Background:
- T.L. Hill's nanothermodynamics describes thermodynamics in small systems.
- Biological macromolecules partition between bulk solution and membranes.
- Understanding these interactions is crucial for molecular behavior.
Purpose of the Study:
- To investigate T.L. Hill's phenomenological nanothermodynamics for small systems.
- To derive nanothermodynamic potentials from standard statistical mechanics.
- To clarify the relationship between nanothermodynamics and statistical mechanics.
Main Methods:
- Utilized a simple model of biological macromolecules partitioning between bulk solution and membrane.
- Introduced a system size-dependent equilibrium constant for the partition.
- Employed standard Gibbsian equilibrium statistical mechanics for computations.
Main Results:
- Derived Hill's differential and integral chemical potentials from statistical mechanics.
- Demonstrated that the difference in potentials relates to equilibrium re-partitioning upon size change.
- Linked potential differences to system fluctuations and inhomogeneity.
Conclusions:
- Provided a clearer understanding of nanothermodynamics for small systems.
- Established a logical connection between nanothermodynamics and statistical mechanics.
- Explained nanothermodynamic phenomena through equilibrium statistical mechanics principles.
More Related Videos
Related Concept Videos
01:20Maxwell-Boltzmann Distribution: Problem Solving
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
01:06Thermodynamic Systems
A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
Consider an example of tea boiling in a kettle. The tea and...
Consider an example of tea boiling in a kettle. The tea and...
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
02:39Entropy
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...
01:14Extraction: Partition and Distribution Coefficients
The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an organic...
For extracting a solute from an aqueous phase into an organic...
01:24System, Surroundings, and State
Thermodynamics studies the relationship between heat, work, temperature, and energy. A key concept in this field is a "system," the macroscopic part of the universe under observation. Systems can interact with their surroundings, leading to three types: open, closed, and isolated systems.Open systems permit the exchange of both matter and energy with their surroundings, like a boiling pot of water.In contrast, closed systems only allow the transfer of energy, restricting the movement of matter...