246
Anal. Chem. 1985, 57,246-253
Determination of Charge and Size of Technetium Diphosphonate Complexes by Anion-Exchange Liquid Chromatography George M. Wilson and Thomas C. Pinkerton*
Department of Chemistry, Purdue University, West Lafayette, Indiana 47907
Anlon-exchange high-performance liquid chromatography has been employed to determine the negative charges on 12 unknown technetium hydroxyethyildene dlphosphonate complexes (Tc-HEDP), prepared from the sodium borohydrlde reduction of pertechnetate in the presence of the ligand. The separated technetium dlphosphonate complexes, each assumed to be polyprotlc, yielded average charges ranglng from -1.5 to -8.0. Approximate partial molar volumes, ranging from 500 to 1600 mL/mol, Indicate the posslbliity of dimeric or polymerlc complexes. Slze-exciusion chromatography and preliminary mass spectrometry support a polynuclear structural hypothesis. I n several cases a reversal of elution order was observed as a result of size discrimlnatlon, as predicted by lon-exchange theory. The acqulstion of component spectra utilizing UV-VIS photodiode array LC detection, along wlth the average charges and partial molar volumes has enabled an assignment of the Tc-HEDP complexes to various groups.
When inorganic transition metal complexes cannot be obtained in crystalline form suitable for structural analysis, it becomes necessary to perform characterization in solution. The determination of physical properties such as complex charge, size, ligand-to-metalratio, and spectral characteristics aid in the elucidation of such complexes. The following work demonstrates the use of ion-exchange high-performance liquid chromatography for the determination of anionic charges and hydrated partial molar volumes on a group of substitution inert technetium diphosphonate complexes. Technetium diphosphonate (Tc-DP) radiopharmaceuticals are a class of inorganic compounds widely used in the diagnostic imaging of skeletal metastases (1, 2) which have remained elusive to conventional methods of characterization. The technetium diphosphonate complexes are prepared from the reduction of pertechnetate (TcO,-) with a suitable reducing agent (e.g. Sn2+,NaBH4, HONH2, etc.) in the presence of excess diphosphonate ligand in aqueous media (3, 4 ) . The resulting compoynds exist as complicated collections of various unknown Tc-DP complexes in aqueous reaction mixtures (3-8). Several liquid chromatographic methods, including anion-exchange ( 3 , 4 ) ,reverse-phase (6), and size-exclusion (3),have been employed to separate Tc-DP reaction mixtures into Tc-DP components. Studies reveal that the relative composition of Tc-DP complexes within a mixture varies greatly with reaction conditions (e.g., pH, Tc concentration, O2concentration, etc.) (3-6). Only one crystal structure determination has been reported for the technetium diphosphonates (9), owing to the extreme difficulty encountered in the purification and crystallization of these compounds. In lieu of being able to easily isolate and crystallize technetium diphosphonates for structural analysis, solution characterization becomes an alternative. Since the Tc-DP complexes can be separated by anion-exchange chromatography ( 4 , 5 ) it is logical to exploit ion-exchange theory to determine the
ionic charges on the separated complexes as a first step in the solution characterization process. Ion-exchangemethods have been utilized to determine the physical properties of ionic species with attention historically given to cations (10, 11). In the case of technetium, batch ion-exchange techniques have been employed to estimate collective charges on unknown cationic and anionic technetium 99m species at tracer concentrations in unseparated mixtures (12-14). Although such batch ion-exchange technique are appropriate when single species are present, the methods are quite unsuitable for complicated solution mixtures. Electrophoretic techniques have also been used to evaluate charge on technetium species (15); however, difficulties in choosing appropriate matrix supports has limited electrophoresis to selected cases. Given the nonspecific nature of the batch ion-exchange methods, the alternative dynamic column chromatographic technique appears more appropriate for solution mixtures. Russell, Crittenden, and Cash (16) have demonstrated the initial feasibility of using ion-exchange column chromatographyfor the determination of the complex charge on technetium complexes by determining the anionic charge on 99mTc-DTPAand gQmTc-EDTA.The method as developed, however, was limited to the use of conventional low-pressure column chromatography and required use of an internal “reference” species. In measuring only charge, Russell chose an implicit thermodynamic approach; therefore, effects arising out of phenomena not described by the model are inherently reflected in the activity coefficients (17). This is a common practice in ion-exchange treatments, and it assumes that discrimination by solvated volume, in partitioning between the ion-exchange resin and mobile phase, is not significant (17). In many circumstancesthis assumption is valid; however, in cases where ionic species differ greatly in solvated volumes, such ion-exchangetreatments cannot fully account for elution order. The aim of this study is to present a rigorous thermodynamicion-exchange treatment for the determination of charge on kinetically stable transition-metal complexes by means of ion-exchangechromatography, with an explicit description of the complex partial molar volumes and their effects on elution order. The method is demonstrated with a high-performance anion-exchangeseparation where the inclusion of an internal “reference” substance is not required. The determination of anionic charges on a group of structurally unknown technetium hydroxyethylidene diphosphonates (Tc-HEDP), along with collaborating UV-vis spectra and preliminary size-exclusion data, provides new insight into the solution chemistry of technetium diphosphonate complexes.
THEORY When considering the equilibrium of a charged species i in an ion-exchange process, the electrochemical potentials of the species in each phase are equal. When qrand ~ i , are ~ l allowed to represent the electrochemical potential of species i within the resin and the eluent phases, respectively, then under localized equilibrium conditions
0003-2700/85/0357-0246$01.50/00 1984 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 57, NO. 1, JANUARY 1985 Vi,,
=
(1)
%,el
In the eluent phase the electrochemical potential can be related to the standard chemical potential by the expression Vi,el
= pi,elo
+ RT
In
ai,el
+ ziF4e1
(2)
Likewise, in the resin phase
v~,, =
+ RT In ai,, + ZiF& + viII
(3)
where pi,elo and are standard chemical potentials for species i in the eluent and resin, respectively, at some defined standard state, the terms ai,eland ai,, are the activities of species i in the eluent and resin. R is the universal gas constant, T is the absolute temperature, Zi is the absolute charge on species i (i.e., lZl),F is the Faraday constant, 4el and 4, are the electrical potentials acting on species in the respective phases, vi is the partial molar volume of the solvated species i, while II is the osmotic pressure of the ion-exchange resin. Assuming that the partial molar volume of species i is the same in the eluent or resin, eq 2 and 3 may be set equal according to eq 1.
+ RT In qel+ ZiF4e1= pi,,o + RT In ai,, + ZiF4, + QII (4)
pi,elo
An expression analogous to eq 4 exists for the counterion A, which is also in equilibrium with the resin and the eluent phase. For a given chromatographic separation under localized equilibrium conditions, the Donnan potential (Le., A4 = 4, - 4el)experienced by species i will be the same as the counterion A; thus combining the expressions yields eq 5
+ ZiF 1n[
Yi,eI
where yi and Ci are the activity coefficient and molar concentration of species i, respectively, and where the changes in standard chemical potentials are ApT = &,do- kcoand &A’ = p~,~lO - PA,,’. Incorporation of the distribution coefficient K,, defined as the ratio of molar concentration of species i in the resin Ci,, to the molar concentration of species i in the eluent Ci,el,yields eq 6.
Combination of eq 6 with a rearranged form of the general chromatographic retention equation
VB In tR’ = In -
F
+ In KD
(7)
where th’ is the “corrected” retention time of species i (defined as the difference between the measured of species i, tR,,and the retention of a nonretained component, tm), V , is the “stationary-phase volume”, and F is the volume flow rate, results in eq 8.
247
The corrected chromatographic retention time of species i can then be measured at different concentrations of counterion in the eluent while maintaining a constant pH, temperature, pressure, and eluent flow rate. Provided that the first three terms remain constant, then eq 8 can be represented in more general terms as log tR’ = intercept - Zi log aA,el (9) Accordingly, a plot of log corrected retention time vs. the log activity of the eluent counterion yields a linear plot with the slope equal to the charge on species i. A closer examination of the terms included in the intercept shows that R, Z,, ApIo, and ApAo remain constant by definition and that F and Tare experimental parameters that can be held constant. Any changes in Vs, q, vA, and aA,,with change in ionic strength are expected to be insignificant if the initial concentration of the counterion in the eluent is high and this concentration is only varied over a narrow range. This requires that the activity of the counterion in the resin phase be significantly greater than the change in activity of the mobile phase. Further, the treatment assumes that the ratio of the activity coefficients of the complexes between the eluent and the resin phase (yi,el/yl,,)remains appreciably unaffected. Considering the requirement that any change in ionic strength be over a narrow range, this assumption is fairly sound. Under these conditions any change in the osmotic pressure, II, which is governed by swelling equilibrium, should also be insignificant. This is important since the terms Vs and uA,, would be indirectly affected by changes in the magnitude of n. Other treatises dedicated to these considerations discuss the relative significance of each of the aforementioned terms in detail (17-21). A more detailed derivation of eq 8 can be obtained upon request. EXPERIMENTAL SECTION HPLC Apparatus. The chromatographicequipment included a low flow rate version ConstaMetricModel I11 (LaboratoryData Control) dual-piston pump, a Rheodyne Model 7125 injection valve with a 20-wL loop, and a Wika 5000-psi pressure gauge. In addition, a Bioanalytical Systems LC-22 temperature controller, LC-23 column heating compartment, HPLC organizer rack, and a DP-1 pulse damper were used. A guard column (40 mm X 4.6 mm i.d.) containing pellicular anion-exchangesupport material (AE-Pellionex-SAX,Whatman, Catalog No. 1461-010,Lot No. 100079) was included prior to the analytical column. In this type of pellicular packing the ion-exchange functionalities are bound to a resin coating of the pellicular as opposed to a porous silica surface. The analytical column consisted of a 150 mm X 4 mm i.d. stainless steel column containing microparticulate (diameter 7.0 h 1.0 pm), 8% cross-linked anion-exchangepolystyrene-dlvinylbenzene quarternary amine resin (Aminex A-29, Bio-Rad Laboratories) with a 1200-psipressure rating. The column was packed in 1.5 M sodium acetate at pH 8.4. Size-Exclusion Apparatus. For the size-exclusion separations a Varian Series 4100 syringe pump was employed in conjunction with an Altex Model 202 rotary injection valve and a 100 cm X 6 mm i.d. glass column packed with poly(acry1imide)BioGel P-10 (200-400 mesh). Detection Methods. An aluminum-housed NaI(T1) well scintillation crystal (Harshaw,Type 7518) was used to detect the y, 6.0-h half-life) and 22Na radiation from the 9 9 m T(143-keV ~ (1.3-MeV y, 2.6-year half-life) radionuclides on elution from the HPLC column. After the analytical column the eluent entered the scintillation detector well through a loop constructed of in. (1.6 mm) 0.d. X 0.01 low-volume 316 stainless steel tubing in. (0.23 mm) i.d.1. An Ortec Model 420A timing single-channel analyzer, Harshaw NA-23 amplifier, and a Harshaw NR-30 linear ratemeter comprised the detection electronics. A fixed wavelength Altex Model 153 UV-vis liquid chromatography detector (8-fiL flow cell) was utilized in-line after the scintillation detector. The fixed wavelength UV-vis detection was conducted at either 254 or 405 nm. A photodiode array spectrophotometer (Hewlett-Packard,Model HP 845019) was used
248
ANALYTICAL CHEMISTRY, VOL. 57, NO. 1, JANUARY 1985
as a liquid chromatographicdetector to record the W-vis spectra (200-800 nm) of the unknown Tc-HEDP complexes during chromatographic elution. An 8-pL “2” configured spectral flow cell (Hellma Cells Inc., Catalog No. 178.32) with quartz windows and a 10-mm path length was employed with the HP 8450A spectrophotometer. Reagents. The eluents for both the HPLC and size-exclusion chromatography were prepared by using HPLC grade sodium acetate (Fisher Scientific) dissolved in distilled deionized water. When necessary, the pH of the solutions was adjusted with microliter quantities of saturated sodium hydroxide. The eluents were filtered (0.22 pm, Millipore) prior to use. The “reductant” solution required for the Tc(NaBH,)HEDP preparation was 3.15 M sodium borohydride (Alfa Products No. 87658,99%pure) in 0.1 M potassium hydroxide,freshly prepared before use. The 99Tc”carrier” was added in the form of potassium pertechnetate. The Kg9Tc04was prepared by a multiple recrystallization procedure beginning with ammonium pertechnetate (Oak Ridge National Laboratories, 99% pure). The 99”Tcused to spike the Tc(NaBH,)HEDP preparation was obtained as NahTc04 in normal saline (Syncor Corp., Indianapolis, IN) on the day of use. A 1 mCi/mL 22NaC1solution (New England Nuclear, Catalog No. NE2081) was used to determine the mobile-phase retention (t,) for the radiometric detection. The solution was diluted 30-fold in filtered (0.22 pm) distilled water prior to injection. A 50% (v/v) methanol solution (HPLC grade, Fisher Scientific) was used to determine the t , with the UV-vis and refractive index detectors. No difference in the determination of column void volume was found with either of these two methods. The disodium salt of 1-hydroxyethylidenediphosphonate (97% Na,H2HEDP, Procter and Gamble) was used both in the Tc(NaBH4)HEDPpreparation and as external standard for evaluation purposes. The standard HEDP samples were prepared by dissolving 0.30 M HEDP in 0.800 M NaOAc, adjusting the pH to 8.5 with saturated NaOH, and then filtering with 0.22-pm nylon filters. Tc(NaBH,)HEDP Sample Preparation. The following describes the general procedure for the preparation of a ggTcFirst, 0.50 mL of 63 (NaBH4)HEDPsample spiked with g9mT~. mM KgSTc04is added to 4.00 mL of an aqueous 397 mM NazHzHEDPsolution in a 10-mL Erlenmeyer flask containing a miniature magnetic stir bar. To this solution 1.00 mL of NaS9mTcO4(-50 mCi in normal saline) is added. Second, 0.50 mL of filtered (0.22 pm) reductant solution is added dropwise over a 4-min time span while permitting the effervescence of hydrogen to subside between additions. The reactant addition proceeds with continuous stirring at ambient temperatures while exposed to air. After the addition of the reductant solution is complete,the reaction mixture is stirred for an additional 30 min prior to filtration (0.22 pm) and HPLC analysis. All solutions are prepared by using distilled deionized water unless otherwise specified. Chromatographic Procedures. Six pH-adjusted sodium acetate mobile phases with ionic strengths of 0.815,0.800,0.785, 0.770,0.755, and 0.740 M were employed during the HPLC charge determination experiments. The column temperature was 28.0 OC,and the flow rate was continuously maintained at 0.134 f 0.001 mL/min. At each ionic strength a minimum of three chromatograms were obtained so that an average retention time,for a given peak could be determined. Each eluent was allowed to equilibrate with the column stationary phase for at least ten column volumes before the first sample was injected at the ionic strength. The pH of the eluent was maintained at 8.53 0.03 for the determination of charge on the HEDP reference sample, and at 8.1 & 0.1 for the determination of charge on the Tc-HEDP species. During the acquisition of the UV-vis spectra of the Tc-HEDP complexes with the photodiode array spectrophotometric detection, a 100-pL sample loop and a 0.755 M acetate eluent (pH 8.1) were employed. Spectra were collected every 20 s throughout a chromatogram.
*
RESULTS AND DISCUSSION Chromatographic Considerations. The judious choice of the chromatographic packing material and operating con-
ditions were critical to the success of determining the anionic charge on the separated unknown technetium diphosphonate complexes by anion-exchange HPLC. The experimental parameters chosen reflect a compromise between the preconditions imposed by the ion-exchange theory and the practical considerations necessary to achieve an adequate separation. Ion-exchange theory dictates that the principal mechanism responsible for changes in corrected retention times (eq 8), that result as the ionic strength of the mobile phase is varied, be due primarily to the ion-exchange equilibria. This does not preclude the existence of other inherent secondary processes such as adsorption and exclusion; instead the theory simply requires that these secondary effects remain constant over the eluent ionic strength range employed. Such secondary phenomena might, however, determine overall elution order independent of ionic strength changes. In particular, the so-called “secondary exclusion” phenomena, which can discriminate between the solvated volumes of species separated on porous cross-linked polystyrene-divinylbenzene ion-exchange resins, has been explicitly included in this theoretical treatment. The microparticulate Aminex A-29 resin was selected in lieu of other anion-exchange supports because of (i) its high exchange capacity, which accommodates millimolar sample concentration necessary for the spectrophotometric detection, (ii) its increased efficiency, which yields greater resolution, and (iii) its hydrophobic polysytrene-divinybenzene base, which exhibits minimum adsorption to these hydrophilic Tc-HEDP complexes (4). Conversely, distinctly hydrophilic ion-exchange supports, such as cellulose, dextrans, and silica, have proven unsatisfactory in separating these particular technetium diphosphonate complexes because of adsorption interactions. Acetate was chosen as the mobile-phase counterion because of its monovalent charge and its anticipated noncomplexing properties, thereby minimizing the probability of ligand exchange with the technetium complexes during the chromatographic process. Nonbuffered but pH-adjusted acetate eluents were employed because of the difficulty in fiding a suitable buffer in the desired pH region which would be noncomplexing with technetium and yet would still enable accurate assessment of the activity in the mobile phases. This precaution was taken even though the complexes are believed to be substitution inert. In order to ensure the linearity of eq 8 and the applicability of ion-exchange theory to the determination of charge on the separated anionic species, several experimental precautions were exercised in accordance with the theoretical considerations discussed above and the constancy of the intercept term. First, a special slow flow rate pump was used to produce a constant, reproducible flow rate of 0.134 0.001 mL/min. Second, a constant operating temperature of 28.0 f 0.1 “C was maintained by a column temperature controller. Third, the system pressure was continuously monitored and was observed to remain constant throughout the range of ionic strengths employed. Fourth, the incremental difference in ionic strength (0.015 M) between each elution was kept small compared to the total counterion concentration of the eluent (0.740-0.815 M). Fifth, the overall range in ionic strength change (0.085 M) was small compared to the counterion concentration in the resin phase, estimated to be somewhere between 2.8 and 4.2 M given a swollen capacity of 1.4 mequiv/mL and a water content range from 35% to 58% (22, 23). Calculation of Activity Coefficients. Utilization of eq 9 requires an estimation of the activity coefficients of the counterion over the concentration range employed. In this study sodium acetate was chosen as the eluent counterion with
*
ANALYTICAL CHEMISTRY, VOL. 57, NO. 1, JANUARY 1985
249
Ionic Charge of HEDP
W
E -2800 W
I
(7 -2600
W
5
-2500
\
-230@i
0 740 M 0755 Ivl
\
24@o/
10
20
30
40
50
0770 M
20
IONIC STRENGTH
0785 M
Figure 1. Average charge on HEDP as a function of ionic strength.
0800 M
a concentration range from 0.740 to 0.815 M. At ionic strengths less than unity, one of the most accepted methods for calculating the mean activity coefficient for a 1:l nonassociated electrolyte is expressed below (24-26)
0815 M
where p is the ionic strength of the solution, Z1 and Zz represent the charges on the electrolyte ions, A and B are constants which include the absolute temperature and dielectric constant of the solvent, ci is an ion-size parameter, and b is an empirical constant. The product Bu (0.9221) and the coefficient b (0.1755) for aqueous sodium acetate were ascertained from previous work (27). Term A (0.514mol-1/2L1l2 K3/2)was calculated by traditional methods (25). Determination of Charge on an External Standard. In order to evaluate the accuracy of the charge determination method relative to the unknown Tc-HEDP complexes, a suitable standard had to be chosen for comparison which would reflect any ancillary phenomena experienced by the technetium complexes. It was with this intent that the HEDP ligand was selected as a standard since it is reasonable to assume that any nonideal processes which could affect retention of the technetium complexes might well be due to the nature of the ligand. Hydroxyethylidene diphosphonate (CH3C(OH)(P03Hz)2) is a tetraprotic acid, for which the acid dissociation constants have been determined (28-31). The 0.3 M HEDP standard solution in 0.800 M NaOAc was prepared at the same pH as the mobile phase, pH 8.5; thus the predominant species a t equilibrium were H3EDP3- >> HzEDP2-> HEDP". As any polyproticweak acid, the HEDP will elute from the anion-exchange chromatographas one peak with an average charge that reflects the percent abundance of the predominant species at the selected pH. When the pK,'s of HEDP are utilized as reported by Collins and Perkins (28) at p = 0 and the pK,'s are corrected for ionic strength in an appropriate manner (241, speciation calculations at pH 8.53 yield the expected average charge on the HEDP over a wide ionic strength range (Figure 1). Typical chromatograms for the HEDP at the selected mobile-phase ionic strengths are illustrated in Figure 2. As the HEDP transverses the column on the average 25% of the time is spent in the mobile phase and the remaining 75% of the time is spent in the stationary phase. This means the effective average ionic strength environment experienced by the HEDP might range from 3.1 to 3.2, if one assumes the ionic strength in the resin phase to be approximately 4.0. This means one would expect the charge on the HEDP at pH 8.53 to range from -2.87 to -2.92. The average charge on the HEDP at pH 8.53, as determined from the slope of eq 9, was found to be -2.8 0.1 with an intercept of 1.84 and a correlation coefficient of 0.9981. This measured value is slightly
*
0
20
10
30
40
Time (minutes)
Flgure 2. Chromatograms obtained for HEDP at various eluent ionic strengths. Changes in the ionic strength (and therefore activity) of the mobile phase causes changes in retention time which are related to the complex charge of the HEDP: eluent, sodium acetate, pH 8.53; flow rate, 0.134 mL/min; temperature, 28.0 O C ; pressure, 950 psi.
-z" I
I1
a m
I
254 nm delectlon
U&&d
0 . 4
RETENTION TIME (minutes1
Figure 3. Tc-HEDP complexes separated by anion-exchange HPLC.
An HP 8450A spectrophotometer was used as the detector: eluent, 0.755 M sodium acetate; flow rate, 0.11 mL/min; temperature, 28.0 'C; Pressure, 950 psi.
RETENTION TIME Iminutesl
Flgure 4. Tc-HEDP components separated by anion-exchange HPLC with spectrophotometric detection at a single wavelength: eluent, 0.755 M sodium acetate; flow rate, 0.1 1 mL/min; temperature, 28.0 'C; pressure, 950 psi.
lower than that predicted; however, the difference is within the precision of the experimental measurement. The determination of average charge on the HEDP as an external standard demonstrates an accuracy of the chromatographic method of AO.1 unit charge. This uncertainty was found to be well within the precision encountered in determining the charge on the Tc-HEDP complexes (hO.1 to *0.4 depending on the component peak measured). Determination of Charge on the Tc-HEDP Complexes. The kinetic stability of these Tc-HEDP complexes has been evidenced by collection and reinjection of the HPLC-separated components, yielding single peaks in most cases. Typical anion-exchange HPLC chromatograms of the Tc-HEDP preparation are illustrated in Figures 3-5 with optical de-
250
ANALYTICAL CHEMISTRY, VOL. 57, NO. 1, JANUARY 1985
Table I. Chromatographic Capacity Factors, Charge Determination Results, and UV-Visible Spectral Characteristics of numerous Tc-HEDP Complexes at pH 8.1 ionic group
I I1 I11 IV V V VI VI1 VI1 VI1 VI11 VI11 IX
peak
capacity factor"
chargeb,2,
S.D.
*
intercept
correlation coeff
Nc
-1.3 -1.6 0.20 2.5 2.5
-0.9953 -0.9980 -0.9950 -0.9985 -0.9953 -0.9802 -0.9993 -0.9997 -0.9998 -0.9939 -0.9965 -0.9980
6 5 5 6 6 6 4 3 3 6 6 6
A
T M Z
Y U V P
Q R S
W X
1.1 1.4 3.5 4.5 4.8 6.3 8.1 8.7 9.4 10.8 12.0 13.6
-5.8 -6.8 -5.2 -1.5 -1.6 -3.5 -6.7 -7.6 -7.9 -6.8 -7.2 -8.0
.3 f .2 f .3 .1 f .1 f .4 f .2 f .2 f .1 f .4 f .3 f .3 2t
*
1.7 0.18 -0.18 -0.28 0.45 0.35 0.02
spectral characteristicsd 255 248 257 254 256 250 240 236 236 236 328 335 280
(s), 536 (w) (vs), 284 (vs),365 IwI (s), 400 (w) (s), 333 (m), 448 IwI (m) (8)
(s), 312 (s), 334 (s) (m), 400 (s) (m), 400 (s) (m), 400 (s) (w), 406 (s) (w), 408 ( 8 ) (w), 315 IwI, 408 (8)
"0.755 M sodium acetate eluent, temp 28 "C, pH 8.1, y detection. *The standard deviation of the slope from eq 9 is reported. CNumber of ionic strengths at which the retention time was measurable. UV-visible peak maxima in nanometers: vs = very strong band, s = strong band, m = moderate band, w = weak band, 1 1 = broad band with ill-defined peak maximum.
RETENTION TIME (minutes)
Figure 5. Anion-exchange HPLC separation of Tc(NaBH,)HEDP sample: eluent, 0.755 M sodium acetate; flow rate, 0.134 mL/min; temperature, 28.0 "C; pressure, 950 psi; full scale, 2 X lo5 countsls.
tection at 254 and 405 nm and %Tc y detection, respectively. Although most of the Tc-HEDP complexes appear to be resolved, a collection of lesser retained components can be seen to overlap. Even though the separation appears complicated, the multiple detection schemes enabled definitive identification of some components owing to the differences in spectral properties. The Tc-HEDP peaks characterized in this study are indicated by letter notation in one or more of the three chromatograms. The average charges on 12 of the Tc-HEDP complexes were measured by the the chromatographicmethod described. The average charges, 2, obtained from plots of eq 9 are shown in Table I along with the corresponding intercepts and spectral characteristics of each peak. The Tc-HEDP complexes have been classified into groups based on similarities of charge progression, chromatographic capacity factor, spectral characteristics, and the magnitude of the intercept terms. Although the charge on peak A could not be measured, it was included in Table I because of its unique UV-vis spectrum. Approximation of Solvated Partial Molar Volumes. Close examination of the intercepts in Table I, generated from the plots of eq 9, reveals low values. This implies that the partial molar volumes of these complexes should be large. Referring to eq 8 one recognizes that the intercept is a complicated function of the partial molar volume of a complex (vi), the partial molar volume of the acetate counterion ( u A ) , the absolute charge on the complex (ZJ, and a variety of other constant column parameters. Although many of these parameters cannot be determined with great precision, they can be estimated within reasonable limits given various assumptions detailed by Marcus and Kertes (18). In order to evaluate the partial molar volumes of the complexes, the following conditions were chosen. First, by convention the standard states are selected so that the activity coefficients are unity at infinite dilution such that ~ 1 , ~ : = w ~ , ~ " and p . ~ , ~=] "PA,?" (i.e., Awi" = 0 and AwA" = 0). Second, the
stationary-phase volume (Vs) was estimated by taking the inverse of the ion-exchange resin capacity. Third, an average activity of counterion in the resin phase was estimated N 1.3 M) given the average of the resin water content, resin counterion concentration, co-ion concentration, and the average eluent activity (18,32). Fourth, the activity coefficients of the complexes in the resin and the eluent (Le., In (yiPl/yis)) were evaluated to a first approximation by means of eq 10, using an ion-size parameter Bd = 1,correction factor b = 0.2, solvent terms A = 0.5, ionic strength in the resin phase p, 3.5, and ionic strength of the mobile phase pel = 0.78. Fifth, the osmotic pressure of the resin II was estimated to be -360 atm at 28 "C, from an empirical relationship II = 0.854 (Vs - 287) derived by Boyd and Soldano (33). Sixth, the hydrated partial molar volume of acetate was taken to be 93 mL/mol given the hydrated radius of the acetate ion to be rhi = 2.96
A
(18).
In the case of the counterion as well as the complexes it is assumed that the species are hydrated to an equal degree both in the resin and the mobile phase. Since these are anionic species, this is a reasonable assumption. Solving for the partial molar volume of the complex (vi) yields eq 11, where Q is the intercept (Table I).
Equation 10 was used to estimate the activity coefficients. The first approximation assumed an ion-size parameter Bci = 1 ( B = 0.329, u = 3.04 A), so species with high charges and large sizes were overestimated. To correct for this the hydrated radius (Phi) of each charged species was calculated after the first approximation from the following relationship derived by Conway et al., (34),vi = 2.51rhf + 3.15rh?. Given an estimated diameter ( d ) of the complexes from the first approximation, the ion-size parameter was recalculated for each size group, and the partial molar volume was reapproximated given new values. The partial molar volumes converged after several approximations. The resulting values are presented in Table 11. Interpretation of Elution Order. In attempting to sort out the elution order of a complex ion-exchange separation such as presented here, it becomes evident that the interdependency of the charge and partial molar volume on the intercept of a plot of In tF/ vs. In u ~will, not ~ enable ~ interpretation by simple inspection, since a reversal of elution order could be caused by differences in either a high charge (af-
ANALYTICAL CHEMISTRY, VOL. 57, NO. 1, JANUARY 1985
Table 11. Charge Progressive Elution Order of the Tc-HEDP Comeonents along with Their Charges and Hydrated Partial Molar Voiumes peak4
charge (2)
5,mL/mol
Y U V T
-1.5 f 0.1 -1.6 f 0.1 -3.5 f 0.4 -5.8 f 0.3 -5.2 f 0.3 -6.8 f 0.2 -6.7 zk 0.2 -6.8 f 0.4 -7.2 f 0.3 -7.6 f 0.2 -7.9 f 0.1 -8.0 f 0.3
510 520 840 1400 1200 1600 1400 1400 1400 1600 1600 1600
Z
M P S
W
Q R X
"Elution order at In aA,el = -2.0 (Figure 6).
.a: I
C
'"
'A$
Flgure 6. Plots of In corrected retention times vs. in activity of counterion in mobile phase for each Tc-HEDP component over wide hypothetical range. Dashed line indicates position of elutions Illustrated in Figures 3-5.
fecting slope) or volume (affecting intercept). Assuming linearity and plotting eq 8 for each complex over a wide range of hypothetical eluent ionic strengths illustrates the crossover of these plots due to the differences in slope and intercept (Figure 6). Furthermore, one recognizes by extrapolation to some dilute mobile-phase condition that the normal charge progressive elution order can be found (Figure 6, Table 11). In reviewing the charges and partial molar volumes given in Table 11,one sees that the complexes increase in their average charge and size proportionally, as one might expect. In the case of components T and 2 one recognized a reversal of the charge progressive elution order. The discrimination by the difference in partial molar volume explains the reversal, exactly as theory would predict. In a like manner the elution order of components M , P, and S of effectively equal charge can be seen with M eluting first, because of ita greater partial molar volume. This demonstrates that the discrimination of partial molar volume (the so-called "secondary exclusion mechanisms") is an integral part of ion-exchange theory. Based on the hydrated partial molar volumes (Table 11) it appears that the complexes fall into three groups: (i) vi N 500 mL/mol (diameter -11 A), (ii) v2 800 mL/mol (diameter -13 A), and (iii) vi N 1200-1600 mL/mol (diameter -15-17 A). This is consistent with the discrimination by volume of 8% crossed-linked anion exchangers, which have an average pore diameter of -50 A.
1 1 /I
0
2
251
264 nm detection
4
6
8
RETENTION TIME (hours)
Flgure 7. Size-exclusion chromatography of Tc(NaBH,)HEDP components: eluent, 0.755 M sodium acetate; flow rate, 0.10mL/min. (A) Tc(NaBH,)HEDP preparation diluted 2:l in the eluent (0.32AUFS). (B) HPLC collected fraction containing group 5 peaks (0.16 AUFS).
These differences in hydrodynamic volume can also be observed with size-exclusionchromatography. A size-exclusion separation of the Tc-HEDP reaction mixture on BioGel-P10 (exclusion limit 20 000 daltons relative to globular proteins) is illustrated in Figure 7A. The BioGel poly(acry1imide)was chosen because it has been demonstrated to be nonadsorptive to Tc-HEDP complexes (3). The pertechnetate (TcO,-), however, is believed to experience adsorption. Isolation of peaks Y and U after the anion-exchange HPLC with subsequent injection onto the size-exclusion column identifies the second peak as the smaller complexes (Figure 7B). The position of component V could not be identified and is suspected to be unresolved from the remainder of the complexes in peak one. Structural Hypothesis. Electrochemical studies on the reduction of pertechnetate in aqueous hydroxyethylidene diphosphonate have identified Tc(V) as the likely higher oxidn. state of technetium (35). Since the sodium borohydride reduced Tc-HEDP reaction is allowed to proceed in the presence of air, it is assumed that the complexes are oxidized to Tc(V) or Tc(1V) from lower oxidation states (e.g., Tc(II1)) with concomitant hydrolysis. Technetium(V) complexes in general have been thoroughly studied. Davison and Jones (36)have proposed a variety of oxotechnetium(V) cores including Tc03+,trans-TcOz+,and the oxo-bridged TCZO~~' and Tc2Oz6+.If such Tc(V) centers were to combine with the diphosphonate ligand (L4-), one could expect a collection of negatively charged complexes: TcOL,~-~',TcO~L,~-~',TC~O~,L:-~', T C O ~ O ~ L ~ ~Also, -~'. Munze (37) has proposed possible hydroxytechnetium(1V) complexes specifically in regard to the HEDP ligand including Tc(OH)3H2L-l,TcO(OH)HL2-,T ~ ~ ( o H ) ~ L ~TC~(OH)~L". -and Of these proposed Tc-HEDP complexes Munze has isolated only one, K2TcOOH(HL). One X-ray structural determination has been reported by Libson, Deutsch, and Barnett (9) on a technetium methylenediphosphonate (MDP), ( [Li (HzO)3] [Tc (OH)(MDP)] I/3H20)', which reveals a polymeric array. Each MDP ligand bridges two symmetry-related technetium atoms, and each technetium atom is bound by two MDP ligands. The Tc/ MDP ratio is one, and the technetium center is approximately octahedral in coordination with a cis-coordinate oxygen bridging the technetiums (Figure 8). The oxidation state of the technetium was presumed to be Tc(IV), and the presence of the proton on the oxo bridge was also assumed. With Tc(V) and the absence of the oxo-bridged proton, another formulation can be proposed, ([Li(H,O),] [TcV(0)MDP]J/,H20), (38).Either of these structures creates an imaginary linear polymeric chain which spirals one direction relative to the configuration about the cis-oxo bridge (Figure 9). From this three-dimensional polymeric array one can also hypothesize
-
252
ANALYTICAL CHEMISTRY, VOL. 57, NO. 1, JANUARY 1985
n
Flgure 11. Postulated Tc-DP octa cluster [TcVO(DP)]t-.
Flgure 8. Oxo-bridged dimerlc unit of technetium methylenediphosphonate crystal structure ([Li(H20)3][Tc(OH)(MDP)] -1/3H20),. (Figure from ref 9.)
ammonium ion-exchange resins can be used to determine the average charges and estimates of partial molar volumes of kinetically stable transition-metal complexes. Measurement of the change in "corrected" retention times (tR,'),upon variation of the activity of the counterion in the mobile phase ( u A , ~ ~yields ), the average charge on each separated complex from the slope of a In th' vs. In aA,el plot. Given approximate values of various constant column parameters, the hydrated partial molar volumes of complexes can be extracted from the intercepts of the same plots.
ACKNOWLEDGMENT
Flgure 0. Proposed linear polymeric array of Tc-DP crystal structure, [TcVO(DP)],'- or [TC'~OH(DP)],'-. For HEDP R and R'are OH and CH3; for MDP R and R'are both H. DP
I
TcHo / \ DP 0
LITERATURE CITED
\
?T ,'c/ /
'
\
OlTc
\I
0
We express our appreciation to N. M. M. Nibbering of the University of Amsterdam for performing the preliminary field desorption mass spectrometry and to C. R. Powell for assistance in performing the size-exclusion chromatography. Registry No. Na2H2HEDP,2809-21-4;KWTcO4,75492-44-3; Nag9Tc0,,23288-60-0; NaBH4, 16940-66-2.
DP
\ /
__ Flgure 10. Postulated Tc-DP hexacluster [TcvO(DP)]
t-.
an alternation of the cis-oxo bridging configuration, thus producing either a hexa cluster [TC~(O)(DP)],~(Figure 10) or octa cluster [TC~(O)(DP)],~(Figure 11). A structural model of the octa cluster, using bond lengths given in ref 9, measures 18 A at its widest point. Preliminary negative ion field desorption mass spectrometry (39) on the sodium borohydride reduced Tc-HEDP reaction mixture, separated in this study, reveals an assortment of technetium components including T C ~ ~ O ( O H ) , ( H E D at P)~m/z 501 and T C ~ ~ ( O H ) ( H E D Pat ) ~m/z ' - 619. Each of these fragments represents the two fundamental units (the former depicted in Figure 8) necessary for a polymeric cluster. It is believed that the technetium hydroxyethylidene diphosphonate complexes separated by anion exchange (Figures 3-5) represent a collection of mixed valence technetium complex monomers, oxo-bridged dimers, and/or polymeric clusters. Assuming the Tc-HEDP complexes to be polyprotic in nature, the nonintegral average charges at pH 8.1 (Table I) can be easily surmised with a polynuclear hypothesis. Definitive identification of the Tc-HEDP complexes awaits the determination of ligand-to-metal ratios and the accurate mass of each separated complex.
CONCLUSION Anion-exchangehigh-performance liquid chromatography on highly cross-linked polystyrene-divinylbenzenequaternary
Fogelman, 1.; Cltrin. D. L.; McKIllop, J. H.; Turner, J. G.; Bessent, R. G.; Greig, W. R. J. Nucl. Med. 1979, 2 0 , 98-101. O'Connel, M. J.; Wahner, H. W.; Ahmann, D. L. Mayo Clln. Roc. 1978, 5 3 , 221. Van Den Brand, J. A. G. M.; Das, H. A.; Dekker, B. G.; Deligny, C. L. Int. J. Appl. Radlat. Isot. 1981, 32, 637-644. Plnkerton, T. C.; Helneman, W. R.; Deutsch, E. Anal. Chem. 1980, 52. 1106-1 110. Tanabe, S.;Zodda, J. P.; Deutsch, E.; Heineman, W. R. Int. J . Appl. Radiat. Isot. 1983, 34, 1577-1584. Srlvastava, S. C.; Melnken, 0. E.; Richards, P.; Ford, L. A.; Benson, W. R., presentation at the Third World Congress of Nuclear Medicine and Biology, Paris, France, Aug 29-Sept 2, 1982. Tofe, A. J.; Fracis, M. D. J. Nucl. Med. 1974, 75, 69-74. Deutsch, E. Coord. Chem. Rev. 1982, 44, 191-227. Llbson, K.; Deutsch, E.; Barnett, B. L. J. Am. Chem. SOC.1080, 102, 2476-2478. Schubert, J. J . Phys. Chem. 1048, 52, 340-350. Schubert, J.; Richter, J. W. J. fhys. Chem. 1948, 5 2 , 350-357. Gorski, B.; Koch, H. J. Inorg. Nucl. Chem. 1970, 3 2 , 3831-3836. Whitney, D. C.; Diamond, R. M. J. Inorg. Nucl. Chem. 1965, 2 7 , 219-225; Inorg. Chem. 1963, 2 , 1284-1295. Owanwanne, A.; et ai. paper presented at the proceedings of the 2nd International Syposium on Radiopharmaceutlcais,Seattle, WA, March 19-22, 1979. Hoffman, 1.; Muenze, R.; Dreyer, I.; Dreyer, R. J. Radloanal. Chem. 1982, 7 4 , 53-81. Russell, C. D.; Crittenden, R. C.; Cash, A. G. J. Nucl. Med. 1980, 27, 354-360. Heifferlch, F. "Ion Exchange"; McGraw-Hill: New York, 1962; Chapter 5. Marcus, Y.; Kertes, A. S. "Ion Exchange and Solvent Extraction of Metal Complexes"; Wiley: New York, 1969. Relchenberg, D. I n "Ion Exchange, a Series of Advances"; Marlnsky, J. A., Ed.; Marcel Dekker: New York,,,1966; Vol. I,Chapter 7. Rieman, W., 111; Walton, H. F. Ion Exchange In Analytical Chemistry"; Pergamon Press: New York, 1970; Chapters 2 and 3. Rothbart, H. L. I n "An Introduction to Separation Science"; Karger, B. L., Synder, L. R., Horvath, G., Eds.; Why: New York, 1973; Chapter 12. Marcus, Y.; Mayan, D. J. fhys. Chem. 1963, 67, 983-986. "Chromatography, Electrophoresis, Immunochemistry and HPLC"; BloRad Laboratories: Richmond, CA, 1983; pp 3-5. Koithoff, I.M., Elvlng, P. J., Eds. "Treatise on Analytical Chemistry": Wlley: New York, 1979, Part I,Vol. 2, Chapter 18. Robinson, R. A,; Stokes, R. H. "Electrolyte Solutions", 2nd Ed.; Butterworths: New York, 1959; Chapter 9, pp 230-231. Stokes, R. H.; Robinson, R. A. J . Am. Chem. SOC. 1948, 7 0 , 1870-1878.
Anal. Chem. 1985, 57,253-257 (27) Dwyer, J. S.; Rosenthal, D. J . Phys. Chem. 1963, 67,779-782. (28) Colllns, A. J.; Perkins, P. G. J . Appl. Chem. Biotechnol. 1977, 27, 651-681. (29) Grabenstetter,R. J.; Quimby, 0. T.; Flautt, T. J. J . Phys. Chem. 1967, 71, 4194-4202. (30) Wada, H.; Fernando, Q. Anal. Chem. 1972, 4 4 , 1640-1643. (31) Carroll, R. L.; Irani, R. R. Inorg. Chem. 1967, 6 , 1994-1998. (32) Dresner, L.; Kraus, K. A. J . Phys. Chem. 1963, 6 7 , 990-998. (33) Boyd, G. E.; Soldano, B. A. Z . Nektrochem. 1953, 57, 162-170. (34) Conway, B. E.; Verrall, R. E.; Desnoyers, J. E. Z . Phys. Chem. (Le@@) 1965, 230, 157-178. (35) Pinkerton, T. C.; Heineman, W. R. J . Nectroanal. Chem. 1963, 158, 323-340. (36) Davlson, A,; Jones, A. G. Int. J . Appl. Radiat. Isot. 1962, 33, 875-881.
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(37) Munze, R. J. Labelled Compd. Radlopharm. 1977, 15, 215-225. (38) Bandoii, G.; Mazzi, U.; Roncari, E. Coord. Chem. Rev. 1962, 4 4 , 191-227. (39) Nlbbering, N. M. M. (University of Amsterdam) and Pinkerton, T. C. (Purdue University), unpublished results.
RECEIVED for review July 2, 1984. Accepted September 19, 1984. This research has been funded in part by contributions from the Procter and Gamble Co., the Showalter Trust Foundation, the Society of Nuclear Medicine, and Mallinckrodt, Inc. In addition fellowship support for G. M. Wilson was provided by the Phillips Petroleum Co.
Ion Penetration through Tubular Ion Exchange Membranes Purnendu K. Dasgupta* and R. Quin Bligh Department of Chemistry, Box 4260, Texas Tech University, Lubbock, Texas 79409
Joseph Lee and Vincent D'Agostino RAI Research Corporation, 225 Marcus Boulevard, Hauppauge, New York 11787
Permnted and Donnan forbldden Ion penetratlon rates through small diameter Ion exchange membrane tubes have been studled for a number of Ions and membrane types. Membranes Include radiation grafted poly(tetrafluoroethy1ene) and poly(ethy1 vlnylacetate) catlon and anion exchangers and perfluorosulfonate (Naflon 81l x and 815x) catlon exchanger tubes. For catlon exchangers, Cu2' was the model permltted catlon and sulfate, dodecylbenzenesulfonate, naphthalenedlsulfonate, naphthalenetrlsulfonate and poly(styrenesulfonate) were the anlons (tested as the correspondlng aclds) for whlch penetratlon rates were determined. For anion exchangers, nltrate was the model permltted anion and Ll', Na', NMer+, NEt,', NPr,,', and poly(dlallyldlmethylammonlum)"' were the catlons (tested as the correspondlng hydroxides) studled. Forbldden Ion penetratlon decreases with Increasing slze and charge of the Ion and Is effectlvely ellmlnated wlth large, multlply charged polymerlc or mlcellar Ions. For a given Ion, the concentratlon dependence of the penetratlon rate Is accurately predlcted by a second-order equatlon.
The success of a ion exchange process employing ion exchange membranes depend on two factors. The first of these is the efficiency with which the desired exchange process takes place. This may be kinetically limited by either the rate of transport of the ion to be exchanged to the membrane or the rate of ion transport through the membrane. The transport rate to the membrane is determined by the hydrodynamics of the velocity field of the fluid carrying the ion to be exchanged; it has been shown that bead packed tubes (1)or membrane tubes (2)and filament filled helices ( 3 , 4 )display excellent mass transport efficiency to the wall. The transport rate through the membrane is determined by the nature of the membrane itself and its thickness. Consideration of structural integrity and useful lifetime introduce practical limits to which the membrane thickness can be reduced. It is of interest therefore to examine different membrane types to determine their permeability to permitted ions. Ions that 0003-2700/85/0357-0253$0 1.50/0
are oppositely charged to the membrane matrix (Le., cations for cation exchanger matrices, which bear, for example, negatively charged sulfonate groups) are exchangeable by the membrane and referred to as permitted ions through the rest of this paper. In contrast, an ion similiarly charged to the membrane matrix (e.g., anions for cation exchangers) is retarded (in a simplistic sense, by the electrostatic field) and such ions are referred to as Donnan forbidden. Note that there is no such barrier to an ion which has been rendered oppositely charged by complexation or other chemical reactions. For example, a cation exchange membrane may pose a barrier for the transport of chloride as C1- across it but no barrier exists toward the transport of chloride as a positively charged complex, e.g., ZnCl+. The barrier to the forbidden ion is not sufficient to completely eliminate its penetration when the concentration differential across the membrane is high. The permeability of the membrane to the undesirable forbidden ions constitutes the second factor that is of interest. Consider, for example, ion exchange membrane suppressors in common use in ion chromatography (5). Sodium carbonate solution is converted to carbonic acid by passing it through a cation exchange membrane tube in H+form, while a dilute sulfuric acid solution flows outside the tube to act as a receiver fluid for the permeated sodium ion and, even more importantly, to keep the cation exchange sites in the membrane rejuvenated in the H+form. While the passage of the regenerant counterion, sulfate, is retarded by the negatively charged membrane matrix bearing sulfonate groups, significant penetration occurs with all but very dilute solutions of sulfuric acid. The penetration rate of a forbidden ion depends on the ionic size which governs its diffusive transport through the membrane matrix. Chloride is smaller than perchlorate, and the former thus penetrates more than the latter under otherwise comparable conditions (3). With a very large forbidden ion, such as dodecylbenzenesulfonate, the penetration rate can be dramaticallyreduced as demonstrated by Japanese investigators (6-8). For any given forbidden ion, the penetration rate is inversely related to the membrane thickness and density of available exchange sites and directly related 0 1984 American Chemical Society
