Percolation Thresholds in Ternary Polymer Melt Blends with Separate Dispersions of the Inner Phases: Mathematical Model

A mathematical model based on a straightforward geometrical background is developed which enables predictions of a transition of one dispersed phase to a cocontinuous one (i.e., the percolation threshold) on addition of another dispersed phase during melt mixing in ternary polymer blends. The present work concerns only ternary blends with two separate dispersions of the inner phases in which no encapsulation takes place. In addition, in order to simplify the model, one of the inner phases was represented by hard, nondeformable microspheres The expression developed describes well an experimental relationship between the percolation threshold, the concentration above which the former dispersed phase transforms to a continuous one, and concentrations of both inner phases. The results agree well with the experimental data obtained in a previous work.     

Rogue wave solutions for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber

In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.     

Phase Diagrams of Semicrystalline Polymer–Crystalline Substances: Polyolefins–1,2,4,5-Tetrachlorobenzene

The full phase diagrams of low-density polyethylene (LDPE), high-density polyethylene (HDPE), and isotactic polypropylene (i-PP) mixtures with 1,2,4,5-tetrachlorobenzene (TeCB), including the solubility curve of TeCB in a solid polymer, were constructed by an optical method. The diagrams contain a eutectic point that corresponds to the situation when the crystallization of TeCB out of its solution in a polyolefin is accompanied by the crystallization of monomer units of the macromolecules. As a result, the polymer acquires a gel structure with crystallites as crosslinks and amorphous regions saturated with TeCB. It is demonstrated that the eutectic point position on the phase diagram can be used for ranking polymers with respect to their thermodynamic affinity to a solvent. For the studied systems, the affinity to TeCB was decreased in the order i-PP, HDPE, and LDPE. Direct experimental evidence was obtained that TeCB crystals can be dissolved in a solid polymer via a vapor phase mechanism, which leads to the polymer amorphization.     

Black phosphorus saturable absorber for ultrafast mode‐locked pulse laser via evanescent field interaction

Black phosphorus, or BP, has found a lot of applications in recent years including photonics. The most recent studies have shown that the material has an excellent optical nonlinearity useful in many areas, one of which is in saturable absorption for passive mode‐locking. A direct interaction scheme for mode‐locking, however, has a potential to optically cause permanent damage to the already delicate material. Evanescent field interaction scheme has already been proven to be a useful method to prevent such danger for other 2‐dimensional nanomaterials. In this report, we have utilized the evanescent field interaction to demonstrate that the optical nonlinear characteristics of BP is sufficiently strong to use in such an indirect interaction method. The successful demonstration of the passive mode‐locking operation has generated pulses with the pulse duration, repetition rate, and time bandwidth product of 2.18 ps, 15.59 MHz, and 0.336, respectively.