scholarly journals Morphological Monte Carlo Simulation for Crystallization of Isotactic Polypropylene in a Temperature Gradient

Crystals ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 213 ◽  
Author(s):  
Chunlei Ruan
Keyword(s):  
Monte Carlo ◽  
Temperature Gradient ◽  
Isotactic Polypropylene ◽  
Isothermal Crystallization ◽  
Numerical Solutions ◽  
Temperature Gradients ◽  
Monte Carlo Algorithm ◽  
Gradient Field ◽  
Conversion Degree ◽  
Central Temperature

Polymers are poor heat conductors, so the cooling of thick-walled shapes results in temperature gradients. Here, isotactic polypropylene (iPP) is chosen as a model polymer for the study of polymer crystallization in a temperature gradient field. The morphological Monte Carlo algorithm is applied, combined with the radius growth model, to predict the growth of spherulites. Through comparison of the two numerical solutions, analytical solution and experimental data, the validity of the morphological Monte Carlo algorithm is demonstrated. In addition, the roles of central temperature, temperature gradient for the evolution of spherulites, and the conversion degree of the melt into spherulites are considered. The results of the study show that increases in central temperature and temperature gradient can increase the anisotropy of spherulites. Isothermal crystallization and crystallization in a temperature gradient field are compared, and the differences are considered. Results show that when the central temperature is below 125 °C, and when the temperature gradients are less than 15 K/mm and 27 K/mm, the differences in the conversion degree of the melt into spherulites are less than 2% and 5%, respectively. Therefore, crystallization under such temperature gradient conditions can be simplified as isothermal crystallization.

scholarly journals A Note for Probabilistic Model of Polymer Crystallization in Temperature Gradients

Crystals ◽  
2019 ◽  
Vol 9 (10) ◽  
pp. 538
Author(s):  
Chunlei Ruan ◽  
Yunlong Lv
Keyword(s):  
Temperature Gradient ◽  
Crystallization Kinetics ◽  
Probabilistic Model ◽  
Polymer Crystallization ◽  
Temperature Gradients ◽  
Kinetics Model ◽  
Gradient Field ◽  
Conversion Degree ◽  
Avrami Equation ◽  
Large Temperature

A polymer crystallization kinetics model is the most important way to characterize the crystallization rate of polymers. Because polymers are poor heat conductors, the cooling of thick-walled shapes results in temperature gradients. Piorkowska (Piorkowska, E. J. Appl. Polym. Sci., 2002, 86: 1351–1362.) derived the probabilistic analytical model of polymer crystallization in temperature gradients based on the Avrami equation. However, there are some misunderstandings when using this model. Here, isotactic polypropylene (iPP) is chosen as a model polymer and its crystallization is studied in a temperature gradient field. Based on the results of the Monte Carlo method, the probabilistic model methodology is discussed. The results show that when the product has a large temperature gradient and a large temperature difference, the probabilistic model cannot be used directly; instead, it is necessary to use the average probabilistic model. This means that the sample should be divided into several smaller parts and the probabilistic model used separately for each small part. The values are then averaged to obtain the mean conversion degree of the melt into spherulites for the whole product. The effects of the division number are also discussed. The goal of the present paper is to better understand the polymer crystallization kinetics model in terms of temperature gradients.

Formation and propagation of a shock wave in a gas with temperature gradients

2002 ◽  
Vol 473 ◽  
pp. 245-264 ◽  
Author(s):  
V. S. SOUKHOMLINOV ◽  
V. Y. KOLOSOV ◽  
V. A. SHEVEREV ◽  
M. V. ÖTÜGEN
Keyword(s):  
Shock Wave ◽  
Temperature Gradient ◽  
Numerical Solutions ◽  
Weak Shock ◽  
Negative Temperature ◽  
Temperature Gradients ◽  
Initial Disturbance ◽  
Weak Shock Wave ◽  
Axial Distance ◽  
Uniform Medium

A theoretical analysis was carried out to study the formation and propagation of a weak shock wave in a gas with longitudinal temperature gradients. An equation describing the formation and propagation of a weak shock wave through a non-uniform medium in the absence of energy dissipation was derived. An approximate analytical solution to the one-dimensional wave propagation equation is established. With this, the thermal gradient effects on the shock-wave Mach number and speed were investigated and the results were compared to earlier experiments. Numerical solutions for the same problem using Euler’s equations have also been obtained and compared to the analytical results. The analysis shows that the time of shock-wave formation from the initial disturbance, for mild temperature gradients, is independent of the gradient. The shock wave forms at a longer axial distance from the initial disturbance when the temperature gradient is positive whereas the opposite is true for a negative temperature gradient.

The Effect of Space-Dependent Thermal Conductivity on the Steady Central Temperature of a Cylinder

2001 ◽  
Vol 124 (1) ◽  
pp. 195-197 ◽  
Author(s):  
Louis C. Burmeister
Keyword(s):  
Thermal Conductivity ◽  
Monte Carlo ◽  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Test Cases ◽  
Two Dimensional ◽  
Central Temperature ◽  
Constant Thermal Conductivity ◽  
Difference Methods ◽  
Peripheral Temperature

A transformation is presented that enables the center temperature of a cylinder to be expressed in terms of an integral of the peripheral temperature distribution for heat conduction with space-dependent thermal conductivity. Its predictions agree with exact answers and with numerical solutions obtained with finite difference methods for four test cases. The new result can be applied to a two-dimensional floating random-walk Monte Carlo procedure which previously was restricted to the case of constant thermal conductivity.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

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