Phase Equilibrium and Optimization Tools: Application for Enhanced Structured Lipids for Foods

Solid-liquid phase equilibrium modeling of triacylglycerol mixtures is essential for lipids design. Considering the alpha polymorphism and liquid phase as ideal, the Margules 2-suffix excess Gibbs energy model with predictive binary parameter correlations describes the non ideal beta and beta` solid polymorphs. Solving by direct optimization of the Gibbs free energy enables one to predict from a bulk mixture composition the phases composition at a given temperature and thus the SFC curve, the melting profile and the Differential Scanning Calorimetry (DSC) curve that are related to end-user lipid properties. Phase diagram, SFC and DSC curve experimental data are qualitatively and quantitatively well predicted for the binary mixture 1,3-dipalmitoyl-2-oleoyl-sn-glycerol (POP) and 1,2,3-tripalmitoyl-sn-glycerol (PPP), the ternary mixture 1,3-dimyristoyl-2-palmitoyl-sn-glycerol (MPM), 1,2-distearoyl-3-oleoyl-sn-glycerol (SSO) and 1,2,3-trioleoyl-sn-glycerol (OOO), for palm oil and cocoa butter. Then, addition to palm oil of Medium-Long-Medium type structured lipids is evaluated, using caprylic acid as medium chain and long chain fatty acids (EPA-eicosapentaenoic acid, DHA-docosahexaenoic acid, gamma-linolenic-octadecatrienoic acid and AA-arachidonic acid), as sn-2 substitutes. EPA, DHA and AA increase the melting range on both the fusion and crystallization side. gamma-linolenic shifts the melting range upwards. This predictive tool is useful for the pre-screening of lipids matching desired properties set a priori.

Liquid-Liquid Equilibrium of Aqueous Two-Phase Systems Containing Some Synthetic Polyelectrolytes and Polyethylene Glycol

Experimental results are presented for the liquid-liquid equilibrium of aqueous two-phase systems containing a synthetic polyelectrolyte (polysodium acrylate, polysodium methacrylate, and polysodium ethylene sulfonate) and polyethylene glycol at (298.2 and 323.2) K. A total of 40 phase diagrams were obtained, comprising data both of the binodal curve (obtained through cloud-point measurements) and of equilibrium compositions. The influences of temperature, the nature of the polyelectrolyte monomer unit, and the chain length of both types of polymers are analyzed and discussed.

Effect of Charge Asymmetry on Adsorption and Phase Separation of Polyampholytes on Silica and Cellulose Surfaces

The relation between the properties of polyampholytes in aqueous solution and their adsorption behaviors on silica and cellulose surfaces was investigated. Four polyampholytes carrying different charge densities but with the same nominal ratio of positive to negative segments and two structurally similar polyelectrolytes (a polyacid and a polybase) were investigated by using quartz crystal microgravimetry using silica-coated and cellulose-coated quartz resonators. Time-resolved mass and rigidity (or viscoelasticity) of the adsorbed layer was determined from the shifts in frequency (Delta f) and energy dissipation (Delta D) of the respective resonator. Therefore, elucidation of the dynamics and extent of adsorption, as well as the conformational changes of the adsorbed macromolecules, were possible. The charge properties of the solid Surface played a crucial role in the adsorption of the studied polyampholytes, which was explained by the capability of the surface to polarize the polyampholyte at the interface. Under the same experimental conditions, the polyampholytes had a higher nominal charge density phase-separated near the interface, producing a soft, dissipative, and loosely bound layer. In the case of cellulose substrates, where adsorption was limited, electrostatic and polarization effects were concluded to be less significant.

Nickel adsorption in two Oxisols and an Alfisol as affected by pH, nature of the electrolyte, and ionic strength of soil solution

Background, aim, and scope The retention of potentially toxic metals in highly weathered soils can follow different pathways that variably affect their mobility and availability in the soil-water-plant system. This study aimed to evaluate the effects of pH, nature of electrolyte, and ionic strength of the solution on nickel (Ni) adsorption by two acric Oxisols and a less weathered Alfisol. Materials and methods The effect of pH on Ni adsorption was evaluated in surface and subsurface samples from a clayey textured Anionic `Rhodic` Acrudox ( RA), a sandy-clayey textured Anionic `Xantic` Acrudox (XA), and a heavy clayey textured Rhodic Kandiudalf (RK). All soil samples were equilibrated with the same concentration of Ni solution (5.0 mg L(-1)) and two electrolyte solutions (CaCl(2) or NaCl) with different ionic strengths (IS) (1.0, 0.1 and 0.01 mol L(-1)). The pH of each sample set varied from 3 to 10 in order to obtain sorption envelopes. Results and discussion Ni adsorption increased as the pH increased, reaching its maximum of nearly pH 6. The adsorption was highest in Alfisol, followed by RA and XA. Competition between Ni(2+) and Ca(2+) was higher than that between Ni(2+) and Na(+) in all soil samples, as shown by the higher percentage of Ni adsorption at pH 5. At pH values below the intersection point of the three ionic strength curves (zero point of salt effect), Ni adsorption was generally higher in the more concentrated solution (highest IS), probably due to the neutralization of positive charges of soil colloids by Cl(-) ions and consequent adsorption of Ni(2+). Above this point, Ni adsorption was higher in the more diluted solution (lowest ionic strength), due to the higher negative potential at the colloid surfaces and the lower ionic competition for exchange sites in soil colloids. Conclusions The effect of ionic strength was lower in the Oxisols than in the Alfisol. The main mechanism that controlled Ni adsorption in the soils was the ionic exchange, since the adsorption of ionic species varied according to the variation of pH values. The ionic competition revealed the importance of electrolyte composition and ionic strength on Ni adsorption in soils from the humid tropics. Recommendations and perspectives The presence of NaCl or CaCl(2) in different ionic strengths affects the availability of heavy metals in contaminated soils. Therefore, the study of heavy metal dynamics in highly weathered soils must consider this behavior, especially in soils with large amounts of acric components.

The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

A wavelet-based adaptive technique for adsorption problems involving steep gradients

A general, fast wavelet-based adaptive collocation method is formulated for heat and mass transfer problems involving a steep moving profile of the dependent variable. The technique of grid adaptation is based on sparse point representation (SPR). The method is applied and tested for the case of a gas–solid non-catalytic reaction in a porous solid at high Thiele modulus. Accurate and convergent steep profiles are obtained for Thiele modulus as large as 100 for the case of slab and found to match the analytical solution.

Computationally efficient solution techniques for adsorption problems involving steep gradients in bidisperse particles

A piecewise uniform fitted mesh method turns out to be sufficient for the solution of a surprisingly wide variety of singularly perturbed problems involving steep gradients. The technique is applied to a model of adsorption in bidisperse solids for which two fitted mesh techniques, a fitted-mesh finite difference method (FMFDM) and fitted mesh collocation method (FMCM) are presented. A combination (FMCMD) of FMCM and the DASSL integration package is found to be most effective in solving the problems. Numerical solutions (FMFDM and FMCMD) were found to match the analytical solution when the adsorption isotherm is linear, even under conditions involving steep gradients for which global collocation fails. In particular, FMCMD is highly efficient for macropore diffusion control or micropore diffusion control. These techniques are simple and there is no limit on the range of the parameters. The techniques can be applied to a variety of adsorption and desorption problems in bidisperse solids with non-linear isotherm and for arbitrary particle geometry.

Adsorption in mesopores: A molecular-continuum model with application to MCM-41

The classical model of surface layering followed by capillary condensation during adsorption in mesopores, is modified here by consideration of the adsorbate solid interaction potential. The new theory accurately predicts the capillary coexistence curve as well as pore criticality, matching that predicted by density functional theory. The model also satisfactorily predicts the isotherm for nitrogen adsorption at 77.4 K on MCM-41 material of various pore sizes, synthesized and characterized in our laboratory, including the multilayer region, using only data on the variation of condensation pressures with pore diameter. The results indicate a minimum mesopore diameter for the surface layering model to hold as 14.1 Å, below which size micropore filling must occur, and a minimum pore diameter for mechanical stability of the hemispherical meniscus during desorption as 34.2 Å. For pores in-between these two sizes reversible condensation is predicted to occur, in accord with the experimental data for nitrogen adsorption on MCM-41 at 77.4 K.

Non-Equilibrium Reaction Rates in the Macroscopic Chemistry Method for DSMC Calculations

The Direct Simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of the reaction rate coefficient, nor is it restricted to a collision cross-section which yields a simple power-law viscosity. For reaction rates of interest in aerospace applications, chemically reacting collisions are generally infrequent events and, as such, local equilibrium conditions are established before a significant number of chemical reactions occur. Hence, the reaction rates which have been used in MCM have been calculated from the reaction rate data which are expected to be correct only for conditions of thermal equilibrium. Here we consider artificially high reaction rates so that the fraction of reacting collisions is not small and propose a simple method of estimating the rates of chemical reactions which can be used in the Macroscopic Chemistry Method in both equilibrium and non-equilibrium conditions. Two tests are presented: (1) The dissociation rates under conditions of thermal non-equilibrium are determined from a zero-dimensional Monte-Carlo sampling procedure which simulates ‘intra-modal’ non-equilibrium; that is, equilibrium distributions in each of the translational, rotational and vibrational modes but with different temperatures for each mode; (2) The 2-D hypersonic flow of molecular oxygen over a vertical plate at Mach 30 is calculated. In both cases the new method produces results in close agreement with those given by the standard TCE model in the same highly nonequilibrium conditions. We conclude that the general method of estimating the non-equilibrium reaction rate is a simple means by which information contained within non-equilibrium distribution functions predicted by the DSMC method can be included in the Macroscopic Chemistry Method.

Adsorption characteristics of carbonized bark for phenol and pentachlorophenol

The potential of using carbonized slash pine bark as a substitute for activated carbon was examined in this study. The bark was carbonized by slow heating in nitrogen for 6.5 h to 672 degrees C. The BET-N-2 surface area, average micropore and mesopore diameter, and micropore volume were 332 m(2) g(-1) 21.7 Angstrom, and 0.125 cm(3) g(-1), respectively. The adsorption capacities for phenol and pentachlorophenol (PCP) at pH 2 and pH 8 were evaluated. The Langmuir equation provided a slightly better fit than the Freundlich equation to two sets of phenol data. The calculated Freundlich constants, K = 0.41 - 0.58 mmol/g/(mmol dm(-3))(1/n) and 1/n = 0.30 - 0.41, were lower and higher, respectively, than literature values for activated carbons. The adsorption capacity of the carbonized bark was much lower for PCP than for phenol. The protonated and anionic PCP isotherms were Type II or III, respectively, in the Brunauer classification. The BET equation provided the best fit to protonated PCP isotherm data. The anionic PCP data were fitted to both the BET model and an equation used in the literature to represent phosphate adsorption on activated carbons. Nonlinear regression of the data for both phenol and PCP adsorption with the Freundlich, Langmuir and BET equations generally gave more accurate parameters, compared with the use of linearized equations to obtain the parameters. (C) 1998 SCI.

Modification of MCM-41 by surface silylation with trimethylchlorosilane and adsorption study

Siliceous MCM-41 samples were modified by silylation using trimethylchlorosilane (TMCS). The surface coverage of functional groups was studied systematically in this work. The role of surface silanol groups during modification was evaluated using techniques of FTIR and Si-29 CP/MAS NMR. Adsorption of water and benzene on samples of various hydrophobicities was measured and compared. It was found that the maximum degree of surface attachments of trimethylsilyl (TMS) groups was about 85%, corresponding to the density of TMS groups of 1.9 per nm(2). The degree of silylation is found to linearly increase with increasing pre-outgassing temperature prior to silylation. A few types of silanol groups exist on MCM-41 surfaces, among which both free and geminal ones are responsible for active silylation. Results of water adsorption show that aluminosilicate MCM-41 materials are more or less hydrophilic, giving a type IV isotherm, similar to that of nitrogen adsorption, whereas siliceous MCM-41 are hydrophobic, exhibiting a type V adsorption isotherm. The fully silylated Si-MCM-41 samples are more hydrophobic giving a type III adsorption isotherm. Benzene adsorption on all MCM-41 samples shows type IV isotherms regardless of the surface chemistry. Capillary condensation occurs at a higher relative pressure for the silylated MCM-41 than that for the unsilylated sample, though the pore diameter was found reduced markedly by silylation. This is thought attributed to the diffusion constriction posed by the attached TMS groups. The results show that the surface chemistry plays an important role in water adsorption, whereas benzene adsorption is predominantly determined by the pore geometry of MCM-41.

Capillary coexistence and criticality in mesopores: Modification of the Kelvin theory

The classical model of capillary equilibrium in cylindrical pores is modified here by the introduction of molecular concepts and the solid fluid interaction potential. The new approach accurately predicts capillary coexistence and criticality, with results quantitatively matching those from density functional theory for nitrogen adsorption, while also predicting condensation pressures in agreement with reported experimental findings for MCM-41. The larger critical pore size for nitrogen adsorption in these materials, however, suggests a modification of the potential function parameters, evaluated here from data for hydroxylated silica.

Analysis and application of an equilibrium model for in vitro bioassay systems with three components: Receptor, hormone and hormone-binding-protein

A simple theoretical framework is presented for bioassay studies using three component in vitro systems. An equilibrium model is used to derive equations useful for predicting changes in biological response after addition of hormone-binding-protein or as a consequence of increased hormone affinity. Sets of possible solutions for receptor occupancy and binding protein occupancy are found for typical values of receptor and binding protein affinity constants. Unique equilibrium solutions are dictated by the initial condition of total hormone concentration. According to the occupancy theory of drug action, increasing the affinity of a hormone for its receptor will result in a proportional increase in biological potency. However, the three component model predicts that the magnitude of increase in biological potency will be a small fraction of the proportional increase in affinity. With typical initial conditions a two-fold increase in hormone affinity for its receptor is predicted to result in only a 33% increase in biological response. Under the same conditions an Ii-fold increase in hormone affinity for receptor would be needed to produce a two-fold increase in biological potency. Some currently used bioassay systems may be unrecognized three component systems and gross errors in biopotency estimates will result if the effect of binding protein is not calculated. An algorithm derived from the three component model is used to predict changes in biological response after addition of binding protein to in vitro systems. The algorithm is tested by application to a published data set from an experimental study in an in vitro system (Lim et al., 1990, Endocrinology 127, 1287-1291). Predicted changes show good agreement (within 8%) with experimental observations. (C) 1998 Academic Press Limited.

Experimental and theoretical investigations of adsorption hysteresis and criticality in MCM-41: Studies with O-2, Ar, and CO2

MCM-41 materials of six different pore diameters were prepared and characterized using X-ray diffraction, transmission electron microscopy, helium pycnometry, small-angle neutron scattering, and gas adsorption (argon at 77.4 and 87.4 K, nitrogen and oxygen at 77.4 K, and carbon dioxide at 194.6 K). A recent molecular continuum model of the authors, previously used for adsorption of nitrogen at 77.4 K, was applied here for adsorption of argon, oxygen, and carbon dioxide. While model predictions of single-pore adsorption isotherms for argon and oxygen are in satisfactory agreement with experimental data, significant deviation was found for carbon dioxide, most likely due to its high quadrupole moment. Predictions of critical pore diameter, below which reversible condensation occurs: were possible by the model and found to be consistent with experimental estimates, for the adsorption of the various gases. On the other hand, existing models such as the Barrett-Joyner-Halenda (BJH), Saito-Foley, and Dubinin-Astakhov models were found to be inadequate, either predicting an incorrect pore diameter or not correlating the isotherms adequately. The wall structure of MCM-41 appears to be close to that of amorphous silica, as inferred from our skeletal density measurements.