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Effective surface coverage of coarse-grained soft matter.

Galen T Craven1, Alexander V Popov, Rigoberto Hernandez

  • 1Center for Computational Molecular Science and Technology, School of Chemistry and Biochemistry, Georgia Institute of Technology , Atlanta, Georgia 30332-0400, United States.

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Macromolecule surface coverage is nonlinear due to overlap. New models quantify this relationship using overlap probability (δ), accurately predicting site occupancy even with soft interactions and multiple occupancies.

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Area of Science:

  • Physical Chemistry
  • Materials Science
  • Computational Modeling

Background:

  • Surface coverage of macromolecules on substrates often deviates from simple proportionality to density due to molecular overlap.
  • Understanding macromolecular interactions and their impact on surface binding is crucial for designing advanced materials and processes.

Purpose of the Study:

  • To develop analytical formulas and computational models to characterize the nonlinear relationship between macromolecule surface coverage and number density.
  • To investigate the role of overlap probability (δ) in governing macromolecular binding and surface occupancy.
  • To provide a framework for predicting surface coverage in systems with soft macromolecular interactions.

Main Methods:

  • Development of analytical formulas based on overlap probability (δ).
  • Implementation of computational models simulating macromolecular interactions with a finite bounded potential.
  • Derivation of exact transition probabilities for sequential configurations.
  • Application of a simplified mean-field (MF) expression for site fraction (ϕ) prediction.
  • Validation against simulation results for a dynamical system with multibody interactions.

Main Results:

  • The study establishes a nonlinear relationship between macromolecule surface coverage and two-dimensional number density, dependent on overlap probability (δ).
  • Soft macromolecular interactions (δ > 0) lead to multiple occupancy, reducing the fraction of occupied sites (ϕ).
  • The simplified mean-field (MF) model shows excellent agreement with exact results for predicting ϕ.
  • Both exact and MF models accurately predict results from a dynamical system simulation.

Conclusions:

  • The developed models provide a robust method for characterizing nonlinear surface coverage of coarse-grained macromolecules.
  • The overlap probability (δ) is a key parameter controlling macromolecular interactions and surface occupancy.
  • The mean-field approximation offers a computationally tractable and accurate approach for predicting surface coverage in complex systems.