Comments and recommendations on the use of the Avrami equation for physico‐chemical kinetics

Khanna, Y. P.; Taylor, Tom

doi:10.1002/pen.760281605

Cited by 96 publications

(81 citation statements)

References 7 publications

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“…Simulations for the Avrami equation (Eq. 1), for various integer values of m and a range of values of A (within the range of experimentally determined values of A and m in the lipid literature), clearly demonstrate that any minor deviation from a perfect sigmoid in the experimentally determined data essentially results in a superposition of different Avrami constants and exponents within the same fit (13)(14)(15). In practice, many approaches in the literature attempt to explain (usually without experimental evidence) lower-than-expected or noninteger Avrami exponents derived from experimentally obtained data.…”

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confidence: 82%

Modification of the Avrami model for application to the kinetics of the melt crystallization of lipids

Narine

Humphrey

Bouzidi

2006

J Americ Oil Chem Soc

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The Avrami model was developed to model the kinetics of crystallization and growth of a simple metal system. The original assumptions of the model do not apply for high-volumefraction crystallizing lipids, although it is incorrectly and frequently applied. A modified form of the Avrami model, wellsuited to complex lipid crystallization kinetics, is developed. It produces excellent fits to experimental data and allows the prediction of physically meaningful parameters, such as changes in nucleation rate and type, growth rate, morphology, and dimensionality. Morphological changes highlighted by time-resolved temperature-controlled polarized light microscopy support its application to crystallizing lipids. The kinetics of crystallization for six separate lipid samples were monitored by pulsed NMR, and fits were performed using the classical and modified Avrami model. In all cases, the modified model provided superior fits to the data compared with that of the classical model. The modified model supports the theory that lipids crystallize and grow into networks via very specific growth modes. Furthermore, the case is made that it is useful for interpreting crystallization kinetics of other systems such as polymer melts, which have nonconstant growth rates, dimensionalities, and nucleation conditions, and whose growth become diffusion-limited within specific regimes.Paper no. J11426 in JAOCS 83, 913-921 (November 2006).The Avrami model is frequently used to evaluate the kinetics of crystallization and growth of lipids, and is purported to relate experimentally determined kinetics to growth modes and structure of the final lipid network. Unfortunately, the application of the Avrami equation in lipid crystallization literature is inconsistent. Three different fits of the Avrami model have produced significantly different values for the Avrami exponent and constant (see below). Some researchers suggest that only a portion of the crystallization curve should be fitted with the model, thereby ignoring important information about the entire crystallization process. It has also been suggested that there are a number of line segments within a typical data set that can each be fitted with the Avrami model, and researchers have arbitrarily chosen one segment to fit with the model, without any justification. In fact, the crystallization kinetics of most lipid systems are not characterized by conditions that the Avrami model assumes are valid.This communication reviews the development of the Avrami model and examines crystallization data from a number of lipid systems. A modification to the Avrami model is proposed that does not violate the assumptions of the original model and provides excellent fits of crystallization data from lipids.Assumptions of the Avrami model. The Avrami equation is used extensively to model the crystallization behavior of metallic melts, polymers, and more recently, lipids, and is related to the problem of impinging waves, a problem first solved by Poisson (1). It is important to note that essentially i...

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confidence: 82%

Modification of the Avrami model for application to the kinetics of the melt crystallization of lipids

Narine

Humphrey

Bouzidi

2006

J Americ Oil Chem Soc

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“…Al 2,62%: 294,5 K (F), 297,5 K (G). En todos los casos el tiempo de cristalizaci6n a la temperatura indicada fue de 30 min despu6s de r. activaci6n asociada al proceso de cristalizaci6n (E~) proporciona resultados err6neos, puesto que su magnitud depende de la magnitud due 11 (Khanna y Taylor, 1988).…”

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“…Posteriormente, se calculo la fracci6n de cristalizaci6n de tripalmitina (F) en función del tiempo (t) como F = (T¡ -T)/(T ~ -T~), donde T es la transmitancia de la soluci6n a tiempo cero, T es la transmitancia a tiempo t y T, es la transmitancia mfnima obtenida durante la cristalizaci6n. Con la ecuaci6n deAvrami (Avrami, 1940) modificada de acuerdo a Khanna y Taylor(Khanna y Taylor, 1988) (Ec. 2) el indice de Avrami (11) y z se calcularon de la regresioiilineal entre Ln[-Ln(1 -F)] y Ln(t) (Ec.…”

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Cálculo de algunos parámetros de la cristalización de triacilglicéridos de aceites vegetales / Determination of some crystallization parameters for triacylglycerides of vegetable oils

Toro‐Vázquez

Dibildox-Alvardo

Charó-Alonso

1999

Food sci. technol. int.

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Se ha desarrollado un sistema modelo de composición heterogénea de triacilglicéridos (TG) donde el componente de mayor temperatura de fusión cristaliza independientemente. Se emplearon, disoluciones de tripalmitina en aceite de ajonjolí (0,98,1,80 y 2,62% p/v) que siguen un comportamiento ideal de cristalización, determinado por calorimetría diferencial de barrido y la ecuación de Hildebrand, Estas disoluciones se emplearon para investigar el efecto del superenfriamiento y la viscosidad (η) en el desarrollo de los estados polimórficos de cristales de TG, su mecanismo de crecimiento, constante de velocidad de cristalización (z) y energia de activación asociada al proceso de cristalización ( E a ). La velocidad de nucleación y de crecimiento de cristales, así como la forma polimórfica desarrollada por los TG dependen predominantemente de la η y del superenfriamiento, que a su vez es función de la concentración del TG de mayor temperatura de fusión en el sistema (ej., tripalmitina). Mediante una regresión multivariable podria evaluarse el efecto conjunto del superenfriamiento, la η del medio y la concentración del componente cristalizable para predecir el tamaño, número y forma polimórfica de los cristales desarrollados durante el proceso industrial de cristalización fraccionada de aceites y grasas vegetales. Asi se establecenán las condiciones de mayor rendimiento y eficacia de separación de la fracción cristalizada.Palabras clave : Aceite de ajonjolí, cristalización, triglicéridos, tripalmitina A model system with a heterogenous composition of triacylglycerides (TG), in which the component with the highest melting temperature crystallized independently, was developed. Thus, tripalmitin solutions in sesame seed oil (0.98, 1.80 and 2.62% w/v) with ideal crystallization behavior, evaluated through differential scanning calorimetry and the Hildebrand equation, were utilized as a model system to investigate the effect of supercooling and viscosity (η) on the development of polymorph states of TG crystals, their crystal growth mechanism, crystal growth rate constant (z), and activation energy associated with the crystallization process ( E a ). Results indicated that a modification of the Avrami equation, as suggested by Khanna and Taylor, provides reliable values of z and, subsequently, correct estimates of E a . This was not the case when the original Avrami equation was used. Subsequent analysis indicated that nucleation and crystal growth, as well as the polymorph states developed by the TG, depend mainly on η and the extent of supercooling. The latter is a function of the concentration of the TG with the highest melting temperature in the system (e.g. tripalmitin). In conclusion, it is feasible to model the combined effect of supercooling, the viscosity of the liquid phase, and the concent...

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“…Some authors [17,18] reparameterized Avrami's approximate equation. The so called Erofeev model was used by Ng [17] to describe the thermal decomposition in the solid state.…”

Section: Introductionmentioning

confidence: 99%

Crystallization Kinetics of Cocoa Fat Systems: Experiments and Modeling

Padar

Jeelani

Windhab

2008

J Americ Oil Chem Soc

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Isothermal crystallization kinetics of unseeded and seeded cocoa butter and milk chocolate is experimentally investigated under quiescent conditions at different temperatures in terms of the temporal increase in the solid fat content. The theoretical equations of Avrami based on one-, two-and three-dimensional crystal growth are tested with the experimental data. The equation for onedimensional crystal growth represents well the kinetics of unseeded cocoa butter crystallization of form a and b 0 . This is also true for cocoa butter crystal seeded milk chocolate. The sterical hindrance due to high solids content in chocolate restricts crystallization to lineal growth. In contrast, the equation for two-dimensional crystal growth fits best the seeded cocoa butter crystallization kinetics. However, a transition from three-to one-dimensional growth kinetics seems to occur. Published data on crystallization of a single component involving spherulite crystals are represented well by Avrami's three-dimensional theoretical equation. The theoretical equations enable the determination of the fundamental crystallization parameters such as the probability of nucleation and the number density of nuclei based on the measured crystal growth rate. This is not possible with Avrami's approximate equation although it fits the experimental data well. The crystallization can be reasonably well defined for single component systems. However, there is no model which fits the multicomponent crystallization processes as observed in fat systems. List of symbols k rate constant in Avrami approximate equation (s -m ) m exponent in Avrami approximate equation N number of germ nuclei per unit volume at any instant of time (m -3 ) N 0 initial number of germ nuclei per unit volume (m -3 ) p probability of growth of germ nuclei per unit time (s -1 ) l length or radius of crystal grain (m) _ l average rate of growth of length or radius of crystal grain (m s -1 ) S mass of crystalline phase per unit mass of lipid phase S m maximum mass of crystalline phase per unit mass of lipid phase S m0 fraction of solid fat at the beginning of bulk crystallization t time (s) T temperature (K) v volume of crystal grain (m 3 ) V volume of crystalline phase per unit volume of suspension V m maximum volume of crystalline phase per unit volume of suspension V e volume of crystal grains per unit volume of suspension formed without growth impediment z dimensionless re-scaled timeGreek letters _ c shear rate (s -1 ) r 1 cross-sectional area of rod-like crystal (m 2 ) r 2 thickness of plate-like crystal (m)

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Comments and recommendations on the use of the Avrami equation for physico‐chemical kinetics

Cited by 96 publications

References 7 publications

Modification of the Avrami model for application to the kinetics of the melt crystallization of lipids

Modification of the Avrami model for application to the kinetics of the melt crystallization of lipids

Cálculo de algunos parámetros de la cristalización de triacilglicéridos de aceites vegetales / Determination of some crystallization parameters for triacylglycerides of vegetable oils

Crystallization Kinetics of Cocoa Fat Systems: Experiments and Modeling

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