Directed walk in probability space that locates mean field solutions to spin models.

Despite their formal simplicity, most lattice spin models cannot be easily solved, even under the simplifying assumptions of mean field theory. In this paper, we present a method for generating mean field solutions to classical continuous spins. We focus our attention on systems with nonlocal interactions and nonperiodic boundaries, which require careful handling with existing approaches, such as Monte Carlo sampling. Our approach utilizes functional optimization to derive a closed-form optimality condition and arrive at self-consistent mean field equations. We show that this approach significantly outperforms conventional Monte Carlo sampling in convergence speed and accuracy. To convey the general concept behind the approach, we first demonstrate its application to a simple system: a finite one-dimensional dipolar chain in an external electric field. We then describe how the approach naturally extends to more complicated spin systems and to continuum field theories. Furthermore, we numerically illustrate the efficacy of our approach by highlighting its utility on nonperiodic spin models of various dimensionality.

Bottlebrush polymers with flexible enantiomeric side chains display differential biological properties.

Chirality and molecular conformation are central components of life: biological systems rely on stereospecific interactions between discrete (macro)molecular conformers, and the impacts of stereochemistry and rigidity on the properties of small molecules and biomacromolecules have been intensively studied. Nevertheless, how these features affect the properties of synthetic macromolecules has received comparably little attention. Here we leverage iterative exponential growth and ring-opening metathesis polymerization to produce water-soluble, chiral bottlebrush polymers (CBPs) from two enantiomeric pairs of macromonomers of differing rigidity. Remarkably, CBPs with conformationally flexible, mirror image side chains show several-fold differences in cytotoxicity, cell uptake, blood pharmacokinetics and liver clearance; CBPs with comparably rigid, mirror image side chains show no differences. These observations are rationalized with a simple model that correlates greater conformational freedom with enhanced chiral recognition. Altogether, this work provides routes to the synthesis of chiral nanostructured polymers and suggests key roles for stereochemistry and conformational rigidity in the design of future biomaterials.