Evaluation of K⊖ from [η]-M-data of binary and ternary polymer systems

Unperturbed dimensions of flexible linear macromolecules can be obtained from [η]-M-data in any solvent, good or poor, single or mixed. Usually K_θ is estimated by a relationship between [η]/M_W^0.5 and M_w^0.5 first proposed by Burchard and by Stockmayer and Fixman. But, it is well-known that the Burchard-Stockmayer-Fixman-plot shows downward curvature, especially for good solvent systems. Various efforts have been made to achieve relations with better linearity. One of the first was the semi-empirical relation between ([η]/M_w^0.5)^0.5 and M_w/[η] by Berry. Predicting a relationship of the excluded volume parameter z to the viscosity expansion factor by α⁵_η instead of α⁵_η Tanaka obtains that ([η]/M_w^0.5)^5/3 is linear in M_w^0.5. By allowing for the dependence of the viscometric interaction parameter B, which is correlated to the second virial coefficient A₂, on molar mass, Gavara, Campos and Figueruelo predict a linear dependence of [η]/M_w^0.5 against A₂.M_w^0.5. It is not our intention here to discuss the validity of these theories, but to compare them with experimental data.     

Complex Formation and Ionic Association in Methanol Solutions of Poly(Ethylene Oxide) and Alkaline Earth Salts

Complex formation of poly(ethylene oxide) (PEO) with divalent barium and strontium salts was investigated in methanol. In these systems the complexation was accompanied by a considerable degree of ionic association. An analytical model for the polymer-ion complexation based on a one-dimensional lattice model was proposed. According to this model, the electrostatic effects between the bound ions were separated from the total free energy change of the binding. Three binding constants, i.e., the ionic association constant K _A, the cation binding constant, K _c, and the anion binding constant, K _a, could be estimated. K _A for barium and strontium salts was comparable, and the effect of counteranions on K _A was not large. K _c for barium salts was almost independent of the kind of counteranion and larger than that for corresponding strontium salts, indicating stronger polymer-ion interaction for barium salts. The anion binding constant, K _a, was strongly dependent upon the kind of anion, and the order was CI^? ? ? 4 ^?. The pronounced ion binding for larger anions may be explained by the more favorable free energy change of desolvation. Finally, the concentration of free and bound ionic species was determined as a function of PEO concentration.     

TiO2和Mg-Fe型类水滑石特征电离/络合平衡常数研究

The intrinsic surface reaction constants, pKa1^int, pKa2^int, p^＊KC^int and p^＊KA^int , were evaluated by a modifieddouble extrapolation （MDE） for TiO2 without structural charge and Mg-Fe hydrotalcite-like compounds （HTlc） with structural charge, respectively. The results of intrinsic surface reaction constants for TiO2 were compared with those obtained by class double extrapolation （CDE） in literature. Furthermore, the values of intrinsic surface reaction constants obtained by MDE were used to simulate the charging behaviors of the materials. The following conclusions were obtained. For TiO2 without structural charge, the pKa1^int and pKa2^int evaluated by MDE are equal to those by CDE, however the p^＊KC^int and p^＊KA^int evaluated by MDE are much different from those by CDE. In principle, the results of the p^＊KC^int and p^＊KA^int evaluated by MDE are more accurate than those by CDE. The values of intrinsic surface reaction constants obtained by MDE can excellently simulate the charging curves for TiO2 with the triple layer model （TLM）. For HTlc with positive structural charge, the results of ^＊KC^int=0 and ^＊KA^int →∞ were obtained by MDE, which means the inert electrolyte chemical binding does not exist; the point of zero net charge （PZNC） of c-independence also exist as the same as solid without structural charge, and the PHPZNC obtained by the acid-base titration can excellently be simulated and the surface charging tendency can be simulated to a great extent using the pKa1^int and pKa2^int evaluated by MDE and the diffuse layer model （DLM）.     

Non-newtonian behavior of polymers with log-normal molecular weight distribution

By choosing suitable approximations to Bueche's function, it is possible to calculate the viscosity versus shear stress for log-normal molecularly distributed linear polymers. For bulk polymers the mixing rules M?_w, M?_w, M?_z are considered. For values of η/η0 > 0.1 and heterogeneities with M?_w/M?_n > 1.5 the result obtained with any mixing rule is η/η0 = erfc [(1/delta;) log (M₀Q^h/aK)], where a = π²/6_pRT and where the δ and K values are dependent on the heterogeneity ratio Q = M?_w/M?_n and on the type of mixing rule; on the other hand, the h value is independent of the heterogeneity, but depends on the mixing rule. Most experimental data should fit the M?_w mixing rule as one would expect from the zero shear stress mixing rule. Experimental data are compared with the theoretical results.     

Activity Coefficient Determinations of KCl in the KCl + Formamide + Water Mixed Solvent System Based on Potentiometric Measurements at 298.2 K

In this work mean activity coefficient measurements for KCl in the KCl + formamide + water system, using the potentiometric method, are reported. The electromotive force measurements were performed on a galvanic cell of the type Ag | AgCl | KCl (m), formamide (w%), H₂O (1−w)% | K-ISE, in solvent mixtures containing w=(0,10,20,30, and 40)% mass percent of formamide over ionic strengths ranging from 0.0010 to 3.9578 mol⋅kg⁻¹. Modeling of the activity coefficients of this ternary system was based on an extended Debye–Hückel equation and the Pitzer ion-interaction model. The resulting values of the mean activity coefficients, the osmotic coefficients and the excess Gibbs energy, together with Pitzer ion-interaction parameters (β ⁽⁰⁾, β ⁽¹⁾ and C ^ϕ ) and Debye–Hückel parameters (a, c and d), are reported for the investigated system.     

Osmotic Coefficients of Aqueous Solutions of Some Poly(oxyethylene) Glycols at the Freezing Point of Solution

Summary. The freezing temperatures of dilute aqueous solutions of some poly(oxyethylene) glycols (PEG, HO–(CH₂CH₂O) _n –H, n varying from 4 to 117) were measured over a solute to solvent mass ratio from 0.0100 to 0.3900. The second and third osmotic virial coefficient (A ₂₂ and A ₂₂₂) of poly(oxyethylene) glycols in aqueous solution were determined. The molecular weight dependence of the second virial coefficient can be described by a simple relation A ₂₂=2×10^–5 M _n ^1.86, and the third virial coefficient is A ₂₂₂=0.038A ₂₂ ². The activity coefficients of the solute were calculated using the Gibbs-Duhem equation as applied by Bjerrum. From the osmotic and activity coefficients the excess Gibbs energies of solution, as well as the respective partial molar functions of solute and solvent and the virial pair interaction coefficients for the excess Gibbs energies were estimated. The second and the third osmotic virial coefficients are correlated with the Mc-Millan-Mayer virial coefficients.     

IONIC STRENGTH EFFECTS ON THE GROUND STATE COMPLEXATION and TRIPLET STATE ELECTRON TRANSFER REACTION BETWEEN ROSE BENGAL and METHYL VIOLOGEN

Abstract— The equilibrium constants, K_c, for complexation between methyl viologen dication (MV²+) and Rose Bengal, or Eosin Y, decrease with increasing ionic strength. At zero ionic strength K_c is 6500 (± 500) mol^?1 dm³ for Rose Bengal and 3200 (± 200) mol^?1 dm³ for Eosin Y, and these values decrease to 1500 (± 100) and 680 (± 40) mol^?1 dm³, respectively, at an ionic strength of 0.1 mol dm^?3. K_c is independent of pH between 4.5 and 10. ΔH is -25 (± 1) kJ mol^?1 for complexation with either dye, whereas ΔS is -15 (± 3) J K^?1 mol^?1 for Rose Bengal, and - 23 (± 3) J K^?1 mol^?1 for Eosin Y. The complexation constant for Rose Bengal and the neutral viologen, 4,4'-bipyridinium-N, N'-di(propylsulphonate), (4,4'-BPS), is 420 (± 35) mol^?1 dm³, and independent of ionic strength. No complexation could be observed for either Rose Bengal or Eosin with another neutral viologen, 2,2'-bipyridinium-N,N'-di(propylsulphonate), (2,2'-BPS). MV²+ quenches the triplet state of Rose Bengal with a rate constant of 7 × 10⁹ mol^?1 dm³ s^?1, and this rate constant decreases slightly as ionic strength increases. The cage escape yield following quenching, Φ_cc is very low (Φ_cc= 0.02 (± 0.005), and independent of ionic strength. 4,4'-BPS quenches the triplet state of Rose Bengal with a rate constant of 2.2 (± 0.1) × 10⁹ mol^?1 dm³ s^?1, and gives a cage escape yield of 0.033 (± 0.006). 2,2'-BPS quenches the Rose Bengal triplet with a rate constant of 6 (± 1) × 10⁸ mol^?1 dm³ s^?1 and gives a cage escape yield of 0.07 (± 0.01). Conductivity measurements indicate that MV²+(Cl^?)₂ is completely dissociated at concentrations below 2 × 10^?2 mol dm^?3.     

Osmotic Coefficients of Aqueous Solutions of Some Poly(oxyethylene) Glycols at the Freezing Point of Solution

The freezing temperatures of dilute aqueous solutions of some poly(oxyethylene) glycols (PEG, HO–(CH₂CH₂O) _n –H, n varying from 4 to 117) were measured over a solute to solvent mass ratio from 0.0100 to 0.3900. The second and third osmotic virial coefficient (A ₂₂ and A ₂₂₂) of poly(oxyethylene) glycols in aqueous solution were determined. The molecular weight dependence of the second virial coefficient can be described by a simple relation A ₂₂=2×10^–5 M _n ^1.86, and the third virial coefficient is A ₂₂₂=0.038A ₂₂ ². The activity coefficients of the solute were calculated using the Gibbs-Duhem equation as applied by Bjerrum. From the osmotic and activity coefficients the excess Gibbs energies of solution, as well as the respective partial molar functions of solute and solvent and the virial pair interaction coefficients for the excess Gibbs energies were estimated. The second and the third osmotic virial coefficients are correlated with the Mc-Millan-Mayer virial coefficients.     

Application of the Bjerrum Association Model to Electrolyte Solutions. IV. Apparent Molar Heat Capacities and Compressibilities in Water and Aprotic Solvents

The Bjerrum association model, which has already been applied successfully to volumes and enthalpies of dilution of electrolyte solutions, has now been extended to apparent molar heat capacities and compressibilities of these systems. The proposed method of calculation, which takes into account the relaxation effect observed in second derivatives of the excess Gibbs free energy, can be used to extrapolate to infinite dilution the experimental data for systems showing a wide range of association constants in acetonitrile, propylene carbonate, and water. The concentration dependence of the thermodynamic properties can be reproduced quantitatively by the addition of one or two virial coefficients. Literature data for C _P,2, and K _S,2, of electrolytes in aprotic solvents were refitted with this equation. For dissociated or slightly associated systems (K _A < 10), the standarY ₂ ^o d infinite dilution quantities () are in excellent agreement with literature values. For systems with high K _A, Y ₂ ^o obtained by the model are systematically lower than those reported in the literature. This is not surprising, since the traditional method of extrapolation using the Debye–Hückel limiting law or the Pitzer equation does not take association into account. A computer software that performs the calculations for the application of the Bjerrum model to thermodynamic properties has been designed and is presented in the appendix.     

Ion association and solvation behavior of some alkali metal acetates in aqueous 2-butanol solutions at T = 298.15, 303.15 and 308.15 K

Molar conductance of lithium acetate, sodium acetate and potassium acetate were studied in aqueous 2-butanol solutions with an alcohol mass fraction (w₂) of 0.70, 0.80 and 0.90 at 298.15, 303.15 and 308.15 K. The conductance data were analyzed with the Fuoss conductance-concentration equation to evaluate the limiting molar conductances (Λ₀), association constants (K_A,c) and cosphere diameter (R) for ion-pair formation. Gibbs energy (ΔG⁰), enthalpy (ΔH⁰) and entropy (ΔS⁰) for ion-association reaction were derived from the temperature dependence of K_A,c. Activation energy for ionic movement (ΔH^#) was derived from the temperature dependence of Λ₀. Based on the composition dependence of Walden products (Λ₀η₀) and different thermodynamic properties (ΔG⁰,ΔH⁰, ΔS⁰ and ΔH^#), the influence of the solvent composition on ion-association and solvation behavior of ions were discussed in terms of ion-solvent, ion-ion interactions and the structural changes in the mixed solvent media.     

Dilute solution properties of styrene–acrylonitrile and styrene–methyl methacrylate copolymers. II. Short-range and long-range interactions from intrinsic viscosity data

Experimental data on styrene–acrylonitrile (St–AN), and styrene–methyl methacrylate (St–MMA) copolymers reported in Part I of this series are tested by “two-parameter” theoretical relations. The Fox–Flory (F–F) parameter K is estimated using the F–F, Stockmayer–Fixman (S–F), and Inagaki–Ptitsyn (I–P) equations. In general, the K values obtained by the F–F equation are low for the three St–AN copolymer samples in the systems studied while the values obtained from S–F and I–P equations agree within the limits of experimental error. Values of K obtained from Kurata–Stockmayer (K–S) equation for sample SA₁ agree with values obtained by the S–F and I–P equations. The specific solvent effect on the K values is discussed. Values of the unperturbed dimension r?0²/M?_w, calculated from the K values estimated from the S–F equation and from the homopolymer data are compared. Except in one case, the calculated r?0²/M?_w values from homopolymer data are low in comparison with the values obtained from experimental data, which shows that the presence of the repulsive interactions between unlike monomer units brings about an expansion of copolymer molecule. The effect of composition on the steric factor σ values is discussed. The long-range interaction parameter B, the excess interaction parameters ΔB_AB, and χAB are calculated. The effects of composition and solvent on these parameters are discussed.     

Copper-indium ordering in RECu6In6 (RE=Y, Ce, Pr, Nd, Gd, Tb, Dy)

The rare earth metal-copper-indides RECu₆In₆ (RE=Y, Ce, Pr, Nd, Gd, Tb, Dy) were synthesized from the elements by arc-melting. Well-crystallized samples were obtained by slowly cooling the melted buttons from 1320 to 670 K in sealed silica tubes in a muffle furnace. They were investigated by X-ray diffraction on powders and single crystals: ThMn₁₂ type, space group I4/mmm, Z=2, a=916.3(2), c=535.8(2) pm, wR₂=0.063, 216 F² values, 15 variables for YCu₆In₆, a=926.5(4), c=543.5(3) pm, wR₂=0.064, 314 F² values, 15 variables for CeCu₆In₆, a=925.7(4), c=540.1(3) pm, wR₂=0.075, 219 F² values, 15 variables for PrCu₆In₆, a=923.1(4), c=540.3(3) pm, wR₂=0.071, 218 F² values, 15 variables for NdCu₆In₆, a=917.7(4), c=540.2(3) pm, wR₂=0.076, 207 F² values, 15 variables for GdCu₆In₆, a=917.0(5), c=540.5(4) pm, wR₂=0.062, 215 F² values, 15 variables for TbCu₆In₆, a=915.2(8), c=540.7(7) pm, wR₂=0.108, 218 F² values, 15 variables for DyCu₆In₆. The structures have been refined with a split position (50% Cu+50% In) for the 8j site. They can be explained by a tetragonal body-centered packing of CN 20 polyhedra (10Cu+10In) around the rare earth atoms. The ordering models of the copper and indium atoms and the limitations/resolution of X-ray diffraction for this topic are discussed.     

Crystal structure of K6CrNb15O42

K_6CrNb_(15)O_(42)crystallizes in the hexagonal system with a=9.126(3)A,c=12.068(3)A,V=870.4(5)A~3,and space group P6_2/mcm,Z=1.The structure was solved using direct method andFourier Techniques.Of the 829 unique reflections measured by counter techniques,448 with I≥3σ(I)were used in the least-squares refinement of the model to R=0.034(R_w=0.044).The structureof KoCrNb_(15)O_(42)may be described as consisting of corner-shared and edge-shared octahedra,the ringunits composed of six octahedra of Nb(1)are corner-shared one another along the c-axis to formhexagonal column octahedra chains which are connected by K~+ and octahedra of Nb(2).     

The x-ray crystal structure,resolution and absolute configuration of thecis-α-dichloro(1, 8-diamino-3, 6-diazaoctane)-ruthenium(III) cation

Summary Acis- configuration for the [RuCl₂(trien)]Cl·2H₂O (trien=1, 8-diamino-3, 6-diazaoctane) complex has been confirmed by an x-ray crystal structure determination. Crystals are monoclinic, space group P2₁/c witha=7.336 (1),b=8.477 (2),c=23.181 (4) Å, =103.3 (1)°, U=1403 (1) Å.³ Z=4 and M=389.7, D_c=1.84 g cm^–3. The structure was refined by full matrix least squares methods to final residual values of R=0.025 and R_w=0.033 on the basis of 3882 unique reflections. The complex has been resolved into its optical isomers using the (+)1, 2-diaminoethanebis(oxalato)cobaltate(III) anion and the absolute configuration assigned.     

On the interpretation of solubilization results obtained from semi-equilibrium dialysis experiments

The interpretation of intramicellar solubilization data obtained from semi-equilibrium dialysis (SED) experiments is described, and methods are presented for determining equilibrium constants for the solubilization of organic species by aqueous surfactant solutions as well as activity coefficients of both the organic solute and the surfactant within the micelle. The solubilization equilibrium constant of an organic solute in an aqueous micellar solution (K) is defined as the ratio of the mole fraction of organic solute in the micellar pseudophase (X) to the concentration of the unsolubilized monomeric organic solute in the aqueous phase (c ₀). Expressions compatible with the Gibbs-Duhem equation are used to represent the concentration dependence of activity coefficients of both the solubilizate and surfactant in the micellar pseudophase; the analysis leads to calculated values of the concentrations of free and intramicellar surfactant and organic solute in both compartments of the equilibrium dialysis cell. Solubilization equilibrium constants for many amphiphiles are well correlated by the simple expressionK=K ₀(1-BX)², whereB is an empirical constant andK ₀ is the limiting value ofK asX approaches 0.     

Solution properties of high molecular weight polystyrene

A series of polystyrenes with weight-average molecular weight M?_w up to 1.3 × 10⁷ was prepared by anionic polymerization in tetrahydrofuran (THF). Each sample was characterized by gel-permeation chromatography, light scattering, and viscometry. It was found that each sample had an almost symmetrical and very narrow molecular weight distribution (M?_w/M?_n < 1.07). The mean-square unperturbed radius of gyration 〈S²〉₀ was determined in trans-decalin at 20.4°C as 〈S²〉₀ = 7.8₆ × 10^?18M?_w (cm²). The particle scattering factor was well represented by the Debye equation irrespective of solvent in the range of M?_w < 4 × 10⁶, and only a small deviation was observed in benzene at higher molecular weights. The penetration function Ψ ≡ A₂M²/4π^3/2N_A〈S〉^23/2 was found to approach a relatively low asymptotic value of 0.21–0.23 at molecular weights above 2 × 10⁶ in benzene at 30°C, where A₂ is the second virial coefficient and N_A is Avogrado's number. It was also found that the theta temperature in trans-decalin was affected by the nature of polymer samples. A difference of about 3°C in the theta temperature was observed between two series of anionic polystyrenes, one prepared in THF and the other in benzene, but there was practically no difference in unperturbed chain dimension.     

Synthesis, Structure, and 31P NMR of Sulfur/Oxygen-Bridged Incomplete Cubane-Type Molybdenum and Tungsten Clusters with Triphenylphosphine Ligands

Sulfur/oxygen-bridged incomplete cubane-type triphenylphosphine molybdenum and tungsten-clusters [Mo₃S₄Cl₄(H₂O)₂(PPh₃)₃]·3THF (1A), [Mo₃S₄Cl₄(H₂O)₂(PPh₃)₃]·2THF (2A), [Mo₃OS₃Cl₄(H₂O)₂(PPh₃)₃]·2THF (1B), and [W₃S₄Cl₄(H₂O)₂(PPh₃)₃]·2THF (1C) were prepared from the corresponding aqua clusters and PPh₃ in THF/MeOH. On recrystallization from THF, procedures with and without addition of hexane to the solution gave 1A and 2A, respectively, while the procedures gave no effect on the formation of 1B and 1C. Crystallographic results obtained are as follows: 1A: monoclinic, P2₁/n, a=17.141(4) Å, b=22.579(5) Å, c=19.069(4) Å, =96.18(2)°, V=7337(3) ų, Z=4, R(R _w)=0.078(0.102); 1C: monoclinic, P2 ₁/c, a=12.635(1) Å, b=20.216(4) Å, c=27.815(3) Å, =96.16(1)°, V=7062(2) ų, Z=4, R(R _w)=0.071(0.083). If the phenyl groups are ignored, the molecule [Mo₃S₄Cl₄(H₂O)₂(PPh₃)₃] in 2A has idealized CS symmetry with the mirror plane perpendicular to the plane determined by the metal atoms, while the molecule in 1A does not have the symmetry. The tungsten compound 1C is isomorphous with the molybdenum compound 2A. ³¹P NMR spectra of 1A, 2A, and 1C were obtained and compared with similar clusters with dmpe (1,2-bis(dimethylphosphino)ethane) ligands.     

Crystal Structure Investigation of RE–Ni–Zn Ternary Compounds (RE = La,Ce, Tb)

The RENiZn (RE = La, Tb), RE₂Ni₂Zn (RE = La, Ce, Tb) and La₃Ni₃Zn ternary compounds were synthesized by two methods: by heating in a resistance furnace evacuated quartz ampoules containing Al₂O₃‐crucibles with element pieces and by induction melting in sealed Ta crucibles with subsequent annealing at 400 °C. Scanning electron microscopy (SEM) coupled with energy dispersive X‐ray spectroscopy (EDXS) was used for examining microstructure and phase composition of some of the alloys. The crystal structures for all the investigated phases were solved or confirmed on single crystal data by applying the direct methods refined by a standard least square procedure: LaNiZn – str. type ZrNiAl, hexagonal, , hP9, a = 0.7285(1), c = 0.3938(1) nm, wR₂ = 0.0534, 257 F² values, 14 variables; a = 0.7044(1), c = 0.3782(1) nm, wR₂ = 0.0447, 236 F² values, 14 variables for TbNiZn; La₂Ni₂Zn – str. type Pr₂Ni₂Al, orthorhombic, Immm, oI10, a = 0.4381(1), b = 0.5459(1) c = 0.8605(2) nm, wR₂ = 0.0824, 223 F² values, 13 variables; a = 0.4365(1), b = 0.5430(1) c = 0.8279(2) nm, wR₂ = 0.0635, 209 F² values, 13 variables for Ce₂Ni₂Zn; a = 0.4209(1), b = 0.5366(1) c = 0.8165 (1) nm, wR₂ = 0.0757, 200 F² values, 13 variables for Tb₂Ni₂Zn; La₃Ni₃Zn – str. type Y₃Co₃Ga, orthorhombic, Cmcm, oS28, a = 0.4276(1), b = 1.0310(2) c = 1.3636(3) nm, wR₂ = 0.0859, 579 F² values, 26 variables. The structural peculiarities of these compounds and their relations are discussed.     

Standard potential of the Ag-AgCl electrode and acidity constant of glycine at constant molality of NaCl in glucose-water mixed solvents from 278.15 to 318.15 K

Standard electrode potentials E° of Ag-AgC1 electrode in molality scale and acidityconstants of glyeine pK_1° at constant molality of NaCl (1.0 mol·kg~(-1)) in 5 and 15 mass%glucose-water mixed solvents over a range of temperatures from 278.15 to 318.15 K weredetermined from precise emf measurements.The dependence of acidity constant on temperatureis given as a function of the thermodynamic temperature T by an empirical equation, pK_1°=A_1(K/T)-A_2+A_3(T/K).The corresponding thermodynamic quantities of the first dissociationprocess of glycine were calculated and the effects of both tho solvent and the salt on themwere also discussed.     

Activity Coefficient Determination for the Ternary Systems CsCl in N-Methylformamide or Urea + Water Mixtures at T = 298.15 K

The mean activity coefficients for CsCl in N-methylformamide or urea (w) + H₂O (1 ? w) systems were determined in this work by potentiometry, using ion-selective electrodes at 298.15 K. The value of mass fraction w was varied between 0.00 and 0.40 in five unit-steps and the molality of CsCl was between 0.0020 and 1.4009 mol·kg^?1. The experimental data have been correlated with the Pitzer, modified Pitzer and the extended Debye–Hückel equations. The resulting values of the mean activity coefficients, the osmotic coefficients and the standard Gibbs energy of transfer, together with the Pitzer ion-interaction parameters (β ⁽⁰⁾, β ⁽¹⁾ and C ^φ), extended Debye–Hückel parameters (a, c and d), and modified Pitzer parameters (b, B _MX, C _MX) are reported for the investigated systems.