Two-dimensional Fourier analysis and quasielastic light-scattering measurements of colloid crystals.

Abstract

Two-dimensional (2D) Fourier transformation was carried out for particle distribution in highly purified polymer latex suspensions by use of a digital-image-processing system. The particle distributions were photographed by an optical microscope for larger particles (g approximately 0.2 \ensuremath{\mu}m in diameter) at various temperatures and particle charges. The interparticle distance (2${D}_{\mathrm{expt}}$) calculated from the halo pattern in the Fourier image hardly changed with increasing temperature (i.e., with decreasing dielectric constant for water), and decreased with particle charges.Preliminary quasielastic light scattering (QELS) was carried out independently for smaller particles (l approximately 0.2 \ensuremath{\mu}m in diameter) and furnished broad peaks in the interference function. The 2${D}_{\mathrm{expt}}$ obtained from the peak of the interference function was smaller than 2${D}_{0}$ (average interparticle distance calculated from concentration). The 2${D}_{\mathrm{expt}}$ was found to decrease with increasing particle charges and with decreasing dielectric constant. The trend observed by QELS was consistent with the results of 2D Fourier transformation, and with our previous claim that there exists electrostatic attraction among the particles through the intermediary of counterions (in addition to short-range repulsion). In the QELS experiments, the effect of the particle sedimentation on 2${D}_{\mathrm{expt}}$ was investigated by changing the specific gravity of the dispersion medium using mixtures of ${\mathrm{H}}_{2}$O and ${\mathrm{D}}_{2}$O. No significant change was detected in the peak position with solvent composition. The 2D Fourier transformation and QELS measurements were carried out finally for the same latex particles (diameter \ensuremath{\sim}0.1--0.2 \ensuremath{\mu}m). The value of 2${D}_{\mathrm{expt}}$ estimated by the two methods was roughly the same and the numbers of halo rings and broad scattering peaks coincided. It is now clear that the broad peaks in the interference function obtained from the QELS measurements corresponded to the two-state structure directly observed by the microscopic method. This provides strong support to our previous interpretation that the single broad peak(s) observed by other scattering methods reflect(s) the translational ordering of ionic species.