Measurement and correlation of mutual diffusion coefficients for molten polystyrene-hydrocarbon systems

The mutual diffusion coefficients for three molten polystyrene(PS)-hydrocarbon systems—PS-in-xylene, PS-n-octane, and PS-n-nonane—were measured by using a sorption apparatus with quartz spring in the temperature region from 130 to 175°C and for mass fraction of hydrocarbon ranging from 0 to 0.15. The mutual diffusion coefficients were correlated with good agreement by the freevolume theory.     

Estimation of diffusion coefficients for trace amounts of solvents in glassy and molten polymers

Two methods based on the free-volume theory of transport are developed for the estimation of diffusion coefficients for trace amounts of solvents in amorphous polymers. The first method uses diffusivity data for a polymer–solvent system above the glass transition temperature to estimate the temperature dependence of the mutual diffusion coefficient below this temperature. In the second method, mutual diffusion coefficients are estimated for a particular polymer–solvent system both above and below the glass transition temperature using no diffusivity data for the system. The predictions of the proposed theory are compared with diffusivity data for the n-pentane–polystyrene and ethylbenzene–polystyrene systems.     

Prediction of binary diffusion coefficients in supercritical CO2 with improved behavior near the critical point

In this work, a predictive model for binary diffusivities at infinite dilution (D₁₂) in SC-CO₂ is proposed. It combines two terms – background and singular – with the objective to represent D₁₂ accurately not only far but also near the critical point, where critical enhancement is always observed. The model provides an average error of 6.20% for a large database including 149 systems and 4469 data points over wide ranges of temperature and pressure. The models selected for comparison (Wilke–Chang, Scheibel, Lusis–Ratcliff, Lai–Tan, Tyn–Calus and Reddy–Doraiswamy) achieve scattered and biased results, with average errors from 11.62% to 75.17%. In the whole, the new model exhibits an excellent performance for any kind of molecules in terms of size, molecular weight, polarity and sphericity, in all critical region. In order to help interested readers, a spreadsheet for the calculation of D₁₂ is given in Supplementary data. The input data is: temperature, pressure, CO₂ viscosity, and solute properties (acentric factor, critical constants, molar volume at normal boiling point, and molecular weight – given in this paper for the systems studied).     

超临界二氧化碳对聚合物的增塑作用及应用

简要介绍了超临界二氧化碳的性质及其与聚合物的相互作用 ,着重论述了超临界二氧化碳对聚合物的增塑作用及应用 ,包括小分子渗透、溶胀聚合、抽提分级、聚合物脱挥及微孔材料的制备等     

Upcycling by grafting onto semi-crystalline polymers using supercritical CO2

The creation of graft copolymers by selectively grafting a second polymer to the amorphous fraction of a semi-crystalline polymer in supercritical CO₂ is demonstrated herein. The graft copolymer is synthesized by free radical polymerization of a vinyl monomer within the semi-crystalline polymer below its melt temperature. Such conditions afford selective grafting on the amorphous regions (block “B”) while leaving the crystalline domains (block “A”) unmodified. Accordingly, unique A-B, A-B-A, A-B-A-B-A, and so forth. block structures are formed. In this work, styrene is polymerized within polyamide 6, polyethylene terephthalate, and isotactic polypropylene. Purification of these material is performed to remove the un-grafted homopolymer, allowing for determination of the graft yield, the portion of polymer which covalently bonds to the semi-crystalline matrix. Grafting yields achieved in polyamide 6, polyethylene terephthalate, and isotactic polypropylene were 98%, 59%, and 15%, respectively. Property enhancements were observed upon further characterization of polystyrene-polyamide 6 copolymers, including high glass transition temperatures, the ability to be remelted, and tunable grafting molecular weight. Additionally, hydrophobicity is controlled by varying polystyrene composition. The remarkable range of accessed properties demonstrates this as a potential route to upcycling plastics.     

Measurement of solubility and diffusion coefficients of ethylene in solid and molten low-density polyethylene with different melt indices

The diffusion behavior of ethylene in polyethylene is of great importance for the polymerization and degassing of polyethylene (PE) industry. Based on the gravimetric sorption and desorption measurement approach, an intelligent gravimetric analyzer is applied to obtain the solubility and diffusion coefficients of ethylene in solid low-density PE (LDPE) with different melt indices at 30°C to 70°C, 0 to 4 atm and in molten LDPE at 160°C to 230°C, 0 to 4 atm, respectively. Results indicate that both the solubility and diffusion coefficients of ethylene in solid LDPE are smaller than those in molten LDPE, while the dissolution enthalpy and diffusion activation energy of ethylene in solid LDPE are higher. In addition, one- and two-dimensional diffusion models are built and the effects of particle size, polymer properties, and operation conditions are systematically investigated on the diffusion behaviors of ethylene in solid and molten LDPE.     

Tracer diffusion coefficients in molten salts—I. Methods

Two different methods for determination of tracer diffusion coefficients in molten salts are presented. Both methods were based on the theory related to diffusion of instantaneously applied, infinitely thin radioactive sources in semi-infinite one-dimensional diffusion media.In the first method, the melt was absorbed in sintered, porous MgO-strips. The labyrinth factors for these “Impregnated Self-supporting Strips” (ISS) were known from calibration measurements.The second method used was a direct method. In this case the melt was kept as a “Cylindrical Thin Layer” (CTL) of thickness 0.025–0.030 cm in a graphite crucible facilitating effective quenching of the melt after the experiment.The results obtained for pure molten NaNO₃ and NaCl are discussed and compared to data reported in the literature.     

Partition coefficients for fatty acid esters in supercritical fluid CO2 with and without ethanol

The complex nature of fish oils was exploited to study the dependence of structural factors upon fatty acid ester solubility in supercritical fluid carbon dioxide (SCF-CO₂). Partition coefficients were determined for a number of components present in two mixtures of fatty cid ethyl esters derived from menhaden oil in SCF-CO₂ at 60°C and 125 bar. Analogous data also were obtained for SCF-CO₂ with 5% (w/w) ethanol added. The addition of ethanol was found to increase partition coefficients for all species, but resulted in a decrease of fluid selectivity. Aside from the chain length of a component, both the degree and position of unsaturation were found to be structural factors that affect the value of the partition coefficient.     

Measurement and prediction of LDPE/CO2 solution viscosity

When CO₂ is dissolved into a polymer, the viscosity of the polymer is drastically reduced. In this paper, the melt viscosities of low‐density polyethylene (LDPE)/supercritical CO₂ solutions were measured with a capillary rheometer equipped at a foaming extruder, where CO₂ was injected into a middle of its barrel and dissolved into the molten LDPE. The viscosity measurements were performed by varying the content of CO₂ in the range of 0 to 5.0 wt% and temperature in the range of 150°C to 175°C, while monitoring the dissolved CO₂ concentration on‐line by Near Infrared spectroscopy. Pressures in the capillary tube were maintained higher than an equilibrium saturation pressure so as to prevent foaming in the tube and to realize single‐phase polymer/CO₂ solutions. By measuring the pressure drop and flow rate of polymer running through the tube, the melt viscosities were calculated. The experimental results indicated that the viscosity of LDPE/CO₂ solution was reduced to 30% of the neat polymer by dissolving CO₂ up to 5.0 wt% at temperature 150°C. A mathematical model was proposed to predict viscosity reduction owing to CO₂ dissolution. The model was developed by combining the Cross‐Carreau model with Doolittle's equation in terms of the free volume concept. With the Sanchez‐Lacombe equation of state and the solubility data measured by a magnetic suspension balance, the free volume fractions of LDPE/CO₂ solutions were calculated to accommodate the effects of temperature, pressure and CO₂ content. The developed model can successfully predict the viscosity of LDPE/CO₂ solutions from PVT data of the neat polymer and CO₂ solubility data.     

Determination of binary diffusion coefficients in supercritical chlorotrifluoromethane and sulphurhexafluoride with supercritical fluid chromatography (SFC)

Binary diffusion coefficients D₁₂ have been determined in supercritical chlorotrifluoromethane and in liquid as well as supercritical sulphurhexafluoride with supercritical fluid chromatography (SFC) using the peak broadening method. D₁₂ values of benzene, methylbenzene, 1,4-dimethylbenzene, 1,3,5-trimethylbenzene, 1,3-dibromobenzene, 2-propanone and tetrachloromethane are reported at temperatures and pressures from 283 to 338 K and 3 to 15 MPa respectively; this corresponds to densities from 400 to 1000 kg m⁻³ for CClF₃ and 300 to 1400 kg m⁻³ for SF₆. The binary diffusion coefficients D₁₂ are of the order of 10⁻⁸ m² s⁻¹. At constant temperature they exhibit a considerable dependence on density whereas the influence of temperature at constant density is relatively small.     

两步扩散模型对超临界CO2萃取丁香油的数值模拟

基于扩散模型方程和集总参数模型方程,首次建立了具有3个可调参数的两步扩散模型方程.该模型同时考虑固体颗粒内扩散阻力与内壁的阻力,能较好地描述超临界流体萃取过程.用两步扩散模型方程模拟了超临界CO<,2>萃取丁香油的动态过程,在实验温度与压力范围内模型计算值与实验数据的平均相对误差AARD在2.33%～19.48%之间,所有实验点的AARD为8.09%.而用扩散模型方程和集总参数模型方程模拟,所有实验点的AARD分别为17.51%和8.13%,表明两步扩散模型对于超临界CO<,2>萃取丁香油的传质过程的模拟效果优于扩散模型方程和集总参数模型方程.     

Investigation of CO2 sorption in molten polymers at high pressures using Raman line imaging

CO₂ sorption in molten poly(ε-caprolactone) (PCL) has been investigated by temporally resolved Raman line imaging, which is introduced here as a new technology for the direct measurement of gas mass fraction profiles inside polymers during transient sorption experiments. Molten PCL was exposed to pressurized carbon dioxide in an optically accessible pressure cell at 80 °C and pressures up to 7.1 MPa. During sorption, Raman spectra were acquired temporally and spatially resolved across the PCL drop, allowing the evaluation of the PCL/CO₂ mutual diffusivity, of the CO₂ solubility in PCL, and the determination of temporal evolution of mass fraction profiles of carbon dioxide inside PCL.     

Estimation of diffusion and solubility coefficients for water and CO2 in reaction injection molded parts

The evolution of gases from Reaction Injection Molded (RIM) parts during painting causes “pinhole” surface defects, which result in scrap. The transport of gases plays a major role in this outgassing. The diffusion rates of CO₂ and water through reaction injection molded parts is measured in this work. Despite the presence of glassy hard domains and dispersed microbubbles of size <25 μm (nucleated parts), the diffusion showed Fickian characteristics, and diffusion coefficients were independent of the concentration of water and CO₂ in nucleated and non-nucleated RIM parts. The presence of microbubbles enhances diffusion, which could be predicted from the diffusion rate through the non-nucleated material by using a simplistic one-dimensional model. The diffusion coefficients of water and CO₂ follow an Arrhenius relationship. The solubility coefficients follow a van't Hoff relationship over a wide range of 20 to 150°C. Apart from predicting diffusion and solubility coefficients, for various RIM materials and processing conditions, the estimated parameters will be used to interpret the outgassing phenomenon in a subsequent paper.     

Predictive correlation of binary diffusion and self-diffusion coefficients under supercritical and liquid conditions

The hydrodynamic equation D/T = αη^β, where D is the infinite dilution binary diffusion or self-diffusion coefficient, T is the temperature, η is the fluid viscosity, and α and β are constants, were demonstrated to be effective for predicting both binary diffusion and self-diffusion coefficients in high density fluids, i.e. liquid and supercritical states. When a solute was specified, the correlation well represented both binary diffusion and self-diffusion coefficients, irrespective of solvent over a wide solvent viscosity range. The solute-dependent constants α and β were determined for 12 solutes with average absolute deviation of 6.2% for 1006 data points.     

Measurement of interfacial tension in PS/LDPE melts saturated with supercritical CO2

The effect of supercritical carbon dioxide (scCO₂) on the interfacial tension between a polymer melt pair—polystyrene (PS) and low density polyethylene (LDPE)—was studied using the pendant drop method at temperatures varying from 200 to 240°C and CO₂ pressures up to 18 MPa. The LDPE melt was prepared in a high pressure optical cell and the PS pendant drop was injected into the LDPE melt with a special high pressure syringe. For measurements with scCO₂, the optical cell was first pressurized with scCO₂ and measurements were taken after the saturation of scCO₂ into both polymer melts. Excellent agreement was found with literature data for the same system without using scCO₂. For the polymer pair saturated with scCO₂, it was found that the interfacial tension decreases significantly with increasing CO₂ pressure and appears to level off at higher CO₂ pressures.     

Prediction of the concentration dependence of diffusion coefficients of polymers in solution

The hydrodynamic volumes of solvated polymers shrink with increasing concentrations in solution until a concentration (c_x) is reached at which the effective dimensions are those of a Theta solvent. A simple model (Ref. 7) can be used to calculate the volume fraction of solvated polymer coils as a function of concentration. From this, the concentration dependence of diffusion coefficients can be estimated (Ref. 5). Calculated data are in very good agreement with experimental values except for some lower molecular weight polymers in poor solvents.     

Determination of diffusion coefficients of depositing ions in molten chlorides by transient electrochemical techniques

The electrochemical reduction of Pb(II), Zn(II) and Mg(II) ions at glassy carbon and tungsten electrodes in molten KCl–LiCl eutectic was studied by linear sweep voltammetry (LSV), convolutive potential sweep voltammetry (CPSV), chronopotentiometry and chronoamperometry. In the case of lead deposition, the initial nucleation stage was found to influence the shape of the voltammetric current peak. CPSV was consequently believed to be a more reliable method than LSV for the calculation of the diffusion coefficient of the Pb(II) ion. Similar complications were not observed for zinc and magnesium since the nucleation overpotentials for these metals were significantly lower than for lead. On the other hand, lithium codeposition made it difficult to interpret the zinc and especially the magnesium convolution voltammograms. Chronopotentiometry yielded practically identical results for D _Pb(II) as the voltammetric techniques. However, due to a substantial residual current, the Sand equation was not obeyed for the Zn(II) and Mg(II) ions. Determination of diffusion coefficients from single potentiostatic current transients and the Cottrell equation was not found to be a very reliable method. Empirical expressions for the temperature dependence of D in the range 400–500 °C were calculated for all three ions.     

葡萄糖水溶液扩散系数的测定与关联

液相扩散系数在化工数据中起着非常重要的作用,由于液体结构及扩散本身的复杂性,至今还没有一个合理的理论模型来预测液相扩散系数,有必要从实验和理论上对不同的体系进行研究.制备了金属膜池,用氯化钾溶液标定了膜池常数,并用已有可靠文献值的蔗糖水溶液验证了装置的可靠性.测定了298.15～328.15 K不同温度下葡萄糖水溶液的积分扩散系数,考察了温度对扩散系数的影响.在实验数据的基础上,提出一个有温度关联项的半经验模型,关联和计算了本实验的数据,结果与实验值吻合很好.