Physicochemical Characterization of Variously Packed Porous Plugs

Langmuir 2006, 22, 1903-1910

1903

Physicochemical Characterization of Variously Packed Porous Plugs of Hydroxyapatite: Streaming Potential Coupled with Conductivity Measurements Kyriaki Skartsila and Nikos Spanos* School of Science and Technology, Hellenic Open UniVersity, 262 23 Patras, Greece ReceiVed September 9, 2005. In Final Form: December 1, 2005 A homemade instrument was used for the measurement of the streaming potential, conductivity, and permeability of plugs packed in different densities with hydroxyapatite (HAP) particles at 25 °C and pH ) 7.0 ( 0.2. KCl solutions with ionic strength values in the range of 0.3-300 mM, equilibrated with HAP for 3 days, were forced to flow through the plugs. It was found that the particle volume fraction of the plug obtained from conductivity measurements was slightly higher than that obtained by weighing the solid. This suggested that, in addition to the volume of the solid itself, the volume of liquid trapped in the cavities of the particles does not contribute to the conductivity of the plug. The pH change recorded in the solution passed through the plug was attributed to the protonation/deprotonation of the HAP surface groups. Denser packing of the HAP crystallites resulted to higher surface conductivities. It was suggested that this trend was due to the easier interparticle ion transport in close-packed plugs. Considering ζ-potential, the values computed by neglecting surface conductivity were significantly underestimated, especially at low ionic strength values and at dense packing. More realistic values for the HAP ζ-potential were obtained taking into account the surface conductivity. These values were practically independent of the material packing during the plug preparation. Finally, the total surface conductivity was found to be limited behind the slipping plane of the electric double layer developed at the interface of HAP in contact with electrolyte solution.

Introduction Hard tissues of higher mammals including bone, dentin, and dental enamel are natural composites that contain hydroxyapatite (Ca5(PO4)3OH; HAP) (or a similar mineral), bound with proteins, other organic materials, and water. The inorganic constituent, HAP, is the most thermodynamically stable crystalline phase of calcium phosphate and is known to be a highly biocompatible material.1,2 The interaction of biomolecules with the surface of HAP is of great importance in systems where biological fluids are in contact with hard tissues. Proteins and/or peptides strongly adsorbed on HAP have been implicated in the mineralization of hard tissues, in some cases as accelerators,3-6 while in others as inhibitors.7-10 The inhibitory activity of some salivary proteins as well as their adsorption onto HAP is associated with the presence of phospho-L-serine in their amino acid sequence.9-13 It has been suggested that phospho-L-serine at low solution concentrations14-16 and L-serine at much higher concentrations17 * Corresponding author. Tel.: +30 2610 367525, fax: +30 2610 367520, e-mail: [email protected]. (1) Bajpai, P. K.; Billote, W. G. Ceramic Biomaterials. In The Biomedical Engineering Handbook; Bronzino, J. D., Ed.; CRC Press Inc.: Boca Raton, FL, 1995; p 558. (2) Osborn, J. F.; Neweseley, H. Biomaterials 1980, 1, 108. (3) Termine, J. D.; Belcourt, A. B.; Conn, K. M.; Kleinman, H. D. J. Biol. Chem. 1981, 256, 10408. (4) Weinstook, M.; Leblond, C. P. J. Cell Biol. 1973, 56, 838. (5) Lee, S. L.; Vers, A.; Glonek, T. Biochemistry 1977, 16, 2971. (6) Lechner, J. H.; Veis, A.; Sabsay, B. In The Chemistry and Biology of Mineralized ConnectiVe Tissue; Veis, A., Ed.; Elsevier: Amsterdam, 1981; p 395. (7) Termine, J. D.; Conn, K. M. Calcif. Tissue Res. 1976, 22, 149. (8) Termine, J. P.; Eanes, E. D.; Conn, K. M. Calcif. Tissue Int. 1980, 31, 247. (9) Hay, D. I.; Moreno, E. C.; Schlesinger, D. H. Inorg. Perspect. Biol. Med. 1979, 2, 271. (10) Moreno, E. C.; Varughese, K.; Hay, D. I. Calcif. Tissue Int. 1979, 28, 7. (11) Moreno, E. C.; Kresak, M.; Hay, D. I. Arch. Oral Biol. 1978, 23, 525. (12) Bennick, A.; Cannon, M.; Madapallimettam, G. Biochem. J. 1979, 183, 115. (13) Moreno, E. C.; Kresak, M.; Hay, D. I. J. Biol. Chem. 1982, 257, 2981. (14) Aoba, T.; Moreno, E. C. J. Colloid Interface Sci. 1985, 106, 110.

adsorb on the surface of HAP, blocking the active crystal growth sites and thus resulting in the inhibition of HAP crystal growth. In the above-mentioned studies, HAP was in the form of dilute suspensions. The interaction of proteins on HAP and artificial dental materials has, moreover, been reported in the literature in studies related to bacteria adhesion on tooth material.18,19 In situ monitoring of the adsorption/desorption of various adsorbates on adsorbents may be done by streaming potential (SP) measurements.20,21 In addition to adsorption/desorption studies, the technique of SP measurements has become a useful tool for studying the interface between electrolyte solutions and macroscopic solid surfaces, owing to its versatility that allows handling planar surfaces, cylindrical capillaries, and packed beds of granular or fibrous materials.22-25 The measurement of SP in packed beds of granular materials is much more elaborate than microelectrophoresis in dilute suspensions, but it has the advantage that the ζ-potentials of large particles can be determined. Furthermore, measurements can be performed at high electrolyte concentrations, (15) Misra, D. N. J. Colloid Interface Sci. 1997, 194, 249. (16) Spanos, N.; Koutsoukos, P. G. Langmuir 2001, 17, 866. (17) Spanos, N.; Klepetsanis, P. G.; Koutsoukos, P. G. J. Colloid Interface Sci. 2001, 236, 260. (18) Matsumura, H.; Kawasaki, K.; Okumura, N.; Kambara, M.; Norde, W. Colloids Surf., B 2003, 32, 97. (19) Kawasaki, K.; Kambara, M.; Matsumura, H.; Norde, W. Colloids Surf., B 2003, 32, 321. (20) Jachowicz, J.; Maxey, S.; Williams C. Langmuir 1993, 9, 3085. (21) (a) Norde, W.; Rouwendal, E. J. Colloid Interface Sci. 1990, 139, 169. (b) Shirahama, H.; Lyklema, J.; Norde, W. J. Colloid Interface Sci. 1990, 139, 177. (c) Somasundaran, P.; Healy, T. W.; Fuerstenau, D. W. J. Phys. Chem. 1964, 68, 3562. (d) Ethe`ve, J.; De´jardin, P. Langmuir 2002, 18, 1777. (e) Zembala, M.; Adamczyk, Z. Langmuir 2000, 16, 1593. (22) Szymczyk, A.; Fievet, P.; Foissy A. J. Colloid Interface Sci. 2002, 255, 323. (23) El-Gholabzouri, O.; Cabrerizo-Vı´lchez, M. A.; Hidalgo-A Ä lvarez, R. J. Colloid Interface Sci. 2003, 261, 386. (24) Gonzalez-Fernandez, C. F.; Espinoza-Jimenez, M.; Gonzalez-Caballero, F. Colloid Polym. Sci. 1983, 261, 688. (25) Walker, L. S.; Bhattacharjee, S.; Hoek, M. V. E.; Elimelech, M. Langmuir 2002, 18, 2193.

10.1021/la0524622 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/13/2006

1904 Langmuir, Vol. 22, No. 4, 2006

Skartsila and Spanos

well above the critical coagulation concentration. Moreover, the measurement of SP, in combination with the electrical conductivity of the porous plug, allows for the evaluation of ζ-potential by accounting for the surface conduction phenomenon. This phenomenon affects strongly the value of ζ-potential determined from SP measurements.22,23 The technique of SP was used in our laboratory for the investigation of the electric double layer (EDL) developed at the interface of closely packed particles of HAP in contact with an electrolyte solution, in the absence and in the presence of biologically interesting molecules adsorbed on the surface of HAP. The apparatus employed made it possible for simultaneous measurements of the SP, conductivity, and permeability of a HAP plug to be curried out. Polycrystalline preparations of HAP were used in the form of closely packed disks to model the mineralized matrix of bones, avoiding the interference of the organic matrix present in the bone vascular channel.26,27 Despite the significance of the HAP interface in contact with biological fluids, reports in the literature related with the parameters of the EDL developed during electrolyte passage through plugs of closely packed HAP particles are, to our knowledge, missing. Work on this subject is currently in progress in our laboratory. The present paper is the first part of this work, where the parameters of the EDL were investigated by using variously packed plugs of HAP equilibrated with a range of concentrations of indifferent electrolyte.

Theory Plug Conductivity. According to the O’Brien and Perrins theory,28 the electrical conductivity K* (µS cm-1) of a plug composed of close-packed monodisperse nonconducting spheres with relatively thin double layers (κR . 1, where κ is the reciprocal Debye length, and R is the particle radius), in a symmetrical electrolyte, is related to the bulk conductivity K∞ as

[

e2z2n∞/f∞ K* ) 1 + 3φ f(0) + (f(Du) - f(0)) ∞ K K∞

]

(1)

where φ is the volume fraction of the solid, z is the valence of the counterion, f∞ is the friction coefficient beyond the double layer, and n∞ is the equilibrium ion density beyond the double layer. According to this theory, only the surface conduction due to the excess of counterions in the double layer is taken into account; that is, the (negative) contribution due to the exclusion of co-ions is considered to be insignificant. K∞ is the electric conductivity of the bulk electrolyte,

K∞ )

absolute surface conductivity, Kσ:

Du )

Kσ RK∞

(3)

Du is in turn related to ζ-potential:28,29

Du )

(

)

3m 2 1 + 2 + Θ [exp(-zeζ/2kT) - 1] κR z

(4)

where m is a dimensionless parameter, accounting for the electroosmotic contribution to the surface conductivity, which, for aqueous solutions at room temperature, is 0.15, and Θ represents the conduction behind the shear plane relative to the conduction due to electromigration beyond the shear plane. At relatively high ionic strengths, where, according to eq 3, Du is small (Du < 1/2), eq 1 can be simplified into eq 5 by assuming f(Du) to be linear between f(0) ≈ -0.4 and f(1/2) ) 0:

K* ) (1 - 1.2φ)K∞ +

2.4φ σ K R

(5)

SP in Plugs. The potential developed in a plug due to an imposed pressure gradient is known as the SP, Estr. O’Brien30 related Estr to Du and the ζ-potential for a close-packed plug of monodisperse nonconducting spherical particles:

{

0RT Fζ Estr 1 ) + [1 + 3φf(0)] ∆P K* ηF RT Fζ 2 - ln 2 g(Du) RT z1

[

] }

(6)

where ∆P is the applied total pressure difference, z1 is the valence of the co-ion, η is the liquid viscosity, and g(Du) is a tabulated function of Du that also depends on the volume fraction and type of packing of the particles. The other symbols have their usual meaning. At low Du values, g(Du)0, and as f(0) ≈ -0.4, eq 6 reduces to the well-known Smoluchowski equation:

0ζ(1 - 1.2φ) Es ) ∆P ηK*

(7)

Liquid Transport. The permeability, which is a measure of the convenience of fluid flow through a porous medium, is a parameter defined by Darcy’s law as

J)

KsA ∆P η l

(8)

2

e2zi2ni∞/fi∞ ∑ i)1

(2)

and f(Du) is a tabulated function of Du, of the particle volume fraction, and of the type of packing of the particles. Du is the relative surface conductivity number, which is related to the (26) (a) Walsh, W. R.; Guzelsu, N. J. Orthop. Res. 1991, 9, 683. (b) MacGinitie, A. L.; Seiz, G. K.; Otter, W. M.; Cochran, G. V. B. J. Biomech. 1994, 27, 969. (c) Mak, F. T. A.; Huang, T. D.; Zhang, D. J.; Tong, P. J. Biomech. 1997, 30, 11. (d) MacGinitie, A. L.; Stanley, D. G.; Bieber, A. W.; Wu, D. D. J. Biomech. 1997, 30, 1133. (27) Griffiths, H.; Morgan, G.; Williams, K.; Addy, M. J. Periodontal Res. 1993, 28, 60. (28) O’Brien, R. W.; Perrins, W. T. J. Colloid Interface Sci. 1984, 99, 20.

where Ks is the specific permeability of the porous medium, J is the liquid flow rate, and A and l respectively denote the crosssection and length of the porous plug. Permeability can be related to the shapes of the flow channels in the porous medium, that is, the morphology of the solid, via the Kozeny-Carman equation:31

Ks )

1 (1 - φ) Kc S 2

3

(9)

V

(29) O’Brien, R. W. J. Colloid Interface Sci. 1983, 92, 204. (30) O’Brien, R. W. J. Colloid Interface Sci. 1986, 110, 477. (31) Han, Q.; Duncan, A. J.; Viswanathan, S. Metall. Mater. Trans. B 2003, 34, 25.

Electrokinetic Measurements on Plugs of HAP

Langmuir, Vol. 22, No. 4, 2006 1905

where SV is the surface area of the solid per unit volume of plug, and Kc is a constant dependent on the characteristics of the solid. In the case where fresh electrolyte of different concentration is pressed through a porous plug, assuming that the mixing of the two electrolyte solutions inside the plug is negligible, the resistance R* of the inhomogeneous plug can be calculated from the two homogeneous plugs placed in series:

R* )

(

)

l2 l l1 1 l ) + / / K* A lK1 lK2 A

(10)

where K/1 and K/2 are the conductivities of the two homogeneous parts, and l1 and l2 their respective lengths. On the basis of eq 10, Minor et al.32 calculated the specific resistance F* of the inhomogeneous plug as a function of time:

{

(

)

1 1 1 V l + /- / t / (1 φ)l 0 e t e V K2 K2 K2 1 ) 1 F* ≡ K* l et K/1 V

(11)

where V is the average velocity, calculated from the liquid flow rate, as J ) VA. Experimental Section Materials and Chemicals. Reagent-grade chemicals were used throughout. HAP used for the preparation of the porous plugs was prepared as follows: 1 L of 0.5 M Ca(NO3)2 and 1L of 0.3 M (NH4)2HPO4 were added simultaneously to 150 mL of triply distilled CO2-free water, which was kept well-stirred at 70 ( 1 °C. The addition was done over a period of 2 h. The pH of the solution was maintained at 10 by the addition of NH3 solution, and carbon dioxide was excluded by bubbling with gaseous nitrogen saturated with water vapor. The precipitate was washed thoroughly with triply distilled water and refluxed at 70 °C until free of NH3. Characterization of the solid was performed by powder X-ray diffraction (XRD, Philips 1830/40), Fourier transform infrared spectroscopy (FTIR; Spectrum BX II, Perkin-Elmer) and scanning electron microscopy (SEM; JEOL ISM 5200 and LEO SUPRA 35VP). The specific surface area (SSA) of the HAP prepared was measured by nitrogen adsorption (multiple-point BET, Gemini, Micromeritics) and was found to be 23 m2/g. The mean particle size measured by laser diffraction (Mastersizer S, Malvern) was found to be 8.3 µm, while examination of the morphology of the crystalline material with SEM showed agglomerates of 50-150 nm prismatic crystallites. FTIR spectra, in addition to the characteristic bands for HAP, showed the presence of a weak peak at 875 cm-1, characteristic of the hydrogen phosphate.33 Powder XRD spectra exhibited reflections corresponding to stoichiometric HAP exclusively. Finally, the molar Ca/P ratio in the obtained solid was determined by chemical analysis for calcium (atomic absorption, AAnalyst 700, Perkin-Elmer) and phosphate (UV-Vis spectroscopy, Lamda 35, Perkin-Elmer) following dissolution of the solid in hydrochloric acid. The respective value was found to be equal to 1.71 ( 0.05. Description of the Equipment/Measurement. The measurements of the SP, conductivity, and permeability of the plugs of packed HAP particles were done in an apparatus built in our laboratory. All measurements were done at 25 °C. The plugs were prepared by centrifugation of suspensions of HAP particles. The particles were directly centrifuged into the poly(methyl methacrylate) (PMMA) plug holder (cylinder with 1.5 cm length and 0.6 cm diameter). HAP plugs with various packing modes were obtained through variation of the conditions of centrifugation (duration and speed). On both (32) Minor, M.; van der Linde, A. J.; Lyklema, J. J. Colloid Interface Sci. 1998, 203, 177. (33) Bett, J. A. S.; Christner, L. G.; Keith Hall, W. J. Am. Chem. Soc. 1967, 89, 5535.

sides of the plug holder, perforated platinized platinum disk electrodes were mounted, and each side was connected to a liquid reservoir. Two porous membranes (Millipore, 0.65 µm) were introduced between the electrodes and the plug to prevent the disintegration of the packed solid upon the application of pressure. The electrolyte solution was forced through the plug by applying a pressure difference (using nitrogen overpressure) across the cell. The desired value of the pressure difference was adjusted by a pressure regulator and was monitored by a pressure transducer. The signal of the cell electrodes was transferred to a high-input impedance voltmeter or to a conductivity meter (Metrohm 712). Before measuring the SP, the signal was amplified and filtered to eliminate noise. The potential difference between the plug electrodes was recorded as a function of time, and the SP was determined from the potential jumps at “pressure on” and “pressure off” settings. The setup is similar to that depicted in Figure 4.18 of ref 34. The SP was measured at six pressure differences, varying between 0 and 0.65 × 105 N/m2. The respective correlation plots showed perfectly straight lines, even at high ionic strength values, where SPs of less than 1 mV were measured. The plug conductivity was calculated from the product of the plug conductance, G*(S), times the conductometric cell constant (cm-1) based on the cell geometry. The geometrically determined value of the cell constant was tested by comparing the conductance of a 0.03 M KCl solution, measured by using the empty plug holder, with the conductivity of the same solution measured by using a commercially available conductivity probe with a known cell constant (Metrohm 6.0908.110, 0.79 cm-1). The values obtained by both methods were in very good agreement. The calibration of the device was performed by using the system of a polystyrene latex plug-KCl solution.32,35 Blank measurements were also done; that is, the SP across the empty cell (without the solid) was measured, so that the contribution of the plug holder and porous membrane to the global signal could be estimated and taken into consideration in the subsequent measurements. The empty cell yielded SP values that should not be neglected. A relatively low signal due to the plug holder was anticipated because the surface of PMMA, in contact with an electrolyte solution, acquires a low electric charge with an isoelectric point (IEP) at pH 4.3 and a value of ζ-potential no higher than 20 mV.25 To minimize any dissolution of HAP constituting the plug, which may occur during the flow of the liquid through the plug, the KCl solutions in the range of the ionic strength values investigated (0.3300 mM) were presaturated with respect to HAP. The solubility of HAP in the saturated solutions was measured by chemical analysis for total calcium and total phosphate. The pH of the saturated solutions was found to be equal to pH ) 7.0 ( 0.2.

Results and Discussion Unlike the conductivity and SP, which are rather insensitive to small cracks in the plug, the velocity of the liquid flow through the plug measured for every electrolyte concentration was used to check the integrity of the plug.32 Flow rate was found to be independent of the electrolyte concentration, indicating that the diffuse double layer does not affect the fluid velocity. Prior to all measurements of the electrolyte flow rate, conductivity, and SP, the plug was rinsed thoroughly with the fresh electrolyte solution until the conductivity attained a constant value. In Figure 1, the conductivity and the specific resistance of one of the plugs used in the present study are shown as a function of time after exchanging the electrolyte solution in the reservoirs from 3.4 to 10.4 mM KCl. The conductivity increased after applying the pressure difference (∆P ) 0.40 × 105 N/m2) because of the higher concentration of the fresh electrolyte. Similar curves were obtained for all cases studied. The time needed to attain a new (34) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: London, 1995; Vol. 2, Chapter 4. (35) Lo¨bbus, M.; Van Leeuwen, H. P.; Lyklema, J. Colloids Surf., A 2000, 161, 103.

1906 Langmuir, Vol. 22, No. 4, 2006

Figure 1. Conductivity and specific resistance of plug5 as a function of time after changing the electrolyte concentration from 3.4 to 10.4 mM KCl.

Skartsila and Spanos

Figure 3. Flow rate of liquid through the plug as a function of pressure difference for plug3 (9) and plug4 (b). Table 1. Particle Volume Fractions Determined by Different Methods and Surface Conductivities Corresponding to the Plugs of HAP Particles Packed in Different Densities

Figure 2. Plug conductivity, K*, versus the bulk conductivity, K∞, corresponding to various ionic strengths, for the plugs compiled in Table 1: plug1 (9), plug2 (b), plug3 (2), plug4 (1), and plug5 (().

stationary state is related to the length of the plug, the particle volume fraction, and the average fluid velocity (eq 11). From the slope of the linear part of the F*(t) curve, the particle volume fraction, φdF*/dt, may be calculated according to eq 11. The particle volume fraction may, moreover, be obtained from the mass of the solid constituting the plug, φw, and from conductivity measurements, φcon. In the former case, the particle volume fraction may be replaced by Vs/Vp, where Vp is the plug volume and Vs is the volume of the particles given by m/d, with m and d standing for the mass and the average density (3.22 g cm-3 for HAP1) of the particles, respectively. φcon and surface conductivity, Kσ, were calculated from the slope and intercept of the linear fitting of the curve obtained by plotting K* versus K∞, which correspond to various ionic strength values, according to eq 5. The plots obtained are shown in Figure 2. The excellent linear fitting demonstrates that slope and intercept are constant over a large range of K∞. In other words, surface conductivity seems to be independent from ionic strength over a large range of ionic strength values. The values of the particle volume fraction obtained by the three different ways described above and of the surface conductivity, corresponding to the plugs packed in different ways, are summarized in Table 1. It may be observed

plug

φdF*/dt

φw

φcon

Kσ/10-8 S

1 2 3 4 5

0.42 0.36 0.33 0.28 0.18

0.38

0.41 0.37 0.31 0.26 0.19

3.9 3.3 2.9 1.8 0.8

0.22 0.15

that, in the cases where the solid was removed from the plug, dried and weighed, the value of φw obtained was smaller than the particle volume fractions that were determined by means of conductivity measurements (i.e., φdF*/dt and φcon). This finding implies that in addition to the volume of the solid itself, there is a volume of liquid trapped in the cavities of the particles that does not contribute to the conductivity of the plug. It may therefore be suggested that the effective volume of the plug that does not contribute to the plug conductivity, Veff s , is larger than the intrinsic volume of the particles, Vs, and an apparent density of the HAP particles constituting the plug may be obtained from conductivity measurements, dcon, by replacing φcon or φdF*/dt by eff con con Veff s /Vp, where Vs is given by m/d . An average value of d -3 equal to 2.76 g cm was found, which, in accordance with the considerations mentioned above, is lower than the intrinsic density of HAP (3.22 g cm-3). Assuming that surface conductivities are indicative of the packing characteristics of the porous plugs, it may be seen in Table 1 that they increase with increasing packing. It should be noted here that, while the volume flow of the liquid tends to be strongly dominated by the wider channels, because Poiseuille’s law predicts a proportionality to the fourth power of the radius, surface conduction currents tend to avoid the wide channels. Close packing of the solid is favorable for surface conduction because that would facilitate the transport of ions from one particle to the next.34 Therefore, the closer the packing of the solid, the higher the respective surface conductivity. As far as the liquid transport through the plug is concerned, the specific permeability of the plug may be estimated from the slope of the linear fitting of the curve resulting from the plot of liquid flow rate versus ∆P, according to eq 8. Figure 3 shows typical curves obtained for the plugs compiled in Table 1. Specific permeability allows for the calculation of the constant Kc, which depends on the characteristics of the solid. The values of Kc

Electrokinetic Measurements on Plugs of HAP

Langmuir, Vol. 22, No. 4, 2006 1907 Table 2. pH of a Fresh Electrolyte Solution Replacing the Old Solution, before (pHinitial) and after (pHfinal) Passage through the Plug ionic strength (mM KCl)

Figure 4. Solubility of HAP determined experimentally after a 3-day equilibration with KCl solutions of various ionic strengths (solid square), and theoretically calculated at various pHs and ionic strengths (straight lines). Ionic strength values are quoted in mM KCl. Also shown is the concentration of HAP in the liquid after passage through the plug at 99.5 (open symbols) and 292.0 (crosscentered symbols) mM KCl, corresponding to the five plugs studied: plug1 (square), plug2 (circle), plug3 (up triangle), plug4 (down triangle), and plug5 (diamond).

obtained increased with the particle volume fraction from a value of 5.1 × 10-3 for plug 5 (minimum packing) to a value of 3.2 for plug 1 (maximum packing), showing a strong dependence of the morphology of the solid on packing. It should be noted that Kc values, which are of the same order of magnitude as those obtained for the maximum packing (φcon ) 0.41), have been reported for plugs composed of hair fibers with φ > 0.50 (Kc ) 5.5)20 and for the mushy zone of aluminum-copper alloys with φ > 0.75 (Kc ) 5.0).36 A possible question is whether any dissolution of the HAP plug material takes place during the liquid flow. The fact that the flow rate of the liquid through the plug is invariable with time demonstrates that, in case any dissolution occurred, this should be negligible. The extent of the dissolution of the plug material was determined by analyzing the electrolyte solution for calcium, before and after passage through the plug. Figure 4 shows the amount of HAP dissolved after equilibration for 3 days in the solutions of different KCl concentrations used in this study (solid square), with relation to the thermodynamic solubility of HAP calculated at 25 °C and at various pH and ionic strength values (straight lines). The ionic strength values shown on the graph refer to the total ionic strength due to KCl and dissolved HAP. Thermodynamic solubility and total ionic strength were calculated by using the computer code HYDRAQL.37 The solubility constant of HAP and the formation constants of the various species formed in the system “electrolyte solution KCl/ HAP” were taken from the NIST database.38 As may be seen, the experimentally obtained solubility (solid square) corresponding to higher ionic strength values (30.4-292.0 mM) was slightly higher than that corresponding to lower ionic strengths (0.7-3.4 mM), in accordance with theory, which predicts increasing solubility with increasing ionic strength (e.g., straight lines (36) Nielsen, O.; Arnberg, L.; Mo, A.; Thevik, H. Metall. Mater. Trans. A 1999, 30, 2455. (37) Papelis, G.; Hayes, K. F.; Leckie, J. O. HYDRAQL: A Program for the Computation of Chemical Equilibrium Composition of Aqueous Batch Systems; Technical Report No. 306; Stanford University: Menlo Park, CA, 1988. (38) NIST Critically Selected Stability Constants of Metal Complexes Database, version 6.0; U.S. Department of Commerce: Gaithersburg, MD, 2001.

old electrolyte

new electrolyte

pHinitial

pHfinal

3.4 0.7 1.4 292.0 99.5 292.0

30.4 1.4 10.4 0.7 1.4 30.4

7.04 6.90 6.88 6.86 6.90 7.04

6.82 6.68 6.62 7.19 7.12 7.25

calculated at various ionic strengths, shown in Figure 4). Provided the dissolution of HAP takes place through equilibrium (eq 12), a slightly higher solubility results in a low shift of pH to higher values, as in our case (Figure 4, solid square, ionic strength 30.4-292.0 mM). The fact that the amount of HAP, dissolved after equilibration for 3 days (solid square), was lower than that corresponding to the thermodynamic solubility (straight lines) suggested that the solution flowing through the plug was undersaturated with respect to HAP. Therefore, dissolution of the plug material to some extent, especially at the high ionic strengths studied, should not be precluded. In fact, as it may also be seen in Figure 4, a slightly increased amount of HAP was dissolved in the solution after passage through the plug, in the cases of the two higher ionic strengths studied (open symbols for 99.5 mM and cross-centered symbols for 292.0 mM). At the lower ionic strength values, no significant change in the amount of the dissolved HAP was observed following passage of the electrolyte solution through the plug. Among the various plugs studied (Table 1), the plugs with the most dense packing, plug1 (square) and plug2 (circle), exhibited the highest solubility. The increased solubility observed in the more dense plugs should be ascribed to the considerably lower values of the liquid flow rate due to the higher packing, resulting in longer contact time of the liquid with the solid.

Ca5(OH)(PO4)3 a 5Ca2+ + 3PO43- + OH-

(12)

The potential-determining ions (PDIs) for HAP are the respective lattice ions. The change in the pH of the solution in equilibrium with the solid is therefore expected to reflect changes in the surface potential related to the measured SP. Typical pH changes measured as a result of the flow of fresh electrolyte solution through the plug, replacing the old solution, are compiled in Table 2. It may be observed that, when the ionic strength of the new solution is higher than the respective value of the old, the pH of the new solution decreased during the electrolyte flow through the plug. On the contrary, when a fresh solution of lower ionic strength permeated the plug, the pH of the solution increased. To explain these observations, we considered the mechanism for development of surface charge in the HAP/electrolyte solution system, which may be described according to the following scheme:

≡OH- + H+ a ≡OH2 (a) ≡PO43- + H+ a ≡HPO42- (b) ≡HPO42- + H+ a ≡H2PO4- (c) ≡CaO- + H+ a ≡CaOH° (d) ≡CaOH0 + H+ a ≡CaOH2+ (e)

(13)

1908 Langmuir, Vol. 22, No. 4, 2006

Figure 5. Variation in SP with the liquid flow rate obtained for plug3, in the presence (solid symbols) and in the absence (open symbols) of the HAP particles, at different ionic strength values: 0.7 (square), 1.4 (circle), and 10.4 (up triangle) mM KCl.

In the reaction presented in Scheme 13, “≡” stands for the surface. When a new electrolyte solution with higher ionic strength is forced to pass through the plug, the surface of the HAP particles is further shielded by the counterions of the EDL, which in turn induce an additional electric charge, thus increasing the absolute surface charge, σo. Since the surface of HAP is negatively charged in the pH range 6-8,16,19 an increase in the absolute value of the surface charge shifts equilibria 13 to the left, that is, deprotonation of the surface groups, thus rendering the surface more negative and releasing protons to the solution. In consequence, the pH of the solution decreases. On the contrary, when the new electrolyte solution permeating the plug is of lower ionic strength, the surface of the HAP particles is less shielded by the counterions of the EDL, and the surface is therefore less negatively charged. Reduction of the negative surface charge entails a shift of equilibria 13 to the right, that is, the surface groups are protonated, rendering the surface less negative, while protons are withdrawn from the solution, causing an increase of the solution pH. It should be also mentioned that, besides the protonation/deprotonation of the surface groups, the potential contribution of the lattice ions of HAP present in the working solution (i.e., phosphate and calcium ions) to the development of surface charge is currently under investigation. As already mentioned in the Experimental Section, the plug holder and the membranes placed at the ends of the plug to prevent the disintegration of the packed solid contribute to the global signal obtained during the measurement of SP. The variation of SP as a function of the volume flow rate, corresponding to plug3 (solid symbols) and to an empty cell (open symbols) at different values of the ionic strength, is shown in Figure 5. Similar curves, with excellent linear fit, were obtained for all plugs and ionic strength values studied. The SP due to the HAP particles themselves may be determined by subtracting the values obtained for the empty plug from those obtained for the entire system (with the HAP particles). Moreover, using the lines obtained from the liquid flow rate versus pressure difference plots (typical curves are illustrated in Figure 3), liquid flow rate may be replaced by the respective pressure difference, thus resulting in the variation of SP, due to the HAP itself, as a function of the applied pressure difference. A typical variation is shown in Figure 6 for plug3 at different values of ionic strength. Similar lines, with excellent linear fit, were also obtained for all plugs

Skartsila and Spanos

Figure 6. Variation in SP, due to the HAP itself, with the pressure difference obtained for plug3, at different ionic strength values: 0.7 (9), 1.4 (b), and 10.4 (2) mM KCl.

Figure 7. Variation in ζ-potential, calculated according to the Smoluchowski approximation (ζSmol; open symbols) and the O’Brien theory (ζcomb; solid symbols), with the ionic strength, corresponding to the plugs shown in Table 1: plug1 (square), plug2 (circle), plug3 (up triangle), plug4 (down triangle), and plug5 (diamond).

and ionic strength values studied. The slope of the linear fitting (Estr/∆P) was then used to calculate the ζ-potential, according to eqs 6 or 7. Figure 7 shows the variation of the ζ-potential, corresponding to the plugs packed in different ways, as a function of the ionic strength. The ζ-potential was calculated, on one hand, according to eq 7 (Smoluchowski approximation, ζSmol) and, on the other hand, on the basis of the O’Brien theory (ζcomb). In particular, ζcomb was obtained by combining the conductivity and SP data, using eqs 1, 3, and 6. Details on the calculation procedure have been reported elsewhere.32 It may be noticed that ζSmol exhibits a spurious maximum, contrary to the monotonic decrease of the absolute ζ-potential, with increasing ionic strength predicted by the Gouy-Chapmann theory. Moreover, ζSmol seems, strangely enough, to depend on the packing of the plug. The paradoxical dependence of ζSmol on packing and the spurious maximum of the variation of ζSmol with ionic strength disappear, and an anticipated trend for the ζ-potential arises in the case of ζcomb. The discrepancy between the ζ-potential values obtained by using

Electrokinetic Measurements on Plugs of HAP

the theories mentioned above is attributed to the fact that the Smoluchowski theory does not take into consideration the polarization of the double layer due to the surface conductivity, resulting in underestimated values for ζSmol. In contrast, the O’Brien theory, which takes into account the effect of surface conductivity, yields more realistic ζ-potential values. Since, as stated in the theoretical section, the effect of surface conductivity is more pronounced at low ionic strength values, it is expected that the lower the ionic strength, the more significant the underestimation of ζSmol. Otherwise, at high ionic strength values, where the contribution of surface conductivity to the conductivity of the entire plug is negligible (Du , 1), it is anticipated that the ζ-potentials calculated are almost identical, regardless of the theory according to which they were calculated. These considerations are in full agreement with our experimental results, as may be seen in Figure 7, demonstrating that the O’Brien theory, in addition to spherical particles, may satisfactorily be applied to prismatic particles, such as those of the HAP crystals investigated in the present work. Concerning the dependence of ζSmol on packing, viz. the shift of ζSmol to more underestimated values with increasing packing density of the plug, it may be ascribed to the increasing surface conductivity with increasing packing density (Table 1), resulting in higher polarization of the double layer. Neglect of the increase in the polarization of the double layer with packing, in the computation of ζ-potential, results in significantly underestimated values of ζSmol. It should also be noted that similar effects of surface conductivity on the variation of ζ-potential as a function of the ionic strength, obtained from SP or streaming current measurements for various materials, have been reported.23,32,39,40 It may thus be strongly recommended that the effect of surface conductivity should be taken into account in the determination of ζ-potential from SP measurements, especially at low ionic strength values. Values of ζ-potential obtained at one value of ionic strength by using different methods have been reported in the literature. Considerably higher ζ-potential values of -25 and -36 mV have been reported from measurements in 0.01 M phosphate buffer at pH 7.0 by using the techniques of SP measurements of HAP platelike crystals18,19 and microelectrophoretic mobility measurements of HAP particles,19 respectively. As may be seen in Figure 7, a value of about -4.1 mV, irrespective of packing, was attained in the present study in 0.01 M KCl at pH 7.0. The more negative values obtained in the presence of phosphate buffer should be attributed to the specific adsorption of negatively charged phosphate species, which in turn, shifted the IEP to lower pH values, thus rendering the ζ-potential more negative. Concerning the discrepancy between the values obtained by the techniques of SP and microelectrophoresis,19 it was anticipated because of the method of calculation of the ζ-potential from the experimentally measured parameters, that is, SP and microelectrophoretic mobility, respectively.28,30 Finally, in view of the success of the Gouy-Stern theory in interpreting static double-layer properties, it is consistent to do the same treatment for the surface conductivity, that is, Kσ ) Kσi + Kσd. To a first approximation, Kσi is determined by the ions within the hydrodynamically stagnant Stern layer, and Kσd is determined by the diffuse part of the EDL; these two parts are distinguishable as “behind” and “beyond” the slipping plane.34 The ratio of these two parts of surface conductivity, Θ ) Kσi/ Kσd, may be determined by replacing the calculated values of (39) Spanos, N.; Koutsoukos, P. G. J. Colloid Interface Sci. 1999, 214, 85. (40) Minor, M.; van der Linde, A. J.; van Leeuwen, H. P.; Lyklema, J. Colloids Surf., A 1998, 142, 165.

Langmuir, Vol. 22, No. 4, 2006 1909 Table 3. Θ Values Calculated from ζcomb and Du According to Eq 4 at Various Ionic Strength Values Corresponding to the Plugs Studied ionic strength (mM KCl)

plug1

plug2

Θ plug3

plug4

plug5

0.7 1.4 3.4 10.4 30.4 99.5 292

108.6 150.5 241.4 131.3 147.2 114.4 97.2

101.6 137.4 147.6 92.3 98.4 117.7 182.2

41.7 81.9 122.9 107.1 113.9 92.7 311.9

84.6 73.6 125.2 107.3 100.8 164.8 114.7

109.4 78.8 115.3 108.4 95.4 118.4 136.9

ζcomb in eq 4. The values of Θ obtained at various ionic strength values for the plugs studied are summarized in Table 3. The remarkably high values of Θ suggested that the total surface conduction is practically limited behind the plane of shear. Similarly, significantly high values have been reported for Θ, determined, on one hand, for titania particles by calculating Kσi and Kσd using the mobilities of the ions and the charge densities behind and beyond the slipping plane39 and, on the other hand, for bacterial cells (Bacillus breVis) on the basis of an equation analogous to eq 4.41 On the contrary, significantly lower values of Θ (on the order of 1) have been reported for polystyrene latex32 and silica particles.40 Work is in progress in our laboratory to determine the surface charge of HAP particles, which, in combination with the results of the present study, allows for an estimate of the lateral mobility of the counterions in the stagnant layer of the EDL (i.e., behind the slipping plane).

Conclusions The particle volume fraction obtained from conductivity measurements was slightly higher than that obtained from the weight of the solid constituting the plug, suggesting that, in addition to the volume of the solid, there is a volume of liquid trapped in the cavities of the particles that does not contribute to the conductivity of the plug. The dissolution of the HAP in the plugs was low enough to not have any effect on the flow rate of the electrolyte. The changes in the pH of the solution passing through the plug were attributed to the mechanism of the development of surface charge on HAP based on the protonation/deprotonation of the surface hydroxyl, phosphate, and calcium ions. Surface conductivity was found to increase with increasing packing density, implying that surface conduction currents tend to prefer the narrow channels of the plug. This finding may be explained by the fact that close packing of the solid facilitates the transport of ions from one particle to the next. In the case of the relatively low SP values obtained for HAP, the contribution of the blank (empty cell) to the total signal should be taken into account. Surface conductivity was found to play a significant role in the determination of the ζ-potential. The values computed according to the Smoluchowski theory, that is, neglecting the surface conduction phenomenon, are seriously underestimated, especially at relatively low ionic strength values, where the contribution of surface conductivity to the total plug conductivity is significant. An additional parameter resulting in the underestimation of the ζ-potential values, calculated according to the Smoluchowski theory, is the higher packing density of the plug, which is accompanied by a higher surface conductivity, the omission of which results in (41) van der Wal, A.; Minor, M.; Norde, W.; Zehnder, A. J. B.; Lyklema, J. J. Colloid Interface Sci. 1997, 186, 71.

1910 Langmuir, Vol. 22, No. 4, 2006

further underestimated values of ζSmol. The underestimation of the ζ-potential may be eliminated, and more realistic values, independent of the packing of the plug, may be obtained when the ζ-potential is computed according to the O’Brien theory, that is, by taking into consideration the effect of surface conductivity. Finally, the considerably high values obtained for the ratio of the two parts of surface conductivity “behind/beyond” the slipping plane suggested that the total surface conduction is practically limited behind the plane of shear.

Skartsila and Spanos

Acknowledgment. Financial support by the European Social Fund, Operational Programme for Educational and Vocational Training II (EPEAEK II), program Pythagoras (contract No. 89188), is gratefully acknowledged. Kind help given by P. G. Koutsoukos from the University of Patras, Greece for the characterization of HAP by powder XRD and SEM is also acknowledged. LA0524622