The solution of electromagnetic scattering by a homogeneous prolate (or oblate) spheroidal particle with an arbitrary size and refractive index is obtained for any angle of incidence by solving Maxwell's equations under given boundary conditions. The method used is that of separating the vector wave equations in the spheroidal coordinates and expanding them in terms of the spheroidal wavefunctions. The unknown coefficients for the expansion are determined by a system of equations derived from the boundary conditions regarding the continuity of tangential components of the electric and magnetic vectors across the surface of the spheroid. The solutions both in the prolate and oblate spheroidal coordinate systems result in a same form, and the equations for the oblate spheroidal system can be obtained from those for the prolate one by replacing the prolate spheroidal wavefunctions with the oblate ones and vice versa. For an oblique incidence, the polarized incident wave is resolved into two components, the TM mode for which the magnetic vector vibrates perpendicularly to the incident plane and the TE mode for which the electric vector vibrates perpendicularly to this plane. For the incidence along the rotation axis the resultant equations are given in the form similar to the one for a sphere given by the Mie theory. The physical parameters involved are the following five quantities: the size parameter defined by the product of the semifocal distance of the spheroid and the propagation constant of the incident wave, the eccentricity, the refractive index of the spheroid relative to the surrounding medium, the incident angle between the direction of the incident wave and the rotation axis, and the angles that specify the direction of the scattered wave.

Light Scattering by a Spheroidal Particle

Biosynthesis and Bioconjugation to Biomedical Application Juan Zhou,‡,§ Yong Yang, and Chun-yang Zhang*,†,§ †College of Chemistry, Chemical Engineering and Materials Science, Collaborative Innovation Center of Functionalized Probes for Chemical Imaging in Universities of Shandong, Key Laboratory of Molecular and Nano Probes, Ministry of Education, Shandong Provincial Key Laboratory of Clean Production of Fine Chemicals, Shandong Normal University, Jinan 250014, China ‡State Key Laboratory of Virology, Wuhan Institute of Virology, Chinese Academy of Sciences, Wuhan 430071, China Single-Molecule Detection and Imaging Laboratory, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China

Toward Biocompatible Semiconductor Quantum Dots: From Biosynthesis and Bioconjugation to Biomedical Application

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We studied the Brownian motion of isolated ellipsoidal particles in water confined to two dimensions and elucidated the effects of coupling between rotational and translational motion. By using digital video microscopy, we quantified the crossover from short-time anisotropic to long-time isotropic diffusion and directly measured probability distributions functions for displacements. We confirmed and interpreted our measurements by using Langevin theory and numerical simulations. Our theory and observations provide insights into fundamental diffusive processes, which are potentially useful for understanding transport in membranes and for understanding the motions of anisotropic macromolecules.

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Brownian Motion of an ellipsoid

The tuning of interfacial properties at selective and desired locations on the particles is of great importance to create the novel structured particles by breaking the symmetry of their surface property. Herein, a dramatic transition of both the external shape and internal morphology of the particles of polystyrene-b-poly(4-vinylpyridine) (PS-b-P4VP) was induced by precise positioning of size-controlled Au nanoparticle surfactants (Au NPs). The size-dependent assembly of the Au NPs was localized preferentially at the interface between the P4VP domain at the particle surface and the surrounding water, which generated a balanced interfacial interaction between two different PS/P4VP domains of the BCP particles and water, producing unique convex lens-shaped BCP particles. In addition, the neutralized interfacial interaction, in combination with the directionality of the solvent-induced ordering of the BCP domains from the interface of the particle/water, generated defect-free, vertically ordered porous channels within the particles. The mechanism for the formation of these novel nanostructures was investigated systemically by varying the size and the volume fraction of the Au NPs. Furthermore, these convex lens-shaped particles with highly ordered channels can be used as a microlens, in which the light can be concentrated toward the focal point with enhanced near-field signals. And, these particles can possess additional optical properties such as unique distribution of light scattering as a result of the well-ordered Au cylinders that filled into the channels, which hold great promise for use in optical, biological-sensing, and imaging applications.

Size-Controlled Nanoparticle-Guided Assembly of Block Copolymers for Convex Lens-Shaped Particles

Multidimensional Design of Anisotropic Polymer Particles from Solvent-Evaporative Emulsion

Shape and morphology of polymeric particles are of great importance in controlling their optical properties or self-assembly into unusual superstructures. Confinement of block copolymers (BCPs) in evaporative emulsions affords particles with diverse structures, including prolate ellipsoids, onion-like spheres, oblate ellipsoids, and others. Herein, we report that the evaporation rate of solvent from emulsions encapsulating symmetric polystyrene-b-polybutadiene (PS-b-PB) determines the shape and internal nanostructure of micron-sized BCP particles. A distinct morphological transition from the ellipsoids with striped lamellae to the onion-like spheres was observed with decreasing evaporation rate. Experiments and dissipative particle dynamics (DPD) simulations showed that the evaporation rate affected the organization of BCPs at the particle surface, which determined the final shape and internal nanostructure of the particles. Differences in the solvent diffusion rates in PS and PB at rapid evaporation rate...

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Confined assembly of block copolymers (BCPs) is receiving increasing attention due to the ability to create unconventional morphologies that cannot be observed in the corresponding bulk systems. Th...

Jae Man Shin

Papers

Size-Controlled Nanoparticle-Guided Assembly of Block Copolymers for Convex Lens-Shaped Particles

Multidimensional Design of Anisotropic Polymer Particles from Solvent-Evaporative Emulsion

Morphological Evolution of Block Copolymer Particles: Effect of Solvent Evaporation Rate on Particle Shape and Morphology

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100th Anniversary of Macromolecular Science Viewpoint: Block Copolymer Particles: Tuning Shape, Interfaces, and Morphology