Light scattering near and from interfaces using evanescent wave and ellipsometric light scattering

Light propagation in layered media in a total reflection geometry: a transfer matrix method using virtually linear basis functions to handle critical conditions

For light propagation in a layered refractive index profile, critical conditions occur when the wave vector perpendicular to the layering becomes zero. Such conditions can occur in a total reflection geometry. Conventional transfer matrix methods become singular, and geometrical optics concepts break down at critical conditions. We introduce two new, to the best of our knowledge, basis systems using virtual linear functions that obey the Helmholtz equation and turn to linear functions required for critical conditions.

Light scattering in TIRF microscopy: A theoretical study of the limits to surface selectivity

In TIRF microscopy, the sample resides near a surface in an evanescent optical field that, ideally, decreases in intensity with distance from the surface in a pure exponential fashion. In practice, multiple surfaces and imperfections in the optical system and refractive index (RI) inhomogeneities in the sample (often living cells) produce propagating scattered light that degrades the exponential purity. RI inhomogeneities cannot easily be avoided. How severe is the consequent optical degradation? Starting from Maxwell's equations, we derive a first-order perturbative approximation of the electric field strength of light scattered by sample RI inhomogeneities of several types under coherent evanescent field illumination. The approximation provides an expression for the scattering field of any arbitrary RI inhomogeneity pattern. The scattering is not all propagating; some is evanescent and remains near the scattering centers. The results presented here are only a first-order approximation, and they ignore multiple scattering and reflections off the total internal reflection (TIR) surface. For simplicity, we assume that the RI variations in the z direction are insignificant within the depth of the evanescent field and consider only scattering of excitation light, not fluorescence emission light. The general conclusion of most significance from this study is that TIR scattering from a sample with RI variations typical of those on a cell culture alters the effective thickness of the illumination to only ∼50% greater than it would be without scattering. The qualitative surface selectivity of TIR fluorescence is largely retained even in the presence of scattering. Quantitatively, however, scattering will cause a deviation from the incident exponential decay at shorter distances, adding a slower decaying background. Calculations that assume a pure exponential decay will be approximations, and scattering should be taken into account. TIR scattering is only slightly dependent on polarization but is strongly reduced for the highest accessible incidence angles.

Foundation of correlation ellipsometry

An experimental strategy for the detection of fluctuation dynamics at interfaces based on a combination of photon correlation spectroscopy (PCS) with a nulling ellipsometry scheme is investigated theoretically. The intensity description of ellipsometry measurements is generalized to PCS time correlation functions. The nulling ellipsometry procedure is applied for every lag time t of the correlation functions, to extract the dynamics connected to the coherent signal which contains the interface dynamics. The classical ellipsometry parameters Δ and tanΨ are generalized to functions and tan [capital Psi, Greek, tilde]_Q(t). A suitable Siegert relation is derived and employed to show that either field correlation functions or intensity correlation functions after baseline subtraction can be used as the starting point for the nulling ellipsometry procedure.

Near-wall dynamics of concentrated hard-sphere suspensions: comparison of evanescent wave DLS experiments, virial approximation and simulations

In this article we report on a study of the near-wall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of ϕ≈ 0.25 which provides us with a fast and non-costly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall.

Translational and rotational near-wall diffusion of spherical colloids studied by evanescent wave scattering

In this article we extend recent experimental developments [Rogers et al., Phys. Rev. Lett., 2012, 109, 098305] by providing a suitable theoretical framework for the derivation of exact expressions for the first cumulant (initial decay rate) of the correlation function measured in Evanescent Wave Dynamic Light Scattering (EWDLS) experiments. We focus on a dilute suspension of optically anisotropic spherical Brownian particles diffusing near a planar hard wall. In such a system, translational and rotational diffusion are hindered by hydrodynamic interactions with the boundary which reflects the flow incident upon it, affecting the motion of colloids. The validity of the approximation by the first cumulant for moderate times is assessed by juxtaposition to Brownian dynamics simulations, and compared with experimental results. The presented method for the analysis of experimental data allows the determination of penetration-depth-averaged rotational diffusion coefficients of spherical colloids at low density.

Optical imaging of liquid crystals at the nanoscale

The instrumentation associated with near-field scanning optical microscopy (NSOM) can be exploited to provide three-dimensional structure and dynamic information about liquid crystals at scales not possible with diffraction-limited tools. This Minireview focuses on our use of NSOM techniques to probe spatial variations of the nematic director and the nematic orientational order parameter on length scales as small as a few nanometers.

Electrochemical reductive desorption of alkyl self-assembled monolayers studied in situ by spectroscopic ellipsometry: evidence for formation of a low refractive index region after desorption

Aggregates formed after reductive desorption of self-assembled monolayers of shorter chained thiols from gold may stabilise hydrogen bubbles.

One-particle correlation function in evanescent wave dynamic light scattering

In order to interpret measured intensity autocorrelation functions obtained in evanescent wave scattering, their initial decay rates have been analyzed recently [P. Holmqvist, J. K. G. Dhont, and P. R. Lang, Phys. Rev. E 74, 021402 (2006); B. Cichocki, E. Wajnryb, J. Blawzdziewicz, J. K. G. Dhont, and P. R. Lang, J. Chem. Phys. 132, 074704 (2010); J. W. Swan and J. F. Brady, ibid. 135, 014701 (2011)]. A theoretical analysis of the longer time dependence of evanescent wave autocorrelation functions, beyond the initial decay, is still lacking. In this paper we present such an analysis for very dilute suspensions of spherical colloids. We present simulation results, a comparison to cumulant expansions, and experiments. An efficient simulation method is developed which takes advantage of the particular mathematical structure of the time-evolution equation of the probability density function of the position coordinate of the colloidal sphere. The computer simulation results are compared with analytic, first and second order cumulant expansions. The only available analytical result for the full time dependence of evanescent wave autocorrelation functions [K. H. Lan, N. Ostrowsky, and D. Sornette, Phys. Rev. Lett. 57, 17 (1986)], that neglects hydrodynamic interactions between the colloidal spheres and the wall, is shown to be quite inaccurate. Experimental results are presented and compared to the simulations and cumulant expansions.

Near-field laser Doppler velocimetry measures near-wall velocities

A new near-wall velocimetry technique is proposed, based on evanescent wave dynamic light scattering, which allows for the measurement of near-wall velocity profile (characterized by an apparent slip velocity and a shear rate) with a resolution of tens of nanometers. A full theoretical expression of the correlation function is derived for the case of linear flow with negligible Brownian motion. The technique is demonstrated for latex spheres dispersed in water-glycerol mixtures.

Mie scattering by soft core-shell particles and its applications to ellipsometric light scattering

Through the use of Mie theory generalized to multiple spheres, the derivatives of the scattering matrix elements and ellipsometric scattering variables are found as a function of shell thickness and nonconcentricity for core-shell particles. In particular, for the case of a core-shell sphere system where the centers are not concentric, the derivatives are taken with respect to the line segment describing the distance between spherical centers. The derivatives of the scattering matrix elements can be used to calculate the changes in ellipsometric light scattering, allowing for sensitivity and precision in quantitative models of fluctuations in core-shell systems. Computed results giving model contrast for a variety of sizes and fluctuation modes are used to design and guide novel light-scattering experiments currently underway.

Resonance enhanced dynamic light scattering

We present a novel light scattering setup that enables probing of dynamics near solid surfaces. An evanescent wave generated by a surface plasmon resonance in a metal layer is the incident light field in the dynamic light scattering experiment. The combination of surface plasmon resonance spectroscopy and dynamic light scattering leads to a spatiotemporal resolution extending a few hundred nanometers from the surface and from microseconds to seconds. The comparison with evanescent wave dynamic light scattering identifies the advantages of the presented technique, e.g., surface monitoring, use of metal surfaces, and biorelevant systems. For both evanescent wave geometries, we define the scattering wave vector necessary for the analysis of the experimental relaxation functions.

Evanescent-wave dynamic light scattering at an oil-water interface: diffusion of interface-adsorbed colloids

A light-scattering goniometer for evanescent-wave dynamic light scattering (EWDLS) measurements at a liquid-fluid interface is introduced, and used for measurements on two charge-stabilized polystyrene colloid systems adsorbed to alkane-water interfaces. The goniometer allows an independent variation of the penetration depth and the scattering vector components parallel and perpendicular to a liquid-fluid interface. The possible illumination geometries are compared. Ellipsometry at the liquid-fluid interface is implemented as a complementary tool. In EWDLS measurements, the absence of diffusive motion perpendicular to the interface is demonstrated, which confirms the adsorption of the particles. The two-step decay of the autocorrelation function is interpreted in terms of diffusion within a two-dimensional interface lattice of colloidal particles, stabilized by repulsive electrostatic interactions, and a desorption process. A significant slowing down of the in-plane diffusion of the colloids as compared to the bulk diffusion is observed.

Dynamics of amphiphilic diblock copolymers at the air-water interface

Two polyisoprene-polyethyleneoxide diblock copolymers with different block length ratios adsorbed to the water surface were investigated by multiple angle of incidence ellipsometry, evanescent wave light scattering, and surface tension experiments. In a semidilute interfacial regime, the transition from a two-dimensional to a "mushroom" regime, in which polymer chains form loops and tails in the subphase, was discussed. A diffusion mechanism parallel to the interface was probed by evanescent wave dynamic light scattering. At intermediate concentrations, the interfacial diffusion coefficient D(∥) scales with the surface concentration Γ, as D(∥) ~ Γ(0.77) in agreement with the scaling observed for polymer solutions in a semidilute regime. At relatively high concentrations a decreasing of D(∥) is discussed in terms of increasing friction due to interactions between polyisoprene chains.

The intensity correlation function in evanescent wave scattering

As a first step toward the interpretation of dynamic light scattering with evanescent illumination from suspensions of interacting spheres, in order to probe their near wall dynamics, we develop a theory for the initial slope of the intensity autocorrelation function. An expression for the first cumulant is derived that is valid for arbitrary concentrations, which generalizes a well-known expression for the short-time, wave-vector dependent collective diffusion coefficient in bulk to the case where a wall is present. Explicit expressions and numerical results for the various contributions to the initial slope are obtained within a leading order virial expansion. The dependence of the initial slope on the components of the wave vector parallel and perpendicular to the wall, as well as the dependence on the evanescent-light penetration depth are discussed. For the hydrodynamic interactions between colloids and between the wall, which are essential for a correct description of the near-interface dynamics, we include both far-field and lubrication contributions. Lubrication contributions are essential to capture the dynamics as probed in experiments with small penetration depths. Simulations have been performed to verify the theory and to estimate the extent of the concentration range where the virial expansion is valid. The computer algorithm developed for this purpose will also be of future importance for the interpretation of experiments and to develop an understanding of near-interface dynamics, at high colloid concentrations.