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Dimerization and structure formation of colloids via capillarity at curved fluid interfaces.

ABSTRACT: Capillary interactions are ubiquitous between colloids trapped at fluid interfaces. Generally, colloids in fluid interfaces have pinned, undulated contact lines that distort the interface around them. To minimize the area, and therefore the energy of these distortions, colloids interact and assemble in a manner that depends on the shape of the host interface. On curved interfaces, capillary interactions direct isolated colloid motion along deviatoric curvature gradients. This directed motion relies on the leading order, long-ranged quadrupolar distortions made by the colloids' undulated pinned contact lines. Here we study pair interactions and dimer formation of colloids on non-uniformly curved fluid interfaces. Pair interaction energies are inferred to be order of 104kBT, and interacting forces are of order 10-1 pN for 10 micron particles adsorbed on interfaces formed around a 250 micron micropost. We compare experiments to analysis for the pair interaction energy, and identify criteria for dimers to form. We also study the formation of trapped structures by multiple particles to discern the influence of the underlying interface shape and the contact line undulations. By comparison to Monte Carlo simulations with potentials of interactions based on analysis, we find that higher order terms in the distortion fields generated by the particles play a major role in the structure formation on the curved interface. These interactions are determined by the particle's contact line and the host interface shape, and can be used to assemble particles independent of their material properties.

SUBMITTER: Read A

PROVIDER: S-EPMC7371263 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.

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Dimerization and structure formation of colloids via capillarity at curved fluid interfaces.

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