Responsive Properties of Grafted Polyanion Chains: Effects of Dispersion Interaction and Salt

Abstract

We study thermodynamic responsive properties of a grafted polyanion layer on a planar surface by using statistical density-functional theory. The structure and electrostatics of the grafted layer are explored by varying the strength (ε) of dispersion interaction (DPI) and salt concentration (ρ salt ). The brush behaviors are determined by the competition and interplay between the DPI and the screening effect of small ions (counterions and salt ions). The DPI has a positive contribution to brush swelling, while the doping salt has either a positive or negative contribution depending on the concentration. At low surface grafting density (ρ g ), the DPI plays a prominent role at low ρ salt ; the screening effect dominates the behavior only at high ρ salt . At high ρ g , the screening effect is always important because the counterion density inside the brush is high; the electrostatic interaction is weak in most cases so that the brush layer is sensitive to the DPI. Both structure and electrostatics of the grafted layer can be regulated and controlled by varying ε and ρ salt . These results provide useful predictions and a fundamental understanding for the thermodynamic properties in a polyelectrolyte-grafted surface.

Phase Behavior of Partially Charged Polyelectrolyte Solutions with Salt: A Theoretical Study

“…To include calcium-binding interactions in the model, we introduced a modified square-well potential for the Ca 2 + and − R-CO 2 pairs, which was then incorporated into the liquid-state theory by an extra Helmholtz free energy from the perturbed-chain statistical associating fluid theory (PC-SAFT), [46,47] following the recent work by Xu and co-workers. [50,51] The system Helmholtz free energy density, f, can generally be written as the sum of an ideal contribution (f id ) and an excess contribution (f ex ) [33] :…”

“…To include calcium‐binding interactions in the model, we introduced a modified square‐well potential for the Ca 2 + and pairs, which was then incorporated into the liquid‐state theory by an extra Helmholtz free energy from the perturbed‐chain statistical associating fluid theory (PC‐SAFT), [ 46,47 ] following the recent work by Xu and co‐workers. [ 50,51 ]…”

Interfacial Microstructure of Neutral and Charged Polymer Brushes: A Density Functional Theory Study

“…In the last few decades, PDFT has been used to study grafted PBs. [30][31][32][33][34][35][36][37] However, the significant deviations in the interfacial density distributions between PDFT and simulations are found in the literature. 38 The accurate and reliable predictions of PDFT leave much to be desired in the relevant thermodynamic and structural properties (e.g., the capacitance of supercapacitors).…”

Phase Behavior of Ion-Containing Polymers in Polar Solvents: Predictions from a Liquid-State Theory with Local Short-Range Interactions

“…Such an LS theory has also been applied to study the phase behaviors of concentration-asymmetric mixtures of polycation and polyanion solutions and has also revealed a wealth of interesting and complex phase separations scenarios [57]. Classical density functional theories (cDFT) for charged polymers have also been developed based on a similar framework and have found wide applications in many polyelectrolyte systems [58][59][60][61][62][63][64][65]. A complete theoretical understanding of the solution phase behaviors of charged polymers, however, remains challenging, not only because of the multi-component nature of the system (which, in the simplest case of a salt-free solution of fully charged polymers, consists of solvent, counterions, and charged polymers), but also because of the delicate interplay among various factors, including the translational entropy of each component, excluded volume interactions, chain connectivity, and more importantly the long-range electrostatic interactions.…”

“…Increasing the length of the neutral side chains shrinks the phase-separated region, while increasing the acid-to-ether ratio expands the phase-separated region. A combination of PC-SAFT and cDFT for charged polymers has found applications in studies of the thermodynamic responsive properties of a grafted polyanion layer on a planar surface [63] and effects of polyelectrolyte surface coating on the energy storage performance in supercapacitors [64].…”