Combined kinetic analysis of thermal degradation of polymeric materials under any thermal pathway

Combined kinetic analysis has been applied for the first time to the thermal degradation of polymeric materials. The combined kinetic analysis allows the determination of the kinetic parameters from the simultaneous analysis of a set of experimental curves recorded under any thermal schedule. The method does not make any assumptions about the kinetic model or activation energy and allows analysis even when the process does not follow one of the ideal kinetic models already proposed in the literature. In the present paper the kinetics of the thermal degradation of both polytetrafluoroethylene (PTFE) and polyethylene (PE) have been analysed. It has been concluded, without previous assumptions on the kinetic model, that the thermal degradation of PTFE obeys a first order kinetic law, while the thermal degradation of PE follows a diffusion-controlled kinetic model.     

On the kinetics of cellulose degradation: looking beyond the pseudo zero order rate equation

The kinetics of cellulose degradation was analysed by means of a two-stage model, characterised by an autoretardant and autocatalytic regime, later tempered by the consumption of glycosidic bonds in the amorphous regions. The proposed model explains the effects on the kinetic equations of different modes of ageing (acid hydrolysis, ageing in ventilated oven or sealed vessels), initial oxidation of cellulose and experimental procedures (with or without reduction of oxidised groups). The autoretardant branch can be analysed in a quantitative way, while the integration of the non-linear autocatalytic branch is allowed in some cases, characterised by the decrease of pH and/or emission of acid volatile organic compounds (VOCs). Most of the controversial results of the literature can be easily explained, but the proposed model offers also a guide for further studies on the kinetics of cellulose degradation.     

Kinetics and mechanism of the epoxide-amine polyaddition

The mechanism and kinetics of the epoxide-amine polyaddition reaction have been studied by isothermal and scanning DSC measurements. The initial concentrations of the reactants (epoxides: bisphenol-A-diglycidyl ether (DGEBA) and phenyl glycidyl ether (PGE), amines: N,N′-dibenzylethylenediamine (DBED) and aniline) in our model systems have been strongly varied. The suggested kinetic model describes the reaction behavior of mixtures with any initial epoxide/amine ratios over the whole range of cure by a single parameter set. To find the optimum kinetic parameters, we have solved the set of differential equations numerically by the technique of multivariate non-linear regression (Mult-NLR). Excellent agreement was obtained between calculated and experimental curves.     

Prediction of paper permanence by accelerated aging I. Kinetic analysis of the aging process

The validity of accelerated aging tests to predict and rank papers on their permanence has been under question, preventing the development of performance-based standards for permanent paper. We conducted a general kinetic analysis to investigate the aging process of paper. A general kinetic model is proposed to describe the depolymerization of cellulose. Experimentally it was shown that in the case of aging, cellulose degradation follows classic first-order kinetics as a special case of our general kinetic model. The Arrhenius equation was critically re-examined for the case of a multiple reaction system. It was shown analytically that the Arrhenius equation is still applicable when certain conditions are met. This was convincingly supported by experimental results. We also analysed the dependence of the degradation rate on the moisture content and hydrogen ion concentration. By conducting systematic experiments on these two factors, a general and quantitative relationship was established to explain the contribution of each factor and their interactions. Finally, based on this kinetic analysis, the effects of storage conditions on the life expectancy of paper were estimated.     

On the degradation evolution equations of cellulose

Cellulose degradation is usually characterized in terms of either the chain scission number or the scission fraction of cellulose unit as a function of degree of polymerisation (DP) and cellulose degradation evolution equation is most commonly described by the well known Ekenstam equations. In this paper we show that cellulose degradation can be best characterized either in terms of the percentage DP loss or in terms of the percentage tensile strength (TS) loss. We present a new cellulose degradation evolution equation expressed in terms of the percentage DP loss and apply it for having a quantitative comparison with six sets of experimental data. We develop a new kinetic equation for the percentage TS loss of cellulose and test it with four sets of experimental data. It turns out that the proposed cellulose degradation evolution equations are able to explain the real experimental data of different cellulose materials carried out under a variety of experimental conditions, particularly the prolonged autocatalytic degradation in sealed vessels. We also develop a new method for predicting the degree of degradation of cellulose at ambient conditions by combining the master equation representing the kinetics of either percentage DP loss or percentage TS loss at the lowest experimental temperature with Arrhenius shift factor function.     

Pyrolysis kinetics of ethylene–propylene (EPM) and ethylene–propylene–diene (EPDM)

The thermal degradation kinetics of several ethylene–propylene copolymers (EPM) and ethylene–propylene–diene terpolymers (EPDM), with different chemical compositions, have been studied by means of the combined kinetic analysis. Until now, attempts to establish the kinetic model for the process have been unsuccessful and previous reports suggest that a model other than a conventional nth order might be responsible. Here, a random scission kinetic model, based on the breakage and evaporation of cleavaged fragments, is found to describe the degradation of all compositions studied. The suitability of the kinetic parameters resulting from the analysis has been asserted by successfully reconstructing the experimental curves. Additionally, it has been shown that the activation energy for the pyrolysis of the EPM copolymers decreases by increasing the propylene content. An explanation for this behavior is given. A low dependence of the EPDM chemical composition on the activation energy for the pyrolysis has been reported, although the thermal stability is influenced by the composition of the diene used.     

The influence of transverse differential swelling stresses on the kinetics of sorption of penetrants by polymer membranes

The influence of transverse differential swelling stresses on the kinetics of sorption of a penetrant in a polymer membrane exhibiting linear viscoelasticity is described by a model developed from the much simpler one of Crank. Sorption and transverse swelling kinetic curves are computed numerically. The character of absorption and desorption curves is examined systematically mainly as a function of (i) the magnitude of the stresses set up and of the stress-dependence of the diffusion coefficient, (ii) the relative rates of stress relaxation and of diffusion, and (iii) the degree of plasticization or “softening” of the polymer by the penetrant. It is shown that important general features of experimental sorption kinetic curves can be reproduced satisfactorily under well defined conditions. Attention is also given to transverse swelling kinetic curves. Their correlation with the corresponding sorption curves is examined briefly but systematically and discussed with reference to experimental data.     

Mass transfer kinetics and breakthrough and elution curves for bovine serum albumin using cibacron blue cellulose membranes

The mass transfer of bovine serum albumin onto a stack of cibacron blue cellulose membranes in the loading and elution stages were studied. The breakthrough curves obtained in the loading stage were fitted to the pore and the lumped kinetic (LK) models, respectively. Then experimental data obtained in the elution stage were described by using the LK model in which the kinetic equation, the initial and the boundary conditions were rewritten according to the operation. For the breakthrough curves it was found that the contribution of the sorption kinetics to band broadening was significant whereas that of axial dispersion was negligible. In contrast, both of these contributions were significant to the profile of the elution curve. By studying the mass transfer kinetics in the elution stage, information about the influence of the module geometry on the performance of affinity membrane separations may be obtained.     

Potential of thermal analysis as applied to studying the kinetics of thermal degradation of polymers

The kinetics of thermal degradation of low-density polyethylene was studied by TGA and DSC at heating rates from 0.5 to 40 deg min^–1. Causes of significant discrepancies in the published effective kinetic constants of the overall reaction of thermal degradation of the polymers, determined using different experimental methods and different data treatment procedures, were analyzed. The possibility of using random break model as an alternative approach to describing polymer thermal degradation curves obtained by thermal analysis methods was demonstrated by the example of polyethylene.     

A Thermogravimetric Approach to Study the Influence of a Biodegradation in Soil Test to a Poly(lactic acid)

Summary: An amorphous grade Poly (lactic acid) (PLA) was selected for an accelerated burial in soil test during 450 days. Thermogravimetric analyses were carried out to study the effects of degradation in soil on the thermal stability and the thermal decomposition kinetics. A single stage decomposition process is observed for all degradation times. It is shown that the thermal stability of PLA is slightly affected by degradation in soil. Concerning the study of the thermal decomposition kinetics, Criado master curves were plotted from experimental data to focus the study of the thermodegradation kinetic model.The kinetic methods proposed by Broido and Chang were used to calculate the apparent activation energies (Ea) of the degradation mechanism. These results were compared to the Ea values obtained by the method developed by Coats and Redfern in order to prove the applicability of the former methods to the kinetic study. As expected, non-linear tendency is found out for Ea variation along the degradation times, which can be explained as an evolution by stages.     

Constant rate thermal analysis for thermal stability studies of polymers

This paper explores the relationship between the shapes of temperature-time curves obtained from experimental data recorded by means of constant rate thermal analysis (CRTA) and the kinetic model followed by the thermal degradation reaction. A detailed shape analysis of CRTA curves has been performed as a function of the most common kinetic models. The analysis has been validated with simulated data, and with experimental data recorded from the thermal degradation of polytetrafluoroethylene (PTFE), poly(1,4-butylene terephthalate) (PBT), polyethylene (PE) and poly(vinyl chloride) (PVC). The resulting temperature-time profiles indicate that the studied polymers decompose through phase boundary, random scission, diffusion and nucleation mechanisms respectively. The results here presented demonstrate that the strong dependence of the temperature-time profile on the reaction mechanism would allow the real kinetic model obeyed by a reaction to be discerned from a single CRTA curve.     

Investigating the kinetics of the adsorption process of polyamideamine on cellulose

The kinetic dependences have been investigated of the adsorption process of polyamideamine on monocarboxyl cellulose, bleached sulphate cellulose pulp of softwood and bleached sulphite cellulose pulp of hardwood. It has been found that the process kinetics can be described by means of the Elovich-Tyomkin exponential kinetic equation; the influence of the entropy factors plays a decisive role in changing the process speed; the activation energy is of the order of 6.5–8.0 kJ/mol.     

Surface and bulk reactions of cellulose oxidation by periodate. A simple kinetic model

The kinetics of periodate oxidation of cellulose was followed by exploiting the β-alkoxy degradation of oxidised units in alkaline medium, that brings about a decrease of viscometric degree of polymerisation. The parallel strong weight loss after NaOH treatment indicates a non-random mechanism of oxidation. The obtained results are interpreted on the basis of an appositely derived kinetic model that can be applied to other mechanisms of bulk and surface degradation.     

Cellulose dissolution: insights on the contributions of solvent-induced decrystallization and chain disentanglement

The dissolution of cellulose is a critical step for the efficient utilization of this renewable resource as a starting material for the synthesis of high value-added functional polymers and chemicals and also for biofuel production. The recalcitrance of semicrystalline cellulose microfibrils presents a major barrier to cellulose dissolution. Despite research efforts, important aspects of cellulose dissolution such as solvent-induced decrystallization and chain disentanglement are not well-understood. Here we address these fundamental issues with the practical goal of gaining insights into the swelling and dissolution of cellulose that cannot be obtained from macroscopic experimental data. To this end, we have used a newly-developed phenomenological model that captures the phenomena governing the dissolution of semicrystalline polymers as well as the thermodynamics and kinetics of dissolution. This model fits well experimental data for swelling and dissolution of cotton fibers in the ionic liquid [bmim]Cl, and allows the quantification of two important aspects, i.e., solvent effectiveness in cellulose (1) decrystallization and (2) chain disentanglement, the balance of which controls the mechanism and kinetics of cellulose dissolution. The activation parameters of cellulose decrystallization, estimated using the obtained decrystallization constant values, reveal that the decrystallization of cellulose in [bmim]Cl is associated with positive enthalpy and entropy and it is also very sensitive to temperature. When the solvent effectiveness in the disruption of cellulose crystals is relatively lower than its ability to disentangle the chains, the kinetics of dissolution are controlled by decrystallization. Furthermore, conditions that facilitate cellulose chain disentanglement, in addition to increasing the rate of dissolution, can result in faster decrystallization. The solvent effectiveness in chain disentanglement is the only factor that determines the decrease of the cellulose fiber radius. In cases where the fiber dissolution rate is lower than the decrystallization rate, the dissolution of cellulose is mostly controlled by the solvent ability to disentangle the chains. The insights obtained from this study improve the understanding of cellulose–solvent interactions underlying decrystallization and disentanglement and their contributions in controlling the kinetics of cellulose swelling and dissolution.     

Test of a model of stress-dependent diffusion by means of combined colored tracer and birefringence profile measurements

In the present paper we further test a model of stress-dependent diffusion previously used with success to simulate the variation from Case I to Case II penetration kinetics in the system liquid methylene chloride-uniaxially oriented cellulose acetate film, according to whether penetration occurs across or along the axis of preferred macromolecular orientation. Data on penetration rates, optical density profiles (using a colored tracer), and the corresponding birefringence profiles, characteristics of these penetration modes in the aforesaid system, are presented and compared with appropriate model uptake kinetic curves and penetrant concentration and compressive differential swelling stress profiles. It is shown that the salient features of the observed experimental behavior are in general accord with model predictions based on physically realistic assumptions.     

Kinetic Study of the Mass Transfer of Bovine Serum Albumin on Cibacron Blue Cellulose Membranes by Using the Multi-Plate and Transport Models

The mass transfer kinetics of bovine serum albumin on Cibacron blue F3GA cellulose affinity membranes has been investigated. It was found that the multi-plate (MP) and transport models successfully described experimental breakthrough curves obtained by single-step frontal analysis. The correlation between the two models was used to estimate the rate coefficients of mass transfer from experimental data. The flow rate was found to have little effect on the performance of affinity membrane separations. The improvement of the performance by increasing the thickness of the membranes was limited. The transport model was simplified by approximating the very sharp Langmuir isotherm determined by a rectangular isotherm and an analytical solution obtained although this was found to be unsuited to describe the experimental data.     

Analysis of DSC Data Relating to Proteins Undergoing Irreversible Thermal Denaturation

New approaches to the analysis of differential scanning calorimetry (DSC) data relating to proteins undergoing irreversible thermal denaturation have been demonstrated. The experimental approaches include obtaining a set of DSC curves at various scanning rates and protein concentrations, and also reheating experiments. The mathematical methods of analysis include construction of a linear anamorphosis and simultaneous fitting of a theoretical expression for the dependence of the excess heat capacity on temperature to a set of experimental DSC curves. Different kinetic models are discussed: the one-step irreversible model, the model including two consecutive irreversible steps, the Lumry and Eyring model with a fast equilibrating first step, and the whole kinetic Lumry and Eyring model. This revised version was published online in July 2006 with corrections to the Cover Date.     

The study of model systems subjected to sub- and supercritical water hydrolysis for the production of fermentable sugars

Bioenergy obtained from lignocellulosic biomass is considered the most efficient way to achieve sustainable development in the future. However, there still are challenges in the cellulose conversion to hexoses, which could be used as raw material for the bioenergy production. Sub- and supercritical water hydrolysis have been researched as emergent technologies to obtain simple sugars from lignocellulosic biomass; however, the reaction pathways and kinetics of the hydrolysis of cellulose into oligomers and monomers, and their degradation under sub- and supercritical conditions, are not completely understood yet. Thus, this review provides an overview of the state-of-the-art on hydrolysis with sub- and supercritical water of model systems, cellulose and starch, in the context of elucidating the reaction pathways and kinetic behavior of the biomass hydrolysis to produce suitable fermentation substrates for the production of second generation bioethanol and other biofuels.     

D301R树脂对水溶液中硝基苯的吸附性质

研究了D301R弱碱性阴离子交换树脂对水中硝基苯的吸附作用,测定了不同温度下吸附的动力学曲线和吸附等温线,提出了吸附动力学模型,计算了平衡吸附量、吸附活化能和吸附焓等。 实验结果表明,吸附动力学符合表面过程控制的准二级反应模型,其速率常数k2在300 K时为3.74×10-2 g/(mg·min),并随温度的升高而升高;平衡吸附量在300 K时为5.02 mg/g,且随温度的升高而降低;吸附活化能为39.02 kJ/mol;吸附等温线符合Langmuir吸附模型,吸附焓为-22.47 kJ/mol,吸附作用力主要是氢键。     

Time-dependence of the polarized intensity ratio in CIDNP investigations

The time-dependence of the polarized intensity ratio within a product molecule has been studied by a kinetic method. The kinetic analysis of polarized product formation shows that considerable changes in CIDNP ratios occur during the reaction but characteristic curves can be obtained under different experimental conditions. A method is proposed to evaluate the relative enhancement coefficients on the basis of these characteristic curves, and to obtain information on the kinetics of the reaction.