Evaluation of light scattering models to characterize concentrated polymer particles embedded in a solid polymer matrix (original) (raw)
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Polymer Journal, 1985
Static and dynamic properties of polymer solutions and melts can be investigated by means of modern scattering techniques. While small angle X-ray scattering (SAXS) and smallangle neutron scattering (SANS) have made advances particularly in studies related to the static structure factor S(K), laser light scattering including the use of Fabry-Perot interferometry and photon correlation spectroscopy has become a standard tool in studying polymer molecular motions. In polymer solutions, the main technique is to use measurements of angular distribution of integrated scattered intensity by means of visible light, SAXS or SANS for S(K) and measurements of angular distribution of the spectrum of scattered light by means of photon correlation spectroscopy for the dynamic structure factor, S(K, w). Recent advances have been made in the method of data analysis related to the ill-posed Laplace inversion problem. The new approaches include the singular value decomposition technique and methods of regularization with different criteria for the smoothing operator. By combining static and dynamic light scattering measurements with appropriate algorithms for the Laplace inversion of the time correlation function, a new analytical technique has been developed for polymer molecular weight characterizations. The nonintrusive method has been applied to determine the molecular weight distributions of linear and branched polyethylene in 1,2,4-trichlorobenzene at 135°C and of poly(l,4-phenyleneterephthalamide) in concentrated sulfuric acid. In addition, a new prism light scattering cell is being developed to integrate the above capabilities with chromatographic and other separation techniques. Aside from translational motions of the center of mass of polymers in dilute solution, photon correlation spectroscopy also permits us to investigate rotational, flexual and internal segmental motions. Polymer molecules entangle in semidilute solution. Light-scattering spectroscopy measures a cooperative diffusion coefficient and a slow mode which has been shown to be different in magnitude from the self-diffusion coefficient. The entanglement behavior varies from coils to rod-like polymers. Static and dynamic properties of polymer solutions in semidilute and semiconcentrated regimes can be related to those of bulk polymer melts where measurements of polarized Rayleigh-Brillouin spectra and depolarized Rayleigh spectra yield information on localized structural relaxation and collective segmentallmolecular orientational motions. Relaxation times covering a very broad frequency range will be discussed.
Particle and Particle Systems Characterization
A method for estimating the particle size distribution (PSD) of dilute latexes from multiangle dynamic light scattering (MDLS) measurements is presented. The estimation procedure includes two main steps: 1) the calculation of the angle-dependent average diameters of the PSD from MDLS measurements, and 2) the estimation of the PSD through an optimization strategy based on a genetic algorithm (GA). First, the capability of the method was tested on the basis of three simulated examples that involved different PSD shapes, widths, and diameter ranges. Then, the method was employed for esti-mating the PSD of three samples: a polystyrene latex standard of narrow PSD and known nominal diameter; a mixture of two polystyrene standards of narrow PSDs; and an industrial latex of unknown composition. For comparison, all examples were also solved by numerical inversion of the MDLS autocorrelation measurements through a linear constrained Tikhonov regularization technique. The proposed method appears as an effective and robust tool for characterizing unimodal and multimodal PSDs, without requiring any a priori assumption on the mode shapes or on the PSD diameter range.
Advances in Colloid and Interface Science, 1997
Analysis and modeling of small-angle scattering data from systems consisting of colloidal particles or polymers in solution are discussed. The analysis requires application of least-squares methods, and the basic principles of linear and non-linear leastsquares methods are summarized with emphasis on applications in the analysis of small-angle scattering data. These include indirect Fourier transformation, square-root deconvolution, size distribution determinations, and modeling. The inclusion of corrections for instrumental smearing effects is also discussed. The most common analytical expressions for model form factors and structure factors are summarized. An example of analysis of small-angle neutron and X-ray scattering data from block copolymer micelles is given. 1 A premous version of this review was used as lecture notes in The Third European Summer School on "Scattering Methods Applied to Soft Condensed Matter",
Inverse Problems in Science and Engineering, 2003
Polymeric emulsions are well characterized by the knowledge of their particle size distributions (PSD). Elastic-light-scattering (ELS) measurements can be inverted to estimate the PSD in the range from 50 nm. up to several micrometers. The relative refractive index of the particles is required in computation procedures to obtain the PSD. Small differences in the assumed refractive index may cause significant differences in the resulting PSD. From the scattering data, the refractive index can be determined. In this paper we present the corresponding technique. We consider polymeric emulsions where the non-absorption assumption is reasonable. We propose a methodology based on Tikhonov regularization applied only to the distribution. However, we solve the minimization problem simultaneously with respect to the distribution and the refractive index. To select the regularization parameter, we include the Generalized Cross Validation technique. From simulated ELS measurements we show that the problem is solved successfully. NOMENCLATURE A matrix form of operator T D particle diameter f particle size distribution (PSD) f vector form of PSD g noisy ELS measurement H matrix form of L I light scattering intensity J functional q smoothing restriction on f m relative particle refractive index n 1 particle refractive index n 2 solvent refractive index S Lorentz-Mie scattering function T Operator that represents the integral equation Greeks ε experimental error γ regularization parameter θ scattering angle Superscript ~ estimated values * adjoint
Optics & Laser Technology, 1999
A laser light scattering system was built to study the scattering parameters of some materials in solution form. The light source used was an argon-ion laser at wavelength 488 nm (all lines). The investigated material was a synthetic polymer which has a wide range of applications in the ®eld of teeth medicine applications. This is polymethyl-methacrylate (PMMA) which is used for the formation of arti®cial clamps. The PMMA was solved in both acetone and methyl-ethyl-ketone (MEK). The acetone solvent is chosen for its high speci®c refractive index increment dn/dc at the same wavelength 488 nm as the argon laser source. The angular distribution of the scattered laser light intensities of PMMA dissolved in acetone was measured at dierent scattering angles from 30 to 1508 for each concentration. The angular distributions have a symmetrical behavior about the scattering angle p/2; by using the scattered intensities the Zimm plot was formed. The weight average molecular weight (WAMW) was determined, the two other scattering parameters like as radius of gyration, h, and the second verial coecient, A 2 were determined. #
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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.
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Polymer Engineering and Science, 1987
A novel approach is described for the noncontact evaluation of structural morphology in polyblends by light scattering. Optical methods are attractive for the on-line characterization of translucent materials because they are noninvasive, rapid, and applicable to high temperature materials. One limitation of conventional light-scattering techniques is their requirement for relatively thin samples in order to avoid multiple-scattering effects that smear out the details of the light diffraction pattern. The approach described in this paper is meant to circumvent this limitation by resorting to turbidimetric measurements, which provide useful information on the average size, shape, concentration, and orientation of the dispersed phase particles even in the presence of multiple scattering. The sample thickness is no longer restricted, and methods are described by which the near-surface volume of infinitely thick parts may be inspected with access to a single side of the material. Results are presented for polypropylenepolycarbonate (PP/PC) samples of different thicknesses and microstructural morphology, including fibrillar-type oriented structures.
Journal of Polymer Science: Polymer Physics Edition, 1977
Hartel's theory for multiple scattering has been generalized to the case of small-angle light scattering (SALS) by polymers having a rodlike morphology. It is shown that multiple scattering tends to make the scattering patterns more diffuse and leads to an underestimation of the size of the units (rods) measured from such patterns. The error induced by neglecting multiple scattering has been estimated at 10% for a transmittance of 75% and at 22% for a transmittance of 50%. A correction method based on Hartel's procedure is suggested.