exploration of the fundamental equilibrium behaviour of calcium exchange with weak acid cation...

Desalination 351 (2014) 27–36

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Desalination

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Exploration of the fundamental equilibrium behaviour of calciumexchange with weak acid cation resins

Graeme J. Millar ⁎, Shannon Papworth, Sara J. CouperthwaiteScience and Engineering Faculty, Queensland University of Technology, Brisbane, Queensland, Australia

H I G H L I G H T S

• Detailed understanding of the behaviour of ion exchange resins for water softening• Demonstration of the usefulness of the Langmuir–Vageler expression• Observation of partial hydrolysis of weak acid cations in aqueous solution• Evidence for super-equivalent ion exchange behaviour• Suggestion that dissolved salts remain in the interior of the resin beads

Abbreviations: ARE, average relative error; Ce, equiliconcentration of ions in solution; EABS, sum of the absofractional error function; ICP, inductively coupled plasmarate coefficient termed the “half value”;m,mass of resin;Mdard deviation; nF, Freundlich exponent; NLLS, non-linealoading of ions on the resin; qmax, maximum (monolayeSAC, strong acid cation; SEIX, super equivalent ion exchanerrors; SSE, sumof the squares of the errors; V, volume of s⁎ Corresponding author at:QueenslandUniversity of Te

706, Gardens Point Campus, Brisbane, Queensland 4001, AE-mail address: [email protected] (G.J. Millar).

http://dx.doi.org/10.1016/j.desal.2014.07.0220011-9164/© 2014 Published by Elsevier B.V.

a b s t r a c t
a r t i c l e i n f o
Article history:Received 7 June 2014Received in revised form 16 July 2014Accepted 17 July 2014Available online xxxx

Keywords:CalciumIon exchangeLangmuir–VagelerSodiumSuper equivalent

This study evaluated the complexity of calcium ion exchange with sodium exchanged weak acid cation resin(DOW MAC-3). Exchange equilibria recorded for a range of different solution normalities revealed profileswhich were represented by conventional “L” or “H” type isotherms at low values of equilibrium concentration(Ce) of calcium ions, plus a superimposed region of increasing calcium uptake was observed at high Ce values.The loading of calcium ionswas determined to be ca. 53.5 to 58.7 g/kg of resin whenmodelling only the sorptioncurve created at low Ce values, which exhibited awell-defined plateau. The calculated calcium ion loading capac-ity for DOW MAC-3 resin appeared to correlate with the manufacturer's recommendation. The phenomenon ofsuper equivalent ion exchange (SEIX) was observed when the “driving force” for the exchange process wasincreased in excess of 2.25 mmol calcium ions per gram of resin in the starting solution. This latter event wasexplained in terms of displacement of sodium ions from sodium hydroxide solution which remained in theresin bead following the initial conversion of the as supplied “H+” exchanged resin sites to the “Na+” version re-quired for softening studies. Evidence for hydrolysis of a small fraction of the sites on the sodium exchanged resinsurface was noted. The importance of carefully choosing experimental parameters was discussed especially inrelation to application of the Langmuir–Vageler expression. This lattermodelwhich compared the ratio of the ini-tial calcium ion concentration in solution to resinmass, versus final equilibrium loading of the calcium ions on theresin; was discovered to be an excellent means of identifying the progress of the calcium–sodium ion exchangeprocess. Moreover, the Langmuir–Vageler model facilitated standardization of various calcium–sodium ionexchange experiments which allowed systematic experimental design.

© 2014 Published by Elsevier B.V.

brium concentration; Co, initiallute errors; HYBRID, composite; KF, Freundlich coefficient; KLV,PSD,Marquardt's percent stan-r least squares; qe, equilibriumr) loading of ions on the resin;ge; SNE, sum of the normalizedolution;WAC,weak acid cation.chnology, P Block, Level 7, Roomustralia. Tel.: +61 7 3138 2377.

1. Introduction

Ion exchange is a technology which spans many fields, from analyti-cal research purposes to industrial streams, and beyond to natural pro-cesses such as the exchange of minerals in soils [1,2]. The exchangermedium comes in various forms, such as naturally occurring zeolitematerials [3,4] to industrially synthesised ion exchange resins [5–7].Regardless of the type of exchanger, ion exchange is understood tooccur at a stoichiometric ratio; that is, one ion of a certain charge in solu-tion migrates into the exchanger phase and replaces ions of equivalentcharge resident on the exchanger surface. The process of ion exchangehas been studied primarily by three experimental methodologies;

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Table 1Summary of error functions used for non-linear least squares (NLLS) analysis of equilibriumexchange data.

Error function Equation

Sum of the squares of the errors(ERRSQ or SSE) ∑

p

i¼1qe;calc−qe;meas� �2

i

Hybrid fractional error function (HYBRID)100p−n∑

p

i¼1

qe;meas−qe;calc� �2

i

qe;meas

" #i

Marquardt's percent standard deviation(MPSD) 100

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

p−n∑p

i¼1

qe;meas−qe;calc

qe;meas

" #2

i

vuut0@

1A

Average relative error (ARE)100p ∑

p

i¼1

qe;calc−qe;meas� �

qe;meas

��i

Sum of the absolute errors (EABS)∑p

i¼1qe;calc−qe;meas� ��

i

28 G.J. Millar et al. / Desalination 351 (2014) 27–36

kinetic [8], equilibrium and column studies [9,10]. Common to all threeapproaches is the use of numerous models to describe the sorptionprocess, some of which are generalized for both adsorption and ionexchange systems [11]. Thus, there can at times exist confusion [12], alack of fundamental understanding [13], and insufficient experimentalrigour [14]. Consequently, our research group has focussed upon devel-oping a systematic approach to investigating the basic experimental pro-cedures used in ion exchange. For example, equilibrium isotherm studiesof singly charged ions with strong acid cation resins have revealed thepitfalls of failing to comprehend the impact of experimental conditionssuch as bottle-point method used and solution/resin ratio [15].

This paper extends the study of ion exchange equilibria to situationswhere multiply charged ions are involved. One of the oldest ion ex-change processes known and also a very common industry applicationis the softening of water using materials such as zeolite A [16] or syn-thetic resins [17]. Zeolite is used as a detergent builder as it is more en-vironmentally benign when compared to phosphate based materials[18]. Costa et al. [19] studied the synthesis of zeolite 4A using kaolinas a starting material, with the aim of preparing more cost effectivedetergent builders. Similarly, Ma et al. [20] attempted the synthesis ofzeolite 4A using bentonite clay. Recently, Xue et al. [16] improved thesoftening performance of zeolite 4A, especially magnesium removal,by enhancing themesoporosity. Hoffmann andMartinola [17] reviewedthe application of various synthetic ion exchange resins to softening ofwater. Ghergheles et al. [21] reported a study using a cationic resin tosoften geothermal water which successfully softened the water to thepoint of suitability for household use. The concept of hybrid ionexchange-reverse osmosiswater treatment plants has also gained inter-est in relation to development of high water recovery units [22]. For ex-ample, Venkatesan and Wankat [23] modelled ion exchange softeningpre-treatment of brackish water prior to reverse osmosis operationand noted an improvement in water recovery from 36 to 90% withoutthe appearance of precipitation. Lipnizki et al. [24] also advocated thecombination of ion exchange softening processes with reverse osmosistreatment of wastewater.

The fundamental representation of the softening process is shown inEq. (1).

Ca2þ aqð Þ þ 2NaþR↔Ca2þR2þ 2Naþ aqð Þ: ð1Þ

However, the assumption of simplicity may not necessarily be cor-rect, since, as noted in Helferrich [2], any ion exchange process is inevi-tably coupled with the process of adsorption. Moreover, when multiplecharged ions are present in solution their exchange behaviour is highlydependent upon the solution normality. For instance, Pabalan andBertetti [25] studied the exchange of various solutions of alkali and alka-line earth cations with clinoptilolite. A strong relationship between thesolution normality and shape of the equilibrium isothermwas reported.In general, with increasing dilution the zeolite material exhibited apreference for the higher charged species, which was referred to asdue to the “concentration–valency” effect.

Surprisingly, for such a common industry application,we have foundrelatively few fundamental sorption equilibrium studies in the openliterature regarding water softening by synthetic resins. Jiang et al.[26] reported the exchange of calcium andmagnesium ions by a chelat-ing resin, and provided examples of kinetic and equilibrium behaviour.However, these authors did not examine weak acid cation resins withcarboxylic acid functional groups, or use non-linear least squares(NLLS) fitting procedures to interpret the data. Instead, they linearizedrelevant equations and introduced known errors associated with thisapproach [14]. Enterazi and Tahmasbi [27] also used linearized isothermmodels, did not investigate the influence of solution normality and onlyconsidered a strong acid cation (SAC) resin. Yi et al. [28] obtained iso-therm data for calcium and magnesium exchange with a chelatingresin, but did not evaluate the impact of solution normality or compare

different isotherm models with the aim of determining which fits thedata optimally.

Therefore, the aim of this publication was to examine the equilibriumexchange behaviour of calcium with a commercially available weak acidcation resin comprising of carboxylic acid functional groups. Particularfocuswas upon themethodology for generating sorption isotherms, rele-vant equations to use, impact of solution normality and appropriatenessof non-linear least squares fitting procedures.

2. Experimental

2.1. Resins

The resin used was termed MAC-3 and supplied by DOW Water &Process Solutions. This resin was characterized by a weak acid cationfunctionality through carboxylic acid groups, a polyacrylic macroporousstructure, and a stated exchange capacity of 3.8 eq./L. The resin wasinitially received in the “H+” form and as such required conversion tothe desired “Na+” form. The transformation procedure was as follows:A quantity of wet resin in the “H+” form was placed into a clear u-PVCion exchange column of 0.05 m diameter and subsequently rinsedwith purified water at a rate of 15 L/h for 30 min. A 4% (w/v) solutionof NaOH was then used to convert the resin to the “Na+” form, againat a flow rate of 15 L/h for 30 min, at which point conductivity and pHmeasurements of the outlet solution had stabilised. Finally, the resinwas again rinsed several times with water to remove any residualNaOH species present. In addition, the bed was ‘lifted’ between eachrinse through a brief period of running the rinse water counter-currentin order to settle the resin beads evenly and prevent channelling.

2.2. Chemicals

Aqueous solutions were prepared using triple distilled water towhich appropriate amounts of salt were added. Analytical reagentgrade calcium chloride was supplied by Rowe Scientific.

2.3. Analysis

Samples were analysed using a Perkin Elmer Optima 8300 DVInductively Coupled Plasma Optical Emission Spectrometer (ICP-OES)for integration times of 0.15 s with 10 replications. Samples werediluted to a concentration between 1 and 100 mg/L using a Hamiltonauto-dilutor with 10 mL and 1 mL syringes. A certified standard fromAustralianChemical Reagents (ACR)wasdiluted to formmulti-level cal-ibration curves. An external reference was used to monitor instrumentdrift and accuracy of the results.

Fig. 1. Model fits for exchange of calcium ions from a 0.01 N calcium chloride solution with DOWMAC-3 weak acid cation resin.

Table 2Non-linear least squares (NLLS) fit of Competitive Langmuir & Freundlich isotherm datafor calcium exchange from a 0.01 N CaCl2 solution with a sodium loaded DOW MAC-3weak acid cation resin. Numbers in bold indicate minimum error values and minimumsum of normalized error values.

SSE HYBRID MPSD ARE EABS

qmax (g/kg) 54.0 58.7 63.5 66.9 56.1KL 671.5 89.0 28.8 17.9 1063.6SSE 2139 4330 6193 6924 2474HYBRID 2025 929 1071 1161 2880MPSD 221 88 71 72 265ARE 72 54 52 51 81EABS 127 193 230 243 105SNE 3.25 2.74 3.11 3.30 3.79

KF 28.2 17.2 9.0 16.5 26.0nF 5.2872 3.4624 2.4395 3.4432 5.0057SSE 2438 3757 6432 3989 2531HYBRID 1278 728 973 733 1075MPSD 161 87 64 84 145ARE 68 44 49 44 61EABS 174 195 258 198 171SNE 4.05 3.88 4.85 3.89 4.80

29G.J. Millar et al. / Desalination 351 (2014) 27–36

2.4. Equilibrium studies

A range of resin masses were placed into centrifuge tubes with40 mL of a known concentration of CaCl2 solution. The samples wereagitated on a rotary shaker unit (RatekModel RSM7DC) at constant rev-olutions of 50 rpm for 24 h at a temperature of ca. 19 °C. After equilibri-um conditionswere achieved the solutionwas separated from the resinbeads and then transferred to a centrifuge to further separate solid fromliquid. Calcium concentrations in solution (Ce (mg/L)) were then mea-sured and the equilibrium calcium loading on the resin (qe (mg/g)) in-ferred from Eq. (2);

qe ¼Vm

Co− Ceð Þ ð2Þ

where: qe = equilibrium loading of calcium ions on the resin (mg/g);V = volume of solution (L);m=mass of resin (g); Co= initial concen-tration of calcium ions in solution (mg/L); and, Ce = equilibrium con-centration of calcium ions in solution (mg/L). Sodium concentrationswere also measured in solution in order to determine the quantityreleased from the resin as a consequence of the exchange process. De-sorption profiles were either shown where the sodium concentrationswere expressed in relation to the mass of resin present (mmol Na/gresin), or in relation to calcium ions in solution under equilibrium (Ce).

3. Background equilibrium isotherm theory

3.1. Langmuir–Vageler model

The Langmuir–Vageler model was first reported by Vageler andWoltersdorf [29,30] and involved the correlation of the starting solutionconditions and the equilibrium loading of the species of interest on thesorbent material as illustrated in Eq. (3).

qe ¼VCo

m

� �:qmax

VCo

m

� �þ KLV

ð3Þ

where: qe= equilibrium loading of calcium ions on the resin (mmol/g);V= volume of solution (L);m=mass of resin (g); Co= initial concen-tration of calcium ions in solution (mmol/L); qmax is the maximum(monolayer) loading of calcium ions on the resin (mmol/g); and,KLV = a rate coefficient termed the “half value”.

3.2. Competitive Langmuir model

The Competitive Langmuir expression is different from other sorp-tion models presented here in that it relates more to an ion exchangeprocess as it takes into account the presence of both ions involved inthe exchange [31]. Based upon the process in Eq. (1) and the law ofmass action, the expression in Eq. (4) can be derived.

qe;Ca2þ ¼ k qmax Ce;Ca

Co þ k−1ð ÞCe;Cað4Þ

Fig. 2. Model fits for desorption of sodium ions during exchange of calcium ions from a 0.01 N calcium chloride solution with sodium loaded DOWMAC-3 weak acid cation resin.


where, qe,Ca represents the loading of the calcium ions on the resin atequilibrium (mg/g) and Ce,Ca is the concentration of calcium ions in solu-tion at equilibrium (mg/L). The systemmust have amass balance where-in qmax (meq/L) = qe,Na (meql/L) + qe,Ca (meq/L) and Co (meq/L) =Ce,Ca (meq/L) + Ce,Na (meq/L).

For the purposes of this paper, wherein the experimental methodol-ogy rather than the detailed theoretical exploration is the mainfocus, it is not necessary to discuss the use of more accurate representa-tions of solutions where activities are calculated rather than molarconcentrations.

3.3. Freundlich model

The Freundlich isotherm expression (Eq. (5)) has been used innumerous studies of sorption systems. Originally it was an empiricalmodel based upon physical observations, but shown in later years tobe based upon fundamental physical principles [32,33]:

qe ¼ KF C1=n Fe ð5Þ

where, qe = equilibrium loading of calcium ions on the resin (mg/g);KF = Freundlich coefficient (mg/g (L/mg)1/n); Ce = concentration ofcalcium ions at equilibrium (mg/L); and, nF = Freundlich exponent(dimensionless).

3.4. Non-linear least squares (NLLS) analysis of equilibrium data

Isotherm models such as Langmuir and Freundlich have commonlybeen linearized in published sorption literature, as this promotes easeof use in software packages such asMicrosoft Excel or similar. However,this latter procedure violates fundamental assumptions of the leastsquares process [14]. Consequently, a non-linear least squares (NLLS)

Fig. 3. Stoichiometry of calcium ion exchange with sodium ions on DOWMAC-3 resin at asolution normality of 0.01 N; dashed line shows ideal stoichiometric exchange.

fitting approach is more appropriate as described by several authors[34,35]. Therefore, this paper followed the methodology recommendedby Ho et al. [36] which used the error functions described in Table 1.

4. Results

4.1. 0.01 N calcium chloride solution

Fig. 1 shows equilibrium isotherm data for calcium exchange withDOW MAC-3 resin from a 0.01 N solution of calcium chloride. Applica-tion of the Langmuir–Vageler expression provided a reasonable fit ofthe data. However, closer inspection of the measured points suggestedthat the calcium loading actually plateaued at a value of approximately1.4 mol Ca/kg resin and upon increasing the “driving force” of theexchange process i.e. increasing the ratio of calcium ions in solution tothe mass of resin present, the calcium loading accelerated. This latterobservation was more evident in the corresponding CompetitiveLangmuir analysis of the equilibrium data (Fig. 1). It was apparent thatthe uptake of calcium ions was extremely favourable as the calciumloading rapidly increased at low values of Ce, with a definite plateaunoted to develop at Ce values between 7.1 and 86.5 mg/L. The“rectangular profile” of the equilibrium isotherm data was indicativeof an exchange process which was practically, almost irreversible [37].At higher Ce values above 86.5 mg/L, the calcium loading on the resinmaterial exhibited a distinct enhancement which was not consistentwith simple Langmuir type sorption behaviour which has the basicpremise of a limited number of sorption sites being available [38]. Alsoshown in Fig. 1was a Competitive Langmuirfit of only the Ce data pointsup to 86.5 mg/L, which indicated a considerably improved representa-tion of the experimental values, albeit the low range Ce points remaineddifficult to model adequately. The maximum loading of calcium ions onthe resin surface was now estimated to be 58.7 g/kg (Table 2). In con-trast, the Freundlichmodel was observed to be inadequate atmodellingthe equilibrium isotherm, especially at low values of Ce (Fig. 1).

It was of interest to also examine desorption of sodium ions as thecalcium ions were exchanged on the resin surface sites. Fig. 2 showedthat the Langmuir–Vageler and Competitive Langmuir isotherm fits ofthe measured data for sodium ion desorption were similar in profile tothose for calcium uptake (Fig. 1). The main difference was the magni-tude of the sodium ions desorbed compared to calcium ions. A clearerindication of the exchange process which occurred between calciumions in solution and sorbed sodium ions on the weak acid cation surfacewas seen by inspection of Fig. 3 which compared the equivalents ofsodium released into solution to the amount of calcium removed fromsolution. Overall, the exchange process appeared to be approximatelystoichiometric in nature. There was a discrepancy from ideal behaviourin that slightly less sodium ionswere released than expected. This latterdeviation may have been due to experimental error, however as will beseen below the behaviour was consistent in several tests and not ran-dom in nature. Thus, an underlying physical phenomenonwas requiredto explain the behaviour observed.

Fig. 4.Model fits for exchange of calcium ions from a 0.025 N calcium chloride solution with DOW MAC-3 weak acid cation resin.



Increasing the solution normality to 0.025 N calcium chloride solu-tion resulted in the equilibrium isotherm profiles illustrated in Fig. 4The shape of the isotherms recorded was similar to those displayed inFig. 1 when a 0.01 N solution was employed. Again, the initial uptakeof calcium ions was rapid and a distinct plateau in the calcium uptakewas noted, followed by a rise in the calcium loading as the “drivingforce” or value of Ce increased. The Competitive Langmuir fit of thedata up until a Ce value of 215 mg/L indicated that the maximum calci-um ion capacity on the resin was now 53.5 g/kg (Table 3), which wasless than the value of 58.7 g/kg noted when 0.01 N calcium chloridesolution was the exchanging solution. Fig. 5 displayed the correlationbetween both sodium ions desorbed and the calcium ions present in





the initial solution (Langmuir–Vageler plot), and versus the equilibriumconcentration of calcium ions in solution (Competitive Langmuir plot).The ejection of sodium ions into solution paralleled the increase in theratio of calcium ions to resin mass in the initial solution. A small plateauregionwas evident in the Langmuir–Vageler plot (Fig. 5) afterwhich thesodium ion release rate increased. The Competitive Langmuir fit of thedata relating to desorbed sodium ions, also indicated the rapid releaseof these latter species into solution as calcium was loaded onto theresin exchange sites. After a plateau region encompassing a calciumion equilibrium concentration in solution (Ce) up to 161.4 mg/L, the so-dium expulsion from the resin was again enhanced. A graph relatingequivalents of calcium loaded on the DOWMAC-3 resin and the quanti-ty of sodium ions released into solution is shown in Fig. 6 As before, therelationship between the amount of calcium ions loaded on the resinsurface and the sodium ions desorbed from the resin bead was approx-imately linear, with a definite indication that less sodium was releasedthan expected based upon process stoichiometry.


The normality of the calcium chloride solution was further elevatedto 0.05 N in order to examine the impact of increasing solution concen-tration upon the exchange behaviour of DOW MAC-3 resin. Fig. 7presents various model fits of the equilibrium exchange data whichmirror those shown in Figs. 1 and 4. Analysis of the isotherm profilessuggested that they were similar to those already recorded for the0.01 and 0.025 N calcium chloride solutions. Applying the CompetitiveLangmuir model to the data for Ce values up to 290.4 mg/L resulted ina prediction for the monolayer exchange capacity of the resin to be57.2 g Ca/kg of resin (Table 4). Not unexpectedly, due to the close cor-respondence between the isotherm profiles noted in Fig. 7 and thosefor lower solution normalities, the sodium desorption profiles in Fig. 8were remarkably similar to those already commented upon in Figs. 2and 5. Logically, these latter observations should have translated into asimilar relationship between calcium ions loaded on the resin and thequantity of sodium ions released into solution, which was indeedwhat was seen (Fig. 9).

Fig. 5.Model fits for desorption of sodium ions during exchange of calcium ions from a 0.025 N calcium chloride solution with sodium loaded DOW MAC-3 weak acid cation resin.

Fig. 6. Stoichiometry of calcium ion exchange with sodium ions on DOWMAC-3 resin at asolution normality of 0.025 N; dashed line shows ideal stoichiometric exchange.


5. Discussion

5.1. Isotherm profile

Sorption isotherms have been classified by several different typesdepending upon the profile obtained from experimental equilibriumstudies. For example, using the classification of Giles et al. [39,40] theequilibrium curves reported in this study appeared to be consistentwith the general “L” type or the subset of “L” which is termed “H”. “L”type isotherms are probably the most common isotherm profilesreported as they are the classic Langmuir pattern wherein a concavecurve is observed which related to progressive saturation of surfacesites and ultimately formation of a monolayer of sorbed species [37].“H” isotherms are a variant of the “L” class wherein the initial gradientof the slope is very high and these are often called “rectangular”isotherms. Indeed, the initial stage of the isotherm profiles in thisstudy wherein a rapid increase in the quantity of sorbed calcium ionswas observed and a distinct plateau noted, was consistent with the“H” isotherm illustrated by Alberti et al. [11]. The subsequent rise incalcium uptake following creation of the plateau in sorption capacityhas been noted by Giles et al. [39] as the sub-groups 3 and 4 of “L” and“H” class isotherms. The fundamental difference between sub-groups3 and 4 was the ever increasing uptake of sorbate in sub-group 3 and

Fig. 7. Model fits for exchange of calcium ions from a 0.05 N calciu

formation of a secondary plateau in sub-group 4. From the isothermprofiles shown in this study it was difficult to conclusively assign theisotherms to either sub-group mentioned due to a lack of data-points.

Several studies have reported inflection points in equilibrium iso-therm curves, where an increase in ion uptake was noted. For example,

m chloride solution with DOWMAC-3 weak acid cation resin.






Pabalan and Bertetti [25] studied the ion exchange behaviour of varioussolutions comprising of both mono- and divalent cations with naturalzeolite. An important aspect of the latter study was the observation ofa strong dependence of the isotherm profile upon solution normality.As the solution normality was lowered the affinity of the zeolite materi-al for the divalent species increased significantly, due to the “concentra-tion–valency” effect. Although, inflectionswere noted in themajority ofisotherms such as those where sodium and strontium ions wereexchanged, no discussion was made of this phenomenon. Similarly,Inglezakis et al. [41] collected ion exchange isotherms for the exchangeof chromium ions from solutionwith clinoptilolite. The isotherm profilewas characterized by an initial increase in sorbate uptake followed by adistinct plateau andfinally a rapid increase in chromium sorption. Theseauthors stated that the exchange process changed from favourable tounfavourable but did not explicitly provide a reason for this behaviour.Bricio et al. [42] hypothesised a “double selectivity”model for equilibri-um isotherms displaying inflection points, which resulted from ex-change of ions with “H+” forms of styrene–divinyl benzene resins. Thekey assumptions were: two different active sites in the resin; distribu-tion of resin capacity related to percentage of divinyl benzene present;and, ion exchange equilibria occurred simultaneously at both types ofsite. The idea of two distinct types of exchange sites has also been enun-ciated by Tamura et al. [43] for weak acid cation resins. These authorswere of the view that one site was located in regions where largepores were present and the other was in the macroporous channels.Limousin et al. [37] also discussed several studies regarding theexchange of potassium and calcium ions with 2:1 clays where the iso-therms showed a preference for potassium uptake initially and then

Fig. 8. Model fits for desorption of sodium ions during exchange of calcium ions from a 0.05

followed the non-preference curve at higher loadings, thus creating aninflection point. Again, a two site model was fitted to the experimentaldata.

5.2. Resin capacity

The resin manufacturer states that the DOWMAC-3 material shoulduptake 1.9 mol Ca/L or 76.15 g/L which was 101.5 g/kg based upon apacking density of 750 g resin/L and resin supplied in the H+ form.The initial procedure used here was to modify the as supplied “H+”

form of the resin with sodium hydroxide in order to obtain the required“Na+” exchanged resin. During this latter exchange process the resinwas expected to expand by 70% and this was thematerial thenweighedfor the bottle-point investigation. During the column conditioning ofthe weak acid cation resin this latter expansion in volume was indeedobserved. Consequently, the resin capacity was now adjusted to1.12 mol Ca/L resin in sodium form, or 1.49 mol Ca/kg resin (assumingpacking density of 0.75) which equated to 59.7 g Ca/kg resin. This latterestimate for calcium loading onDOWMAC-3 resinwas remarkably sim-ilar to the value of 58.7 g Ca/kg resin determined in this studywhen theexchange capacity calculation was applied for example in Fig. 1 to Cevalues less than 86 mg/L calcium ions.

Consequently, one must consider what principle explained theincrease in calcium uptake post-formation of the plateau region in theequilibrium isotherm plots. One possible explanation was the conceptof “super equivalent ion exchange” which has been reviewed in depthby Kokotov [44]. This author elucidated that the inclusion of electrolytewas enhancedwhen: using solutions of high concentration; the capacityof the sorbate decreased; and, the cross-linking of the resin structurewas low. Christensen and Thomsen [45] highlighted the importance ofthe uptake of co-ions and solvent when working with concentrated so-lutions during ion exchange processes. This latter situation was compa-rable to our studywhen a large concentration of calcium ions in solutionwas exchanged with a small amount of resin. Christensen and Thomsen[45] for example contacted a calcium loaded resinwith a solution of cal-cium chloride. Evidencewas obtained which showed that uptake of cal-cium chloride salt into the resin structure improved as the solutionmolality increased. The relative amount of salt included in the resinbeads depended upon the Donnan potential [46] and size of the ions in-volved. Similarly, Soldatov et al. [47] examined the non-exchange ofvarious electrolyteswith anionic resin and again reported that the inclu-sion of electrolyte in the resin was promoted by increasing the concen-tration of the external solution. To account for the sorption degreeof electrolytes it was required not only to include Donnan or Nernstdistribution effects but also to allow the possibility for formation ofhydrated ionic associates.

Donnan equilibrium theory predicts that the chloride ions should beexcluded from the resin bead at low salt concentrations (“Donnanexclusion”) but progressively be included as the aqueous concentrationincreased (“Donnan inclusion”) [48].

N calcium chloride solution with sodium loaded DOWMAC-3 weak acid cation resin.

Fig. 9. Stoichiometry of calcium ion exchange with sodium ions on DOWMAC-3 resin at asolution normality of 0.05 N: dashed line shows ideal stoichiometric exchange.


5.3. Process stoichiometry

The question of process stoichiometry has to be addressed to gain aninsight into the exchange behaviour. For example, in the case illustratedwhere a sodium loaded resin was placed into a solution containing cal-cium ions, ion exchange theory dictated that for each calcium ion thatmoved from solution into the exchanger, two sodium ions shouldmove in the opposite direction. All three plots of calcium loaded onthe resin versus the quantity of sodium released suggested an approxi-mately linear relationship over all conditions studied (Figs. 3, 6 and 9),with a slight upward trend noted toward the final stages of the plot per-haps indicating an increased displacement power of Ca ion at increaseddriving force conditions. As previously discussed, the plateau region inthe isotherm plots appeared to correlate to monolayer exchange ofcalcium ions with sodium ions on the resin surface.

To gain an insight to the deviation in stoichiometry noted above, anexperiment was conducted involving addition of sodium exchangedresin to pure water. The presence of sodium ions in solution followingequilibration between sodium exchanged weak acid cation resin andpure water (Fig. 10) suggested that partial hydrolysis of the resinsurface had occurred according to Eq. (6).

NaþR þH2O↔HþR þ Naþ þ OH−: ð6Þ

Lehto and Harjula [49] discussed the fact that weak acid cation ex-change resins typically exchanged a small proportion of sodium ionson the resin surface with hydronium ions from solution. The concomi-tant rise in solution pH was consistent with Eq. (6), and calculationsbased upon the quantity of sodium ions in solution suggested that thepH should have been in the range 9.8 to 10.2. The latter pH range wasin agreement with the measured data and in harmony with the workof Lehto and Harjula [49] which highlighted the significant impactupon pH even a limited degree of hydrolysis can have. Consequently,the hydrolysis effect explains why the calcium–sodium exchange

Fig. 10. Equilibrium data for DOW MAC-3

process in this study indicated less ejection of sodium ions from theresin surface than expected, as the exchange process in Eq. (7) probablyoccurred in addition to Eq. (1).

Ca2þ aqð Þ þ 2HþR↔Ca2þR2þ 2Hþ aqð Þ: ð7Þ

Therefore, it was pertinent to inspect for example, the dataconcerning solution pH during the equilibrium exchange of the 0.01 Ncalcium chloride solution with DOW MAC-3 resin in this study(Fig. 11). Notably, the pHvalueswere depressed relative to the situationwhen the sodium exchanged resin was immersed in pure water. Thislatter behaviour was consistent with two processes, namely exchangeof the sodium ions for calcium specieswhichwere probably less suscep-tible to hydrolysis and release of protons (hydronium ions) due toEq. (7).

The additional uptake of calcium ions aftermonolayer exchangewaspostulated to be due to inclusion of calcium ions from the calciumchloride electrolyte at high ratios of calcium in solution to resin mass.Consequently, it can be deduced that inclusion of electrolyte in theresin beads concomitantly resulted in the expulsion of non-exchangedsodium ions already present within the resin pores. The source ofthese non-exchanged sodium ions was presumably from the sodiumhydroxide used in the initial resin regeneration stage as shown inEqs. (8) and (9).

HþR þ Naþ þ OH−↔NaþR þ H2O ð8Þ

NaþR þ Naþ þ OH−↔NaþR � NaOH: ð9Þ

Despite the fact that extensive rinsingwith purified water was com-pleted following the sodium hydroxide regeneration procedure untilthe effluent solution pH stabilised, evidently some sodium hydroxidewas retained within the resin structure. In order to ascertain whethersodium chloride entered the resin beads or simply sodium ions fromthe external solution, the concentration of chloride ions in the equilibri-um solutionswasmeasured (Fig. 12). The data suggested that the quan-tity of chloride present in the bulk solution remained reasonablyconstant. This evidence indicated that the chloride ions were unable toenter the resin pore structure despite evidence showing a super ionexchange taking place, whichwas in accordwith Donnan exclusion the-ory. Consequently, a charge balancing anionic species must have beenpresent inside the resin bead in order to maintain electroneutrality.The only possibility appeared to be hydroxide ions from inclusion ofsome of the sodium hydroxide regenerant.

5.4. Experimental procedures

As shown in the Results section the equilibrium isotherms can becomplicated. Evidence has been presentedwhich showed that changingthe solution concentration or amount of resin used had consequences

weak acid cation resin in pure water.

Fig. 13. Comparison of Langmuir–Vageler fits of equilibrium data for various solutionnormalities.

Fig. 11. pHas a function of DOWMAC-3 resinmass in a 0.01 N aqueous solution of calciumchloride.


on the data produced. As outlined by Lehto and Harjula [49], withion exchange a common mistake was the labelling of equilibria as“isotherms” since ion exchange required conditions not only of constanttemperature but also of constant solution normality. Moreover, theequilibrium data obtained was representative for only the specificexperimental conditions used to produce the data. Indeed, it can evenbe the case that only a portion of the ion exchange equilibrium isothermcurve was measured as often test conditions were chosen arbitrarily.Lehto andHarjula [49] have noted the difficulty in choosing appropriateratios of solution to sorbent material present for ion exchange process-es. The Langmuir–Vageler equation which has not been the subject ofsignificant attention in previous literature, was shown in this publica-tion to be a critical method for normalizing the experimental conditionsemployed in relation to generation of isothermplots. The “driving force”used in the bottle-point technique needed to be at least 2 mmol Ca2+

ions in the initial solution relative to resinmass for a plateau in the sorp-tion profile to be observed. Increasing the exchange “driving force” to2.5 mmol Ca2+ ions per gram of resin resulted in an inflection point ascalcium was loaded at an increased rate. When all three Langmuir–Vageler plots were overlaid, as shown in Fig. 13, it was observed that aperfect overlap of measured data was present up until a “drivingforce” of 1.27 mmol calcium ions per g of DOW MAC-3 resin. Conse-quently, for the current experimental conditions it could be concludedthat the “driving force” was a key experimental parameter.

6. Conclusions

This study has demonstrated that even well-known and longestablished ion exchange processes such as water softening can exhibitrelatively complex behaviour. We have shown that an arbitrary choiceof experimental parameters for isotherm generation, which is inherentto a substantial quantity of published literature, could be potentially

Fig. 12. Solution concentration of chloride ions as a function ofDOWMAC-3 resinmass in a0.01 N aqueous solution of calcium chloride.

responsible for incomplete data sets and a source of misinterpretationof the true situation. In this respect, the “driving force” employed inthe exchange process was demonstrated to be a key factor and that ap-plication of the Langmuir–Vageler expression was useful in analysingthe impact of varying the ratio of calcium ions in the initial solution tothe resin mass, to the final equilibrium loading of calcium ions on theresin. The Langmuir–Vageler equation although known for the past80 years has been relatively ignored until now. Nevertheless, its em-ployment to interpret equilibrium data in conjunction with traditionalisotherm models such as Langmuir and Freundlich appears justified,even essential. Evidence was obtained which suggested that in additionto ion exchange between calcium ions in solution and sodium ions onresin sites, at high driving force conditions calcium ions could alsoenter the resin beads and exchange with sodium ions present due toinclusion of sodium hydroxide. The isotherm profiles obtained in thispaper highlighted the impact of experimental parameter choice andthe benefit of measuring all ions in solution, including the anionicspecies in this case, in order to gain a comprehensive process under-standing. Assumptions that a simple ion exchange process is occurringshould not automatically be assumed, aswe have shown both structuraland non-structural ion exchange processes can occur. Correspondingly,the history of the resin used for testing purposes should be evaluated asit is likely that salts are present within the pore structure of the resinbeads. The need to consider hydrolysis effects was also found to be ofsignificance when studying weak acid cation resins, and incorporationof this latter process allowed more accurate determination of ionexchange stoichiometry conditions.

Acknowledgements

Provision of an MSc scholarship from the Institute for FutureEnvironments is acknowledged. Support from the Faculty of Scienceand Engineering for some of the equipment in this study is alsorecognised. The comments of the reviewers were helpful in improvingthe quality of this manuscript.

References

[1] C.A. Lucy, Evolution of ion-exchange: from Moses to the Manhattan project tomodern times, J. Chromatogr. A 1000 (1–2) (2003) 711–724.

[2] F.G. Helfferich, Ion Exchange, McGraw-Hill, New York, 1962.[3] D. Caputo, F. Pepe, Experiments and data processing of ion exchange equilibria

involving Italian natural zeolites: a review, Microporous Mesoporous Mater. 105(3) (2007) 222–231.

[4] P. Misaelides, Application of natural zeolites in environmental remediation: a shortreview, Microporous Mesoporous Mater. 144 (1–3) (2011) 15–18.

[5] A.N. Nikoloski, K.L. Ang, Review of the application of ion exchange resins for therecovery of platinum-groupmetals from hydrochloric acid solutions, Miner. Process.Extr. Metall. Rev. 35 (6) (2014) 369–389.

[6] J. van Deventer, Selected Ion exchange applications in the hydrometallurgicalindustry, Solvent Extr. Ion Exch. 29 (5–6) (2011) 695–718.

http://refhub.elsevier.com/S0011-9164(14)00403-2/rf0005














[7] I.M. Abrams, J.R. Millar, A history of the origin and development of macroporousion-exchange resins, React. Funct. Polym. 35 (1–2) (1997) 7–22.

[8] W. Plazinski, W. Rudzinski, A. Plazinska, Theoretical models of sorption kineticsincluding a surface reaction mechanism: a review, Adv. Colloid Interf. Sci. 152(1–2) (2009) 2–13.

[9] C.E. Borba, E.A. Silva, S. Spohr, G.H.F. Santos, R. Guirardello, Application of the massaction law to describe ion exchange equilibrium in a fixed-bed column, Chem. Eng. J.172 (1) (2011) 312–320.

[10] A. Ma, J.P. Barford, G. McKay, Application of the BDST model for nickel removal fromeffluents by ion exchange, Desalin. Water Treat. (2013) 1–12 http://dx.doi.org/10.1080/19443994.2013.833869 .

[11] G. Alberti, V. Amendola, M. Pesavento, R. Biesuz, Beyond the synthesis of novel solidphases: review on modelling of sorption phenomena, Coord. Chem. Rev. 256 (1–2)(2012) 28–45.

[12] K.H. Chu, Fixed bed sorption: setting the record straight on the Bohart–Adams andThomas models, J. Hazard. Mater. 177 (1–3) (2010) 1006–1012.

[13] C. Tien, Remarks on adsorption manuscripts revised and declined: an editorial, J.Hazard. Mater. 150 (1) (2008) 2–3.

[14] M.I. El-Khaiary, G.F. Malash, Common data analysis errors in batch adsorptionstudies, Hydrometallurgy 105 (3–4) (2011) 314–320.

[15] G.J. Millar, S.J. Couperthwaite, C.W. Leung, An Examination of Isotherm Generation:Impact of Bottle-Point Method Upon Potassium Ion ExchangeWith Strong Acid Cat-ion Resin, 2014. (submitted for publication).

[16] Z. Xue, Z. Li, J. Ma, X. Bai, Y. Kang, W. Hao, R. Li, Effective removal of Mg2+ and Ca2+

ions by mesoporous LTA zeolite, Desalination 341 (2014) 10–18.[17] H. Hoffmann, F. Martinola, Selective resins and special processes for softening water

and solutions; a review, React. Polym. Ion Exch. Sorbents 7 (2–3) (1988) 263–272.[18] M.J. Schwuger, M. Liphard, Sodium-aluminium-silicates in the washing process part

X. Cobuilders and optical brighteners, Colloid Polym. Sci. 267 (4) (1989) 336–344.[19] E. Costa, A. De Lucas, M.A. Uguina, J.C. Ruíz, Synthesis of 4A zeolite from calcined

kaolins for use in detergents, Ind. Eng. Chem. Res. 27 (7) (1988) 1291–1296.[20] H. Ma, et al., Synthesis of zeolite of type A from bentonite by alkali fusion activation

using Na2CO3, Ind. Eng. Chem. Res. 49 (2) (2010) 454–458.[21] C. Ghergheles, V. Ghergheles, T. Romocea, M.A. Roman, E. Pantea, M. Ion, A. Iovi,

Softening of waste geothermal water using ion exchange resins for environmentprotection, J. Environ. Prot. Ecol. 13 (3) (2012) 1553–1559.

[22] H.A. Abdulgader, V. Kochkodan, N. Hilal, Hybrid ion exchange — pressure drivenmembrane processes in water treatment: a review, Sep. Purif. Technol. 116(2013) 253–264.

[23] A. Venkatesan, P.C. Wankat, Simulation of ion exchange water softening pretreat-ment for reverse osmosis desalination of brackish water, Desalination 271 (1–3)(2011) 122–131.

[24] J. Lipnizki, B. Adams, M. Okazaki, A. Sharpe, Water treatment: combining reverseosmosis and ion exchange, Filtr. Sep. 49 (5) (2012) 30–33.

[25] R.T. Pabalan, F.P. Bertetti, Experimental and modeling study of ion exchangebetween aqueous solutions and the zeolite mineral clinoptilolite, J. Solut. Chem.28 (4) (1999) 367–393.

[26] S. Jiang, B. Gao, B. Dong, Ion exchange behaviors of Ca(II) and Mg(II) on LewatitMonoPlus TP 207 and TP 208 chelating resins, Advanced Materials Research,2012, pp. 937–951.

[27] M.H. Entezari, M. Tahmasbi, Water softening by combination of ultrasound and ionexchange, Ultrason. Sonochem. 16 (3) (2009) 356–360.

[28] W.-t Yi, C.-y Yan, P.-h. Ma, Removal of calcium and magnesium from LiHCO3 solu-tions for preparation of high-purity Li2CO3 by ion-exchange resin, Desalination249 (2) (2009) 729–735.

[29] P. Vageler, J. Woltersdorf, Beitrage zur Frage des Basenaustausches und derAziditaten II Vorversuche an Permutiten, Z. Pflanzenernahr. Dungung Bodenk. A15(1930) 184–204.

[30] P. Vageler, J. Woltersdorf, Beitrage zur Frage des Basenaustausches und derAziditaten I. Einletung, Z. Pflanzenernahr. Dungung Bodenk. A15 (1930) 329–342.

[31] R. Petrus, J.K. Warchoł, Heavy metal removal by clinoptilolite. An equilibrium studyin multi-component systems, Water Res. 39 (5) (2005) 819–830.

[32] M. Goto, R. Rosson, J.M.Wampler,W.C. Elliott, S. Serkiz, B. Kahn, Freundlich and dualLangmuir isothermmodels for predicting 137Cs binding on Savannah River Site soils,Health Phys. 94 (1) (2008) 18–32.

[33] J. Skopp, Derivation of the Freundlich adsorption isotherm from kinetics, J. Chem.Educ. 86 (11) (2009) 1341–1343.

[34] A. Gunay, Application of nonlinear regression analysis for ammonium exchange bynatural (Bigadiç) clinoptilolite, J. Hazard. Mater. 148 (3) (2007) 708–713.

[35] K.V. Kumar, S. Sivanesan, Comparison of linear and non-linear method in estimatingthe sorption isotherm parameters for safranin onto activated carbon, J. Hazard.Mater. 123 (1–3) (2005) 288–292.

[36] Y.S. Ho, J.F. Porter, G. McKay, Equilibrium isotherm studies for the sorption ofdivalent metal ions onto peat: copper, nickel and lead single component systems,Water Air Soil Pollut. 141 (1–4) (2002) 1–33.

[37] G. Limousin, J.P. Gaudet, L. Charlet, S. Szenknect, V. Barthès, M. Krimissa, Sorptionisotherms: a review on physical bases, modeling and measurement, Appl. Geochem.22 (2) (2007) 249–275.

[38] I. Langmuir, The adsorption of gases on plane surfaces of glass, mica and platinum, J.Am. Chem. Soc. 40 (9) (1918) 1361–1403.

[39] C.H. Giles, D. Smith, A. Huitson, A general treatment and classification of thesolute adsorption isotherm. I. Theoretical, J. Colloid Interface Sci. 47 (3) (1974)755–765.

[40] C.H. Giles, T.H. MacEwan, S.N. Nakhwa, D. Smith, 786. Studies in adsorption. Part XI.A system of classification of solution adsorption isotherms, and its use in diagnosisof adsorption mechanisms and in measurement of specific surface areas of solids,J. Chem. Soc. (1960) 3973–3993.

[41] V.J. Inglezakis, M.D. Loizidou, H.P. Grigoropoulou, Equilibrium and kinetic ionexchange studies of Pb2+, Cr3+, Fe3+ and Cu2+ on natural clinoptilolite, WaterRes. 36 (11) (2002) 2784–2792.

[42] O.J. Bricio, J. Coca, H. Sastre, Modelling equilibrium isotherms for styrene–divinylbenzene ion exchange resins, Chem. Eng. Sci. 53 (7) (1998) 1465–1467.

[43] H. Tamura, M. Kudo, R. Furuichi, Polyfunctionality of resin carboxyl sites in ionexchange with alkali metal ions, Anal. Chim. Acta. 271 (2) (1993) 305–310.

[44] Y.A. Kokotov, Generalized thermodynamic theory of ion-exchange isotherm,Solvent Extr. Ion Exch. 17 (4) (1999) 1001–1082.

[45] S.G. Christensen, K. Thomsen, Experimental measurement and modeling of thedistribution of solvent and ions between an aqueous phase and an ion exchangeresin, Fluid Phase Equilib. 228–229 (2005) 247–260.

[46] F.G. Donnan, J.T. Barker, An experimental investigation of Gibb's thermodynamicaltheory of interfacial concentration in the case of an air–water interface, Proc. R.Soc. Lond. Ser. A 85 (1912) 557–574.

[47] V.S. Soldatov, E.M. Polhovski, Z.I. Sosinovich, Non-exchange sorption of electrolytesby ion exchangers: I. Sorption of hydrochloric and perchloric acids and their sodiumsalts by Dowex 1 × 8 resin, React. Funct. Polym. 60 (2004) 41–48.

[48] B.D. Bowes, et al., Insights into protein sorption and desorption on dextran-modifiedion-exchange media, Chem. Eng. Technol. 35 (1) (2012) 91–101.

[49] J. Lehto, R. Harjula, Experimentation in ion exchange studies — the problem ofgetting reliable and comparable results, React. Funct. Polym. 27 (1995)121–146.





























































































































exploration of the fundamental equilibrium behaviour of calcium exchange with weak acid cation...

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