Thermodynamics of Association in Interacting Charged Polymers

Ghosh, Souradeep (2024) Thermodynamics of Association in Interacting Charged Polymers. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Souradeep Ghosh (18RS089)) 18RS089.pdf - Submitted Version Restricted to Repository staff only Download (5MB)

Abstract

This thesis presents a theoretical analysis of polyelectrolyte chains in dilute solutions and their interactions with other flexible polymer chains. The first part of the thesis focuses on the size and charge of a single polyelectrolyte chain in dilute solutions, with particular emphasis on the effect of excluded volume of counterions on the chain conformation. A modified Debye-Huckel approach is utilized to investigate the behavior of point-sized and bulky counterions. The results show that the excluded volume of bulky counterions prevents the collapse of the chain and leads to a swollen chain conformation, with the gyration radius of the PE chain complexed with bulky counterions larger than that of its uncharged analog. The second part of the thesis presents a comprehensive theoretical framework for investigating the interactions between two flexible polymer chains, specifically polyelectrolytes. The free energy of the system is calculated by utilizing a center-of-mass separation approach, taking into account the position-dependent mutual interactions and conformations of the individual chains. This approach provides insight into the position-dependent local dielectricity of the system as the two PEs undergo mutual overlap, emphasizing the fundamental differences between the two-body interactions of soft, interpenetrating macromolecules and those of rigid particles. The final part of the thesis presents a theoretical framework to analyze the total charge and size of the complex and thermodynamics of the complexation of two symmetric, ionizable, oppositely charged polyelectrolyte chains. The free energy of the system is derived using a variational extremization of the Edwards’ Hamiltonian for the two-chain system that explicitly accounts for the screened Coulomb and non-electrostatic interactions among monomers within individual chains and between two chains. The results show that the thermodynamic drive for complexation increases with the charge density of the symmetric chains and is maximum for symmetric chain lengths for fully ionizable chains. The interplay of the most significant thermodynamic effects - the free ion entropy and ion pair enthalpy - marks a crossover Coulomb strength, whereas regimes of enthalpy- and entropy-driven complexation are found, respectively, for low and high Coulomb strengths.

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