Optical microscopy measurement of pair correlation functions

Abstract

We studied the pair correlation function g͑r͒ of silica particles with a fluorescent core and a nonfluorescent shell which were confined between two glass plates by optical video microscopy. To investigate the possible role of optical artifacts due to overlapping particle images, we compared experiments, where, first, the whole particle ͑white image͒ and then, only the fluorescent core ͑fluorescent image͒ was used for determining particle positions. While under white-image conditions the observed g͑r͒ exhibits a main peak at about 1.2 times the particle's diameter; under fluorescent image conditions the obtained g͑r͒ resembles a short-ranged repulsive system where the main peak is close to contact. This discrepancy points towards artifacts of video microscopy, leading to erroneous g͑r͒ and in turn to erroneous effective-pair potentials. Optical microscopy methods are currently used extensively in colloidal science to determine various physical properties of colloidal systems under different conditions ͓1-6͔. Of particular interest has been the study of quasi-twodimensional ͑Q2D͒ systems, where a colloidal suspension is confined between two parallel plates separated a distance only slightly larger than the particles' size ͓7-9͔. Under such conditions, the particles form a single layer between the plates and one can use optical methods to image all the particles in the field of view at the same time. In this way one can directly sample the equilibrium configurations of the system which allows us to calculate several thermodynamic properties Thus, one of the key steps in those experiments is the accurate determination of the particles' positions from which various quantities of interest are determined. It has been recently demonstrated that at small particle distances under bright field illumination conditions, optical artifacts due to overlapping particle images can occur leading to an erroneous determination of the particles' positions and thus, to a deviation ⌬r͑r͒ of the actual interparticle distance ͓10͔. Although such deviations are close to the experimental accuracy of the optical video microscopy, they can lead to considerable artifacts in other quantities, e.g., the effective-pair potential.It has been suggested that particle image overlapping can be avoided by using core-shell particles with a fluorescent core and a nonfluorescence shell ͓10͔. In this work we use such particles to investigate the effect of ⌬r͑r͒ on physical quantities, such as the static pair correlation function g͑r͒ in Q2D colloidal systems. This is an important issue since the pair correlation function, measured by optical microscopy, has been used in the literature to obtain a more fundamental quantity, namely, the pair interparticle potential u͑r͒ in confined geometries ͓7-9,11͔. Here we report measurements of g͑r͒ of Q2D colloidal systems, consisting of core-shell silica spherical particles, suspended in water and confined between two glass plates. The core-shell particles' diameter is = 1.4 m, having a fluorescent core of diameter ...

Pair interaction potentials of colloids by extrapolation of confocal microscopy measurements of collective suspension structure

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A new tracking algorithm for multiple colloidal particles close to contact

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