Pair Interaction Parameters Research Articles

Mixed adsorption and surface tension prediction of nonideal ternary surfactant systems

To deal with the mixed adsorption of nonideal ternary surfactant systems, the regular solution approximation for nonideal binary surfactant systems is extended and a pseudo-binary system treatment is also proposed. With both treatments, the compositions of the mixed monolayer and the solution concentrations required to produce given surface tensions can be predicted based only on the γ-LogC curves of individual surfactants and the pair interaction parameters. Conversely, the surface tensions of solutions with different bulk compositions can be predicted by the surface tension equations for mixed surfactant systems. Two ternary systems: SDS/Hyamine 1622/AEO7, composed of homogeneous surfactants, and AES/DPCl/AEO9, composed of commercial surfactants, in the presence of excess NaCl, are examined for the applicability of the two treatments. The results show that, in general, the pseudo-binary system treatment gives better prediction than the extended regular solution approximation, and the applicability of the latter to typical anionic/cationic/nonionic nonideal ternary surfactant systems seems to depend on the combined interaction parameter, \( {\mathop {(\beta }\nolimits_{an}^s } + {\mathop \beta \nolimits_{cn}^s })/2 - {\mathop \beta \nolimits_{ac}^s }/4 \): the more it deviates from zero, the larger the prediction difference. If \( {\mathop {(\beta }\nolimits_{an}^s } + {\mathop \beta \nolimits_{cn}^s })/2 - {\mathop \beta \nolimits_{ac}^s }/4 \)→0, good agreements between predicted and experimental results can be obtained and both treatments, though differently derived, are interrelated and tend to be equivalent.

Thermodynamic characterization of ternary solutions of uncharged polymers

The thermodynamic interactions in aqueous solutions of uncharged polymers were studied. Using a gel-deswelling method, the water activities (chemical potentials) in binary and ternary (two polymers in one solvent) solutions of methylcellulose (MC), polyvinyl alcohol (PVA) and polyvinyl pirrolidone (PVP), respectively were determined at various polymer volume fractions (1.0 × 10 −2 < v 2 < 1.0 × 10 −1). On the theoretical basis of the Flory–Huggins approximations, the relevant solvent–segment ( χ 12 or χ 13) and segment–segment pair interaction parameters ( χ 23) have been calculated. The solvent activity curves (ln a 1 versus polymer volume fraction) can be well described by a polynomial of third-degree in both the binary and the ternary solutions of the polymers. The solvent–segment interaction parameters exhibit a slight dependence on the polymer concentration. For each binary solution, the χ 12− v 2 function can be fitted by a straight line wich has a small positive slope. In the mixtures of two polymers, the values of the segment–segment ( χ 23) interaction parameters were close to zero or sligthly negative ( χ 23 ∼0 ± 0.03), indicating that under the studied conditions, the polymers in the ternary solutions are compatible.

Nature and origin of lamellar magnetism in the hematite-ilmenite series

Grains consisting of finely exsolved members of the hematite-ilmenite solid-solution series, such as are present in some slowly cooled middle Proterozoic igneous and metamorphic rocks, impart unusually strong and stable remanent magnetization. TEM analysis shows multiple generations of ilmenite and hematite exsolution lamellae, with lamellar widths ranging from millimeters to nanometers. Rock-magnetic experiments suggest remanence is thermally locked to the antiferromagnetism of the hematite component of the intergrowths, yet is stronger than can be explained by canted antiferromagnetic (CAF) hematite or coexisting paramagnetic (PM) Fe-Ti-ordered ( R 3) ilmenite alone. In alternating field demagnetization to 100 mT, many samples lose little remanence, indicating that the NRM is stable over billions of years. This feature has implications for understanding magnetism of deep rocks on Earth, or on planets like Mars that no longer have a magnetic field. Atomic-scale simulations of an R 3 ilmenite lamella in a CAF hematite host, based on empirical cation-cation and spin-spin pair interaction parameters, show that contacts of the lamella are occupied by “contact layers” with a hybrid composition of Fe ions intermediate between Fe2+-rich layers in ilmenite and Fe3+-rich layers in hematite. Structural configurations dictate that each lamella has two contact layers magnetically in phase with each other, and out of phase with the magnetic moment of an odd non-self-canceling Fe3+-rich layer in the hematite host. The two contact layers and the odd hematite layer form a magnetic substructure with opposite but unequal magnetic moments: a lamellar “ferrimagnetism” made possible by the exsolution. Because it is confined to magnetic interaction involving the moments of just three ionic layers associated with each individual exsolution lamella, lamellar magnetism is unique and quite distinct from conventional ferrimagnetism. Simulation cells indicate that the magnetic moments of contact layers are locked to the magnetic moments of adjacent AF hematite layers and are parallel to the basal plane (001). Thus, lamellar magnetism is created at the temperature of chemical exsolution, and is a chemical remanent, rather than thermal remanent, magnetization. However, in thermal demagnetization experiments, too short for lamellar resorption, demagnetization temperatures are those of the CAF hematite, considerably higher than temperatures of original lamellae formation. Internal crystal structure cannot dictate that the contact layers of different lamellae will form magnetically in phase with each other to give the highest net magnetic moment, but magnetic moments of lamellae can be made to form in phase by the external force of the magnetizing field at the time of exsolution. A thesis of this paper is that an external magnetic field can dictate the magnetic moments and hence the chemical location of ilmenite lamellae in a hematite host, and that once in place, neither the location nor the magnetic moment will be easily disturbed. In an ilmenite host, the external magnetic field cannot control the chemical location of a hematite lamella, which is dictated by the enclosing ilmenite, but once lamellae have formed, the field can dictate their magnetic moments. These moments, however, are not locked chemically to the host, resulting in lower coercivity. The effectiveness of the external force in single crystals is dictated by their orientation with respect to the magnetizing field. In grains with (001) oriented parallel to the field, it would be effective in producing in-phase magnetic moments and very strong remanence. In grains with (001) normal to the field, the field would be less effective in producing in-phase magnetic moments, hence producing weak remanence. The most intense lamellar magnetism per formula unit occurs with in-phase magnetization, high lamellar yields, and the largest number of lamellae per unit volume (i.e., smallest lamellar size). Compared to the magnetic moment per formula unit ( M pfu) and magnetic moment per unit volume ( M V) of end-member magnetite ( M pfu = 4 μB, M V = 480 kA/m) and hematite ( M pfu = 0.0115 μB, M V = 2.1 kA/m), results for some atomic models reasonably tied to natural conditions are M pfu = 0.46–1.36 μB and M V = 84–250 kA/m.

Studies of Activity Coefficients for Ternary Systems: Water + 18-Crown-6 + Alkali Chlorides at 298.15 K

Osmotic vapor pressure measurements have been carried out for three ternary systems, H2O + 0.2 m 18-crown-6 + LiCl, H2O + 0.2 m 18-crown-6 + NaCl and H2O + 0.2 m 18-crown-6 + KCl at 298.15 K using vapor pressure osmometry. Water activities for each ternary system were measured and used to calculate the activity coefficients of 18-crown-6 (18C6) and its salts following the methodology developed by Robinson and Stokes for isopiestic measurements. In the concentration range studied, it was found that (in NaCl and KCl solutions) there is considerable lowering of activity coefficients of one component in the presence of other solutes that has been attributed to the formation of the complexed 18C6:Na+ (or 18C6:K+) species in solution. The Gibbs energies of transfer of alkali chlorides from water to aqueous 18C6 solutions and that of 18C6 from water to aqueous electrolyte solutions have been calculated. These were further used to evaluate the pair and triplet interaction parameters. The calculation of thermodynamic equilibrium constants using the pair interaction parameter, gNE (i.e., the nonelectrolyte–electrolyte pair interaction) for the studied complexation of cations yields values which are in good agreement with those reported in literature obtained by using ion-selective potentiometry and calorimetry. The results are discussed in terms of water structural effects, complex formation, and hydrophobic interactions.

Microscopic Protonation Equilibria of Poly(amidoamine) Dendrimers from Macroscopic Titrations

Poly(amidoamine) (PAMAM) dendrimers of generations G0, G1, G2, G3, G4, and G6 are investigated by potentiometric (acid−base) titrations. The data are interpreted with a site binding model, which offers the possibility to model the titration curves for all generations of the dendrimers and to describe all dendrimers within a common parameter set. These parameters involve the microscopic ionization constants for each group in the fully deprotonated state and nearest-neighbor pair interaction parameters. From this model we can further obtain all microscopic ionization constants as well as conditional microstate probabilities. The protonation of PAMAM dendrimers first involves protonation of primary amine groups at the outer rim of the dendrimer at high pH, while the tertiary amine groups in the dendrimer core protonate at lower pH. The last group to protonate at low pH is a central tertiary amine.

Phase state diagrams of the poly(dimethylsiloxane)—poly(diethylsiloxane) system

Phase equilibria in the poly(dimethylsiloxane)(PDMS)—polydiethylsiloxane (PDES) system in the amorphous and liquid-crystal states were studied by optical interferometry. The findings obtained were compared with the data of calorimetric measurements. The experiments were carried out in a wide range of molecular weights and temperatures, and the phase diagrams were constructed. Thermodynamic analysis of the experimental data was performed in the framework of the Flory—Haggins theory for polymeric solutions. The analytical expressions for calculation of the pair interaction parameter using the binodal and liquidus curves were obtained. The pair interaction parameters of polymers and their dependences on the temperature and molecular weight were determined. The pair interaction parameter was shown to decrease with increasing the molecular weight of the oligomer component, approaching asymptotically a limiting value, which characterizes the interaction of the high molecular-weight PDMS and PDES. It was shown that the phase equilibria in the PDMS—PDES systems can be predicted quantitatively and qualitatively.

Thermodynamic parameters of the interaction of CsCl with monosaccharide ( d-glucose, d-galactose, d-xylose, and d-arabinose) in water at [formula omitted

A non-liquid-junction electrochemical cell composed of a potassium ion selective electrode(K-ISE) against a chloride ion selective electrode (Cl-ISE) as a reference electrode was employed to study the thermodynamic parameters of weak interactions between aqueous cesium chloride and the monosaccharides ( d-glucose, d-galactose, d-xylose, and d-arabinose) at T=298.15 K . Activity coefficients for this system obtained from electromotive force measurements indicate that they have a close relationship with the stereostructure of the saccharide. The Gibbs free energy pair interaction parameters and salting constants were also evaluated; these can characterize the interaction between the saccharides and CsCl in water. The results were interpreted on the basis of a model of structural and electrostatic interaction and the hydration effect of the hydroxyl ion of these saccharides.

The enthalpy and entropy interaction parameters of cesium chloride with saccharides ( d-glucose, d-fructose and sucrose) in water at 298.15 K

The transfer enthalpies have been measured for cesium chloride from pure water to aqueous saccharides ( d-glucose, d-fructose and sucrose) solutions at 298.15 K. The McMillan–Mayer theory was employed to relate the excess thermodynamic function with a series of interaction parameters of solutes to obtain the enthalpy pair interaction parameters of cesium chloride with saccharides in water. Entropy interaction parameters can be evaluated through the enthalpy interaction parameters and the Gibbs free energy parameters. These parameters are discussed in detail to provide some information for the interaction of solute–solute and solute–solvent in CsCl–saccharide–water ternary system, and to investigate the influence of the size of metal ions and the number of hydroxyl in saccharides on these parameters.

Interactions of HCl with 1-Butanol and Group Additivity Analysis for the HCl–Alcohol Interactions

An electromotive force (emf) method was used to determine thermodynamic parameters of interaction of HCl with normal 1-butanol (n-BuOH) in water between 5 and 45°C. A comparison of pair interaction parameters for HCl–n-BuOH with those for HCl–t-BuOH (tert butyl alcohol) showed that there is an obvious difference between them. This was interpreted in terms of steric structure of their carbon chains. The group Gibbs free energy parameters (\(G_{HCl} - {CH}_{2} \) and \(G_{HCl} - {OH} \)) for the HCl–alcohol–water systems were derived according to the Savage–Wood group additivity principle. These group parameters can be used to evaluate pair interaction parameters of HCl with alcohol molecules.

Short-range order in Ni-8.4 at.% Au above the miscibility gap

The elastic diffuse neutron scattering was measured for a Ni-8.4 at.% Au single crystal above the miscibility gap at 1083 K. The Ni-58 isotope was used to reduce the incoherent scattering. In contrast to previous x-ray investigations, short-range order scattering reflects local atomic arrangements characteristic of decomposition. This can be uniequivocally concluded from the diffuse scattering within the first Brillouin zone. For larger scattering vectors, the diffuse scattering is dominated by the displacement scattering due to the large difference in atomic sizes. The magnitudes of the extracted Warren-Cowley short-range order parameters show a smooth decrease with increasing distance. Crystals modeled on the basis of these parameters reveal basic arrangements of small Au clusters consisting of a tetrahedron and an attached fifth Au atom. The effective pair interaction parameters obtained from an inverse Monte Carlo analysis give no hint for a metastable state with ${L1}_{2}$ structure.

Streptavidin Tetramerization and 2D Crystallization: A Mean-Field Approach

A mean-field theoretical approach is applied to streptavidin tetramerization and two-dimensional (2D) crystallization. This theory includes, in particular, solvent–residue interactions following the inhomogeneous Flory–Huggins model for polymers. It also takes into account residue–residue interactions by using tabulated pair interaction parameters. This theory allows one to explicitly calculate the entropy of the inhomogeneous system. We show that hydrophobic interactions are responsible for the stability of tetramerization. Within the present theory, the equilibrium distance between the two dimers is the same as that determined experimentally. The free energy of tetramerization (i.e., dissociation of the two dimers) is 50 k B T. Unlike tetramerization, hydrophobic interactions alone are not sufficient to stabilize the 2D crystal C 222 , but solvent-mediated residue–residue interactions give the most important contribution.

Synthesis and Protonation Behavior of Carboxylate-Functionalized Poly(propyleneimine) Dendrimers

Five generations of carboxylate-functionalized poly(propyleneimine) dendrimers have been synthesized starting from a double Michael addition of amine-functionalized poly(propyleneimine) dendrimers to methyl acrylate followed by basic hydrolysis using LiOH in a water/methanol mixture. The dendritic compounds have been characterized using 1H NMR, 13C NMR, IR, and ESI−MS spectroscopy. Subsequently, the protonation behavior of these potential complexing agents is studied with potentiometric titrations in 0.1 and 1.0 M KCl solutions. The carboxylate-functionalized dendrimers show a characteristic onionlike shell protonation behavior. The titration curves for different ionic strengths cross at pH 8.5 which is exactly after protonation of the outermost shell of amines (θ ∼ 0.25). This crossing point is found not to be identical to the point of zero charge θ ∼ 0.5, which is observed at pH 4.5. The Ising model was used to rationalize the complete set of titration data simultaneously for five generations with only one microscopic pK value for each additional shell and a set of three nearest neighbor pair interaction parameters.

Determination of Vapor Liquid Equilibrium from the Kovats Retention Index on Dimethylsilicone using the Wilson Mixing Model

Non-ideal mixing in a dimethylsilicone stationary phase is modeled according to the Wilson activity coefficient. Pure liquid vapor pressures of alkylated compound series are calculated from capillary GLC retention with the functional group heat of solution in a polymer solvent. The new method uses the Kovats index, molar mass, and functional group to determine the bubble line of a compound. Boiling points at reduced and normal pressure are compared to literature values of 194 gasoline components. An unlike molecular pair interaction parameter is derived, using only bubble line data of the pure liquids. Binary phase diagrams are constructed and compared to vapor liquid equilibrium data.

Partial molar volumes of some α-amino acids in aqueous sodium acetate solutions at 308.15 K

The apparent molar volumes V 2,φ have been determined for glycine, dl-α-alanine, dl-α-amino-n-butyric acid, dl-valine and dl-leucine in aqueous solutions of 0.5, 1.0, 1.5 and 2.0 mol kg −1 sodium acetate by density measurements at 308.15 K. These data have been used to derive the infinite dilution apparent molar volumes V 0 2,φ for the amino acids in aqueous sodium acetate solutions and the standard volumes of transfer, Δ t V 0, of the amino acids from water to aqueous sodium acetate solutions. It has been observed that both V 0 2,φ and Δ t V 0 vary linearly with increasing number of carbon atoms in the alkyl chain of the amino acids. These linear correlations have been utilized to estimate the contributions of the charged end groups (NH 3 +,COO −), CH 2 group and other alkyl chains of the amino acids to V 0 2,φ and Δ t V 0. The results show that V 0 2,φ values for (NH 3 +,COO −) groups increase with sodium acetate concentration, and those for CH 2 are almost constant over the studied sodium acetate concentration range. The transfer volume increases and the hydration number of the amino acids decreases with increasing electrolyte concentrations. These facts indicate that strong interactions occur between the ions of sodium acetate and the charged centers of the amino acids. The volumetric interaction parameters of the amino acids with sodium acetate were calculated in water. The pair interaction parameters are found to be positive and decreased with increasing alkyl chain length of the amino acids, suggesting that sodium acetate has a stronger dehydration effect on amino acids which have longer hydrophobic alkyl chains. These phenomena are discussed by means of the cosphere overlap model.

Surface modification strategies for multicomponent polymer systems,VI:acid–base interactions as a strategy for interfacial modification in immiscible polymer blends

Three copolymers with different emulsification efficacies were used as potential interface modifiers for an immiscible blend of linear low density polyethylene (LLDPE) and poly(vinyl)chloride (PVC). The specific interaction between blend components and the modifying copolymers was determined by measurements of interfacial tension and by inverse gas chromatographic (IGC) data, characterizing the acid–base properties of the polymers. Additional information on modifier effectiveness was obtained from blend morphology data. Acid–base pair interaction parameters, computed from IGC results, predicted the modifying potential of the two copolymers which emulsified the system, and were consistent with the morphology and interfacial tension results. IGC, however, did not distinguish between the emulsification qualities of the two good modifiers. The best of the three modifiers (P4VP-PIP) also increased the impact strength of the modified LLDPE/PVC system. The results indicate that specific (acid–base) interactions at component interfaces may represent a promising strategy for the choice of emulsifying agents for some immiscible polymer blends.

The type of order in Cu–10 at.% Au—evidence from the diffuse scattering of X-rays

In a recent publication, Kuhlmann et al. ( Acta mater., 1997, 45, 3319) claimed Cu–10 at.% Au to be long-range ordered at temperatures above 473 K and as high as 723 K. This is in contrast to the generally accepted phase diagram where this region is attributed to the range of solid solutions. To clarify this problem, a three-dimensional diffuse X-ray scattering experiment was performed at room temperature on a Cu–10 at.% Au single crystal aged at 573 K. The Warren–Cowley short-range order parameters derived from this experiment show conclusively that only short-range order is present. Effective pair interaction parameters determined by the inverse Monte-Carlo method are somewhat different from those obtained for Cu–25 at.% Au in the short-range ordered state.

Predicting liquid–liquid transitions in polymer solutions using the GCLF equation of state

Group contribution lattice fluid equation of state (GCLF-EOS) have been extended and used to calculate phase equilibria in polymer solutions. Group parameters for three group contributions and nine new group contributions have been calculated. Saturation vapor pressure for pure solvent and weight fraction activity coefficients in polymer solutions have been calculated and the agreement obtained with experimental data indicated the accuracy of the parameters. A combining rule consisting a pair interaction parameter with temperature dependency was proposed. The area method was used with GCLF-EOS to obtain phase diagram for liquid equilibrium (LLE) of polymer solutions. The method was able to predict both lower critical solution temperature (LCST) and upper critical solution temperature (UCST).

Diffusion on a honeycomb lattice: Real-space renormalization-group approach

A two-dimensional lattice-gas model with honeycomb symmetry is investigated by using the real-space renormalization group (RSRG) approach with a number of RSRG transformations based on clusters of different symmetries and sizes (up to 42 sites). The accuracy of calculations is found to be a nonmonotonic function of the size of a cluster, and to depend strongly on its symmetry. The highest obtained accuracy with respect to the determination of the critical value of the pair interaction parameter is 0.38%. The phase diagram of the Ising antiferromagnetic spin model and of the corresponding lattice-gas model is constructed with this accuracy. The ordered phase in the lattice system is shown to appear in the very narrow density interval, $0.447lnl0.553.$ In addition, the coverage dependence of the chemical diffusion coefficient and mean-square density fluctuations are studied at temperatures below the critical one. Both quantities are demonstrated to exhibit singularities at the critical coverages. The type of singularities (in particular, the critical slowdown of diffusion) is in agreement with the predictions of the scaling theory and also with recent results obtained for a model treating the effect of surface reconstruction on diffusion.

Thermodynamics of the interaction of HCl with D-galactose in water at 278.15–318.15 K

Thermodynamic parameters of the interaction of HCl with D-galactose in water have been determined from electromotive force measurements at 10 K intervals from 278.15 to 318.15 K. Standard Gibbs energies of transfer of HCl from water to aqueous solutions of 5, 10, 15 wt.% D-galactose were evaluated. Comparison of pair interaction parameters of HCl–D-galactose was made with those of HCl–D-glucose and HCl–D-arabinose. The difference between these parameters was interpreted in terms of the stereochemistry of these monosaccharides. An enthalpy–entropy compensation has been observed with the pair interaction parameters for the HCl–sugar–water systems at each given temperature studied. The salting constants, kS, of D-galactose, D-glucose, D-fructose, D-arabinose, and sucrose by HCl in water were calculated from (a) the Debye–MacAulay theory (DMT); (b) Conway–Desnoyers–Smith theory (CDST); (c) the internal pressure theory developed by McDevit–Long (IPT); (d) the scaled particle theory (SPT). The results show that the calculated values of kS are reasonably in agreement with the experimental ones.

Mechanism of “Order-Order” Kinetics in Ll2 Superstructure Studied by Computer Simulation

ABSTRACTMonte Carlo simulations of the isothermal long-range order (LRO) relaxation in A3B system with Ll2 superstructure have been performed within a model based on a vacancy jump mechanism between nearest neighbour lattice sites. The studies aimed at the explanation of the origin of two simultaneous LRO relaxation processes experimentally observed in Ni3Al. An effect of pair interaction energies and saddle-point energies (assigned to jumping atoms) was studied. The preference of vacancies for the A-sublattice (face centres), commonly postulated for Ni3Al, occurred only for a narrow range of pair-interaction energies within the domain corresponding to Ll2 ordering. It was found that the appearance of the fast relaxation process is definitely correlated with the efficiency of B-atom jumps, as well as with the values of the saddle-point energies. The results lead to a microscopic model of the “order-order” relaxation in Ll2 superstructure and yield new indications for the choice of pair-interaction energy parameters applied in Monte Carlo simulations of atomic migration in Ll2 intermetallic compounds.