Calculated Interaction Parameters Research Articles

Removal of chlorinated volatile organic contaminants from water by pervaporation using a novel polyurethane urea–poly (methyl methacrylate) interpenetrating network membrane

Polymer membranes are potentially selective for separation of organic compounds from a mixture by pervaporation. A novel crosslinked hydroxyterminated polybutadiene based (HTPB) polyurethane urea (PUU)–poly (methyl methacrylate) (PMMA) interpenetrating network (IPN) membrane has been developed for the selective removal of chlorinated volatile organic compounds (VOCs) such as 1 , 1 , 2 , 2 -tetrachloroethane, chloroform, carbon tetrachloride, trichloroethylene present in water in very low concentration by pervaporation. IPNs of different PMMA content and also different crosslink density were used. Since the selective permeation and diffusion of the VOCs through the membrane are dependent on their interaction with the membrane material, their sorption and diffusion behaviors through the membrane were also investigated by swelling the membrane in pure VOCs. The sorption and diffusion behaviors were explained with the help of their solubility parameter data and calculated interaction parameter data of the membrane polymers with the VOCs. From the swelling kinetics data, diffusion coefficients of the VOCs through the membrane were calculated. Diffusion coefficients increased with the increase in crosslink density and PMMA content in the membrane. In pervaporation experiment, concentrations of chlorinated organic compounds in feed were varied from 100 ppm (0.01%) to 1000 ppm (0.1%). All the three IPN membranes showed excellent separation performances of the chlorinated VOCs from water. One IPN containing 26% PMMA (PUU–PMMA-3) produced 88.7% trichloroethylene in permeate, 0.2 kg / m 2 h trichloroethylene flux and a separation factor of 7842 from a 0.1% aqueous feed after a pervaporation run of 3 h at 30 ∘ C . All the three IPN membranes of different compositions have shown the separation performances, viz., flux and separation factor for all the VOCs in the order 1 , 1 , 2 , 2 - tetrachloroethane < carbon tetrachloride < chloroform < trichloroethylene .

Mathematical calculation of binodal curves of a polymer/solvent/nonsolvent system in the phase inversion process

Four methods of calculating Flory–Huggins interaction parameters from solubility parameters were examined by comparing calculated binodal curves with experimental data. This is a promising method to calculate interaction parameters from solubility parameters because of the wide use of solubility parameters. The fitting results were satisfactory after the optimization of the correction constant according to the membrane casting systems mentioned. The optimized correction constants were 0.09 and 1.01 for the polymer/solvent and polymer/nonsolvent, respectively. The constants were obtained from PES/solvent and PSF/solvent systems and checked with PSF/DMAc/nonsolvent systems. Calculation was carried out, based on Flory–Huggins solution theory, to analyze the behavior of the polymer/solvent/nonsolvent system phase diagram with the influence of parameter sets in a wide range. It was found that with the increment of solvent/polymer interaction parameters or nonsolvent/polymer interaction parameters the miscibility gaps decreased. However, the miscibility gaps increased with the increment of nonsolvent/solvent interaction parameters.

Modeling of the phase equilibria of polystyrene in methylcyclohexane with semi-empirical quantum mechanical methods I

A method for calculating interaction parameters traditionally used in phase-equilibrium computations in low-molecular systems has been extended for the prediction of solvent activities of aromatic polymer solutions (polystyrene+methylcyclohexane). Using ethyl-benzene as a model compound for the repeating unit of the polymer, the intermolecular interaction energies between the solvent molecule and the polymer were simulated. The semiempirical quantum mechanical method AMI, and a method for sampling relevant internal orientations for a pair of molecules developed previously were used. Interaction energies are determined for three molecular pairs, the solvent and the model molecule, two solvent molecules and two model mole-cules, and used to calculated UNIQUAC interaction parameters, a ij and a ji. Using these parameters, the solvent activities of the polystyrene 90,000 amu+methylcyclohexane system, and the total vapor pressures of the methyl-cyclohexane+ethylbenzene system were calculated. The latter system was compared to experimental data, giving qualitative agreement.

The interaction between polymer and AOT or NaDEHP in aqueous solution: mesoscopic simulation study and surface tension measurement

The interaction of polyvinylpyrrolidone (PVP) with sodium bis(2-ethylhexyl) sulfosuccinate (AOT) and sodium bis(2-ethylhexyl) phosphate (NaDEHP) in the solution was investigated by dissipative particle dynamics (DPD) simulation. The calculated interaction parameters between PVP and AOT or NaDEHP showed that AOT is in favor to form polymer–surfactant complex with PVP in contrast to NaDEHP. The experiment of surface tension measurement proved the computational results. In DPD simulation, the mean square end-to-end distance 〈 r 2〉 of polymer chain firstly increases in size, then reduces and increases again. And some polymer–surfactant complexes were also shown. One conclusion is that mesoscopic simulation can be considered as an adjunct to experiment and provide other valuable information for the experiment.

Modeling of the phase equilibria of polystyrene in methylcyclohexane with semi-empirical quantum mechanical methods I.

A method for calculating interaction parameters traditionally used in phase-equilibrium computations in low-molecular systems has been extended for the prediction of solvent activities of aromatic polymer solutions (polystyrene+methylcyclohexane). Using ethylbenzene as a model compound for the repeating unit of the polymer, the intermolecular interaction energies between the solvent molecule and the polymer were simulated. The semiempirical quantum chemical method AM1, and a method for sampling relevant internal orientations for a pair of molecules developed previously were used. Interaction energies are determined for three molecular pairs, the solvent and the model molecule, two solvent molecules and two model molecules, and used to calculated UNIQUAC interaction parameters, a(ij) and a(ji). Using these parameters, the solvent activities of the polystyrene 90,000 amu+methylcyclohexane system, and the total vapor pressures of the methylcyclohexane+ethylbenzene system were calculated. The latter system was compared to experimental data, giving qualitative agreement. Figure Solvent activities for the methylcylcohexane(1)+polystyrene(2) system at 316 K. Parameters aij (blue line) obtained with the AM1 method; parameters aij (pink line) from VLE data for the ethylbenzene+methylcyclohexane system. The abscissa is the polymer weight fraction defined as y2(x1)=(1mx1)M2/[x1M1+(1mx1)M2], where x1 is the solvent mole fraction and Mi are the molecular weights of the components.

Mesoscopic simulation study on the interaction between polymer and C 12 NBr or C 9 phNBr in aqueous solution

The interaction of partially hydrolyzed polyacrylamide (HPAM) with dodecyl-oxypropyl-β-hydroxyl trimethyl-ammonium bromide (C12NBr) and nonyl-phenyl-oxypropyl-β-hydroxyl trimethyl-ammonium bromide (C9phNBr) in the solution was investigated by the Dissipative Particle Dynamics (DPD) method. The calculated interaction parameters between HPAM and C12NBr or C9phNBr showed that C12NBr is most likely to form polymer/surfactant complex with HPAM in contrast to C9phNBr. The experiment of binding isotherm was used to validate the DPD results via surfactant-selective electrode and equilibrium dialysis method. In DPD method, the mean square end-to-end distance of polymer chain firstly increased, then reduced, and finally increased again. In addition, some polymer/surfactant complexes were also shown. One conclusion is that mesoscopic simulation can be considered as an adjunct to experiments and provide otherwise inaccessible (or not easily accessible) information in the experiment.

A new theory for polymer/solvent mixtures based on hard-sphere limit

Based on hard-sphere limit of binary mixtures with different molecular size of components a theory has been developed for calculating activities of solvents in polymer/solvent mixtures. The theory considers various chain configurations for polymer molecules, varying from extended chain to the coiled chain. According to this theory the activity of solvent can be calculated from molecular weights (MWs) and densities as the only input data. The only adjustable parameter in the calculations, is the hard-sphere diameter of polymer, which provides useful criteria for the judgement on the chain configuration of polymer. The activity calculations have been performed for seven binary mixtures of polymer/solvent and compared with experimental data at various temperatures and for a varying range of MWs of polymers. The solvents in the mixtures were both of polar and nonpolar natures. The activity calculations for the same systems were performed by the well-known Flory–Huggins theory. Comparing the results of calculations with those of Flory–Huggins theory indicates that, the proposed theory is able to predict the activities of the solvent with good accuracy. The radius of gyration, excluded volume and interaction parameter for polymer chain have been calculated using the parameter obtained in the new theory. The calculated interaction parameter in the new theory, is interpreted in terms of attraction, repulsion and interchange energy of polymer and solvent in the mixture.

Investigations on the predictability of the formation of glassy solid solutions of drugs in sugar alcohols

A prerequisite for the formation of glassy solid solutions prepared by the melting method is the miscibility of the respective drug and the carrier in the molten state. As could be shown experimentally, all investigated drug/sugar alcohol combinations miscible in the molten state form to some extent glassy solid solutions, dependent on their tendency to recrystallize during preparation. Therefore, the present study focuses on the evaluation of factors that govern the miscibility of molten drugs and sugar alcohols as carriers. In this context, solubility parameters are discussed as a means of predicting miscibility in comparison to a new approach, using calculated interaction parameters derived from molecular dynamics (MD) studies. There is evidence that a Coulomb interaction term C SR, comprising short-range electrostatic interactions and hydrogen bonding energy is essential for the miscibility of drug and carrier in the molten state. To relate C SR to the molecular volume, a non-dimensional parameter P i is defined. For this parameter, a limiting value for miscibility exists. Contrary, calculated solubility parameter differences between drug and sugar alcohol in the range of 8–15 MPa 1/2 are not suitable for a prediction of miscibility or immiscibility, since the mixtures deviate from regular solution behavior. In irregular mixtures of drugs and sugar alcohols, an excess entropy and the formation of hydrogen bonds between unlike molecules favor miscibility, that cannot be predicted by regular solution theory.

Molecular simulation studies on the interaction between different polymers in aqueous solution

A molecular dynamics simulation was performed to investigate the aggregates of mixing and the interaction between different polymers in aqueous solution. These polymers include partially hydrolyzed polyacryamide (HPAM), hydroxyethylcellulose (HEC) and polyvinylpyrrolidone (PVP). The structures of mixed aggregates were analyzed from the dihedral angle distribution of: (1) pure HPAM; (2) HPAM in aqueous solution; (3) HPAM with small segments of PVP or HEC in aqueous solution. At the same time, the simulated IR spectra and the calculated interaction parameters were used to distinguish the different interactions between HPAM and PVP or HEC. In order to confirm the validity of the simulated predictions, experimental IR spectra of polymer systems were made, and the specific viscosity of the HPAM and PVP or HEC system was measured using capillary viscometry. It can be seen from the viscosity measurements that the viscosity of the HPAM/PVP system in aqueous solution decreases linearly with an increase in concentration of PVP, whereas a maximum viscosity value appears with the increase in concentration of HEC in the HPAM/HEC system. The conclusion was drawn that the interaction between HPAM and HEC is stronger than the one between HPAM and PVP, and that molecular simulation can be considered as an adjunct to experiments and can provide otherwise inaccessible (or, not easily accessible) microscopic information that experimentalists can use.

Mixed monolayer and mixed micelle formation in binary mixture of surfactants—Systems for trioxyethylenated dodecyl sulfonate and some polyoxyethylenated fatty alcohol ether nonionic surfactants

AbstractThe interaction and synergism of some polyoxyethylenated fatty alcohol ether (POE) nonionic surfactants (C12E2, C12E3, C10E5, C10E7, where Cx indicates number of carbon atoms in the chain and Ey indicates number of oxyethylene glycol ethers) with trioxyethylenated dodecyl sulfonate (C12E3S) in mixed monolayer formation at the surface and in mixed micelle formation in aqueous solutions were studied at 25 and 40°C by calculating interaction parameters (βα, βM) from surface tension‐concentration data by use of Rosen's equations based on the nonideal solution theory. All the systems investigated adapt reasonably well to the nonideal model, with negative values of βσ and βM (where M means micelle and σ refers to the air‐liquid interface) indicating a favorable interaction between the mixed surfactants. Either at a monolayer or in a mixed micelle, the attractive interaction becomes stronger when the alkyl chain in the POE surfactant is longer, i.e., when the POE becomes more hydrophobic. The interaction increases in the order C10E7&lt;C10E5&lt;C12E3, C12E2. For the two C10En (n= 5,7)/C12E3S systems, as temperature increases from 25 to 40°C, the interaction increases in a mixed micelle, but it decreases in a mixed monolayer. Synergism in mixed micelle formation exists for C12E3S/C10En mixtures when X1M, the mole fraction of POE in a mixed micelle, is ≈0.4–0.8, whereas synergism does not occur in the systems of C12E3S/C12Em due to the large difference between CMC1 and CMC2, i.e., large |In(C1M/C2M)| value (where CMC=critical micelle concentration). The degree of synergism in mixed micelle formation is temperature independent and is 0.23, 0.18, and close to zero for C10E5/C12E3S, C10E7/C12E3S, and C12Em(m=2,3)/C12E3S systems, respectively. Synergism in surface tension reduction effectiveness occurs in C12E3S/C12E2 and C12E3S/C12E3 systems. The mole fractions of POE in the solution phase are 0.302 and 0.333 for the two mixtures at the point of maximum synergism.

The determination of interaction parameters in the characterization of polyetherimide gas separation membranes using the Horvath-Kawazoe model

The Horvath-Kawazoe (HK) model is widely used to characterize microporous carbons and zeolites. The use of the HK model in this application has been extensively studied and interaction parameters exist to relate gas adsorption isotherms to the microporosity of these materials. However, interaction parameters for the HK model do not exist for polymeric materials, which limits its use in characterizing such systems. In this work, the HK parameters for the nitrogen-polyetherimide system were determined from molecular properties and computational chemistry. The interaction energy coefficients required to calculate interaction parameters in the HK model were determined from the polarizability and diamagnetic susceptibility of PEI using the Kirkwood-Muller equations. The parameters were used in the HK method to model a nitrogen adsorption isotherm at 77.2°K and determine the micropore size distribution of a PEI gas separation membrane. The relation between the differential heat of adsorption and pore size distribution, which is the basis of the HK model, was studied for nitrogen adsorption on PEI using different interaction parameters and estimates of the diameter of the PEI chain. The influences of these parameters on the calculated pore size distribution were discussed. The validity of the pore size distribution was examined by comparing the dominant pore size with the d-spacing obtained from X-ray diffraction on PEI. Good agreement was obtained between these values on using a suitable structural model that represents the wall thickness of the adsorbent and includes the polar property of PEI in determining HK parameters.

Theoretical predictions of unstable two-phase regions in wurtzite group-III-nitride-based ternary and quaternary material systems using modified valence force field model

Group-III (B, Al, Ga, and In)-nitride quaternary alloys and group-III (Al, Ga, and In)-nitride-based mixed anion (As, P, and Sb) quaternary alloys are useful for blue and green light emitting devices and high-temperature, high-power, and high-frequency electronic devices. It is known that these alloys are very difficult to grow in certain compositional regions. The thermodynamical stability of these alloys is studied with respect to an unstable two-phase region in the phase field. The unstable two-phase region is predicted based on a strictly regular solution model. The interaction parameter used in our model is obtained analytically using the valence force field (VFF) model modified for wurtzite structures. The calculated interaction parameters, which are required to predict the unstable two-phase region, agree well with experimental results for related alloy systems. The modified VFF model can also be used to predict the microscopic crystal structure, such as first neighbor anion–cation bond lengths. In order to verify our calculations, we compare the calculated and experimental results for the first neighbor anion–cation bond lengths in the InGaN system. The calculated results agree well with the experimental results. From our calculation results, the unstable two-phase regions for four A1−x−yBxCyD type group-III-nitride quaternary alloys and nine A1−xBxC1−yDy type group-III-nitride mixed anion quaternary alloys are calculated. The predicted unstable two-phase regions agree well with experimentally observed regions of phase separation in ternary alloys, which suggests our model calculations can provide useful guidance in ternary and quaternary systems where there is no experimental data.

Analysis of phase-separation region in wurtzite group III nitride quaternary material system using modified valence force field model

The group III (B, Al, Ga, In) nitride quaternary alloy systems are potentially useful for ultraviolet, blue, and green light-emitting devices, or high-temperature, high-power, and high-frequency electronic devices. There have been significant challenges to the epitaxial growth of these alloys and we have investigated the unstable mixing region in the phase field. The existence of an unstable mixing region is predicted based on a strictly regular solution model. The interaction parameter used in our model is analytically obtained by the valence force field model modified for wurtzite structures. From our calculations, among the group III nitride quaternary alloy systems, we find that InGaAlN system has the narrowest unstable mixing region, and that the BInAlN system has the widest unstable mixing region. The calculated interaction parameters which are the important to predict the unstable mixing region agree well with the best-fit line of experimental results for various alloy systems.

Modeling of the phase equilibria of polyisobutylene in diisobutylketone with molecular mechanics

A method of calculating interaction parameters used in phase equilibrium calculations has been extended for predicting solvent activities of polymer solutions. A pair of interaction parameters are determined by calculating interaction energies between all pairs of molecules in the solution of interest with a molecular mechanics method known as the consistent force field (CFF). The conformational space of a pair of molecules is sampled with a Monte Carlo algorithm followed by energy minimizations. In this paper, the method is used to calculate interaction parameters and solvent activities for the diisobutylketone/polyisobutylene system, using 2,2,4-trimethylpentane as a model compound for the polymer molecule.

Diffusion and partitioning of humic acid in a porous ultrafiltration membrane

Surface imaging of wet polysulfone (PM30) ultrafiltration membranes with atomic force microscopy indicates a relatively smooth but porous surface in the aqueous environment. The average pore radius was 9.7±0.8 nm, and the average porosity was 10%. Therefore, for the case of adsorption of humic acid on the membrane (J. Membr. Sci. 97 (1994) 37–52), we hypothesize here that the transport of humic materials in the membrane can be modeled as one-dimensional diffusion and linear partitioning in a porous medium. An interaction parameter was developed using the model to characterize the strength of interaction between the humic acid and the membrane as a function of pH and calcium concentration. The mass of humic acid adsorbed and the calculated interaction parameter were found to increase with decreasing pH and increasing calcium concentration; hence, the strength of interaction between humic acid and membrane is now simply parameterized. The kinetics of adsorption of humic acid was also modeled, and fitted diffusion time scales showed that the humic acid diffusion coefficient increased with decreasing pH and increasing calcium concentration, which is consistent with a compaction of the humic molecule. These effects were also consistent with a previous study of humic acid diffusion coefficients in activated carbon (J. Colloid Interface Sci. 110 (1) (1986) 149–164).

Vapor-liquid equilibria of polymer solutions determined by molecular mechanics

A method of calculating interaction parameters used in phase equilibrium calculations was extended for predicting solvent activities of polymer solutions. A pair of interaction parameters are determined by calculating interaction energies between all pairs of molecules in the solution of interest with a molecular mechanics method called the consistent force field (CFF). The conformational space of a pair of molecules is sampled with a Monte Carlo algorithm followed by energy minimizations. The method is used to calculate solvent activities for the diethylketone/polypropylene system, giving results in good agreement with experimental values. In addition, solvent activities are predicted for the diethylketone/polyethylenesystem for which no experimental data are available. The method is fully predictive, as no fitting to experimental phase-equilibrium data is carried out.

Measurement and prediction of water activity in electrolyte solutions by a modified ASOG group contribution method

A set of new ionic type functional groups for the prediction of water activities ( a w) in aqueous solutions of electrolyte solutes using the ASOG group contribution method is proposed. Previously published experimental data on water activities, osmotic coefficients and freezing temperatures for binary solutions of electrolyte salts and water at different temperatures were used to calculate interaction parameters. With such parameters, values of a w for binary (14), ternary (28) and quaternary (3) systems, at different temperatures, were predicted and compared with experimental data. This data included both published and new data, measured with an electric hygrometer, for sodium nitrate (at 20°C) and potassium nitrate (at 20°C and 30°C). Calculated average relative deviations of a w predictions using the ASOG method were 0.21%, 0.28% and 0.20% respectively.

On the thermodynamic treatment of poly(vinylidene fluoride)/polystyrene blend under liquid—liquid phase separation conditions

This paper deals with experimental and theoretical investigations on the compatibility of binary of polymer blends in solution. The experimental phase boundary of a crystalline polymer such as poly(vinylidene fluoride) with polystyrene (an amorphous polymer) in dimethylformamide as solvent has been determined by size-exclusion chromatography at 25°C. The composition of the coexisting phases has been used to calculate interaction parameters by means of the Flory—Huggins-type function for the free energy of mixing, including composition dependence of the polymer-polymer interaction parameter and a first correction term denoted as ternary interaction parameter. The calculation of these parameters involves the solution of a system of equations that should be equal to the number of unknown parameters. Diverse approximations have been proposed in order to reduce the number of equations to be solved; they are mainly concerned with the composition dependence of both binary polymer-polymer and ternary interaction parameters and of their derivatives.

Control of the chromium-oxygen reaction in pure iron melts

en

VLE data and UNIFAC-parameters of binary mixtures with methylisocyanate

Vapor pressures of binary mixtures of methylisocyanate with hexane and benzene in the temperature range of −5°C to 200°C have been measured. There was no indication of thermal instability or polymerisation within that range. Based on the experimental VLB data, UNIFAC interaction parameters have been correlated for the new main group of isocyanate. The parameters allow good prediction of VLE from different binary systems composed of molecules with the same functional groups. In addition, literature data of binary mixtures were taken to calculate interaction parameters of chlorine-substituted aliphatic hydrocarbon-groups with the isocyanate group.