Non-Einstein Viscosity Phenomenon of Acrylonitrile–Butadiene–Styrene Composites Containing Lignin–Polycaprolactone Particulates Highly Dispersed by High-Shear Stress

Lignin powder was modified via ring-opening polymerization of caprolactone to form a lignin–polycaprolactone (LPCL) particulate. The LPCL particulates were mixed with an acrylonitrile–butadiene–styrene (ABS) matrix at an extremely high rotational speed of up to 3000 rpm, which was achieved by a closed-loop screw mixer and in-line melt extruder. Using this high-shear extruding mixer, the LPCL particulate size was controlled in the range of 3395 nm (conventional twin-screw extrusion) down to 638 nm (high-shear mixer of 3000 rpm) by altering the mixing speed and time. The resulting LPCL/ABS composites clearly showed non-Einstein viscosity phenomena, exhibiting reduced viscosity (2130 Pa·s) compared to the general extruded composite one (4270 Pa·s) at 1 s–1 and 210 °C. This is due to the conformational rearrangement and the increased free volume of ABS molecular chains in the vicinity of LPCL particulates. This was supported by the decreased glass transition temperature (Tg, 83.7 °C) of the LPCL/ABS composite specimens, for example, giving a 21.8% decrement compared to that (107 °C) of the neat ABS by the incorporation of 10 wt % LPCL particulates in ABS. The LPCL particulate morphology, damping characteristics, and light transmittance of the developed composites were thoroughly investigated at various levels of applied shear rates and mixing conditions. The non-Einstein rheological phenomena stemming from the incorporation of LPCL particulates suggest an interesting plasticization methodology: to improve the processability of high-loading filler/polymer composites and ultra-high molecular weight polymers that are difficult to process because of their high viscosity

Shadow prices and well-posedness in the problem of optimal investment and consumption with transaction costs

We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we reformulate and reduce the Hamilton-Jacobi-Bellman equation for this singular stochastic control problem to a non-standard free-boundary problem for a first-order ODE with an integral constraint. Having shown that the free boundary problem has a smooth solution, we use it to construct the solution of the original optimal investment/consumption problem in a self-contained manner and without any recourse to the dynamic programming principle. Furthermore, we provide an explicit characterization of model parameters for which the value function is finite.Comment: 31 pages, 20 figure