Some new operational modes and parameters of stress relaxation for the viscoelastic characterization of solid polymers. II. The “vertical‐shift” mode and intrinsic “time–strain clock”

As in part I of this study, in the same manner in the present part II as well, by the same modus operandi way, an attempt was made to introduce, by means of a given operational mode, some further practical parameters for a “by‐eye” but well‐proven experimental viscoelastic characterization of a polymeric solid. Thus, through consideration of the peculiar vertical shift behavior of the apparent modulus (?) of isotactic polypropylene (iPP) and based on the KWW model, it is shown that, in an empirical and a formalistic sense, a relevant effective or equivalent (single) characteristic relaxation time can be introduced which can give some new interpretations for the linear and nonlinear viscoelastic behavior of a polymeric material, as that of a “time–strain clock,” which, as an intrinsic function, is responsable for a functional time–strain shift of the relaxation time and, at the same time, for a shift toward to a more linear or to a more nonlinear behavior. In the above context of attempts, another functional relationship was shown, the so‐called spectral shift function and its corresponding parameter of nonlinearity strength, through which some further interpretations and characterizations connected with the existence of the permanent internal stress could be made. Finally, the introduction of the so‐called spectral isostrains and their corresponding “spectral inversion point” complete the “set” of the operative parameters proposed for the above‐mentioned purpose. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 138–148, 2003     

An accelerated successive substitution method for single stage flash calculations

An acceleration technique, based on the Dominant Eigenvalue Method of Orbach and Crowe (1971), is proposed to accelerate a successive substitution method in which liquid and vapor compositions are used as the iteration variables. The performance of this scheme is compared with the accelerated successive substitution method of Mehra et al. (1983) and the General Dominant Eigenvalue Method (GDEM) of Crowe and Nishio (1975) as implemented by Michelsen (1982, 1987) which iterate upon the equilibrium ratios. The proposed acceleration scheme exhibits a less oscillatory behavior during convergence, and requires less storage than the accelerated methods using the K-factors as the iteration variables. However, the number of thermodynamic evaluations is comparable with that of Mehra et al. (1983) and is more than that of Michelsen (1982, 1987).     

Model reduction for linear simulated moving bed chromatography systems using Krylov‐subspace methods

Simulated moving bed (SMB) chromatography is a well‐established technology for separating chemical compounds. To describe an SMB process, a finite‐dimensional multistage model arising from the discretization of partial differential equations is typically employed. However, its relatively high dimension poses severe computational challenges to various model‐based analysis. To overcome this challenge, two Krylov‐type model order reduction (MOR) methods are proposed to accelerate the computation of the cyclic steady states (CSSs) of SMB processes with linear isotherms. A “straightforward method” that carefully deals with the switching behavior in MOR is first proposed. Its improvement, a “subspace‐exploiting method,” thoroughly exploits each reduced model to achieve further acceleration. Simulation studies show that both methods achieve high accuracy and significant speedups. The subspace‐exploiting method turns out to be computationally much more efficient. Two challenging analyses of SMB processes, namely uncertainty quantification and CSS optimization, further demonstrate the accuracy, efficiency, and applicability of the proposed methods. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3773–3783, 2014     

A QUASI-NEWTON ALGORITHM FOR SOLVING MULTIPHASE EQUILIBRIUM FLASH PROBLEMS

A new algorithm has been developed for solving the multicomponent vapor-liquid-liquid equilibrium Mash problem. The algorithm is an extension of the “inside-out” approach proposed by Boston and Britt for the vapor-liquid equilibrium flash problem.

Conventional flash algorithms use temperature, pressure, composition, and phase fraction as the problem independent variables, In the inside-out approach a new set of independent variables is introduced in place of the conventional variables. The new variables are chosen to be as independent as possible of the conventional variables and as free as possible of mutual interaction. Complex phase equilibrium models are used only to generate parameters for a simple equilibrium ratio model. These parameters become the problem independent variables. The Quasi-Newton method of Broyden is employed to promote convergence of these variables.

The algorithm first obtains a solution for the vapor-liquid equilibrium flash. By examining the liquid phase, a heuristic algorithm is employed which quickly locates a two liquid phase composition region of reduced total system free energy when the original liquid is unstable. The solution of the vapor-liquid-liquid equilibrium flash is initiated only when this occurs.

The performance of the algorithm is demonstrated by a number of problems which exhibit varying degrees of nonideality.     

Crystallization behavior of “wet brush” and “dry brush” blends of PS‐b‐PEO‐b‐PS/h‐PEO

The crystallization behavior of the blending system consists of homopolymer poly(ethylene oxide) (h‐PEO) with different molecular weights, and polystyrene‐block‐poly (ethylene oxide)‐block‐polystyrene (PS‐b‐PEO‐b‐PS) triblock copolymer has been investigated by DSC measurements. The crystallization of PEO block (b‐PEO) in block copolymer occurs under much lower temperature than that of the h‐PEO in the bulk (ΔT > 65 °C), which is attributed to the homogeneous nucleation crystallization behavior of the b‐PEO microdomains. In both the “dry‐brush” and the “wet brush” blending systems, the homogeneous nucleation crystallization temperature of PS‐b‐PEO‐b‐PS/h‐PEO blends increases due to the increase of the domain size. The heterogeneous nucleation crystallization temperatures of h‐PEO in the wet brush blending systems are higher than that of the corresponding h‐PEO in the bulk. At the same time, the heterogeneous nucleation crystallization temperature of b‐PEO10000 decreases from 43°C to 30°C and 40°C in the h‐PEO600 and h‐PEO2000 blending systems, respectively, because of the stretching of the PEO chains in the wet brush. However, this kind of phenomenon does not happen in the dry brush blending systems. The self‐seeding procedure was used to further ascertain the nucleation mechanism in the crystallization process. As a result, the self‐seeding domains have been confirmed, and the difference between the dry brush and wet brush systems has been observed. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Steady states for chemical process plants: A legacy code,time‐stepping approach

Given a legacy dynamic simulator of a chemical process plant, we construct a computational procedure that can be “wrapped around” the simulator to compute its steady states (both stable and unstable) and their dependence on input parameters. We apply this approach to the Tennessee Eastman (TE) challenge problem presented by Downs and Vogel, who also provided a FORTRAN process model. Using the FORTRAN simulator as a black‐box input‐output map, we enable it to systematically converge to isolated solutions and study their stability and parametric dependence within the equation‐free framework. The presence of neutrally stable modes in TE problem (due to so‐called inventories), their interplay with the problem formulation and the convergence of the solution procedure is explored and rationalized. Interestingly, our time‐stepper formulation can automatically take advantage of separation of time scales, when present, to enhance computational convergence. The approach enables legacy dynamic simulators to calculate several dynamic problem characteristics useful for controller design and/or process optimization. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3308–3321, 2013     

A linear model predictive control algorithm for nonlinear large‐scale distributed parameter systems

This work provides a framework for linear model predictive control (MPC) of nonlinear distributed parameter systems (DPS), allowing the direct utilization of existing large‐scale simulators. The proposed scheme is adaptive and it is based on successive local linearizations of the nonlinear model of the system at hand around the current state and on the use of the resulting local linear models for MPC. At every timestep, not only the future control moves are updated but also the model of the system itself. A model reduction technique is integrated within this methodology to reduce the computational cost of this procedure. It follows the equation‐free approach (see Kevrekidis et al., Commun Math Sci. 2003;1:715–762; Theodoropoulos et al., Proc Natl Acad Sci USA. 2000;97:9840‐9843), according to which the equations of the model (and consequently of the simulator) need not be given explicitly to the controller. The latter forms a “wrapper” around an existing simulator using it in an input/output fashion. This algorithm is designed for dissipative DPS, dissipativity being a prerequisite for model reduction. The equation‐free approach renders the proposed algorithm appropriate for multiscale systems and enables it to handle large‐scale systems. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

原油蒸馏塔的内外不可行路径优化方法

针对原油蒸馏塔的特点 ,将蒸馏塔模拟的内外法与优化的不可行路径法结合 ,提出原油蒸馏塔的内外不可行路径法 .对某原油蒸馏塔的优化计算表明该方法能提高计算速度 ,并取得较好的优化效果 .     

Nonlinear viscoelasticity of “hard elastic” polypropylene fibers

“Hard elastic” polypropylene fibers respond nonlinearly to stress at all strains. Low tenacities at break (less than 1 g/denier), low moduli of elasticity (slopes of stress-strain curves from 2.8 to 28 g/denier), and large breaking extensions (over 800 percent) are characteristic of “hard elastic” fibers. Behavior in simple extension, cyclic extension, and stress relaxation can be represented by a quasi-linear viscoelastic model which uses a continuous relaxation spectrum and a quasilinear relation between stress history T(t)and strain history λ(t): where T^e[λ(t)] is the elastic response. When creep data are available, this model should provide a unified representation of experimental observations.     

Computational fluid dynamics simulations of heat transfer between the dense‐phase of a high‐temperature fluidized bed and an immersed surface

The transient process of heat transfer between a high‐temperature emulsion packet and the wall of an immersed surface is simulated using computational fluid dynamics (CFD). From these simulations, the total heat transfer coefficient and its radiant contribution due to the emulsion (dense) phase are evaluated. The results are compared with experimental data (Ozkaynak et al., “An experimental investigation of radiant heat transfer in high temperature fluidized beds,” in Fluidization IV, 1983:371–378) and with predicted values from the generalized heterogeneous model (GHM), (Mazza et al., “Evaluation of overall heat transfer rates between bubbling fluidized beds and immersed surfaces,” Chem Eng Commun., 1997;162:125–149). The CFD simulations are in good agreement with both, experimental data and theoretical GHM predictions and provide a reliable way to quantify the studied heat transfer process. Also, the GHM is validated as a practical tool to this end. © 2011 American Institute of Chemical Engineers AIChE J, 58: 412–426, 2012     

Monte Carlo real coded genetic algorithm (MC‐RGA) for radioactive particle tracking (RPT) experimentation

Radioactive particle tracking (RPT) technique is a non‐invasive velocimetry technique, extensively applied to study hydrodynamics of dense multiphase systems. In this technique, the position of a radioactive tracer particle, designed to mimic the phase of interest, is followed as a Lagrangian marker of point velocity. Computational limitations encountered during tracer particle position reconstruction (which is an inherently slow process) have thus far restricted the use of this versatile technique only to small‐scale process vessels. Here, we present a noteworthy improvement over the classical Monte Carlo algorithm for tracer particle position reconstruction, whereby we enhance the convergence and computational speed of the algorithm using Real Coded Genetic Algorithm optimization. This modification results in drastic reduction in computational time required for detector parameter estimation, and altogether eliminates the need for the “distance‐count map,” which was earlier inherent to RPT experimentation. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2850–2863, 2017     

Identification of parameters in systems of ordinary differential equations using quasilinearization and data perturbation

Given a set of observed data for a particular physical phenomenon, the problem of computing the “best fit” parameters for the mathematical model describing the phenomenon is a common problem in process or reaction mechanism identification. If the mathematical model comprises a set of non-linear ordinary differential equations, this leads to a non-linear boundary value problem. A very powerful way of attacking this class of problem uses an adaptation of the Newton-Raphson-Kantorovich procedure, called quasilinearization, which regards the non-linear problem as the limit of a sequence of linear problems. Starting from an initial trial solution, convergence if it does occur, occurs rapidly; further, convergence is assured if the initial guess is “close enough” to the true solution. The difficulty of making a good initial guess, a serious limitation of the method in the past, can in principle be overcome by the algorithm proposed. When a given vector may not be within the domain of convergence of the original problem, it must be within the domain of convergence of some other derived problem. The latter may then be perturbed towards the original problem in a finite number of steps. In the case of process identification, new data points are derived; these are subsequently adjusted until they coincide with the original data. The algorithm has been successfully applied to several examples from recent chemical engineering literature.     

Desiccant wheel system modeling improvement using multiple population genetic algorithm training of neural network

Since the physical modeling method for the desiccant wheel system (DWS) is complex and costly for calculations, the modeling method based on neural network (NN) gains attention for its simplicity and effectiveness. The previous NN models of DWS are mostly based on backpropagation (BP) NN and adopt the gradient searching method to obtain the weights and thresholds. However, the gradient searching method results in “overfitting” easily. In this paper, a novel neural network training algorithm, trainmpga, is proposed. The algorithm searches the optimal weights and thresholds of NN by making use of the multiple population genetic algorithm, thereby conquering the “overfitting” of the gradient searching method and the “prematurity” of the genetic algorithm. Meanwhile, related configurations of NN, such as parameters and framework, are studied. Finally, the proposed modeling method trainmpga proves to have high training and prediction accuracy in comparison to the training algorithms in the MatLab toolbox and has good application prospects.     

“In-out” recursive probability modeling of branched step-growth polymerizations

This paper presents the derivation of mathematical formulae for molecular and network parameters of branched step-growth polymerizations. Weight-average molecular weight, gel point, and weight fractions of soluble, pendant and elastically-effective material in a gel are derived. The direct “in-out” recursive analysis of Macosko and Miller is applied to four general step-growth polymerization systems. The method is introduced using the simple case of A_f homopolymerization. Two new systems are then modeled; a homopolymerization of A_fB_g monomers with two types of reactive groups, and an A_f+B_g+C_h terpolymerization. The fourth system presented is a general A_f+B_g copolymerization of polydispersed reactants; we have partially analyzed this system before, but we give a new and complete presentation here to show the generality of the “in-out” analysis. We also survey some additional polymer systems that have been analyzed in the literature. Then, we discuss limitations of this modeling approach, the use of the models and their implementation in software. We give two numerical examples: a silicone rubber system and a segmented polyurethane network system. Appendices present the small amount of elementary probability theory and polymer distribution theory needed to support the analysis. This paper serves as an introduction to the “in-out” method; after reading this paper, the reader should be able to apply the “in-out” method to many step-growth polymer systems.     

Highly Practical “Ligand‐Free‐Like” Copper‐Catalyzed N‐Arylation of Azoles in Lower Nitrile Solvents

In lower nitrile solvents, the N‐arylation of azoles with aryl halides was achieved efficiently in the presence of copper powder without any additional ligands. Thus, the first nitrile type of monodentate ligand‐mediated, “ligand‐free‐like” copper‐catalyzed N‐arylation procedure was established.     

ESTIMATION OF MULTIVARIATE TIME SERIES

Abstract. The algorithm proposed here is a multivariate generalization of a procedure discussed by Pearlman (1980) for calculating the exact likelihood of a univariate ARMA model. Ansley and Kohn (1983) have shown how the Kalman filter can be used to calculate the exact likelihood function when not all the observations are known. In Shea (1983) it is shown that this algorithm is much quicker than that of Ansley and Kohn (1983) for all ARMA models except an ARMA (2, 1) and a couple of low-order AR processes and therefore when we have no missing observations this algorithm should be used instead. The Fortran subroutine G13DCF in the NAG (1987) Library fits a vector ARMA model using an adaptation of this algorithm. Experience in the use of this routine suggests that having reasonably good initial estimates of the ARMA parameter matrices, and in particular the residual error covariance matrix, can not only substantially reduce the computing time but more important improve the convergence properties of the minimization procedure. We therefore propose a method of calculating initial estimates of the ARMA parameters which involves using a generalization of the concept of inverse cross covariances from the univariate to the multivariate case. Finally theory is put into practice with the fitting of a bivariate model to a couple of real-life time series.     

Factors that enable the formation of porous strut morphology in “Swiss Cheese” viscoelastic polyurethane foam technology

Several factors were investigated that affect porous strut morphology in the Highly Porous Supersoft Viscoelastic Foam. Porous strut morphology and high air permeability of the Swiss‐Cheese TDI VE technology were found to be enabled by the combination of immiscible polyether polyols mixed with a third, highly hydrophobic polyol of high equivalent weight that is immiscible with either of the first two polyether polyols. Completely “punctured through” pores in struts were observed more frequently in foam samples where an isocyanate index of 90 versus 100 was employed. When isocyanate index is fixed to 90, it was found that a poly(1,2‐butylene oxide) (“PBO”) monol level of ≥3.0 parts per hundred polyol (pphp) was needed to see the first signs of a “punctured” pore strut morphology. Studies show that a “high‐Eq.Wt.‐hydrophobic‐polyol‐leaving‐voids” model is consistent with observed results. Hydrophobic polyols that allowed the formation of porous strut morphology included BO‐4000 monol (Eq.Wt. ～ 4000) and PBD‐10000 diol (Eq.Wt. ～ 5000). The use of these hydrophobic polyols also yielded air flows that were significantly higher than those obtained with the “standard” viscoelastic foam formulations that were prepared at the same isocyanate index. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44449.     

Storage hardening and “abnormal” groups in guayule rubber

The hardening process of natural (Hevea brasiliensis) rubber, that takes place when this rubber is stored in dry conditions over long periods of time, has been correlated with the presence of reactive “abnormal” groups directly grafted on the polymeric chain and in the serum of the latex. In the present work, natural Hevea (HR) and Guayule (Parthenium argentatum) rubber (GR) were stored under accelerated conditions and the changes in Mooney viscosity and molecular weight measured. The results showed that while HR undergoes hardening, GR keeps its Mooney viscosity constant, as does a constant viscosity (CV) Hevea rubber. These results are explained by the absence of functional “abnormal” groups that sustain the hardening reactions.     

Optimal periodic control of a continuous “living” anionic polymerization II. New theoretical results

In a previous publication¹, a suboptimal technique was developed to solve the problem of producing polymers with prespecified values of the number-average chain length and the polydispersity, through “living” anionic polymerizations carried out in continuous stirred-tank reactors. The solution of that problem involved the periodic operation of the monomer solution feed and of the initiator solution feed, as well as readjustments in their feedstock concentrations. The present work solves the problem directly, without resorting to laborious “optimization-rescaling” procedures. The objective functional considers not only the polymer quality, but also the required polymer production. Compared with the previous results¹, the present solutions are better and obtained with less computational effort. The proposed technique may be applicable to other optimal periodic control problems with nonconventional objective functionals.     

Interrogation of “surface,” “skin,” and “core” orientation in thermotropic liquid‐crystalline copolyester moldings by near‐edge X‐ray absorption fine structure and wide‐angle X‐ray scattering

Injection molding thermotropic liquid‐crystalline polymers (TLCPs) usually results in the fabrication of molded articles that possess complex states of orientation that vary greatly as a function of thickness. “Skin‐core” morphologies are often observed in TLCP moldings. Given that both “core” and “skin” orientation states may often differ both in magnitude and direction, deconvolution of these complex orientation states requires a method to separately characterize molecular orientation in the surface region. A combination of two‐dimensional wide‐angle X‐ray scattering (WAXS) in transmission and near‐edge X‐ray absorption fine structure (NEXAFS) spectroscopy is used to probe the molecular orientation in injection molded plaques fabricated from a 4,4′‐dihydroxy‐α‐methylstilbene (DHαMS)‐based thermotropic liquid crystalline copolyester. Partial electron yield (PEY) mode NEXAFS is a noninvasive ex situ characterization tool with exquisite surface sensitivity that samples to a depth of 2 nm. The effects of plaque geometry and injection molding processing conditions on surface orientation in the regions on‐ and off‐ axis to the centerline of injection molded plaques are presented and discussed. Quantitative comparisons are made between orientation parameters obtained by NEXAFS and those from 2D WAXS in transmission, which are dominated by the microstructure in the skin and core regions. Some qualitative comparisons are also made with 2D WAXS results from the literature. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007