Experimental and theoretical investigation of solubility and diffusion of ethylene in semicrystalline PE at elevated pressures and temperatures

The solubility and diffusivity of ethylene in semicrystalline polyethylene were experimentally measured using a magnetic suspension microbalance. The sorption measurements were carried out at temperatures up to 80°C and pressures up to 66 atm. The experimentally measured solubilities were found to decrease with increasing temperature and increased with ethylene pressure in good agreement with the predictions of the Sanchez–Lacombe lattice‐fluid model. The diffusivity of ethylene in semicrystalline polyethylene films was estimated from the reduced sorption curves using the half‐time method. The experimentally determined diffusivities were compared with theoretical values predicted by a new molecular hybrid model, which combines the characteristic features of the Pace–Datyner diffusion model with those of the Kulkarni–Stern free‐volume model. The ethylene diffusion coefficient was found to increase with temperature and/or the ethylene‐sorbed concentration. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 87: 953–966, 2003     

Thermodynamic model for the permeability of light gases in glassy polymers

The permeability of light gases in a series of different glassy polymers is analyzed through a thermodynamic‐based approach for solubility and diffusivity. The nonequilibrium thermodynamic model for glassy polymers describes the solubility of the different penetrants; diffusivity is given as the product of a mobility factor and a thermodynamic factor. The latter is predicted by the nonequilibrium lattice fluid thermodynamic model, while the mobility coefficient is determined using the experimental permeability data. For rather soluble penetrants (e.g., CO₂), a plasticization factor is also accounted for, considering the mobility to depend exponentially on penetrant concentration, as often observed experimentally. The model is able to describe accurately the experimental behavior in a simple and effective way, considering only two adjustable parameters. The mobility coefficient is found to depend on the penetrant size (critical volume) and on the fractional free volume of the polymer matrix, following rather general and reasonable correlations. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2776–2788, 2015     

Characterization of temperature‐dependent moisture diffusivity in PMR‐15 resin

The temperature‐dependent moisture diffusion behavior of high‐temperature polyimide resin, PMR‐15, is presented. Adsorption and high temperature desorption tests are used to experimentally determine moisture diffusivity at several temperatures. Diffusivity is determined from the weight change based on the initial slope and using a nonlinear regression technique with Fickian diffusion assumption. The basic test procedures and diffusivity values are presented in this study. The results also include the relative humidity (RH) dependent equilibrium moisture concentration and a relationship between the RH and equilibrium moisture concentration. As direct measurement at typical operating temperature may be precluded by blistering, an Arrhenius‐type temperature‐diffusivity relationship is used to estimate the temperature‐dependent moisture diffusivity for the PMR‐15 resin. The moisture diffusivity of PMR‐15 tested is estimated to be 6.64 E ?10 m²/s at 288°C. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

Determination of sorption kinetic parameters using the relaxation‐dependent solubility model in the methanol vapor—Poly(methyl methacrylate) system

The relaxation‐dependent solubility model was applied to simulate the experimentally observed sorption kinetic behavior of the PMMA–vapor MeOH system at 25°C, to obtain the main transport parameters. Application of the model in series of successive sorption kinetic runs covering small concentration intervals revealed certain trends in the concentration dependence of the diffusion coefficient of the system, not detectable by a previous simpler analysis of the data. Following excess free volume fill up, relaxation frequencies exhibit a weak exponential dependence on concentration. The functional dependence of the thermodynamic diffusivity on the concentration, deduced from the aforementioned simulation procedure, was tested and found to reproduce reasonably well the series of sorption kinetic runs covering considerably larger concentration intervals. In addition, this analysis indicates a strong dependence of the relaxation mechanism on the concentration interval. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2278–2288, 2006     

Molecular transport of aromatic hydrocarbons through lignin‐filled natural rubber composites

The diffusion and transport of organic solvents through lignin‐filled natural rubber composites have been studied in the temperature range 25–45°C. The diffusion of aromatic solvents through these samples were studied with special reference to the effect of filler concentration, penetrant size, and temperature. Transport coefficients such as diffusion, permeation, and sorption coefficients were estimated. The van't Hoff relationship was used to determine the thermodynamic parameters. The first order kinetic rate constant has been evaluated. A correlation between theoretical and experimental sorption results was evaluated. POLYM. COMPOS., 28:15–22, 2007. © 2007 Society of Plastics Engineers     

Theoretical analysis and experimental study on SO2 adsorption onto pistachio‐nut‐shell activated carbon

The adsorption study of SO₂ onto the activated carbon prepared from pistachio‐nut shell was studied theoretically and experimentally. A single‐particle sorption model known as concentration‐dependent surface diffusivity micropore, surface and macropore diffusion control model incorporating micropore, macropore and surface diffusions, together with a nonlinear isotherm at the micropore mouth, has been derived and solved by a finite difference method. The effects of different types of nonlinear isotherms and concentration dependent surface diffusivities have been thoroughly studied. The effects of adsorbate concentration and temperature on adsorption were studied experimentally. Good agreement was found between the model predictions and the experimental results. The value of the tortuosity factor and the extracted diffusion coefficients obtained are consistent with their corresponding values reported. © 2008 American Institute of Chemical Engineers AIChE J 2009     

Diffusivity of n-hexane in poly(ethylene-stat-octene)s assessed by molecular dynamics simulation

Molecular dynamics simulations have been used to study diffusion of n-hexane in wholly amorphous poly(ethylene-stat-octene)s with comonomer contents ranging from 0 to 11.5 mol%. The branches in the polymer increased the specific volume by affecting the packing of the chains in the rubbery state in accordance with experimental data. The diffusion of n-hexane at penetrant concentrations between 0.5 and 9.1 wt% was simulated within time-scales between 0.1 and 0.2 μs. The penetrant diffusivity unexpectedly decreased with increasing comonomer content. The penetrant molecule motion statistics showed that systems with high comonomer content showed a greater tendency for short distance motion (over a sampling period of 3 ps) whereas the systems with lower comonomer content showed penetrant motion over longer distances. It seems that the branches retarded local chain mobility of the polymer thereby trapping the penetrant molecules. All systems studied showed a minimum in penetrant diffusivity at ca. 1 wt% n-hexane and a marked increase in diffusivity at higher penetrant concentrations. The volumetric data for the different polymer-penetrant systems were consonant with additional volumes of the different components. Comparison between simulated diffusivities (for a wholly amorphous polymer) and experimentally obtained diffusivity data for semicrystalline polymers showed that constraining effect of the crystals were substantial for the highly crystalline systems and that it gradually decreased with decreasing crystallinity.     

A Combined Experimental and Theoretical Approach to Study Temperature and Moisture Dynamic Characteristics of Intermittent Paddy Rice Drying

Intermittent drying of paddy rice is fully investigated both theoretically and experimentally. A model is developed to describe simultaneous heat and mass transfer for the drying stages and mass transfer for the tempering ones. The model is considered for both cylindrical and spherical geometries. The model excels in considering non-constant paddy rice and air physical properties as well as surface vaporization and convection. The consequent equations are numerically solved with finite-difference method of line using implicit Runge–Kutta. Furthermore, a set of experiments is conducted in a laboratory-scale fluidized bed dryer to estimate the moisture diffusivity of rice and evaluate the effects of different parameters. Two correlations for moisture diffusivity are derived for each geometry based on the experimental results. It is noteworthy that the geometry choice leads to significantly different moisture diffusivities. As a result, the diffusivity values obtained for spherical presentation is 2.64 times greater than that of cylinder. Moreover, the cylindrical model fits the experimental results more precisely, especially for tempering stage (AARD_cyl = 1.03%; AARD_sph = 1.53%). Model results reveal that thermal equilibrium is quickly reached within the first 2 min. Air velocity shows no influential effect on drying upon establishment of fluidized condition. In addition, drying rate is drastically improved after applying the tempering stage. A definition for tempering stage efficiency is also proposed which shows that 3 h tempering will be 80% efficient for the studied case. Rising temperature significantly improves the drying rate, while it does not contribute much in the tempering efficiency.     

Sorption and transport of aqueous salt solution in polyurethane membrane at 25, 44, and 60°C

Sorption and transport of aqueous salt solutions in polyurethane elastomer has been investigated over the temperature interval of 25–60°C by using an immersion/weight gain method. The size of the ions has no significant effect on the penetrant transport coefficients. The sorption data have been explained in terms of the simple Fickian model. Attempts have also been made to estimate the transport parameters by applying corrections to include the spatial diffusivity of the liquids within the polymer sample. Temperature dependence of the transport coefficients has been used to estimate the activation parameters from the Arrhenius plots.     

Process monitoring and kinetics of rigid poly(urethane–isocyanurate) foams

Process temperature profiles of a two‐component rigid poly(urethane–isocyanurate) foam system were studied and compared with the predictions of a one‐dimensional numerical simulation. This model is based on experimentally determined thermophysical properties including thermal diffusivity, enthalpy of reaction, and rate of reaction. Temperature profiles were measured at three positions within the foam and at the foam surface for mold temperatures of 25°C and 55°C. A high rate of reaction and heat of reaction, along with low thermal diffusivity, cause temperatures near the foam center to be insensitive to mold temperatures for thick samples. Thermal analysis was used for determination of thermophysical properties. Temperature‐dependent heat capacity, reaction kinetics, and heat of reaction were evaluated using temperature‐scanning DSC. Thermal conductivity was analyzed from steady‐state heat profiles. The system reaction kinetics indicated much faster kinetics than reflected by process cure temperature profiles made using thermocouples. The simulations accurately predict experimental results, allowing determination of demold time dependence on process conditions, including feed temperature, mold temperature programming, and sample thickness. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 374–380, 2000     

A free-volume interpretation of the influence of the glass transition on diffusion in amorphous polymers

A new version of the free-volume theory of diffusion is used to describe polymer–solvent diffusion both above and below the glass transition temperature. Expressions are derived for the temperature dependence of the mutual diffusion coefficient and for the effective activation energy in the limit of zero penetrant concentration. The theory also describes the effect of the glass transition on the diffusion process. Predictions of the theory are compared with available diffusivity data for amorphous polymer–solvent systems.     

Modeling solubility of gases in semicrystalline polyethylene

An absorption model of gases in semicrystalline polymer was built that was based on the activity coefficient theory in polymer solution and associated with crystallinity dependent on temperature. The solubility of ethylene, isopentane, and n‐hexane in three types of polyethylene (PE) were obtained by the use of a pressure‐decay method at temperatures of 333–363 K and pressures of up to 2 MPa, 80–300 KPa, and 19–100 KPa, respectively. Experimental data from three gases in each PE sample were used for the single‐parameter fitting, and fitting error was within about 12%. It was found that a single parameter was merely dependent on the properties of PE used. It was shown that, unlike with the Flory–Huggins model and the UNIFAC–M‐H method, correlation between the crystallinity of the semicrystalline polymer and temperature had to be taken into account in order for the solubility data of alkane, olefin, and aromatic hydrocarbons in polyethylene to fit well, especially in the temperature range near the melting point of the polymer. The four free‐energy contributions to the total gas activity were experimentally determined to be about 47%–60% combined, the free‐volume contribution about 12%–25%, and the elastic effect about 22%–35%, but the interactional contribution was zero. The contributions changed with the size of the gas molecules. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1737–1744, 2007     

A kinetic study of the reaction between terephthalic acid and ethylene oxide in a nonsolvent system

Kinetics of the reaction between terephathalic acid and ethylene oxide, catalysed by triethylamine, was studied in a high-pressure reactor without using solvent. This reaction was carried out at a temperature range of 80–100°C and at a pressure range of 10–15 Kg/cm² beyond the corresponding vapor pressure of ethylene oxide. Effects of temperature, catalyst concentration, mole ratio of ethylene oxide to terephthalic acid, particle size of terephthalic acid, pK value of the tertiary amine and stirrer speed were experimentally investigated on the yield of bis(2-hydroxyethyl) terephthalate and reaction rates. It was found that the bulk reaction of terephthalic acid with ethylene oxide occurred in the liquid phase. Based on experimental results a reaction mechanism to synthesize bis(2-hydroxyethyl) terephthalate from terephthalic acid and ethylene oxide in a nonsolvent system was proposed, and rate constants were obtained with a model based on this proposed reaction mechanism. The activation energy of the reaction was found to be between 3.67–8.28 kcal/mole in the temperature range of 80–95°C.     

Osmotic Dehydration of Apple Cylinders: II. Continuous Medium Flow Heating Conditions

Mass transfer of apple cylinders during osmotic dehydration was quantitatively investigated under continuous medium flow conditions. The influences of the main process variables (solution concentration, operation temperature, contact time, and solution flow rate) were determined. A second-order polynomial regression model was used to relate weight reduction (WR), moisture loss (ML), solids gain (SG), and mass diffusivity (D _m and D _s ) to process variables. The conventional diffusion model using a solution of Fick's unsteady state law involving a finite cylinder was applied for moisture diffusivity and solute diffusivity determination. Diffusion coefficients were in the range of 10^?9–10^?10 m²/s, and moisture diffusivity increased with temperature and flow rate, increased with solution concentration (> 50°Brix), and decreased with increasing solution concentration (< 50°Brix), but solids diffusivity increased with temperature and concentration and decreased with increasing flow rate. A continuous-flow osmotic dehydration (CFOD) contactor was developed to be a more efficient process in terms of osmotic dehydration efficiency: time to reach certain weight reduction (T _w ) and moisture loss (T _m ) were shorter than that of conventional osmotic (COD) dehydration processes. Effectiveness evaluation functions used in this study could be widely applied to osmotic dehydration system evaluation.     

Diffusion of saturated hydrocarbons in low density polyethylene (LDPE) films

The diffusion coefficients at zero penetrant concentration, D₀, of n-heptane, n-heptane, n-octane, n-decane, and 2,2,4-trimethylpentane (TMP) in LDPE were obtained in the range of 25–50°C, using the desorption method. The dependence of D₀ on the size and shape of the penetrant is reported. It was found that D₀ decreases with increasing penetrant molecule size. The activation energies of diffusion in the temperature range of 25–50°C increase with increasing penetrant molecule size and are independent of temperature. The results are interpreted in terms of the free volume theory and semiquantitative estimates of the free volume parameters are reported.     

The influence of temperature on effective diffusivity and adsorption kinetics for humid air—porous alumina

The kinetics of water adsorption from an air stream on porous alumina is studied experimentally in a differential bed at five temperatures in the range 9·8–64·0°C. The mass transfer rate is calculated theoretically by means of a model, which considers simultaneous resistance to mass transfer in the pore system of the solid and in a film surrounding the particle. The adsorption equilibrium is described by the non-linear Freundlich isotherm. Comparison of experiments with theory shows that the model describes the adsorption kinetics adequately and allows the effective diffusivity in the porous solid to be calculated. This leads to the result that the effective diffusivity is decreased by a factor 3 when temperature is increased from 9·8–64·0°C.     

Determination of the diffusion coefficients of organic solvents in polyepichlorohydrin: A comparative study of inverse gas chromatography and sorption methods

The diffusivity of organic solvents in polyepichlorohydrin was studied with two different experimental setups: inverse gas chromatography (IGC) with packed columns and sorption measurements in gravimetric experiments monitored in a Cahn electrobalance. The aim of this work was to test the possibility of solving an inherent problem in the data reduction of IGC measurements, that is, the necessity of characterizing the morphology of the polymer coated on the support (usually given in the so‐called geometric factor of the column). Temperatures between 35 and 65°C were used in the IGC experiments, whereas the sorption measurements were performed between 30 and 40°C. Glass beads were used as supports in IGC for obtaining data concerning the variation of the plate height with the average gas velocity, with which the use of the Van Deemter equation allowed the determination of the diffusion coefficient if the geometric factor was known. In the sorption experiments, the diffusion coefficients at different penetrant activities were directly measured. For their extrapolation within the same concentration range used for IGC (infinite dilution of the penetrant), the theoretical model of Vrentas and Duda was used. By a combination of sorption and IGC experiments, the geometric factor of an IGC column could be adjusted, and this allowed the determination of the diffusion parameters of any other solvent in the same column. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 2216–2223, 2003     

WATER ADSORPTION AND DRYING CHARACTERISTICS OF OKRA Hibiscus Esculentus L

ABSTRACT

Moisture adsorption characteristics of okra were evaluated at 10, 20, 30° C. Isotherms were found to be of type III. Monolayer moisture contents were evaluated with GAB model. Drying was carried out at 60, 70, 80° C and drying data were analysed to obtain diffusivity values from the period of first felling drying rate. Effective diffusivity increased with increasing temperature. Calculated values of the effective diffusivity showed an Arrhenius type temperature dependence.     

Membrane distillation for propanone removal from aqueous streams

The use of air‐gap membrane distillation for the selective removal of propanone from aqueous solutions was tested. The effect of the following operating conditions upon flux and selectivity was experimentally examined: feed concentration, feed flow rate, feed temperature, and coolant temperature. Although the PVDF membranes tested performed well at the propanone feed concentrations encountered in fermentation processes, they demonstrated wetting limitations at higher concentrations. Within the feed temperature range of 40–70 °C, and propanone concentration up to 6 wt%, propanone selectivities of 2–6 were achieved. A mathematical model of the process was developed and validated. © 2000 Society of Chemical Industry