Size distribution analysis of polymer latex systems by use of the extrema in the angular light scattering pattern. III. Unpolarized and horizontally polarized scattered light

The extrema in the unpolarized and the horizontally polarized angular scattering patterns are used as a basis for size-distribution analysis of polymer latex systems composed of single, spherical, optically isotropic particles. The method of analysis is similar to that recently proposed for vertically polarized scattered light and the polarization ratio, where the modal diameter and a distribution width parameter are determined from the experimental angular scattering pattern and prepared theoretical diagrams obtained by Mie theory calculations. The method of analysis, based on all four scattering functions, is illustrated by use of a Dow polystyrene latex sample.     

Size-distribution analysis of polymer latex systems by use of the extrema in the angular light-scattering pattern: II. The polarization ratio

Previously, the angular positions of the extrema of the polarization ratio have been utilized in light-scattering studies as a method of particle-size analysis under the assumption of monodisperse, spherical particles. Since the consequences of the existing finite polydispersity on this method of analysis was not assessed, the results are questionable. This work is concerned with (1) reporting the quantitative effects of a finite polydispersity on the method of analysis, (2) pointing out previous misuse of the method, and (3) revising the method of analysis to include polydispersity and the exact Mie calculations. The method will then permit the characterization of a scattering system in terms of a modal diameter and a distribution-width parameter by utilizing prepared diagrams for a particular relative refractive index.     

Particle size analysis of polymer latexes by light scattering. V. The significance of an assumed distribution in the analysis of angular scattering data

In the analysis of light scattering data from polymer latex systems or other systems of spherical particles, it is necessary to assume a particle size distribution function. Theoretical angular scattering functions based on the assumed distribution and representing a wide range of size distribution parameters are compared to experimental data in order to obtain a best fit. In previous work, it has been shown that as the polydispersity increases beyond certain limits the uncertainty in the assignment of the size distribution parameters (i.e., the best fit) increases. This report is concerned with the analysis of angular scattering from unimodal systems and simulated cases where theoretical scattering functions for wide, negatively skewed distributions are used as “experimental data,” are analyzed by utilizing four different distribution functions. These functions represent different degrees of skewness and include negatively, positively, and normally skewed distributions. The results from the use of the various distribution functions are discussed with respect to the uncertainly in the assignment of distribution parameters resulting from the loss of structure in the angular scattering pattern due to increased polydispersity. Scattering data from the bimodal distribution are analyzed by assuming a unimodel distribution, and the consequences of this assumption are assessed.     

A thermodynamic analysis on the coincidence of extrema conditions in the sorption equilibrium for ternary polymer systems

Flory-Huggins theory of polymer solutions has been used to express the condition of extrema values in the total sorption, as well as the inversion point in the preferential adsorption parameters for termary polymer systems. Two approaches have been followed, the first considers the binary and ternary interaction parameters independent of polymer concentration and solvent composition. In the second one, this dependence has been introduced. Our attention is focused on the volume fraction of solvent mixture dependence of the above parameters, in order to confirm or not the coincidence between the extrema values and the inversion point. Several cosolvent and cononsolvent ternary polymer systems, have been used to test the validity of the equations obtained. Also, it has been verified, from an experimental point of view, that in cosolvent ternary polymer systems there is coincidence in both compositions while in cononsolvent ternary polymer systems, such coincidence does not appear.     

Size distribution analysis of single and bi-component polymer and inorganic particle systems by comparison of two analysis methods in analytical ultracentrifuge

Sedimentation velocity runs were performed on organic and inorganic particles with analytical ultracentrifugation and the diameter and diameter distribution analysis was carried out with Sedfit and VelXLAI data analysis programs. The particles were measured either as pure components or as mixtures of different organic or inorganic particles using different weight ratios of these components. Polymer particles with peak diameters of ≈15 and 32-35 nm and inorganic particles with peak diameters of ≈5 and ≈32 nm were used and the particles also differed in the extent of polydispersity. The mixtures of particles in the weight ratios of 50:50, 90:10 and 95:5 of smaller to larger particles or vice versa were studied. The aim was to compare the performance of the analysis programs to characterize the various polymer and inorganic particle samples of varying complexity. The analysis programs were compared with each other not only for peak particle diameters and their size distributions, but also for the cumulative fractions of components of the particle mixtures.     

Concentration distribution of elements in heterogeneous polymer systems determined by electron microprobe analysis

A technique for analysis of composition variations in heterogeneous polymer systems permits investigation of materials with both uniform and nonuniform distribution of heterostructural components. To illustrate the method, determinations have been made of concentration profiles of dibromo-diallyl-phthalate formed in porous PVC in two different ways.     

Morphological analysis of polymer systems with broad particle size distribution

This contribution is focused on precise determination of particle size distribution in polymer blends with complex morphology by means of our new program called MDISTR. Standard determination of the particle size distribution is usually achieved by measurement of particle sizes in (a single set of) electron micrographs. We show why this method fails for two frequent cases: (i) blends with very broad particle size distribution and (ii) blends that are composed of domains with different particle sizes. On real-life examples, we demonstrate that program MDISTR yields accurate particle size distributions in both the above-mentioned cases, while the standard image analysis gives average particle sizes differing by >100 % from the correct result. We describe MDISTR calculations which are based on a linear combination of standard particle size distributions from two (or more) sets of micrographs with different magnifications, different locations within the sample and precisely defined statistical weights.     

Transformation of phase size distribution into scattering intensity

A practical method of calculating the small-angle scattering intensity and the density correlation function from the phase size distribution is presented for a sample with a random two-phase morphology. The correlation function can be calculated in terms of joint probability distribution functions of the phase size distributions of the two individual phases with information from the chord length distribution. The phase size distribution is approximated as a weighted sum of exponentials, which is then transformed analytically into the correlation function and hence the small-angle scattering for any combination of phase size distributions of the two phases. This represents an extension of the Debye method for materials with more complex phase size distributions. The inverse problem of calculating the phase size distributions from the small-angle scattering requires a thermodynamic model or simplifying approximation. An example of the reverse transformation is given for a nanoporous polymer thin film. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3070–3080, 2004     

Ion distribution around electrostatically stabilized polystyrene latex particles studied by ellipsometric light scattering

The ion distribution around electrostatically stabilized polystyrene latex spheres for different ionic strengths is investigated by ellipsometric light scattering. This method is sensitive to the refractive index profile around colloidal particles, which is affected by the local salt content. At an average salt concentration of c* = 10(-4) mol L(-1), the ion concentration at the particle interface increases discontinuously, and a layer of high salt content with 20-30 nm thickness is built up. The observation cannot be explained within the framework of the Poisson-Boltzmann equation; it rather resembles a prewetting transition. Interactions that could possibly lead to a stabilization of the observed layer of high salt content are discussed.     

Remarks on the angular distribution of light scattering from absorbing solid surfaces

We have shown that within the approximate “backward” Raman scattering geometries used with absorbing cubic crystals there are significant variations of the scattered powder due to geometrical factors. Angular dispersion curves are derived for the scattered power in terms of the optical constants n and k and the angles of incidence and detection. The results are rather insensitive to the absorption constant and carrier concentration but depend critically on the index of refraction n and its dispersion. Experimental results for typical cubic materials are in agreement with the model.     

Application of interface distribution functions to the evaluation of the small angle x-ray scattering of multicomponent polymer systems

A method for correcting the small angle x-ray intensity of multi-component polymer systems to compute the interface distribution function is presented. The resolution of this function can be improved to a great extent by evaluating the interference function from the measured intensity corrected for fluctuation scattering by use of a function which is proportional to the gas scattering of the investigated system. The method is applied successfully to polymer blends composed of components having similar morphology.Presented at the Spring Meeting of the Deutsche Physikalische Gesellschaft, Hamburg, March 14–16, 1988.     

Application of interactive image analysis to light scattering patterns of some polymer systems

In this paper we describe a system for interactive picture analysis useful for extraction of various types of physical information from both real- and Fourier-space images. The possibility of hardware and software operations are illustrated, with examples of applications such as analysis of light scattering patterns from phase separated systems, semicrystalline polymer films with significant supermolecular morphology and from less regular polymer systems with a pronounced speckle effect. The analysis concentrates on both spatial and time dependent scattering processes and measurements of intensity correlation of scattered light. Although the present examples of application are limited to light scattering patterns of polymer systems, the technique of interactive picture analysis is useful for quantitative extraction of information from real-and Fourierspace images of arbitrary structure.     

Contribution to polymer nanoparticles analysis by laser light scattering

The applications of laser light scattering (LLS) to polymer physics and colloid science have been extensive and noteworthy, especially in particle-size analysis. The study presents an example of LLS application to the characterization of interpolymer complexation of poly(aspartic acid) with a vinylic polymer, by particle size and zeta potential evaluation. The LLS technique is complemented by oscillatory rheological data. The complexes have a potential biomedical application by bioactive substances attachment.     

Determination of the width of the domain boundaries in polymer two-phase systems by X-ray small-angle scattering

An accurate determination of the width of domain boundaries presupposes an unambigous elimination of the intensity component due to density fluctuations within the domains. The theoretical aspects of this problem are discussed and an application is demonstrated in an SAXS study of a styrene-isoprene-styrene blockcopolymer. The widths of the domain boundaries depend on the history of the sample, its values are, in general, smaller than theoretically predicted. The domain sizes correspond to the theoretical values, its variance is of the same order as the variance of the molecular weight of the domain-building blocks.Dedicated to Prof. Dr. Dr. h. c. O. Kratky on the occasion of his 80th birthday.     

Photoelectron angular distribution in valence shell ionization of heteroaromatic molecules studied by the continuum multiple scattering xalpha method

Photoelectron angular distributions are calculated for the valence shell ionization of heteroaromatic molecules of pyridine, pyrazine, pyrimidine, pyrrole, and furan by the continuum multiple scattering Xalpha method. The asymmetry parameters exhibit strong energy dependences in ionization from pi orbitals but are almost invariant in ionization from sigma orbitals, in good agreement with experimental results. The asymmetry parameters in ionization from nonbonding orbitals appear generally higher than those in ionization from bonding orbitals. These features are interpreted in terms of the Coulomb phase and photoelectron angular distribution in the molecular frame.     

Evaluation of the dynamic properties of polymer latex particles interacting with quartz interface by evanescent wave dynamic light scattering

The diffusion behavior of polymer latex particles in dispersion near the quartz interface has been estimated by evanescent wave dynamic light scattering (EVDLS) technique. The diffusion coefficient of the particles was measured as a function of the distance between the particle and interface. The apparent diffusion coefficient estimated by EVDLS was small for particles near the interface and increased upon increasing the distance from the interface, and then saturated at a certain value which is close to the value expected for free-motion. The range of the distance over which diffusion was affected by interaction with the interface depended on the added salt concentration. This means that the diffusion of the particle is influenced by an electrostatic interaction between the particle and quartz interface in addition to the hydrodynamic effect near the wall. This range was found to be more than 800?nm at 0?M salt condition but about 400?nm at 10^-4 and 10^-3?M salt conditions. Hence it is appropriate to say that the hydrodynamic effect reaches up to 400?nm and the electrostatic effect is longer ranged, more than 800?nm, for the system studied here. The EVDLS technique is a very powerful tool for quantitative estimations of the dynamic behavior of the particle near the interface and for estimation of the range where the wall effect is dominant. EVDLS will give us an answer to the question of “where is the ‘interface’ and where is the ‘bulk’?”.     

Necessary and sufficient conditions for the appearance of extrema on concentration distribution curves in complex equilibrium systems

It is shown that species distribution curves with at least one minimum may be found in most equilibrium systems with three or more components. Whether such concentration minima are actually observed then depends on the values of the equilibrium constants and on the total (analytical) concentrations of the components. A general algorithm is given for the necessary and sufficient conditions for the appearance of extrema in multicomponent systems. Three-component systems are studied in more detail and special attention is given to the limiting case of a horizontal inflection, i.e., the point where the concentration minimum just disappears. Two well-studied chemical examples, the Cu(2+)-diethylenetriamine-OH(-) and Hg(2+)-Cl(-)-OH(-) systems are discussed, along with a simple model system showing as many as five extrema on a single distribution curve.     

Average cluster size determination in supersonic beams from angular distribution measurements after scattering by a buffer gas

A method for the determination of average cluster size in supersonic beams is presented. Based on angular distribution broadening of the beams caused by passing through a buffer gas, this method is well suited for in situ determination of the mean cluster size when the apparatus contains a movable detector with sufficient spatial resolution. The shape and width of the beam profile after scattering by a buffer gas are evaluated theoretically as functions of buffer gas pressure and atom-cluster collision cross-section. Experimental results are presented for an argon beam, yielding average cluster sizes between 300 and 7000 atoms depending on the stagnation pressure. Simple criteria to assess the applicability of the method to a given experimental situation are discussed. The average cluster sizes determined in this work agree quite satisfactorily with previously published values for similar beam generation conditions.