Model For Crystallization Kinetics Research Articles

Hydration Kinetics and Microscopic Analysis of Calcium Oxide Expansion Clinker

Hydrating and calcining method combined with the kinetic equation were adopted to describe the hydration kinetics process of the laboratory-calcined CaO expansion clinker, XRD and SEM were used to test and analysis its mineral compo-sition and microstructure as well. The results show that, hydration reaction process in pure water of f-CaO contained in the CaO expansion clinker meets the Avrami isothermal crystallization kinetics model, and the hydration degree increases with temperature, with the relation between reaction rate constant and temperature conforming to Arrhenius law; the CaO expansion clinker powder contains a large number of particles in which f-CaO, CaSO4, Ca4Al6O12SO4(partly still containing calcium silicates) phases existing at the same time, by the impact of the presence of impurity phases and the difference of calcining conditions, the hydration activity of f-CaO contained in CaO expansion clinker was different from that of pure CaO and that of f-CaO wrapped in cement clinker or high-calcium fly ash.

Mathematical Model of Dynamic Crystallization of Ethylene/1‐Octene Copolymers

SummaryDynamic crystallization (DC) is a fractionation technique to enhance physical separation of polymers with different chain crystallizabilities by crystallizing polymer chains from solution in a column under a constant flow rate. In this work, a mathematical model for describing fractionation mechanism of dynamic crystallization based on the concept of population balance, crystallization kinetic, and dispersion models is proposed by the first time. The model was validated with experimental DC analysis of three ethylene/1‐octene copolymers. The simulated DC profiles were found to describe experimental results well.

Mathematical Modeling of Temperature Rising Elution Fractionation (TREF) of Polyethylene and Ethylene/1-Olefin Copolymers

Temperature rising elution fractionation (TREF) is a characterization technique widely used to estimate chemical composition distribution (CCD) of semicrystalline copolymers. Although several mathematical models have been previously proposed to elucidate the TREF fractionation mechanism, all previous TREF models assume equilibrium fractionation; thus, they cannot describe important kinetics effects observed in TREF experiments. In this work, a new TREF model is developed incorporating crystallization and dissolution kinetic models during the fractionation process. The proposed model describes the effects of molecular weight, comonomer content, cooling rate, heating rate, and solvent flow rate on experimental TREF profiles for both polyethylene and ethylene/1-olefin copolymers very well.

A multifunctional device to determine specific volume, thermal conductivity and crystallization kinetics of semi-crystalline polymers

The control and optimization of heat transfer during the forming of thermoplastic parts is of primary importance since they impact on the quality of final parts. The modelling of this transfer requires accurate knowledge of the polymer thermo-physical properties, and also of the parameters describing the crystallization, this latter data being very sensitive to the thermal history for semi-crystalline polymers. The experimental determination of these parameters requires the use of many instruments, which is time consuming. To address this issue, a home-built instrumented mould was designed to measure and identify several properties from a single experiment. Specific volume, transverse thermal conductivity in amorphous and solid states can be estimated as a function of the temperature. Parameters of a crystallization kinetics model are identified with a non invasive procedure. Our methodology is illustrated on a well-known semi-crystalline thermoplastic. Identified parameters are compared with literature results.

A Differential Scanning Calorimetry Method for Construction of Continuous Cooling Transformation Diagram of Blast Furnace Slag

The continuous cooling crystallization of a blast furnace slag was studied by the application of the differential scanning calorimetry (DSC) method. A kinetic model describing the correlation between the evolution of the degree of crystallization with time was obtained. Bulk cooling experiments of the molten slag coupled with numerical simulation of heat transfer were conducted to validate the results of the DSC methods. The degrees of crystallization of the samples from the bulk cooling experiments were estimated by means of the X-ray diffraction (XRD) and the DSC method. It was found that the results from the DSC cooling and bulk cooling experiments are in good agreement. The continuous cooling transformation (CCT) diagram of the blast furnace slag was constructed according to crystallization kinetic model and experimental data. The obtained CCT diagram characterizes with two crystallization noses at different temperature ranges.

Crystallization kinetics modeling of high density and linear low density polyethylene resins

AbstractThis paper describes isothermal and nonisothermal crystallization kinetics of a Ziegler‐Natta catalyzed high density polyethylene (HDPE) and linear low density polyethylene (LLDPE) resins. Standard techniques such as differential scanning calorimetry (DSC) and light depolarization microscopy (LDM) techniques were used to measure isothermal kinetics at low supercoolings. DSC was also used to measure nonisothermal crystallization kinetics at low cooling rates. Extrapolation of isothermal crystallization half‐times of Z‐N catalyzed LLDPE resin using the isothermal half‐time analysis led to erroneous predictions, possibly due to Z‐N LLDPE consisting of a mixture of molecules having different amounts of short chain branching (comonomer). However, predicted reciprocal half‐times at high supercoolings, using isothermal half‐time analysis and using nonlinear regression of nonisothermal crystallization kinetics measured at low cooling rates using the differential Nakamura model, of the HDPE were similar to measured reciprocal half times at high supercoolings of a similar HDPE by Patki and Phillips. It is also shown that the differential Nakamura model can be effectively used to model nonisothermal crystallization kinetics of HDPE resins. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012

An SPICE model for phase-change memory simulations

Along with a series of research works on the physical prototype and properties of the memory cell, an SPICE model for phase-change memory (PCM) simulations based on Verilog-A language is presented. By handling it with the heat distribution algorithm, threshold switching theory and the crystallization kinetic model, the proposed SPICE model can effectively reproduce the physical behaviors of the phase-change memory cell. In particular, it can emulate the cell's temperature curve and crystallinity profile during the programming process, which can enable us to clearly understand the PCM's working principle and program process.

Improved Kinetic Model of Crystallization for Isotactic Polypropylene Induced by Supercritical CO2: Introducing Pressure and Temperature Dependence into the Avrami Equation

Supercritical carbon dioxide (SC-CO2) provides a highly tunable technique to induce changes in morphology and crystallization kinetics of various polymers. In this study, the effect of SC-CO2 treatment on the crystallinity of isotactic polypropylene (i-PP) was analyzed by differential scanning calorimetry (DSC). The Avrami equation is suitable for describing crystallization kinetics of various solids. However, the assumption that the crystallinity approaches 1.0 as the time approaches infinity is not valid for semicrystalline polymers, especially in the atmosphere of SC-CO2. An improved kinetic model for the CO2-induced crystallization of i-PP was purposed by introducing equilibrium crystallinity, as well as temperature- and pressure-dependent terms into the Avrami equation. The parameters of the crystallization kinetics model were obtained by least-squares fitting of the DSC data. The results show that the improved kinetic model provides a reasonable description of the crystallization behavior of i-PP induced by SC-CO2. The successful application of the improved kinetic model to the CO2-induced crystallization of i-PP suggests that this model may be adopted to other SC-CO2-semicrystalline polymer systems.

Evaluation of nonisothermal crystallization kinetic models for linear poly(phenylene sulfide)

The nonisothermal crystallization kinetics of linear Poly(phenylene sulfide) (PPS) was studied with differential scanning calorimetry. Ozawa theory, Jeziorny model, and Mo equation were applied to describe the crystallization kinetics and to determine the crystallization parameters and mechanism of the linear PPS resin. The crystallization activation energies were also calculated using Kissinger formula and Flynn-Wall-Ozawa equation, respectively. According to the Ozawa model, it is found that instantaneous nucleation takes place during crystallization of PPS; the Ozawa exponent m is 3 in initial stage of crystallization; as the crystallization temperature decreases, the value of m reduces, and the growth rate of crystal almost keeps a constant. The Avrami exponent n obtained from Jeziorny model fluctuate around 1.84. Based on the Jeziorny model, the crystallization rate increases with increasing the cooling rate, but it does not change any longer when the cooling rate rise to a certain value. Mo equation also exhibits great advantages in treating the nonisothermal crystallization kinetics of PPS. The activation energy E of nonisothermal crystallization process of PPS is calculated to be −162.73 kJ/mol by the Kissinger formula, and the mean value of E determined by Flynn-Wall-Ozawa equation is −152.40 kJ/mol. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011

Crystallization Kinetics and Excess Free Energy of H2O and D2O Nanoscale Films of Amorphous Solid Water

Temperature-programmed desorption (TPD) and reflection absorption infrared spectroscopy (RAIRS) are used to investigate the crystallization kinetics and measure the excess free energy of metastable amorphous solid water films (ASW) of H(2)O and D(2)O grown using molecular beams. The desorption rates from the amorphous and crystalline phases of ASW are distinct, and as such, crystallization manifests can be observed in the TPD spectrum. The crystallization kinetics were studied by varying the TPD heating rate from 0.001 to 3 K/s. A coupled desorption-crystallization kinetic model accurately simulates the desorption spectra and accurately predicts the observed temperature shifts in the crystallization. Isothermal crystallization studies using RAIRS are in agreement with the TPD results. Furthermore, highly sensitive measurements of the desorption rates were used to determine the excess free energy of ASW near 150 K. The excess entropy obtained from these data is consistent with there being a thermodynamic continuity between ASW and supercooled liquid water.

Effects of carbon nanofibers on the crystallization behavior of polyethylene oxide

AbstractDifferential scanning calorimetry (DSC) was used to investigate the crystallization behavior of polyethylene oxide (PEO) and carbon nanofiber (CNF) filled PEO systems under non-isothermal experimental conditions. The dispersion and distribution of CNF of the composites were studied using scanning electron microscopy. Studies showed the uniform segregation of CNFs in PEO. Different crystallization kinetic models (the modified Avrami equation and the combined approach of Avrami and Ozawa) were used to study the dependence of crystal nucleation on the filler content. Analysis showed that inclusion of CNF to PEO retards the crystallization of PEO at all CNF loading under study

Crystallization behavior of poly(trimethylene terephthalate)-poly(ethylene glycol) segmented copolyesters/multi-walled carbon nanotube nanocomposites

Poly(trimethylene terephthalate)-poly(ethylene glycol) segmented copolyester (PTEG)/multi-walled carbon nanotube (MWCNT) nanocomposites with various MWCNT content and copolyester composition were prepared by solution blending and the effect of MWCNTs on the crystallization behavior of PTEG copolymers was explored by differential scanning calorimetry (DSC), depolarized light intensity (DLI) technique and polarized light microscopy (PLM). The dynamic crystallization and the crystallization morphology of the nanocomposites are discussed. The isothermal crystallization kinetics was analyzed by means of a two stage crystallization kinetics model. The results showed that MWCNTs take the role of an effective nucleating agent during composite crystallization and can expedite the process of crystallization of the PTEG matrix by providing more nucleation sites to the crystallizing phase, which results in the formation of smaller spherulites.

Effects of carbon nanofibers on the crystallization kinetics of polyethylene oxide

Differential scanning calorimetry (DSC) was used to investigate the crystallization behavior of polyethylene oxide (PEO) and carbon nanofiber (CNF) filled PEO systems under non-isothermal experimental conditions. The dispersion and distribution of CNF of the composites were studied using scanning electron microscopy. Studies showed the uniform segregation of CNFs in PEO. Different crystallization kinetic models were used to study the dependence of crystal nucleation on the filler content. Modified Avrami analysis showed that PEO undergoes change of crystallization from 3-D to 1-D crystal while going from primary to secondary crystallization. The crystallization kinetic of PEO reversed at CNF loading higher than 1 wt% of PEO. Based on modified Avrami and the combined approach of Avrami and Ozawa, it is concluded that the CNF retards the crystallization of PEO at all CNF loading under study.

Crystal nucleation and cluster-growth kinetics in a model glass under shear

Crystal nucleation and growth processes induced by an externally applied shear strain in a model metallic glass are studied by means of nonequilibrium molecular dynamics simulations, in a range of temperatures. We observe that the nucleation-growth process takes place after a transient, induction regime. The critical cluster size and the lag-time associated with this induction period are determined from a mean first-passage time analysis. The laws that describe the cluster-growth process are studied as a function of temperature and strain rate. A theoretical model for crystallization kinetics that includes the time dependence for nucleation and cluster growth is developed within the framework of the Kolmogorov-Johnson-Mehl-Avrami scenario and is compared with the molecular dynamics data. Scalings for the cluster-growth laws and for the crystallization kinetics are also proposed and tested. The observed nucleation rates are found to display a nonmonotonic strain rate dependency.

Nonisothermal crystallization behavior and kinetics of isotactic polypropylene/ethylene–octene blends. Part II: Modeling of crystallization kinetics

By applying the experimental data described in Part I, the non-isothermal crystallization kinetics of isotactic polypropylene/ethylene–octene blends have been mathematically modeled. The commonly used Avrami, Ozawa, Mo and Urbanovici–Segal models were used to model the crystallization kinetics, and it appears that Mo and Urbanovici–Segal models can well describe the non-isothermal crystallization kinetics of PP/POE blends. The data processing indicates that a small amount of POE can enhance the kinetic crystallizability because of heterogeneous nucleation, but excessive POE would in turn reduce the kinetic crystallizability by blocking the crystallization of PP.

Modeling of specific structure crystallization coupling with dissolution

In this paper, the research framework for specific structure crystallization modeling has been proposed in which four steps are required in order to investigate the rigorous crystallization modeling by thermodynamics. The first is the activity coefficient model of the solution, the second is Solid-Liquid equilibrium, the third and fourth are the dissolution and crystallization kinetics modeling, respectively. Our investigations show that the mechanisms of complex structure formation and microphase transition can be analyzed by combining the dissolution and crystallization kinetics modeling. Moreover, the formation mechanism of the porous KCl has been analyzed, which may provide a reference for the porous structure formation in the advanced material synthesis.

Thermally and flow induced crystallization of polymers at low shear rate

Abstract In semi-crystalline thermoplastic products, final properties are strongly dependent on the thermo-mechanical history experienced by the polymer melt during processing. More precisely, structural heterogeneities such as rigidity gradients and shrinkage anisotropy are directly related to the crystalline microstructure. Therefore, accurate prediction of part properties by a processing computer simulation code requires the implementation of an appropriate crystallization kinetics model, including both the effects of thermally and flow induced structure development. One issue is the necessity to improve the modeling of shear/extensional experimental data by relating the crystallization accelerating factors to an easily accessible material related variable. Several authors modeled the effect of the flow on the crystallization kinetics by using the isokinetic approach of Nakamura. Often, the resulting kinetic equations of these models account only for the evolution of the crystallinity fraction α leaving the influence of crystalline morphology aside. We may quote the work of Guo and Narh [1] , which connects the flow influence on the crystallization rate to the increase in the thermodynamic melting temperature in the Nakamura model. In 2005, R.I. Tanner presented a comparison of some models describing the polymer crystallization at low shear deformation rates under isothermal conditions. Based on Tanner's study, we developed a model of crystallization at low shearing, applied to non-isothermal flows, using only macroscopic measurable parameters. The key features of the concentrated suspension theory were used to characterize the effect of crystallization on the viscosity. In addition, we assumed that the flow generates additional crystallization nuclei via a parameter which combines the deformation and the deformation rate. The concept of germination-growth is introduced using the fundamentals of the Avrami–Kolmogorov theory, coupled with a modified Schneider's approach. The model is applied to a polypropylene, in a cooled Couette flow configuration. The results show the enhancement of the crystallization kinetics due to the shearing. The definition of global parameters simplifies the type and the number of experiments needed for the model parameter identification. The use of Schneider's approach leads to a new way of discriminating the relative roles of the flow and the temperature on the crystallization phenomenon. The competition between the two driving causes is presented and discussed: at low cooling rate or at high temperature, the shearing effect predominates. Other interesting results show the size distribution of the spherulites as well as the volume proportion for each crystalline size in the polymer.

Analytical Model for Heterogeneous Crystallization Kinetics of Spherical Glass Particles

An analytical model developed to describe the crystallization kinetics of spherical glass particles has been derived in this work. A continuous phase transition from three‐dimensional (3D)‐like to 1D‐like crystal growth has been considered and a procedure for the quantitative evaluation of the critical time for this 3D–1D transition is proposed. This model also allows straightforward determination of the density of surface nucleation sites on glass powders using differential scanning calorimetry data obtained under different thermal conditions.

Application of a crystallization kinetics model to simulate the effect of operation conditions on Crystaf profiles and calibration curves

AbstractCrystallization analysis fractionation (Crystaf) is a polymer characterization technique used to estimate chemical composition distributions (CCDs) of semicrystalline copolymers. The Crystaf profile can be transformed into a CCD using a calibration curve that relates average comonomer content to peak crystallization temperature. The calibration curve depends on copolymer molecular properties and Crystaf operation conditions. In this investigation, we applied a crystallization kinetics model to simulate Crystaf calibration curves and to quantify how Crystaf calibration curves depend on these factors. We applied the model to estimate the CCDs of three ethylene/1‐hexene copolymers from Crystaf profiles measured at different cooling rates and showed that our predictions agree well with the CCDs described by Stockmayer's distribution. We have also used this new methodology to investigate the effects of cooling rate, molecular weight, and comonomer type on Crystaf profiles and calibration curves. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 866–876, 2009

Warpage–crystallinity relations in rotational molding of polypropylene

AbstractThe authors present a study of the crystalline properties of selected series of polypropylene (PP) materials in relation to their warpage at conditions relevant for rotational molding. The PP materials have different crystallization temperatures and kinetics. The authors study the crystalline features of the materials using hot‐press experiments and differential scanning calorimetry (DSC). In the DSC, the authors do constant cooling rate runs as well as isothermal crystallization and subsequent heating. A multimode crystallization kinetics model was fitted to the DSC cooling runs. Regression analysis was done to relate the results from the crystallization experiments to warpage. The derived empirical model shows that the crystallization temperature, crystallization half‐time, and heat of fusion are the most significant parameters influencing warpage. Materials with warpage deviating from the model average are discussed taking aspects of the multimode kinetics into account. The present work could represent a basic platform for understanding and predicting the warpage during rotational molding process. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers