Recent advances in the aqueous chemistry of the calcium(II)-gluconate system – Equilibria, structure and composition of the complexes forming in neutral and in alkaline solutions

Of the sugar carboxylates, D-gluconate is clearly the most signiﬁcant representative: the world’s annual production of this organic compound is estimated to be in the order of 10 5 tonnes. The reason of its mass production is due to its outstandingly broad range of practical (medical, pharmaceutical, industrial, etc. ) applications. D-gluconate is a well-known and exceptionally popular complexing agent; accordingly, it has been the subject of a large number of coordination chemical research investigations. Its complexation properties are specially remarkable in alkaline to hyperalkaline pH conditions, where the deprotonation of one or more of its alcoholic OH groups provides a favourable frame for the formation of very stable chelate complexes with a large variety of metal cations. With the aim to show the state of the art of some relevant issues in the aqueous chemistry of the D-gluconate ion, the current paper focusses on the acid- base properties and calcium(II) complexation of the compound encompassing the entire experimentally available pH-range in water. The accessible literature on the deprotonation of carboxylic and alcoholic OH groups is collected and critically evaluated. The lactonization equilibria of D-gluconic acid are also scrutinized. The available data on the calcium complexes forming in neutral and in (hyper)alkaline solu- tions (both in terms of composition, formation constants and solution structure) are also discussed. Where feasible, some of these properties are compared with those of D-glucose and its derivatives as well as some less common sugar carboxylates, structurally related to D-gluconate, ( i.e., D-heptagluconate, L-gulonate and a -D-isosaccharinate). Special emphasis is laid on the relationship between complex stabil- ity and the type of metal-binding groups.

In the food and pharmaceutical industries, trace elements are often administered in the form of gluconate salts/complexes due to their ready absorption and appropriate tolerance by the body. Calcium(II) gluconate is used as a source of calcium for treating calcium deficiency by oral or intravenous treatment [2,32,33]. Iron(II/ III) complexes with gluconate have been proposed as mediators for indirect electrochemical reduction of dyestuffs in textile dyeing processes ( [34] and references therein). In this field, Bechtold and co-workers investigated the influence of Ca 2+ ions on the redox chemistry of the Fe(III)/Fe(II) couple in the presence of Gluc -. The study was motivated by the expected formation of binary (Ca(II)/ gluconate) and ternary (Ca(II)/Fe(III)/gluconate) complexes altering the mediator properties of Fe(II/III) gluconate aqueous species, especially under alkaline conditions [35,36]. Note that the formation of similar type of ternary complexes with aldarate ligands (polyhydroxy dicarboxylates) was observed at basic pH for the systems Ca(II)/Al(III)/aldarate [37] and Ca(II)/B(III)/aldarate [38], respectively.
As for the metal industry, gluconate is commonly used in the galvanic deposition of nickel-cobalt onto aluminium, in the baths required for preparing surface plating of nickel, tin and zinc [1,[39][40][41], but also as cleansing agent removing calcareous and rust deposits from metals or other surfaces (e.g., galvanized iron, stainless steel, glass, among others) [1,2,42]. In many of these applications, gluconate is dissolved in very alkaline solutions. This combination benefits from the caustic nature of the solution and the ability of gluconate to solubilize calcium, magnesium and iron salts at high pH.
Sodium gluconate is widely used in the cement industry as an additive retarding the curing process. Gluconate-bearing cementitious materials retain a very high workability and plasticity, despite using a reduced content of water, and show increased stability upon setting [2,[43][44][45][46]. The presence of gluconate in cement and concrete, and the planned use of these materials in some of the concepts for nuclear waste disposal (i.e., repositories for low-and intermediate-level waste, L/ILW) have also brought awareness during the last two decades upon the complexation of gluconate with radionuclides and the potential mobilization of these complexes from the repository into the biosphere. Several studies have confirmed the strong complexation of gluconate with actinides (An) and fission products [47][48][49][50][51][52][53][54][55][56][57]. For An(III) and An(IV), these complexes are further stabilized in the presence of calcium, where the formation of ternary Ca(II)/An(III/IV) gluconate species has been proposed for Nd(III)/Cm(III) [58] and Th(IV) [59].
An accurate and complete knowledge of the thermodynamic properties of gluconate aqueous species and solid compounds arises as very useful in most of the gluconate applications summarized above. In spite of this, there is no recent comprehensive thermodynamic evaluation of the gluconate system available in the Scheme 1. Chemical formula of D-gluconic acid (HGluc), as well its five-(c-HGluc) and six-membered (d-HGluc) lactones. Additionally, the nucleophilic attack of the OH group being the initial step in the acid-catalyzed lactonization is indicated.
literature. Sawyer reviewed all the literature published on gluconate until December 1963 and summarized the resulting thermodynamic data, although no critical evaluation of the original experimental studies was conducted by the author [1].
In similar terms, the last release of the NIST Standard Reference Database 46 in 2004 provided a very comprehensive compilation of thermodynamic data of gluconate (among many other organic ligands) and its complexes with many metal cations [60]. In the context of nuclear waste disposal, it is also noteworthy the work performed within the thermochemical database (TDB) project of the Nuclear Energy Agency (NEA). The 9th volume of this series was dedicated to the critical evaluation of the thermodynamic data available on the complexation of organic ligands with radionuclides relevant in nuclear waste disposal [61]. Although HGluc was not evaluated in this volume of the NEA-TDB, the review conducted on a-D-isosaccharinic acid ((2S,4S)-2,4,5-trihydroxy-2-(hy droxymethyl)pentanoic acid, HIsa, close analogue of HGluc) provides a very detailed overview of the type of complexes and stability expected for the former ligand.
Generally speaking, considerable knowledge has been accumulated on the coordination chemistry, that is: the structure and equilibria of complexes comprising polyhydroxy carboxylates and alkaline earth metal ions (in particular Ca 2+ ), forming in aqueous solutions of 2 < pH < 10 [13,[24][25][26][27]29,[62][63][64][65][66][67][68][69][70]. The interactions in this pH range involve weak chelation of the metal ion by the OH and COO À functionalities, where the carboxylate moiety acts as anchor group. Usually, the formation constants of these simple, mononuclear 1:1, or in some cases 1:2 type stepwise calcium complexes are low. This situation changes dramatically under hyperalkaline conditions. In solutions of pH > 12, Ca 2+ forms bi-and trinuclear complexes with Gluc À [26,28,30] as well as with a range of sugar carboxylate type ligands structurally related to Gluc À (e.g., with Dheptagluconate and L-gulonate [30,71], but not with Disosaccharinate [72]). These polynuclear Ca-complexes are of surprisingly high stability, so much so, that in solutions pH > 12, Ca 2+ will be predominantly present in the form of complexes like Ca 2 L 2 H À4 À2 (or Ca 2 LH À3 0 ) and Ca 3 L 2 H À4 0 (besides, the minor species CaLH À1 0 is formed to a minor extent). It is also noticeable that quite a few of these multinuclear species are charge-neutral.
The present work aims at providing a comprehensive review of the literature available for the aqueous solutions containing gluconate, calcium ions and supporting electrolytes (from dilute to highly saline) and encompassing the entire experimentally available pH-range (from acidic to hyperalkaine), from the perspective of solution thermodynamics and coordination chemistry. An attempt will be made to summarize the literature findings relating to the protonation (both carboxylate and alcoholate), lactonization and Ca(II) complexation of gluconate (Scheme 1). For the latter, close-to-neutral and hyperalkaline systems will be discussed separately. The structure of the complexes (both in the solution and in the solid state), when there are data available for them, will also be discussed. Also, the complexation properties of some gluconate-related ligands will be briefly assessed.

General aspects and experimental methods
The protonation reaction of Glucand the corresponding equilibrium constants, K p 0 and K p , can be defined by the following equations: where K p 0 is the thermodynamic protonation constant, referring to infinite dilution, expressed in terms of dimensionless activities (a), while K p is the conditional protonation constant, expressed in terms of equilibrium molar concentrations (brackets) and c ø is the standard molar concentration (1 mol•dm À3 or M). The activities and molar concentrations of a given species are connected via the socalled activity coefficients (c). As for K p , the term ''conditional" means that the constant is valid only under the experimental conditions used for its determination (i.e., a given ionic strength (I) and type of background electrolyte) [61]. In practice, it is desirable to keep the c coefficients constant to avoid the variation of K p throughout the measurement. Having these constants determined, K p 0 is obtained by extrapolating them to infinite dilution (I ? 0).
The protonation equilibrium (Eq. (1)) has been widely investigated in the literature. Potentiometric techniques have been largely preferred to quantify this equilibrium, often in combination with polarimetric and coulometric methods. Recently, the use of NMR ( 1 H and 13 C) has gained relevance to study this system, especially in view of the ability of this technique to provide accurate speciation information based on the variation of the chemical shifts in the 1 H and 13 C NMR spectra of Glucand HGluc molecules. A relevant limitation of the technique is the high detection limit (at least millimolar range), imposing the use of relatively high gluconate concentrations in the experiment. In turn, this can affect the properties of the matrix solution and needs to be taken into account in the interpretation of the data.
HGlucd-HGluc þ H 2 O ð7Þ where K c/d 0 and K c/d are the lactonization constants at infinite dilution and at finite ionic strengths, respectively; a w represents the activity of water. It is important to note that as in the case of K p , K c/d is expressed in terms molar concentrations; hence, their actual value depend on the ionic strength and the type of the inert electrolyte used [61].
Because the formation of a lactone involves the reorganization of the gluconic acid molecule, lactonization is a much slower process compared to the deprotonation of HGluc to form Gluc -. Both lactones can form (Scheme 1), although several studies have indicated that the formation of d-HGluc is kinetically favoured, at least under acidic conditions. Due to the coupling of the protonation (Eq. (1)) and lactonization (Eqs. (4) and (7)) reactions, an adequate knowledge of the latter is necessary for the determination of log K p . If sufficient time is allowed for both reactions to achieve equilibrium (typically ranging from hours to days, depending on the pH), and speciation techniques permit the quantification of protonation and lactonization processes, both log K p and log K c/d can be evaluated simultaneously. However, if equilibria are achieved but the experimental techniques do not allow distinguishing between HGluc and c/d-HGluc, an ''apparent" protonation constant (log K p,app ) is determined according to the overall reaction: where HGluc* represents all species (HGluc and c/d-HGluc) that are formed when the protonation of Gluctakes place. Combining Eqs.
(3), (6) and (9), the following relationship can be deduced: Eq. (12) indicates that log K p,app > log K p in all cases. In many of the available studies assessing protonation and lactonization reactions simultaneously (see Section 2.2), log K p was determined from log K p,app and log K c/d . With this approach, the underestimation of the latter results in an overestimation of log K p . Such an issue has been identified in several of the reviewed experimental studies, where the time considered in the experiment was insufficient to reach the equilibrium between HGluc and c/d-HGluc, especially in view of the very slow kinetics for the formation/hydrolysis of c-HGluc (see Mitchell and Duke [75]). Motivated by the desire to describe the system under non-equilibrium conditions, too, several studies aimed at studying the time-dependence of the lactonization processes, utilizing polarimetry, coulometry, highperformance liquid chromatography or electrospray ionization mass spectrometry [74,75,77,78,81]. Since the reaction rates of the forward (lactone formation) and backward (lactone hydrolysis) are equal in equilibrium, the following relationship holds: where k 1,c and k 1,d (s À1 ) are the rate coefficients for lactone formation, and k -1,c and k -1,d (s À1 ) are those for lactone hydrolysis. In most cases, k -1,d was determined for the fast hydrolysis of d-HGluc. Given that K d is known from independent measurements, k 1,d can be calculated. On the other hand, the slow lactonization kinetics as compared to the rapid protonation represents an advantage for the determination of log K p when approaching the system with fast titrations, starting from alkaline conditions. This approach allows for the study of the thermodynamic equilibrium between HGluc and Glucwithout generating significant amounts of c/d-HGluc, and thus provides more accurate values of log K p at the cost of disregarding the quantification of log K c/d . Furthermore, the accurate determination of log K p is indispensable when studying complex formation reactions under acidic conditions. Since both H + and the metal ion compete for the COOgroup of Gluc -, the protonation and complexation reactions are not independent from each other. Consequently, using an inaccurate value of log K p yields an inaccurate binding constant for Ca 2+ , too.
In the following Section, all log K p and log K c/d constants as well as the k 1,c/d and k -1,c/d rate coefficients reported in the literature are listed in Tables 1 and 2, respectively. Furthermore, the meanings of the different terms of pH used throughout this work are the following: pH will be used when it is discussed in a general context, pH c is referred to as -log ([H + ]/c ø ), while pH obs means the experimentally observed value, recorded directly from the pH meter. The latter differs from pH c , when the calibration and the measurements are performed at different ionic strengths and/or in different medium. Namely, these parameters affect the activity of H + and the liquid junction potential of the electrode, hence pH obs [61].
2.2. Review of available thermodynamic data for the system c/d-

HGluc/HGluc/Gluc -
The pioneering work in the field was reported by Cannan and Kibrick [62], who studied the complex formation between Gluc -(among other carboxylates) and Zn 2+ , Mg 2+ , Ca 2+ , Sr 2+ as well as Ba 2+ in acidic medium. The authors determined also log K p in Table 1 Conditional protonation constants (log K p , Eq. (3)) reported in the literature, organized by increasing background electrolyte concentration. The data correspond to t = 25°C unless indicated differently. Where reported, triple standard errors are included in parentheses. , Eq. (2)), obtained by extrapolating data for log K p to infinite dilution. d Thermodynamic protonation constant (log K p 0 , Eq. (2)), obtained experimentally. e Suggested to be log K p,app instead of log K p by the authors of Ref. [19]. f The temperature was not indicated in Refs. [62] and [83]. The temperature was 20°C in Refs. [7] and [35], 22°C in Ref. [81] and 37°C in Ref. [84] 0.2 M KCl for all the carboxylic acids under investigation. The titrations were conducted from acidic to alkaline conditions using NaOH as titrant. In the case of gluconate and despite working within the pH c range 3-4.5, the authors did not consider the lactone formation in their data evaluation. Furthermore, the description of further relevant experimental details (e.g., the length of the potentiometric titration) is missing in the paper. The value of log K p reported by the authors is considered in this review to be higher than the real protonation constant. Heinz [83] performed potentiometric titrations with HGluc (among other carboxylic acids) in the absence and presence of Ca 2+ . The titrations were carried out in the pH c range of 3-6, using 0.015 M KCl as background electrolyte. Although the length of the measurement was not indicated in the paper, the titration from acidic to alkaline conditions likely promoted the presence of relevant amounts of lactones in the system. Since the lactonization was not considered, the log K p reported by Heinz is presumably overestimated.
Sawyer and Bagger [74] carried out a very comprehensive study on the lactone-acid-salt equilibria of HGluc combining polarimetric, potentiometric and coulometric methods. In the first step, the authors equilibrated the aqueous solutions of pure and halfneutralized d-HGluc for 72 h, and determined the ''apparent" disso-ciation constant (= -log K p,app ) by measuring the pH c . In the second step, the authors measured the optical rotation of lactone samples of different concentrations, equilibrated again for 72 h. The pH c values ranged between 2.36 and 3.96 and were set using organic buffers of different concentrations. Using the molar rotation of d-HGluc, HGluc and Gluc -(also discussed in this review, see Table 3) and considering the value of -log K p,app , the authors were able to determine log K p and log K d .
The rate of d-HGluc hydrolysis was also quantified by polarimetry and coulometry with and without the use of organic pH buffers, respectively. Significantly divergent rate constants were determined depending on the pH c , as well as on the buffer and experimental method used. Despite the comprehensiveness of this study, the log K p and log K d data reported by the authors are considered inaccurate due to the insufficient equilibration time considered in the experiment (see Mitchell and Duke [75]) and the limitations in the calibration/measurement of molar rotations (see Combes and Birch [78] and Table 3).
Mitchell and Duke [75] studied the equilibrium and kinetics of c-HGluc and d-HGluc hydrolysis using a combination of polarimetric and potentiometric techniques. The authors employed 0.1 M HCl and several pH buffers of different concentration to set the pH c in the polarimetric characterization of the lactone hydrolysis.  Table 2 Kinetic rate coefficients of formation (k 1,c/d ) and hydrolysis (k -1,c/d ) of cand d-HGluc (Eq. (13)), respectively, and conditional equilibrium constants for the lactonization of HGluc (log K c/d , Eqs. (6) and (9)); organized by increasing background electrolyte concentration. The data correspond to t = 25°C unless indicated differently. Where reported, triple standard errors are included in parentheses. The authors calculated log K p,app as well as log K c and log K d at different ionic strengths, which allowed them to obtain log K p . They found that only log K p depends on the ionic strength, and they extrapolated their data to determine the thermodynamic constant at infinite dilution. The specific rotations reported by the authors for d-HGluc, HGluc and Glucdiffer significantly from those reported in Sawyer and Bagger [74] (Table 3). In contrast to Sawyer and Bagger, the authors observed that c-HGluc becomes relevant after sufficiently long equilibration times, and concluded that a contact time of 72 h (as considered by Sawyer and Bagger) was insufficient to attain thermodynamic equilibrium within the system c/d-HGluc/HGluc. The authors also observed that k -1,d is strongly dependent on [H + ] and [OH -], and thus different contact times are required for the equilibration of the system at different pH c . Also, the authors suggested the lactone hydrolysis to take place via an uncatalyzed, an acid-and a base-catalyzed pathway, respectively. Felty [76] studied the lactonization equilibria of numerous aldonic acids, including HGluc. To separate the free acid and the two lactones as well as to determine their concentrations, GC analyses were carried out for the O-trimethylsilylated derivatives. The results obtained at 25°C agree very well with those of Mitchell and Duke [75] and Kutus et al. [82], respectively. Extending the temperature range from 0 to 45°C, valuable insights into the thermodynamics of lactonization were gained. Namely, that the lactone formation reaction is endothermic (i.e., it becomes more favorable with increasing temperature) and accompanied by an increase in the entropy. Being lactonization de facto a dehydration process explains the positive enthalpy change. Furthermore, the overall number of molecules increases during the reaction, yielding positive entropy. It can also be concluded from these thermodynamic parameters that the formation of c/d-HGluc is enthalpy-driven.

Reaction
Pocker and Green [77] investigated the hydrolysis of d-HGluc by means of polarimetry, potentiometry and spectrophotometry. Contrary to Mitchell and Duke [75], the authors determined specific rotations for d-HGluc, HGluc and Glucto be very similar to those reported by Sawyer and Bagger. The samples were equilibrated for 72 h before the reading of the optical rotation. Similarly to the case of Sawyer and Bagger [74], log K p and log K d data reported by the authors are considered inaccurate due to the insufficient equilibration time considered in the experiment and the limitations in the calibration/measurement of molar rotations (see Combes and Birch [78] and Table 3). The authors also evaluated the kinetics of d-HGluc hydrolysis, and concluded that the overall pseudo-firstorder rate constant includes an uncatalyzed (zeroth order) component. Additionally, k -1,d is a function of [H + ] and [OH -], but also of the type and concentration of the pH buffer in solution. Consequently, the hydrolysis of d-HGluc takes place via general acid/base catalysis, in line with previous findings of Sawyer and Bagger [74] as well as Mitchell and Duke [75].
Roos and Williams [84] conducted a series of potentiometric experiments to assess the acid-base properties of citric, folic, gluconic and succinic acid and the corresponding complexation with Mn, Zn and Fe. All experiments were performed in 0.15 M NaClO 4 at 37°C. The log K p reported by the authors is also included in Table 1, although acknowledging the relevant differences expected with respect to thermodynamic functions derived at t = 25°C.
Coccioli and Vicedomini [85] studied the protonation of Glucand the complex formation with Pb(II) by a series of potentiometric titrations in the pH c range of 1.5-5, using 1.0 M NaClO 4 as inert electrolyte. No account of the equilibration time allowed for each titration point was provided by the authors. Coccioli and Vicedomini acknowledged the possible formation of c-HGluc and/or d-HGluc under more acidic conditions, and therefore disregarded all experimental points with pH c 3.5 in the fitting process to determine log K p . Remarkable quantities of lactone (5-15%) are expected to co-exist with HGluc at pH c 4.5, especially if titration has been initiated from the acidic range. Consequently, the log K p reported by Coccioli and Vicedomini is likely an overestimation of the protonation constant.
Motekaitis and Martell [18] investigated the complexes of Al(III) with hydroxycarboxylic acids by means of potentiometric titrations. The authors also assessed the log K p of the carboxylic acids studied. In both cases, 0.1 M KNO 3 and KOH were used as background electrolyte and titrant solution, respectively. Titrations were performed within 2 pH c 11, but no information on the equilibration time allowed for each titration point was provided in the paper. In the case of HGluc, the possible formation of c/d-HGluc was not considered in the interpretation of the acid-base equilibrium. Provided that the titration of gluconate accomplished from acidic to alkaline conditions, significant quantities of lactone are to be expected below pH c = 4.5.
Blomqvist and Still [6] assessed the complexation of Cu(II) and Cd(II) with Gluc -, and complemented their study with the determination of log K p . Potentiometric titrations were performed with KOH at t = 25°C, using 0.5 M KNO 3 as background electrolyte. The concentration of H + was calculated from the pH readings using the relationship pH c = pH obs -0.14. Although expected at pH c 4.5, the possible formation of c/d-HGluc was not considered in the calculations of log K p . Neither pH c range nor length of the titrations were reported in the manuscript. The log K p value determined by the authors (Table 1) is likely to be overestimated due to the contribution of the lactonization reaction.
Combes and Birch [78] conducted a very comprehensive study on the hydrolysis of d-HGluc using HPLC (Fig. 1), optical rotation and conductometry. As previously indicated by Pocker and Green [77], Combes and Birch confirmed the strong impact of the background electrolyte on the optical properties of gluconate and its derivatives. Hence, the specific rotation of HGluc in pure water was quantified as -5.11°, in contrast to the values of Sawyer and Bagger [74] as well as Pocker and Green [77], but in agreement with the one reported by Mitchell and Duke [75] as well as Kutus et al. [82] (Table 3). This indicates that previous publications [74,77] using higher specific rotation of HGluc likely overestimated its concentration, thereby overestimating log K p and underestimating log K d . The authors were able to quantify k 1,d and k -1,d for the d-lactonization of HGluc (via polarimetry), and also demonstrated that 140 h are not sufficient to reach the equilibrium of the formation of c-HGluc. Escandar and Sala [7] studied the dissociation constant of HGluc and its complexes with Cu(II) by potentiometry. Experiments were performed at t = 20°C using 0.10 M NaNO 3 as background electrolyte. Both solid NaGluc and d-HGluc were used as initial source of gluconate, dissolved in standard base and back-titrated by stepwise addition of standard acid. Both titration curves led to similar results ( Table 1). The back-titration approach is considered to provide reliable log K p due to the minimization of the presence of lactone in the aqueous solution.
Best et al. [19] assessed the acid-base properties of gluconate (among other hydroxycarboxylic acids) and its complexation with Al(III) using a series of potentiometric titrations in 0.1 M NaCl. d-HGluc was chosen as initial source of gluconate in the experiments. The authors indicated that 3 to 4 h were necessary for the equilibration of some titration points, although no exact reference is provided to the case of gluconate. Best and co-workers did not specify either whether HCl or NaOH were used as titrating solutions, although the good agreement with other studies suggests that a back-titration with HCl was performed. Due to the use of d-HGluc as source of gluconate, the authors indicated that log K p,app rather than log K p was obtained from their experimental data.
Gajda et al. [10] investigated the role of hydroxy groups in the coordination chemistry of polyhydroxy carboxylic acids, including HGluc. Using potentiometric titrations at t = 25°C and I = 0.1 M NaClO 4 , the authors determined the log K p of Gluc -. In the case of aldonic acids (such as HGluc), a back-titration with HClO 4 starting from alkaline pH was used to avoid the error caused by lactonization.
Zubiaur et al. [79] studied the equilibrium d-HGluc/HGluc/Glucby means of potentiometric titrations. The authors conducted their experiments in 0.1 M I 3.0 M NaClO 4 . All titrations were performed from acidic to alkaline conditions, starting in all cases from d-HGluc. The authors observed strong kinetic effect on the pH readings within 3.8 pH c 6.5, and consequently allowed an equilibration time of 4 h for each titration step and thus approximately 2 weeks for each titration series. The authors, however, did not use any speciation technique to identify the different gluconate species in solution, but they assumed the lactonization reaction to be the formation d-HGluc and they fitted their potentiometric data optimizing log K p and log K d at different ionic strengths. This approach allowed them to obtain the thermodynamic constants by extrapolating the conditional constants to zero ionic strength.
Giroux et al. [11] combined potentiometry, UV-vis spectrophotometry, circular dichroism experiments as well as 1 H and 13 C NMR to assess the acid-base properties of Glucand its complexes with Pr(III). Experiments were performed in 0.1 M NaClO 4 at t = 25°C via performing potentiometric titrations under acidic to alkaline conditions. A fast initial acidification of the starting gluconate solution and the optimization of the titration speed (to avoid lactone formation and allow a good stabilization of the measurements) were considered to minimize the interference caused by lactonization. The log K p reported in this publication is in good agreement with other potentiometric studies conducted by back-titration, indicating that the authors probably succeeded in minimizing the amount of c/d-HGluc in their experiments.
Bechtold et al. [35] studied the stability of Ca(II)/Fe(III) gluconate complexes and their electrochemical properties by a series of potentiometric titrations. As a first step in the study, the authors determined the acidity constant of HGluc in the absence of calcium (II) and iron(III). Experiments were performed at t = 20°C in 0.1 M KNO 3 as background electrolyte. Titrations were conducted within 2 pH c 11.6 using a back-titration approach with 0.1 M HNO 3 . Considering the overall short duration of one measurement (~1 h), the log K p determined in this work is realistic.
Zhang et al. [16] studied the protonation of gluconate and its complexation with Np(V) in acidic to near neutral pH conditions using potentiometric titrations and UV-vis spectrophotometry. Experiments were performed in 1.0 M NaClO 4 at t = 25°C. Fast potentiometric back-titrations (60 s per titration point) were conducted at 3 pH c 6 with HClO 4 (Fig. 2). This approach was aimed at minimizing the impact of lactonization on the determination of log K p .
Zhang et al. [81] investigated the lactonization and deprotonation of HGluc using 13 C NMR, potentiometric titrations and ESI-MS techniques. 13 C NMR measurements were performed to assess the equilibrium described in Eq. (1). All samples were prepared in D 2 O, whereas DNO 3 and NaOD were used to adjust the pH. All solutions were prepared as 0.1 M NaGluc and let equilibrate for 3 days. Provided the very slow kinetics of the lactonization/hydrolysis reactions, the lactone 13 C NMR peaks (both for c-HGluc and d-HGluc) appear separately from those of HGluc/Gluc -. Furthermore, the peak positions of the lactones are pH-independent. Consequently, given the pH c is known, log K p can be deduced from the variations of the chemical shifts of HGluc/Gluc -, regardless of the amount of lactones formed. This property renders NMR spectroscopy to be an important tool to study acid-base equilibria without the interference of the lactonization.
Independent batch samples of different pH c and at constant concentration of NaGluc (0.05 M) were prepared in 0.1 M NaClO 4 and let equilibrate for at least 3 days. The concentration of the hydrogen ion in each solution was measured with a combination pH electrode, and the resulting log K p,app apparent data were fitted taking log K p determined by 13 C NMR into consideration. This approach made the determination of log K d possible, however, a discrepancy has been identified affecting the estimation of log K d , which was quantified using log K p and log K p,app determined in In the final step, Zhang and co-workers determined the rate coefficient of the d-lactonization of HGluc (k 1,d ) by ESI-MS (Fig. 3). Based on Eq. (13) and using the value of log K d determined by potentiometry, the authors were also able to calculate the rate constant of the lactone hydrolysis (k -1,d ).
Lakatos and co-workers [20] reported on the complexation of Glucwith Al(III) in the pH c range of 2-10 at t = 25°C and I = 0.2 M KCl. They calculated log K p by conducting potentiometric titrations starting from acidic pH. To avoid lactonization, the samples were acidified just before the measurements. Additionally, the pH c was always kept higher than 2, hence, the rate of lactonization / lactone hydrolysis processes was expected to be markedly slower than that of protonation / deprotonation reactions.
Pallagi et al. [25] studied the acid-base properties of gluconate and its complexation with Ca 2+ using 1 H, 13 C and 43 Ca NMR. Experiments were performed in 1.0 M NaCl-NaGluc mixtures, with 0.2 M NaGluc in most of the cases. D 2 O was present in all samples in a concentration of 20% v/v. The pH of the mixture solution was calculated as pH mixt = pH obs + 0.08, considering that pD = pH + 0.40, independently of the ionic strength. It is noteworthy that pH mixt is not equal to pH c as it was recorded in solutions of I = 1 M, while the electrode was calibrated with dilute buffer solutions. The protonation constant of Glucwas obtained from the variations of the 1 H and 13 C NMR chemical shifts upon decreasing the pH mixt from 6.6 to~1.8. As in the case of Zhang et al. [81], Pallagi and coworkers observed the development of additional lactone peaks in the 13 C NMR spectra upon decreasing the pH mixt below~3.8. Kutus et al. [14] studied the complexation of gluconate with neodymium(III) at 2 pH c 8 using a combination of experimental methods (spectrophotometry, potentiometry, freezing point depression, conductometry and NMR spectroscopy). Because of the pH c range considered for the study of the complexation, the authors determined the protonation constant of Gluc -, too, by fitting the potentiometric and photometric data simultaneously. Titrations were performed with HCl and started from weakly alkaline conditions to minimize the impact of lactonization, while in the case of photometric measurements, the spectra were recorded directly after sample preparation.
Kutus and co-workers performed a comparative study on the protonation and lactonization of HGul and HGluc using various experimental methods [82]. Fast potentiometric titrations and polarimetric measurements were used for the quantification of the protonation equilibria. Based on their polarimetric measurements, the authors reported the specific rotation of HGluc in 1.0 M NaCl as -(5.7 ± 0.8)°. This value agrees well with the specific rotation reported by Combes and Birch [78] in pure water (-5.11°).
Additionally, the pH-dependence of the specific rotation of the HGluc/Glucsystem was used to calculate log K p . As opposed to the potentiometric titrations, the pH obs (measured together with the optical rotation) is not equal to pH c , as in the case of Pallagi et al. [25]. Thus, the difference between pH obs and pH c is a plausible explanation for the discrepancy between log K p (POL) and log K p (POT) ( Table 1). The latter was chosen as the real protonation constant by the authors and within experimental error, it is identical with the one obtained by the same group at I = 1 M NaCl [14].
Furthermore, 13 C NMR spectroscopy was used to distinguish between the two lactones and to determine log K d and log K c (Fig. 4). The values reported in this work are in good agreement with those from Refs. [75,76,78,81]. Furthermore, they clearly show that the lactones are formed to the same extent. Using log K p (POT) as well as the two lactonization constants, the value of 3.53 is obtained as log K p,app , which is higher by 0.16 than log K p (POT). This difference sets an upper limit to which extent the log K p can be overestimated at I = 1 M NaCl by neglecting lactonization equilibria.
Kutus et al. [31] reported on the complexation of gluconate with Mg 2+ ions in the pH c range of 2-13 studied by potentiometry, infrared, 1 H and 13 C spectroscopies. As for the pH c measurements, fast titrations were performed at t = 25°C and I = 4 M using NaCl as background electrolyte. Using the data obtained in the acidic range, the authors deduced log K p .
In summary, a plethora of data regarding the protonation of gluconate and the lactonization of gluconic acid have accumulated over the past five decades. It is apparent from the magnitude of the lactonization constants that under strongly acidic conditions, the formation of cand d-lactones has to be taken into account for a proper thermodynamic description of gluconate-containing  systems. Resolving the parallel (de)protonation, cand d-lactone formation (or reverse hydrolysis) processes is possible with careful experimentation as well as with the combination of various experimental means, including NMR spectroscopy. As for the lactonization kinetics, the formation d-HGluc is much faster. Despite this, the formation constants of cand d-HGluc are essentially the same (within their reported uncertainties), indicating that (via Eq. (13)) the hydrolysis of the c-isomer is much slower. The higher stability of the five-membered ring is in line with the observaation made for the diastereomeric L-gulonic acid c-lactone [82]. Carbohydrates and their derivatives (e.g., aldoses, ketoses, sugar alcohols) interact weakly with calcium as well as with other alkaline earth metal ions. This is due to the relatively low electron density of the oxygen donor atoms, present in hydroxy, formyl and oxo groups, which are not strong competitors of the H 2 O molecules bound to the metal ion. Consequently, the complexes, which are formed in weakly acidic to weakly alkaline solutions are of low stability and are of almost exclusively 1:1 stoichiometry [86].
As for Ca(II) complexes, these features lead to difficulties in the quantitative characterization of complexation equilibria with conventional methods (such as potentiometry, spectrophotometry, conductometry and calorimetry). First, the use of high metal and ligand concentrations is required. Second, such complexes are not detectable by UV-vis. A further complication is associated with the simultaneous formation of conformational isomers in these aqueous solutions. That is, when the association reactions between Ca 2+ ions and carbohydrate derivatives are studied, only the average variations are detectable, hence, only the macroscopic equilibrium constants can be determined.
Molecular properties, such as electron density, optical activity or X-ray absorption can also be utilized when studying solution equilibria and structure. Polarimetry and NMR spectroscopy have been proven to be useful to extract complex formation constants. Furthermore, given the different conformers are long-lived enough on the NMR timescale, their metal-binding processes can be quantified independently. As for solution structure, various methods, such as NMR, X-ray absoprtion fine structure (EXAFS), infrared and Raman spectroscopies can be applied to identify the metalbinding sites of the ligands as well as to provide additional structural information (e.g., bond lengths and angles, coordination numbers). The two vibrational spectroscopies are also essential, together with X-ray diffraction, to characterize the coordination compounds in the solid phase. Additionally, in the past few decades, structure optimization employing quantum chemistry emerged as an important tool to elucidate the nature of such metal-ligand interactions.
To separate the effects of different functional groups on the complex stability and solution structure, first gluconate-related compounds having only OH groups are discussed. Due to the weak binding ability of the OH moieties, the stability of the Ca(II) complexes forming with D-glucose and sugar alcohols heavily depends on the steric arrangement of these groups, as identified by Angyal and others [87][88][89][90][91][92][93][94][95][96]. In general, the favorable arrangement of at least three OH groups is desirable for complexation both for cyclic and open-chain ligands. For ring structures, the most stable structures are a) six-membered / pyranose rings having three nonadjacent OH groups in triaxial (ax-ax-ax) arrangement or b) three adjacent OH groups in axial-equatorial-axial (ax-eq-ax) sequence or c) five-membered / furanose rings with OH functions with the same ax-eq-ax motif (Scheme 2a-c). Acyclic polyols, whose OH groups are situated on the same side of the plane (threo-threo), exhibit stronger binding than those having erythro-threo or erythro-erythro arrangement (Scheme 2d-f). Accordingly, the order of complex stability is expected to be ax-ax-ax (sixmembered) > ax-eq-ax (six-membered) > ax-eq-ax (five membered) as well as threo-threo > erythro-threo > erythro-erythro.
The association reaction between the Ca 2+ ion and a sugar-type ligand (L) as well as the corresponding thermodynamic (b 11 0 ) and conditional (b 11 ) 1:1 stability constants are defined as where a, c denote activities and activity coefficients, brackets stand for molar concentrations of a given species in equilibrium and c ø is the standard molar concentration (1 M).
As for D-glucose ((2R,3S,4R,5R)-2,3,4,5,6-pentahydroxyhexanal, Glu, Scheme 3), however, neither the anor the b-Dglucopyranose isomer (Scheme 3) has a favourable steric arrangement, thus, Glu is not able to form stable complexes with Ca 2+ . Indeed, the log b 11 constant could not be deduced from 1 H NMR spectroscopic [88], thin-layer chromatographic [97] and potentiometric (employing Ca 2+ -ion selective electrode, Ca-ISE) [66,70,98] measurements. The value of log b 11 was suggested to be smaller than -1 in Ref. [66] which agrees with the one (-1.12) obtained from conductometric experiments performed at 30°C [99]. Contrary to the observations reported by Angyal [88], Pallagi and co-workers were able to determine the stability constant both for the a (log b 11 = 0.18) and b (log b 11 = 0.23) anomeric forms from the gradual upfield shift of the 13 C NMR peaks upon the addition of CaCl 2 at t = 25°C [100]. These constants, however, should be considered with care. First, they were obtained by assuming that either the aor the b-anomer is solely present, therefore they are Scheme 2. Steric arrangements of the OH groups for calcium(II) complexation in the order of decreasing complex stability. For cyclic triols: a) 1,3,5-ax-ax-ax triol and b) 1,2,3-ax-eq-ax triol on a six-membered ring; c) 1,2,3-ax-eq-ax triol on a fivemembered ring. For acyclic triols: d) threo-1,2-threo-2,3, e) erythro-1,2-threo-2,3 and f) erythro-1,2-erythro-2,3 sequences. upper estimates and refer to an average effect of the Ca(II) complexation on the 13 C chemical shifts. Second, although the ionic strength was adjusted to 1 M in each sample using NaCl, the ionic medium was replaced almost completely to CaCl 2 at the highest concentrations of Ca 2+ . Considering this ''medium effect", the constants obtained can be regarded as semi-quantitative estimates at best.
In the same work, insights into the structure of the CaGlu 2+ solution species have been gained as well. Based on the variation of the peak areas of the two isomers, the authors concluded that the relative weight of a-anomer increases upon metal ionbinding. Using the 1 H- 43 Ca heteronuclear multiple quantum coherence (HMQC) two-dimensional NMR technique, the interaction between the Ca 2+ ion and the C(1)OH group (adjacent to the ethereal oxygen) was revealed for both anomers. On the other hand, molecular modeling performed at the HF/6-31G(d,p) level suggested the additional coordination of the ethereal oxygen as well as C(6)OH. In conclusion, the binding of Ca 2+ is likely to take place to a small extent in aqueous solutions; however, the formation constant is too low rendering its quantitative determination to be difficult. Similarly to D-glucose, it can be stated that the extent of association is small, thus, the actual value of the formation constant is very sensitive to the experimental method, the ionic strength and the concentrations of the metal ion / ligand applied. The majority of the literature data [70,84,95,96,100,101], however, is consistent with the average value of 0.0 ± 0.3 for log b 11 . Additionally, comparing the results obtained for Glu and Sor, it can be stated that the second forms more stable complexes with the Ca 2+ ion. This can be explained by the favorable threo-threo arrangement of Sor (Schemes 2 and 3) and by the flexibility of this ligand. That is, the large number of coexisting conformations results in more favored reactions in view of entropy.
As for the structure of the CaSor 2+ complex, the metal-binding sites were proposed to be the C(1)OH, C(2)OH, C(4)OH and C(6) OH groups, based on the long-range couplings observed in the 1 H-43 Ca HMQC spectrum [100]. Conversely, C(3)OH should be the coordinating group due to the threo-2,3-OH motif. Owing to the very broad 1 H peaks, however, the peak assignment was not obvious. Based on the assignment of the 1 H NMR peaks reported previously [102], the most probable binding sites are, indeed, the C(1)OH, C(2)OH and the C(3)OH groups, while the fourth one can be either the C(4)OH or C(6)OH.
Expectedly, introduction of a negatively charged anchoring group (e.g. carboxylate) into the ligand will result in the formation of complex(es) with significantly higher stability. Oxidizing the terminal CH 2 OH group of D-glucose, the D-glucuronic acid or its deprotonated form, the D-glucuronate ion ((2S,3S,4S,5R)-2,3,4,5-tet rahydroxy-6-oxohexanoate, Glucur -, Scheme 4) can be obtained. Due to the presence of the CHO group, Glucuris known to exist in a and b pyranose forms. Since this ligand provides an interplay between structural rigidity and strong binding affinity, studying its Ca(II) complexation is useful to understand which factor has stronger impact on complex stability. Gould (15)), calculated by extrapolating from the data for log b 11 obtained at I = 1 M and 2-4 M (not shown), and from those of Refs. [33], [63] and [66]. d Thermodynamic formation constant (log b 11 0 , Eq. (15)), obtained by extrapolating data for log b 11 to infinite dilution. e Thermodynamic formation constant (log b 11 0 , Eq. (15)), calculated from the data for log b 11 , reported in Ref. [63]. f This constant has been recalculated in this work from the one reported in Ref. [26], assuming the formation of the Ca 2 Gluc 2 H -4 0 complex [28]; for discussion, see lower constant was determined by Kutus and co-workers [70] (log b 11 = 0.80, t = 25°C, I = 1 M NaCl), which is consistent with the higher ionic strength employed. Although there is a considerable uncertainty in the formation constant, it can be safely deduced that log b 11 (CaGlucur + ) is higher not only than log b 11 (CaGlu 2+ ) but also than log b 11 (CaSor 2+ ). Consequently, the presence of a strong binding group overcomes the destabilizing effect caused by the rigid structure (CaGlucur + vs. CaSor 2+ ). D-gluconate exhibits both enhanced metal ion-binding and flexibility, also possesses the favorable threo-threo configuration adjacent to the COOgroup (Schemes 1 and 4). Regarding the Ca(II) complexation equilibria of Gluc -, a great body of research has been devoted to determine the stoichiometry of the Ca(II) complex as well as to quantify its binding strength. Under near-neutral to slightly alkaline pH conditions, the complex formation takes place between Ca 2+ and Gluc -, mainly (in fact, almost exclusively) 1:1, although the formation of the 1:2 complex was also detected at very high [Gluc À ] T /[Ca 2+ ] T ratios.
For the CaGluc + aqueous species, the thermodynamic association constant, log b 11 0 , was found to be in the range of 1.7-1.9 [25,27,65,67] when extrapolating the experimental data to zero ionic strength. These constants are listed in Table 4. Conversely, the log b 11 0 values obtained for the Ca 2+ complexes of monocarboxylate compounds is about one order of magnitude lower [106]. This is most probably due to the absence of alcoholic OH groups on the ligand, which rules out the possibility of the formation of chelate structures. At finite ionic strengths, a plethora of data for the formation constant have been published applying various experimental methods. The values of log b 11 vary in the range of 0.70-1.36 and were obtained from potentiometric titrations employing platinized platinum hydrogen [26,66], glass [13] and Ca 2+ ion-selective electrode [33,38,66,[68][69][70]95], ion-exchange [63] and 13 C NMR spectroscopic [25] measurements. All these constants are presented in Table 4.
Contrary to the CaGlu 2+ , CaSor 2+ and CaGlucur + complexes, there is a lower uncertainty in the stability constants for the CaGluc + species, given that the ionic strength is the same (or very similar). By way of example, the log b 11 varies between 1.08 and 1.21 at I = 1 M, corresponding to NaCl [25,68,70] or NaClO 4 [70]. The only exception is the value of 0.37 [26], which has been recalculated to be 0.70 in this work (see Section 4.2). Still, this value is probably underestimated, since it was obtained from potentiometric titrations applying a platinum electrode, which is less sensitive to this pH-independent complexation reaction than a Ca 2+ ion-selective electrode.
Based on the majority of literature data, it can be concluded that the stability of the 1:1 complexes follows the order of Gluc -% Gul -% Hpgl -> Glucur -) Sor ) Glu, which reflects the crucial role of COO -(Glucvs. Sor as well as Glucurvs. Glu) and ligand flexibility (Glucvs. Glucuras well as Sor vs. Glu) on the binding strength.
At higher [Gluc À ] T /[Ca 2+ ] T ratios, the formation of the 1:2 calcium complex, CaGluc 2 0 , was claimed to be observed first by polarimetric measurements performed by Sipes [64]. Later, Ca-ISE potentiometric measurements carried out by Masone and Vicedomini [33] yielded log b 12 = 1.88 (t = 25°C, I = 0.5 M NaCl). Additionally, further Ca-ISE [69] and 13 C NMR [25] measurements implied its formation, though, the variations were too small preventing a quantitative evaluation. A recent study by Kutus et al. [70] was aimed at clarifying whether the formation of the CaGluc 2 0 complex really takes place and attempts were made to accurately determine its formation constant. The same research group carried out analogous measurements with Gul - [107] and Hpgl - [70]. During the potentiometric titrations using Ca-ISE (e.g., the Ca 2+ -Glucsystem, Fig. 5), the observed cell potentials were found to shift towards smaller [Ca 2+ ] values to a much higher extent than those observed with uncharged ligands, like Glu and Sor [70,84]. Moreover, the titration curves obtained for Gluccontaining  systems were found to be essentially identical to those measured for Hpgland Gulcontaining solutions. Accordingly, the stability constants for the complexes of Gluc -, Guland Hpglwith calcium(II) are (not surprisingly) similar. The results of the calculations assuming solely the formation of the CaGluc + species are depicted as dashed lines in Fig. 5. The log b 11 constant obtained (1.23, not shown in Table 4) [70] agrees reasonably well with other values obtained via Ca-ISE titrations [13,25,33,63,66] especially if one considers the different ionic strength applied.
It is obvious, however, that there are systematic deviations between the observed and calculated data (even for the points falling in the linear section of the calibration curve), when only the formation of the 1:1 complex is assumed. (The same observations were made for the titration curves of the other two ligands, Guland Hpgl -, too). Thus, in the next step, formation of the 1:2 complex (CaL 2 0 ) was also considered: Including the 1:2 complex, the abovementioned errors practically disappear (demonstrated by the solid lines in Fig. 4). Thus, this model was accepted in this study and the corresponding computed stability products for the 1:1 and 1:2 complexes are presented in Table 4. The Ca(II) concentration distribution diagram calculated for the Ca 2+ -Glucsystem (Fig. 6) attests that the formation of the 1:2 species exceeds 30% of [CaCl 2 ] T at high ligand to metal ratios and similar values were computed for the other two ligands (Guland Hpgl -) as well.
Regarding CaGluc 2 0 , the value obtained in this work for log b 12 is commensurate with that reported previously [33] and the difference can be accounted for the various ionic strength applied (0.5 M NaCl in Ref. [33] vs. 1 M NaCl in Ref. [70]). In conclusion, this hitherto uncertain species was proposed by different experimental methods [25,33,64,69,70] therefore its existence can be postulated. In light of these findings and structural similarity, the formation of CaHpgl 2 0 and CaGul 2 0 is not surprising (see their formation constants in Table 4).

The structure of the complexes forming in or crystallized from neutral solutions
The association of alkaline metal ions is known to affect the optical activity of the interacting ligand [108]. The optical rotation of such solutions (exemplified in Fig. 7) gradually decreases with increasing calcium concentration indicating that upon complexation, the optically active complexes formed have a specific rotation smaller than that of the uncomplexed anion. Although the direction of this variation is well-defined, its magnitude (0.5°for Gluc À ) is rather small, despite that about 75% of Gluc À is bound in the two complexes at the highest CaCl 2 concentration (calculated from the formation constants listed in Table 4). In conclusion, the specific rotations of the free ligand and that of the complexes are only slightly different entailing that accurate determination of the formation constants via polarimetry is not possible.
On the other hand, the experimental optical rotations (Fig. 7) could be fitted well by using the formation constants of CaGluc + and CaGluc 2 0 obtained from Ca-ISE titrations (Table 4) [109]. This calculation indeed yielded specific rotations being not very much different for the complexed and uncomplexed forms of gluconate. Polarimetric measurements resulted in the same outcome for heptagluconate and gulonate, too. (The specific rotations are listed in Table 5.) In conclusion, the formation of the 1:1 and especially the 1:2 complexes affects the equilibrium conformation of Gluc À to a minor extent.
Regarding the structure of the CaGluc + solution species, the coordination of the COO -, C(2)OH and C(4)OH (originally interpreted as C(3)OH) was suggested on the basis of the variation of 13 C NMR chemical shifts [24]. In a recent publication, the 1 H-43 Ca HMQC NMR measurement (Fig. 8) attested the coordination of C(2)OH and C(3)OH groups [25]. The authors suggested the simultaneous formation of linkage isomers in which either the C(2)OH or both C(2)OH and C(3)OH functions act as binding sites. Quantum chemical calculations suggested that the second is more stable, which can be elucidated that in this isomer, two five-membered chelates are formed, while only one (sixmembered) chelate is present in the first structure. It has to be noted that Gluchas the threo-2,3-threo-3,4-triol sequence, therefore the Ca(II) chelation by C(2)OH, C(3)OH and maybe C(4)OH is preferred.
From recent quantum chemical calculations by Bugris et al. [29] (taking implicit and explicit solvent effects into account), it was demonstrated that the most stable structure of the aqueous CaGluc + complex involved the binding of the O1, O2 and O3 oxygen atoms. For the lowest-energy structure (Fig. 9), the Ca 2+ ion is bound to one oxygen of the COOgroup and also coordinated by the C(3)OH moiety, yielding the coordination number of 6. When the Ca 2+ is assumed to be bound to the COOand C(2)OH groups, the free energy of this isomer is only 3.4 kJÁmol À1 higher than that of the previous one. This difference is not significant considering that the energy of thermal motion is 2.48 kJÁmol À1 at 25°C. This finding supports the previous assumption of Pallagi et al. [25], namely, the co-existence of these two isomers. Furthermore, in both isomers, Glucacts as a bidentate ligand, and several intramolecular hydrogen bonds contribute to the stabilization of the overall structure.
In the case of Hpgl -, two-dimensional 1 H- 43 Ca NMR measurements revealed the probable coordination of all the three OH functions [71] inferring the coexistence of coordination isomers. The Ca(II) ion, on the other hand, is bound to four heptagluconate anions acting as bidentate ligands and to a water molecule in the CaHgpl 2 Á4H 2 O single crystal [110]. The carboxylate group binds Ca 2+ in a monodentate manner, in line with the findings for the CaGluc + aqueous complex [25,29].
The significance of the calcium salt of D-gluconic acid has already been mentioned. Therefore it is somewhat surprising that the crystal structure of CaGluc 2 ÁH 2 O(s) has been determined and published only recently [29]. The reason for this may be that slow cooling of an aqueous solution yields fine needles that are unsuitable for single crystal X-ray diffraction studies. The hanging drop vapour diffusion method however resulted in almost isometric single crystals with the size of approximately 0.05 mm Â 0.02 mm Â 0.01 mm. The CaGluc 2 ÁH 2 O crystallizes in orthorhombic system, forming coordination polymers (Fig. 10). The coordination number of the Ca 2+ ion was found to be nine, considered to be surprisingly high compared to the majority of other Ca(II) containing structures [111], (e.g., it was found to be 7 in the lactobionate complex of Ca(II), where the metal ion is coordinated to the gluconate part of the lactobionate ion [112]). Furthermore, the coordination polyhedron of Ca 2+ is that of a distorted triaugmented triangular prism. Similarly to Hpgl - [110], bidentate coordination of the carboxylate ion was not discernible. Conversely, two of these groups act as a bridging ligand by binding two metal ions simultaneously, in a monodentate manner (Fig. 10). Such coordination motic has been deduced from the infrared analysis of the solid CaGluc 2 salt [24].

Acid-base equilibria and Ca(II) complexation of Gluc À in alkaline solutions
Alkaline conditions are of paramount relevance in the field of the coordination chemical interactions between calcium(II) and gluconate ions. As it was already mentioned, the underground repositories for the deposition of low-and intermediate-level radioactive waste are of general importance due to safety reasons. As repositories make frequent use of cement-based materials, alkaline pore water may form by incidental water intrusion [113][114][115]. Gluconate, being an additive to Portland cement [2,[43][44][45][46], is likely to be present in these systems [53]. The ability of Glucto bind metal ions (as it will be shown below) becomes more pronounced in these alkaline systems, therefore the quantitative description of complexation processes between Glucand the constituents of concrete, e.g., calcium(II) ions is of particular interest.
Furthermore, Glucwas proposed to be the model compound of different organic substances (e.g., humic substances) that might be present in strongly caustic Bayer liquors [116,117]. It has also been  reported, that the solubility of Ca(OH) 2 (s) (used for NaOH recovery) is severely affected by a range of complexing ligands, in particular Gluc - [116][117][118].
The enhanced complexing ability of Glucis certainly associated with the involvement of alcoholate (O À ) moieties in the metal ionbinding (beside that of the COO À group). First, we summarize our current knowledge on the acid-base properties of the alcoholic hydroxy groups of Gluc -. For comparison, data for some hydroxycarboxylates closely related to Glucare also discussed.

Deprotonation of the alcoholic OH of Gluc À in strongly alkaline medium
Alcohols are weak acids, and for the acid dissociation reaction the acid dissociation constant log K a is -15.5 and -16.0 for methanol and ethanol, respectively [119]. The acidity of simple hydroxycarboxylates are usually similar to these values or even smaller [120,121]. For statistical reasons, polyhydroxy carboxylates are stronger acids, since each additional OH group decrease the pK a with 0.3 logarithmic unit [122].
The conditional acid dissociation constant, K a , for a hydroxycarboxylate anion, L À , in general can be expressed as: where K p is the protonation constant of AH -1 2and c ø again stands for the standard molar concentration, 1 mol•dm À3 or M. To demonstrate how the acidity of Glucchanges in the presence of Ca 2+ under alkaline conditions, the log K a instead of log K p will be discussed in this Section. Most probably due to experimental challenges, only a few data are available in the literature for the log K a of Gluc -. The available methods for determining K a are limited to potentiometry using H 2 -Pt electrode or NMR titrations. As it can be seen, potentiometric effects caused by alcohol deprotonation (Fig. 11) may reach pH c % 0.2 units (% 12 mV), which is (using careful experimentation) readily and accurately measurable and expected to provide reliable values for log K a values. The values discussed in this Section are listed in Table 6.
In the first report on the deprotonation of Gluc À to form GlucH -  NaClO 4 ) was published by Roos and Williams, who used glass electrode [84]. Combining this method with 13 C NMR, a value of -13 ± 1 (t = 22°C, I = 0.1 M NaClO 4 ) was proposed by Zhang and coworkers [81]. The considerably high uncertainty of log K a is reasonable in light of that pH c measurements were limited to < 13, due to the poor performance of the glass electrode at such high pH c . Hence, the authors observed only partial deprotonation of Glucand their value can be regarded as a semi-quantitative estimation.
Employing H 2 -Pt electrode, known to be more accurate for pH measurements in alkaline solutions, similar values of log K a (t = 25°C, I = 1 M) were reported by two different groups [23,26]. Coccioli and Vicedomini [23] also concluded that GlucH -1 2can be further deprotonated, yielding GlucH -2 3-(t = 25°C, I = 1 M NaClO 4 ). In a recent study, Buckó et al. [28] conducted H 2 -Pt potentiometric and 13 C NMR studies at t = 25°C and I = 4 M (using NaCl as inert electrolyte). The log K a deduced from the titrations is in excellent agreement with the one obtained by Kutus et al. [31] under identical experimental conditions, using however glass electrode.
As for the NMR experiments, inclusion of the two-fold deprotonated Glucwas necessary to obtain an acceptable fit for the 13 C chemical shifts (see the dashed and solid lines in Fig. 12). This finding confirms that of Coccioli and Vicedomini [23], whose value is however higher by 0.7 logarithmic units. This discrepancy can be attributed to the difference in the ionic strength as well as well as to the different methods employed. In case of H 2 -Pt potentiometric titrations in Ref. [28], the ratio of [NaOH] T /[NaGluc] T was limited to lower values as compared to the 13 C NMR experiments. Consequently, the formation of the GlucH -2 3was not observed by this technique. The log K a for GlucH -1 was also determined at t = 50 and 75°C (Table 6) by Buckó et al. [28]. The temperature-dependent constants thus obtained allowed the calculation of the enthalpy and entropy changes of deprotonation applying the van't Hoff equation (DH = 57 kJ mol À1 and DS = -79 J•mol À1 K À1 ). With regard to hydroxycarboxylates closely related to Gluc -, log K a was reported to be -13.41 for Hpgl -, determined by H 2 -Pt potentiometric measurements (t = 25°C, I = 1 M NaCl) [71]. The higher acidity of Hpglcan be explained by the statistical effect of the higher number of OH functions [122]. With regard to the deprotonation of Gul -, H 2 -Pt electrode and 13 C NMR studies (t = 25°C, I = 1 M) yielded log K a = -13.72 and -13.75, respectively [30]. The latter values are practically identical to those found for Glucunder identical experimental conditions. Contrary to this, the log K a value for Isa -(at t = 25°C, I = 1 M NaCl) was found to be almost one order of magnitude lower from 13 C NMR measurements [72], which indicate that Isais significantly weaker acid than Gluc -. These observations (and others, see Section 4.2) led to the conclusion, that ''caution should be exercised when using gluconate as a thermodynamic model for isosaccharinate" [123].

Formation of complexes between Ca(II) and Gluc À under alkaline conditions
When the pH of a solution, containing Ca 2+ -ions in a concentration of around 0.1 M, is raised to pH % 13, the formation of a large amount of Ca(OH) 2 (s) (portlandite) precipitate can be observed. Addition of NaGluc (in excess relative to Ca 2+ ) to this precipitate was found to result in instantaneous dissolution of the solid. This simple test-tube experiment served as the starting point for studying interactions between Ca(II) and gluconate in alkaline solutions. Table 6 Conditional deprotonation constants (log K a , Eq. (20)) for D-gluconate (Gluc -), D-heptagluconate (Hpgl -), L-gulonate (Gul -) and a-D-Isosaccharinate (Isa -), organized by the reaction and background electrolyte concentration. Data correspond to t = 25°C unless indicated differently. Where reported, triple standard errors are included in parentheses.
Upon deprotonation of the OH group, an alcoholate (O À ) is formed, which (due to its increased basicity) is a much more effective binding site for bi-, tri-and tetravalent metal ions, than the OH moiety. Metal ions (i.e., Ca 2+ ), in turn, facilitate the deprotonation of the OH groups and the parallel complex formation. In other words, Ca 2+ decreases the pK a of the ligand, that is, increases the acidity of the alcohol group, since it is a strong competitor of H + for the O À moiety. This process is the well-known metal-ioninduced (or promoted) ligand deprotonation.
For metal-ion polyhydroxy carboxylate complexes, van Duin et al. proposed a generalized scheme [124]. According to this, at first the deprotonation of the COOH group takes place, which is followed by the dissociation of the neighboring a-OH group. Finally, a further H + is displaced from another (not necessarily the b-) OH functional group, resulting in the coordination of the metal ion by a diolate moiety. It was predicted that for alkaline earth metal ions, the OH deprotonation occurs in solutions of pH ! 10.
Ca(II)-complexes forming via ligand deprotonation have higher stability, as the Ca(II)-alcoholate interactions are plausibly stronger than those with OH. In some early works, it was already stated that with increasing pH, the calcium sequestering capacity is enhanced in alkaline solutions containing Glucand Hpgl - [125].
For calcium complexation, the general complexation reactions and the corresponding b pq-r conditional stability products can be expressed as: where Lstands for polyhydroxy carboxylate anions. Sipes [64] in his Ph.D. thesis observed the displacement of the alcoholic proton from the CaGluc + complex in the pH range of 10-11, using polarimetry. In the same work, the formation of a Ca(II) gluconate complex of 2:1 metal:ligand stoichiometry was invoked at higher pH.
The interactions between calcium ions and Gluc À at high pH were studied in detail in the work of Pallagi et al. [26]. Systematic pH-potentiometric measurements (Fig. 13) using the H 2 -Pt electrode revealed the simultaneous formation of both mono-and polynuclear complexes containing calcium ion(s) and deprotonated Gluc À molecule(s). When only the plausible CaGlucH -1 0 species was included in the speciation model, the experimentally observed cell potential values were not correctly reproduced. The very pronounced dependence of the titration curves on the metal ion concentration (Fig. 13) already strongly indicated the possible formation of polynuclear complex(es). This is not unprecedented, as the removal of protons from hydroxycarboxylates and the simultaneous formation of remarkably stable polynuclear complexes were reported for other metal ions, e.g., for Cu(II) [3,7,10]. From these potentiometric titrations, the best chemical model included the following species: CaGluc + , CaGlucH -1 0 , Ca 2 GlucH -3 0 and Ca 3 Gluc 2 H -4 0 , in addition to the monohydroxido complex of Ca(II), namely, CaOH + [126]. Recently, it was found that the solution equilibrium of Ca(II) is dominated by the Ca(OH) 2 0 aqueous complex in ligand-free solutions (hence, CaOH + is a minor species) [127]. Furthermore, recent calculations revealed that Ca 2 GlucH -3 0 can be replaced by Ca 2 Gluc 2 H -4 2À (yielding the same fitting quality), which was shown to form in a broad temperature range (see below) [28]. Although, the 2:1:-3 and 2:2:-4 species are apparently not easily distinguishable under the experimental conditions in Ref. [26], here the model consisting of CaGluc + , CaGlucH -1 0 , Ca 2 -Gluc 2 H -4 2À and Ca 3 Gluc 2 H -4 0 is chosen. Accordingly, the original dataset were reevaluated using this speciation model and the for-mation constants of CaOH + and Ca(OH) 2 0 [127]; the corresponding stability products are shown in Table 7.
In addition to potentiometric titrations, the existence of the biand trinuclear gluconate-containing species was supported by freezing point depression, ESI-MS and EXAFS measurements as well as by conductometry (proving the formation of charge neutral complexes) [26]. A representative species distribution diagram for this system is shown in Fig. 14.
As for the CaGlucH -1 0 aqueous species, the metal-ion-induced ligand deprotonation can be quantified as well. The deprotonation of Glucin the CaGluc + complex is defined by the following reaction: while the corresponding deprotonation constant, K 11-1 , can be deduced from log b 11 (Eq. (16)) and log b 11-1 (Eq. (22)): Using log b 11 = 1.08 (Table 4) and log b 11-1 = -10.76 (Table 7), log K 11-1 is -11.84. That is, the pK a of the bound Gluc -(11.84) is approximately lower by two orders of magnitude than the pK a of the free ligand (13.68, see Table 6). This clearly shows that the formation of an alcoholate group is significantly facilitated by an already bound Ca 2+ . The driving force of this reaction is (1) the very strong interaction between the Ca 2+ ion and the Omoiety and (2) the concurrent formation of a stable chelate structure.
Furthermore, the direct binding of GlucH -1 2to Ca 2+ can also be characterized: From log K a = -13.68 (Eq. (20), Table 6), and log b 11-1 = -10.76 (Eq. (22), Table 7), log K 11 is found to be 2.74, indicating that deprotonation of the OH moiety results in roughly two orders of magni-  Table 7 for discussion. The figure has been replotted based on the data of Ref. [26].
tude increase in the stability of the complex species formed, relative to that containing hydroxyl group (that is CaGluc + , for which log b 11 = 1.08, see Table 4)). Beside Gluc -, the formation constants of further 1:1:-1 Ca-sugar carboxylate complexes were determined, and all of these were found to be formed in the alkaline pH-range. In an early work, Makridou et al. [105] reported the formation constant of log b 11-1 = -10.40 for the mononuclear Ca-complex of D-glucuronate. In more recent studies, the formation constants of CaHpglH -1 0 (log b 11-1 = -10.35 [71]) and the CaIsaH -1 0 (log b 11-1 = -11.36 [72]) were determined at t = 25°C and I = 1 M NaCl. Gluc À was proven to form polynuclear Ca-complexes in alkaline solutions at elevated temperatures, too. In the recent work of Buckó et al. [28], the formation constants of the CaGlucH -1 0 , complex. Furthermore, the authors found that the abstraction of a Ca 2+ ion by the 2:2:-4 complex is accompanied by DH % 0. The formation of polynuclear calcium complexes similar to those with gluconate both in terms of composition and stability, were also observed in alkaline solutions containing sugar carboxylates that are structurally closely related to Gluc À . In alkaline solutions containing calcium(II) ions and Hpgl À , the formation of Ca 3 Hpgl 2 H -4 0 was observed by Pallagi et al. [71]. In analogous solutions containing Gul À , the existence of the Ca 3 Gul 2 H -4 0 and Ca 3 Gul 2 H -3 + were concluded from potentiometric titrations by Kutus et al. [30]. Both studies were performed at t = 25°C and I = 1 M, employing NaCl as background electrolyte. Remarkably, at significantly higher ionic strength (4 M NaCl), beside the Ca 3 Hpgl 2 H -4 0 complex, the Ca 3 Hpgl 2 H -3 + species was also found to be formed [128], analogous to the case of Gul -. (The respective stability products are also listed in Table 7.) It is also important to note, that polynuclear calcium(II) complexes were not detected in alkaline solutions containing Isa À [72], confirming again that the analogy between Glucand Isashould be handled with caution [123]. From these observations, the following general picture emerges. In hyperalkaline (pH > 12) aqueous solutions, Ca 2+ ions form unusual solution complexes with certain (but not all) carbohydrates containing carboxylate and alcohol(ate) donor groups. These polynuclear (bi-or trinuclear) solution species are of surprisingly high stability, for example, the polynuclear complexes of gulonate (Ca 3 Gul 2 H -4 0 and Ca 3 Gul 2 H -3 + ) are so stable, that the formation of  Table 7 for discussion.

The structure of the complexes forming in alkaline solutions
The coordination sites of Glucin the bi-and three nuclear Cacomplexes were found to be the COO -, C(2)-Oand C(3)-Ogroups. This was proven by Ca(II) concentration-and temperaturedependent 1 H NMR spectra [26]. The structure of the Ca 3 Gluc 2 H -4 0 complex was optimized by quantum chemical calculations at the HF/6-31(d,p) level (the structure is displayed in Fig. 15). Accordingly, the central Ca 2+ is bound by one oxygen of each carboxylate and by the two C(2)-Ogroups, establishing two five-membered chelate rings. The other two metal ions are coordinated by the other oxygen of the COOand by the C(3)-Omoieties, thereby forming six-membered chelate structures. As a result, each carboxylate acts as a bridging ligand between two (chemically non-equivalent) metal ions. The prerequisite structural motif which makes the gluconate ion capable of forming these polynuclear complexes is the ability of the carboxylate group to act as a bridging ligand and, at the same time, the presence and contribution of the two adjacent alcoholate moieties (i.e., C(2)-Oand C(3)-O -). In the mononuclear CaGlucH -1 0 complex, just like for the parent CaGluc + species, the formation and coexistence of the two binding isomers can be inferred with the five-or the six-membered chelate structure. This makes possible the simultaneous binding of two calcium ions from the opposite directions to the same gluconate molecule. The formation of the complex, however, does not end at this point as the uncoordinated sides of the calcium ions are still available for binding to the next gluconate unit. Ultimately, this results in the formation of ''Ca-L-Ca-L-Ca" type short chains as schematically represented in Fig. 16. The relative positions of the alcoholate functionalities determine their availability for complexation and seem to be the key. For gluconate, it makes possible to bind two calcium ions simultaneously by C(2)-Oand C(3)-Owith the carboxylate as bridge. For Isa À , this was found not to be the case. The C(2)-Odoes but the C(6)-OH (situated on the carbon atom second from the carboxylate group) does not participate in the Ca 2+ binding, as it was proven by 13 C NMR measurements (that is, the 13 C NMR signal of C6 remained unchanged upon Ca 2+ complexation in strongly alkaline solutions). This is suspected to be the structural reason why Isadoes not form polynuclear complexes with calcium ions. On this basis, it was suggested that the readily available gluconate is not a good model compound of isosaccharinate, both in terms of structure and stability [72].
The structures of the Ca 3 Hpgl 2 H -4 0 and Ca 3 Gul 2 H -4 0 have been recently scrutinized by Kutus et al. [30]. Initially, from temperature-dependent 1 H NMR spectra, it was suggested [71] that the in this type of complex, the binding sites in Gluc À and Hpgl À are identical (that is, COO -, C(2)-O À and C(3)-O À groups.) However, more detailed 1 H NMR measurements proved that the coordination sites of Hpglseem to be same as those of Gul -, i.e., COO -, C(2)-O À and C(4)-O À groups (as the H2 peak is shifted downfield, while the H4 peak is shifted upfield for both ligands upon Ca 2+ complexation). This leads to the conclusion that the analogy in the binding sites stems from the similarity of the arrangement of the OH groups. Although Gul À and Hpgl À differ in their relative configuration, the C(2)-OH and C(3)-OH groups are in erythro, while the C(3)-OH and C(4)-OH groups are in threo position in both anions. It is striking that in Glucthe C(2)-OH and C(3)-OH groups are in threo position. It seems therefore likely that the threo or erythro configuration accounts for the differences in the coordination mode of Gluc À and Gul À /Hpgl À . In other words, after the formation of the -OOC-C(2)-Obinding moiety, the steric arrangement (or spacing) of the C(3)-OH group relative to that of C(2)-OH determines whether the C(3)-OH or the C(4)-OH group will be coordinated to the Ca 2+ ion. These results are in accordance with the rules proposed by Angyal et al. for sugar alcohols [94], i.e., in neutral medium the complex formed threo-1,2-threo-2,3 triol is more stable than that with threo-1,2-erythro-2,3 triol. For sugar carboxylates, both the C(2)-OH and C(3)-OH groups can participate in the Ca 2+ ion coordination in threo-threo case (Gluc À ), while the C(2)-OH and C(4)-OH groups are preferred in threo-erythro arrangement (Gul À and Hpgl À ). From these observations it can be concluded that configuration plays crucial role in the formation of deprotonated Ca(II) complexes. These statements may hold for other metal complexes of carbohydrate derivatives, too.

Summary
The thermodynamic and structural characterization of the Ca 2+ / Gluc À / H 2 O system emerges as a multifold and scientifically challenging exercise. In acidic solutions, the carboxyl deprotonation and lactonization takes place in parallel. Under (hyper)alkaline conditions the formation of one or more alcoholate groups on gluconate gives rise to the formation of a variety of monomeric and polynuclear Ca 2+ complexes.
Acidic and neutral medium With careful experimentation and applying various experimental methods simultaneously, it proved to be possible to separate the experimental effects caused by carboxyl deprotonation and lactonization, and to accurately characterize the underlying multiple chemical equilibria and kinetic processes. The subtleties of the lactonization of gluconic acid have been revealed in great detail, including the separate evaluation of the formation of cand d-lactones.
It has been shown that in weakly acidic to alkaline conditions, calcium ions form both 1:1 and 1:2 complexes with gluconate, and that the formation of the 1:2 species is related to the flexibility of the organic ligand. Recently, the crystal structure of the solid CaGluc 2 ÁH 2 O has also been determined.
It has been experimentally demonstrated (and supported by quantum mechanical calculations), that in the CaGluc + solution species the calcium ions are simultaneously chelated by COO À / C(2)-OH and COO À /C(3)-OH, and therefore the two binding isomers coexist in solution.
Alkaline (hyperalkaline) medium The acid dissociation constants of the alcoholic OH of gluconate and those of some structurally related ligands have been determined and were found to correlate with the stability of the calcium complex formed with the alcoholate functionality. Deprotonation of the OH group results in a ca. hundredfold increase in the stability of the corresponding solution species.
In (hyper)alkaline aqueous solutions, Ca 2+ ions were found to form polynuclear solution species with gluconate as well as with certain (but not all) structurally related sugar-carboxylates; the complexes identified are of remarkably high stability, predominantly bi-or trinuclear and quite a few (but not all) of them are charge-neutral; calcium ions are simultaneously bound to the COO À /C(2)-O À and COO À /C(3)-O À of the gluconate, giving rise to the formation of short Ca-L-Ca-L-Ca chains. Upon comparison with other sugar carboxylic acids, the COO À /C(2)-O À motif always participates in metal-binding, while the actual configuration is determines whether the second alcoholate binding site is the C(3)-O À or the C(4)-O À group.

Outlook
The thermodynamic description of the binary Ca(II)-gluconate system is considered to be essential in the development of thermodynamic models of more complex systems, i.e. ternary systems including different metals, lanthanides (Ln) and actinides (An) of the type Ca(II)/M(II/III/IV)/Gluc À with M = Ni(II), Fe(III), Al(III), Ln (III)/An(III), An(IV), etc. The current review demonstrates that several (but not all) building blocks are now available for constructing these models. In aqueous solutions (in particular in alkaline ones), when polyhydroxy carboxylate ions, Ca 2+ and further tria-or tetravalent cations are simultaneously present, binary as well as high stability heteropolynuclear (or ternary) complexes of Ca n M m L p type are formed. It is possible that in aqueous solutions various binary complexes (both mono-and polynuclear) comprising Ca 2+ and sugar carboxylates serve as precursors of these highly stable ternary species. Their formation, nature and stability is determined by the chemical properties of the ligand as well as by that of the metal ions. The knowledge of the chemical motifs determining the stability and the structure of these solution species (both binary and ternary) is a prerequisite for the construction of thermodynamic models describing the abundance and distribution of the contributing components among the various complex species forming. Albeit considerable efforts are currently being made to elucidate the thermodynamics, composition and structure of these heteropolynuclear species, our current knowledge on them is limited. Therefore, and especially in view of their manifold practical relevance (such as the thermodynamic modelling of the aqueous chemistry certain radioactive waste repositories, or understanding the fundamental aspects of certain industrial processes in, e.g., alumina refining, corrosion inhibition or textile dyeing), the detailed study of such systems is warranted.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.