Investigation of clay modifier effects on the structure and rheology of supercritical carbon dioxide‐processed polymer nanocomposites

Superior property enhancements in polymer–clay nanocomposites can be achieved if one can significantly enhance the nanoclay dispersion and polymer–clay interactions. Recent studies have shown that nanoclays can be dispersed in polymers using supercritical carbon dioxide (scCO₂). However, there is need for a better understanding of how changing the clay modifier affects the clay dispersability by scCO₂ and the resultant nanocomposite rheology. To address this, the polystyrene (PS)/clay nanocomposites with “weak” interaction (Cloisite 93A clay) and “strong” interaction (Cloisite 15A clay) have been prepared using the supercritical CO₂ method in the presence of a co‐solvent. Transmission electron microscopy images and small‐angle X‐ray diffraction illustrate that composites using 15A and 93A clays show similar magnitude of reduction in the average tactoid size, and dispersion upon processing with scCO₂. When PS and the clays are coprocessed in scCO₂, the “dispersion” of clays appears to be independent of modifier or polymer–clay interaction. However, the low‐frequency storage modulus in the scCO₂‐processed 15A nanocomposites is two orders of magnitude higher than that of 93A nanocomposites. It is postulated that below percolation (solution blended composites), the strength of polymer–clay interaction is not a significant contributor to rheological enhancement. In the scCO₂‐processed nanocomposites the enhanced dispersion passes the percolation threshold and the interactions dictate the reinforcement potential of the clay–polymer–clay network. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 823–831, 2010     

Quadrature formulas for the generalized Riemann-Stieltjes integral

In this paper we propose a technique of approximation for the generalized Riemann-Stieltjes integral and we found an analogue for Newton-Cotes formulas in the case n = 2 and n = 3. *Beneficiary of a Socrates fellowship at the Department of Mathematics, University of Study of Cagliari, Via Ospedale, n. 72, Cagliari, 09124, Italy, in the period February – July 2002.     

Analytic continuation of the exponential transform from convex cavities

The analytic continuation of the exponential transform of a domain in Rn is proved under some global geometric assumptions on the boundary. Two approximation schemes of the continued transform (one based on a Taylor series truncation, the other on a global eigenfunction expansion) are also discussed.     

PAN composite membrane with different solvent affinities controlled by surface modification methods

Polyacrylonitrile (PAN) composite membranes with surface properties designed by either a chemical modification with ethylenediamine (EDA), or layer‐by‐layer (LbL) polyelectrolyte adsorption were investigated in this paper. Fourier‐transformed infrared (FTIR) spectroscopy and streaming potential measurements showed that the first step of the reaction with EDA in gas phase was the formation of ammonium salts with the reactive carboxylic groups present on the surface of the starting membrane. Part of the ammonium carboxylate groups was transformed in secondary amide linkages by a heat‐induced reaction. Poly(sodium styrenesulfonate) (NaPSS) and a polycation containing about 95 mol % of N,N‐dimethyl‐2‐hydroxypropyleneammonium chloride units in the backbone (PCA₅) were used as opposite polyions in the LbL film construction. The adsorbed polyion amount per every layer was controlled by the nature and concentration of the supporting electrolyte in polyelectrolyte deposition solution (NaBr and KBr). An almost linear increase of the adsorbed polyion amount versus the layer pair number was observed. The swelling degree (SD) in pure alcohols of the LbL‐modified PAN composite membrane decreased with the increase of the solvent polarity and with the decrease of the pore volume by pore filling with polyelectrolyte complex multilayer. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4161–4171, 2005     

An Extremal Problem Arising in the Dynamics of Two-Phase Materials That Directly Reveals Information about the Internal Geometry

In two-phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. Motivated by this, and to obtain an algorithm for designing appropriate driving fields, we find approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [-1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [-1,1] and, to simplify the analysis, Chebyshev approximation is used. This allows one to obtain explicit estimates of the error of the approximation, in terms of the number of points and the minimum distance of the points to the interval [-1,1]. Assuming this minimum distance is bounded below by a number greater than 1/2, the error converges exponentially to zero as the number of points is increased. Approximate linear relations are also obtained that incorporate a set of moments of the measure. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markov-type functions with a positive semidefinite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the time-dependent boundary potentials are suitably tailored. © 2022 Wiley Periodicals, Inc.     

Constraint groups

The complete list of constraint manifolds having the group structure is given.