Effects of linker flexibility on phase behavior and structure of linked colloidal gels

Abstract

Colloidal nanocrystal gels can be assembled using a difunctional “linker” molecule to mediate bonding between nanocrystals. The conditions for gelation and the structure of the gel are controlled macroscopically by the linker concentration and microscopically by the linker’s molecular characteristics. Here, we demonstrate using a toy model for a colloid–linker mixture that linker flexibility plays a key role in determining both phase behavior and the structure of the mixture. We fix the linker length and systematically vary its bending stiffness to span the flexible, semiflexible, and rigid regimes. At fixed linker concentration, flexible-linker and rigid-linker mixtures phase separate at low colloid volume fractions, in agreement with predictions of first-order thermodynamic perturbation theory, but the semiflexible-linker mixtures do not. We correlate and attribute this qualitatively different behavior to undesirable “loop” linking motifs that are predicted to be more prevalent for linkers with end-to-end distances commensurate with the locations of chemical bonding sites on the colloids. Linker flexibility also influences the spacing between linked colloids, suggesting strategies to design gels with desired phase behavior, structure, and, by extension, structure-dependent properties.

Colloidal Nanocrystal Gels from Thermodynamic Principles

“…When the average end-to-end distance of the linker is close to the average patch−patch distance on an NC, a large number of linkers form loops rather than bridges, which is enough to completely suppress gelation in the case of intermediate linker flexibility (Figure 3b−d). 4 First-order TPT fails to capture this qualitative change in phase behavior, so we have extended TPT to retain loop and higher-order graphs in the graphical expansion of the free energy. 31 This furnishes predictions for the fraction of linkers forming bridges and loops, which are in good agreement with our simulations (Figure 3c,d).…”

“…This observation is consistent with our predictions that looping hinders gelation by wasting linker (Figure 3). 4,31 The structure factor S obtained from small-angle X-ray scattering (SAXS) measurements provides details about the assembled microstructure and confirms a percolated network with a fractal dimension of ∼2, as evidenced by the power law behavior of S at small wavevectors, q (Figure 6c). Sn:In 2 O 3 does not fuse during assembly, and because the TORC chemistry is reversible, the gel could be disassembled by navigating the phase diagram from the spinodal region to the homogeneous dispersed region.…”

“…Chem. Phys.2021154 . This paper uses thermodynamic perturbation theory and coarse-grained simulations to explore the implications of the rigidity of linker molecules on the conditions promoting gelation and on microscopic structure in linked nanocrystal assemblies.…”

“…The dashed line indicates the distance between NC patches. Adapted with permission from ref , copyright 2021 AIP Publishing.…”

“…Linkers with end-to-end distances incommensurate with the patch− patch spacing form few loops and readily induce gelation, suggesting that strategies for reducing looping should increase the predictability of and propensity for gelation. 4,31 A viable linking strategy for reversible gelation requires NCs, ligands, and linker molecules to be cooperatively designed so that NC dispersions are stable, the linking bonds are reversible, and the byproducts do not interfere with assembly. An alternative, chemically nonspecific approach is to use the added molecule as a depletant instead of a linker, which has been well-studied for MPs.…”