Coupling of isotropic and directional interactions and its effect on phase separation and self-assembly

Abstract

The interactions of molecules and particles in solution often involve an interplay between isotropic and highly directional interactions that lead to a mutual coupling of phase separation and self-assembly. This situation arises, for example, in proteins interacting through hydrophobic and charged patch regions on their surface and in nanoparticles with grafted polymer chains, such as DNA. As a minimal model of complex fluids exhibiting this interaction coupling, we investigate spherical particles having an isotropic interaction and a constellation of five attractive patches on the particle’s surface. Monte Carlo simulations and mean-field calculations of the phase boundaries of this model depend strongly on the relative strength of the isotropic and patch potentials, where we surprisingly find that analytic mean-field predictions become increasingly accurate as the directional interactions become increasingly predominant. We quantitatively account for this effect by noting that the effective interaction range increases with increasing relative directional to isotropic interaction strength. We also identify thermodynamic transition lines associated with self-assembly, extract the entropy and energy of association, and characterize the resulting cluster properties obtained from simulations using percolation scaling theory and Flory-Stockmayer mean-field theory. We find that the fractal dimension and cluster size distribution are consistent with those of lattice animals, i.e., randomly branched polymers swollen by excluded volume interactions. We also identify a universal functional form for the average molecular weight and a nearly universal functional form for a scaling parameter characterizing the cluster size distribution. Since the formation of branched clusters at equilibrium is a common phenomenon in nature, we detail how our analysis can be used in experimental characterization of such associating fluids.

Self-assembly of polymer-grafted nanoparticles in solvent-free conditions

“…Typical examples of equilibrium formation of clusters can be found in: mixtures of star and linear chains, 67 dendrimers, 68 ring polymers 69–71 and microgels. 72,73,74–78 Equilibrium polymerization was previously observed by GNPs in a solvent, i.e., simulations of grafted poly(ethylene oxide) (PEO) chains in aqueous solutions. 22,79 …”

Universal interrelation between measures of particle and polymer size

“…Both types of non-equilibrium cluster are rather spherical on average. In (c), we show lattice animals or swollen branched equilibrium polymers from the recent study of Audus et al 35 We contrast these results for swollen branched polymers with "percolation clusters" and equilibrium branched polymers with screened excluded volume interactions. Percolation clusters have been extensively studied before 36 and we refer to the work of Mansfield and Douglas 26 for illustrative images of the percolation clusters utilized in the present analysis.…”

Limiting the valence: advancements and new perspectives on patchy colloids, soft functionalized nanoparticles and biomolecules

“…13,[16][17][18][19][20][21][22] Such a directionality generally stems from the overall shape of the folded protein, the distribution of hydrophobic residues on the protein surface and the distribution of charged residues. At physiological pH values, this results in a heterogeneous surface charge, with the range of the electrostatic interactions being set by the screening provided by ions in solution.…”

“…15 Complex interactions between biomolecules, such as lysozymes and other proteins, or supramolecular complexes, such as viruses, have been recently described as patchy, meaning that the effective interactions in these systems are characterized by limited valence and directionality. 13,[16][17][18][19][20][21][22] In this review, we present a selection of recent advancements in the field of anisotropically interacting units, focusing on patchy colloidal systems, recently developed soft functionalized nanoparticles and biomolecules. A selection of the limited valence systems discussed here is represented in Fig.…”