Square-Gradient Model for Inhomogeneous Systems: From Simple Fluids to Microemulsions, Polymer Blends and Electronic Structure

  • Jianzhong WuEmail author
Part of the Molecular Modeling and Simulation book series (MMAS)


The square-gradient approximation for describing the thermodynamic and structural properties of inhomogeneous systems was first proposed many years ago by van der Waals in his celebrated work on capillarity. Because it entails no a priori knowledge on inter-particle interactions, the mathematical procedure is generically applicable to a wide variety of seemingly unrelated phenomena, regardless of whether the system contains classical or quantum particles. This chapter presents a few common concepts underlying different incarnations of the square-gradient model for simple fluids, microemulsions, polymer blends as well as electronic systems. Pedagogical examples are given to illustrate its applications to describing the physical properties of various inhomogeneous systems including surface tensions, x-ray scattering from microemulsions, and spinodal decomposition in polymer blends. By emphasizing similar ideas used in different subfields of statistical mechanics, the tutorial material may help better understand connections among similar theoretical methods established in different contexts.


Monte Carlo Vertex Function Inhomogeneous System Uniform System Helmholtz Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author is indebted to Dr. Liu Yu for comments and suggestions. For the financial support, we are grateful to the U.S. National Science Foundation (NSF-CBET-1404046).


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Copyright information

© Springer Science+Business Media Singapore 2017

Authors and Affiliations

  1. 1.Department of Chemical and Environmental Engineering and Department of MathematicsUniversity of CaliforniaRiversideUSA

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