Physico-chemical aspects of polyethylene processing in an open mixer. Part 29: Experimental kinetics and mechanisms of γ-lactone formation

The experimental kinetics for γ-lactone formation shows more complexity than that for acids. Nonetheless, it can be concluded to the existence of a constant rate of formation from the beginning of the experiments with polyethylene melts. There is an additional term contributing to γ-lactone formation in the initial stages that is cubic in processing time. In the advanced stages of processing, in the high temperature range (170-200 °C), the concentration of γ-lactones increases linearly with the processing time.There are many mechanisms susceptible to give γ-lactones on polyethylene melt processing. Some of them are based on decomposition of intermediates formed directly on chain propagation. This is so for the α,γ-keto-hydroperoxides in 4-position to hydroxyl groups. Since decomposition of these intermediates is very fast, the reaction might account for a constant rate of γ-lactone formation from the beginning of polyethylene processing. Decomposition of the α,δ-keto-hydroperoxides formed on intramolecular reactions on chain propagation is not so fast as that of the α,γ-keto-hydroperoxides. Nonetheless, it might account for part of the delayed formation of γ-lactones. The same is valid for the mechanisms based on peroxidation of aldehydes and γ-hydroxy trans-vinylene groups that involve intermediates that are formed on polyethylene peroxidation. They might be important for explaining the cubic term as well as γ-lactone formation in the advanced stages of polyethylene processing.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 18: Mechanisms and kinetics of trans-vinylene group formation

Numerous reactions can yield trans-vinylene groups on polyethylene oxidation. The first problem on data interpretation consists in the separation of the experimental data into components corresponding to well-defined mechanisms. This is achieved by fitting the experimental data into an equation comprising a linear and a parabolic term. The linear term corresponds to trans-vinylene formation at a constant rate from the beginning of the experiments. It can be attributed to trans-vinylene formation on direct decomposition of polyethylene peroxy radicals. The second term accounts for trans-vinylene group formation on cage reactions of various free radicals resulting from hydroperoxide decomposition.The first mechanism can be interpreted by formal homogeneous kinetics. Formation of trans-vinylene groups according to the second mechanism can be accounted for by the heterogeneous kinetics. It proceeds in parallel with the formation of alcohols and ketones. However, reaction of the double bonds with various reactive species in the oxidizing polymer melt does not only lead to a limiting value of the concentration in the advanced stages of polyethylene processing, but also affects the accuracy of the calculations already in the early stages.     

STUDY ON THE ADSORPTION OF PHENOL BY CHITOSAN FROM AQUEOUS SOLUTION

The effects of pH, initial concentration and temperature on the adsorption of phenol by chitosan were investigated in this paper. The isothermal data was applied to Langmuir linear and the Freundlich linear isotherm equation, and the thermodynamic parameters （AH, AG, AS） were calculated according to the values of binding Langmuir constant, KL. Results indicated that the adsorption between chitosan and phenol was significantly physical in nature, the negative ΔH constant at lower temperature confirmed that more phenol was adsorbed by chitosan at lower temperature. The kinetics of the sorption process of phenol on chitosan was investigated using the pseudo-first order and pseudo-second order kinetics, and results showed that the second order equation model provided the best correlation with the experimental results.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 28: Formal kinetics of aldehyde and carboxylic acid formation in the advanced stages

The rate of acid formation at high temperature is constantly increasing but temperature independent. Two main mechanisms can account for this behavior in the advanced stages of polyethylene processing. The first mechanism is based on free radical induced oxidation of aldehyde pairs that are formed on acid-catalyzed decomposition of allylic hydroperoxides. The last will be formed essentially on mechanical stress-induced oxygen addition to trans-vinylene groups. Peroxidation of one of the aldehydes might yield an acyl-peroxy radical that is likely to abstract the labile hydrogen atom from the second aldehyde. The acyl radical formed in the reaction will abstract a hydroxyl group from the peracid formed in the same reaction. This yields an acid and an acyl-oxy radical that will give a primary alkyl radical on decarboxylation. The second mechanism involves oxidation of ketones and alcohols that accumulate in the oxidizing melt. Acid-catalyzed decomposition of the α-keto-hydroperoxides yields simultaneously an acid and an aldehyde. Formal kinetics based on each mechanism shows that they do not involve significant activation energy, as it is required by the experimental data. The dependency on the oxygen concentration deduced from the formal kinetics for the oxidation of aldehyde pairs is in agreement with the experiments.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 26: Formal kinetics of aldehyde and carboxylic acid formation at a constant rate

Formation of carboxylic acids at a constant rate can be easily explained. It seems to result from the formation and decomposition of α,γ-keto-hydroperoxides. Formal kinetics based on formation and decomposition of these structural units is in agreement with the experimental findings. The activation energy deduced from the calculations is negligible, in agreement with the experimental data showing the constant rate to be practically temperature independent. Comparison of the acids with the hydroperoxides and ketones formed initially shows that the rate of oxygen addition to alkyl radicals is significantly smaller than in low molecular mass liquids. The same conclusion is reached on comparing directly the acids formed on decomposition of α,γ-keto-hydroperoxides in polyethylene melt and in hexadecane. The rate of oxygen addition in polyethylene melt is closer to 2 × 10⁵ than to 6 × 10⁵ (s⁻¹) that is valid in hexadecane.It is possible to attribute the relatively small amount of aldehydes that might be formed at a constant rate to different reactions of alkoxy radicals that are not in a cage with other radicals. These alkoxy radicals result from the addition of peroxy radicals to unsaturated bonds. This addition is followed mainly by epoxide formation and simultaneous release of an alkoxy radical.     

半结晶聚合物注射成型中结晶动力学的数值模拟

对半结晶聚合物注射成型过程及其结晶过程进行偶合模拟,分析了二者的相互影响.具体是在注射成型数值模拟中考虑结晶动力学效应,分别在本构方程、能量方程及材料物性参数方程中引入反映结晶效应的参数;同时在结晶动力学计算中考虑流动诱导效应,从能量的角度提出并使用修正的动力学模型,用材料流动过程的耗散能表征流动对结晶的影响.通过对等规聚丙烯(iPP)和聚对苯二甲酸乙二醇酯(PET)两种半结晶聚合物注射过程模拟结果的分析比较,证实成型过程具有加速结晶的作用.同时,材料的结晶也对注射成型加工过程,尤其是保压与冷却过程的温度场分布有较大的影响.     

Thermodynamic properties of polar fluids from a perturbed-dipolar-hard-sphere equation of state

Based on theoretical results for a system of hard spheres with dipoles, a new equation of state is applied to the correlation of thermodynamic properties for four fluids: argon, ammonia, water and acetonitrile. The reference system has the same dependence on density as that given by the Carnahan-Starling equation, but the coefficients are now functions of temperature through the reduced dipole moment. These coefficients are chosen to match the Padé approximant developed by Rushbrooke, Stell and Hoye for the Helmholtz energy of dipolar hard spheres. The reference system proposed here shows a phase transition for reduced dipole moments greater than 1.9. A simple, empirical perturbation term is added to the reference system to account for induction and dispersion forces. For polar fluids, the equation gives results significantly better than those obtained from conventional cubic equations of state, when using the same limited experimental data for determining equation-of-state parameters.     

Aqueous solubility calculation of aromatic acids within a wide temperature range using a modified regular solution model

Abstract  

The modified RSFH model, based on the regular solution theory coupled with the Flory-Huggins entropy term, was extended to calculate the solubility of aromatic acids in water within wide temperature ranges. The aqueous solubility data on aromatic acids from the published literature were assembled and validated. A total of 1,009 aqueous solubility data points for 25 aromatic acids within the temperature range of 273–463 K were selected for modeling. The calculation results showed that the solubility of aromatic acids in water could be well represented by the proposed four-parameter solution model within a wide temperature range. The overall absolute average deviation (δ _AAD) is 6.76%. The estimated cohesive energies of the aromatic acids were found to be about 20–30 kJ mol⁻¹. For the majority of the aromatic acids investigated, the cohesive energy could be considered as a constant. Strong temperature dependency, however, was also observed for a few aromatic acids, and misleading results may be obtained if this dependency is neglected. The model also has a certain prediction ability and could be extrapolated to a high temperature range where no experimental solubility data are available.     

EPR line shifts and line shape changes due to spin exchange of nitroxide-free radicals in liquids 4. Test of a method to measure re-encounter rates in liquids employing 15N and 14N nitroxide spin probes

EPR line shifts due to spin exchange of perdeuterated 2,2,6,6-tetramethyl-4-oxopiperidine-1-oxyl (14N-PDT) in aqueous solutions and the same probe isotopically substituted with 15N (15N-PDT) were measured from 293 to 338 and 287 to 353 K, respectively. Nonlinear least-squares fits of the EPR spectra yielded the resonance fields of the nitrogen hyperfine lines to high precision from which the shifts were deduced. The shifts are described by two terms: one linear and the other quadratic in the electron spin-exchange frequency, omegae. The quadratic term is due to spin exchange that occurs when two spin probes diffuse together and collide. A linear term is predicted for spin exchanges that occur upon re-encounter of the same two probes while they occupy the same "cage" before diffusing apart. The quadratic term has no adjustable parameters, while the linear term has one: the mean time between re-encounters, tauRE. The theory is cast in terms of the spin-exchange-induced line broadening that can be measured from each spectrum independently of the line shifts, thereby removing the explicit dependence of omegae on the temperature and the spin-probe concentration. In this form, theoretically, the value of the linear term is about a factor of 2 larger for 15N-PDT than for 14N-PDT for all temperatures; however, tauRE must be the same. Experimentally, we find that both of these expectations are fulfilled, providing strong support that the linear term is indeed due to re-encounter collisions. Values of tauRE derived from 14N-PDT and 15N-PDT are of the same order of magnitude and show the same trend with temperature as a hydrodynamic estimate based on the Stokes-Einstein equation.     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 17. Effect of oxygen availability

The gas in contact with polyethylene has considerable impact on its oxidation. The rate of oxidation product formation is mostly larger with oxygen blanketing than in air. Similarly, the rate in air is larger than that under nitrogen blanketing. Moreover, the relative effect of the surrounding gas is depending heavily on the particular oxidation product considered. The effect on the alcohol concentration on passing from air to pure oxygen is the same as that on the hydroperoxide concentration. It is only under pure nitrogen that alcohol formation is relatively more affected than hydroperoxide formation. The overall carbonyl groups as well as the ketones show the expected ranking, i.e. faster rate in pure oxygen than in air and faster rate in air than under pure nitrogen. However, carboxylic acids are formed much faster in oxygen than in air. For the acids the results in air and under nitrogen are significantly closer in the initial stages of processing than the results obtained under pure oxygen. This is different for γ-lactones for which formation is faster in oxygen than in air where it is faster than under nitrogen. With trans-vinylene groups the situation is opposite to that observed for carboxylic acids: the rate of formation is close for the experiments performed under air and under oxygen and significantly faster than under nitrogen. The results for hydroperoxides, alcohols and ketones are easily interpreted taking into account the kinetics developed in previous work. Fitting the data to the heterogeneous kinetics shows the effect of the oxygen concentration on this kinetics. It is especially unexpected with respect to its impact on the initiation rate. It is discussed taking into account various possibilities. The only one that is compatible with all the data envisages chain initiation resulting from interaction of oxygen with strained polymer molecules.     

Mutual Solubilities of Water and Alkanes

Summary.  The evaluation of mutual solubility data for systems water with n-alkanes, isoalkanes, and cycloalkanes along the three phase line is reported and a formula for the prediction of solubility of alkanes in water is developed. Then a cubic equation of state with an added term, which accounts for hydrogen bonding is used for correlation of liquid–liquid equilibrium data and for prediction of solubility of water in hydrocarbons using alkane in water solubility data. Comparison of the predicted and experimental solubilities is performed using all accessible experimental data. With this approach it is possible to predict the solubilities of water in alkanes with good accuracy over the temperature range up to about 20 K below critical temperature. Solubility of alkanes in water can also be calculated using experimental data for solubility of water in alkanes but results of these calculations are more sensitive to experimental errors of the data. Corresponding author: E-mail: macz@ichf.edu.pl Received August 5, 2002; accepted (revised) September 13, 2002 Published online March 13, 2003 RID="a" ID="a" Dedicated to Prof. Dr. H. Gamsj?ger on the occasion of his 70^th birthday anniversary     

Vapor–liquid equilibria and densities of CO2 with four unsaturated fatty acid esters at elevated pressures

In this study experimental P–T–x–y equilibrium data for four binary mixtures over a wide range of pressure (10.44–23.54 MPa) were determined at 313 K and 333 K. Liquid and vapor densities of carbon dioxide + four fatty acid ester systems, including oleic acid methyl ester, linoleic acid methyl ester, eicosapentaenoic acid ethyl ester, and docosahexaenoic acid ethyl ester were measured by using two circulating systems consisting of two vibrating tube densitometers. The vapor-phase density was observed to increase more significantly with pressure than the liquid-phase density at constant temperature. Experimental equilibrium constants of oleic acid methyl ester and linoleic acid methyl ester were found to be larger than those of eicosapentaenoic acid ethyl ester, docosahaxaenoic acid ethyl ester, linoleic acid, triolein, and tocopherol. This indicates that the two methylated fatty acids would be extracted easier than the other compounds in a separation process using supercritical CO₂ extraction. The equilibrium data were successfully correlated using the Peng–Robinson and modified Soave–Redlich–Kwong equations of state with quadratic (two parameters), Panagiotopoulos–Reid (three parameters), and Adachi–Sugie (three parameters) mixing rules. In general, the Soave–Redlich–Kwong equation of state with the Panagiotopoulos–Reid mixing rules and the quadratic mixing rules give the best correlation for methylated fatty acids and ethylated fatty acids, respectively.     

A Fractal-Like Kinetic Equation to Investigate Temperature Effect on Cellulose Hydrolysis by Free and Immobilized Cellulase

According to fractal-like theory in the heterogeneous system, a cellulase-catalyzed kinetic equation that contained two parameters (rate constant k and fractal dimension h) was deduced. The equation described directly the mathematical relationship between reducing sugar concentration and hydrolytic time, and accurately fitted the experimental data of free/immobilized cellulase at 37, 40, 44, 47, and 50?°C (R (2)?>?0.99). The fitted h value is estimated as a constant (0.6148) in these tested temperatures. The fitted k value increased with temperature increase, and the relationship agreed with Arrhenius equation (R (2)?>?0.98). The fractal-like equation could predict accurately the experimental data at low temperature 34?°C for free/immobilized cellulase and high temperature 53?°C for immobilized cellulase, but the prediction at 53?°C for free cellulase was not accurate enough due to its lower stability than immobilized cellulase. The application of fractal-like theory in cellulase kinetics is successful.     

弹道明胶老化初级阶段的模型

用流变震荡模式研究了10 wt%浓度的弹道明胶在冷却和等温下的老化行为.对明胶从sol-gel点冷却到某个目标温度的过程,通过不同冷却速率的实验,建了一个弹性模量与温度的线性关系.不同温度下明胶的等温老化实验表明,弹性模量-时间曲线具有相似的形状.依据Normand提出的二级反应动力学模型,引入一个表征明胶老化行为的速率常数,构建了一个预测弹道明胶在老化初级阶段的弹性模量演化的模型.该模型中模量-温度关系在初始和无穷大时是直线,其他模量-温度线是近似直线,并交于sol-gel点.老化速率常数和过冷度之间符合Flory-Weaver方程.对弹性模量和老化时间进行归一化处理,可将不同温度下的老化曲线叠加成一条主曲线.     

The dynamics of water vapor sorption on a composite sorbent in the presence of unsorbable components

Preliminary mathematical processing of the experimental data on the dynamics of water vapor adsorption on a composite adsorbent was performed. The approximate time dependence of water vapor pressure was constructed. An analytic equation describing changes in the mean temperature of adsorbent grains as a function of the duration of measurements depending on water vapor pressure was obtained, and an asymptotic approximation equation was suggested. The system under consideration was shown to pass two “diffusion” stages in the dynamics of pressure changes and changes in the mean temperature of grains. The characteristic times of the diffusion stages monotonically increased as the fraction of an unadsorbable component in the gas phase of the system grew.     

Adsorption integral equation via complex approximation with constraints: The Langmuir kernel

The relationship between the measured adsorption isotherm and unknown energy distribution function is described by so‐called adsorption integral equation, a linear Fredholm integral equation of the first kind. We consider the case of the Langmuir kernel when the equation can be reduced to the Stieltjes integral equation. A new method for solving the Stieltjes equation is developed. The method is based on the ideas of complex approximation with constraints. The numerical algorithms constructed on the base of this method allow reduction of the problem under consideration to linear or linear‐quadratic programming problems. The method is compared with the usual regularization methods. The obtained results can be useful for the evaluation of the experimental adsorption energy distribution from experimental data. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 191–200, 2000     

Physico-chemical aspects of polyethylene processing in an open mixer. Part 30: Formal kinetics of γ-lactone formation at a constant rate

There are only few mechanisms susceptible to explain γ-lactone formation at a constant rate. The formal kinetics based on these mechanisms proves to be a useful tool in the attempt to estimate the likeliness and possible relative amount of their contribution. The α,γ-keto-hydroperoxides formed in 4-position to hydroxyl groups are decomposed very rapidly at the temperatures of the experiments. The decomposition yields a carboxylic acid group in 4-position to the alcohol group and is first choice for explaining γ-lactone formation at a constant rate. However, the activation energy deduced from the formal kinetics developed for this mechanism is rather small with about 3.6 kcal/mol and hardly in agreement with the experimental value of 29.8 kcal/mol. This leads to the re-examination of the experimental data. Separate fitting of the data for the low temperature range yields the value of 4.1 kcal/mol. This value is sufficiently close to the value deduced from the formal kinetics to be compatible with it. The formal kinetics indicates also that on passing from air to pure oxygen the rate should increase by a factor of about 1.7. This is sufficiently close to the experimental value of about 2 for agreement. It is concluded that the mechanism examined can account for the bulk of the γ-lactone formed at a constant rate.The calculations for 1-peroxy-2,5-di-hydroperoxides and 1,4-keto-hydroperoxides do not yield conclusions that are as straightforward as those for the α,γ-keto-hydroperoxides in 4-position to hydroxyl groups. Although the estimated activation energies are roughly compatible with the experimental value for the low temperature range, the increase with the oxygen concentration is significantly larger than that observed experimentally. Hence, the contribution of these intermediates to the constant rate of γ-lactone formation can only be minor.     

Study on kinetics of combustion of brick-shaped carbonaceous materials

Combustion of brick-shaped carbonaceous materials (carbon deposits from coke oven, coke and electrographite) was carried out in thermobalance in static air. Analysis of kinetics of the process was carried out using both classical (Arrhenius law) and newer (three-parametric equation) methods. In classical approach two types of kinetic equations were used in calculations: differential and integral. The results obtained show that, independently on kinetic variables (α – conversion degree or m – mass of sample) used in differential equations, kinetics of combustion of brick-shaped carbonaceous materials is characterized by only one pair of Arrhenius coefficients: activation energy (E) and pre-exponential constant (A). At the same time the integral equation demonstrates distinction in relation to methods based on differential equations, generating higher activation energies and separate isokinetic effect (IE). Parallel IE shows that kinetic analysis has to encompass activation energy in connection to second coefficient, pre-exponential constant A, depending on assumptions made for kinetic equations. On the other hand three-parametric equation allows describing kinetic of combustion in alternative way using only one experimental value – initial temperature in form of point of initial oxidation (PIO) – and also offers new methods of interpretation of the process.     

Optimization of Parameters for Cr(VI) Adsorption on Used Black Tea Leaves

Dynamic characteristics of Cr(VI) sorption on used black tea leaves (UBTLs) as a low-cost adsorbent are studied. Batch experiments were conducted to evaluate the effects of Cr(VI) concentration, solution pH and temperature on the removal process. Both of adsorption and reduction, involved in the process, are affected by the processing parameters. The adsorption kinetics is described successfully using pseudo-second order rate equation and the rate constant decreases with increasing the initial concentration of Cr(VI) up to 150 mg/L (for 0.1 g/L UBTLs) then becomes slow. Experimental and calculated kinetic data for equilibrium are well expressed by Langmuir isotherm. The solution pH has a profound effect on the adsorption rate. The rate constant increases linearly with an increase in temperature, and the low value of activation energy of adsorption, 16.3 kJ/mol, indicates that Cr(VI) is easily adsorbed on UBTLs. The maximum Cr(VI) adsorptive conditions, with a minimum reduction, were achieved from the dynamics of operational parameters: the initial Cr(VI) concentration < 150 mg/L (for 0.1 g/L UBTLs); the initial solution pH = 1.54–2.00 and the processing temperature < 50 ^∘C, for the possibility of its practical application.     

Non-linear calibration functions in ion chromatography with suppressed conductivity detection using hydroxide eluents

The linearity of calibration curves in ion chromatography with suppressed conductivity detection using hydroxide eluents was investigated. Theoretical calibration curves were derived for strong electrolytes and weak monobasic acids and the results compared with experimental data. At low concentrations up to 1 micromol l(-1) the autoprotolysis of water induces left-curved calibration functions even for strong electrolytes like nitrate. The experimental data are best described by a quadratic function, the differences between linear and quadratic regression being up to 10%. At higher concentrations the calibration curves for strong electrolytes are linear. Due to incomplete dissociation, the calibration curves for weak mono- and dibasic acids show a right curvature. Thus, depending on the analyte and the concentration range of interest, analysts should carefully choose between a linear and a quadratic regression function.