Combinatorial effect of rolling and carbonaceous nanoparticles on the evolution of crystallographic texture and structural properties of ultra high molecular weight polyethylene

Ultra high molecular weight polyethylene (PE) is a structural polymer widely used in biomedical implants. The mechanical properties of PE can be improved either by controlled crystalline orientation (texture) or by the addition of reinforcing agents. However, the combinatorial effect has not received much attention. The objective of this study was to characterize the structure and mechanical properties of PE composites incorporating multiwall carbon nanotubes (MWCNT) and reduced graphene oxide (RGO) subjected to hot rolling. The wide angle X-ray diffraction studies revealed that mechanical deformation resulted in a mixture of orthorhombic and monoclinic crystals. Furthermore, the presence of nanoparticles resulted in lower crystallinity in PE with smaller crystallite size, more so in RGO than in MWCNT composites. Rolling strengthened the texture of both orthorhombic and the monoclinic phases in PE. Presence of RGO weakened the texture of both phases of PE after rolling whereas MWCNT only mildly weakened the texture. This resulted in a reduction in the elastic modulus of RGO composites whereas moduli of neat polymer and the MWCNT composite increased after rolling. This study provides new insight into the role of nanoparticles in texture evolution during polymer processing with implications for processing of structural polymer composites.

Belief propagation for minimum weight many-to-one matchings in the random complete graph

In a complete bipartite graph with vertex sets of cardinalities n and n', assign random weights from exponential distribution with mean 1, independently to each edge. We show that, as n -> infinity, with n' = n/alpha] for any fixed alpha > 1, the minimum weight of many-to-one matchings converges to a constant (depending on alpha). Many-to-one matching arises as an optimization step in an algorithm for genome sequencing and as a measure of distance between finite sets. We prove that a belief propagation (BP) algorithm converges asymptotically to the optimal solution. We use the objective method of Aldous to prove our results. We build on previous works on minimum weight matching and minimum weight edge cover problems to extend the objective method and to further the applicability of belief propagation to random combinatorial optimization problems.

THEORY OF NEWFORMS OF HALF-INTEGRAL WEIGHT

We set up the theory of newforms of half-integral weight on Gamma(0)(8N) and Gamma(0)(16N), where N is odd and squarefree. Further, we extend the definition of the Kohnen plus space in general for trivial character and also study the theory of newforms in the plus spaces on Gamma(0)(8N), Gamma(0)(16N), where N is odd and squarefree. Finally, we show that the Atkin-Lehner W-operator W-4 acts as the identity operator on S-2k(new)(4N), where N is odd and squarefree. This proves that S-2k(-)(4) = S-2k(4).

Minuscule weight percent of graphene oxide and reduced graphene oxide modified Ag3PO4: new insight into improved photocatalytic activity

Designing and fabricating hybrid systems with a visible light active semiconductor as one of its components is an important research area for the development of highly efficient photocatalysts. Herein, we report visible-light driven photocatalytic activity of graphene oxide (GO) and controllably reduced GO (rGO) modified Ag3PO4 composites fabricated by an in situ method. Concentration of graphene derivatives in GO/rGO-Ag3PO4 composites was in the range of 0.13-0.52 wt% which is very minute compared to those reported previously. The optimal concentration of GO in Ag3PO4 with a kinetics (k = 1.23 +/- 0.04 min(-1)) for the degradation of rhodamine B is 0.26 wt%. GO-Ag3PO4 photocatalysts display an improved catalytic activity compared with pristine and rGOs modified Ag3PO4. In line with this, GO/rGO-Ag3PO4 composites show improved photocatalytic activity for the degradation of 2-chlorophenol compared with Degussa P-25. Our experiments with GO reduced to different extents show that, rGO with more polar functional groups exhibits a higher photocatalytic efficiency. The photocatalytic activity in the presence of different scavengers reveals that holes and O-2(-center dot) reactive species play major roles in the degradation phenomenon. In view of our experimental results and reported theoretical studies, a change in conduction band energy level and variation in the contribution of different charge orbitals (C 2p and O 2p) to the conduction band in the composite favours electron flow from graphene derivatives to the semiconductor, enhancing its photocatalytic response.