On inferring liquid-liquid phase boundaries and tie lines from ternary mixture light scattering

We investigate the possibility of using light scattering data in the single-phase regions of a ternary liquid mixture phase diagram to infer ternary mixture coexistence curves, and to infer tie lines joining the compositions of isotropic liquid phases in thermodynamic equilibrium. Previous analyses of a nonlinear light scattering partial differential equation (LSPDE) show that it provides for reconstruction of ternary [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008); C. Wahle, D. Ross, and G. Thurston, J. Chem. Phys. 137, 034201 (2012)] and quaternary [C. Wahle, D. Ross, and G. Thurston, J. Chem. Phys. 137, 034202 (2012)] mixing free energies from light scattering data, and that if the coexistence curves are already known, it can also yield ternary tie lines and triangles [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008)]. Here, we show that the LSPDE can be used more generally, to infer phase boundaries and tie lines from light scattering data in the single-phase region, without prior knowledge of the coexistence curve, if the single-phase region is connected. The method extends the fact that the reciprocal light scattering intensity approaches zero at the thermodynamic spinodal. Expressing the free energy as the sum of ideal and excess parts leads to a natural family of Pade? approximants for the reciprocal Rayleigh ratio. To test the method, we evaluate the single-phase reciprocal Rayleigh ratio resulting from the mean-field, regular solution model on a fine grid. We then use a low-order approximant to extrapolate the reciprocal Rayleigh ratio into metastable and unstable regions. In the metastable zone, the extrapolation estimates light scattering prior to nucleation and growth of a new phase. In the unstable zone, the extrapolation produces a negative function that in the present context is a computational convenience. The original and extrapolated reciprocal light scattering are jointly used as input to solving the LSPDE to deduce the mixing free energy and its convex hull. When projected onto the composition triangle, the boundary of the convexified part of the free energy is the phase boundary, and lines on the convexified region along which the second directional derivative is zero are the tie lines. We find that the tie lines and phase boundaries so deduced agree well with their exact values. This work is a step toward developing methods for inferring phase boundaries from real light scattering intensities measured with noise, from mixtures having compositions on a coarser grid.     

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.     

On the interpretation of ternary diffusion measurements in low-molecular weight fluids by dynamic light scattering

Dynamic light scattering (DLS) allows for efficient measurement of physical transport properties in fluids. It is now a well established technique for determination of mutual mass diffusion coefficients in binary mixtures and multicomponent macromolecular solutions. More recently, ternary systems of low-molecular weight compounds have been analyzed by DLS where it was found that only one of the two mass diffusion modes can be observed. In this work, a theoretical interpretation of these findings is provided. For this purpose, a simple theory is developed that describes the observed signals. Thereby, it can be shown that both diffusion modes contribute to the signal but one mode is strongly enhanced for situations typically encountered in DLS experiments. The developed theory thus clarifies the relationship between ternary DLS measurements and other diffusion experiments. It provides the practical basis for quantitative analysis of DLS experiments in ternary low-molecular weight fluids.     

Agglomeration of particles in a binary latex mixture,according to dynamic light scattering data

The effect of additions of methyl methacrylate latexes on agglomeration of butadiene-styrene latex was examined.     

Static and dynamic light scattering in turbid suspensions

The application of static and dynamic light scattering to many colloidal systems of practical interest has often been considered too complicated due to strong multiple scattering. There are two new approaches to overcome this problem. One of them aims at suppressing contributions from multiple scattering using novel cross‐correlation schemes. While this relies on the suppression of multiple scattering, the so‐called diffusing wave spectroscopy (DWS) works in the limit of very strong multiple scattering. DWS can be used for the characterization of dynamic and static properties of colloidal systems on a large range of time and length scales ranging from a few Ångstroms to hundreds of nanometers. We demonstrate that a wealth of information can be obtained from these methods on the structure, dynamics, interaction effects, stability, aggregation, and sol‐gel transition in colloidal dispersions.     

Dynamic light scattering in liquid and supercooled diphenylmethane

We use a dynamic light scattering technique to measure both polarized (VV) and depolarized (VH) spectra of liquid diphenylmethane (DPM) between 288 and 362 K, covering both normal and supercooled liquid ranges. Our results allow extracting information on structural relaxation processes, rotational motions, rotation-translation couplings, and molecular reorientation phenomena in liquid DPM. The VV spectra are modeled according to the microscopic theory of Wang, which assumes that a structural relaxation process dominates the spectrum. We find that the relaxation time of the structural relaxation in DPM follows an Arrhenius behavior. The Rayleigh dip was observed in the VH spectra, which are described using the Andersen-Pecora theory. Our results are discussed in terms of the rotation-translation coupling parameter, which we find independent of temperature over the experimental range. The collective reorientation time also follows an Arrhenius behavior with temperature. Finally, we calculate the hydrodynamic volumes for the reorientation process from geometric molecular models in two hydrodynamic limits: slip and stick boundary conditions. Our results suggest that the DMP molecule reorientates in quasi-slipping conditions in the bulk liquid.     

Stimulated light scattering in smectic A liquid crystals

The non-linear interaction of arbitrary polarized light with smectic layer deformations in smectic A liquids (S_A) is considered. It is shown that the combined effect of anisotropy, fluidity and a characteristic kind of deformation cause a number of specific non-linear optical phenomena. Two-wave mixing in S_A transforms into a partly degenerate four-wave mixing (FWM) when the polarization and the direction of propagation of the coupled electromagnetic (EM) waves are arbitrary. The interference of the EM waves gives rise to a dynamic grating of layer deformations without a change of mass density of S_A. In the resonant case a propagating mode of a second sound (SS) is excited. The non-linear phenomena are analysed by solving the self-consistent system of the Maxwell equations for the non-linear anisotropic inhomogeneous medium and the hydrodynamic equations of S_A in the external EM field. The explicit expressions of the EM and SS waves amplitudes are obtained. It is shown that the coupled fundamental EM waves undergo the parametric amplification and the phase cross-modulation, and their amplitudes as well as the SS wave amplitude are spatially localized. The energy transfer between the coupled EM waves is non-reciprocal. The scattering of the fundamental EM waves by the dynamic grating results in the appearance of additional harmonics with combination frequencies and wavevectors. The light induced dynamic grating also generates a longitudinal electric field due to the flexoelectric effect.     

圣草次苷-CTAB-DNA三元体系共振光散射光谱研究及应用

基于圣草次苷和十六烷基三甲基溴化胺(CTAB)的二元体系增强DNA的共振光散射(resonance light scattering,RLS)信号,提出了一种测定纳克级小牛胸腺DNA(ctDNA)的新方法.研究了圣草次苷、CTAB与DNA的结合方式并讨论了三元体系的最佳反应条件.增强的RLS信号与DNA浓度具有良好的线性关系,线性方程为ΔIRLS=28.33+1241c,r=0.9953.采用该方法对合成样品进行了分析测定,回收率和RSD分别为96.51%~101.38%和2.56%~3.90%,检出限为1.942μg·L^-1.     

Anomalous light scattering in photonic cholesteric liquid crystals

ABSTRACT

We have carried out polarisation and angle-resolved measurements of the light scattered from photonic cholesteric liquid crystals. Both in samples doped with laser dyes and in inactive (non-doped) samples we have observed pronounced directional dependences of the scattered light, finding angular ranges where the scattering is greatly enhanced and regions where the effect is almost suppressed. Moreover, the total amount of scattered light has also been found to depend strongly on the polarisation and direction of the incident beam. All the results have been interpreted successfully in terms of a simple expression proposed for the scattering cross section, in which the density of states of the ingoing and outgoing beams plays a major role. The expression would be applicable not only to cholesteric liquid crystals but to any one-dimensional photonic material.     

Dynamics of supercooled van der Waals liquid under pressure. A dynamic light scattering study

Dynamics of 1,1-di(p-methoxyphenyl)cyclohexane (BMPC) was studied in a temperature range of 253–313 K and a pressure range of 0.1–180 MPa by means of depolarized dynamic light scattering-photon correlation spectroscopy. The temperature dependence of the mean structural relaxation times measured at constant pressures was analyzed using the Vogel-Fulcher-Tamman (FVT) equation. From the FVT analysis the values of the fragility and the glass transition temperature T_g and T₀ as well as their pressure dependence dT_g/dP and dT₀/dP were obtained and compared with the corresponding quantities obtained for a chemically similar but dynamically different liquid 1,1-di(4-methoxy-5-methylphenyl)cyclohexane (BMMPC), in which two additional intramolecular relaxations were previously reported. The temperature and pressure dependence of the mean structural relaxation times was also analyzed using the Avramov model.List of abbreviations BMMPC 1,1-Di(4-methoxy-5-methylphenyl)cyclohexane - BMPC 1,1-Di(p-methoxyphenyl)cyclohexane - KWW Kohlrausch-Williams-Watts - VFT Vogel-Fulcher-Tamman     

Study of dynamic light scattering in nematic liquid crystal and its optical,electrical and switching characteristics

In the present study, the polarisation-independent dynamic light scattering (DLS) in a nematic liquid crystal (LC) with a negative dielectric anisotropy has been compared in two operating modes by applying DC voltage or AC voltage to LC cells with a vertical and hybrid alignment. The attenuation of light transmittance and the DLS optical threshold without polarizers as well as a phase retardation of LC bend–splay deformation and a Fredericks threshold voltage with polarizers have been determined. Diffuse scattering of a light beam and broadband transmittance spectra of LC cells have been examined using the DC voltage in the interval of 0–40 V. Multi-domain structures and turbulent flows in the LC cells have been observed by polarisation optical microscope. The results show that the enhancement of the diffuse scattering of light in the LC cells correlate with ion density increase. The largest attenuation of the light intensity in the LC cells with a vertical alignment was 16.4 dB at a wavelength of 650 nm with a minimum decay time equal to 2.5 ms at DC voltage of 60 V. Our study has been shown that switching from a diffuse light scattering state to a transparent state can be twice accelerated by applying AC voltage with high frequency to LC cells.     

A comparison of diffusion coefficients for ternary mixed micelle solutions measured by macroscopic gradient and dynamic light scattering techniques

Taylor dispersion is used to measure ternary mutual diffusion coefficients (D(ik)) for aqueous solutions of decylsulfobetaine (SB10) (1) + dodecylsulfobetaine (SB12) (2), SB10 (1) + SB14 (2), and SB12 (1) + SB14 (2) mixed zwitterionic micelles. Cross-coefficient D(21) for the coupled flow of surfactant 1 produced by a concentration gradient in surfactant 2 is relatively small for these solutions, but D(12) reaches values as large as the main D(ii) coefficients. The results are interpreted by using the equation D(ik) = partial differential(C(i)D(i))/ partial differentialC(k) to relate the ternary mutual diffusion coefficients to the concentration-weighted average diffusion coefficients D(i) of the micellar and free-monomer forms of the surfactants. The macroscopic-gradient Taylor measurements are compared with diffusion coefficients measured by dynamic light scattering (DLS), which monitors microscopic concentration fluctuations. At most compositions, the intensity autocorrelation function G(tau) is a single exponential decay in D((2)), the smaller eigenvalue of the mutual diffusion coefficient matrix. A contribution from D((1)) is identified at high solute fractions of surfactant 1. The DLS results are consistent with contributions to G(tau) from uncoupled fluctuations in the concentrations of eigencomponents defined as the linear combinations of surfactants 1 and 2 that diagonalize the D(ik) matrix. A procedure for the rapid and convenient DLS measurement of ternary mutual diffusion coefficients, including the cross-coefficients for coupled diffusion, is suggested, using the Onsager reciprocal relation together with the eigenvalues and pre-exponential factors from G(tau).     

Transient light scattering in helix ferroelectric liquid crystal cells

The static model to describe coherent (regular) transmittance in helix ferroelectric liquid crystal cells under the transient light scattering mode is proposed. It can be used to develop three-dimensional volumetric and two-dimensional liquid crystal displays. The dependence of coherent transmittance on cell parameters and the amplitude of the applied electric field is analysed. Conditions for increasing scattering efficiency and contrast ratio enhancement through an interference quenching effect of the coherent transmittance are indicated.     

On the design of experiments for determining ternary mixture free energies from static light scattering data using a nonlinear partial differential equation

We mathematically design sets of static light scattering experiments to provide for model-independent measurements of ternary liquid mixing free energies to a desired level of accuracy. A parabolic partial differential equation (PDE), linearized from the full nonlinear PDE [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008)], describes how data noise affects the free energies to be inferred. The linearized PDE creates a net of spacelike characteristic curves and orthogonal, timelike curves in the composition triangle, and this net governs diffusion of information coming from light scattering measurements to the free energy. Free energy perturbations induced by a light scattering perturbation diffuse along the characteristic curves and towards their concave sides, with a diffusivity that is proportional to the local characteristic curvature radius. Consequently, static light scattering can determine mixing free energies in regions with convex characteristic curve boundaries, given suitable boundary data. The dielectric coefficient is a Lyapunov function for the dynamical system whose trajectories are PDE characteristics. Information diffusion is heterogeneous and system-dependent in the composition triangle, since the characteristics depend on molecular interactions and are tangent to liquid-liquid phase separation coexistence loci at critical points. We find scaling relations that link free energy accuracy, total measurement time, the number of samples, and the interpolation method, and identify the key quantitative tradeoffs between devoting time to measuring more samples, or fewer samples more accurately. For each total measurement time there are optimal sample numbers beyond which more will not improve free energy accuracy. We estimate the degree to which many-point interpolation and optimized measurement concentrations can improve accuracy and save time. For a modest light scattering setup, a sample calculation shows that less than two minutes of measurement time is, in principle, sufficient to determine the dimensionless mixing free energy of a non-associating ternary mixture to within an integrated error norm of 0.003. These findings establish a quantitative framework for designing light scattering experiments to determine the Gibbs free energy of ternary liquid mixtures.     

Phase separation mechanism in gelling aqueous biopolymer mixture probed by light scattering

Using time-resolved static and dynamic light scattering (DLS) we have studied the kinetics of phase separation in an aqueous gelatin/maltodextrin mixture upon fast cooling. The time evolution of the droplet radius is modelled for the monodisperse case under reaction-limited and diffusion-limited conditions and compared with the observed evolution of the mode associated with the droplet diffusion. For quenches to above the gelatin ordering temperature, nucleation and rather reaction-limited than diffusion-limited growth and late-stage coalescence of droplets with diameters up to 90 μm were concluded. Quenches to well below the gelatin ordering temperature seem to induce diffusion-limited growth or (delayed) spinodal decomposition (SD) to a phase-separated microstructure with slow late-stage coarsening. In deep quenches, a second slow SD or diffusion-limited cluster aggregation (DLCA) process becomes apparent from the evolution of the static structure factor; the process seems to be related to the maltodextrin gelation in the composite.     

Brownian dynamics in strongly scattering porous media - dynamic light scattering with single-mode matching

Brownian motions in porous media represent a challenging problem not only from a theoretical but also from an experimental point of view. A very powerful technique for the measurement of Brownian motions is Dynamic Light Scattering (DLS). For our problem, however, the classic version of DLS is useless because the porous matrix scatters very strongly and the particles to be measured are completely masked. Sometimes it is possible to suppress the background scattering by matching the refractive indices of the matrix and the confined liquid, but this restricts the applicability to a handful of suitable model systems. We have introduced a new technique which overcomes this difficulty: The keyword is single-mode matching and the idea is to select from the complicated random light field generated by the strongly scattering medium only a single mode so that the contribution from the matrix to the selected mode vanishes because of destructive interference. The first experimental results on the dynamics of latex particles in aqueous suspensions confined in a packing of glass beads are very promising. Their quantitative analysis demonstrates clearly the feasibility of measuring the diffusion coefficient within an opaque strongly scattering porous medium.     

Dumbbell-shaped polyelectrolyte brushes studied by depolarized dynamic light scattering

We present the synthesis and comprehensive characterization of dumbbell-shaped polyelectrolyte brushes (DPB). The core of these particles consists of poly(methyl methacrylate) (PMMA) and poly(styrene) onto which a dense brush shell of poly(styrene sulfonate) is grafted. The morphology of DPB particles is studied in solution by cryogenic-transmission electron microscopy. We demonstrate that well-defined DPB are generated that react to external stimuli such as surfactant and salt concentration. The rotational diffusion and collective relaxations of the DPB particles were monitored by depolarized dynamic light scattering (DDLS). Here we found a new relaxation mode in the DDLS-signal that can be ascribed to collective fluctuations of the polyelectrolyte layer affixed to the surface of the dumbbells.     

Theory of dynamic light scattering by polymers and gels

It is shown under very general conditions that the intermediate scattering function for the generalized Rouse—Zimm model always takes the simple form G(K, t) α exp[?K²(k_BT/f)t], when the scattering vector K becomes sufficiently large. (Here k_B is Boltzmann's constant, T is the absolute temperature and f is the individual bead friction factor.) A microscopic formulation for the bulk modulus and friction factor density of a gel network is incorporated into the viscoelastic continuum model of Tanaka et al. The resulting expression for the apparent long-wavelength diffusion coefficient of the gel is D_G = (k_BT/f)2(1 - 2/Φ), where Φ is the network functionality.     

Determination of microscopic interaction parameters of ternary polymer solutions with light scattering data

Using a renormalized form of the Random Phase Approximation (or Tree Graph Approximation) we analysed data on the zero angle scattering intensity and the apparent radius of gyration for the system polystyrene-poly(methyl methacrylate)-bromobenzene. Since the microscopic parameters of this system are known from the analysis of the zero-angle scattering data, the theory yields a parameterfree prediction of the apparent radius of gyration which fits the data very well. To show the influence of renormalization we also analyse the data by an unrenormalized version of RPA.