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The average glass transition temperatures, Tg, of thin homopolymer films exhibit a thickness dependence, Tg(h), associated with a confinement effect and with polymer-segment-interface interactions. The Tg's of completely miscible thin film blends of tetramethyl bisphenol-A polycarbonate (TMPC) and deuterated polystyrene (dPS), supported by SiO(x)/Si, decrease with decreasing h for PS weight fractions phi >0.1. This dependence is similar to that of PS and opposite to that of TMPC thin films. Based on an assessment of Tg(h, phi), we suggest that the Tg(h, phi) of miscible blends should be rationalized, additionally, in terms of the notion of a self-concentration and associated heterogeneous component dynamics.

Thin polystyrene (PS) liquid films supported by oxidized silicon (SiO x /Si) substrates may be unstable or metastable, depending on the film thickness, h. In the metastable thickness regime, holes nucleate throughout the surface of the films and subsequently grow under the action of capillary forces. Recent studies show that the hole growth rate in thin PS films is suppressed with the addition of small concentrations of C 60 fullerenes, due to pinning at the line of contact. We examined the hole growth dynamics in thin film polystyrenes with functionalized single-walled carbon nanotubes (PS-SWNT) supported by SiO x /Si substrates. The hole growth velocities in PS films containing 0.75 wt % functionalized single-walled nanotubes, V PS - SWNT, were appreciably slower than V PS, the hole-growth velocities of holes in polystyrene films of the same thickness. Moreover, V PS - SWNT and V PS decreased with decreasing film thickness, for h < 50 nm, with thickness dependencies which exceed theoretical predictions. In addition, V PS(h)/V PS - SWNT(h) increased with decreasing h, for h < 50 nm, and approached a constant value for larger h. We show that the suppression of the hole-growth rates in the PS−SWNT films are associated with larger viscosities of the PS−SWNT films and that the film thickness-dependent velocities are associated with film thickness-dependent viscosities.

This paper addresses industrial gases supply chains involving multiple products at multiple plants that must be coordinated with multiple depot-truck-routes in order to satisfy customer demands. The full-space optimization problem corresponds to a large-scale mixed-integer linear programming model (MILP). To solve large-scale industrial problems, this paper proposes a rolling horizon approach with two aggregation strategies for solving the smaller subproblems. The first one relies on the linear programming (LP) relaxation for which the binary variables (complicating variables) of the distribution problem are treated as continuous, while the second one uses a novel tailored model for the distribution side constraints that leads to improved solutions. A real case study of an industrial gases supply chain has been addressed obtaining good results in both objective value and with lower computational effort compared with the full-space solution. The extension to longer time horizons through a receding horizon is also considered.

Thin polystyrene films supported by oxidized silicon (SiOx/Si) substrates may be unstable or metastable, depending on the film thickness, h, and can ultimately dewet the substrate when heated above their glass transition. In the metastable regime, holes nucleate throughout the film and subsequently grow due to capillary driving forces. Recent studies have shown that the addition of a second component, such as a copolymer or miscible polymer, can suppress the dewetting process and stabilize the film. We examined the hole growth dynamics and the hole morphology in thin film mixtures composed of polystyrene and tetramethyl bisphenol-A polycarbonate (TMPC) supported by SiOx/Si substrates. The hole growth velocity decreased with increasing TMPC content beyond that expected from changes in the bulk viscosity. The authors show that the suppression of the dewetting velocity is primarily due to reductions in the capillary driving force for dewetting and to increased friction at the substrate-polymer interface. The viscosity, as determined from the hole growth dynamics, decreases with decreasing film thickness, and is connected to a depression of the glass transition of the film.