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New information on the state of water molecules and ions in the alkali ion forms of sulfostyrene resins have been obtained by joint application of thermodynamic and quantum chemistry methods to treatment of experimental water sorption isotherms taken from the literature. The theoretical water sorption isotherms have been computed from suggested earlier model of Predominant Hydrates. The model parameters were obtained with the help of quantum chemical calculations of structures of the swollen ion exchangers. Ab initio non-empirical SCF MO LCAO method has been used. The molecular models included fragments of the polystyrene chain with two sulfonic groups and the number of water molecules identical to that in the resins with 10% divinylbenzene. The theoretical water sorption isotherms for all alkali metal forms accurately describe the experimental data in the assumption of presence in the resin three (Li+ and Na+) or two (K+, Rb+ and Cs+) predominant hydrates. The calculations allowed obtaining the following characteristics of the molecular models: binding energy of the water molecules to the swollen ion exchanger, Gibbs' energy of the hydrates formation, distances between the water molecules and ions, lengths of the hydrogen bonds and some other parameters. These data allowed explaining physical reasons for the difference in properties of the alkali ions related to the water “structure forming” and “structure breaking” subgroups. The results of the quantum chemistry calculations clearly indicate separation of water molecules in the resin into several groups differing in the binding energy and the distances to the cations. The number of hydrogen bonds per water molecule in the ion exchanger is about 25% less than in the bulk water, but the total number of intermolecular bonds (hydrogen and ion-molecular) is approximately the same as in the bulk water. Intermolecular bonds in the ion exchanger form an integrated net in which the mobile and the fixed ions function as the knots.

Information on the state of proton and water molecules in sulfostyrene ion exchangers was obtained by joint application of thermodynamic and quantum chemistry methods to experimental water sorption isotherms from paper B.R. Sundheim , M.H. Waxman , H.P. Gregor , J. Phys. Chem. , 57 : 9 ( 1953 ) 974–978 . The model of Predominant Hydrates in combination with non-empirical quantum chemical calculation was used for calculation of theoretical water sorption isotherms. The experimental water sorption isotherms can be accurately described by the model accounting for the presence in the resins with different cross-linkages (0.4–23% DVB) of four hydrates (H 3 O + ; H 3 O + ·H 2 O; H 3 O + ·2H 2 O; H 3 O + ·6H 2 O) with practically the same Gibbs energy formation (stability constants). The IR and Raman spectra of dry and hydrated resins were interpreted by comparing theoretically calculated spectra of p-ethylbenzene sulfonic acid and experimental ones. Some corrections to their interpretation were suggested. The spectra show that complete dissociation of sulfonic groups occurs after sorption by the resin three water molecules per sulfonic group.

Valuable information on the state of water molecules in the ion exchanger can be obtained by joint application of thermodynamic and quantum chemistry methods to treatment of water sorption isotherms. An improved variant of the Predominant Hydrates model accounts for competitive process of formation in the resin of several hydrates forming an ideal mixture with the free water. The parameters of the model are number of hydrates, number of water molecules in each hydrate and Gibbs energies of the hydrates formation. The first two parameters can be obtained from quantum chemical calculation of structure of the molecular model of swollen ion exchanger and the energy state of the water molecules. The new approach was illustrated by its application to experimental data of Gregor H . P ., Sundheim B . R ., Held K . M ., Waxman M . H . Studies on ion-exchange resins . V . Water vapor sorption , J . of Coll . Sci ., 7 : 5 ( 1952 ) 511–534 on isopiestic data of water sorption by Li + and Na + forms of sulfostyrene resin with 10% DVB. The experimental water sorption isotherms can be accurately described by the model accounting for the presence in the resin of two hydrates with the same number of water molecules for Li + and Na + forms. The difference in the intensity of hydration reveals in the different Gibbs energy of the hydrates formation. The mole fraction of water in different hydrates and the free water was calculated. It appeared that more than a half of water molecules in both cases are free and enter the resin phase due to the entropy increase upon distribution of the free water between the solution and the resin.

Comparative studies of the state of water molecules in carboxylic acid resins were carried out using classic thermodynamics and ab initio quantum chemical calculation of the structure of representative fragments of their polymeric matrix in the presence of different amounts of water molecules. Water sorption isotherms were obtained for H + , Li + , Na + , K + Mg 2+ , Ca 2+ and Ba 2+ forms of the carboxylic acid ion exchanger Lewatit S8227 using the isopiestic method. Quantum chemistry calculations were performed by the Firefly QC package, which is partially based on the GAMESS (US) source code, on the theory level RHF/MINI. Atomic structures of fragments of the resin interior containing 1–6 monomeric residues and 0–10 water molecules per functional group were computed. It has been shown that the water sorption isotherms are well described by the previously derived equation on the assumption of the presence in the swollen ion exchanger of one or two formal hydrates. Quantum chemistry calculations allow independent evaluation of the number of water molecules in the hydrates and in so doing reduce the number of fitting parameters needed for quantitative description of the water sorption isotherms. They also allow classifying the water molecules in the resin according to the type of interaction with fixed ion–counter-ion ion pair.

Weak base polyfunctional fibrous anion exchangers, containing small amount of carboxylic acid groups were obtained on the base of industrial modacrylic fibers Kanecaron (40% acrylonitrile, 60% vinylchloride) (Kaneka Ltd., Japan) by their reacting with aqueous solutions of diethylenetriamine (DETA). The sample obtained at optimal condition (DETA concentration 70–80%, process time 2–7 h, temperature 95 °С) have anion exchange capacity 3–5 meq/g and water uptake 0.3–0.4 gH2O/g. Their chemical stability in different media has been studied. On the base of studies of their ion exchange capacity, elemental analysis, potentiometric titration and IR spectra the structure of these ion exchangers has been clarified. Predominant reaction of the modification is substitution of the Cl atoms by nitrogen in DETA molecules with formation of tertiary and secondary amino groups. All three atoms of nitrogen react and the ratio of incoming N atoms and outgoing Cl atoms is close to one.

Acid–base properties, kinetics and equilibrium sorption of Ca 2+ , Cu 2+ , Pb 2+ , Cd 2+ , Ni 2+ and Mn 2+ ions on fibrous chelating ion exchanger FIBAN X-1 containing iminodiacetic group have been studied. The structural and electronic characteristics of ion-polymeric complexes have been obtained by non-empirical quantum chemical calculations. The rate of sorption processes was extremely high; the half-process time of the sorption process was equal to 24 s. The isotherms of ion sorption are described by the Langmuir equation what allowed deriving equation for dependence of the distribution coefficient on the ion concentration and accurate extrapolation of these value to zeros concentration. The concentration range the Henry’s law applicability was determined theoretically and proved experimentally. The sorption selectivity series in a neutral medium was Cu > Ni > Pb > Cd > Mn > Ca. The same series follows the pH at which the sorption begins. Complete extraction of all heavy metal ions occurs at pH > 4. The quantum chemical calculations have shown that the selectivity of sorption is determined by the number of coordination bonds between the cation and fixed anion, the length of the bonds and degree of their covalence. The way of combining of these factors is individual for each specific cation and can be revealed by quantum chemical calculations.

Ion exchange equilibria Cl−– NO 3 - , Cl−– SO 4 2 - , NO 3 - – SO 4 2 - on fibrous strong base anion exchangers on the basis of graft copolymer of styrene and divinylbenzene to polypropylene fibers with groups of benzyl trimethyl- (TMA), triethyl- (TEA), and tributyl- (TBA) ammonium have been studied and characterized by values of the equilibrium coefficients and separation factors. They were compared with the same equilibria on ion exchange resins Dowex1 with different cross-linkage. An equation allowing calculating the separation factor for different ionic concentrations and ratios of the ions in solutions of uni- and divalent ions from the equilibrium coefficient invariant to the concentration has been derived. The selectivity of nitrate and chloride sorption increases with increasing size of alkyl radicals in the functional group and with increasing percent of divinylbenzene in the resins. A quantity characterizing selectivity of ion exchanger to bivalent ion against the univalent ion named concentration of zeroth selectivity (CZS) has been suggested to describe the efficiency of ion exchangers in processes of water purification from univalent ions, specifically nitrates in waters containing sulfates. At concentrations above the CZS the univalent ion is absorbed selectively compared to the bivalent one; the “dumping effect” in frontal chromatograms of mixtures of such ions is not possible above the CZS point and this criterion can be used for choosing the ion exchanger for selective removal of univalent ions from mixtures with polyvalent ones. The CZS values for conventional strong base ion exchangers in ion exchange NO 3 - – SO 4 2 - is higher than typical total ionic concentrations in drinking waters (1–3 × 10−3 eq/L). For Dowex1 × 10 it was found equal 1.3 × 10−2 eq/L. For the fibrous ion exchanger with benzyltributylammonium groups CZS = 3.3 × 10−6 eq/L. This ion exchanger is suitable for selective removal of nitrates from the solutions with concentrations higher than this value and has exceedingly high selectivity to nitrates which makes the process of its regeneration difficult. The most suitable fibrous ion exchangers for application in drinking waters purification from nitrates with guarantied absence of the nitrate dumping appeared FIBAN A-1 TEA having the CZS values 4.3 × 10−4 eq/L.

It has been established that fibrous polymeric ion exchangers can be impregnated with nanoparticles of hydrated ferric oxide (HFO) which serves as a selective sorbent for As(III) and As(V) species from aqueous solutions. The screening studies have shown that the largest amount of Fe(III) can be loaded into a weak base anion exchanger with ternary amino groups (up to 1.4 mmol Fe/gram of dry fiber). The fibrous composite sorbent on the base of such anion exchanger possess a high selectivity toward both As(III) and As(V) species combined with a high sorption capacity (∼2.9 g As/kg till As concentration in outlet solution becomes more than 10 μg/L). The sorbent does not release Fe into contacting solution and does not require backwashing in column operations. Its specific feature is extremely high rate of the sorption processes. The process rate is controlled by diffusion of the arsenic species into HFO particles uniformly spread in the fiber. The half process time appeared equal 23 s which allows column operation with empty bed contact time down to 10 s. The sorption of As(III) at pH values admissible for drinking water is not affected by the foreign anions ( Cl − , SO 4 2 − , H 2 PO 4 − / HPO 4 2 − ) . Sorption of As(V) decreases with phosphates concentration increasing. Column experiments with model and natural waters containing As in concentrations 50–100 ppb have shown that the new sorbent can be used for production of small water household filters with the filtering bed volume about 0.5 L. The filter allow purification of 200 L of water per hour and obtaining 2.5–5 tons (5000–10 000 bed volumes) of purified from As(III) and As(V) water without correcting pH and pre-oxidation of As(III). The field experiment on purification of natural water containing 60 ppb of As allowed purification of 10 000 bed volumes of water to 10 ppb of As in the effluent.

In the studies, ion exchange substrates prepared from new (standard) and spent ion exchange resins were used as fertilisers introduced into sand that served as a model of degraded soil. The obtained results showed a strong effect of the additions of standard ion exchange substrates on grass yield. It progressively increased with the increase of substrate fraction in the sand at its low content (up to 5–7%). One percent additions only of ion exchange substrates into sand increased plant yield from three to nine times. It was also noticed that an addition of one volume percent of the substrate brought the fertility of sand to that of commercially available garden soil. Results of the experiments with spent ion exchangers exhibited their fertiliser utility as an ion exchange substrate (the Mp substrate) and as monoionic forms containing potassium, nitrate and phosphate ions (the NPK monoionic forms). The plant yield obtained on sand enriched with the Mp substrate or with the NPK monoionic forms was from 1.5 to 4.5 times higher than that obtained on sand alone. At the same time the boost to growth to be attributed to the introduction of the standard substrate into sand was from two to four times greater than that caused by an addition of the Mp substrate or the NPK monoionic forms. The higher efficacy of the standard substrate compared to that of the Mp resulted from greater potassium and phosphorus contents in that substrate. The lower plant biomass on sand fertilised with the NPK monoionic forms compared to that obtained on sand enriched with the standard substrate was caused by a lower content of nitrogen, potassium and phosphorus and a lack of calcium, magnesium and sulphur in the mixture of the NPK forms.

The anion exchange fibers on the basis of industrially produced polyacrylonitrile fiber NITRON with different strong and weak base groups have been described in the paper. Their acid–base properties were characterized by the acidity parameters calculated from the potentiometric titration curves. The method of computer analysis of the titration curves described elsewhere was used. It was established that the ion exchange fibers are polyfunctional and contain at least four types of functional groups. Their capacities and the acidity parameters have been calculated. The fibers have full ion exchange capacity about 3.5 meq/g. The capacity according to the strong base quaternary aminogroups (p K ≅ 2) is usually about 2.5 meq/g. The water uptake, stability in hydrogen peroxide solutions, strong acids and alkalis of different concentrations at the ambient temperature and 100 °C have been studied. The fibers do not loose significantly their anion exchange capacities and mechanical properties except for the most extreme regimes of their treatment. At the same time they accumulate carboxylic acid groups in their structure due to hydrolysis of the residual nitrile groups in the fiber.

Sorption of sulfuric acid and lithium sulfate by the sulfate form of ion exchanger Dowex 1×8 have been studied in the range of concentrations 0.025–2 M. The regularities observed were described with the help of mathematical and computer models similar to those used for description of sorption of HCl and HClO4 in the previous communication [Soldatov et al. React. Funct. Polym. 60 (2004) 41]. The models account for the site sharing effect, Donnan distribution and dimerisation of hydrosulfate ion in the resinous phase. The main introduction in the sorption of sulfuric acid in the studied concentration range is done by conversion of sulfate to hydrosulfate counterion. Dimerisation of hydrosulfate and Donnan distribution becomes important at a concentration of the external H2SO4 solution above 1 M. Sorption of lithium sulfate is entirely controlled by the Donnan distribution.

Sorption of hydrochloric and perchloric acids and their sodium salts was studied by Cl− and ClO4− forms of ion exchanger Dowex 1×8 in the concentration range of the external electrolyte 0.25–4 mol/l. Sorption of water and the total amount of the solution were also studied. Sorption of the acid appeared markedly higher than that of the respective salts. A mathematical modeling and computer simulation of the processes were performed. The overall sorption was represented as a superposition of the Donnan membrane distribution and formation associates type RAn · (AnKt)i · (H2O)n in the homogeneous resin phase. The model expresses non-ideality of the resin phase in explicit form as formation of the above associates characterized by the constants of their formation. A good agreement between the experimental and calculated sorption in the whole concentration range was obtained in the assumption of two associates with i=1, 2 and n=1–3. The same factors control sorption of the acids and the salts and the difference in their behavior has a quantitative character. The main introduction into the overall sorption of the salts makes the Donnan distribution up to concentration of the external electrolyte 4 M, while the main part of the absorbed acids is contained in the associates.

A method for determination of the acidity parameters of ion exchangers with arbitrary functionality from potentiometric titration data was developed. Titration of ion exchanger RH (ROH) with alkali KtOH or acid HAn is considered as superposition of ion exchange H + –Kt + (OH − –An − ) and the reaction of neutralization. The method is based on the assumption of linear dependence of logarithm of the equilibrium coefficient of the ion exchange as a function of the neutralization degree. The acidity parameters are two constants of this dependence. They are thermodynamic equilibrium constant of ion exchange, p K and the difference between logarithm of the equilibrium coefficient at the complete and zeroth neutralization of the ion exchanger, Δp k . Specially developed computer program allows reconstruction of the potentiometric titration curve from the sets of the acidity parameters of each type of the functional groups in the resin. The theory was tested on a number of ion exchangers with different functionalities: sulfonic and carboxylic acid cation exchangers, polyfunctional weak base anion exchangers of different structures. The ion exchange capacity of each type of groups can be determined with precision higher than 0.1 meq/g. The p K i values of the groups present in macroamounts are determined with precision at least ±0.2 p K units.

A mathematical model establishing relations between the selectivity, degree of ion exchange and structure of spatial polyelectrolytes has been developed. The structure is expressed through two parameters: radius of interaction (that is a maximal distance at which the exchange sites influence each other) and the number of exchange sites situated in the sphere of interaction (neighbors). A larger number of neighbors should result in more complicated shape of property-composition dependencies of the ion exchange system. A computer model allowing estimation of the probability of the presence of different numbers of neighbors in different elements of the polymer network as a function of distance from the exchange site was suggested. The polymer network is represented as a body obtained by integration of fragments with eight to ten monomeric units of different shapes: linear chains, H and T shape units and small rings. The theory was applied to interpreting dependencies of selectivity of cation exchange on sulfonic styrene-divinylbenzene cation exchangers and strong base anion exchangers on the same matrix. Dependencies of selectivity on degree of ion exchange and cross-linkage of the resins are in good agreement with the prediction of the theory if the predominant number of neighbors in different particular cases is ranging between two and four. The non-equivalence of exchange sites of spatial polyelectrolytes is their inherent property because different exchange sites have different amounts of the neighbors. The difference in the selectivity dependence on the cross-linkage of cation and anion exchangers on styrene-divinylbenzene matrix finds a simple and natural explanation.

A simple method for calculating acidity parameters, suggested in a previous publication (React. Funct. Polym. 38 (1998) 73), as well as constants for the modified Henderson–Hasselbach equation, is described. It follows from analysis of the shape of potentiometric titration curves of ion exchangers that along with the vertical inflection at the equivalence point, they have a horizontal inflection at half neutralization. The pH value and the tangent of the titration curve at that point are simply related to the acidity parameters of resins. The derived equations allow ready determination directly from the titration curve.

Equilibria of ion exchange of neutral aliphatic amino acid cations (A + =Gly + , Ala + , Val + , Leu + ) and H + have been studied on a liquid sulfonic type ion exchanger — dinonylnaphthalene sulphonic acid dissolved in heptane. It has been established that the difference in selectivity of extraction of these cations is much greater than on sulphostyrene resins, which is a favourable precondition for their selective extraction. The selectivity coefficients of the H + –A + exchange have a region of a low dependence on the degree of loading of liquid ion exchanger ( X =0 –0.5) and a region of a sharp decrease ( X >0.5) . This phenomenon is explained as a result of formation of very stable complexes of the amino acid cations and the anion of dinonylnaphthalene sulphonic acid containing one unsubstituted proton per 3–6 A + cations. The IR spectra confirm this assumption. The dependence of the selectivity coefficient on the degree of H + –A + exchange has been described using the previously developed mathematical model of ion-exchange processes. The model is consistent with the experimental data in an assumption that four nearest neighbours of an exchange centre in the associates of the liquid ion exchanger influence the energy of ion exchange on a given exchange site.

Simplest ion exchange systems, containing two phases and three components (two electrolytes of the exchangeable ions and a solvent), are considered from the viewpoint of thermodynamics of mixtures. Specific of these systems is the presence at the ion exchange phase of a spatially infinite, osmotically inactive matrix carrying an electrical charge. Application of some important concepts and equations of chemical thermodynamics of mixtures, such as chemical potential, activity coefficients, Gibbs free energy, equations of Gibbs-Duhem and of the equilibrium constant, have been discussed. It is concluded that ion exchange is a process combining features of heterogeneous chemical reaction and osmotic distribution. It can be equally well described as a chemical reaction complicated by osmotic phenomena as vice versa, depending on the properties of the ion exchanger and the statements of the theoretical approach.