Small-angle light scattering from thin polymer films: Multiple scattering from samples with rodlike morphology

Hartel's theory for multiple scattering has been generalized to the case of small-angle light scattering (SALS) by polymers having a roadlike morphology. It is shown that multiple scattering tends to make the 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.     

Scattering of light from thin polymer films. I. Multiple scattering

A general method is described to take into account the multiple scattering effect in a small-angle light scattering from thin polymer films. It is seen that multiple scattering tends to make the scattering envelope more diffuse, reducing the intensity in the high intensity regions and increasing it in the low intensity regions. The method is applied here to a spherulitic system, but it is valid for any other system where the principal scattering is in the forward direction.     

The scattering of light from thin polymer films: Multiple scattering. II. Effect of depolarization

A procedure is described to include the effect of depolarization of the originally plane-polarized incident light beam as it passes through a thin polymer sample on the intensity of multiple light scattering. The multiple scattering gives rise to “polarization scrambling” in which, for example, H_v scattering measurements involve multiple scattered rays which may have undergone some V_v scattering. These phenomena reduce the angular dependence of scattering since large intensities originally occurring at small values of θ are rescattered so as to enhance intensities at other angles. Correction factors for both H_v and V_v scattering are presented.     

Small-angle light scattering and crystallization processes in solid polymer films

Information, not previously measurable, about the internal crystallization processes occurring within spherulitic films can now be obtained by combining refractive index, birefringence, and small-angle light-scattering measurements. The surroundings of a spherulite in a solid film are composed of both the adjacent spherulites and their interstices (boundaries), and it is shown that different crystallization processes can occur in each of these regions. Upon annealing a quenched isotactic polypropylene film, the rate of crystallization within the interstices of the space-filling spherulites is observed to be greater than the rate of crystallization within the spherulites themselves.     

Small-angle polarized light scattering from amorphous spheres

Small-angle light-scattering measurements have been made using micron-diameter isotropic and spherical polymer latex particles placed between crossed polarizers. Four-leaf clover patterns are obtained, reminiscent of those commonly found for spherical birefringent scatterers. The experimental results compare closely with predictions of Mie scattering theory for isotropic spheres.     

Dynamics of thin polymer films: Recent insights from incoherent neutron scattering

Incoherent neutron scattering is presented as a powerful tool for interpreting changes in molecular dynamics as a function of film thickness for a range of polymers. Motions on approximately nanosecond and faster timescales are quantified in terms of a mean-square atomic displacement (〈u²〉) from the Debye–Waller factor. Thin-film confinement generally leads to a reduction of 〈u²〉 in comparison with the bulk material, and this effect becomes especially pronounced when the film thickness approaches the unperturbed dimensions of the macromolecule. Generally, there is a suppression (never an enhancement) of 〈u²〉 at temperatures T above the bulk calorimetric glass-transition temperature (T_g). Below T_g, the reduction in the magnitude of 〈u²〉 depends on the polymer and the length scales being probed. Polymers with extensive segmental or local mobility in the glass are particularly susceptible to reductions of 〈u²〉 with confinement, especially at the Q vectors probing these longer length scales, whereas materials lacking these sub-T_g motions are relatively insensitive. Moreover, a reduced 〈u²〉 value correlates with reduced mobility at long time and spatial scales, as measured by diffusion in these thin polymer films. Finally, this reduced thin-film mobility is not reliably predicted by thermodynamic assessments of an apparent T_g, as measured by discontinuities or kinks in the T dependence of the thermal expansion, specific volume, index of refraction, specific heat, and so forth. These measurements illustrate that 〈u²〉 is a powerful and predictive tool for understanding dynamic changes in thin polymer films. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3218–3234, 2004     

Multiple scattering of light from polymer dispersed liquid crystal material

Light scattering from polymer dispersed liquid crystal (PDLC) material has been studied experimentally and by Monte Carlo simulation. Light scattering was measured as a function of both scattering angle and cell thickness. The cell thicknesses of practical interest are in an intermediate regime where neither single scattering nor light diffusion applies. Both the angular and the thickness dependence of the scattering intensity can be described accurately by a Monte Carlo simulation of multiple scattering from a homogeneous distribution of independent scatterers. The model smoothly interpolates between the single scattering limit for thin cells and the diffusion limit for thick cells. It can easily be extended to include any specific feature of a scattering display system.     

Small-angle light scattering from a distribution of spherulite sizes

Depolarized small-angle light scattering from spherulites in semicrystalline polymers gives rise to a characteristic cloverleaf pattern. For scattering from a single spherulite, the position of the maximum in scattered intensity is readily related to the spherulite radius. For a distribution of spherulites, the maximum should be related to some characteristic measure of the distribution. It is shown for a wide variety of distributions that this characteristic radius is a ratio of high moments of the size distribution, specifically R* ≈ 〈R⁷〉/〈R⁶〉. The shape of the light-scattering profile should in principal be related to the nature of the spherulite distribution. Calculations of scattering profiles from a variety of distributions fail to demonstrate this, owing to the strong dependence of scattering power on spherulite size. Exceptions are noted for the case of certain bimodal distributions.     

Small-angle polarized light scattering by spherulites

The light-scattering matrix for a three-dimensional spherulite is derived within the Ray-leigh-Gans-Debye light-scattering approximation. New expressions for the polarized, small-angle light-scattering intensities I_VV and I_VH are derived from the scattering matrix. These expressions are compared with the I_VV and I_VH expressions derived for a spherulite by Stein and Rhodes. For the case of a weakly anisotropic spherulite having an average refractive index mismatch with its surroundings, the two sets of expressions predict different I_VV and I_VH intensities. In particular, our expressions show that the I_VVand I_VH patterns usually attributed to the spherulitic anisotropy and crystallinity are also predicted for an isotropic sphere. This is in accord with recent experiments.     

Effect of birefringence on light scattering from deformed spherulitic polymer films

Light scattering from oriented samples of crystalline polymers is affected by the birefringence of the sample. An extension of the theory for scattering from uniaxially deformed two-dimensional and three-dimensional spherulites is made so as to include the retardation of the incident and scattered beams in passing through the birefringent sample. Strain influences scattering, in that it changes the birefringence of the sample and it also changes the anisotropy and shape of the spherulites. Scattering intensities are calculated for both crossed and parallel polarizers as a function of Ω, χ, and Φ, where Ω is the angle between the stretching direction of the sample and the horizontal direction, and χ and Φ are the angles between the stretching direction and the polarization directions of the polarizer and analyzer, respectively. It is shown that for crossed polarizers with Φ = 45° and χ = 45° birefringence changes largely influence the results but that for the polarizers parallel at Φ = 0° and χ = 0° or crossed at Φ = 90° and χ = 0° the birefringence effect is minimized. The intensity distributions for crossed polarizers at Φ = 45° and χ = 45° from polyethylene films stretched to give retardations up to several wavelengths, are found to be in good agreement with the calculated results.     

Brillouin scattering from polymer films

Many polymers cannot be prepared as clear amorphous blocks suitable for classical light scattering studies. However, most linear polymers can be prepared as films which are somewhat transparent. With the advent of high contrast multipass interferometers, these films can now be studied by Brillouin scattering. This work demonstrates the wide range of polymeric materials that can now be studied by Brillouin spectroscopy.     

New apparatus for studies on supermolecular structures of thin polymer films by small-angle light scattering

The construction and principle of operation of small-angle light scattering apparatus for studies of supermolecular structure in thin polymer films is described. The apparatus can be used to study changes in spherulite structure during crystallization and changes in films subjected to steady or sinusoidal strain. Typical results with polyethylene films are given.     

Small-angle light scattering from an anisotropic sphere: The mueller matrix approach

The explicit form of the Mueller scattering matrix, which characterizes the small-angle light scattering from an anisotropic sphere when the requirements of the Rayleigh-Gans-Debye (RGD) approximation are fulfilled, contains all information obtainable about the RGD scattering from an anisotropic sphere taken as a model for a spherulite. A comparison of angular dependences of single matrix elements for the Lorenz-Mie sphere, the Rayleigh particle, and the simplified form of the presented matrix (taking a sphere without inherent anisotropy, i.e., Δn = 0) shows very good agreement within the limits of RGD approximations. The polarized small-angle light scattering intensities Hυ and Vυ are combinations of the single matrix elements. Their explicit form is in accord with the expressions for Hυ and Vυ intensities recently rederived from a 2 × 2 amplitude scattering matrix. It has been shown that the angular dependence of matrix elements is determined by the (n? — 1)/Δn parameter, where n — is the mean refractive index andδ n is the anisotropy, both measured relative to the surrounding medium. The expressions for Hυ and Vυ intensities derived by Stein and Rhodes fail for a sphere without inherenet anisotropy ( δ n = 0); and the commonly used procedure of size determination from a maximum of Hυ intensity has limited validity (it holds only approximately under the condition of a small phase shift and small (n?-1)/ δ n). Further theoretical work must be done to understand and construct scattering models for situations where the RGD approximately is inappropriate.     

Small-angle scattering of circularly polarized light from an anisotropic sphere

A theory of the small-angle scattering of circularly polarized light from an anisotropic sphere has been derived. The validity of the theory has been verified, and a relationship between the structural information thus obtained and the structural information obtained with linearly polarized light has been demonstrated.