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Langmuir 2009, 25, 2294-2301
Kinetics and Thermodynamics of Adsorption on Hydroxyapatite of the [160Tb]Terbium Complexes of the Bone-Targeting Ligands DOTP and BPPED Christoph Rill,†,‡ Zvonimir I. Kolar,*,‡ Guido Kickelbick,† Hubert Th. Wolterbeek,‡ and Joop A. Peters§ Institute of Materials Chemistry, Vienna UniVersity of Technology, A-1060 Vienna, Austria, Radiation and Isotopes for Health section, Delft UniVersity of Technology, 2629 JB Delft, The Netherlands, and Biocatalysis and Organic Chemistry, Department of Biotechnology, Delft UniVersity of Technology, 2628 BL Delft, The Netherlands ReceiVed October 27, 2008. ReVised Manuscript ReceiVed December 9, 2008 The temperature-dependent adsorption on hydroxyapatite (HAP) of the Tb complexes of two macrocyclic DOTAlike ligands containing HAP-binding phosphonate groups was studied by a radiotracer method using 160Tb as the label. One ligand (DOTP) contains four separate phosphonate groups, while the second ligand (BPPED) contains a single bisphosphonate group coupled via a phosphinate spacer group. The equilibrium isotherms were fitted by models according to Langmuir, Freundlich, Langmuir-Freundlich, To´th, and Dubinin-Radushkevich, with the Langmuir-Freundlich and the To´th models resulting in the best fits. These models take into account the energetic surface heterogeneity of HAP for the binding of the complexes, which was confirmed by the dependence of the reversibility of the adsorption on the complex concentration. The affinity of the Tb-BPPED complex toward the HAP surface was substantially higher than that of the Tb-DOTP complex. Thermodynamic parameters obtained from the temperature-dependence of the adsorption and the Van’t Hoff relation showed that the adsorption of both complex types is endothermic and entropy-driven, due to dehydration of the complex and the HAP surface during adsorption. The kinetics of the adsorption were very fast, and of the tested models (pseudo-first-order, pseudo-second-order, intraparticle diffusion, and Elovich) only the Elovich model described the experimental data suitably. The activation energy of the adsorption was calculated by application of an Arrhenius-type relation, showing chemisorption for both complex types. Adsorption rates were reduced when HAP with larger particle size was used.
1. Introduction Hydroxyapatite (HAP) is a major constituent of bone mineral and is thus often used as a model for bone in medical research.1-3 The goal of many studies is the selective attachment of molecules for therapeutic and diagnostic purposes to the bone surface. HAP presents a valuable bone model for in Vitro studies on these systems. Phosphates and the closely related phosphonic acids are known to have a very high affinity for various inorganic hydroxidic and oxidic materials,4,5 which makes them ideal targeting groups for HAP and bone. This is even more pronounced for the geminal bisphosphonates, that is, methylene-bridged diphosphonates, because of the chelating effect of the two phosphonate groups. Various bisphosphonates were studied and successfully applied clinically for modulation of bone metabolism by inhibiting the resorption of bone material.6,7 By including phosphonate groups in molecules with other coordinating moieties, it is possible to * To whom correspondence should be addressed. E-mail: Z.I.Kolar@ tudelft.nl. Telephone: +31-15-27 86619. Fax: +31-15-27 83906. † Vienna University of Technology. ‡ Radiation and Isotopes for Health section, Delft University of Technology. § Department of Biotechnology, Delft University of Technology. (1) Yang, Y.-Q.; Luo, S.-Z.; Pu, M.-F.; He, J.-H. Nucl. Sci. Technol. 2002, 13, 98–104. (2) Peru, L.; Daculsi, G. Clin. Mater. 1994, 15, 267–272. (3) Ehrick, R. S.; Capaccio, M.; Puleo, D. A.; Bachas, L. G. Bioconjugate Chem. 2008, 19, 315–321. (4) Guerrero, G.; Mutin, P. H.; Vioux, A. Chem. Mater. 2000, 12, 1268–1272. (5) Mutin, P. H.; Guerrero, G.; Vioux, A. J. Mater. Chem. 2005, 15, 3761– 3768. (6) Ebetino, F. H.; Francis, M. D.; Rogers, M. J.; Russell, R. G. G. ReV. Contemp. Pharmacother. 1998, 9, 233–243. (7) Page, P. C. B.; Moore, J. P. G.; Mansfield, I.; McKenzie, M. J.; Bowler, W. B.; Gallagher, J. A. Tetrahedron 2001, 57, 1837–1847.
introduce various metal ions to the bone which can have different functions depending on the nature of the ions. For diagnostic purposes with molecular imaging techniques paramagnetic, Gd(III) chelates have been used as magnetic resonance imaging (MRI) contrast agents,8 while the phosphonate complexes of the radionuclides 99mTc and 86Y have been used for bone single photon emission computed tomography (SPECT)9 and positron emission tomography (PET),10 respectively. It is known that selective attachment of radionuclides such as 186/188Re, 153Sm, or 166 Ho to the bones of cancer patients afflicted with bone metastases may have a pain palliative effect.11 It is often necessary to use a substantial excess of the ligand to prevent metal loss from the complex and thus the presence of free metal ions which may be toxic.11 This is not the case for the well-studied macrocyclic ligand 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetra(acetic acid) (DOTA) because it forms kinetically inert complexes by enclosing the metal ions in a rigid cage.12 Structurally similar ligands including 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetra(methylenephosphonic acid) (DOTP), which contains four phosphonate groups, and 10-((diphosphonoethyl(hydroxy)phosphoryl)methyl)-1,4,7,10-tetraazacyclododecane-1,4,7-tri(acetic acid) (BPPED, see Chart 1 for structures of ligands), which carries a phosphinate-coupled bisphosphonate (8) Caravan, P.; Ellison, J. J.; McMurry, T. J.; Lauffer, R. B. Chem. ReV. 1999, 99, 2293–2352. (9) Suzuki, A.; Togawa, T.; Kuyama, J.; Nakahara, T.; Yui, N.; Iuchi, T.; Oga, M.; Osato, K. Ann. Nucl. Med. 2002, 16, 495–498. (10) Roesch, F.; Herzog, H.; Plag, C.; Neumaier, B.; Braun, U.; MuellerGaertner, H.-W.; Stoecklin, G. Eur. J. Nucl. Med 1996, 23, 958–966. (11) Volkert, W. A.; Hoffman, T. J. Chem. ReV. 1999, 99, 2269–2292. (12) Desreux, J. F. Inorg. Chem. 1980, 19, 1319–1324.
10.1021/la803562e CCC: $40.75 2009 American Chemical Society Published on Web 01/16/2009
Adsorption of DOTA-Based Tb Complexes on HAP Chart 1. Structures of the Ligands Discussed
group, were found to form 1:1 complexes with lanthanide ions of comparable or even higher stability.13-15 Unfortunately, not much is known about the thermodynamics and especially the kinetic nature of the attachment of these functional molecules to the surface of HAP. This knowledge, however, is important for correct predictions of, for example, dosage of the pharmaceutical or its pharmacokinetics. It is the goal of this study to obtain more information about the interaction of the HAP surface with two model complexes using DOTP and BPPED as ligands. The investigation was done by a radiotracer method using 160Tb as the label. This radionuclide was selected as representative for the entire series of lanthanides, which are all known to form structurally virtual identical complexes with this type of ligand.13 The advantages of the 160Tb radionuclide are its high natural abundance (100%) and the high cross section for thermal neutron capture of its precursor 159Tb. Additionally, the half-life of 72 days of 160Tb allows for relatively comfortable handling.
2. Experimental Section Hydroxyapatite. Two types of hydroxyapatite were used, “high resolution” (HR-HAP) and “fast flow” (FF-HAP). Both materials were purchased from Fluka Biochimica and were used without drying. Nitrogen sorption Brunauer-Emmett-Teller (BET) analysis showed that HR-HAP had a specific surface area of 69.7 m2 g-1, an average pore width of 25.7 nm, and a Barrett-Joyner-Halenda (BJH) adsorption diameter of 18.3 nm. For FF-HAP, these numbers were determined to be 68.4 m2 g-1, 28.7 nm, and 15.2 nm, respectively. Microscopic images show that HR-HAP has a particle size of about 20 µm and FF-HAP of about 200 µm (see the Supporting Information, Figure S5). Unless specified otherwise in the text, the discussion concerns HR-HAP. Preparation of Radioactive Tb Complexes. 160Tb-labeled Tb(NO3)3 · 6H2O was prepared by thermal neutron irradiation of Tb(NO3)3 · 6H2O target (Aldrich, 99.9%) in a nuclear reactor (thermal neutron flux: 4.49 × 10-12 cm-2s-1; irradiation time: 1.5 h; Reactor Institute Delft, Delft University of Technology). The irradiated material (specific activity: ∼59 GBq mol-1) was dissolved in demineralized water to form a stock solution with a concentration of 2.0 mmol L-1. DOTP (291.8 mg, 515 µmol) was suspended in 40 mL of water and slowly heated to 80 °C, which led to complete dissolution of the ligand. The pH of the resulting solution was adjusted to 8.9 with a 3 mol L-1 NaOH solution. A stock solution of both labeled and unlabeled Tb(NO3)3 · 6H2O (total amount of Tb3+ 500 µmol) in 10 mL of water was added dropwise to the DOTP solution at 80 °C under stirring, while maintaining the pH of the solution between 8 (13) Geraldes, C. F. G. C.; Sherry, A. D.; Kiefer, G. E. J. Magn. Reson. 1992, 97, 290–304. (14) Qi, Y. H.; Zhang, Q. Y.; Xu, L. J. Chem. Inf. Comput. Sci. 2002, 42, 1471–1475. (15) Vitha, T.; Kubícˇek, V.; Hermann, P.; Kolar, Z. I.; Wolterbeek, H. T.; Peters, J. A.; Lukesˇ, I. Langmuir 2008, 24, 1952–1958.
Langmuir, Vol. 25, No. 4, 2009 2295 and 9. After 3 h of stirring at 80 °C, the solution was cooled to room temperature and then 4 mL of 2.5 mol L-1 tris-hydroxymethylaminoethane buffer (Tris, p.A., Merck) was added. The pH was adjusted to 7.4 using 5 mol L-1 HCl and 3 mol L-1 NaOH. The solution obtained was diluted with water to 100 mL, resulting in a final Tb(III) concentration of 5 mmol L-1 and a total 160Tb activity of ∼12 MBq L-1. A sample of the Tb-BPPED complex was prepared similarly; 160 mg (261 µmol) of the ligand BPPED was suspended in 20 mL of water and brought into solution by addition of 3 mol L-1 NaOH. This solution was slowly dropped into 15 mL of an aqueous solution of Tb(NO3)3 · 6H2O (11.1 mg irradiated and 104.4 mg nonirradiated, total of 255 µmol), while maintaining the pH at 9. After stirring at room temperature overnight, 2 mL of a 2.5 mol L-1 solution of Tris buffer was added and the pH was adjusted to 7.4. The solution was diluted with water to a total volume of 50 mL, resulting in a Tb(III) concentration of 5.1 mmol L-1 and a total 160Tb activity of ∼29 MBq L-1. The formation of the complexes was verified by paper chromatography using Whatman 1 Chr paper developed by normal saline solution. The activity on the dried paper strips was scanned using a Geiger-Mu¨ller (GM) counter with a narrow collimator slit (4 mm). Additionally, iodine vapors were used to visualize the organic ligand components. Determination of Equilibrium Adsorption Isotherms. For a typical adsorption isotherm experiment, 50.0 mg of HAP (Fluka, BioChemika, “high resolution”) was suspended in 0.1 mol L-1 Tris buffer in a 10 mL plastic vial. Tris buffer (0.1 mol L-1) and radioactive Tb-DOTP complex solution were added to obtain a total volume of 3 mL and a Tb3+ concentration ranging between 0.1 and 4.0 mmol L-1. After mild agitation for 3 days, the suspension was filtered through a 0.2 µm syringe filter (Rotilab, mixed cellulose ester). The 160 Tb activity in 1 mL of the filtrate was determined by measuring the γ-ray activity of 160Tb using a Wallac 1480 Wizard 3′′ counter based on a NaI(Tl)-scintillation detector. The temperature for the sample equilibration ranged from room temperature (i.e., 20 °C) up to 60 °C and was controlled to within (1 °C by performing the experiments inside an incubator. Plastic vials were used at room temperature, and sealable glass ones at higher temperatures. To verify the experimental data obtained from the analysis of the samples’ γ-activity, some of the samples were analyzed by inductively coupled plasma-optical emission spectroscopic (ICP-OES) measurements on a PerkinElmer Optima 4300 DV. The samples were diluted to a Tb3+ concentration in the order of a few ppm (∼5-30 µmol L-1), and the emission was measured at the two characteristic wavelengths of 350.9 and 384.9 nm. The results were in excellent agreement with the values obtained through γ-ray activity measurements, validating the application of γ-counting to this study (see the Supporting Information for details). Determination of the Adsorption Kinetics. The adsorption kinetics were investigated in a batch adsorption setup with samples taken from the suspension at specific time intervals. Preliminary experiments showed that the adsorption of the Tb-DOTP complex on the surface of HAP is a very rapid process: within only a few seconds after contacting the complex solution with HAP, about 30% of the complex was already removed from the supernatant. Therefore, an experiment setup was constructed comprising a reactor vessel and a filtration system with separate filtration stations allowing fast sampling times down to an interval of 10 s for up to 10 consecutive samples. The suspension was stirred mechanically rather than magnetically in order to avoid alteration of the particle size of the HAP during the course of the experiment, due to grinding between the stirrer bar and the glass walls. To ensure a steady state at the start of the measurement, the influence of initial HAP conditioning in Tris buffer was examined. Furthermore, the effect of the stirrer speed (200-600 rpm) on mass transport was checked. For a typical run, 165 mg of HAP was suspended in 0.1 mol L-1 Tris buffer, and the complex stock solution was quickly added to start the adsorption process. The amounts of Tris buffer and complex solution were chosen such that a final liquid volume of 10 mL with a complex concentration of 0.825 mmol L-1 was obtained. A number
2296 Langmuir, Vol. 25, No. 4, 2009 of samples of ∼0.75 mL was drawn from the suspension at time intervals ranging from 10 s at the beginning to several hours at the end of a run. The samples were immediately filtered through 0.2 µm membrane filters (Whatman, mixed cellulose ester) to freeze the adsorption process, and the activity of 0.5 mL of the filtrate was measured as above. The kinetics were examined at various temperatures ranging from 0 to 60 °C, and the temperature deviation during each of the series was kept within 1 °C. When performing the experiments in a singlewalled reaction flask, evaporation and recondensation of water on the vessel walls was problematic especially during the later phase of the heated experiments, because the complex concentration in the suspension was gradually increasing, distorting the resulting kinetics data. Therefore, a double-walled reactor was applied, allowing exact thermostatic control of the temperature of the entire vessel. The dependence of the complex concentration on the time was negligible at 60 °C with this setup (see the Supporting Information). Mathematical fitting of the various models to the experimental data for both the isotherms and the kinetics was done with the OriginPro 7.5G SR6 software using the built-in nonlinear leastsquares fitting routine based on the Levenberg-Marquardt algorithm. Reversibility of the Adsorption. The reversibility of the adsorption process for both the Tb-DOTP and the Tb-BPPED complexes, which can be an important factor in the choice of the correct adsorption model, was tested in experiments similar to the isotherm experiments. In 10 mL centrifuge tubes, an adsorption equilibrium was obtained by slowly agitating a suspension of 50 mg of HAP in 5 mL of the respective complex solution for 3 days. The suspension was centrifuged, and 4.5 mL of the supernatant was removed and replaced by 4.5 mL of fresh Tris buffer containing no complex. The HAP was resuspended and agitated for another 3 days to reach the new equilibrium. The concentration of the complex in the solution after both equilibration steps was determined by measuring the γ-ray activity of the samples. The results obtained were verified with samples prepared according to the method used for the collection of isotherm data. After equilibration for 3 days, the resulting concentration of radiolabeled complex in the solution was measured. To observe an exchange between adsorbed complex and the complex in solution, a solution containing only the unlabeled complex at a concentration equal to the liquid phase of the equilibrated sample was added to the adsorption system. After equilibration for another 3 days, the final concentration of radiolabeled complex was determined. Theoretical Models. Both the isotherm and the kinetics data were fitted to a number of different models in order to obtain comparable and physically interpretable parameters, which describe the adsorption process. The models of Langmuir,16 Freundlich,17 Langmuir-Freundlich (also known as Sips, L-F),18 To´th,19 and Dubinin-Radushkevich (D-R)20 were tested for the isotherms. The kinetics data were examined by the adsorption models of pseudofirst-order (Lagergren),21 pseudo-second-order,22 intraparticle diffusion,23 and Elovich.24 The curves were fitted to the experimental data using a nonlinear least-squares fitting algorithm to obtain the model parameters. To determine which of the models most accurately describes the observed experimental data, the Akaike Information Criterion with a second order correction for small sample sizes (AICc)25,26 was used. This method calculates a numerical score for every model and (16) Langmuir, I. J. Am. Chem. Soc. 1918, 40, 1361–1403. (17) Freundlich, H. M. F. Z. Phys. Chem. 1906, 57, 385–471. (18) Sips, R. J. Chem. Phys. 1948, 16, 490–495. (19) To´th, J. AdV. Colloid Interface Sci. 1995, 55, 1–239. (20) Dubinin, M. M.; Radushkevich, L. V. Dokl. Akad. Nauk SSSR 1947, 55, 327–329. (21) Lagergren, S. K. SVen. Vetenskapsakad. Handl. 1898, 24, 1–39. (22) Ho, Y. S.; McKay, G. Process Biochem. 1999, 34, 451–465. (23) Zou, W.; Han, R.; Chen, Z.; Zhang, J.; Shi, J. Colloids Surf., A 2006, 279, 238–246. (24) Low, M. J. D. Chem. ReV. 1960, 60, 267–312. (25) Akaike, H. IEEE Trans. Autom. Control 1974, 19, 716–723. (26) Burnham, K. P.; Anderson, D. R. Model Selection and Multimodel Inference, 2nd ed.; Springer: New York, 2002.
Rill et al. data set based on the resulting residuals and the degrees of freedom of the fitting procedure according to eq 1; the lowest AICc value indicates the preferred model.
( SSRl ) + 2j + 2j( l -j +j -1 1 )
AICc ) l ln
(1)
Here, l is the number of experimental data points, SSR is the sum of squared residuals of the fit, and j is the number of fit parameters increased by 1. Isotherm Models. The models of Langmuir, LangmuirFreundlich, and To´th are special cases of the generalized Langmuir model27 in eq 2 where ce and qe are the complex concentration in solution and the amount of complex adsorbed on HAP, respectively, in equilibrium, qm is the maximum saturation load, K is a constant often regarded as an affinity constant, and m and n are surface heterogeneity parameters.
[
qe ) qm
(Kce)n 1 + (Kce)n
]
m ⁄n
(2)
For the Langmuir model, the heterogeneity parameters m and n are both equal to 1 (see eq 3), where KL is the Langmuir affinity constant).16 This basic model assumes an energetically homogeneous surface with the same adsorption energy for every adsorption site. The maximum adsorption capacity is a full monolayer coverage, and interaction between adsorbed species is not allowed.
qe ) qm
(KLce) 1 + (KLce)
(3)
The Langmuir-Freundlich18 and To´th19 models take into account that the adsorption energy is not equal for all sites, as expressed by deviations of m and n from a value of 1. Both models use a Gaussianshaped energy distribution, with the Langmuir-Freundlich model (m ) n, eq 4) using a symmetric energy curve and the To´th model (m ) 1, eq 5) using an energy distribution with a stronger tail toward low adsorption energies. KLF and KT are the respective affinity constants of these two models.
qe ) qm
[
qe ) qm
(KLFce)n
(4)
1 + (KLFce)n (KTce)n
1 + (KTce)n
]
1 ⁄n
(5)
The Freundlich isotherm model17 (eq 6), where KF is the Freundlich affinity constant) is an empirical model similar in form to the Langmuir-Freundlich model; however, it does not limit the adsorption to a monolayer and is often applicable to adsorption on heterogeneous surfaces.
qe ) KFce1 ⁄n
(6)
20
The Dubinin-Radushkevich model (eq 7) is based on the micropore volume filling theory and describes adsorption inside a single type of uniform pore.
qe ) qm exp -KD(RT ln(1 + 1⁄ce))2
[
]
(7)
Here, KD is a constant, R is the general gas constant (8.314 J mol-1 K-1), and T is the absolute temperature. From the values of qe and ce obtained with a particular model describing an adsorption isotherm, the temperature-dependence of the distribution coefficient Kdis ) qe/ce can be calculated, and from the latter parameter the thermodynamic parameters of the adsorption can be evaluated via the Van’t Hoff equation in its integrated form (eq 8). The free energy of the adsorption is given by ∆G° ) ∆H° (27) Marczewski, A. W.; Jaroniec, M. Monatsh. Chem. 1983, 114, 711–715.
Adsorption of DOTA-Based Tb Complexes on HAP
Langmuir, Vol. 25, No. 4, 2009 2297
Figure 1. Room temperature (20 °C) isotherms for the adsorption of Tb-DOTP (a) and Tb-BPPED (b) on HAP and the different best-fit model curves. Separate points are experimental data; curves are as follows: dotted green, D-R; solid green, Langmuir; solid red, L-F; dashed blue, To´th; solid gray, Freundlich.
- T∆S° with the standard Gibbs free energy of adsorption ∆G° and the standard adsorption enthalpy ∆H° and entropy ∆S°.
ln(Kdis) )
∆S° ∆H° R RT
(8)
Kinetic Models. Adsorption kinetics are often expressed in the form of a pseudo-first-order process driven by a concentration gradient. In its integrated, linearized form, this results in the socalled Lagergren equation21 (eq 9) with the adsorption time t, the adsorbed amount of complex q ) q(t), and the first-order adsorption rate k1.
ln(qe - q) ) ln(qe) - k1t
(9)
Another equation often used for the description of adsorption kinetics is the respective pseudo-second-order equation22 (eq 10); here, the adsorption rate is proportional to (qe - q)2 with the secondorder adsorption rate k2.
q)
(
1 1 + qe q 2k t e 2
)
-1
(10)
A simple intraparticle diffusion model23 (eq 11) which can be applied for spherical, porous adsorbent particles is related to the adsorbent particle size and the diffusion of the adsorbate within the particles. Although fast kinetics can be problematic for this model, it has been tested to fit our adsorption data.
q ) kp√t + c
(11)
Here, kp is the intraparticle diffusion rate constant. For fast kinetics, the intercept c of this linear relationship represents an apparent initial amount of adsorbate on the surface. The empirical Elovich adsorption model24 (eq 12), which has found wide applicability for numerous adsorption systems, is based on the assumption of energetic heterogeneity of the adsorption sites in the form of a rectangular distribution:
q)
ln(t + t0) ln t0 β β
(12)
with the Elovich time constant t0 ) (Rβ)-1, the Elovich adsorption rate R, and β which is a system constant related to the adsorption energy. For small t0 (i.e., t0 , t), this equation simplifies to
q)
ln(Rβ) ln t + β β
(13)
For low surface coverage (q f 0, in the beginning of the process), the derivative form (dq)/(dt) ) R e- βq reduces to (dq)/(dt) ) R, giving the parameter R the physical meaning of the initial adsorption rate. After selection of the most appropriate model, the Arrhenius equation (eq 14) allows the calculation of the activation energy of
the adsorption from the adsorption rate constant k as a function of the temperature. The activation energy can give an indication whether the adsorbate is chemi- or physisorbed.
k)p e
-Ea
⁄RT
(14)
Here, p is the Arrhenius prefactor and Ea the activation energy of the adsorption.
3. Results and Discussion Formation of the Tb Complexes. The ligands DOTP and BPPED displayed in Chart 1 were used to coordinate Tb3+ ions for which the radioactive 160Tb nuclide served as radiotracer. For both ligands, the applied methods resulted in clear and homogeneous solutions, which were stable for at least several weeks. The successful formation of the complexes was confirmed by paper chromatography, which indicated that no free Tb3+ ions were present in the solution (see the Supporting Information for details). Equilibrium Isotherm Data. The room temperature (20 °C) isotherms recorded for the adsorption of the Tb-DOTP and the Tb-BPPED complexes and the respective curves calculated with the best-fit parameters are displayed in Figure 1. It can already be seen from the graphical evaluation that in both cases the To´th and L-F models give the best fit, which is confirmed by the AICc values (see the Supporting Information, Table S3). These two models fit the data equally well. It is evident that the adsorption sites along the HAP surface are energetically heterogeneous, which is a major aspect in both models. The adjustable parameters in the fitting procedure are highly correlated as is also reflected in high standard deviations of the resulting best-fit parameters, which are compiled in Table 1. Since the lowest standard deviations were obtained with the L-F model, all further fitting procedures were performed with this model. The specific surface area of the HR-HAP particles used in the current study was determined to be 69.7 m2 g-1 by BrunauerEmmett-Teller (BET) nitrogen sorption experiments. The best-fit value of qm for the L-F model at 20 °C (see Table 1) then corresponds with a maximum adsorption capacity Xm of 0.819 ( 0.014 µmol m-2. Previously, Vitha et al.15 have investigated the room temperature equilibrium adsorption behavior of the Tb-BPPED complex on HAP particles and used the Langmuir as well as the L-F models to fit their experimental data. The L-F isotherm gave the better fit of their data with best-fit values of KLF ) 129 ( 21 L mmol-1, Xm ) 0.778 ( 0.018 µmol m-2, and n ) 0.46 ( 0.03, which is in good agreement with the presently reported values. The constant KLF, which can be viewed as a measure for the affinity of the complex toward the HAP surface, is significantly
2298 Langmuir, Vol. 25, No. 4, 2009
Rill et al.
Table 1. Best-Fit Parameters for the Fits of the Experimental Adsorption Data of Tb-DOTP and Tb-BPPED and the Langmuir-Freundlich (L-F) and To´th (T) Modelsa Tb-DOTP model -1
L-F, qm [mmol g ] L-F, KLF [L mmol-1] L-F, n [ - ] T, qm [mmol g-1] T, KT [L mol-1] T, n [ - ] a
Tb-BPPED
20 °C
37 °C
60 °C
20 °C
37 °C
0.102 (0.021) 0.355 (0.383) 0.370 (0.038) 0.221 (0.124) 5.2 (11.4) 0.148 (0.043)
0.085 (0.010) 6.57 (4.78) 0.347 (0.046) 0.108 (0.024) 23.9 (49.9) 0.196 (0.049)
0.143 (0.016) 2.39 (1.88) 0.297 (0.024) 0.255 (0.081) 2085.3 (5395.2) 0.127 (0.027)
0.057 (0.001) 112.1 (11.7) 0.474 (0.020) 0.0602 (0.0010) 3.5 (0.7) 0.354 (0.015)
0.097 (0.025) 7.86 (15.06) 0.302 (0.079) 0.119 (0.049) 167.7 (727.8) 0.177 (0.080)
Values in parentheses are standard errors.
Figure 2. Adsorption isotherms of Tb-DOTP (hollow, dashed) and Tb-BPPED (solid) at a temperature of 20 °C (blue, b), 37 °C (red, 2), and 60 °C (green, 9).
larger for the Tb-BPPED complex than for the Tb-DOTP complex. This is most likely caused by the presence of the bisphosphonate group with two phosphonates in very close proximity to each other, causing an additional chelating effect. Although the Tb-DOTP complex contains four separate phosphonate groups and it is known that all of these groups bind to the HAP surface,28 strong coordination to the central Tb3+ ion also occurs via these groups. On the other hand, the bisphosphonate in Tb-BPPED is not bound to the Tb3+ ion and thus is entirely free for interaction with the HAP surface.29 Figure 2 displays the isotherms for the adsorption of both complexes on HAP at various temperatures. It can be seen that upon increase of the temperature the amount of adsorbed complex at equal equilibrium concentration in solution increases for both complexes. This indicates that the adsorption is an endothermic process. The saturation of the surface (i.e., the plateau of the isotherm, qm) is reached for lower equilibrium concentrations ce in the case of Tb-BPPED, again reflecting the higher affinity of this complex toward the HAP surface. However, the final amount of adsorbed complex is generally higher for the slightly more compact Tb-DOTP complex. A similar dependence of qm on the complex size was previously reported by Vitha et al.15 Equilibrium Thermodynamics. The thermodynamic parameters of the adsorption process were calculated using the Van’t Hoff relationship between the distribution coefficient and the adsorption enthalpy and entropy (eq 8). Since the calculations require data sets with equal initial complex concentrations, these were constructed by means of the L-F model and the best-fit parameters. Figure 3 displays the linearized Van’t Hoff plots for typical initial complex concentrations ranging from 0.1 to 5.0 mmol L-1. (28) Alves, F. C.; Donato, P.; Sherry, A. D.; Zaheer, A.; Zhang, S.; Lubag, A. J. M.; Merritt, M. E.; Lenkinski, R. E.; Frangioni, J. V.; Neves, M.; Prata, M. I. M.; Santos, A. C.; Lima, J. J. P. d.; Geraldes, C. F. G. C. InVest. Radiol 2003, 38, 750–760. (29) Kubícˇek, V.; Rudovsky´, J.; Kotek, J.; Hermann, P.; Vander Elst, L.; Muller, R. N.; Kolar, Z. I.; Wolterbeek, H. T.; Peters, J. A.; Lukesˇ, I. J. Am. Chem. Soc. 2005, 127, 16477–485.
Figure 3. Van’t Hoff plots for the adsorption of Tb-BPPED (green hollow, dashed) and Tb-DOTP (blue solid) based on typical complex starting concentrations of 0.1 (9), 0.5 ([), 1.0 (2), and 5.0 mmol L-1 (b). Table 2. Thermodynamic Parameters of the Adsorption for an Initial Concentration of the Complexes of 1 mmol L-1 -1
-1
∆S° [J mol K ] ∆H° [kJ mol-1] ∆G° [kJ mol-1]
Tb-DOTP
Tb-BPPED
88.4 (0.6) 16.6 (0.2) -9.32 (0.39)
69.3 (n/a)a 10.3 (n/a)a -10.0 (n/a)a
a Estimated standard errors cannot be presented for the Tb-BPPED data, since the parameters were calculated from two data points.
The Tb-DOTP adsorption isotherms were investigated at three different temperatures, and the graphs clearly show linear relationships. For Tb-BPPED, however, only two temperatures were examined, and therefore, the thermodynamic parameters for the adsorption of this complex have to be considered with some caution. The thermodynamic parameters calculated for an initial concentration of 1.0 mmol L-1 are listed in Table 2. The parameters obtained for the two complexes are similar, and the higher overall free energy of the adsorption ∆G° for Tb-BPPED reflects the observed difference in surface affinity between the two complexes. As qualitatively observed from the temperaturedependence of the adsorption, it is an endothermic process with a negative free energy of adsorption in both cases; that is, the adsorption proceeds spontaneously and is entropy-driven. This is most likely caused by the release of a large number of water molecules from the solubilized, negatively charged complexes as well as from the polar HAP surface upon adsorption, an effect previously reported for lanthanide-DOTP complexes.28 Additionally, this dehydration of the complex and hydroxyapatite surfaces was previously described as a major cause for the endothermic nature of the adsorption process. Moreno et al.,30 who investigated the thermodynamics of the adsorption of phosphoproteins on HAP, reported that the adsorption was endothermic and entropy-driven. The positive ∆H was attributed (30) Moreno, E. C.; Kresak, M.; Hay, D. I. J. Biol. Chem. 1982, 257, 2981– 2989.
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Table 3. Reversibility of the Complex Adsorptiona method 1 (desorption) method 2 (exchange)
Tb-DOTP
Tb-BPPED
32/2 51
19/4 33
a The data represent the amount of actually desorbed or exchanged complex as percentage of the amount expected for full reversibility. The data pairs given for method 1 correspond to the low- and high-concentration equilibria, respectively.
to a combination of a change in hydration and structural changes of the proteins during adsorption. Since the DOTA-type complexes of the lanthanides are known for their rigidity, structural changes of the complexes are expected to play only a minor role in this study. Very similar observations were made for the adsorption of DNA strands on HAP via their phosphate backbones31 as well as the adsorption of entirely inorganic phosphate species such as peroxydiphosphate32 or phosphate ions.33 Reversibility of the Adsorption. The reversibility of the adsorption of the complexes was tested in two ways. The first one is based on the assumption that a fully reversible system in equilibrium (i.e., forming a point on the isotherm, qe as function of ce) will return to another point located on the isotherm (ce′, qe′) upon disturbance of the equilibrium. The disturbance was introduced by dilution of the liquid phase of the equilibrated system with Tris buffer. In this way, the complex concentration is reduced, whereas the adsorbed amount of complex initially remains unchanged. Two concentrations were tested, one with small amounts of complex corresponding to the early part of the isotherms and the second with higher complex concentration corresponding to the late part of the isotherms close to the maximum adsorption levels. The second method does not disturb the adsorption equilibrium but rather the ratio of labeled-to-unlabeled complex. In this way, exchange of complex between the solution and the HAP surface can be observed. After initial equilibration of the system, a solution of unlabeled complex with the system’s equilibrium concentration was added, thus keeping both the complex concentration ce and the adsorbed amount qe unchanged. If the system is reversible, the activity measured in the solution will be changed because labeled complex adsorbed on the surface is replaced by unlabeled complex until the specific activity of adsorbed complex and complex in solution are equal. The results of both methods (see Table 3) revealed that the process was only partially reversible (see the Supporting Information for calculation details). Irreversibility was reported earlier for the adsorption of phosphate ions onto hydroxyapatite.33 This behavior was attributed to the strong coordination of the phosphate ions to more than one Ca2+ ion at the surface and, thus, a preferred orientation of the phosphate ions. Furthermore, a recent 31P NMR study has shown that, upon addition of the bisphosphonate pamidronate to a suspension of human bone powder, inorganic phosphate is released into the supernatant, suggesting that at least in part this be the result of displacement by a PO43- function of the bisphosphonate group.34 Similar effects are likely to play a role here. Method 1 shows a concentration-dependence of the reversibility; that is, the adsorption is more reversible at lower complex concentrations. This may be explained by the occurrence of two (31) Chen, W.-Y.; Lin, M.-S.; Lin, P.-H.; Tasi, P.-S.; Chang, Y.; Yamamoto, S. Colloids Surf., A 2007, 295, 274–283. (32) Moreno, E. C.; Kresak, M.; Gaffar, A. J. Colloid Interface Sci. 1994, 168, 173–182. (33) Shimabayashi, S.; Fukuda, H.; Aoyama, T.; Nakagaki, M. Chem. Pharm. Bull. 1982, 30, 3074–3081. (34) Mukherjee, S.; Song, Y.; Oldfield, E. J. Am. Chem. Soc. 2008, 130, 1264– 1273.
Figure 4. Kinetics of the adsorption of Tb-DOTP on HAP at 20 °C and the best-fit model curves resulting from nonlinear least-squares fitting of the experimental data (green, intraparticle diffusion; blue, Lagergren; purple, PSO; red, Elovich). The dashed line represents the amount of complex remaining in the solution as a function of the adsorption time (second ordinate) according to the Elovich model.
types of interactions. At low concentrations, predominantly weak intermolecular interactions between the phosphonates and the HAP surface occur, whereas at higher concentrations in addition chemical displacement reactions of phosphate groups in HAP by the phosphonate functions of Tb-DOTP or Tb-BPPED take place. Both methods show that the adsorption of Tb-DOTP is reversible to a higher degree, which is consistent with this hypothesis and which again reflects the previously mentioned higher affinity of the Tb-BPPED bisphosphonate complex toward the HAP surface. Kinetics of the Adsorption. A number of preliminary experiments was carried out to ensure a stable experiment setup before data collection of the adsorption kinetics was started (see the Supporting Information for details). It was found that the error introduced by the sampling procedure, that is, drawing consecutive samples from a dispersion with the requirement of keeping a constant liquid-solid ratio, was negligible. The influence of the stirring speed (200, 400, and 600 rpm) was statistically insignificant, which shows that the adsorption is not limited by mass transport within the solution. All presented kinetics data were obtained with a stirring rate of 600 rpm. “Preconditioning” of the HAP by suspending the particles in Tris buffer prior to the kinetics experiment overnight led to slightly slower adsorption kinetics and increased adsorption capacity. The former is explained by Ostwald ripening of the HAP particles leading to a reduction of surface area exposed to the complex solution, while the latter is ascribed to more complete wetting of the particles at early stages of the experiment. On the basis of the findings, all further experiments were carried out with preconditioned HAP. The data obtained for the adsorption of Tb-DOTP on HAP at room temperature (20 °C) is displayed in Figure 4 together with the curves resulting from a fit to the different kinetic models. The graphs show that only the Elovich model adequately simulates the experimental data. This observation is confirmed by the AICc values calculated for the fittings with the various models; the Elovich model resulted in the lowest value (see the Supporting Information, Table S4). The adsorption was found to be an extremely fast process with approximately 80% of the finally reached amount adsorbed within the first 5 min of the experiment. The estimated standard error of the Elovich initial adsorption rate R is rather large: 42 and 58% for Tb-DOTP and Tb-BPPED, respectively. This is caused by the interdependence of the model parameters R and β, which was confirmed by comparing the fit of the two best-fitting models (Elovich and PSO) to computergenerated data sets (see the Supporting Information). Thus, the
2300 Langmuir, Vol. 25, No. 4, 2009
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Figure 5. Temperature-dependence of the kinetics of the adsorption of Tb-DOTP on HAP in (a) nonlinear (q vs t) and (b) linearized form (q vs ln(t)). From bottom to top, the temperature increases in the order 0-10-20-30-37-50-60 °C.
Figure 6. Temperature-dependence of the kinetics of the adsorption of Tb-BPPED on HAP in (a) nonlinear (q vs t) and (b) linearized form (q vs ln(t)). From bottom to top, the temperature increases in the order 10-20-37-50 °C. Table 4. Best-Fit Parameters Obtained from Fitting of the Experimental Data with the Elovich Model Tb-DOTP Tb-BPPED
R [mmol g-1 min-1]
β [g mmol-1]
8800 (3720) 5850 (3410)
811 (21) 475 (18)
parameters calculated for the experimental kinetics data were treated with due respect; however, clear trends could be extracted from the data. The kinetics of the adsorption was investigated as a function of the temperature. Figures 5 and 6 display the respective experimental data together with the curves calculated with the Elovich model using the best-fit parameters. An increase in temperature leads to the adsorption of larger amounts of complex for both complex types, as was previously observed in the equilibrium isotherm experiments. Table 5 contains the complete parameter set calculated by fitting the Elovich model to the data collected under various conditions. The initial adsorption rate R is very similar for the two complexes and tends to increase with the temperature, especially for temperatures > 40 °C. From the R values obtained and an Arrhenius type relationship (eq 14; see Figure 7), the activation energy of the adsorption Eads for Tb-DOTP and Tb-BPPED was determined to be 74.9 ( 12.2 and 58.1 ( 29.8 kJ mol-1, respectively. These values indicate that both complexes are chemisorbed on the surface, as the rough borderline between chemi- and physisorption is generally considered to lie between 10 and 50 kJ mol-1 (or ∼0.1 and 0.5 eV per molecule). This is also in line with the observation that the adsorption is only partially reversible. The lower activation energy of the adsorption of the Tb-BPPED complex might be caused by the higher flexibility of this system as well as the free availability of the bisphosphonate group for attachment to the HAP surface.29
Comparison of the adsorption behavior of the complexes on both of the two different types of HAP (i.e., “fast-flow” and “high-resolution”; see Table 5) shows that the adsorption on the “high-resolution” HAP proceeds faster by several orders of magnitude. Nitrogen sorption BET analysis showed that the specific surface area of the two HAP types is almost identical (69.7 and 68.4 m2 g-1 for HR- and FF-HAP, respectively), which is in agreement with the fact that the final amounts of adsorbed complex on these types of HAP are quite similar (Figure 8). The sedimentation of the HAP from a stirred dispersion is much faster for the FF-HAP than for HR-HAP, suggesting a significantly larger particle size for the “fast-flow” type. A microscopic characterization of the two HAP types confirmed that the particle size of the FF-HAP was in the range of 200 µm and the HR-HAP has a particle size of ∼20 µm (see the Supporting Information). This means that the external surface in direct contact with the stirred liquid phase, that is, the surface immediately accessible for adsorption, is larger for the HR-HAP, while much of the surface of the FF-HAP is actually inner surface which is only accessible through the particle pores, causing a limitation by diffusion within the HAP particles. Thus, especially the initial adsorption rate R, which is the main parameter calculated by the Elovich model, was expected to be higher for the HR-HAP. The direct comparison of the two different complexes displayed in Figure 8 shows that the amount of complex adsorbed on the HAP surface is larger for the Tb-BPPED complex, which again confirms the higher overall affinity of this complex for HAP, already observed in the equilibrium experiments.
4. Conclusions The adsorption of Tb3+ complexes of both DOTP and BPPED is an endothermic and entropy-driven process. The LangmuirFreundlich and the To´th isotherm models give the best fits for
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Table 5. Elovich Parameters for the Adsorption Kinetics of Tb-DOTP and Tb-BPPED
R [mmol g-1 min-1] est std error β [g mmol-1] est std error R [mmol g-1 min-1] est std error β [g mmol-1] est std error a
0 °C
10 °C
20 °C
20 °C FFa
1450 (850) 1015 (40)
1200 (450) 842 (22)
8800 (3720) 811 (21)
Tb-DOTP 7.2 (3.4) 512 (28)
5340 (4360) 504 (27)
5850 (3410) 475 (18)
Tb-BPPED 1.9 (0.7) 242 (14)
30 °C
37 °C
50 °C
60 °C
4300 (1770) 602 (16)
1380 (370) 619 (12)
33 630 (35 270) 592 (36)
68 700 (93 460) 557 (44)
5770 (2540) 431 (13)
24 680 (21 800) 454 (24)
Data denoted as “FF” were collected using the “fast-flow” HAP in contrast to the “high-resolution” HAP used for all other data series.
Figure 7. Arrhenius plots of the Elovich initial adsorption rate R as function of the temperature T; hollow symbols (]) and dashed line are experimental data and best-fit Arrhenius curve for Tb-BPPED; solid symbols (2) and line represent data for Tb-DOTP.
Figure 8. Comparison of the kinetics of the adsorption of the Tb-BPPED (black) and the Tb-DOTP (gray) complexes on the two different types of HAP (FF, dashed; HR, solid). For the sake of simplicity, only the fitted Elovich curves are displayed.
the experimental data, which suggests that different adsorption sites for these phosphonate complexes are present at the HAP surface. This is also evident from the tests for the reversibility of the adsorption, which was found to be incomplete and concentration-dependent for both complexes.
While the adsorption was very fast with similar adsorption rates for both of the complexes, the Tb-BPPED complex exhibited a much higher affinity toward the HAP surface than the Tb-DOTP complex. This was ascribed to the presence of the bisphosphonate group of the BPPED ligand: on one hand, it has a chelating effect, and on the other hand the group is not involved in binding the central Tb3+ ion and is thus more available for surface attachment than the DOTP phosphonate groups. For both complexes, the adsorption can be described as a combination of physisorption and chemisorption leading to the observed incomplete reversibility. These phenomena are consistent with the occurrence of a chemical displacement reaction of the phosphate groups in HAP by phosphonate groups of the complexes studied, as proposed by Oldfield et al.34 In summary, the detailed investigation of both the kinetics and the equilibrium thermodynamics of the adsorption process provided important new insights into these medically highly relevant systems. Acknowledgment. The authors kindly thank Prof. Ivan Lukesˇ from the Charles University, Prague, and Prof. Carlos Geraldes from the University of Coimbra for supplying the BPPED and DOTP ligands, respectively. We greatly appreciate the BET measurements done by Dr. Ralf Supplit from the Vienna University of Technology. Financial support by the Marie Curie mobility program of the European Union (MEST-CT-2004007442) is gratefully acknowledged. This work was done in the frame of COST Action D38 “Metal-Based Systems for Molecular Imaging Applications” and the EU Network of Excellence European Molecular Imaging Laboratory” (EMIL, LSCH-2004503569). Supporting Information Available: Validation of γ-counting measurements by ICP-OES measurements; paper chromatography of the complex solutions; calculation of adsorption reversibility data; preliminary kinetics experiments; AICc values for fitting results of the experimental absorption isotherms with various models; AICc values for fitting results of the experimental kinetic adsorption data with various models; fitting of Elovich and PSO models to synthetic data sets; and optical micrographs of HAP. This material is available free of charge via the Internet at http://pubs.acs.org. LA803562E
