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.

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 Metamorphism of Dry Snow as a Result of Temperature Gradient and Vapor Density Differences

1983 ◽  
Vol 4 ◽  
pp. 3-9 ◽  
Author(s):  
E. E. Adams ◽  
R. L. Brown
Keyword(s):  
Temperature Gradient ◽  
Heat Conduction Equation ◽  
Temperature Gradients ◽  
Large Temperature ◽  
Local Minima ◽  
Vapor Density ◽  
Snow Density ◽  
Local Maxima ◽  
The Difference

A heat conduction equation for the determination of the temperature profile in a snowpack is developed. The magnitude of the temperature gradient tends to increase as the snow surface is approached, with local minima through layers of high snow density and local maxima above and below these layers. Calculations are made of the difference in vapor density in the pore and over the ice grain surfaces which border the pore. In the presence of sufficient temperature and temperature gradient, faceted crystals will develop near the top of the pore, as ice is sublimed away from the surfaces in the lower region. There will be a reduction in the percentage of rounded grains as the faceted form develops. The process is demonstrated to be enhanced at warm temperatures and large temperature gradients in low density snow.

End Thermal Stresses in a Long Circular Rod

1968 ◽  
Vol 35 (2) ◽  
pp. 267-273 ◽  
Author(s):  
W. H. Chu ◽  
F. T. Dodge
Keyword(s):  
Temperature Gradient ◽  
General Solution ◽  
Thermal Stresses ◽  
Linear Interpolation ◽  
Temperature Gradients ◽  
Characteristic Functions ◽  
Large Temperature ◽  
End Effect ◽  
Title Problem ◽  
Characteristic Values

The title problem is solved by the method of collocation utilizing complex nonorthogonal characteristic functions. It is shown that the characteristic values can be obtained by repeated linear interpolation without much difficulty. Ten roots are given for the case of Poisson’s ratio equaling 0.3. For large temperature gradients, an example is given which shows high end stresses. The general solution due to the end effect dies down at the rate of exp (–2.722 z/a) or faster, but its magnitude depends on the steepness of the temperature gradient. This paper also shows that the Saint-Venant principle may not always be sufficient, that the end stress could be critical, and that, therefore, it should be calculated.

scholarly journals Metamorphism of Dry Snow as a Result of Temperature Gradient and Vapor Density Differences

1983 ◽  
Vol 4 ◽  
pp. 3-9 ◽  
Author(s):  
E. E. Adams ◽  
R. L. Brown
Keyword(s):  
Temperature Gradient ◽  
Heat Conduction Equation ◽  
Temperature Gradients ◽  
Large Temperature ◽  
Local Minima ◽  
Vapor Density ◽  
Snow Density ◽  
Local Maxima ◽  
The Difference

A heat conduction equation for the determination of the temperature profile in a snowpack is developed. The magnitude of the temperature gradient tends to increase as the snow surface is approached, with local minima through layers of high snow density and local maxima above and below these layers. Calculations are made of the difference in vapor density in the pore and over the ice grain surfaces which border the pore. In the presence of sufficient temperature and temperature gradient, faceted crystals will develop near the top of the pore, as ice is sublimed away from the surfaces in the lower region. There will be a reduction in the percentage of rounded grains as the faceted form develops. The process is demonstrated to be enhanced at warm temperatures and large temperature gradients in low density snow.

Role of substrate shape on thermal energy transmission in robotized wire and arc additive manufacturing

2019 ◽  
Vol 25 (7) ◽  
pp. 1285-1294 ◽  
Author(s):  
Rong Li ◽  
Jun Xiong
Keyword(s):  
Additive Manufacturing ◽  
Temperature Gradient ◽  
Thermal Energy ◽  
Molten Pool ◽  
Temperature Gradients ◽  
Maximum Temperature ◽  
Large Temperature ◽  
Energy Transmission ◽  
Content Type ◽  
Thin Walled

Purpose The purpose of this study is to present how the thermal energy transmission of circular parts produced in robotized gas metal arc (GMA)-based additive manufacturing was affected by the substrate shape through finite element analysis, including distributions of thermal energy and temperature gradient in the molten pool and deposited layers. Design/methodology/approach Three geometric shapes, namely, square, rectangle and round were chosen in simulation, and validation tests were carried out by corresponding experiments. Findings The thermal energy conduction ability of the deposited layers is the best on the round substrate and the worst on the rectangular substrate. The axial maximum temperature gradients in the molten pool along the deposition path with the round substrate are the largest during the deposition process. At the deposition ending moment, the circumferential temperature gradients of all layers with the round substrate are the largest. A large temperature gradient usually stands for a good heat conduction condition. Altogether, the round substrate is more suitable for the fabrication of circular thin-walled parts. Originality/value The predicted thermal distributions of the circular thin-walled part with various substrate shapes are helpful to understand the influence of substrate shape on the thermal energy transmission behavior in GMA-based additive manufacturing.

scholarly journals Morphology and crystallization kinetics of Rubber-modified Nylon 6 Prepared by Anionic In-situ Polymerization

2020 ◽  
Vol 27 (1) ◽  
pp. 204-215
Author(s):  
Hongkai Zhao ◽  
Dengchao Zhang ◽  
Yingshuang Li
Keyword(s):  
Crystallization Kinetics ◽  
In Situ Polymerization ◽  
Good Description ◽  
Nylon 6 ◽  
Avrami Equation ◽  
Infrared Analysis ◽  
Chain Segment ◽  
The Impact ◽  
Kinetics Of

AbstractIn this work, we modified nylon 6 with liquid rubber by in-situ polymerization. The infrared analysis suggested that HDI urea diketone is successfully blocked by caprolactam after grafting on hydroxyl of HTPB, and the rubber-modified nylon copolymer is generated by the anionic polymerization. The impact section analysis indicated the rubber-modified nylon 6 resin exhibited an alpha crystal form.With an increase in the rubber content, nylon 6 was more likely to generate stable α crystal. Avrami equation was a good description of the non-isothermal crystallization kinetics of nylon-6 and rubber-modified nylon-6 resin. Moreover, it is found that the initial crystallization temperature of nylon-6 chain segment decreased due to the flexible rubber chain segment. n value of rubber-modified nylon-6 indicated that its growth was the coexistence of two-dimensional discoid and three-dimensional spherulite growth. Finally, the addition of the rubber accelerated the crystallization rate of nylon 6.

scholarly journals Analysis of the Crystallization Kinetics and Thermal Stability of the Amorphous Mg72Zn24Ca4 Alloy

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3583
Author(s):  
Bartosz Opitek ◽  
Janusz Lelito ◽  
Michał Szucki ◽  
Grzegorz Piwowarski ◽  
Łukasz Gondek ◽  
...  
Keyword(s):  
Metallic Glass ◽  
Crystallization Kinetics ◽  
Crystallization Process ◽  
Isothermal Annealing ◽  
Amorphous Structure ◽  
Avrami Equation ◽  
Temperature Phase ◽  
Scanning Calorimetry ◽  
Human Body Temperature ◽  
End Times

The aim of this study was to analyze the crystallization of the Mg72Zn24Ca4 metallic glass alloy. The crystallization process of metallic glass Mg72Zn24Ca4 was investigated by means of the differential scanning calorimetry. The glass-forming ability and crystallization are both strongly dependent on the heating rate. The crystallization kinetics, during the isothermal annealing, were modelled by the Johnson–Mehl–Avrami equation. Avrami exponents were from 2.7 to 3.51, which indicates diffusion-controlled grain growth. Local exponents of the Johnson–Mehl–Avrami equation were also calculated. In addition, the Mg phase—being the isothermal crystallization product—was found, and the diagram of the time–temperature phase transformation was developed. This diagram enables the reading of the start and end times of the crystallization process, occurring in amorphous ribbons of the Mg72Zn24Ca4 alloy on the isothermal annealing temperature. The research showed high stability of the amorphous structure of Mg72Zn24Ca4 alloy at human body temperature.

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