Chain entanglement in thin freestanding polymer films

When a thin glassy film is strained uniaxially, a shear deformation zone (SDZ) can be observed. The ratio of the thickness of the SDZ to that of the undeformed film is related to the maximum extension ratio, lambda, which depends on the entanglement molecular weight, M(e). We have measured lambda as a function of film thickness in strained freestanding films of polystyrene as a probe of M(e) in confinement. It is found that thin films stretch further than thick films before failure, consistent with the interpretation that polymers in thin films are less entangled than bulk polymers, thus the effective value of M(e) in thin films is significantly larger than that of the bulk. Our results are well described by a conceptually simple model based on the probability of finding intermolecular entanglements near an interface.     

X-ray scattering from polymer nematic liquid crystals

X-ray scattering from main chain polymer nematics is discussed from the point of view of its use in studying the ordering and fluctuations of the polymer chains that make up the nematic phase. An example of data from poly-γ-benzyl glutamate is given, with a discussion of the important features of the data, in terms of the current understanding of the nature of nematic ordering in main chain polymer systems. This includes analyses of the angular distribution function for the polymer segments, long wavelength fluctuations dictated by elastic phenomena, the effects of finite chain lengths, and effects due to the short range interactions and packing of the chains.     

X-ray scattering from freely suspended smectic-A films

This work is devoted to a theoretical analysis of specular reflection and diffuse scattering of x-rays from a freely suspended smectic-A film, taking into account its spatial inhomogeneity and deviations of orientational and position ordering in smectic layers from ideal ordering. The results of the calculations are compared with the experimental data on small-angle scattering of x-rays from freely suspended films of 7 AB liquid crystals. It is found that the theoretical results agree with the experimental data.     

Mean-field theory for polymer adsorption on curved surfaces

We discuss the influence of polymer adsorption on the curvature energy of an interface. Following an article by Clement and Joanny (J. Phys. II 7, 973 (1997)), a mean-field theory is used to calculate the surface tension, rigidity constants and spontaneous curvature associated with both reversible and irreversible polymer adsorption. In the case of irreversible polymer adsorption it is assumed that the amount of adsorbed polymer remains constant upon curving the interface. Unfortunately, constraining the amount of polymer by adding a Lagrange multiplier affects the thermodynamic state of the (free) polymer far away from the interface. Clement and Joanny solve this problem by removing the polymers in the bulk. We allow for the presence of free polymers, but to achieve this we have to apply a local external field to keep the adsorbed amount fixed. The results of the two approaches are compared and a physical interpretation is given. Received 25 July 2001 and Received in final form 5 December 2001     

X-ray scattering studies of liquid surfaces

X-ray reflectivity experiments on the structure of the liquid-vapor interface that were recently carried out by our group will be described. Systems that were studied include thin wetting layers adsorbed onto a solid substrate, the interfacial electron density profile of superfluid ⁴He, and preliminary measurements of the roughness of the surface of liquid gallium. The fundamental theoretical background to these experiments will be reviewed.     

A high-order tangential basis algorithm for electromagnetic scattering by curved surfaces

We describe, analyze, and demonstrate a high-order spectrally accurate surface integral algorithm for simulating time-harmonic electromagnetic waves scattered by a class of deterministic and stochastic perfectly conducting three-dimensional obstacles. A key feature of our method is spectrally accurate approximation of the tangential surface current using a new set of tangential basis functions. The construction of spectrally accurate tangential basis functions allows a one-third reduction in the number of unknowns required compared with algorithms using non-tangential basis functions. The spectral accuracy of the algorithm leads to discretized systems with substantially fewer unknowns than required by many industrial standard algorithms, which use, for example, the method of moments combined with fast solvers based on the fast multipole method. We demonstrate our algorithm by simulating electromagnetic waves scattered by medium-sized obstacles (diameter up to 50 times the incident wavelength) using a direct solver (in a small parallel cluster computing environment). The ability to use a direct solver is a tremendous advantage for monostatic radar cross section computations, where thousands of linear systems, with one electromagnetic scattering matrix but many right hand sides (induced by many transmitters) must be solved.     

Temperature factor of X-ray diffraction and diffuse scattering from helical polymer crystal

A theoretical treatment for the effect of thermal vibration on the X-ray scattering intensity for a helical polymer crystal is presented. The treatment involves assumptions that (1) the unit cell of the crystal contains only one polymer chain and (2) fluctuations of the atomic positions are small. The temperature factor of the intensity of Bragg reflections is expressed in terms of mean squares of fluctuations of helical parameters. The diffuse scattering is also considered in a special case.     

Viscoelastic dynamics of polymer thin films and surfaces

The strain relaxation behavior in a viscoelastic material, such as a polymer melt, may be strongly affected by the proximity of a free surface or mobile interface. In this paper, the viscoelastic surface modes of the material are discussed with respect to their possible influence on the freezing temperature and dewetting morphology of thin polymer films. In particular, the mode spectrum is connected with mode coupling theory assuming memory effects in the melt. Based on the idea that the polymer freezes due to these memory effects, surface melting is predicted. As a consequence, the substantial shift of the glass transition temperature of thin polymer films with respect to the bulk is naturally explanied. The experimental findings of several independent groups can be accounted for quantitatively, with the elastic modulus at the glass transition temperature as the only fitting parameter. Finally, a simple model is put forward which accounts for the occurrence of certain generic dewetting morphologies in thin liquid polymer films. It demonstrates that by taking into account the viscoelastic properties of the film, a morphological phase diagram may be derived which describes the observed structures of dewetting fronts. It is demonstrated that dewetting morphologies may also serve to determine nanoscale rheological properties of liquids.Received: 1 January 2003, Published online: 14 October 2003PACS: 47.50. + d Non-Newtonian fluid flows - 68.47.Mn Polymer surfaces - 68.60.Dv Thermal stability; thermal effects     

Inelastic light scattering and X-ray diffraction from thick free-standing porous silicon films

The results of Raman scattering and X-ray diffraction studies of thick, free-standing, porous Si layers with thickness up to 500 μm are presented. The Raman scattering spectra have a distinctive difference from previous data for porous Si films on Si substrate and for thin, free-standing, porous Si layers. The experimental data can be explained by a modified phonon confinement model that accounts for a comprehensive strained Si nanocrystal. The comprehensive strain is a tensile one, and the value of stress can be up to 3 GPa. This interpretation is supported by data of X-ray diffraction measurements.     

Liquid crystal films on curved surfaces: An entropic sampling study

The confining effect of a spherical substrate inducing anchoring (normal to the surface) on rod-like liquid crystal molecules contained in a thin film spread over it has been investigated with regard to possible changes in the nature of the isotropic-to-nematic phase transition as the sample is cooled. The focus of these Monte Carlo simulations is to study the competing effects of the homeotropic anchoring due to the surface inducing orientational ordering in the radial direction and the inherent uniaxial order promoted by the intermolecular interactions. By adopting an entropic sampling procedure, we could investigate this transition with a high temperature precision, and we studied the effect of the surface anchoring strength on the phase diagram for a specifically chosen geometry. We find that there is a threshold anchoring strength of the surface below which uniaxial nematic phase results, and above which the isotropic fluid cools to a radially ordered nematic phase, besides of course expected changes in the phase transition temperature with the anchoring strength. In the vicinity of the threshold anchoring strength we observe a bistable region between these two structures, clearly brought out by the characteristics of the corresponding microstates constituting the entropic ensemble.     

Modelling microwave scattering from long curved leaves

This paper describes the theoretical simulations carried out with a model of the backscattering coefficient of crops, where the leaf geometry is represented by a curved rectangular dielectric sheet. A general formulation is introduced for the bistatic scattering cross section of the curved sheet, and numerical results based on this approach are compared with those obtained by considering disc shaped leaves.     

Modelling microwave scattering from long curved leaves

Abstract

This paper describes the theoretical simulations carried out with a model of the backscattering coefficient of crops, where the leaf geometry is represented by a curved rectangular dielectric sheet. A general formulation is introduced for the bistatic scattering cross section of the curved sheet, and numerical results based on this approach are compared with those obtained by considering disc shaped leaves.