Mean-field games with a major player

We introduce and study mathematically a new class of mean-field-game systems of equations. This class of equations allows us to model situations involving one major player (or agent) and a “large” group of “small” players.     

Encapsulation of magnetic self-assembled systems in thermoreversible gels

We describe two different ways of encapsulating within the fibrils of thermoreversible polymer gels the filaments of a supermolecular polymer formed by self-assembly of a bicopper complex. Heterogeneous nucleation is brought about with gels made from isotactic poly(styrene) while compound formation occurs with gels made from poly(hexyl isocyanate). These ways depend upon the interaction between the wings of the supermolecular polymer and the side groups of the polymer. In all cases, the filaments retain their 1-D structure. Preliminary results from magnetic susceptibility measurements show a striking difference between the pure and the encapsulated supermolecular polymer.     

Kinetics of styrene uptake by a polyurethane network during the formation of interpenetrating polymer networks

Due to insolubility of the components, formation of interpenetrating polymer networks (IPNs) requires particular ways of synthesis. Among others, IPNs can be prepared by the sequential technique where a network is swollen in a monomer and its crosslinker, which are then polymerized in situ. The simplest case is to swell at equilibrium; however this leads to IPNs of a given composition. For obtaining other compositions, swelling has to be stopped before equilibrium, or the swollen network (gel) has to be deswollen to a certain extent. Therefore, diffusivity of the monomer within the gel has to be known. The kinetics of monomer uptake was studied for a polyether urethane/styrene-divinylbenzene system which gives transparent materials despite the difference in refractive indexes. This allows direct visual observations of the monomer progress within the network. The results are not fully in agreement with the theories of Tanaka and of Candau which both predict the progression of a solvent in a polymeric gel. Two regimes of swelling depending on the concentration distribution of the monomer within the gel were found.     

Thermoreversible gelation of isotactic poly(methyl methacrylate) in butyl acetate: a differential scanning calorimetry study

The thermal behaviour of thermoreversible gels prepared well below room temperature from isotactic poly(methyl methacrylate) (i-PMMA) in butyl acetate (BAC) was investigated by means of differential scanning calorimetry. Gel-formation and gel-melting enthalpies together with melting enthalpy of the solvent were determined as functions of polymer concentration. The results are consistent with the existence of a polymer/solvent complex with a stoichiometry of 1,5–2 BAC molecules per i-PMMA monomeric unit.     

Investigations of Miscibility in Interpenetrated Systems of Polyurethane and Polystyrene Obtained at Room Temperature

Interpenetrating polymer systems based on crosslinked polyurethane (PU) and polystyrene (PS) were prepared at room temperature by a one-shot (in situ) method, starting from an initial homogeneous mixture of reagents via non interfering mechanisms. Both polymerizations were performed either simultaneously or one after the other. Crosslinks and/or covalent bonds between components were deliberately introduced by the addition of appropriate monomers, in order to tailor the degree of microphase separation. Depending on the formation process, transluscent or transparent films were obtained, despite the difference in refractive index of the components. The maximum of miscibility, taken as from the glass transition criterion, was obtained for sequential tightly graft interpenetrating networks.     

In situ ATR-FTIR Spectroscopy of Poly(ethylene terephthalate) Subjected to High-Temperature Methanol

Summary: In situ ATR-FTIR (attenuated total reflection Fourier transform infrared) spectroscopy combined with a high-pressure cell has been applied to measure IR spectra of polymers subjected to superheated or near-critical methanol (100– 200 °C). Spectra of poly(ethylene terephthalate) (PET) have been measured under exposure to high temperature methanol using this ATR-FTIR approach to understand at a molecular level the recycling process of PET. The evolution of the structure and the morphology of the polymer has been studied during the methanolysis. The quantity of trans PET conformer is generally used as a tracer of the crystallinity of PET. During depolymerisation of PET the evolution of crystallinity and of trans conformer appears to be different. The dependence of the rate constant on reaction temperature was correlated by Arrhenius plot, which shows activation energy of 5.8 kJ/mol.     

Conformational changes in poly(vinyl alcohol)-graft-polyacrylamide in aqueous solutions vs graft content

Conformational changes have been studied in intramolecular polymer-polymer complexes (intraPC) of graft copolymers of poly(acrylamide) and poly(vinyl alcohol) (PVA-g-PAA) with various numbers of grafts (4-42) per molecule as a function of temperature and copolymer concentration. It is shown that the magnitude of conformational change depends on the grafts content while the temperature range over which the conformation changes occur is essentially determined by copolymer concentration. The conformational changes are reversible on heating and cooling.