Fractal Evolving Theory and Growing Model of Olefin Polymerization Process

The surface morphology of Ti-Mg supported catalyst and the polyethyleneparticles are studied using scanning electron microscope(SEM) technology. The results show thateithen the catalyst's surface or polymer particle's surface is irregular and has fractalcharacteristics, which can be described by fractal parameter. The more interesting discovery is thatthe surface fractal dimension values of the polymer particles vary periodically with thepolymerization time. We call this phenomenon fractal evolution, which can be divided into the'revolution' stage and the 'evolution' stage. And then we present polymerization fractal growingmodel (PFGM), and successfully describe and/or predict the whole evolving process of thepolyethylene particle morphology under the different slurry polymerization (includingpre-polymerization) conditions without H_2.

Compressed wormlike chain moving out of confined space: A model of DNA ejection from bacteriophage

The molecular biomechanics of DNA ejection from bacteriophage is of interest to not only fundamental biological understandings but also practical applications such as the design of advanced site-specific and controllable drug delivery systems. In this paper, we analyze the viscous motion of a semiflexible polymer chain coming out of a strongly confined space as a model to investigate the effects of various structure confinements and frictional resistances encountered during the DNA ejection process. The theoretically predicted relations between the ejection speed, ejection time, ejection length, and other physical parameters, such as the phage type, total genome length and ionic state of external buffer solutions, show excellent agreement with in vitro experimental observations in the literature.

MODELING OF LASER MACHINING ON POLYMETHYL METHACRYLATE TO FABRICATE MICROFLUIDIC CHIP

The use of a CO2 laser system for fabrication of microfluidic chip on polymethyl methacrylate （PMMA） is presented to reduce fabrication cost and time of chip. The grooving process of the laser system and a model for the depth of microchannels are investigated. The relations between the depth of laser-cut channels and the laser beam power, velocity or the number of passes of the beam along the same channel are evaluated. In the experiments, the laser beam power varies from 0 to 50 W, the laser beam scanning velocity varies from 0 to 1 000 mm/s and the passes vary in the range of 1 to 10 times. Based on the principle of conservation of energy, the influence of the laser beam velocity, the laser power and the number of groove passes are examine. Considering the grooving interval energy loss, a modified mathematical model has been obtained and experimental data show good agreement with the theoretical model. This approach provides a simple way of predicting groove depths. The system provides a cost alternative of the other methods and it is especially useful on research work of rnicrofluidic prototyping due to the short cycle time of production.

Prediction of Henry's constant in polymer solutions using PCOR equation of state coupled with an activity coefficient model

In this paper,the polymer chain of rotator(PCOR) equation of state(EOS) was used together with an EOS/G^E mixing rule(MHV1) and the Wilson's equation as an excess-Gibbs-energy model in the proposed approach to extend the capability and improve the accuracy of the PCOR EOS for predicting the Henry's constant of solutions containing polymers.The results of the proposed method compared with two equation of state(van der Waals and GC-Flory) and three activity coefficient models(UNIFAC,UNIFAC-FV and Entropic-FV) indicated that the PCOR EOS/Wilson's equation provided more accurate results.The interaction parameters of Wilson's equation were fitted with Henry's constant experimental data and the property parameters of PCOR,a and b,were fitted with experimental volume data(Tait equation).As a result,the present work provided a simple and useful model for prediction of Henry's constant for polymer solutions.

Viscoelastic modeling of the diffusion of polymeric pollutants injected into a pipe flow

This study focuses on the transient analysis of nonlinear dispersion of a polymeric pollutant ejected by an external source into a laminar pipe flow of a Newtonian liquid under axi-symmetric conditions.The influence of density variation with pollutant concentration is approximated according to the Boussinesq approximation and the nonlinear governing equations of momentum,pollutant concentration are obtained together with and Oldroyd-B constitutive model for the polymer stress.The problem is solved numerically using a semi-implicit finite difference method.Solutions are presented in graphical form for various parameter values and given in terms of fluid velocity,pollutant concentration,polymer stress components,skin friction and wall mass transfer rate.The model can be a useful tool in understanding the dynamics of industrial pollution situations arising from improper discharge of hydrocarbon pollutants into,say,water bodies.The model can also be quite useful for available necessary early warning methods for detecting or predicting the scale of pollution and hence help mitigate related damage downstream by earlier instituting relevant decontamination measures.

Numerical Analysis of PRISM-PY Calculations for Hard-and Soft-Core Generic Polymer Models

Generic polymer models capturing the chain connectivity and excluded-volume interactions between polymer segments can be classified, according to whether or not the 3D integral of the latter diverges, into hard- and soft-core models. Taking homogeneous systems of compressible homopolymer melts (or equivalently homopolymer solutions in an implicit, good solvent) in the continuum as an example, we recently compared the correlation effects on the structural and thermodynamic properties of the hard- and soft-core models given by the polymer reference interaction site model (PRISM) theory with the Percus-Yevick (PY) closure (Polymers 2023, 15, 1180). Here we analyzed in detail the numerical errors and behavior of the interchain pair correlation functions (PCFs) given by the PRISM-PY calculations of these models using an efficient numerical approach that we proposed. Our numerical approach has the least number of independent variables to be iteratively solved, analytically treats the discontinuities caused by the non-bonded pair potential (such as that of the hard spheres) and takes only the inverse Fourier transform of the interchain indirect PCF between polymer segments (which is continuous and decays towards 0 with increasing wavenumber much faster than both the interchain direct and total PCFs), and is essential for us to accurately solve the PRISM-PY theory for chain length N as large as 106. To capture the correlation-hole effect, the real-space cut-off in the PRISM calculations should be proportional to the square root of N.

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa- tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site model with Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode- coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.

Wind farm polymerization influences on security and economic operation in power system based on Copula function

Wind speed dependences on different areas in a wind farm have influences on security and economic operation in power system.In order to simulate the correlation of wind speed series between different positions,this paper applies Copula function and rank correlation matrix methods to measure the coherence of wind speed in a wind farm.The correlated wind sample space is established.According to active power output characteristics of wind turbines,the polymerization model in a wind farm can be achieved.Monte Carlo optimal power flow is applied to IEEE-30 and IEEE-300 bus systems based on the principle of energy saving dispatching.The study shows that the accuracy of outputs is improved,thus reducing the fluctuation ranges in unit generating costs and power flow in branches while considering wind speed polymerization.This approach provides a new method to improve the effectiveness of energy saving dispatching and system operation arrangement.Results have been tested to be effective.

Simulation of secondary nucleation of polymer crystallization via a model of microscopic kinetics

We present simulations of the mechanism of secondary nucleation of polymer crystallization,based on a new model accounting for the microscopic kinetics of attaching and detaching.As the key feature of the model,we introduced multibody-interaction parameters that establish correlations between the attaching and detaching rate constants and the resulting thickness and width of the crystalline lamella.Using MATLAB and Monte Carlo method,we followed the evolution of the secondary nuclei as a function of various multibody-interaction parameters.We identified three different growth progressions of the crystal：（i） Widening,（ii） thickening and（iii） simultaneously thickening and widening of lamellar crystals,controlled by the corresponding kinetic parameters.

Three-dimensional Numerical Simulation of Viscoelastic Phase Separation under Shear: the Roles of Bulk and Shear Relaxation Moduli

The morphological, dynamic and rheological characteristics in the viscoelastic phase separation（VPS） of sheared polymer solutions are investigated by three-dimensional（3D） numerical simulations of viscoelastic model. The simulations are accelerated by graphic process unit（GPU） to break through the limitation of computation power. Firstly, the morphological and dynamic characteristics of VPS under shear are presented by comparing with those in classic phase separation（CPS）. The results show that the phase inversion and phase shrink take place in VPS under shear. Then, the roles of bulk and shear relaxation moduli in VPS are investigated in details. The bulk relaxation modulus slows down the phase separation process under shear, but not affects the dynamic path of VPS. The dynamic path can be divided into three stages： freezing stage, growth stage and stable stage. The second overshoot phenomenon in the shear stress is observed, and explained by the breakdown and reform of string structures. The shear modulus affects morphology evolution in the late stage of VPS under shear.