FULL PAPER Reversible Equilibrium Deposition www.advtheorysimul.com Shape Dependent Colloidal Deposition and Detachment Isaac Torres-D´ ıaz, Huda A. Jerri,* Daniel Bencz´ edi, and Michael A. Bevan* Models of deposition and detachment dynamics of different shaped anisotropic colloids are reported to understand how equilibrium deposited amounts compare to spherical colloids. For different shaped colloids including spheres, ellipsoids, toroids, and buckled particles with varying aspect ratios, interaction potentials with substrates are computed using the Derjaguin approximation. Using these potentials, the Smoluchowski equation is used to model the dynamics of deposition and detachment versus particle–substrate attraction and aspect ratio for each particle shape. Average times for deposition and detachment and their ratio show steady-state deposited amounts can be enhanced by several orders of magnitude for different particle shapes compared to spherical colloids of the same volume. From a mechanistic standpoint, the present findings indicate how local Gaussian curvature of different particle shapes can lead to stronger adhesive interactions, longer detachment times, and higher deposited amounts compared to spherical colloids, which provides general design rules for controlling and optimizing colloidal deposition. 1. Introduction The ability to synthesize a variety of colloidal particle shapes on the micro- and nanoscale has existed for many years [1] and has continued to significantly expand in recent years, [2,3] which has enabled the use of different shaped colloids in diverse techno- logical areas. For example, it is known that colloid shape can enhance drug circulation [4] and cell internalization, [5] fragrance capsule deposition in consumer products, [6,7] hydrodynamic sep- aration processes, [8] environmental transport, [9,10] and specificity in natural systems such as pollen. [11] Beyond this representative list of illustrative examples, a vast literature too expansive to sum- marize here documents a rich and complex landscape of novel Dr. I. Torres-D´ ıaz, Prof. M. A. Bevan Chemical & Biomolecular Engineering Johns Hopkins University Baltimore, MD 21218, USA E-mail: mabevan@jhu.edu Dr. H. A. Jerri R&D Division Firmenich Inc. Plainsboro, NJ 08536, USA E-mail: huda.jerri@firmenich.com Dr. D. Bencz´ edi Corporate Research Division Firmenich SA., 1217 Meyrin 2, Geneva 1217, Switzerland The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adts.201900085 DOI: 10.1002/adts.201900085 behaviors and properties of nonspherical colloids. However, the basic mechanisms of how shape determines colloidal interac- tions and properties are not sufficiently well understood to design and optimize shape in specific applications, which limits the po- tential impact of different shaped particles. To focus on a particular application, the present study is motivated by deposition of fragrance delivery capsules onto hair. Fragrance capsules are highly engineered to control their stability within formula- tions, deposition on substrates, and re- lease of fragrant contents. For example, contact adhesion can be increased by chem- ical surface modification, including species adsorbed from solution [7] as well as spe- cific interactions mediated by peptides. [12] In an example of another design con- straint, composite capsule shells can be carefully designed to retain fragrant oils until capsules are ruptured for fragrance release. [13] Such core–shell capsules have been shown to buckle into nonspherical shapes, which has been shown to produce en- hanced deposition on hair compared to spherical capsules. [6] To exploit and optimize this shape effect, it is essential to understand how nonspherical capsules and their surface chemistry mediate deposition. To understand the net amount of colloids that can be deposited on a substrate, it is essential to understand both deposition and detachment processes. Deposition is a transient process that oc- curs by transport of colloidal particles to surfaces where they experience repulsive and attractive colloid–surface interactions, which determines whether or not particles come into adhesive contact with substrates. After deposition, it is possible for col- loidal particles to experience the reverse process of detachment, which can result in their transport away from substrates. Be- tween the limits of no deposition and irreversible deposition (no detachment), relative deposition and detachment rates de- termine the degree of reversibility and total deposited amounts at steady state. Irreversible deposition of spherical colloids on substrates is conceptually similar to bulk irreversible aggregation of Brownian colloids and is well understood. [14] Irreversible de- position of different shaped particles has received considerably less attention, but representative findings have shown ellipsoids have no orientation dependence since they adhere on contact [15] and yield lower deposited amounts than spheres due to packing effects. [16] Models of irreversible deposition inherently exclude detachment of colloids from surfaces. Modeling reversible deposition necessarily requires consider- ing detachment. Escape of a particle from an energy well (i.e., Adv. Theory Simul. 2019, 1900085 C  2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1900085 (1 of 9)