Treating the polyelectrolytes as polymers with a draining effect. II. The behavior in the gel permeation chromatography

The behavior of the polyelectrolytes in the gel permeation chromatography (GPC) can be better understood if the modified universal calibration (log([η]M/Φ) vs. elution volume) is used instead of the “classical” universal calibration (log[η]M vs. elution volume). The value of Flory's parameter Φ is obtained from an equation established for nonionic polymers presenting a draining effect, considering that polyelectrolytes also behave as polymers with a draining effect. The modified universal calibration does not apply as successfully to polyelectrolytes as to nonionic polymers, because of their electrostatic exclusion in the pore surface of the GPC columns. Nevertheless, when polyelectrolytes are found in a high salt concentration solution, the modified universal calibration can be used to obtain their molecular mass, using nonionic hydrosoluble polymers as standard polymers. Moreover, considering polyelectrolytes as polymers presenting a draining effect and applying the modified universal calibration provides a better explanation for the electrostatic exclusion of these polymers from the pores of the GPC columns, using the Dubin–Tecklenburg model. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1106–1113, 2006     

Ionic association in acetonitrile and in formamide

In a recent derivation of relaxation effects in the Debye-Hückel-Onsager theory of electrolyte conductance, with a length parameter a, terms are included which have been omitted in earlier treatments (see Appendix). The new expression was applied earlier in a reanalysis of conductance data for aqueous solutions and is applied here to solutions in acetonitrile and in formamide, representing respectively dielectric constants considerably lower and higher than water. As in aqueous solutions, a minimum standard deviation is found over a wide range of (K _A,a) pairs without much effect on A ₀ , so that only approximate determinations ofK _A are possible. On the whole, the most appropriate length parametera is the physical contact distance between counterions, not a fixed radius, independent of ionic size, such as the Bjerrum value, nor a much larger radiusR serving as a boudary between free and associated ions in the ionic atmosphere about a central ion. Relaxation effects calculated by the new analysis are smaller than those from previous expressions for equal values ofa, and this leads to considerably larger values ofK _A than in the original papers. As a consequence, specific short-range ion-ion and ion-solvent forces in most solutions predominate over electrostatic attraction between counterions in their contribution toK _A. A table of limiting equivalent conductance based on the A ₀ values obtained is presented; this differs little from previous tables since A ₀ values obtained by the new analysis are similar to those obtained originally.     

Thermodynamic analysis of the phase separation during the polymerization of a thermoset system into a thermoplastic matrix. II. Prediction of the phase composition and the volume fraction of the dispersed phase

A thermodynamic simulation of the phase‐separation process of an off‐critical blend, based on a thermoplastic matrix with a reactive epoxy system undergoing polycondensation at a constant temperature, was performed. The model considered the composition dependence of the interaction parameter, χ(T,Φ₂) (where T is the temperature and Φ₂ is the volume fraction of polystyrene), along with the polydispersity of both polymers. For every level of conversion, the simulation provided the amount, composition, stoichiometric ratio, and conversion of each phase present. The accuracy of the model was proved by the good agreement between the experimental and predicted glass‐transition temperatures and heat capacity changes at the glass‐transition temperatures for both phases. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1361–1368, 2004     

Rheological properties of multisticker associative polyelectrolytes in semidilute aqueous solutions

Multisticker associative polyelectrolytes of acrylamide (≈86 mol %) and sodium 2‐acrylamido‐2‐methylpropanesulfonate (≈12 mol %), hydrophobically modified with N,N‐dihexylacrylamide groups (≈2 mol %), were prepared with a micellar radical polymerization technique. This process led to multiblock polymers in which the length of the hydrophobic blocks could be controlled through variations in the surfactant‐to‐hydrophobe molar ratio, that is, the number of hydrophobes per micelle (N_H). The rheological behavior of aqueous solutions of polymers with the same molecular weight and the same composition but with two different hydrophobic block lengths (N_H = 7 or 3 monomer units per block) was investigated as a function of the polymer concentration with steady‐flow, creep, and oscillatory experiments. The critical concentration at the onset of the viscosity enhancement decreased as the length of the hydrophobic segments in the polymers increased. Also, an increase in the N_H value significantly enhanced the thickening ability of the polymers and affected the structure of the transient network. In the semidilute unentangled regime, the behavior of the polymer with long hydrophobic segments (N_H = 7) was studied in detail. The results were well explained by the sticky Rouse theory of associative polymer dynamics. Finally, the viscosity decreased with an increase in the temperature, mainly because of a lowering of the sample relaxation time. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1640–1655, 2004     

Properties of vinylpyrrolidone-tert-butylphenyl methacrylate copolymers in solution

Copolymers of vinylpyrrolidone-p-tert-butylphenyl methacrylate (VP-MBPh) of several compositions were prepared by polymerization in benzene at 50°C using α′α′-azobisisobutyronitrile as initiator. Three of the copolymers were fractionated. Number-average molecular weights of fractionated samples were determined by osmotic pressure in benzene or 2-propanol. Kuhn–Mark–Houwink relations were established in benzene, chloroform, and 2-propanol. From the relation between M _n and the intrinsic viscosity (η), it appears that these random copolymers behave as predicted by the theory for flexible polymers. Abnormal viscometric behavior shown by one of the copolymers in nitromethane at 29°C (the theta temperature) is discussed. The Stockmayer–Fixman semiempirical method was used for estimating unperturbed dimensions from viscosity data obtained in chloroform, a good common solvent. Values of the viscosity parameter K_θ increase with the content of p-tert-butylphenyl methacrylate. In general, experimental K_θ values are higher than those calculated for the homopolymers. Excluded-volume parameters are estimated and discussed in relation to repulsive interactions between unlike monomer units.     

Ionic organic/inorganic materials. II. New linear and crosslinked poly(ethylene oxide)‐based ionomers by quaternization with chloroalkyl‐functionalized siloxanes

Siloxane‐modified cationic polyelectrolytes were synthesized through the quaternization reaction of a poly(ethylene glycol)‐based polymer containing tertiary amine groups in the chain with chloroalkyl‐functionalized siloxanes. Linear or crosslinked structures were obtained, depending on the functionality of the siloxane: a chloroalkyl‐monofunctionalized or ‐polyfunctionalized siloxane was used. The reaction occurred in solution with n‐propanol as a solvent and NaI as a catalyst. All products were characterized with elemental analysis and IR and ¹H NMR spectrometry. Viscometric measurements of the linear polymer in dilute aqueous solutions revealed typical polyelectrolyte behavior. The swelling capacities in various solvents of the crosslinked structures were determined. The thermal stability of the crosslinked cationic structures obtained with a polyfunctional siloxane as a quaternization agent was much higher than that of the parent polymer. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3720–3728, 2004     

Well‐defined polymers containing high density of pendant viologen groups

Atom transfer radical polymerization (ATRP) of a viologen‐containing methacrylate, 1‐propyl‐1′‐[2‐(methacryloyloxy)ethyl]‐4,4′‐bipyridinium dihexafluorophosphate, is reported. To achieve good polymerization control, it was essential to use the viologen‐based monomer with a hexafluorophosphate instead of halide counterion, and 2,2′‐bipyridine as the ligand for the Cu‐based ATRP catalyst. The solubility of produced cationic polymers could be tuned by anion metathesis: the polymers with hexafluorophosphate counterions were soluble in organic solvents (e.g., acetone, DMF), and those with chloride counterions were water‐soluble. In aqueous solutions, the polymers (chloride salts) formed large aggregates, the sizes of which ranged from about 200 to about 400 nm (based on dynamic light scattering measurements) depending on the molecular weight. Upon addition of electrolytes (e.g., NaCl), the aggregates underwent dissociation. The apparent diffusion coefficients of the aggregates existing in aqueous solutions and the products of their electrolyte‐induced dissociation were measured by diffusion‐ordered NMR spectroscopy. The association–dissociation processes were also studied by fluorescence spectroscopy: the aqueous polymer solutions, which were originally fluorescent (λ _em = 402 nm at λ _ex = 350 nm), lost their fluorescence in the presence of NaCl. The addition of small amounts of the viologen‐containing polyelectrolytes to solutions of inorganic salts (NaCl) altered the crystal morphology of the salts due to interaction of the multiple charged pendant groups with small ions. In the presence of reducing agents, the pendant viologen groups were converted to viologen radical‐cations, which are prone to dimerize reversibly in aqueous solutions. Indeed, marked dimerization of viologen radical cations (with absorbance maxima at 520 and 870 nm) was observed in relatively dilute aqueous solutions (4 mg mL^?1) upon addition of reducing agents (hydrazine). © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 55 , 1173–1182     

Solution properties of NR/PU block copolymers by size‐exclusion chromatography and viscometry

Soluble block copolymers based on natural rubber and polyurethane oligomers derived from 1,3 butane diol and toluene diisocyanate were synthesized for the first time. The dilute solution properties of these block copolymers dissolved in tetrahydrofuran (THF) were studied by viscometry and gel permeation chromatography (GPC). The Mark–Houwink constants K and a of the block copolymer system were determined by the molecular weight data from GPC combined with the viscosity data. Both the values were found to be in the range usually given by flexible elastomers. The intrinsic viscosity values were found to decrease successively with a decrease in the NCO/OH ratio from 1.12 to 1.05. The unperturbed chain parameters, K_θ and B were determined from the viscosity data. The K_θ calculated was used to get the unperturbed end‐to‐end distance and radius of gyration of the block copolymer systems in THF. The viscosity data were also used to study the chain conformation in dilute solutions. It was found that the molecules adopt a compressed core and shell conformation in which the higher molecular weight component, NR, forms the shell, which compresses the PU core. All the block copolymers assume a compressed segregated core and shell model which changes to a partially segregated core and shell conformation, or partially Gaussian conformation, at the transition temperature located at 70 °C. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2104–2111, 2006     

The effect of salts on the conformation and microstructure of poly(N‐isopropylacrylamide) (PNIPA) in aqueous solution

We present an experimental investigation of the conformation and microstructure of Poly(N‐isopropylacrylamide) (PNIPA) in aqueous solution in the presence of salts. As a model, a strong salting–out salt (Na₂SO₄) and a strong salting–in salt (NaSCN) were chosen. Light scattering measurements show that Na₂SO₄ decreases the radius of gyration of PNIPA compared to its value in water, whereas NaSCN increases it. Moreover, the NaSCN solution was found to be a better solvent for PNIPA compared to water, whereas Na₂SO₄ solution is worse. Small‐angle neutron scattering measurements of semidilute PNIPA solutions, at temperatures well below the phase‐transition temperature, exhibit the behavior predicted by the model of dynamic concentration fluctuations characterized by a single correlation length. Excess scattering at low angles is observed in salt solutions at temperatures that are near, yet below, the phase‐transition temperature. This may indicate intrachain heterogeneities on the scale of 6–8 nm. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3713–3720, 2004     

Rod-like polyelectrolyte adsorption onto charged surfaces in monovalent and divalent salt solutions

We analyze the adsorption of strongly charged polyelectrolytes onto weakly charged surfaces in divalent salt solutions. We include short-range attractions between the monomers and the surface and between condensed ions and monomers, as well correlations among the condensed ions. Our results are compared with the adsorption in monovalent salt solutions. Different surface charge densities (σ), and divalent (m) and monovalent (s) salt concentrations are considered. When the Wigner-Seitz cells diameter (2R) is larger than the length of the rod, the maximum amount of adsorption scales like n_max ∼ σ^4/3 in both monovalent and divalent solutions. For homogeneously charged surfaces, the maximum adsorption occurs at s* ∼ σ² when s* > ϕ, where ϕ is the monomer concentration, the counterpart for divalent salt solution, m* roughly scales as σ^2.2 when m* > ϕ. The effective surface charge density has a maximum absolute value at m′ < m*. A discrete surface charge distribution and short-range attractions between monomers and surface charge groups can greatly enhance surface charge inversion especially for high salt concentration. The critical salt concentration for adsorption in divalent salt solution roughly scales as m_c ∼ bσ^1.9, where b is the distance between two neighboring charged monomers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3642–3653, 2004     

Temperature‐responsive linear polyelectrolytes and hydrogels based on [2‐(methacryloyloxy)ethyl] trimethylammonium chloride and N‐isopropylacrylamide and their complex formation with potassium hexacyanoferrates (II,III)

Water‐soluble temperature‐responsive polyelectrolytes and hydrogels have been synthesized by γ‐radiation copolymerization of [2‐(methacryloyloxy)‐ethyl]trimethylammonium chloride with N‐isopropylacrylamide. Complex formation of soluble copolymers with potassium hexacyanoferrates (II, III) was studied in aqueous solutions. It was shown that, depending on the concentration and temperature, the formation of soluble or insoluble polycomplexes is observed. The hydrogels show good ability to absorb potassium hexacyanoferrates (II, III) from aqueous solutions. Sorption ability of hydrogels depends on the content of cationic monomer in copolymer and the nature of coordination ion. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 515–522, 2004     

Synthesis and properties of blue light‐emitting,silicon‐containing,regio‐ and stereoregular conjugated polymers

This article concerns the hydrosilylation polyaddition of 1,4‐bis(dimethylsilyl)benzene ( 1 ) with 4,4′‐diethynylbiphenyl, 2,7‐diethynylfluorene ( 2b ), and 2,6‐diethynylnaphthalene with RhI(PPh₃)₃ catalyst. Trans‐rich polymers with weight‐average molecular weights (M_w's) ranging from 19,000 to 25,000 were obtained by polyaddition in o‐Cl₂C₆H₄ at 150–180 °C, whereas cis‐rich polymers with M_w's from 4300 to 34,000 were obtained in toluene at 0 °C–r.t. These polymers emitted blue light in 4–81% quantum yields. The cis polymers isomerized into trans polymers upon UV irradiation, whereas the trans polymers did not. The device having a layer of polymer trans‐ 3b obtained from 1 and 2b demonstrated electroluminescence without any dopant. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2774–2783, 2004     

Adiabatic compressibility of polyelectrolytes in aqueous solutions. II. Poly(4-vinyl-N-n-butylpyridinium bromide)

The adiabatic compressibility for two samples (F-1 with DP-3748 and F-2 with DP-2114) of poly(4-vinyl-N-n-butylpyridinium bromide) in aqueous solution has been determined from ultrasonic velocity and density data. The sample (F-1) with the higher degree of polymerization shows comparatively higher velocity and density in solution. However, the evidence for the difference in compressibility is not very decisive. The apparent molal volume ΦV₂ and apparent molal compressibility ΦK₂ for F-1 are found to be slightly higher than for F-2. In aqueous solution, the decrement of adiabatic compressibility per unit concentration, (β₁ ? β)/c, is found to be almost constant throughout the entire concentration range, whereas in the presence of excess added electrolyte (1.0M KBr solution), the compressibility decrement shows a decrease with dilution. The latter values are lower than those found in water, since the molecules, in the presence of excess electrolyte, are coiled up more and are less compressible. The ΦV₂ and ΦK₂ values in water are constant throughout the entire concentration range, as the free counterions formed on dissociation in the dilute region are not solvated and hence contribute little to the compressibility. On the other hand, in the presence of excess KBr (1.0M), the ΦV₂ and ΦK₂ values show a sharp decrease with increase of polyelectrolyte concentration and finally attain a constant value. This is explained by the fact that because of the formation of a charge-transfer complex between the bromide ion and the polycation, more than the equivalent number of bromide ions is bound, leaving free an equal amount of K⁺ ions which are solvated and cause the lowering of apparent volumes and compressibilities. Condensation of charges begins at a certain polyelectrolyte concentration, and no further increase of K⁺ ions is observed. A special situation arises in 0.1M KBr solution. The ΦV₂ and ΦK₂ values at first increase sharply with increase of polyelectrolyte concentration, but then level off to attain a constant value, at comparatively high concentration. In 2.0% poly(4-vinyl-N-n-butylpyridinium bromide) solution, the concentration of polymer repeat unit (0.08M) is almost equal to the concentration of the added electrolyte (0.1M KBr) used to suppress dissociation. As the polyelectrolyte concentration in 0.1M KBr solution is progressively decreased, more bromide ions are made available for forming the charge-transfer complex with the polycation, leaving the K⁺ ions free to contribute to the compressibility.     

Polyampholytes

Polyampholytes are charged polymers with both positively and negatively charged groups. The conformation of these polymers in solutions strongly depends on the distribution of charged monomers along the polymer backbone and their environment. In this review we summarize the current level of understanding of such amphoteric polymers in solutions and their interactions with surfaces and polyelectrolytes. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3513–3538, 2004     

Synthesis and solution properties of a pH‐responsive cyclopolymer of zwitterionic ethyl 3‐(N,N‐diallylammonio)propanephosphonate

The zwitterionic monomer, ethyl 3‐(N,N‐diallylammonio)propanephosphonate, was cyclopolymerized in aqueous solutions using t‐butylhydroperoxide or ammonium persulfate as initiators to afford a polyphosphonobetaine (PPB). The protonation of P(?O)OEtO^– and deprotonation of ? NH⁺ groups in PPB by HCl and NaOH, gave the corresponding cationic polyphosphononic acid (CPP) and anionic polyphosphonate (APP). The presence of two pH‐responsive functionalities in APP has led to establish the equilibria: APP ? PPB ? CPP, the position of which very much dictates the viscosity behavior of its aqueous solution. The PPB demonstrated “antipolyelectrolyte” viscosity behavior; however, in contrast to many polycarbo‐ and polysulfo‐betaines, it was found to be soluble in salt‐free water as well as in salt‐added solutions. Basicity constant (K₁) of the amine group in APP, as determined by potentiometric technique, were found to be “apparent,” and as such followed the modified Henderson‐Hasselbalch equation. The study demonstrated a correlation between the basicity constants and viscosity values. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Electrical conductivity of some cationic polysaccharides. I. Effects of polyelectrolyte concentration,charge density,substituent at the ionic group,and solvent polarity

Electrolytic conductivity behavior of some cationic polysaccharides in water, methanol, and the mixtures water/methanol is presented. The polyelectrolytes investigated contain quaternary ammonium salt groups, N‐alkyl‐N,N‐dimethyl‐2‐hydroxypropyleneammonium chloride, attached to a dextran backbone. This study considers the influences of polymer concentration (1 × 10^?6 < C < 1 × 10^?2 monomol L^?1) and the charge density (ξ = 0.48–3.17) modified either by changing charge distance (b) or dielectric constant of the solvent (ε) on polyion–counterion interaction in salt‐free solutions. Above the critical value, ξ_c = 1, the variation of the equivalent conductivity (Λ) as a function of concentration is typical for a polyelectrolyte behavior. The conductometric data in water were analyzed in terms of the Manning's counterion condensation theory. The presence of longer alkyl chains at quaternary N atoms was found to have a negligible influence on the Λ values. The results show that the decrease of the medium polarity results in the decrease of the number of free ions and, consequently, of the equivalent conductivity values. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3584–3590, 2005     

Hydrodynamic invariant of polymer molecules

The theories of hydrodynamic properties of macromolecules in solution leading to an invariant relationship between the values of the intrinsic viscosity, [η], the molecular weight, M, and the translational friction coefficient of the molecule, f, have been considered. The review of experimental data comprising as much as about 2000 fractions of various polymers suggests that for all flexible-chain and moderately rigid-chain molecules the hydrodynamic parameter A₀ = kη₀(M[η]/100)^1/3f^?1 is actually an invariant independent of the chain length and the thermodynamic strength of the solvent and for moderately polydisperse samples also independent of the degree of their polydispersity. For polymers with very rigid chains the parameter A₀ has a high value over the experimentally investigated range of M. These conclusions make it possible to recommend the use of the following average experimental values of the invariant A₀ for the determination of M of polymers from the values of [η] and f: for flexible-chain and synthetic polymers with moderately high chain rigidity (3.2 ± 0.2) · 10^?10, for polymers with high chain rigidity (3.7 ± 0.4) · 10^?10, and for cellulose derivatives and other polysaccharides with molecular dispersity of nonelectrolyte solutions (3.30 ± 0.30) · 10^?10 erg deg^?1 mol^?1/3. The fact that the experimental value of A₀ = 3.2 · 10^?10 does not coincide with the value of A_∞ = 3.8 · 10^?10 erg deg^?1 mol^?1/3 predicted by the theories of translational friction and viscosity of macromolecules implies that the theoretical values of P_∞ = 5.11 and Φ_∞ = 2.8 · 10²³ mol^?1 are mutually incompatible and these theories require further development.     

Water‐soluble hyperbranched polyelectrolytes with high fluorescence quantum yield: Facile synthesis and selective chemosensor for Hg2+ and Cu2+ ions

New water‐soluble hyperbranched polyfluorenes bearing carboxylate side chains have been synthesized by the simple “A2 + B2 + C3” protocol based on Suzuki coupling polymerization. The linear polyfluorene analogue LPFA was also synthesized for comparative investigation. The optical properties of the neutral precursory polymers in CHCl₃ and final carboxylic‐anionic conjugated polyelectrolytes in buffer solution were investigated. The obtained hyperbranched polyelectrolyte HPFA2 with lower content of branch unit (2%) showed excellent solubility and high fluorescence quantum yield (?_F = 89%) in aqueous solution. Fluorescence quenching of HPFA2 by different metal ions was also investigated, the polyelectrolyte showed high selectivity for Hg²⁺ and Cu²⁺ ions relative to other various metal ions in buffer solution. The Stern‐Volmer constant K_sv was determined to be 0.80 × 10⁶ M^?1 for Hg²⁺ and 3.11 × 10⁶ M^?1 for Cu²⁺, respectively, indicating the potential application of HPFA2 as a highly selective and sensitive chemosensor for Hg²⁺ and Cu²⁺ ions in aqueous solution. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3431–3439, 2010     

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.     

Application of the Bjerrum Association Model to Electrolyte Solutions. III. Temperature and Pressure Dependencies of Association Constants

The Bjerrum association model, developed in 1926, is now incorporated in many conductance theories of electrolyte systems to extract ₀ and K _A from experimental data. The Bjerrum concept is simply a convenient way of taking into account short-range electrostatic interactions between ions. The equations of the Bjerrum model can be applied to the prediction of the temperature and pressure dependencies of K _A from the value of K _A at a reference T and P and from the dielectric properties of the solvent. This feature will be essential when the relaxation effect is taken into account when applying the model to heat capacities and compressibilities. These equations were tested against literature K _A values (obtained from treatment of conductance data by equations that incorporate the Bjerrum concept) in aqueous electrolyte solutions at high temperatures and pressures and in some electrolyte systems in acetonitrile, 2-butanone, propylene carbonate, -butyrolactone, and propanol. In the absence of specific interactions in solution, the agreement between experimental and predicted K _A are generally quite good. Notable exceptions are acids and bases in water, lithium perchlorate in most solvents, and the majority of electrolytes in propylene carbonate, suggesting that specific interactions in these systems may cause the model to fail.