Kinetics Study of the Thermal Decomposition of Post-consumer Poly(Ethylene Terephthalate) in an Argon Atmosphere

The thermal decomposition of post-consumer samples of a carbonated water bottle made of poly(ethylene terephthalate), PC-PET, was examined by linear temperature programing under an argon atmosphere to determine its mass loss kinetics. A simple kinetic model, called the first order pseudo single-component model, was used. The total weight-loss of each sample assumed to be in two periods, with each period corresponding to a one step decomposition of the PC-PET to volatiles. Three methods for determining the kinetic parameters by thermal gravimetric analysis were examined: differential analysis at a constant heating rate (differential), temperatures of a given conversion at a number of heating rates (isoconversional), and the maximum rate at multiple heating rates (peak temperature). The latter two multiple heating rates methods results were comparable to each other but they were not in agreement with the results from the differential method. The results of the differential method were insensitive to the heating rate and consistent with kinetics data reported in the literature for PET.     

Disentangling stochastic signals superposed on short localized oscillations

We introduce a procedure for separating periodic oscillations superposed on a stochastic signal. The procedure combines empirical mode decomposition (EMD) of a signal with tools of data analysis based on stochastic differential equations, namely nonlinear Langevin equations. Taking the set of modes retrieved from the EMD of the signal, our procedure is able to separate them into two groups, one composing the periodic signal and another composing the stochastic signal. The framework is robust for a broad family of localized oscillations, in the range of large frequencies. In particular, we show that, in this context, the EMD method outperforms a low-pass filter and is robust for a wide interval of different frequency ranges and amplitudes of the periodic oscillation, as well as for a broad family of different non-linear Langevin processes.     

Generalization of the Kelvin equation for arbitrarily curved surfaces

Capillary condensation, which takes place in confined geometries, is the first-order vapor-to-liquid phase transition and is explained by the Kelvin equation, but the equation's applicability for arbitrarily curved surface has been long debated and is severe problem. Recently, we have proposed generic dynamic equations for moving surfaces. Application of the equations to the vapor/fluid interfaces in chemical equilibrium conditions nearly trivially solves the generalization problem for the Kelvin equation. The equations are universally true for any surfaces: atomic, molecular, micro or macro scale, real or virtual, Riemannian or pseudo-Riemannian, active or passive.     

角锥棱镜谐振腔激光模式模拟研究

为了探究角锥棱镜谐振腔激光模式,以角锥-平面镜腔为例,将角锥棱镜等效为衍射光栅,考虑角锥镜棱宽在谐振腔中的衍射效应以及二面角误差引起的附加相位分布对谐振腔激光模式的影响,在光学谐振腔理论的基础上,建立了求解本征模式的理论分析模型.采用快速傅里叶法数值模拟不同腔长、角锥镜棱宽和二面角误差情况下该无源谐振腔激光输出模式分布情况.结果表明,在腔长30 cm、角锥镜棱宽小于75μm、二面角误差在-10′~5′之间时,可实现光斑完整的圆形分布输出模式,且有较好的光束质量;棱宽不小于0.4 mm,二面角误差在-40′~10′之间时,光斑为TEM 03阶横模,光场呈六瓣分布;当角锥镜棱宽为0.4 mm、二面角误差为3′,腔长从30~90 cm范围内增加时,该谐振腔输出的激光模式从TEM 03转换成TEM 10.     

Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.     

Construction of Charring-Functional Polyheptanazine towards Improvements in Flame Retardants of Polyurethane

Nitrogen-containing flame retardants have been extensively applied due to their low toxicity and smoke-suppression properties; however, their poor charring ability restricts their applications. Herein, a representative nitrogen-containing flame retardant, polyheptanazine, was investigated. Two novel, cost-effective phosphorus-doped polyheptazine (PCN) and cobalt-anchored PCN (Co@PCN) flame retardants were synthesized via a thermal condensation method. The X-ray photoelectron spectroscopy (XPS) results indicated effective doping of P into triazine. Then, flame-retardant particles were introduced into thermoplastic polyurethane (TPU) using a melt-blending approach. The introduction of 3 wt% PCN and Co@PCN could remarkably suppress peak heat release rate (pHRR) (48.5% and 40.0%), peak smoke production rate (pSPR) (25.5% and 21.8%), and increasing residues (10.18 wt%→17.04 wt% and 14.08 wt%). Improvements in charring stability and flame retardancy were ascribed to the formation of P–N bonds and P=N bonds in triazine rings, which promoted the retention of P in the condensed phase, which produced additional high-quality residues.