Size of Elastic Single-Chain Nanoparticles in Solution and on Surfaces

Abstract

We introduce herein a simple model of covalent-bonded single-chain nanoparticles (SCNPs) by considering these intrachain cross-linked nano-objects as elastic unimolecular networks. According to this model, each SCNP is regarded as a network of elastic strands connected by cross-links. The free energy of the SCNP is decomposed in two contributions: (i) an elastic free energy due to the presence of these strands and (ii) an excluded volume contribution arising from the balance of monomer–monomer and monomer–solvent interactions. We provide scaling law expressions for the size (R), diffusion coefficient (D), apparent molar mass (Mapp), and shrinking factor (⟨G⟩) of elastic SCNPs in good, theta, and bad solvents. Also, we derive scaling laws for the height (H) of elastic SCNPs deposited on both low- and high-surface free energy substrates. A comparison of experimental results to model predictions for covalent-bonded polystyrene SCNPs in solution of narrow molecular weight distribution (1.09 ≤ Đ ≤ 1.26), different amount of reactive groups (0.025 ≤ x ≤ 0.3), and varying precursor molar mass (44 ≤ M ≤ 235 kDa) is performed based on literature data. For the same system, a similar comparison of experimental and theoretical H data corresponding to the case of SCNPs deposited on low- and high-energy substrates is also carried out. This simple elastic model provides a useful framework for connecting the amount of reactive groups and precursor molar mass with the size upon intrachain cross-linking for a variety of covalent-bonded SCNPs both in solvents of different quality and on substrates of different surface free energy.