Photon correlation spectroscopy is a powerful light scattering technique for studying the properties of suspensions and solutions of colloids, macromolecules and polymers. The principle of the technique is explained and the associated instrumentation is described. A number of developments in the instrumentation, which will have a substantial impact on the future application of the technique, are discussed.

The principles of dynamic light scattering (DLS), applied to size analysis of submicron particles suspended in liquid, are reviewed. A comparison is made between two methods of inversion of the autocorrelation function data (cumulants analysis and Laplace transform inversion); choice of the appropriate method depends on the complexity of the underlying particle size distribution (PSD). Representative results are discussed and illustrate the current state-of-the-art of particle size analysis by DLS. Examples include polymer latexes, oil/water emulsions, surfactant micelles and small proteins.

To gain insight into the migration of photons in optically dense heterogeneously structured media, scattering models have been developed which consist of polystyrene latex particles suspended in solutions containing varying amounts of absorptive dye. The amount and distribution of the dye affect the mean pathlength of emergent photons, the latter being proportional to < (eta) >, the average number of collisions of photons with moving scatterers. The quantity < (eta) > has been determined by cumulant analysis of the measured time autocorrelation function for photons which are injected and detected with a pair of fiber optodes positioned at the surface of the scattering medium. In agreement with theoretical predictions, < (eta) > is found to vary linearly with the spacing between the optodes if the medium is homogeneous. Moreover, when the scattering medium is composed of layers whose optical absorptions differ, the detected autocorrelation functions indicate that the photons which successfully traverse the medium move along paths which minimize the absorption probability.

The technique of Brownian dynamics simulation is used to study polarized dynamic light scattering from semi-stiff models of polymers. The primary objective is to determine how sensitive the dynamic scattering form factor, S(q, t), is to dynamic flexibility as opposed to static flexibility (average conformation). S(q, t) over a range of experimentally accessible scattering vector (q) are derived from the dynamical trajectories of many different chains initially selected from an equilibrium ensemble. In order to minimize noise, which is of crucial importance in order to accurately characterize the low amplitude, fast decay components of S(q, t), the center of diffusion or mass is subtracted from the polymer coordinates in most simulations. This procedure, which is valid for systems that have weak coupling between overall translational and rotational motions, has the additional advantage of simplifying S(q, t) since the contribution of overall translation has been factored out. In the analysis of experimental data, premultiplying S(q, t) by exp (+q2 Dt) where D is the translational diffusion constant has the same effect. Simulations are described for dynamically rigid and flexible wormlike chains with variable persistence length (P equals 40 to 100 nm) and contour length corresponding to 762 bp DNA. S(q, t)'s with and without overall translation are analyzed with CONTIN in order to determine lifetime distributions. For large P (> 70 nm), rigid and flexible models are indistinguishable. However, differences are observed when P is less than 70 nm as far as the faster decay components are concerned. The amplitude of the faster decay components are the same for rigid and flexible models but the lifetimes are significantly shorter for the flexible case. For the rigid case, the 'first internal time' corresponds to <(60)-1> where (theta) is the end-over-end rotational diffusion constant. Finally, the simulation results are compared with actual light scattering experiments on 762 bp DNA. A flexible model with P equals 50 nm is in best agreement with experiment. All of the rigid models predict a first internal time that is too long by 40% or more.

The theory of the dynamics of wormlike chains based on the pure bending equation is reviewed. The normal mode solution obtained with the neglect of hydrodynamic interactions has been used to compute correlation functions for the forward depolarized dynamic light scattering, fluorescence polarization anisotropy, and the q dependent polarized dynamic light scattering of wormlike chains. The depolarized light scattering results are also applicable to the field free decay of the transient electric birefringence. Corrections to the relaxation rates due to hydrodynamic interactions are included. Extensive computer simulations based on Brownian dynamics for depolarized light scattering and fluorescence polarization anisotropy have been carried out with full and preaveraged hydrodynamic interaction, as a function of the ratio L/P of the contour length to persistence length of the chain. Flexibility was studied in the range 1 ≤ L/P ≤ 20 which spans relatively rigid to fairly flexible chains. The simulations are compared to theory in order to.study the validity of the assumptions used. It was found that the longest relaxation time observed in the simulations for all the experiments could be interpreted as the rotational diffusion of the chain, in agreement with the assumptions of the theory and the Yamakawa-Yoshisaki formulas for the rotational diffusion coefficient, even in the very flexible case. In the case of fluorescence, the data may show the presence of a small amount of coupling of flexing and rotation. The fast relaxation times in the rigid region are also in good agreement with theory, but the analysis of the data for greater flexibilities is not straightforward due to the resolution limitations of the exponential analysis programs and the large number of relaxations that contribute. The simulations show that, in general, the coupling between the degrees of freedom is small perhaps up to L/P ≤ 4, and is unknown beyond that. The difference between full and preaveraged hydrodynamic interactions was systematic but small.

A new method for studying the internal dynamic behavior of linear, flexible polymer coils in solution using photon correlation spectroscopy (PCS) is presented. Two applications of the method to the study of a high molecular weight polystyrene in good and theta solvents are featured.

Actin plays a major role in the structural integrity and motility of cells as well as in the intracellular dynamics of other macromolecules. Photon Correlation Spectroscopy (PCS) has been used to monitor the diffusion of polystyrene latex spheres (PLS) of different sizes within in vitro polymerized actin solutions under a variety of conditions. Specific actin-binding proteins were added to regulate the actin filament lengths as well as to cross-link filaments together. PCS measurements give information on the mobility of PLS over probing distances equal to the inverse scattering vector magnitude which range from 40 to 420 nm for the data. Results allow estimation of the mean pore sizes within the actin networks as a function of both actin concentration (0.4 - 5 mg/ml) and the presence of actin-binding proteins. Probe diffusion coefficients were measured for PLS samples in length-regulated actin networks at a fixed actin concentration, c (0.65 mg/ml) as c*, the semi-dilute overlap concentration, was varied. There was a change in the dependence on c/c* near the value 1 at which the filaments just overlap. Quasi-static low-angle diffraction patterns from actin solutions have been detected and quantified using a CCD video camera/frame grabber system to study the spatial and slow temporal variations in the intensity patterns.

The results of a theory of noise on photon correlation data is presented for the rather general case of a detector signal which can be modeled as a Gamma process. This model includes finite intercept effects and may even be used for heterodyne measurements. Multiple sample time measurements are considered with particular care and significant decreases of noise with increasing sample time are typically found at small as well as at large lag (and sample) times, if the standard normalization procedure is replaced by the symmetric or compensated normalization schemes. Large estimator covariances are observed across lag time ranges up to one coherence time. This type of correlated noise is typical for correlation measurements and may easily lead to overfitting problems. Experimental verifications are included for the noise calculations.

Applications of quasi-elastic light scattering spectroscopy (QELSS) to the study of protein and polymer solutions are discussed. In binary systems, quasielastic light scattering measures the mutual diffusion coefficient Dm of the macromolecules. For spherical macromolecules, Dm and its concentration dependence can be quantitatively interpreted in terms of hydrodynamic and direct interactions between the diffusing particles in solution. Also discussed are optical probe experiments, in which QELSS spectra of ternary probe: matrix polymer: solvent systems are obtained. The diffusion of dilute probes through a complex probe:matrix system reveals detailed information about the dynamics of the matrix. A direct extension of the orthodox theory for interacting, diffusing spheres successfully describes the dynamics of random-coil polymers in solution. Probe diffusion and other measurements of polymer transport coefficients suffice to reject some alternative models of polymer dynamics.

Diffusion of polystyrene latex and the sodium salt of fluorescein represent the macroscopic and microscopic limits, respectively, of probe diffusion in aqueous hydroxypropylcellulose. In both cases, chemical complexities, such as surface interactions leading to probe aggregation or the solvation characteristics of the polymer matrix, can obscure the general physical information that can be extracted. But when these details are taken into account, a rational picture of probe diffusion in hydroxypropylcellulose begins to emerge. At the same time certain observations, especially the rapid decay mode present in some dynamic light scattering experiments, remain difficult to interpret.

This work is concerned with the identification of the modes in dynamic light and neutron scattering experiments on binary polymer solutions, or on incompressible ternary polymer melts.

After a brief review of the static and dynamic light scattering theory from large particles, an experimental situation of a vesicle distribution in equilibrium with large aggregates is presented. It is shown that light scattering results in this complicated situation can be properly interpreted only if dynamic data are combined with absolute intensity measurements.

Light scattering measurements are made on a mixture of a Side Chain Liquid Crystalline Polymer (SCLCP) and a low molecular weight liquid crystal 5CB (pentyl cyanobiphenyl) in the nematic phase. Results obtained from two different scattering geometries are presented and discussed.

The recognition that the transmission of light through a concentrated, opaque system can be treated as a diffusion process has extended the application of photon correlation techniques to the study of particle size, mobility and interactions in such systems. Solutions of the photon diffusion equation are sensitive to the boundary conditions imposed by the geometry of the scattering apparatus. The apparatus, incorporating a bifurcated fiber optic bundle for light transmission between source, sample and detector, takes advantage of the particularly simple solution for a back-scattering configuration. Its ability to measure particle size using monodisperse polystyrene latices and to respond to concentration dependent particle interactions in a study of casein micelle mobility in skim and concentrated milks is demonstrated. Finally, the changes in dynamic light scattering behavior occurring during colloidal gel formation are described and discussed.

Aerogels are exceptionally light foams formed by extraction of the solvent from a gel under supercritical conditions where surface tension forces are greatly reduced. This results in very little shrinkage of the gels when dried. The dried aerogels have extremely high surface area and have applications as catalyst supports and thermal and acoustic insulators. While most studies have used aerogels formed from silicon dioxide, the authors focused on organic aerogels obtained by the reaction of resorcinol and formaldehyde (RF). The kinetics of the gel formation have been studied using dynamic light scattering. These studies encompass three areas:(1) initial reaction of RF into branched 'clusters' as a function of resorcinol/catalyst (Na2CO3) ratio; (2) aggregation of the clusters into linear chains to form the gel network; and (3) the modulus of the completely gelled sample. The initial particle size increases linearly with R/C ratio as was observed by TEM on dried samples. The scattering intensity increases exponentially as the gel is formed as is observed for polymer gels formed by spinodal decomposition. The cooperative diffusion coefficient (which is directly related to the gel modulus) scales with concentration to a power of approximately unity, which is larger than the 3/4 usually observed for polymer networks.

Polyelectrolyte solutions exhibit unusual or unexpected properties in the limit of low salt concentrations. Consequently, theoretical treatment and interpretation of results obtained by various experimental techniques meet many difficulties. Application of photon correlation spectroscopy to this problem is discussed on the basis of numerous results obtained in a wide variety of experimental conditions (charge density on chains, concentration, molecular weight, temperature, dielectric permittivity of solvent). Linear flexible macromolecules, poly(methacrylic acid) and sodium polystyrene sulfonate were used as samples. The multicomponent character of the solution, i.e., the interaction between charged macromolecules and counterions, is shown to be very important. Experimental results are compared with existing (rather controversial) theoretical concepts.

The aqueous system comprised of poly(dimethylammonium chloride) (a strongly cationic polymer) and a mixture of sodium dodecyl sulfate and Triton X-100 (anionic/nonionic mixed micelles) forms polyelectrolyte-micelle complexes. At suitable micelle compositions and ionic strengths, soluble complexes are formed, which may be studied by a variety of solution techniques, including quasielastic light scattering. In this report, the authors examine the influence of polymer molecular weight and micelle composition on the nature of these complexes. Multiangle measurements were made with two different instruments (hence different procedures for extracting apparent size distributions from measured autocorrelation curves). At the concentrations employed, multipolymer complexes appear to form. The QELS data, taken in conjunction with limited electrophoretic light scattering results, suggest that the main determinant of the extent of higher-order aggregation are those factors influencing the net charge of a 'primary' i.e. intrapolymer complex, with molecular weight per se playing a secondary role.

Applications of the Poisson-Boltzmann (P-B) equation to simple electrolytes and polyelectrolytes, and Manning's two-state theory for counterion condensation on rodlike polyions are reviewed. A modified Scatchard approach applied to generate binding isotherms for the association of univalent ions of finite size to a linear lattice of unite charges, where two equilibrium conditions are taken into consideration: the number of stacks (ns), and the fraction of bound sites (0). Calculations indicate a rapid change in free ion concentration occurs in the range 0.75 < 0 < 0.9 for site separation values (b) less than the Bjerrum length of 7.12 $A. The apparent observation that counterion condensation does not obey a 'mass-action' law may therefore be an 'experimental illusion'.

We examine in more detail the "three-region" model recently proposed to explain the dependence of the persistence length of linear polyions as a function of small ion concentration under low ionic conditions. The three regions approximated as step functions are: (1) "condensed counterions" on the surface of the polyion whose function is simply to reduce the effective charge of each polyion site; (2) a counterion sheath in the vicinity of the polyion that may extend tens of angstroms from the polyion surface; and (3) the "bulk" solution concentration. Incorporated in this model is the property that the concentration of ions in region (2) increases relative to the concentration of ions in region (3) as the polyion concentration is decreased.