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Updated: May 9, 2026

Atomic Layer Deposition of Vanadium Dioxide and a Temperature-dependent Optical Model
11:10

Atomic Layer Deposition of Vanadium Dioxide and a Temperature-dependent Optical Model

Published on: May 23, 2018

Self-consistent analytical solutions to the Voorn-Overbeek model.

Marco Di Mambro1, Thomas C T Michaels1

  • 1Department of Biology, Institute of Biochemistry, ETH Zurich, Otto-Stern-Weg 3, 8093 Zurich, Switzerland and Bringing Materials to Life Initiative, ETH Zurich, Zurich, Switzerland.

The Journal of Chemical Physics
|May 8, 2026
PubMed
Summary
This summary is machine-generated.

Researchers developed an analytical solution for complex coacervation, a process driven by electrostatic interactions in charged polymers. This provides accurate phase boundary predictions, simplifying the study of liquid-liquid phase separation in biopolymers.

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Last Updated: May 9, 2026

Atomic Layer Deposition of Vanadium Dioxide and a Temperature-dependent Optical Model
11:10

Atomic Layer Deposition of Vanadium Dioxide and a Temperature-dependent Optical Model

Published on: May 23, 2018

Area of Science:

  • Physical Chemistry
  • Polymer Science
  • Biophysics

Background:

  • Complex coacervation, driven by electrostatic interactions between oppositely charged macromolecules, is crucial for the phase behavior of charged polymers like nucleic acids and intrinsically disordered proteins.
  • The Voorn-Overbeek model offers a fundamental mean-field description, integrating polymer mixing entropy and Debye-Hückel level electrostatics.
  • Traditional analysis of the Voorn-Overbeek model for phase coexistence relies on numerical methods or approximations due to the lack of closed-form solutions.

Purpose of the Study:

  • To derive a self-consistent analytical solution for the binodal concentrations in the simplest Voorn-Overbeek model.
  • To provide explicit analytical expressions for phase boundaries in systems of two oppositely charged polymers in a neutral solvent.
  • To establish an analytically tractable framework for studying complex coacervation.

Main Methods:

  • Reformulating phase coexistence conditions as a fixed-point problem.
  • Deriving self-consistent analytical solutions for binodal concentrations.
  • Applying Debye-Hückel theory for electrostatic interactions under local electroneutrality.

Main Results:

  • Obtained explicit analytical expressions for phase boundaries of the simplest Voorn-Overbeek model.
  • Demonstrated accuracy of the derived expressions across the entire phase-separated regime.
  • Developed a self-consistent analytical solution for binodal concentrations.

Conclusions:

  • The derived analytical solution provides an accessible framework for understanding complex coacervation.
  • This work simplifies the study of liquid-liquid phase separation in charged polymer systems.
  • The findings lay the groundwork for future research incorporating more complex electrostatic and compositional factors.