Perimeter shell properties of branched polymer adsorbents in various conformational states

Abstract

The structural accessibility and perimeter shell properties of branched macromolecules are studied using Monte Carlo simulations on a simple cubic lattice. Constituent polymer chains of these macromolecules are constructed in an algorithmic way as: a set of collinear monomers; a self-avoiding walk (SAW); tigthly packed monomers. These mimic the ground states for a rigid rod, flexible chain, and collapsed chain conformational states, respectively. We analyzed the set of observables that are related to adsorption, such as perimeter shell size (number of available sites for particle adsorption) per monomer $\langle \bar{n}_a \rangle$, mean coordination number of perimeter shell $\langle n_{\rm bond} \rangle$ (average number of contacts per adsorbed particle), and coordination accessibility per monomer $\langle \bar{n}_s \rangle$. Our results demonstrate that branching reduces the perimeter shell size while it increases mean coordination number of perimeter shell across all conformational states, due to higher local monomer density near branching cores and formation of shared adsorption sites or microcages. Stiff extended structures yield the highest values for $\langle \bar{n}_a \rangle$ (approaching $4$ in the limit of long chains), whereas the flexible ones provide the largest values for $\langle n_{\rm bond} \rangle$. We can note that the collinearity of monomers in constituent chains works in the same direction as reduction of branching ($\langle \bar{n}_a \rangle$ grows), whereas the { tight packing of them} -- in the same direction as the increase of branching ($\langle \bar{n}_a \rangle$ decreases)