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Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
Published on: August 13, 2019
Reconciling lattice and continuum models for polymers at interfaces
1Laboratory of Physical and Colloid Science, Wageningen University, 6703 HB Wageningen, The Netherlands.
The Journal of Chemical Physics
|April 10, 2012
Summary
This study establishes a quantitative link between lattice and continuum polymer models. It reveals that finite segment volume is crucial for adsorption, while depletion models are generally valid for non-ideal chains across various conditions.
Area of Science:
- Polymer Physics
- Surface Science
- Statistical Mechanics
Background:
- Lattice and continuum models for polymers at interfaces are theoretically equivalent but require a quantitative relation for comparison.
- Previous comparisons were limited to ideal chains with zero segment volume in dilute solutions.
- Existing models fail to account for volume filling in real chains, leading to unrealistic predictions for strong adsorption.
Purpose of the Study:
- To establish a quantitative relationship between the inverse extrapolation length (c) from continuum theories and the lattice adsorption parameter (Δχ(s)).
- To extend the comparison to real polymer chains with finite segment volume at finite concentrations, considering both good and theta solvents.
- To provide a unified analytical framework for describing polymer adsorption and depletion phenomena.
Main Methods:
- Analytical extension of existing models to include finite segment volume and concentration effects.
- Matching boundary conditions between lattice and continuum models.
- Comparison with numerical self-consistent field (SCF) calculations for validation.
Main Results:
- For depletion, the ideal-chain relation Δχ(s) = ln(1 + c/5) is found to be generally valid for non-ideal chains, regardless of concentration, chain length, or solvency.
- Depletion profiles are accurately described using two length scales: depletion thickness (δ) and proximal length (p), which depend on chain properties and interaction parameters.
- For adsorption, finite volume filling limits the inverse extrapolation length to c ≈ -0.5, consistent with numerical SCF results.
Conclusions:
- The derived relation Δχ(s)(c) provides a crucial quantitative bridge between continuum and lattice polymer theories.
- This enables the application of analytical continuum results to lattice chains, facilitating the study of adsorption and mechanical desorption.
- The study offers practical methods for experimentally determining polymer-surface interaction parameters.
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