Constitutive equation to describe the nonlinear elastic response of aqueous foams and concentrated emulsions J. Rheol. 48, 679 (2004) Prediction of bubble growth and size distribution in polymer foaming based on a new heterogeneous nucleation model J. Rheol. 48, 439 (2004) Theory for drop deformation in viscoelastic systems SynopsisOften, blends of two immiscible polymers have a morphology with one component building a matrix in which spherical inclusions of the other component are embedded. The rheological response of such blends contains an elastic contribution which can be attributed to the form relaxation of the inclusions. This process has a characteristic relaxation time which is proportional to the radius of the inclusions divided by the interfacial tension between the blends' components. Thus a distribution of radii leads to a distribution of relaxation times. It is shown that rheological data together with an emulsion model can be used to determine the volume weighted sphere-size distribution up to a scaling depending on the interfacial tension. The procedure is applied to data of four PMMAJPS blends and the results are compared with the corresponding distributions obtained from transmission electron microscopy (TEM). If the concentration of the spherical inclusions is small, both results are in excellent agreement. For larger concentrations, deviations between the results from rheology and TEM are observed.
SYNOPSISThe blending of two immiscible polymer samples can lead to spherical inclusions of one component in a matrix of the other component. The mechanical solid-state properties as well as the flow behavior of the melt depend on the size of the spheres in the blend. For that reason, the sphere-size distribution is of major interest. Information about this distribution is often obtained by analyzing thin slices of the blend with transmission electron microscopy. In that way, however, the sphere-size distribution itself is not obtained. The reconstruction of the sphere-size distribution is introduced as a stereological problem, well known in fields as metallurgy, biology, geology, and medicine. It is shown that the spheresize distribution can be reconstructed using a regularization method as implemented in the program FTIKREG. 0 1994 John Wiley & Sons, Inc. I NTRO DU CTlO NMany polymeric materials consist of two or more immiscible polymers. In most of these materials, one component builds a matrix in which particles of the other components are embedded. In the case of twophase materials, the particles are often approximately spheres randomly dispersed in the matrix. Two well-known examples are rubber-toughened polymers like high-impact polystyrene lS2 and polymer blends of two immiscible thermoplastic^.^-^ Naturally, all the particles do not have the same size and a sphere-size distribution must be used to characterize them. This distribution depends on the conditions during the preparation of the material. It influences the mechanical solid-state properties 7-10 as well as the flow behavior of the melt."-'3 For that reason, the sphere-size distribution is of major interest and many experimental methods have been developed to characterize it.One widespread method to obtain this morphological information is miscroscopy, especially trans- CCC 0021-8995/94/0l0039-12 mission electron microscopy (TEM). To study a polymer blend with TEM, thin slices of 50-200 nm thickness have to be prepared, whereas typical particle radii range from about 50 nm up to several micrometers. Obviously, only a two-dimensional profile of the three-dimensional structure can be observed with TEM: Image-analysis of thin slices yields the radii of profiles of the particles rather than the radii of the spherical particles themselves. Similar problems arise in metallurgy, biology, geology, and medicine. Out of the common interest in such problems, the discipline of stereology was founded in the 1960s. In general, stereology deals with mathematical problems concerning the determination of parameters characterizing a three-dimensional structure from data obtained by studying two-dimensional profile^.'^^'^ The reconstruction of sphere-size distributions from so-called profile size distributions is a well-known problem in stereology and many scientists have dealt with the derivation of the relation between both distributions and with methods for reconstructing sphere-size distributions. '6-26 In this contribution, we show that stereological results ...
SYNOPSISIn this article, symmetrical, narrow distribution P ( S-b-MMA ) block copolymers are characterized rheologically, using a dynamic spectrometer and a stress rheometer. The shear induced morphology changes are investigated by off-line electron microscopy and SAXS. We tried to correlate the results of dynamics and long-time creep experiments with morphological and rheological features. Summarizing, one can point out that the examined block copolymers reveal the well-known low frequency behavior of phase separated blends. Additionally, we observed a significant shear influence on the morphology, i.e. a shear induced structuring and alignment of lamellae. This considerable change in morphology is also reflected by characteristic rheological properties ( retardation time, yield stress). Therefore, problems concerning the validity range of linear viscoelastic behavior arise, which are discussed in brief.
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