Isothermal Induction Time Research Articles

Machine Learning-Derived Correlations for Scale-Up and Technology Transfer of Primary Nucleation Kinetics.

Scaling up and technology transfer of crystallization processes have been and continue to be a challenge. This is often due to the stochastic nature of primary nucleation, various scale dependencies of nucleation mechanisms, and the multitude of scale-up approaches. To better understand these dependencies, a series of isothermal induction time studies were performed across a range of vessel volumes, impeller types, and impeller speeds. From these measurements, the nucleation rate and growth time were estimated as parameters of an induction time distribution model. Then using machine learning techniques, correlations between the vessel hydrodynamic features, calculated from computational flow dynamic simulations, and nucleation kinetic parameters were analyzed. Of the 18 machine learning models trained, two models for the nucleation rate were found to have the best performance (in terms of % of predictions within experimental variance): a nonlinear random Forest model and a nonlinear gradient boosting model. For growth time, a nonlinear gradient boosting model was found to outperform the other models tested. These models were then ensembled to directly predict the probability of nucleation, at a given time, solely from hydrodynamic features with an overall root mean square error of 0.16. This work shows how machine learning approaches can be used to analyze limited datasets of induction times to provide insights into what hydrodynamic parameters should be considered in the scale-up of an unseeded crystallization process.

Probability distributions of gas hydrate formation

Induction time distributions for gas hydrate formation were measured for gas mixtures of methane + propane at pressures up to 11.3 MPa using a high‐pressure automated lag time apparatus (HP‐ALTA). Measurements were made at subcooling temperatures between 4.3 and 13.5 K and, while isothermal induction times between 0 and 15,000 s were observed, the median isothermal induction times for the distributions ranged from 100 to 4000 s. A hyperbolic relationship between median induction time and subcooling was used to correlate the data. A graphical interpretation is presented that relates the two types of data that can be acquired by using the HP‐ALTA in one of two modes to study hydrate formation: induction time distributions at constant subcooling and formation temperature distributions observed during linear cooling ramps. The equivalence of these two modes provides a robust method for studying the variation of formation phenomena in different hydrate systems. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2640–2646, 2013

Metastable Zone Widths, Conformational Multiplicity, and Seeding

The propensity for crystallisation of acetanilides and propionanilides was compared both by polythermal metastable zone width measurements and by isothermal induction time measurements. Although there were clear relationships between the metastable zone widths and the conformational multiplicity in some cases, they broke down for the chloroacylanilides. This failure could not be fully accounted for by the difference in the crystal structures of the chloro compounds. A surprising dependence of crystal size on seeding effectiveness could explain some of the crystallisation behaviour, particularly for the induction period measurements.

Cure Kinetics Study of Unfilled and Carbon Black Filled Synthetic Isoprene Rubber

Abstract The reversion type cure kinetic and induction time models were successfully utilized to predict the isothermal and nonisothermal evolution of the state of cure in vulcanization of the unfilled and carbon black (CB)-filled IR compounds measured by APA 2000. The rate constants for the reversion reaction and the formation of the stable and unstable crosslinks and the parameters of the induction time function with the Arrhenius temperature dependences were determined from the isothermal cure measurements. The equation was proposed to adequately describe the measured dependence of the difference between the maximum and minimum torques as a function of isothermal curing temperature. The measured induction time as a function of heating rate and step temperature variation was successfully predicted based on parameters of the isothermal induction time model. Isothermal cure modeling at each curing temperature individually or at all the curing temperatures simultaneously showed the excellent agreement with the experimental data for both curing and reversion. More severe reversion in the CB-filled IR in comparison with the unfilled IR was explained by comparing their reversion rate constants.

Crystallization kinetics for simulation of processing of various polyesters

AbstractThe approach to determine crystallization kinetic parameters based on the DSC nonisothermal crystallization experiments is applied to poly(butylene terephthalate) (PBT) and poly(ethylene‐2,6‐naphthalate) (PEN). The differential form of the Nakamura equation and master curve approach are used. The isothermal induction times are obtained from nonisothermal induction times according to the concept of induction time index. The correction of temperature lag between the DSC furnace and the sample is incorporated. The corrected nonisothermal crystallization kinetic data is shifted with respect to an arbitrarily chosen reference temperature to obtain the master curve. By fitting the obtained master curve with the Hoffman‐Lauritzen equation, the model parameters for the crystallization rate constant are obtained. The relative crystallinity measured at different cooling and heating rates is described by these model parameters. © 2006 Wiley Periodicals, Inc. J Appl PolymSci 102: 2847–2855, 2006

A comparison of induction time and crystallization rate for syndiotactic polystyrene

AbstractOne objective of this study was to measure the crystallization parameters for syndiotactic polystyrene (MW = 244,000) to support a computer simulation of this material in an injection molding application. A second objective was to introduce a new crystallization rate equation that adequately predicts crystallization rates over a broader temperature range than the Hoffman‐Lauritzen equation. A third objective was to establish a new clearly defined method for determining the true induction time of a semicrystalline polymer as a function of temperature. The new crystallization rate equation introduced in this study has been formulated to give appropriate crystallization rate constants for all the temperatures currently usable with the Hoffman‐Lauritzen equation. In addition, this new equation also predicts appropriate crystallization rate constants outside the range of the Hoffman‐Lauritzen equation from temperatures significantly below the glass transition temperature, Tg, to temperatures significantly above the melting point, Tm. Interestingly, the isolation of the true isothermal induction times from apparent induction times in this study nicely mirrored the isothermal crystallization rates at each specific temperature. Both the true induction time and the crystallization rate curves were found to be similarly unsymmetrical as a function of temperature. Also, the temperature at the minimum induction time and the temperature at the peak crystallization rate determined from nonisothermal crystallization rate measurements were found to be nearly identical. Consequently, the results from this study strongly suggest that there is a significant and potentially very useful relationship between induction time analysis and crystallization rate kinetics.

Quiescent polymer crystallization: Modelling and measurements

AbstractThe problem of predicting nonisothermal crystallization kinetics based on isothermal data is considered, with reference to the difficulties involved, both experimental and theoretical. The kinetic model used is the differential form of the Nakamura equation which is an extension of the Avrami equation so as to apply to nonisothermal crystallization. Nonisothermal induction times are obtained from isothermal induction times according to the concept of induction time index. The theory of Hoffman Lauritzen is used to extrapolate the limited isothermal crystallization rate data. Good agreement between DSC (differential scanning calorimetry) nonisothermal crystallinity results and model predictions is obtained for our own data on poly(ethylene terephthalate) (PET) and some literature data on nylon‐6, if the temperature lag between the sample and the DSC furnace is taken into account. The advantages of the present approach in process modeling are pointed out. Quenching experiments have also been performed in which PET slabs are allowed to cool and crystallize from the melt under quiescent conditions. The resulting crystallinity distributions in the thickness direction are measured and predicted by using kinetic parameter values obtained from isothermal DSC measurements alone.

Application of isothermal calorimetry and UV spectroscopy for stability monitoring of pentaerythritol tetranitrate

Thermal stabilities for three pentaerythritol tetranitrate (PETN) samples with variable surface areas were monitored by isothermal calorimetry and UV spectroscopy over the range 363–408 K. Isothermal induction times measured with constant volume calorimetry under an air atmosphere, and NO evolution rates monitored by UV absorbance at 213 nm under vacuum correlated with the PETN surface area at temperatures equal or exceeding 383 K. Rate data measured at 383 K are in accord with predictions based on detailed kinetic modeling. Below 383 K, NO evolution data suggested that additional geometric factors may be significant in controlling PETN stability. Mechanisms for the influence of surface area upon the rate-determining step are addressed.

Influence of carbon black type and concentration upon thermooxidation of the amorphous phase in high and low density polyethylenes

AbstractThermooxidation in solid and molten state of HDPE and LDPE loaded with different types of carbon black is studied by DSC measurements on mill rolled specimens and tensile test on compression moulded specimens by considering the isothermal induction times at 210 to 250°C and the elongation at break at room temperature, respectively. The terms of morphology stability and compatibility between PE and carbon black species are defined on the basis of recently established topoenergetic principles according to which the notions have meaning only in respect to a transformation process revealed in a measuring system which includes the standard experimental conditions. The universal representation allows to determine by iteration the threshold temperature T0 = (240 ± 10) K below which the thermooxidation of the amorphous phase is practically inhibited. This value fairly corresponds to the glass transition temperature like for other polymers and transformation processes studied on topoenergetic basis.

Further study on the prediction of isothermal induction time by dynamic differential scanning calorimetry

To test the applicability of dynamic DSC for predicting isothermal oxidation induction time, further study was carried out on butadiene rubber samples. Similar to the natural rubber samples, various Arrhenius plots of the butadiene rubber samples could be superimposed to form a single plot using a shift factor dependent on the oxidation peak temperature obtained from a dynamic DSC test. The superimposed plot can then be used to predict the oxidation induction times of other butadiene rubber samples from dynamic DSC test results.

Thermoanalytical studies of rubber oxidation: Correlation of activation energy, isothermal induction time and oxidation peak temperature

The activation energy of oxidation, E a, isothermal oxidation induction time, t, and oxidation peak temperature, T p, obtained from DSC/DTA, are widely used to evaluate the oxidative stability of rubbers and the effectiveness of antioxidants. Based on the analysis of 127 sets of data, E a, t and T p were found to be correlated by the following equations E a = 443.13 − 1.545 × 10 5/ T p log t = 15.177 − 5.809 × 10 3/ T p log t = 0.0363 E a − 1.377 A good correlation is obtained if T p is based on a slow heating rate.

Thermoanalytical studies of rubber oxidation: Prediction of isothermal induction time

The oxidation induction times of natural rubber stabilized by various antioxidants were measured by differential scanning calorimetry (DSC). Various Arrhenius plots could be superimposed to form a single plot by using a shift factor dependent on the oxidation peak temperature obtained from a dynamic DSC test. The superimposed plot provides a simple means to predict the induction time from a dynamic DSC test result.