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Updated: Apr 27, 2026
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Synthesis of Information-bearing Peptoids and their Sequence-directed Dynamic Covalent Self-assembly
Published on: February 6, 2020
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Binding polynomial in molecular self-assembly
Andrew A Mosunov1, Kristina A Rybakova1, Olga V Rogova1
1Department of Physics, Sevastopol National Technical University, Sevastopol 99053, Russia.
Summary
The binding polynomial for self-assembling identical molecules relates to the grand partition function. Under weak self-assembly conditions, it simplifies to a molecular partition function, but can be misleading otherwise.
Area of Science:
- Physical Chemistry
- Supramolecular Chemistry
- Statistical Mechanics
Background:
- The binding polynomial is a theoretical construct used to describe self-assembly processes.
- Self-assembly of identical molecular units is a fundamental process in various scientific fields.
- Understanding the relationship between binding polynomials and partition functions is crucial for accurate thermodynamic descriptions.
Purpose of the Study:
- To revisit and clarify the concept of the binding polynomial in the context of identical molecular unit self-assembly.
- To establish a direct link between the binding polynomial and the grand partition function of self-assembling systems.
- To define the conditions under which the binding polynomial accurately represents the system's molecular partition function.
Main Methods:
- Reconstruction of the binding polynomial for self-assembly of identical molecular units.
- Mathematical derivation connecting the binding polynomial to the grand partition function.
- Analysis of the binding polynomial's interpretation under varying self-assembly strengths (equilibrium constant and monomer concentration).
Main Results:
- A direct link between the binding polynomial and the grand partition function for self-assembling identical molecular units was established.
- When self-assembly is not pronounced (equilibrium constant × monomer concentration ≈ 0), the binding polynomial equals the molecular partition function.
- The binding polynomial's interpretation as a molecular partition function is valid only under specific, limited conditions.
Conclusions:
- The binding polynomial is a valid representation of the molecular partition function only in the limit of weak self-assembly.
- In cases of significant self-assembly, the concept of the binding polynomial may be misleading and requires careful interpretation.
- This work clarifies the utility and limitations of the binding polynomial in the study of molecular self-assembly.
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