Tobin Models Research Articles

Dynamic crystallization behavior of PA-12/PP-MWCNT nanocomposites: non-isothermal kinetics approach

Abstract The effect of multi-walled carbon nanotubes (MWCNT) loading on the crystallization behavior of matrix polyamide 12 (PA-12), in PA-12/polypropylene-MWCNT (PP-MWCNT)-based nanocomposites were analyzed for their non-isothermal crystallization behavior at various cooling rates of 2.5–20 °C/min in differential scanning calorimetry (DSC). Several kinetic models such as Jeziorny (modified-Avrami), Mo and Tobin models were employed to analyze the crystallization behavioral trend with respect to time and temperature of the nanocomposites. The crystallization rate increased half-time of crystallization with MWCNT content as estimated from the Jeziorny theory. The linear agreement between Jeziorny model and experimental relative crystallinity outperforms the Tobin analysis where the coefficient of linear regression was found to be considerably trailing behind and off the satisfactory mark. The Mo model accounts for the percentage crystallinity and thereby successfully explained the crystallization behavior of PA-12 where the kinetic parameters increased with crystallinity indicating higher cooling rate for higher crystallinity. The MWCNT induced crystallization (nucleation activity) values were close to zero irrespective of MWCNT loading which reiterates the enhanced crystallization (rate) of PA-12 in the nanocomposites. Estimations based on Friedman approach showed inter-relationship between activation energy and crystallinity where the later was found to be governed by major (matrix) PA-12 phase.

Modeling the crystallization kinetics of polymers displaying high levels of secondary crystallization

The isothermal crystallization of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) was evaluated using a range of models, namely, Avrami, simplified Hillier, Tobin, Malkin, Urbanovici–Segal, Velisaris–Seferis, and Hay. Two methods of model evaluation were used: determination of the parameters through traditional double log plots and curve fitting via nonlinear, multivariable regression. Visual inspection of the cumulative crystallization curves, calculation of the R2 value and standard error of the regression, and evaluation of the returned parameters were used to assess which model best describes the experimental data. The Hay model was found to generate the best fit, closely followed by the Velisaris–Seferis parallel model, suggesting that primary and secondary crystallization occur concurrently. The Avrami, Malkin, and Tobin models were found to perform well when the data is restricted to the region where primary crystallization dominates; however, they could not be used to successfully model the entire crystallization process. This work highlights the importance of selecting the most appropriate model for analyzing kinetics, especially when high levels of lamellar thickening and infilling occur during crystallization.

Non-isothermal cold crystallization kinetics of cork–polymer biocomposites based on polylactic acid for fused filament fabrication

Cork–polymer composites (CPC) based on polylactic acid (PLA) matrix were prepared for the development of filaments for fused filament fabrication. The non-isothermal cold crystallization behaviours of PLA and CPC were investigated by differential scanning calorimetry. Cold crystallization kinetic behaviours of PLA and CPC with 15 mass/% of cork powder residues at different heating rates (1.25, 2.5, 5 and 7.5 K min−1) were studied. Results showed that cold crystallization temperature (Tcc) of PLA matrix decreased with the addition of cork. Crystallization kinetic behaviour was studied by Avrami and Tobin models. It was shown that cork powder surface acts as a nucleating agent during non-isothermal cold crystallization, by accelerating the crystallization rate and, therefore, by reducing the half-time crystallization (t1/2) values. Polarized optical microscopy and X-ray diffraction were used to evaluate the crystalline structure of PLA and CPC. Kissinger and Friedman methods were employed to determine the crystallization activation energy (Ec).

Evaluation of thermal degradation and melt crystallization behavior of taro mucilage and its graft copolymer with poly(lactide)

This communication presents the thermal degradation behavior and non-isothermal crystallization kinetics of taro mucilage (CEM) and its graft copolymer polylactide (CEM-g-PLA) by thermogravimetric analysis (TGA/DTG coupled techniques) and differential scanning calorimetric. Isoconversional degradation analysis for CEM and CEM-g-PLA performed with the aid of Friedman, Kissinger (KSS), Flynn–Wall–Ozawa (FWO), and Kissinger–Akahira–Sunose (KAS) methods. The energy profiles and Criado plots over specific conversion (α) were able to predict that both CEM-g-PLA and CEM followed multi step kinetics and different degradation mechanisms. The Ozawa model fitted the melt crystallization data for CEM-g-PLA and its exponent (m) complements those for the modified Avrami and Tobin models. The crystallization of CEM-g-PLA was characterized with the formation of two distinct crystal growths. Further, the negative isoconversional activation energy suggested the occurrence of melt crystallization in CEM-g-PLA. Thus, the grafting of PLA onto CEM resulted into a material that shows thermal properties entirely different from that of its precursor (CEM) besides having an increased shelf life and not compromising with biodegradability. The analyzed data from the isoconversional equations (viz. Friedman, FWO and KAS models) and Ozawa model could be useful in modelling the degradation stability/mechanism and crystallization behavior of polylactide-grafted copolymer.

Effect of graphene oxide on features of functionalizable Poly(Butylene fumarate) and functional Poly(Butylene succinate) doped polyaniline

A novel material that obtained through combining a biodegradable polymer with a conductive polymer, has been successfully developed by graphene oxide (GO). For the first time, unsaturated poly(butylene fumarate) grafted reduced GO (PBF:RGO) was synthesized via in-situ polymerization method and simultaneous in-situ thermal reduction of GO. It was modified through post-polymerization modification to form sulfonated poly(butylene succinate) grafted reduced GO (PBSS:RGO). Then, PBSS:RGO was incorporated as a polymeric dopant in the synthesis of polyaniline (PANI) to prepare the conductive and anticorrosive compound. Functionalizable PBF and PBF:RGO along with functional PBSS and PBSS:RGO were characterized by 1HNMR. Thermal and crystallization properties of PBF and PBF:RGO were studied using thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC) with Avrami and Tobin models. Further investigation of crystallinity and dispersion of graphene sheets in the polymer matrix was carried out by X-ray diffraction (XRD). PBF:RGO exhibits higher thermal stability, higher crystallization rate, and lower crystallinity compared with pristine PBF. Final composites (PANI:PBSS and PANI:RGO:PBSS) were also characterized through Fourier transform infrared (FT-IR), contact angle analysis, electrochemical impedance spectroscopy (EIS) and electrical conductivity measurements. PANI:RGO:PBSS indicates a higher conductivity, higher inhibition efficiency and more hydrophilicity than PANI:PBSS.

Non-isothermal crystallization of biopolyesters of poly(butylene succinate) formed via in-situ polymerization in presence of poly(vinyl butyral)

Poly(vinyl butyral) (PVB) was incorporated as a nucleating agent into the monomers prior to polymerization of poly(butylene succinate) (PBS) for accelerating crystallization and enhancing mechanical properties. The effects of the PVB content and molecular weights on non-isothermal crystallization and mechanical properties were examined in detail. Adding PVB greatly reduced spherulitic sizes and increased the peak temperature of crystallization by 8.8 °C. An optimal content was observed for a minimal size of spherulites, and the PVB with a low molecular weight led to a smaller spherulitic size than did its counterpart of a high molecular weight. Both the modified Avrami and Tobin models were found to better describe the kinetics of non-isothermal crystallization. A molecular model was proposed to explain accelerated nucleation and spherical growth from PVB's structural perspective. The nucleated PBS exhibited a considerable improvement in mechanical properties: 26% in tensile modulus, 30% in tensile strength, and 82% in elongation at break.

Kinetic modelling of thermal degradation and non-isothermal crystallization of silk nano-discs reinforced poly (lactic acid) bionanocomposites

The present work investigates the effect of novel biofiller, ‘crystalline silk nano-discs (CSNs)’, on thermal stability and crystallization behaviour of melt-processed poly (lactic acid) (PLA)/CSN nanobiocomposites which are very much important for polymer processing. The PLA/CSN nanobiocomposites are obtained through melt extrusion technique. Thermogravimetric (TGA) data revealed that incorporation of ~ 1 wt.% CSNs in PLA enhanced onset degradation temperature (Tonset) ~ 10 °C, and this improvement in thermal stability is due to the formation of network-like structures. Activation energies (Ea) of nanobiocomposites, determined from model-free (Flynn–Wall–Ozawa, Kissinger–Akahira–Sunose methods) and model fitting (Coats–Redfern method) approaches, increased in comparison with PLA, indicating that CSNs impede thermal degradation process. Possible mechanism is proposed for thermal degradation process of nanobiocomposites using Criado’s method. Hyphenated TGA-Fourier transform infrared is utilized to identify evolved gaseous products during degradation of silk, CSNs, PLA and nanobiocomposites. Differential calorimetry data was analysed by Jeziorny, Liu-Mo and Tobin models. It was found that CSNs act as heterogeneous nucleating agents, hence improve non-isothermal crystallization kinetics of PLA.

Analysis of modern approaches to the formation of the portfolio investor shares stock

The object of research is an investment portfolio consisting of a set of investment instruments (securities, assets, projects, etc.) in which the investor's finances are distributed. The main purpose of forming an investment portfolio is its maximum return, but income is always directly proportional to risk. The paper proposes an approach in which the user can manage the values of profitability and risk, and thus determine for himself the optimal composition of the investment portfolio. This is achieved by using a combination of financial asset valuation methods. The study used models that are the basis of portfolio theory and include the choice of investment assets and the optimization of the composition of the portfolio, methods for assessing the investment qualities of assets and the effectiveness of portfolio investment. In particular, Markowitz, Sharpe and Tobin models are used to ensure greater efficiency in making investment decisions in the stock market, including those related to the formation and management of the share portfolio. And in assessing the investment qualities of financial assets. Tests of the method and models on real investment assets have confirmed their effectiveness. In particular, when forming a portfolio of shares, it is determined that the maximum profitability is ensured in the investment portfolio, which is characterized by the maximum risk. Compared to other variants of portfolios with average and minimum returns, it is determined that the value of risks differ by 3–5 %. This is due to the fact that the proposed method is based on a combination of models that take into account various aspects of the stock market. Thus, an optimal portfolio is formed that provides the investor with the desired level of profitability at a fixed level of risk. The results obtained in this work allow to propose a general methodology for the formation of an optimal investment portfolio containing various shares of the most reliable and attractive financial assets in the conditions of modern uncertainty and volatility of the Ukrainian stock market.

Nonisothermal Crystallization Kinetics of Poly(lactic acid) Nucleated with a Multiamide Nucleating Agent

Addition of a commercial available multiamide compound (N,N′,N′′-tricyclohexyl-1,3,5- benzenetricarboxylamide, defined here as TMC) into ecofriendly poly(lactic acid) (PLA) can accelerate the crystallization rate of the material remarkably and broaden its applications. In this paper, the nonisothermal crystallization behavior of biodegradable PLA nucleated by 0.3 wt.% of TMC was investigated by differential scanning calorimetry (DSC). The modified Avrami, Tobin, Ozawa, and Mo models were applied to describe the kinetics of the crystallization process. Various parameters of nonisothermal crystallization, such as the crystallization half-time and crystallization rate constant, reflected that TMC significantly accelerated the crystallization process. The activation energy values of the neat PLA and PLA/TMC blend, determined by the Kissinger method, increased with the addition of TMC. The study should be helpful for understanding the relationship between processing and properties of this material.

Thermal, Mechanical and Rheological Properties of Polypropylene/Poly(ethylene-co-methyl acrylate) Blends

Isotactic polypropylene (PP) has been blended with poly(ethylene-co-methyl acrylate) (EMA) (75/25 wt/wt%) in a single-screw extruder. The compatibilizing effect of polypropylene grafted with maleic anhydride (PP-g-MAH) has been examined. The nonisothermal crystallization of the developed blends has been investigated using differential scanning calorimetry (DSC) and analyzed using Avrami, Tobin and Liu models. The thermal stability of the blends was assessed through thermogravimetric analysis (TGA). The tensile and impact properties, as well as the melt viscosity, have also been determined. The presence of rubber accelerates the crystallization of PP. The thermal stabilities of the blends are intermediate between those of their constituents. Tensile strength and modulus are reduced upon incorporation of EMA into PP, but ultimate elongation and impact strength are improved. The melt viscosity variation with shear rate for all the systems was typical of shear-thinning behavior. The compatibilizing agent has a pronounced effect on enhancing the thermal and mechanical properties of the blend.

Crystallization kinetics and nucleation parameters of Nylon 6 and poly(ethylene-co-glycidyl methacrylate) blend

Blend of Nylon 6 and poly(ethylene-co-glycidyl methacrylate) (PEGMA) were prepared by a twin-screw extruder. Morphology observed with scanning electron microscopies (SEM) show PEGMA is well dispersed in Nylon 6 matrix. Isothermal and nonisothermal crystallization of the blend was investigated by differential scanning calorimeter (DSC) and crystallization kinetics was described by Avrami and Tobin models. Equilibrium melting temperatures were estimated from linear Hoffman–Weeks relationship. All analyses showed that the reaction between PEGMA and Nylon 6 reduced the molecular mobility and reduced the crystallization rate. Expand K g and U * in the Hoffman–Lauritzen equation by Vyazovkin's method demonstrated that Nylon 6/PEGMA had higher K g and U * values and provided another supportive evidence to the above interpretation.

Isothermal crystallization of high density polyethylene and nanoscale calcium carbonate composites

AbstractHigh density polyethylene (HDPE) and calcium carbonate (CaCO3) nanocomposites with maleic anhydride grafted HDPE (manPE) as a compatibilizer were prepared via compounding in a twin‐screw extruder. The CaCO3 are well dispersed in the HDPE matrix from the observation of transmission electron microscope. The isothermal crystallization kinetics was studied by differential scanning calorimetry and simulated by Avrami and Tobin models. The nucleation constants and fold surface free energy were estimated from Lauritzen–Hoffman relation. The results indicate that both manPE and well‐dispersed CaCO3 particles would act as nuclei to induce heterogeneous nucleation and enhance crystallization rate. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Nonisothermal crystallization kinetics of PBT nanocomposites

Nonisothermal crystallization kinetics of virgin poly(butylene terephthalate) (PBT), PBT/nanoclay (NC) and PBT/carbon nanofiber (CNF) composites were investigated. The experimental data on crystallinity versus temperature were collected using a differential scanning calorimeter (DSC) at four different cooling rates (2.5, 5, 10 and 20 °C/min). The data were analyzed using nonlinear multi-variable regression method and fitted to Avrami, modified Avrami, and Tobin models. The addition of carbon nanofiber and nanoclay in general improved the crystallization rate and lowered the onset and peak crystallization temperatures of the filled systems. These effects were dependent on the amount of reinforcement used and on the cooling rate applied, with more pronounced changes noticed at higher cooling rates. Previous results showed enhanced crystallization of polypropylene (PP) systems containing nanoreinforcements. The Avrami model proved to be the best fitting model among those investigated. The activation energies describing the overall nonisothermal crystallization process was also calculated using two different models: Kissinger and Takhor. The values obtained from these models were found to be almost identical. The addition of heterogeneous nuclei (carbon nanofibers or nanoclay platelets) to the PBT melt was found to lower the activation energy of virgin PBT. This result was related to an increased crystallization rate of filled PBT.

Isothermal crystallization studies of poly(butylene terephthalate) composites

AbstractDifferent crystallization kinetic models (Avrami and Tobin) have been applied to study the crystallization kinetics of virgin poly(butylene terephthalate) (PBT) and filled PBT systems under isothermal experimental conditions. The experimental data have been analyzed with a nonlinear, multivariable regression program. The kinetic parameters for the isothermal crystallization have been determined. The analysis results indicate that both models satisfactorily represent the isothermal crystallization kinetics. PBT crystallizes most slowly. The presence of nanoclays or nanofibers, added as fillers, enhances the crystallization rate of PBT composites. An analysis of the kinetic data with the Avrami and Tobin models has shown little change in the crystallization exponent compared with that of virgin PBT. The crystallization rate constant decreases with a rise in the temperature for the two models. This trend has been observed for similar polyester systems reported in the literature. The dispersion of the clay layers in the PBT nanocomposites has been characterized with wide‐angle X‐ray diffraction and transmission electron microscopy. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1344–1353, 2007

Characterization of the Kinetic Phase Transition of Phospholipids Using Avrami and Tobin Models

AbstractMechanism of the lamellar crystalline phase formation of distearoyl‐phosphatidylethanolamine (DSPE) dispersed in excess glycerol has been examined by differential scanning calorimetry. It was found that transformation of liquid‐crystal phase to a crystalline phase must be mediated by a lamellar‐gel phase. Further examination of the kinetic phase behavior using Avrami and Tobin models suggested a single dimensional growing pattern and a three‐step mechanism of the crystallization, consisting of nucleation, normal growth, and restricted growth.

Application of the Avrami, Tobin, Malkin, and Urbanovici–Segal macrokinetic models to isothermal crystallization of syndiotactic polypropylene

Various kinetic equations, namely the Avrami, Tobin, Malkin, and Urbanovici–Segal models, have been applied to describe the kinetics of primary crystallization from the melt state of syndiotactic polypropylene (s-PP) under isothermal conditions. Analysis was carried out using a data-fitting procedure, in which the experimental data were fitted directly to each model using a non-linear multi-variable regression program. The results suggested that the experimental data of s-PP can be best described by the Urbanovici–Segal model, followed by the Avrami, Malkin, and Tobin models, respectively.

Application of the Avrami, Tobin, Malkin, and Simultaneous Avrami Macrokinetic Models to Isothermal Crystallization of Syndiotactic Polypropylenes

Various macrokinetic models (the Avrami, Tobin, Malkin, and simultaneous Avrami models) were applied to describe the primary crystallization of syndiotactic polypropylene (sPP) under isothermal conditions. Analysis of the experimental data was carried out using a direct-fitting method such that the experimental data were fitted directly to each macrokinetic model using a nonlinear multivariable regression program. Comparison of the kinetics parameters obtained from the program to those obtained from the traditional analytical procedure suggested that applicability and reliability of the direct-fitting method are satisfactory. Prediction of the time-dependent relative evolution of crystallinity at other crystallization temperatures was demonstrated based on the bulk kinetics parameters obtained from the analysis.

Nonisothermal bulk crystallization and subsequent melting behavior of syndiotactic polypropylenes: Crystallization from the melt state

Various macrokinetic models, namely, the Avrami, the Tobin, and the Ozawa models, were applied to describe the crystallization process of syndiotactic polypropylene (s-PP) under nonisothermal conditions. Both Avrami and Tobin models were shown to provide a fair description of the experimental data. The Avrami exponent na was found to range from 2.4 to 5.3, while the Tobin exponent nt was found to range from 3.1 to 6.7. The Ozawa model was found to describe the nonisothermal crystallization kinetics of s-PP very well. The Ziabicki's kinetic crystallizability, suggesting the crystallization ability of polymers from the melt when cooled at a unit cooling rate, was also evaluated and was found to range from 0.93 to 1.40°C s−1. The energy barrier for nonisothermal crystallization, based on the Augis–Bennett method, was found to range from −78.6 to −108.1 kJ mol−1. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 338–354, 2000

Polymer crystallization kinetics: Poly(ethylene terephthalate) and poly(phenylene sulfide)

AbstractAnalysis of isothermal crystallization data of PET and PPS was carried out using Avrami and Tobin models. The models gave fractional values of exponent n and the standard deviation varied between 1 and 4%. No improvement in the standard deviation could be obtained even after incorporating the nucleation rate in these models. The Hillier model gave a good fit only to the isothermal crystallization data of PET. A simple model considering primary and secondary crystallization has been proposed. The model is verified using isothermal crystallization data of PPS. © 1993 John Wiley & Sons, Inc.

Non – Isothermal Crystallization Crystallization of Polymers

Abstract The kinetics of non-isothermal crystallization, taking into account both formation and growth of nuclei, is formulated in terms of rate equations. Depending on whether Avrami's or Tobin's models of impingement are applied, sets of, respectively, (m + 1) and (m + 2) first-order differential equations are obtained, where m is the number of spatial dimensions of growth. The number of rate equations reduces to one if the activation of nuclei is much faster than their growth. Avrami's well-known formula is re-obtained from isothermal limiting cases.