Hierarchical Model of Weak Polyelectrolytes with Ionization and Conformation Consistency

Abstract

Conventional models of weak polyelectrolytes are formulated in terms of either an average degree of ionization or a rigid polymer conformation. While the decoupling of segmentlevel ionization and polymer structure simplifies the theoretical procedure and is beneficial from a computational perspective, it misses intrachain correlations (i.e., interactions beyond adjacent monomers) that are important for systems at a low polymer concentration with strong electrostatic interactions. In this work, we propose a hierarchical method that incorporates the liquid-state theories with the site-binding model to account for the effects of the local ionic environment on both inter-and intrachain correlations. A wormlike-chain model is introduced to describe the coupling of polymer conformation and monomeric ionization with the long-range electrostatic interactions accounted for by using the Gibbs−Bogoliubov variational principle. Through an extensive comparison of the theoretical predictions with experimental titration curves for poly(acrylic acid) in different alkali chloride solutions, we demonstrate that the hierarchical model is able to quantify the charging behavior of weak polyelectrolytes over a broad range of solution conditions.

Exploration of Phase Behavior in Asymmetric Semiflexible Polyelectrolyte Mixtures Using Polymer Field Theory

“…The WLC model presents an accurate depiction of semiflexible polymers and serves as a comprehensive model that captures multiscale behavior across length scales relevant to polyelectrolyte solution thermodynamics. Incorporating the WLC model within the RPA framework facilitates a more precise understanding of how polymer structure and interactions influence the phase behavior in polyelectrolyte systems . In our previous paper, we confirm that the Gaussian chain model overpredicts the phase separating domain for semiflexible polymers by undercounting the small length-scale fluctuation effects, which have been previously explored …”

“…Incorporating the WLC model within the RPA framework facilitates a more precise understanding of how polymer structure and interactions influence the phase behavior in polyelectrolyte systems. 60 In our previous paper, 61 we confirm that the Gaussian chain model overpredicts the phase separating domain for semiflexible polymers by undercounting the small length-scale fluctuation effects, which have been previously explored. 62 While there is an extensive research effort in understanding polyelectrolyte complex coacervation, there is also a large parameter space in which to parse.…”

Site-Specific Charge Regulation Model for Amino Acids in Aqueous Solutions

“…Thus, the apparent equilibrium constant measured in experiments is related to the average contribution of each configuration K X ( N ) ′ = false⟨ c X [ + 1 , s O , s X ] false⟩ false⟨ c X [ 0 , s O , s X ] false⟩ 1 c H + where ⟨···⟩ denotes the thermal (or Boltzmann) average (i.e., the expected value) of the quantity of interest (in this case, the concentration of the amino acid with its backbone amine group either charged or uncharged). The thermal average of the concentration is given by false⟨ c X [ s N , s O , s X ] false⟩ = c X t o t exp true{ prefix− β ∑ i μ X false( i false) H false[ s i false] − β u X ...…”

“…As discussed in our recent work for the ionization of weak polyelectrolytes, we can specify the activity coefficient γ i of the amino acid in different charge states as k normalB T nobreak0em0.25em⁡ ln nobreak0em.25em⁡ γ X [ s N , s O , s X ] = μ N e x ( s N ) + μ O e x ( s O ) + μ X e x ( s X ) − k normalB T nobreak0em0.25em⁡ ln nobreak0em.25em⁡ y X [ s N , s O , s X ] The first three terms on the right side of eq are the excess chemical potential of each segment, μ ex (i.e., the deviation from the chemical potential of species i in an ideal solution resulting from the intra- and intermolecular interactions). According to 3bAPM, the excess chemical potential can be decomposed into the contributions due to the hard-sphere repulsion (hs), electrostatic correlation (el), and solvent-mediated interactions (sw), respectively, μ i e x = μ i …”

“…Thus, the apparent equilibrium constant measured in experiments is related to the average contribution of each configuration where ⟨···⟩ denotes the thermal (or Boltzmann) average (i.e., the expected value) of the quantity of interest (in this case, the concentration of the amino acid with its backbone amine group either charged or uncharged). The thermal average of the concentration is given by where μ X ( i ) H ( s i ) = s i [pH – log K X ( i ) T ] ln 10 is the chemical binding energy, and pH = −log­[ c H + γ H + ] is the negative logarithm of the proton activity. The electrostatic pair interaction u X el is given by the direct Coulombic interaction between the segments in their respective states.…”