Abstract: Better understanding the mechanisms of nanoparticle permeation through membranes and packaging polymers has important implications for the evaluation of drug transdermal uptake, in food safety and the environmental implications of nanotechnology. In this study, permeation of 21 nm diameter silver nanoparticles (AgNPs) was tested using Side-Bi-Side and Franz static diffusion cells through hydrophilic 0.1 and 0.05 lm pore diameter 125 μm thick synthetic cellulose membranes, and 16 and 120 μm thick low-density polyethylene (LDPE) films. Experiments performed with LDPE films discarded permeation of AgNPs or Ag ions over the investigated time-frame in both diffusion systems. But controlled release of AgNPs has been quantified using semipermeable hydrophilic membranes. The permeation followed a quasi-linear time-dependent model during the experimental time-frame, which represents surface reaction-limited permeation. Diffusive flux, diffusion coefficients, and membrane permeability were determined as a function of pore size and diffusion model. Concentration gradient and pore size were key to understand mass transfer phenomena in the diffusion systems.

Abstract: Starting from a molecular picture for the X(3872) resonance, this state and its J(PC) = 2(++) heavy-quark spin symmetry partner [X-2(4012)] are analyzed within a model which incorporates possible mixings with 2P charmonium (c (c) over bar) states. Since it is reasonable to expect the bare chi(c1)(2P) to be located above the D (D) over bar* threshold, but relatively close to it, the presence of the charmonium state provides an effective attraction that will contribute to binding the X(3872), but it will not appear in the 2(++) sector. Indeed in the latter sector, the chi(c2)(2P) should provide an effective small repulsion, because it is placed well below the D*(D) over bar* threshold. We show how the 1(++) and 2(++) bare charmonium poles are modified due to the D-(*)(D) over bar ((*)) loop effects, and the first one is moved to the complex plane. The meson loops produce, besides some shifts in the masses of the charmonia, a finite width for the 1(++) dressed charmonium state. On the other hand, X(3872) and X-2(4012) start developing some charmonium content, which is estimated by means of the compositeness Weinberg sum rule. It turns out that in the heavy-quark limit, there is only one coupling between the 2P charmonia and the D-(*)(D) over bar ((*)) pairs. We also show that, for reasonable values of this coupling, leading to X(3872) molecular probabilities of around 70-90%, the X2 resonance destabilizes and disappears from the spectrum, becoming either a virtual state or one being located deep into the complex plane, with decreasing influence in the D*(D) over bar* scattering line. Moreover, we also discuss how around 10-30% charmonium probability in the X(3872) might explain the ratio of radiative decays of this resonance into psi(2S) gamma and J/psi gamma Finally, we qualitatively discuss within this scheme, the hidden bottom flavor sector, paying a special attention to the implications for the X-b and Xb(2) states, heavy-quark spin-flavor partners of the X(3872).

Abstract: We compute the two-loop QED corrections to the Altarelli-Parisi (AP) splitting functions by using a deconstructive algorithmic Abelianization of the well-known NLO QCD corrections. We present explicit results for the full set of splitting kernels in a basis that includes the leptonic distribution functions that, starting from this order in the QED coupling, couple to the partonic densities. Finally, we perform a phenomenological analysis of the impact of these corrections in the splitting functions.