Modeling adsorption processes on the core-shell-like polymer structures: star and comb topologies

TL;DR

The study models coagulation-flocculation and heavy-metal chelation as adsorption of obstacles on core-shell-like polymers, comparing star-like ($d_c=0$) and comb-like ($d_c=1$) topologies across varying branch counts $f$, branch lengths $N$, and separations $S$ using a 3D lattice PERM growth framework. It analyzes two obstacle regimes—immobilized and diffusive—and evaluates adsorption capacity ${ar{n}_a}$, adsorption bonds ${ar{n}_ ext{bond}}$, and bridging effects via ${ar{n}_s}$, showing that comb-like architectures generally maximize adsorption capacity while star-like structures maximize adsorption strength, with these effects amplified by branch separation $S$. The results explain how branching geometry and crowding alter accessibility and bonding, and reveal that diffusion dynamics favor more extended comb-like structures for faster adsorption; bridging and gyration-radius correlations further illuminate the trade-offs. Practically, the findings guide design of branched adsorbents, suggesting that hybrid/dendritic architectures may synergistically combine high capacity and strong binding for efficient pollutant capture and metal chelation.

Abstract

Coagulation-flocculation of pollutants and chelation of heavy metal ions are two widely used techniques in wastewater purification. Despite the differences between their respective mechanisms and inherent length scales, they bear much similarity on a larger scale, and can both be treated as adsorption of obstacles on a polymer structure. In this regime, their adsorbing efficiency is predominantly affected by conformation statistics of involved polymers, and this approach has been used in our previous studies based on lattice polymer model for a linear polymer adsorbent. There is a strong experimental evidence that branched adsorbents are more efficient than their linear counterparts. In this study we focus on two simplest representatives of the core-shell branched architectures: the star-like (with zero-dimensional point-like core) and comb-like polymers (with one-dimensional rigid core) with various number of branches, $f$, branch lengths, $N$, and branches separations, $S$ (for the case of comb-like structure). The polymers are grown on a lattice using the Monte Carlo simulations with the pruned-enriched Rosenbluth algorithm. The quantitative estimates for adsorption capacity in terms of adsorbed obstacles per monomer and the average number of bonds per adsorbed particle (average adsorption strength) have been evaluated in a wide range of parameters $f$, $N$, and $S$. Both the case of implicit diffusion of obstacles (with averaging over different arrangements of immobilized obstacles) and explicit diffusion of obstacles (allowing to study dynamics of adsorption process) have been analyzed. We found that comb-like polymers display the higher adsorption capacity but lower adsorption strength, comparing to the star-like polymers, and these effects are more pronounced with increasing branches separations $S$.

Figures (14)

• Figure 1: Two simplest core-shell-like structures of star- and comb-like polymers considered in this study.
• Figure 2: A few examples of polymeric architectures of the same molecular weight, given by the number of adsorbing monomers, $N_\mathrm{total}$, as considered throughout this study. Star- and comb-like architectures with $f=2-4$ ligands are shown, separation between ligands along a backbone of the latter is denoted by $S$.
• Figure 3: Snapshots of two core-shell-like structures: $d_c=0$, $f=3$ (top) and $d_c=1,f=3,S=4$ (bottom) immersed into the lattice with obstacles (as shown by small blue dots). The lattice sites belonging to the cores are shown with red symbols, while those occupied by monomers are displayed in green.
• Figure 4: a) Average number of "free" nearest neighbor sites around the monomers with the topological distance $n$ from the branching point of star-like structures (at $N=6$). b) The total accessibility ${\overline {n_{\mathrm{free}}}}$ of a star-like structure as a function of its total molecular weight at different $f$.
• Figure 5: a) Average number of "free" nearest neighbor sites around monomer with position $n$ along the single branch of comb-like structures with $N=6$, $S=4$. b) The total accessibility ${\overline {n_{\mathrm{free}}}}$ of the comb-like structure with $S=4$ as function of its total molecular weight at different $f$.