J Incl Phenom Macrocycl Chem DOI 10.1007/s10847-013-0323-0
ORIGINAL ARTICLE
Model of phase distribution of hydrophobic organic chemicals in cyclodextrin–water–air–solid sorbent systems as a function of salinity, temperature, and the presence of multiple CDs
William J. Blanford
Received: 22 January 2013 / Accepted: 15 April 2013 Ó Springer Science+Business Media Dordrecht 2013
Abstract Environmental and other applications of calculating HOC phase distribution in air–water–CD–solid cyclodextrins (CD) often require usage of high concentra- sorbent systems for a single HOC and between water and tion aqueous solutions of derivatized CDs. In an effort to CD for a system containing multiple HOCs as well as reduce the costs, these studies also typically use technical multiple types of cyclodextrin. grades where the purity of the CD solution and the degree of substitution has not been reported. Further, this grade of Keywords Cyclodextrin Hydrophobic organic CD often included high levels of salt and it is commonly chemicals Henry’s Law constants Molar volume applied in high salinity systems. The mathematical models Model Freundlich isotherm NAPL for water and air partitioning coefficients of hydrophobic organic chemicals (HOC) with CDs that have been used in these studies under-estimate the level of HOC within CDs. Introduction This is because those models (1) do not take into account that high concentrations of CDs result in significantly Cyclodextrins (CD) are macro-ring molecules composed of lower levels of water in solution and (2) they do not glucopyranose units that have a variety of uses as carriers account for the reduction in HOC aqueous solubility due to of hydrophobic organic chemicals (HOCs), chromato- the presence of salt. Further, because they have poor graphic separating agents, and as viscosity additives [1]. knowledge of the CD molar concentration in their solu- The torodially shaped molecules have a polar exterior and a tions, it is difficult to draw comparisons between studies. nonpolar interior cavity where HOCs of an appropriate size Herein is developed a mathematical model where cyclo- and shape can form inclusion complexes. Native CDs are dextrin is treated as a separate phase whose relative volume non-toxic naturally occurring compounds, but their negli- is calculated from its apparent molar volume in solution gible aqueous solubility in comparison with synthetic CD and the CD concentration of the solution. The model also derivatives has limited their application to groundwater accounts for the affects of temperature and the presence of remediation [2, 3]. There are over 1500 synthetic CD salt in solution through inclusion of modified versions of derivatives [1] among which 2-hydroxypropyl-b-cyclo- the Van’t Hoff and Setschenow equations. With these dextrin (HP-b-CD) is the most commonly used due to its capabilities, additional equations have been developed for relatively low cost and HOC solubility enhancement characteristics. Since 1993 [4], it has been systematically evaluated as an agent for remediation of hazardous waste Electronic supplementary material The online version of this sites. That CD and other derivatives were initially inves- article (doi:10.1007/s10847-013-0323-0) contains supplementary material, which is available to authorized users. tigated for their ability to increase desorption and disso- lution of HOCs and has evolved to evaluation of CD W. J. Blanford (&) derivatives for remediation of mixed metal and HOC sites School of Earth and Environmental Sciences, Queens College, [5], increasing biodegradation of HOCs [6] and as a The City University of New York, 65-30 Kissena Blvd., Flushing, NY 11367, USA mechanism for increasing the efficiency of oxidants and e-mail: [email protected] their applications [7]. 123 J Incl Phenom Macrocycl Chem
Compared to other fields of chemistry and environmental solid sorbent phases as a function of the concentration of a science, publications that employed high concentrations of single salt and temperature and (2) develop equations to modified CDs such as those typically used in environmental describe phase distribution between water and a single restoration studies ([100 g L-1)[3, 8–10] have rarely drawn cyclodextrin for mixtures of HOCs and the distribution of a comparisons with their results and those of other studies. The single HOC between water and multiple types of cyclodextrin. primary reasons for this arise from the inherent variability in the purity the CDs and the average degree of substitution of the modified CDs that those studies used and the poor of reporting of this information when it is known. This fact is Mathematical models of HOC distribution not completely the fault of the authors. In the past, CD in air–water–cyclodextrin systems manufacturers often did not provide this information because of variation within the quality of their CD production and due Because applications of cyclodextrin for environmental to cost concerns the choice by environmental studies to use restoration typically employ highly concentrated solutions, less pure technical-grade CDs rather than high-purity grades a model is needed that does not treat CD as non-volume that often used in pharmacology studies. As an example, contributing pseudo-phase within water [11, 13–16]. To modified CDs used in lab studies range in purity from 85 to have CD as a distinct separate phase then it needs to be 99 % and in case of HP-b-CD the average degree of sub- included in a mass balance equation beside other envi- stitution range from 0.9 to 5.6 and higher. Thus, two studies ronmental phases such as air and water. The total mass of both using the same mass per volume concentration of single component HOC in a system consisting of air, water, 100 g L-1 HP-b-CD could differ in their molar concentra- and CD phases can be found using the mass balance and tion with values ranging from 55 and 82 mM. volume balance Eqs. 1 and 2:
Because knowledge of the purity, degrees of substitution, MAT ¼ CA1V1 þ CA2V2 þ CA3V3 ð1Þ and level of salts within the CD powder or liquid as it was V ¼ V þ V þ V ð2Þ received was lacking, the equations being used in environ- t 1 2 3 mental CD studies relating guest interactions with CDs did where the subscript A is the designation for the HOC and not take into account the influence of salt impurities and used the numbers 1, 2, and 3 are the respective designations for concentration units of mass of CD powder per volume of the air, water, and CD phases. MAT is the total mass of the solution [3, 4, 8–11] rather than molar or molal units which HOC in the system (molesA), the various C terms are -1 make guest host interactions far simpler to explain. Further, concentrations (molesA L ), and the V terms are the the equations that were used in these studies were largely volumes of the phases (L). Because the purity of the CD borrowed from the existing literature where it was most powder is typically given in mass terms rather than volume commonly used to describe the interactions of potential guest of the CD phase, V3, is the net volume of CD rather than compounds with native CDs that are present in solution at the powder and is calculated from the measured masses of comparatively dilute concentrations [12]. However, CD the solution components, the purity and molar mass of the suppliers have improved the precision of their manufacturing CD powder, and from partial molar volumes. Water is methods and are now applying recently developed tech- assumed to be completely held within V2 because the niques for compositional analysis of modified CD. As such, amount within the cavities of CD is negligible. It has been conditions now exist for new models to be created which shown in X-ray studies of aqueous CD solutions that water meet the needs of environmental and other high CD con- molecules can be present within the cyclodextrin cavity centration applications to accurately assess guest–host where they are theorized to form hydrogen bonds with the interactions. Requisite in the design of these models is the walls of the torus [17]. However, the number of water capability of providing precise relationships for calculating molecules within individual cyclodextrin molecules has HOC distribution in environmental systems where multiple been found to be only 5 to 6 for a-CD and 6 to 7 for b-CD phases such as air, water, and solid sorbents are present and [17]. Using a median value of 6.5 water molecules per HP- which rightfully treat CD as a distinct separate phase due to b-CD molecule, then in a 75 mM aqueous solution of this its high concentration. Further, these models would need to cyclic sugar (*100 g L-1 solution of HP-b-CD with a be sufficiently robust to account for the influences of tem- degree of substitution of 2.7) the fraction of water mole- perature and the presence of salts, multiple HOCs, and cules that are within the cavity would be approximately multiple types of cyclodextrin which affect guest–host HOC 0.9 % of the total in solution and less when partially dis- CD interactions in environmental systems. placed by inclusion of guest HOCs. Thus, it can be The goals of this paper are: (1) to develop a mathematical neglected. Because most CDs, including HP-b-CD, are also model capable of accurately predicting the distribution of a nonelectrolytes [17], they do not produce large hydration single component HOC between air, water, cyclodextrin, and spheres where HOC levels would likely be reduced. 123 J Incl Phenom Macrocycl Chem
0 Therefore, these CDs should have a negligible change on apparent HLC, KA12, equating to the actual HLC, KA12. the effective volume of water in that distinct phase avail- With this relationship for apparent HLC, the mass balance able to the HOC and the presence of cyclodextrins should equation Eq. 1 can now be written as a two phase equation: not greatly alter the relative density of water outside of the C M ¼ C V þ A1 V ð9Þ CD molecules (V2). This is a fundamentally different affect AT A1 1 K0 liq than dissolved salts have on the aqueous solubility of A1liq HOCs. Due to their charged nature, salt ions create The fact that cyclodextrin commonly represents a hydration spheres which effectively reduce the net volume significant fraction of the liquid volume when it is of water available to accommodate and thus provide for the employed as an agent for environmental restoration can solubility of HOCs in aqueous solutions. be accounted for with knowledge of the molar In a three phase air/water/CD system, the relative distribu- concentration of this solution component and the tion of HOCs between air and water has commonly been apparent or partial molar volume of cyclodextrin and a assumed to follow the standard Henry’s Law equation [13–16]: relationship between the Vliq, V2, and V3 for pure solutions
CA1 can be found. KA12 ¼ ð3Þ CA2 V2 ¼ 1 VmCDCCD ð10Þ Vliq where KA12 is the air/water partitioning coefficient which is more commonly known as the standard Henry’s Law V3 -1 ¼ VmCDCCD ¼ /CD ð11Þ Constant (HLC) (units of Lwater Lair ). In these same Vliq publications, the relative HOC distribution between air and CD and between water and CD are also thought to have where VmCD is the apparent molar volume of one mole of similar linear relationships: the subject CD in solution, CCD is the concentration of cyclodextrin in molar units, and /CD equals the volumetric CA1 fraction of the liquid accounted for by cyclodextrin. KA13 ¼ ð4Þ CA3 Incorporating Eqs. 10 and 11 into 8 results in a
CA2 relationship between the apparent and actual HLCs, KA23 ¼ ð5Þ CA3 cyclodextrin concentration and the water/CD partitioning -1 coefficient: where KA13 is the air/CD partitioning coefficient (LCD Lair ) -1 KA12 and KA23 is the water/CD partitioning coefficient (LCD Lwater). K0 ¼ ð12Þ -1 A1liq VmCDCCD 1 VmCDCCD þ The high aqueous solubility of HP-b-CD ([800gL )and KA23 the relatively large molecular mass of the molecule likely Extending from the molar volume of CD, the fraction of greatly limit its vapor pressure and presence in the gas phase to the potential host molecules occupied with a guest HOC, level sufficiently low enough to ignore. As Lantz et al. [14] f , is given by Eq. 13: showed, the three partitioning coefficients can be related to ACD each other through: CA2 f ACD ¼ CA3VmCD ¼ VmCD ð13Þ KA23 KA13 KA23 ¼ ð6Þ In a single component HOC saturated aqueous solution, KA12 the concentration of the HOC in the water phase, CA2, For air in contact with CD solutions, the apparent HLC equals equilibrium aqueous solubility and f ACD equals the is defined in the terms of this model as: maximum fraction of CD molecules occupied under
0 CA1 CA1Vliq equilibrium conditions. KA1liq ¼ ¼ ð7Þ CAliq CA2V2 þ CA3V3 Using measurements obtained with a densitometer, Zielenkiewicz et al. [18] reported a relationship for the 0 -1 where KA1liq is the apparent HLC (units of Lliquid Lair ) and apparent molar volume of CDs in solution with the con- the total volume of liquid, Vliq, equals the volume of the centration of the cyclic sugars in units of molality. Their water and CD phases. The apparent HLC can be related to relationship can be adapted to the molarity units and the the other partitioning coefficients through: choice of water as the solvent in the model developed here: 3 CA1Vliq KA12Vliq V ¼ m =q þ 10 q q = C x q q ð14Þ K0 ¼ ¼ ð8Þ mCD CD liq liq 2 CD 2 liq 2 A1liq CA1 CA1 V3 V2 þ V3 V2 þ KA12 KA13 KA23 where mCD is the molar mass of the subject CD, CCD is the For solutions absent the presence of cyclodextrin concentration of CD in solution in molarity units, x2 is the (i.e.,V3 = 0 and V2 = Vliq), this equation reduces to the mass of water per volume of liquid, qliq is the density of the
123 J Incl Phenom Macrocycl Chem liquid, and q2 is the density of the solvent which in this to the particular elemental composition of the salt and the case is water. While Blanford et al. [3] measured the specific HOC and salting out coefficients for slightly polar density of aqueous solutions of HP-b-CD at ambient room molecules such as toluene are non-additive [22]. The ionic temperature, they did not analyze density as a function of strength for the salting out equation is normally calculated temperature. But more importantly, the inherent variability from the Lewis and Randall’s equation: in the purity and degree of substitution of CD derivatives X 1 2 may require that density values be subject specific. Riberio Cs ¼ CiZ ð17Þ 2 i et al. [19] reported density measurements of aqueous solutions of unmodified c-cyclodextrin at two temperatures where Ci is the molar or molal concentration of ionic (298.15 and 310.15° K) and a range of CD concentrations species i and Zi is the charge of the species. For salt -1 (0.002–0.010 mol L ). For the conditions of their study, solutions, Cs equals the molar or molal concentration of they projected a relationship between the solution density total salt, but because the choice affects the value of ks the and CD concentration in molar units to be slightly non- units of Cs need to be clearly stated. Several groups [23– linear and well approximated by the below equation: 25] have adapted the Setschenow salting out equation to Henry’s coefficients through multiplying by the saturated 2 qliq ¼ q2 1 þ b1CCD þ b2CCD ð15Þ vapor pressure. where b1 and b2 are calibrated coefficients. While they did CA2 KA12salt ln ¼ ln ¼ ksCs ð18Þ find that the 10 °C temperature increase reduced the density CA2salt KA12DI of solution by an average of 0.4 %, they did not include a temperature dependence in their equation. In the case of the where KA12salt is the apparent HLC for an air/salt water solvent water, equations for calculating the density of water system and KA12DI is the HLC for pure deionized water as function of temperature and salinity are readily available which is the same as KA12. Reworking equation 18 yields:
[20] and Eqs. 14 and 15 can be further refined. ksCs KA12salt ¼ KA12e ð19Þ Under the conditions of their study, Zielenkiewicz et al. [18] found for an aqueous solution of uncomplexed Literature values on salting out coefficients are inherently HP-ß-CD with a degree of substitution of 0.6 at a variable where some have observed a temperature sensitivity -2 -1 concentration of 4 9 10 mol kg and a density of water for ks [26] while others have found for their systems it is -1 of 997.04 g L that VmCD for HP-ß-CD equaled functionally insensitive temperature [27, 28]. Because this 0.861 L mol-1. In addition, their methods permitted cal- issue is potentially in doubt, the salting out coefficient is culation of the volume of their subject HP-ß-CD when ascribed in this model as being temperature sensitive. complexed with p-aminobenzoic acid which resulted in a Because the interior of the cyclodextrin cavity is non- value of 0.879 ± 0.0008 L mol-1. As with many HOCs, polar, it is unlikely that any meanfully levels of salt ions will their results show HOCs may only be partially encapsu- enter the CD torus and thus should remain within the water lated within the cavity of cyclodextrins. phase. As a result, the air/CD partitioning coefficient, KA13, should not be affected by the presence of salt. If the assumption that the vapor pressure above a HOC saturated Influence of salt on HOC distribution in CD liquids saline solution is the same as that above a pure water made by Peng and Wan [23], Falabella et al. [25], and Falabella and The effect of salt reducing the aqueous solubility of organic Teja [27] is accurate, then the HOC concentration within the chemicals has long been known and has historically been CD cavities, CA3, under HOC saturated conditions should be defined by the Setschenow salting out equation [21]. It is the same for both saline and pure water CD solutions. normally written as a logarithmic formula, but to make it Therefore: more readily employed in this derivation it is shown in the CA2 KA23 C form of a natural log: A3 ksðTÞCs ¼ C ¼ e ð20Þ KA23salt A2salt CA3 CAo ln ¼ ksCs ð16Þ CAsalt Thus, modifying the apparent HLC for the presence of salt would give: where CAo is the saturated aqueous solubility of the HOC, ksðTÞCs CAsalt is the solubility limit of the HOC as a function of salt 0 KA12e KA1liqsalt ¼ k ðTÞC ð21Þ concentration, k is the salting out constant, and C is the VmCDCCDe s s s s 1 VmCDCCD þ K ionic strength of the particular salt solution. In the literature, A23 0 0 ks and Cs appear in both molar and molal units. It should be Because KAliq, KAliqsalt, KA12, VMCD, Cs, ks(T),and CCD noted that ks values have repeatedly been found to be unique can be measured Eq. 12 can be rearranged to provide an
123 J Incl Phenom Macrocycl Chem equation to determine the CD/water partitioning coefficient Fraction in water: (K ). A23 K eksCs uðÞ1 V C A12 mCD CD ð29Þ VmCDCCD k C uVmCDCCD 1 þ KA12e s s uðÞþ1 VmCDCCD KA23 ¼ ð22Þ KA12KA23 KA12 K0 1 þ VmCDCCD A1liq Fraction in CD:
And the salt water/CD partitioning coefficient, KA23salt, uVmCDCCD can be found to be equal to: KA12KA23 ð30Þ ksCs uVmCDCCD 1 þ KA12e uðÞþ1 VmCDCCD K K VmCDCCD A12 A23 KA23salt ¼ k ðTÞC ð23Þ KA12e s s 0 1 þ VmCDCCD KA1liqsalt Relationship of KA23 with existing CD reaction models The temperature dependence of the above partitioning coefficients can be found with van’t Hoff equation [29]: In the literature, the interaction of cyclodextrin with a HOC E ð 1þE Þ in water has widely been described by reaction models [1, K ¼ e T 2 ð24Þ 4, 30, 31]. Equation 31 gives the most widely used model
Modifying the apparent HLC equation to include this for a 1:1 complexation between CD and a HOC where S(aq) basic temperature dependence gives: is the aqueous concentration of the HOC outside of the CD cavity (uncomplexed), CD(aq) is the concentration of E1A12 exp þ E2A12 þ ksðTÞCs uncomplexed CD in solution, S-CD is the concentration K0 ¼ T (aq) A1liqsalt E1A23 of the HOC–CD complex in solution and K is referred to 1 VmCDCCD 1 þ exp ksðTÞCs T E2A23 2 as the association binding constant or the stability constant. ð25Þ K ½ S CD S þ CD $2 S CD K ¼ ð31Þ ðaqÞ ðaqÞ ðaqÞ 2 ½ S ½ CD HOC mass fraction by phase While Eq. 31 is usually written with brackets which Determination of the equilibrium phase distribution of would normally imply chemical activity, in practice HOCs between air, water, CD, and sorbent phases provides concentration units of mass S, CD, or S–CD per total information on the potential performance of CDs in an liquid volume are used instead of activities. As stated environmental application and enables optimization of the earlier, Rekharsky et al. [17] reported that because most design of CD delivery and treatment systems. For ternary CDs are nonelectolytes their activities will be close to one, phase diagrams, the below equations give the HOC mass but they stated that applies to low CD concentration fraction in the air, water, and CD phases. First the mass solutions. Using activities would permit the equation to balance equation: applied to relatively high CD concentration solutions C where the mass of water in solution is greatly reduced A1 -1 MAT ¼ CA1V1 þ VliqðÞ1 VmCDCCD ksCs due to the level of CD (e.g. 100 g L CD solution has a KA12e -1 CA1 reduction of *7 % in the mass of water over a 0 g L þ VliqVmCDCCD ð26Þ solution). However, in practice the activity coefficients of KA12KA23 constituents are assumed to be equal to one and in effect Equation 26 can be reorganized by dividing through by Eq. 31 uses concentrations. As a result, this model assumes the air concentration and the air volume and substituting u the volume of water is equal the volume of solution. This is as the liquid to gas volume ratio. potentially misleading in the application of Wang and M uV C AT ksCs mCD CD Brusseau [4] CD reaction equation by McCray et al. [11] ¼ 1 þ KA12e uðÞþ1 VmCDCCD CA1V1 KA12KA23 where they created HOC saturated solutions to determine ð27Þ water-CD distribution coefficients. In their work, they assumed that the mass of uncomplexed HOC in solution From here the fractions of the HOC mass in each phase equals literature values for aqueous solubility multiplied by can be found by normalizing each of the three terms on the the total solution volume rather than the volume of solution right hand side of Eq. 27 by the summation of that side. after deducting the portion of the total volume accounted Thus, the fraction in the air phase becomes: for by the added cyclodextrin. Thus, their water-CD 1 partitioning coefficients underestimate the proportion of ð28Þ k C uVmCDCCD 1 þ KA12e s s uðÞþ1 VmCDCCD HOC molecules within cyclodextrin cavities. KA12KA23
123 J Incl Phenom Macrocycl Chem
Previous efforts by Kashiyama and Boving [13], Lantz are occupied with this HOC). However, in CD systems et al. [14], and Szaniszlo et al. [15] to determine air/CD with low HOC concentrations or in HOC saturated CD solution phase partitioning coefficients by headspace GC systems where the HOC has a low aqueous solubility then also made an effort to relate those coefficients to K2. Both fACD 1 and the above equation can be reduced to: Kashiyama and Boving [13] and Szaniszlo et al. [15] 1 K2 ffi ð35Þ designed their experiments with low levels of HOC so that 1 KA23 CCD they could assume that the concentration of complexed CD, VmCD [G-CD], is far less than the uncomplexed CD concentration, [CD], and thus the uncomplexed CD concentration equals Solubility enhancement factor the total CD concentration which is known from preparation. This design limits the applicability of their equation to low McCray et al. [11] applied the concept of the solubility HOC concentration solutions. Szaniszlo et al. [15] did not enhancement factor to define the degree to which sol- report the values of the Henry’s Law constants they used in ubility of an HOC is improved by an aqueous CD their analysis and they report a range of total guest mass in solution over that of pure water. Their model was based their preparations of their samples rather than an exact value, on the equation in Wang and Brusseau [4]inwhichthe but attempts to produce a similar level of difference between water/CD partitioning coefficient where the concentra- uncomplexed and complexed CD using their methods were tion of complexed cyclodextrin molecules are low. unsuccessful which shows the limitation of this method. While the Lantz et al. [14] model did have separate volumes SA ¼ SWðÞ¼1 þ KCWCCD SWE ð36Þ for water and CD in the formulations of their partitioning where SA equals the apparent solubility in aqueous CD coefficients, their equation relating K2 and to their water/CD solutions, SW is the solubility in water, KCW is the parti- partitioning coefficient went against their own model’s tioning coefficient between water and CD, and E is the design by again assuming that the volume of water was equal solubility enhancement factor. to the volume of solution. While the methods of McCray et al. [11] show the Using the nomenclature of this paper, below are the effective increase in apparent solubility, they provide equivalent equations for reaction a model. misleading information on the water/CD partitioning V2 V3 coefficient and their model can be misinterpreted where the ½ ¼S CA2 ½ ¼CD CCD CA3 V V fraction of HOC mass in water equals 1/E and fraction in liq liq ð32Þ V3 CD is equal to (E-1)/E. Despite this, the idea of a solu- ½ ¼S CD CA3 Vliq bility enhancement factor is useful especially when pro- posing cyclodextrins as a remedial alternative. Thus: In the nomenclature of this paper, the enhancement CA3V3 factor can be determined from assuming the lack of an air Vliq K2 ¼ phase and normalizing the remaining terms in the original CA2V2 CA3V3 CCD mass balance equation by the volume of the liquid. Vliq Vliq VmCDCCD ¼ ð33Þ MAT VmCD KA23ðÞ1 VmCDCCD ðÞCCD CA3VmCDCCD ¼ CA2 1 þ VmCD CCD ð37Þ Vliq KA23 After reorganizing: The left-hand side of Eq. 37 equals SA, the apparent VmCDCCD solubility in CD solutions. Since in a HOC saturated CD K2 ¼ KA23CCDðÞ1 VmCDCCD ðÞ1 CA3VmCD solution the HOC concentration in the water portion equals the / aqueous solubility, C equals S .Thereby,theremaining ¼ cd ð34Þ A2 W KA23CCDðÞ1 /cd ðÞ1 fACD terms fulfill the notion of a solubility enhancement factor envisioned by McCray et al. [11]. It should be noted that where f again equals C V , the fraction of CD ACD A3 mCD parameters held within the inner parentheses equal the water/ molecules occupied with a HOC, and u again equals CD CD partitioning constant of McCray et al. [11]. VmCDCCD, the fraction of the total solution volume accounted for by cyclodextrin.
The value of fACD is often high in saturated solutions of high aqueous solubility HOCs. (e.g. using the experimental Enhanced solubilization of organic-liquid mixtures results of McCray et al. 2000 and correcting for CD vol- ume, in a TCE saturated 100 g L-1 HP-b-CD solution with McCray and Brusseau [11] applied Raoult’s Law to their an assumed DS of 4.9 results in 71 % of the CD molecules earlier formula (36) to develop an equation to determine
123 J Incl Phenom Macrocycl Chem the saturated levels of HOCs in a cyclodextrin aqueous HOC distribution in a system of water and multiple solution when exposed to an excess liquid containing types of CD multiple HOCs. Equation shows their model where Xi is the mole fraction of the ith HOC component in a multi- Native and derivatized CDs have different affinities for component HOC liquid, SAi is the saturated concentration various types of HOCs and metals and they have sharply in the CD solution, and the other terms are specific to that different commercial costs. To take advantage of dif- HOC. ferent affinities and reduce the expense of application, circumstances could exist where multiple CDs would be SAi ¼ XiSWiðÞ¼1 þ KCWiCCD XiSWiEi ð38Þ used to address a mixture of HOCs or a metal/HOC While this equation does permit accurate estimation of mixture. As an example Hoffman et al. [6] found that the total amount of each component in solution, it again 2-carboxymethyl-b-cyclodextrin (CM-b-CD) mitigates over estimates the HOC amount in the water portion of the the toxicity of cadmium, cobalt, and copper during bio- liquid. Below is a version of Raoult’s Law for CD solutions degradation of naphthalene, but compared to HP-b-CD, using the nomenclature of this paper. CM-b-CD has a lower affinity for HOCs and is far more expensive [4, 5]. Thus, an application of both CDs may VmCD make sense. As a further example, 2-hydroxypropyl-c- SAi ¼ XiSWi 1 þ VmCD CCD ¼ XiSWiEi KAi23 cyclodextrin has greater affinity for large polycyclic ð39Þ aromatic hydrocarbons (PAHs) than HP-b-CD, but is far more expensive [33]. Thus, a mixture of these two CDs may make sense for application to a coal-tar site where a HOC distribution in a water–CD–absorbent porous range of PAHs are present. media system If the CDs being chosen were known not to polymerize, then they would act independently and the equations for Gao and Blanford [32] found in batch studies that the HOC distribution would be straight forward. The additional presence of 2-hydroxypropyl-beta-cyclodextrin in aqueous CDs would simply be additional phases and the distribution solutions decreased the sorption trichloroethylen to gran- coefficients with water would have the same form as the ulated activated carbon (GAC). Specifically, they found first CD. Thus for the same system as Eq. 37, the addition that phase distribution between water and GAC followed a of a multiple types CDs would follow the form of: Freundlich isotherm. ! M Xnþ2 V C ¼ K Cn ð40Þ AT ¼ C 1 þ mCDi V C ð42Þ AS f A2 V A2 K mCDi CDi liq i¼3 A2i where CAS is the adsorbed concentration of the HOC on the -1 where n is the number of distinct types of CDs. Since the adsorbent (molHOC kgadsorbent), Kf, is the Freundlich -1 process of derivatizing cyclodextrin results in a population adsorption coefficient (Lwater kgadsorbent), which indicates the adsorption ability and n is a constant indicative of of cyclic oligosaccharides with varying degrees of substi- adsorption affinity. From their batch studies, they found tution, this equation also elegantly describes the complex that if the HOC mass associated with CD was removed behavior even of aqueous solutions containing a single type from consideration, then the parameters for the isotherm of modified CD. describing the distribution of the HOC between water and the adsorbent phases was statistically the same as the isotherm parameters in the absence of cyclodextrin. Thus, Summation in the nomenclature of this paper, the absorbent would function as another phase in the mass balance equation and The development of derivatives of native cyclodextrins in the distribution between the water and adsorbent phase technical grades has resulted in a series of studies inves- would follow Eq. 40 and thus Eq. 37 would become: tigating the potential of CD as an agent to improve the remediation of hazardous waste sites. However, the varia- MAT VmCD n 1 MS ¼ CA2 1 þ VmCD CCD þ KfCA2 tion in the purity and degree of substitution of derivatized Vliq KA23 Vliq CDs and a lack of reporting of this information has ð41Þ inhibited the development of models to uniformly assess where MS is the mass of the adsorbent. Over short ranges in the results of these studies. Because that information is concentration a linear isotherm is appropriate and Eqs. 40 becoming widely available, the above model provides a and 41 further simplify. means to evaluate HOC/CD interactions on a molar basis
123 J Incl Phenom Macrocycl Chem and improves the ability of environmental scientists to of all partition/association constants for highly volatile solute- reproduce and compare their results. cyclodextrin-water systems. Anal. Bioanal. Chem. 383(2), 160–166 (2005) 15. Szaniszlo, N., Fenyvesi, E., Balla, J.: Structure-stability study of Acknowledgments Support for Dr. Blanford’s cyclodextrin cyclodextrin complexes with selected volatile hydrocarbon con- research program has been given by the U.S. Department of Defense taminants of soils. J. Incl. Phenom. Macrocycl. Chem. 53(3–4), Environmental Security Technology Certification Program (ESTCP), 241–248 (2005) the U.S. Air Force Center for Environmental Excellence, and Wacker 16. Gao, H., Blanford, W.J., Birdwell, J.E.: The pseudophase Chemie AG. 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