R. Pecora

Dynamic light scattering measurement of nanometer particles in liquids

Dynamic light scattering (DLS) techniques for studying sizes and shapes of nanoparticles in liquids are reviewed. In photon correlation spectroscopy (PCS), the time fluctuations in the intensity of light scattered by the particle dispersion are monitored. For dilute dispersions of spherical nanoparticles, the decay rate of the time autocorrelation function of these intensity fluctuations is used to directly measure the particle translational diffusion coefficient, which is in turn related to the particle hydrodynamic radius. For a spherical particle, the hydrodynamic radius is essentially the same as the geometric particle radius (including any possible solvation layers). PCS is one of the most commonly used methods for measuring radii of submicron size particles in liquid dispersions. Depolarized Fabry-Perot interferometry (FPI) is a less common dynamic light scattering technique that is applicable to optically anisotropic nanoparticles. In FPI the frequency broadening of laser light scattered by the particles is analyzed. This broadening is proportional to the particle rotational diffusion coefficient, which is in turn related to the particle dimensions. The translational diffusion coefficient measured by PCS and the rotational diffusion coefficient measured by depolarized FPI may be combined to obtain the dimensions of non-spherical particles. DLS studies of liquid dispersions of nanometer-sized oligonucleotides in a water-based buffer are used as examples.

Fluorescence correlation spectroscopy as a probe of molecular dynamics

A general theory of fluorescence correlation spectroscopy (FCS), including the effects of translational and rotational motions and chemical reactions, in ideal solutions, is given. The development is carried out explicitly for symmetric rotors of parallel transition moments and generalized to arbitrary configurations of the moments and to asymmetric rotors in the appendices. In addition, the effects of experimental geometry on the measured FCS correlation function are discussed in detail and the optimum geometries, for experiments seeking to measure different quantities, are given. We conclude with a brief discussion of signal‐to‐noise ratios and prospects for applications.

Time‐correlation functions for restricted rotational diffusion

The dynamical model of rotational diffusion of rod‐shaped molecules in a conical volume is applied to the calculation of time autocorrelation functions of 1st and 2nd order spherical harmonic functions of the rod’s orientation angles. Numerical results are obtained for the various correlation functions as a function of the polar angle ϑ0 within which the molecule’s axis is confined. Applications to dielectric relaxation, dynamic light scattering, and fluorescence depolarization experiments are pointed out.

Depolarized Rayleigh scattering and orientational relaxation of molecules in solution. I. Benzene, toluene, and para‐xylene

Measurements of orientational relaxation rates of benzene, toluene, and para‐xylene in a variety of solvents have been made by depolarized light scattering. A plot of reorientational relaxation time of each solute versus solution viscosity was found to fit a straight line with nonzero intercept. The slopes of the lines are compared with those predicted by the Stokes‐Einstein relation.

Spectral Distribution of Light Scattered from Flexible‐Coil Macromolecules

The spectral distribution of light scattered from monodisperse, infinitely dilute solutions of optically isotropic, flexible‐coil macromolecules in the free‐draining approximation of the pearl‐necklace model is related to the macromolecular translational diffusion coefficient D and the set of intramolecular relaxation times, τk. The spectral distribution for scattering parameter x   3 (large scattering angle and molecules with end‐to‐end distance ≳1000 A), additional Lorentzian terms each with half‐width dependent on D and some of the τk become important in the equations for the scattered spectral density. At x = 3, these terms are 15% of the total integrated scattered intensity. They rise to 50% at x = 7. Although the resultant line shape is complex, it is shown that the dominant contribution to this “intramolecular” spectral density comes from terms con...

Spectral Distribution of Light Scattered by Monodisperse Rigid Rods

The spectral distribution of light scattered from an infinitely dilute solution of monodisperse, optically isotropic, rigid rods is investigated. The contributions to the total scattered intensity of terms dependent on the rotational diffusion coefficient are calculated as a function of the product of lengths of the rod and the scattering vector. It is found that rotational diffusion contributions become important in scattering from long rods at large scattering angles.

Theory of dynamic light scattering from polydisperse systems

Analytical expressions for the light scattering autocorrelation function of Schulz distributed Rayleigh–Debye particles are presented. The theory is shown to be valid for spheres, thin rods, disks, and Gaussian coils executing translational diffusion. The polydisperse form factors for these shapes are also given. Analysis of polydisperse data with the expressions given yields the diffusion coefficient of the number average species and the Schulz polydispersity parameter. The effects of polydispersity on the angular dependence of the decay time and the conditions under which the form factor can be neglected are discussed.

Soft Matter Characterization

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Doppler Shifts in Light Scattering. II. Flexible Polymer Molecules

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Resonance enhanced dynamic Rayleigh scattering

The light‐scattering spectrum for the bead‐and‐spring model of flexible polymers is computed. The spectrum is shown to consist of a sum of Lorentzians centered about the incident frequency each with a half‐width proportional to the relaxation time of a given normal mode. The contribution of each normal mode to the spectrum is proportional to the ratio of the equilibrium mean‐squared length of a mode to the square of the incident‐light wavelength.