No Access Submitted: 15 October 2020 Accepted: 20 December 2020 Published Online: 11 January 2021
J. Chem. Phys. 154, 024905 (2021);
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  • Michael P. Howard
  • Zachary M. Sherman
  • Delia J. Milliron
  • Thomas M. Truskett
We extend Wertheim’s thermodynamic perturbation theory to derive the association free energy of a multicomponent mixture for which double bonds can form between any two pairs of the molecules’ arbitrary number of bonding sites. This generalization reduces in limiting cases to prior theories that restrict double bonding to at most one pair of sites per molecule. We apply the new theory to an associating mixture of colloidal particles (“colloids”) and flexible chain molecules (“linkers”). The linkers have two functional end groups, each of which may bond to one of several sites on the colloids. Due to their flexibility, a significant fraction of linkers can “loop” with both ends bonding to sites on the same colloid instead of bridging sites on different colloids. We use the theory to show that the fraction of linkers in loops depends sensitively on the linker end-to-end distance relative to the colloid bonding-site distance, which suggests strategies for mitigating the loop formation that may otherwise hinder linker-mediated colloidal assembly.
M.P.H. thanks Ryan Jadrich for introducing him to Wertheim’s elegant theory. This research was primarily supported by the National Science Foundation through the Center for Dynamics and Control of Materials: an NSF MRSEC under Cooperative Agreement No. DMR-1720595, with additional support from an Arnold O. Beckman Postdoctoral Fellowship (Z.M.S.) and the Welch Foundation (Grant Nos. F-1696 and F-1848). We acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources.
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