Some aspects of nonisothermal crystallization of polymers. II. Consideration of the isokinetic condition

Nakamura, Katsuyuki; Katayama, Ken‐ichi; Amano, Toshihiko

doi:10.1002/app.1973.070170404

Cited by 399 publications

(210 citation statements)

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“…The nucleation rate (27b) is proportional to the growth rate (27a) if Q = P 2 , which corresponds to the isokinetic assumption of the Nakamura equation. 69 Correspondingly, one can show that the rank of the matrix R, which represents the number of physically distinct processes, drops from two for Q P 2 to one for Q = P 2 . Only in the former case can one speak of a true physical distinction between nucleation and growth.…”

Section: Consequences For Thermodynamic Driving Forcesmentioning

confidence: 97%

Crystal shapes and crystallization in continuum modeling

Hütter

Armstrong

2004

Physics of Fluids

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A crystallization model appropriate for application in continuum modeling of complex processes is presented. As an extension to the previously developed Schneider equations [W. Schneider, A. Köppel, and J. Berger, "Non-isothermal crystallization of polymers," Int. Polym. Proc. 2, 151 (1988)], the model presented here allows one to account for the growth of crystals of various shapes and to distinguish between one-, two-, and three-dimensional growth, e.g., between rod-like, plate-like, and sphere-like growth. It is explained how a priori knowledge of the shape and growth processes is to be built into the model in a compact form and how experimental data can be used in conjunction with the dynamic model to determine its growth parameters. The model is capable of treating transient processing conditions and permits their straightforward implementation. By using thermodynamic methods, the intimate relation between the crystal shape and the driving forces for phase change is highlighted. All these capabilities and the versatility of the method are made possible by the consistent use of four structural variables to describe the crystal shape and number density, irrespective of the growth dimensionality.

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Section: Consequences For Thermodynamic Driving Forcesmentioning

confidence: 97%

Crystal shapes and crystallization in continuum modeling

Hütter

Armstrong

2004

Physics of Fluids

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“…The simplest model is a parallel of two kinetic processes noninteracting and competing for the available molten material. The kinetic equation adopted here for both processes is the nonisothermal formulation by Nakamura et al 9,10 of the KolmogoroffAvrami-Evans model. [27][28][29][30] The model is based on the following equation:…”

Section: Theory: Crystallization Kinetics Modelmentioning

confidence: 99%

“…7,8 Several attempts have been made to describe nonisothermal crystallization kinetics with simplifying assumptions [9][10][11][12][13] and procedures have also been developed to determine the relevant rate parameters with no concern on the experimental conditions encountered during processing where drastic solidification conditions are determined by large pressures, stresses, and temperature gradients. 9,10 As a matter of fact, the data obtained from traditional techniques, such as calorimetric cooling ramps, are restricted to few degrees Celsius per second. Such cooling rates are orders of magnitude lower than those experienced by the material during polymer processing.…”

Section: Introductionmentioning

confidence: 99%

Crystallization kinetics of iPP: Influence of operating conditions and molecular parameters

Carrubba

Piccarolo

Brucato

2007

J of Applied Polymer Sci

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An analysis of the crystallization kinetics of different grades of isotactic polypropylene (iPP) is here presented. To describe the crystallization kinetics as a function of molecular and operating parameters, the methodological path followed was the preparation of quenched samples of known cooling histories, calorimetric crystallization isotherms tests, differential scanning calorimetry cooling ramps, wide angle X-ray diffraction (WAXD) measurements, and density determination. The WAXD analysis performed on the quenched iPP samples confirmed that during the fast cooling at least a crystalline structure and a mesomorphic one form. The diffractograms were analyzed by a deconvolution procedure, to identify the relationship between the cooling history and the distribution of the crystalline phases. The whole body of results (including calorimetric ones) provides a wide basis for the identification of a crystallization model suitable to describe solidification in polymer-processing operations, based on the KolmogoroffAvrami-Evans nonisothermal approach. The kinetic parameters, determined for all the materials, are discussed, highlighting the effect of molecular parameters on the crystallization kinetics: molecular mass and distribution, tacticity, nucleating agents, and ethylene units content.

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“…Conhecido K(T) e assumindo novamente n ser igual a 3, pode-se usar então a equação de Nakamura [15], equação 11, para simular as curvas de dθ/dt versus T. A integração de dθ/dt permite então a obtenção das curvas de θ versus T, que podem ser comparadas com as curvas obtidas experimentalmente, verificandose então a validade do método da Curva Mestre para obtenção da constante K(T).…”

Section: Método Da Curva Mestre Aplicado à Cristalizaçãounclassified

Cristalização não isotérmica de poliamida 66: Determinação dos parâmetros da Equação de Nakamura via Método da Curva Mestre

Galera¹,

Mathias²,

Koppen³

et al. 2016

Matéria (Rio J.)

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RESUMOPoliamida é uma família de termoplásticos utilizada na fabricação de peças com tolerância dimensional relativamente estreita, como engrenagens em produtos eletrônicos, pequenos filtros de combustíveis na indústria automobilística e etc. O controle dimensional está intimamente relacionado à contração que acompanha o processo de cristalização do polímero em peças moldadas por injeção. Assim, o propósito do presente trabalho foi determinar a constante de cristalização não-isotérmica de amostra de poliamida 66 empregando-se o Método da Curva Mestre visando seu emprego em conjunto com a equação de Nakamura para simulação do processo de solidificação na moldagem por injeção. Para tanto, experimentos de cristalização não isotérmica foram realizados em um Calorímetro Diferencial de Varredura, DSC, em várias taxas de resfriamento, na faixa de 5 a 40º C/min. As curvas originais de DSC foram corrigidas em termos da defasagem de temperatura entre a amostra e o forno do DSC antes da aplicação do método. A equação de Nakamura e a constante de cristalização não isotérmica obtida pelo método da Curva Mestre foram empregados para simular as curvas de cristalinidade relativa em função da temperatura para as diferentes taxas de resfriamento. Também foi avaliada a influência do uso de diferentes valores de cristalinidade relativa inicial nas simulações via modelo de Nakamura, análise esta normalmente não encontrada na literatura. As curvas geradas pela constante de cristalização calculada via Método da Curva Mestre apresentaram uma boa concordância com os dados experimentais para esta amostra de poliamida 66 usando-se 10 -5 como cristalinidade relativa inicial para a forma diferencial da equação de Nakamura. Desse modo, o modelo de Nakamura, juntamente com sua constante determinada pelo Método da Curva Mestre, se mostrou uma boa opção para a simulação do processo de cristalização na moldagem por injeção de poliamida 66.Palavras-chave: cristalização não isotérmica, método da curva mestre, poliamida 66, defasagem de temperatura. ABSTRACTPolyamide is a family of thermoplastics used for producing components with tight dimensional tolerance, such as gears for electronics products and small filters for fuels in the automotive industry. The dimensional control of these parts is intrinsically related to the contraction associated to the crystallization process during their injection molding . Therefore, the purpose of the present work was to calculate the non-isothermal crystallization constant of a polyamide 66 sample using the Master Curve Approach for simulation of processing. Non-isothermal crystallization experiments were carried out in a differential scanning calorimeter, DSC, at several cooling rates. The original DSC curves were corrected for the temperature lag between the sample and the DSC furnace. The Nakamura equation and the non-isothermal crystallization constant obtained by the Master Curve Approach were employed to simulate the curves of relative crystallinity as a function of temperature, for the different cooling r...

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Some aspects of nonisothermal crystallization of polymers. II. Consideration of the isokinetic condition

Cited by 399 publications

References 0 publications

Crystal shapes and crystallization in continuum modeling

Crystal shapes and crystallization in continuum modeling

Crystallization kinetics of iPP: Influence of operating conditions and molecular parameters

Cristalização não isotérmica de poliamida 66: Determinação dos parâmetros da Equação de Nakamura via Método da Curva Mestre

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