Biomaterials 26 (2005) 271–283

ARTICLE IN PRESS

*Correspondin

6936.

E-mail addres

0142-9612/$ - see

doi:10.1016/j.bio

Nanoscale variation in surface charge of synthetic hydroxyapatitedetected by chemically and spatially specific high-resolution

force spectroscopy

Jennifer Vandivera, Delphine Deanb, Nelesh Patelc, William Bonfieldc, Christine Ortiza,*aDepartments of Materials Science and Engineering, RM13-4022, Massachusetts Institute of Technology, 77 Massachusetts Avenue,

Cambridge, MA 02139, USAbElectrical Engineering and Computer Science, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

cDepartment of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK

Received 23 October 2003; accepted 16 February 2004

Abstract

The normal intersurface forces between nanosized probe tips functionalized with COO�- and NH3+-terminated alkanethiol self-

assembling monolayers and dense polycrystalline phase pure synthetic hydroxyapatite (HA) were measured via a powerful

nanomechanical technique called chemically specific high-resolution force spectroscopy. The data taken on approach of the probe

tip to the HA surface was compared to the nonlinear Poisson–Boltzmann-based electrostatic double layer theory to predict the

surface charge per unit area of the HA, sHA (C/m2), as a function of ionic strength, position within a variety of grains, and across

grain boundaries. The average sHA was found to be B�0.02C/m2 and to vary from �0.0037 to �0.072C/m2 with nanoscale

position in relation to grain boundaries and crystal planes up to �0.19C/m2/mm. Positional measurement of nanoscale surfaceproperties holds great promise in elucidating the molecular origins of physicochemical processes occurring at the biomaterial

interface.

r 2004 Elsevier Ltd. All rights reserved.

Keywords: Hydroxyapatite; Surface analysis; Bioactivity; Atomic force microscopy; Bone repair; Biocompatibility

1. Introduction

Currently, there is a significant need for improvedsynthetic materials, for use as orthopedic implants, toreplace human bone lost and damaged due to disease(e.g. osteoporosis) and/or injury. Certain ceramics, likecalcium phosphates, have the special property of beingbioactive, meaning that an interfacial bond between theimplant and the surrounding bone forms, leading togood fixation, and generally no fibrous tissue encapsula-tion [1–3]. One such ceramic, hydroxyapatite (HA)(Ca5(PO4)3OH), the stable phase of calcium phosphateat body temperature and pH>4.2 [1], is one of the mainconstituents of natural bone (B70wt%) [4] and isbeing investigated in a wide variety of forms foruse in different bone implant applications [1,3–5]. The

g author. Tel.: +1-617-548-9658; fax: +1-617-258-

s: cortiz@mit.edu (C. Ortiz).

front matter r 2004 Elsevier Ltd. All rights reserved.

materials.2004.02.053

nanoscale surface chemical properties (e.g. surfacefunctional groups, charge distribution), and morpholo-gical structure (e.g. grain size, shape, distribution,roughness) will critically influence the implant’s inter-action with the biological environment, and how wellthe implant subsequently performs in vivo [2].

When HA is implanted into a bony site, a cascade ofphysiochemical interactions takes place with the biolo-gical environment upon exposure to extracellular fluid,resulting in the build up of interfacial layers that bondthe bone tissue to the implant material [5–7]. The threemain processes thought to occur upon implantation areadsorption of ions and biomolecules, formation ofcalcium phosphate (apatite) layers, and interactionswith various cells [6]. Transmission electron microscopy(TEM) suggests the precipitation of microcrystals ofCO3-apatite directly onto the implant surface [2] fromcalcium and phosphate ions released from partiallydissolving ceramic HA and ions such as CO3

2� from thebiological fluid. The precipitation of apatite onto the

ARTICLE IN PRESSJ. Vandiver et al. / Biomaterials 26 (2005) 271–283272

HA could be a form of epitaxy [2,5,8] or be controlledby electrostatic interactions [9–12], thus yielding abioactive apatite layer [2,6,13,14]. It is expected thatsurface charge will have a strong influence on theprocesses of inorganic and organic deposition andstructural evolution on the implant material, especiallyin the initial stages of implantation. Reports of increasedcrystal growth of bone-like HA [15], cell adhesion [16],and osteobonding [17] to negatively charged surfaces ofelectrically polarized HA support this hypothesis. Si-substituted HA is known to have improved bioactivityboth in vitro and in vivo [18–20], which has beensuggested to be due to increased negative surface chargefrom substitution of PO4

3� groups with SiO44� groups

[18]. Stoichiometric HA (bulk Ca/P ratio 1.67 [3]) hasbeen shown to have a negative charge though zetapotential measurements of powder suspensions withgranule sizes 5–50 mm [9,18] which is thought to arisefrom the preferential concentration of PO4

3� groups tothe top few nanometers [18] of the surface [3,21]. It isbelieved this Ca deficient surface layer (Ca/P ratio B1.5[21]) is caused by solid–solution equilibrium during theprecipitation used to form stoichiometric HA wherebythere is the creation of a vacancy on one of the 10 Casites, the creation of a vacancy on one of the twohydroxyl sites, and protonation of one of the six PO4

3�

groups [21].Typically, surface charge is measured via the zeta

potential method [22,23] which yields an averaged, bulkvalue for colloidal dispersions, fibers, films, and othermicroscopic structures. Here, we employ the comple-mentary and relatively new technique of chemicallyspecific high-resolution force spectroscopy (HRFS) [24]that allows for the direct measurement of piconewton(pN) level forces in fluid between a nanosized probe tipfunctionalized with molecules of uniform and knownstructure, chemistry, and charge (e.g. self-assemblingmonolayers (SAMs)) as a function of separationdistance from a sample of interest. By comparing HRFSdata on approach of the probe tip to the sample surfaceto appropriate electrostatic double layer theory [25–27],an estimation of the surface charge per unit area, s (C/m2), of the sample of interest can be made. In this paper,we measure, for the first time, the normal electrostaticdouble layer forces between COO�- and NH3

+-termi-nated alkanethiol SAM-functionalized probe tips andbioactive dense, polycrystalline, phase pure syntheticHA via chemically specific HRFS with new nanome-chanical instrumentation [28] that allows for both high-resolution topographic imaging and HRFS withnanoscale spatial resolution. Nanomechanical data onapproach were compared to the nonlinear Poisson–Boltzmann-based electrostatic double layer theory forsurfaces of constant surface charge to predict sHA (C/m2) as a function of ionic strength (IS), position within avariety of grains, and across grain boundaries. This new

methodology allows for precise and positionally sensi-tive measurement of nanoscale surface properties thatcontrol bioactivity.

2. Materials and methods

2.1. Preparation of hydroxyapatite pellets

Synthetic HA pellets were prepared by an aqueousprecipitation reaction between calcium hydroxide(Ca(OH)2) and phosphoric acid (H3PO4) solution asdescribed in detail previously [2,29]. Analytical gradereagents (BDH AnalaR, Merck Ltd., Lutterworth, UK)were used. To ensure purity of the samples, the reactionvessels were thoroughly cleaned and rinsed withdeionized (DI) water prior to use. The precipitationprocess proceeded as follows: a calcium hydroxidesolution was made up by initially stirring 0.5mol ofCa(OH)2 in 1L of DI water. Similarly, 0.299mol ofH3PO4 solution was dissolved in 1L of DI water. Theprecipitation reaction occurred when the H3PO4 solu-tion was added dropwise to the Ca(OH)2 solution over aperiod of 2–3 h at ambient temperature. During theprecipitation process the pH of the reaction wasmaintained at 10.5 by small additions of 25% ammoniasolution. The precipitate was filtered under vacuum,thoroughly washed with approximately 100ml of DIwater, and then placed in a glass drying dish to dry at80�C for 24 h in air. The dried HA filter-cake was thencrushed using a pestle and mortar and sieved to aparticle size less than 75 mm in diameter. The greenpowder was then pressed into pellets using an isostaticpress and subsequently sintered to 1200�C for 2 h in air.The pellets have an average width of 3.8mm, an averagediameter of 8.64mm, and are >98% of the theoreticaldensity (3.1370.015 g/cm3) as measured by waterdisplacement.

2.2. General characterization

Purity of the HA pellets was determined via wideangle X-ray diffraction (WAXD) and X-ray fluorescencespectroscopy (XRF). Surface wettability was assessedvia contact angle measurements with DI water onadvancing and receding (Video Contact Angle System2000, AST Inc.). Grain size analysis, via grain diametermeasurements, was performed using a FEI/Philips XL30FEG environmental scanning electron microscopy(ESEM). To prepare the sample for ESEM, the HApellet was polished to a 3 mm finish using an aluminumoxide film on a uni-pol polisher (Geoscience InstrumentsCorp.) and then etched in 10% H3PO4 for 10 s. ThreeSEM images of different sites were then taken at10,000� and these images were analyzed using ScionImage (Scion Corporation) to determine grain size and

ARTICLE IN PRESSJ. Vandiver et al. / Biomaterials 26 (2005) 271–283 273

distribution. Surface topography was imaged using aDigital Instruments Nanoscope IIIA System Controllerwith multimode atomic force microscope in contactmode in air (CMAFM) with a Thermomicroscopes Si3N4V-shaped cantilever with a spring constant (kc)B0.01N/m (Appendix Tables 1 and 2).

2.3. Chemically specific HRFS with SAMs

2.3.1. Functionalization of probe tips with SAMs

HRFS experiments were performed with electroplatedAu-coated [30] Si3N4 cantilever probe tips chemicallyfunctionalized with alkanethiol SAMs terminated witheither COO� groups (11-mercaptoundecanoic acid, HS-(CH2)10-COOH, Aldrich—used as received) or NH3

+

groups (11-aminoundecanethiol, HS-(CH2)11-NH3, Do-jindo Laboratories—used as received). The Au-coatedcantilever probe tips were cleaned in O2 plasma for 10 sand immediately placed in 1mm SAM solutions in 100%ethanol for 18 h, after which they were rinsed with 100%ethanol and stored in Millipore water (18MO cmresistivity).

2.3.2. Probe tip end-radius measurements

The probe tip end-radius, RTIP; was measured by a JEOL6320FV field-emission high-resolution SEM. Tip radii weredetermined by digitally drawing a circle on a 100,000�SEM image within the point of the tip and comparing theradius of the circle to the scale bar on the image.

2.3.3. Averaged (blind) high-resolution force

spectroscopy

HRFS experiments were conducted using a 1-Dmolecular force probe (1DMFP) [28], to measure force,F (nN), vs. tip–sample separation distance, D (nm), onapproach and retract (F2D curves). A full description ofthis instrument, its limits, procedures for spring constantcalibration and raw data conversion, and details ofmeasurement errors are given in previous work [30]. In allHRFS experiments described in this paper, the springconstant of the cantilever is much less than the stiffness ofthe substrate such that little or no deformation occurs,leading to the D ¼ 0 vertical region of apparent infiniteslope in the high-force constant compliance regime.HRFS experiments were performed using two cantilevers(Thermomicroscopes, V-shaped, kc ¼ 0:01N/m); one witha COO�-terminated SAM probe tip (RTIP=64nm) andthe other with NH3

+-terminated SAM probe tip(RTIP=37.5 nm). HRFS experiments for the COO

�-terminated SAM probe tip (pKa(COO

�)B4.75) werecarried out in aqueous electrolyte solutions having ISs of0.001–1m NaCl and constant pH=5.9870.043 (hence-forth, referred to as pHB6), which were prepared bydissolving NaCl crystals in DI water. An equilibrationtime of 20min was allowed during solution changes andthe order of experiments was from low to high IS. HRFS

experiments for the NH3+-terminated SAM probe tip

(pKa(NH3+)B5.5) were carried out in aqueous electrolyte

solutions having IS of 0.01–1m formate buffer,pH=4.0270.005 (henceforth referred to as pHB4),prepared by mixing formic acid (HCHO2) with DI waterand adding NaCl crystals to get desired IS. Both NaCland formate buffer create only monovalent electrolytesolutions. The probe tip–surface force as a function oftip–sample separation distance on approach and retractwas measured at a z-piezo rate of 2mm/s. HRFSexperiments using each of these probe tips were firstconducted on Au-coated Si substrates [30] functionalizedwith the same SAM as the probe tip in varied IS solutionsof constant pH (pHB6 for COO�-terminated SAM andpHB4 for NH3

+-terminated SAM as described above) todetermine the surface charge per unit area of the SAM(described in detail in a later section) and then used toprobe the HA pellet. Approximately 30 individual HRFSprobes were performed and averaged at each of threerandom locations on the samples of interest.

2.3.4. Positionally specific high-resolution force

spectroscopy

HRFS was additionally performed using a 3-Dmolecular force probe (3DMFP) [28] which has all thesame features as the 1DMFP but additional capabilitiesto image the surface and perform positionally sensitiveHRFS in the plane of the sample surface. An Au-coatedSi3N4 cantilever probe tip (Thermomicroscopes, V-shaped, kc ¼ 0:03N/m, RTIP ¼ 89 nm) chemically func-tionalized with COO�-terminated SAM was used toimage and probe an HA sample simultaneously within avariety of grains and across grain boundaries in order tocompare forces to observed topographical surfacefeatures. The experiment was carried out in 0.01m NaClsolution (pH=5.94). The probe tip–surface forces as afunction of tip–sample separation distance were mea-sured on approach and retract at a z-piezo rate of 2mm/s.

2.3.5. Electrostatic double layer theory

HRFS data on approach were compared to thenumerical solutions of the full nonlinear electrostaticdouble layer theory based on a Poisson–Boltzmannformulation for a surface of constant charge per unit area[31]. The setup and parameters for this analysis are shownin Fig. 1. The Poisson–Boltzmann equation gives anexpression for the electrical potential, F (V), between twocharged planar surfaces in an electrolyte solution. For amonovalent 1:1 electrolyte, the solution has the form:

r2F ¼2fC0

ewsinh

fFRT

� �; ð1Þ

where f is the Faraday constant (96,500C/mol), C0 is thebulk concentration of ions (mol/m3), ew is the dielectricpermittivity of water (6.9� 10�10C/Nm2), R is the

ARTICLE IN PRESS

DεW

F

R TIP

chemicallyfunctionalized

probe tip

aqueous solution(IS= 0.001M−1M, pH = 6)

σsurface

RTIP

Charged Surface

σtip

Fig. 1. Schematic of chemically specific HRFS experiments showing

parameters used in Poisson–Boltzmann electrostatic double layer

model: stip is the charge per unit area of a hemispherical probe tip,ssurface is the charge per unit area of the surface, ew is the dielectricpermittivity of water, RTIP is the probe tip end-radius measure by

SEM, F is the measured probe tip–surface interaction force, and D is

the probe tip–sample separation distance.

4.0%

6.0%

8.0%

10.0%

ntag

e of

Gra

ins

(a)

J. Vandiver et al. / Biomaterials 26 (2005) 271–283274

universal gas constant (8.314 J/molK), and T is theabsolute temperature (K) [25–27]. Constant chargeboundary conditions were used such that the electric fieldat the substrate and probe tip surfaces was related to thesurface charge per unit area (i.e.rFjsurface¼ ssurface=ew andrFjtip¼ �stip=ew). In this study, constant charge bound-ary conditions on both bounding surfaces are employedbecause in the experiments, neither the probe tip nor thesubstrate is electrically connected to any source that wouldmaintain them at a constant potential [32]. A numericalmethod, known as the Newton method on finitedifferences, was used to solve the full nonlinear Poisson–Boltzmann equation [31]. For the 1DMFP experiments,control HRFS experimental data of the COO�-terminatedSAM probe tip vs. a COO�-terminated SAM planarsubstrate were compared to the theory (data not shown)and sCOO� was estimated to be �0.0084C/m

2 where thefixed parameters in the analysis were RTIP and the IS.Analogous NH3

+-terminated SAM HRFS experimentsand theoretical fits (data not shown) yieldedsNHþ

3=+0.0207C/m2. For the 3DMFP experiment on

HA sCOO� of �0.0178C/m2 was used. These probe tips of

known s were then used to test HA in varied IS solutionsand this experimental data were fit to the theoreticalsolution using sHA as the only free fitting variable.

0.0%

2.0%

.3-.

4

.6-.

7

.9-1

1.2-

1.3

1.5-

1.6

1.8-

1.9

2.1-

2.2

2.4-

2.5

2.7-

2.8

3.0-

3.1

Grain Size (µm)

Per

ce

(b)

Fig. 2. (a) ESEM image of acid etched HA pellet (10,000� ) and (b)grain size distribution of acid etched HA pellet (1.4870.68mm).

3. Results

3.1. General characterization: WAXD, contact angle,

ESEM, and AFM

The XRD experiments demonstrated the HA pelletsto be phase pure while XRF analysis confirmed that the

pellets had a Ca/P molar ratio of approximately 1.67and did not reveal any unexpected elements. Contactangle measurements with DI water gave an averaged(n ¼ 6 different positions on sample) advancing contactangle of 65.2�70.85� and an averaged receding contactangle of 18.1�72.9�, demonstrating that the HA surfaceis slightly hydrophilic. The large variation between theadvancing vs. receding contact angles (hysteresis)observed is likely due to water absorption throughinteraction with hydroxyl vacancies near the surface ofHA [21]. Grain size analysis was performed on theESEM images (e.g. Fig. 2a) where the diameter of everydistinct grain on three separate digital images wasmeasured, for a total of 93 grains. The grain sizedistribution (Fig. 2b) was found to have a mean value of1.4870.68 mm. Five 5 mm� 5 mm AFM scans wereanalyzed, and each scan encompassed several grains.The grain sizes determined via CMAFM images agreedwell with the ESEM images where 28 separate grainswere measured giving an average size of 1.1770.76 mm.The average root mean squared (RMS) surface rough-ness of the five 5 mm scans was 113.6721.0 nm, whichtakes into account several grains and grain boundaries.

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1 m1 µm1 m1 m1 µm

748 nm

1 m 20 0 n m20 0 n m200 nm

103 nm

1 µm

(a) (b)

(c) (d)

Fig. 3. CMAFM (Digital Instruments Multimode) images of as-

received HA pellet taken in air with Thermomicroscopes Si3N4 V-

shaped cantilever (kcB0:01N/m). (a) 2-D deflection image of a 5 mmscan across several grains (RMS surface roughness=113.6721.0 nm),(b) 3-D height image of image shown in (a), (c) 2-D deflection image of

single grain in image (a), and (d) 3-D height image of internal surface

of grain shown in image (c) (RMS surface roughness=17.973.2 nm).

(a)

0

0.05

0.1

0 5 10 15

Distance from Surface (nm)

Fo

rce

(n

N)

0.0

0.6

1.2

Fo

rce

/Ra

diu

s (m

N/m

)

IS=0.001M AverageIS=0.01M AverageIS=0.1M AverageIS=1M Average

(b)

-0.03

0

0.03

0 5 10 15

Distance from Surface (nm)

Fo

rce (

nN

)

-0.8

-0.4

0.0

0.4

0.8

Fo

rce/R

ad

ius

(mN

/m)

IS=0.01M AverageIS=0.1M AverageIS=1M Average

Fig. 4. 1DMFP HRFS data. Averaged data on HA as a function of IS

for (a) COO�-terminated SAM probe tip (RTIP ¼ 64 nm, pHB6) and(b) NH3

+-terminated SAM probe tip (RTIP ¼ 37 nm, pHB4).

J. Vandiver et al. / Biomaterials 26 (2005) 271–283 275

Additional scans inside five different grains wereperformed in order to quantify the surface roughnessinside the grains and the average RMS surface rough-ness was found to be 17.973.2 nm. Typical AFMimages are shown in Fig. 3.

3.2. Chemically specific HRFS: charged SAM probe tips

vs. HA

3.2.1. Averaged (blind) HRFS with 1DMFP

3.2.1.1. Approach. The averaged F2D curves withstandard deviations for the COO�-terminated SAMprobe tip vs. an HA pellet surface at pHB6 and variedIS (Fig. 4a) all show a purely repulsive, nonlinear forceson approach of the probe tip to the HA surface. Therepulsive forces observed in the 0.1 and 1m IS solutionsare observed to be significantly less in both magnitudeand range than the lower IS solutions of 0.01 and0.001m. A small attractive ‘‘jump-to-contact’’ wasobserved B20% of these 1DMFP data and the distance,Djump-to-contact ¼ 4:39 nm at 0.01m IS was used toestimate the Hamaker constant (A) of the surface [33]and found to be 4.33� 10�20 J. The averaged F2Dcurves with standard deviations for the NH3

+-termi-nated SAM probe tip vs. HA at pHB4 and varied IS

(Fig. 4b) all show an attractive, nonlinear force thatbegins at increasingly smaller distances from the samplesurface with increasing IS, i.e. 10.8, 9.2, and 6.9 nm at0.01, 0.1, and 1m IS, respectively, and exhibit minimumvalues of F=RTIPB0:20; B0.17, and B0.25mN/m atDB3:4; DB3:7; and DB1:9 nm, respectively. Theseresults clearly suggest an electrostatic double layerorigin for the surface interaction force with the HApossessing a net negative surface charge. One observa-tion of note was that the variance in the HRFS data forthe COO�-terminated SAM probe tip with position onthe HA surface (Fig. 5a) was significantly greater thanthe variance of HRFS curves with position on theCOO�-terminated SAM (Fig. 5b). Hence, the effect ofposition was investigated further using the 3DMFP anddiscussed in the following section.

In order to estimate sHA; the averaged HRFS curvesshown in Fig. 4 were fit to the numerical solution of thePoisson–Boltzmann theory for surfaces of constantcharge per unit area using the following fixed parameters:surface charge of probe tips (sCOO�=�0.0084C/m

2 orsNHþ

3=+0.0207C/m2), IS=0.01m, RTIP (RTIP(COO�)=

64nm or RTIP(NH3+)=37nm), and sHA (C/m

2) as theonly free variable fitting parameter [33]. HRFS data of

ARTICLE IN PRESS

0

0.02

0.04

0.06

0 5 10 15 20 25

Distance from Surface (nm)

For

ce (

nN)

0.0

0.3

0.6

0.9 Force/R

adius (mN

/m)

Position 1Position 2Position 3

0

0.02

0.04

0.06

0 5 10 15 20 25

Distance from Surface (nm)

For

ce (

nN)

0.0

0.3

0.6

0.9 Force/R

adius (mN

/m)

Position 1Position 2Position 3

(a)

(b)

Fig. 5. 1DMFP HRFS data. Averaged data for COO�-terminated

SAM probe tip at three randomly selected positions (pH=5.94,

IS=0.01m) vs. (a) HA and (b) COO�-terminated SAM planar surface.

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

0 5 10 15 20 25 30

Distance from Surface (nm)

For

ce (

nN)

-0.2

0.1

0.4

0.7

1.0

1.3

Force/R

adius (mN

/m)

MFP DataStd DevTheoretical Fit

-0.03

-0.01

0.01

0.03

0.05

0.07

0.09

0 5 10 15 20 25 30

Distance from Surface (nm)

For

ce (

nN)

-0.8

-0.2

0.4

1.0

1.6

2.2

Force/R

adius (mN

/m)

MFP DataStd DevTheoretical Fit

(b)

(a)

Fig. 6. 1DMFP HRFS data. (a) Averaged data for COO�-terminated

SAM probe tip vs. HA (pH=5.94) and Poisson–Boltzmann theoretical

fit (fixed parameters: sCOO� ¼ �0:0084C/m2, IS=0.01m,

RTIP ¼ 64 nm-sHA=�0.005C/m2). (b) Averaged data for NH3

+-

terminated SAM probe tip vs. HA (pH=4.01) and Poisson–

Boltzmann theoretical fit (fitting parameters: sNHþ3=+0.0207C/m2,

IS=0.01m, RTIP ¼ 37 nm-sHA ¼ �0:0048C/m2).

J. Vandiver et al. / Biomaterials 26 (2005) 271–283276

the COO�-terminated SAM probe tip vs. HA in 0.01m ISfit reasonably well to the theoretical Poisson–Boltzmanntheory as shown in Fig. 6a which yielded a best fitparameter of sHA ¼ �0:0050C/m

2. HRFS data of anNH3

+-terminated SAM probe tip vs. HA in 0.01m ISsolution, through comparison with Poisson–Boltzmanntheory, yielded a similar result of sHA ¼ �0:0048C/m

2

(Fig. 6b).

3.2.1.2. Retract. The retract F2D curves were alsoexamined and the average adhesion forces and distanceswith standard deviations for the COO�-terminatedSAM probe tip probing HA vs. solution IS werecalculated (Fig. 7). The adhesion force magnitudes at0.1 and 1m are statistically lower (po0:01) than theadhesion force magnitudes at 0.001 and 0.01m althoughthe forces between 0.1 and 1m were not statisticallydifferent, nor were the forces between 0.001 and 0.01m.The adhesion pull-off distances ranged up to 60 nm andwere also statistically lower (po0:01) at higher IS exceptfor 0.001 compared to 0.01. The adhesion distances aresimilar to the surface roughness within individual grains(17.973.2 nm).

The Derjaguin–Muller–Toporov elastic contact me-chanics theory [34,35] can provide an upper limit

estimate for the number of molecular contacts that existat the maximum compressive force and contribute to theadhesive interaction. The elastic contact area betweenthe probe tip and a planar surface, Acontact ¼ pa2; can becalculated from a; the elastic contact area radius, asfollows:

a ¼ðF þ FadhesionÞRTIP

K

� �1=3;

K ¼4

3

1� n21E1

þ1� n22

E2

� ��1; ð2Þ

where K is the reduced elastic modulus, n the Poisson’sratio, E the Young’s (elastic) modulus, E1(Au)=64G-GPa, n1(Au)=0.44, E2(HA)=95GPa, and E2(HA)=0.28. Taking a maximum compressive force of B1 nN atD ¼ 0 and a maximum observed adhesive force ofB1 nN, Acontact was found to be B5.2 nm

2 for the 64 nmradius COO�-terminated SAM probe tip used for the1DMFP experiments. Since the area per SAM moleculeis approximately 0.216 nm2 [36], the number of mole-cules within the maximum elastic contact area corre-sponds to 24. Hence, the maximum adhesive force perSAM molecule within this elastic contact area is

ARTICLE IN PRESS

-1.6

-1.2

-0.8

-0.4

0.0

0.0001 0.001 0.01 0.1 1 10

Ionic Strength (M)

Adh

esio

n F

orce

(nN

)

-25

-20

-15

-10

-5

0 Adhesion Force/R

adius(m

N/m

)0

20

40

60

80

0.0001 0.001 0.01 0.1 1 10

Ionic Strength (M)

Adh

esio

n D

ista

nce

(nm

)

(a)

(b)

Fig. 7. Analysis of 1DMFP HRFS retract data (RTIP ¼ 64 nm,pHB6) vs. IS: (a) averaged adhesion forces and (b) averaged adhesiondistances on retract between COO�-terminated SAM probe tip and

HA vs. solution IS.

J. Vandiver et al. / Biomaterials 26 (2005) 271–283 277

B42 pN, an upper limit since the contact radius willdecrease from the maximum value before piezo reversaland upon retract, as well as the fact that the adhesionforce taken was the maximum observed.

3.2.2. Positionally specific HRFS with the 3DMFP

3.2.2.1. Approach. As mentioned previously, when per-forming HRFS experiments with the 1DMFP, avariance in the experimental data with position on theHA surface was noticed which was significantly greaterthan the variance of HRFS curves with position on theCOO�-terminated SAM (Fig. 5). Hence, further inves-tigation was carried out with the 3DMFP where AFMimaging and HRFS could both be performed together,making it possible to correlate intersurface forces withtopographical features. The first set of HRFS experi-ments (labeled Scan 1) traversed three different grainson the HA surface corresponding to the positions shownas ‘‘x’s’’ in the CMAFM deflection (topographical)image given in Fig. 8a. Underneath the AFM image inFig. 8a, a topographical profile of the surface height vs.horizontal distance across the image (corresponding tothe horizontal black line in the top image of Fig. 8a) isgiven and shows the surface geometry of the probedarea. A second smaller scan (labeled Scan 2) was made

at the grain boundary between probe positions 5 and 6of Scan 1, and the surface locations of the HRFSexperiments taken across the grain boundary are shownas ‘‘x’s’’ in Fig. 8b. Fig. 8c shows the averaged F2Dcurves including maximum standard deviation for theprobe positions of Scan 1. Fig. 8d shows the averagedF2D curves including maximum standard deviation forthe probe positions of Scan 2. Position 5 on Scan 1 andposition 1 on Scan 2 probe the same topographical face.The probe at point 4 on Scan 2 showed unusualnanomechanical behavior, most likely due to geometricand interlocking effects between the probe tip and thegrain boundary. A positional variance of the surfaceforces was observed in both of these data sets and so thedata were analyzed in this context. In particular, thepositions were grouped by facet as shown in Fig. 9,where a facet was defined as a distinct topographicalface whose area had a relatively constant slope.

Generally, the 3DMFP HRFS data and the 1DMFPHRFS data taken at 0.01m IS were consistent inmagnitude and range, even using different probe tipswhere variations always arise due to geometry and othernanoscale factors such as variations in surface rough-ness, SAM density, etc. The 3DMFP data show slightlylarger F=RTIP correlating with a higher probe tip surfacecharge density than that used for the 1DMFP.

Using the same process as for the 1DMFP data, the3DMFP HRFS data on approach were compared toelectrostatic double layer theory and sHA for eachposition was calculated by averaging the fitted sHA forthree individual curves at that position. Figs. 10a and bshow the averaged sHA for each probe position forScans 1 and 2, respectively, along with standarddeviations. The sHA of each facet was examined sincefacets likely have different exposed crystallographicplanes with differing numbers of exposed chargedgroups causing sHA variations. Statistical analysis showsthe average sHA for each facet to be significantlydifferent from the others in nine out of 10 comparisons(po0:05). The average sHA over all positions in bothscans was calculated in this experiment to be�0.018870.0198C/m2. The magnitude of the forceand hence, the fitted value of sHA; showed variationswithin individual grains, between differing grains, andacross the grain boundary. Fig. 10c shows sHA vs. thedistance of the probe position from the grain boundary(left side of grain boundary, including data from bothscans). A linear regression of these data points gives acorrelation factor of >98% which is statisticallysignificant (po0:05) and a slope of �0.19C/m2/mm.This trend is consistent with surface charge being due toion arrangements in crystallographic planes whichbecome disordered and shifts from one plane to anotherat grain boundaries.

Since the surface charge calculation is based on anapproximated fit to the HRFS data, specific data from

ARTICLE IN PRESS

Fig. 8. (a) Scan 1 CMAFM deflection image taken using 3DMFP with COO�-terminated SAM probe tip in fluid (RTIP ¼ 89 nm, IS=0.01m,pH=5.94) showing specific positions (X ’s) in three grains probed via HRFS. Below is a plot showing the height profile along the solid black line in

the image. (b) Scan 2 CMAFM deflection image taken using 3DMFP with COO�-terminated SAM probe tip in fluid (RTIP ¼ 89 nm, IS=0.01m,pH=5.94) showing specific positions (X ’s) in two grains probed via HRFS. Below is a plot showing the height profile along the solid black line in the

image. (c) Averaged HRFS data of seven probe locations in Scan 1 labeled in (a) (each position, n ¼ 5). (d) Averaged HRFS data of six probelocations in Scan 2 labeled in (b) (each position, n ¼ 5).

1 m

Face t 1

Fa cet 2

1

23

45 6

7

Face t 3

Face t 4

Fa cet 5

1µm

Facet 1

Facet 2

1

23

45 6

7

Facet 3

Facet 4

Facet 5

Fig. 9. Labeling for different facets among the grains imaged in Scan 1.

J. Vandiver et al. / Biomaterials 26 (2005) 271–283278

each individual curve was also examined. The forcebetween the probe tip and HA at one Debye length awayfrom the surface (k�1 ¼ 3 nm) was recorded for eachcurve (n ¼ 5) at each position in each scan (data notshown). An increase in this force would indicate a largersurface charge per unit area if the force is caused mainlyby electrostatics. The trends for surface charge and forcebetween the probe tip and HA at one Debye length awayfrom the surface were consistent.

3.2.2.2. Retract. Similar to the 1DMFP data, theretract F2D curves were also examined and the averageadhesion forces and distances for the COO�-terminatedSAM probe tip probing HA were recorded. The averageadhesion force magnitudes and the adhesion pull-offdistances were similar to the values obtained from the1DMFP experiment and although they differed per facet

ARTICLE IN PRESS

-0.08

-0.06

-0.04

-0.02

0.00

0 3 6 7

Position

Sur

face

Cha

rge

(C/m

2 )

Facet 1 Facet 2 Facet 3 Facet 5

-0.08

-0.06

-0.04

-0.02

0.00

0 2 3 4 6

Position

Sur

face

Cha

rge

(C/m

2 )

Facet 3 Facet 4

y= -0.1877x - 0.0044 R2 = 0.9843

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.0 0.1 0.2 0.3 0.4

Distance from Center of Grain Boundary (µm)

Sur

face

Cha

rge

(C/m

2 )

1 2 4 5

1 5

(c)

(a)

(b)

Fig. 10. Approximation of surface charge per unit area from 3DMFP

HRFS data (fixed parameters: sCOO� ¼ �0:0178C/m2, IS=0.01m,

RTIP ¼ 89 nm, pH=5.94). (a) Averaged (n ¼ 3) surface chargecalculated from fitting HRFS data at each specific probe position on

Scan 1 shown in Fig. 8a to the Poisson–Boltzmann theoretical model.

(b) Averaged (n ¼ 3) surface charge calculated from fitting HRFS dataat each specific probe position on Scan 2 shown in Fig. 8b to the

Poisson–Boltzmann theoretical model. (c) Linear regression of

Poisson–Boltzmann fitted 3DMFP HRFS data to left of grain

boundary between facet 3 and 4.

J. Vandiver et al. / Biomaterials 26 (2005) 271–283 279

there were no obvious correlations with surface charge.Similar to the 1DMFP experiments, Acontact wascalculated to be B6.5 nm2 for the 89 nm radiusCOO�-terminated SAM probe tip used for the 3DMFPexperiments, corresponding to 30 SAM molecules and amaximum adhesive force per SAM molecule of 33 pN.

4. Discussion

In this paper, we have shown how the sensitive andpowerful nanomechanical technique of chemically andspatially specific HRFS can measure the nanoscale forcesthat exist at the interface between a biomaterial surfaceand physiological fluids. Nanosized probe tips of knownchemistry and geometry were used to test a promisingbone implant material, i.e. phase pure, dense, polycrystal-line synthetic HA, and fits of these data on approach toelectrostatic double layer theory [25–27] enabled approx-imation of the HA surface charge per unit area, sHA: Onretract of the probe tip away from the surface, nanoscaleadhesive interaction forces, Fadhesion; were measured. Oneof this most unique aspects of the methodology presentedin this paper is that it allows for the determination of localnanoscale variations in sHA and Fadhesion within grains andacross grain boundaries, important information unable tobe obtained by other standard techniques such as zetapotential measurements. Nanoscale variations in the localinterface potential are certain to affect the adsorptionprocess of ions and biomolecules, formation of calciumphosphate (apatite) layers, and interactions with variouscells which determine the build up of interfacial layers thatbond the bone tissue to the implant material. With the newcapabilities presented in this paper, the relation of suchlocal nanoscale parameters to bioactivity will be able to beexplored, for example by correlating sHA and Fadhesionmeasured by HRFS measurements with the kinetics ofapatite-layer growth when the same samples are incubatedin simulated body fluid (SBF) or implanted in vivo. Inaddition, chemically specific HRFS will be able to detect atextremely high resolutions the differences in nanoscalesurface properties between the original HA surface and theprecipitated bone-like apatite layer for example, in SBF.Lastly, the same experimental and theoretical methodol-ogy can be used for studying the nanoscale interactionsbetween biomaterial surfaces and proteins and cells sincethe nanosized probe tips can be functionalized accordingly.Overall, it is clear that this method holds great potentialfor fundamental research on the physicochemical processesoccurring at biomaterial interfaces and elucidating themolecular origins of bioactivity. Following is a discussionof specific aspects of the data presented in this paper.

4.1. Approach HRFS data

All trends in HRFS experimental data with IS andtheoretical fits support the fact that on approach theintersurface interaction is dominated by electrostaticdouble layer forces and that HA has a net negativesurface charge per unit area, sHA; ranging from �0.0037to �0.072C/m2 with an average value of �0.019C/m2,which is similar to that found for the COO�-terminatedSAM probe tip (sCOO�B0.018C/m

2). The net negativesurface charge of HA is consistent with previous reports

ARTICLE IN PRESSJ. Vandiver et al. / Biomaterials 26 (2005) 271–283280

[9,18,37,38] and as mentioned in Section 1 has beensuggested to be due to preferential surface migration ofPO4

3� groups [3,21]. Considering the maximum magni-tude of sHA (�0.072C/m

2) obtained by HRFS, forcomparison, if one was to consider an alkanethiolSAM of Ca2+ and PO4

3� terminal groups with roughly 1group/0.22 nm2 [36] and a Ca/P ratio of B1.5,equivalent to the surface Ca/P ratio in HA [21], thisSAM would have a fully ionized charge density of�0.74C/m2. Therefore, the HA surfaces measured havea B10� smaller charge density than would be expectedfrom a densely packed collection of phosphate andcalcium ions with a Ca/P ratio of 1.5.

4.2. Spatial heterogeneity of surface charge of

hydroxyapatite

Geometrical calculations have ruled out the variancein apparent surface charge being due to the slope of thesample surface as shown in Appendix A. Unlike SAMlayers, the HA pellets do not present a uniform chargeover its surface but is locally (at the nanoscale level)heterogeneous. The degree to which these nanoscaleheterogeneities are relevant to Ca2+ binding, apatiteprecipitation, protein adsorption, and ultimately bio-compatibility is an area of great interest and is currentlybeing investigated further.

4.3. Relation of HRFS data to zeta potential

measurement

Until recently, the majority of surface charge mea-surements have been accomplished through zeta poten-tial measurements. Zeta potential is dependant onsurface charge density and is defined as the electrostaticpotential at the hydrodynamic shear plane which islocated approximately at the Stern surface. The Sternsurface is the boundary between a layer of more rigidlybound counterions and the diffuse electrostatic doublelayer of highly mobile, hydrated counterions, and istypically a few molecular diameters from the surface[22]. Zeta potential measurements are averaged, bulkmeasurements most often performed via electrophoresison dilute colloidal suspensions or by the streamingpotential method on fibers, films, and other macroscopicstructures [39], and have the variability of particle size[9,40] and IS dependence [22].

The negative sign for surface charge of phase pure HAmeasured in this paper is in agreement with zetapotential measurements of HA in the literature[9,37,38,41]. In previously reported work [18], the zetapotentials of pure, synthetic, dense polycrystalline HAparticles were measured at varied pH. At pH 6, similarto the pH at which the experiments in this paper werecarried out, and IS 0.0001m, the zeta potential for theseHA particles was measured to be approximately

�35mV [18]. When the surface potential is calculatedvia the nonlinear Poisson–Boltzmann equation from theaverage surface charged measured by 3DMFP in thispaper, s(HA) =�0.0188C/m2, a value of �64mV isobtained. Previous zeta potential measurements areB50% of the potential calculated from the HRFS data,which is consistent with previously published data [42,43]that found zeta potential measurements to be 30–50% ofHRFS derived surface potentials for zirconia surfaces inpoly(acrylic acid) solutions probed with spherical zirconiacolloidal probe tips and poly(ether ether ketone) probedwith Si3N4 probe tips, respectively. It has been hypothe-sized that the disagreement between zeta potentialmeasurements and HRFS derived surface potentials isdue to the potential drop in the immobilized liquid layerclose to the surface which moves with the particle in zetapotential measurements, but is not included in Poisson–Boltzmann theory [42]. The surface charge calculated inthis paper via HRFS data compared to Poisson–Boltzmann theory is the effective charge at the Sternsurface since electrostatic double layer theory is validonly within the diffuse double layer that begins at theStern surface [22]. The HRFS surface charge model usedin this paper should more closely resemble the electro-static interaction of a biomacromolecule or cell ap-proaching a biomaterial surface, where the effectivecharge at the Stern surface is what the biomacromoleculeor cell feels inside the diffuse double layer.

4.4. Retract HRFS data

Both the 1DMFP and 3DMFP data produced similaradhesion forces and distances, with a maximum adhesiveforce per SAM molecule of 42pN, clearly typical of anoncovalent interaction (e.g. hydrogen bonding, van derWaals, or ionic). The adhesion forces measured are likelynot hydrophobic interactions since HA is relativelyhydrophilic as seen in the contact angle measurements.Scarcity of jump-to-adhesion occurrences indicates vander Waals forces to be minimally important and the lackof consistent trend in adhesion forces and distances withsurface charge indicates the interactions is unlikely tohave a significant component that is electrostatic innature. Adhesion interactions most likely have contribu-tions from both surface forces and surface topologywhich can be difficult to deconvolute.

5. Conclusions

The average surface charge for the phase pure,polycrystalline hydroxyapatite studied here was foundto be B�0.02C/m2 which correlates reasonably wellwith zeta potential measurements reported in theliterature [9,37,38,41]. The surface charge varies withnanoscale position on the surface and across grain

ARTICLE IN PRESS

Table 2

Definition of abbreviations

Abbreviation

AFM Atomic force microscopy

CMAFM Contact mode atomic force microscopy

J. Vandiver et al. / Biomaterials 26 (2005) 271–283 281

boundaries and is most likely associated with exposedcrystal plane since different facets in the same grain havestatistically different surface charges. Extra PO4

3�

groups at the surfaces cause all surfaces to have anegative charge and variance is most likely due todifferent arrangements on each crystal plane of theadditional charged ions making up the HA lattice. It isexpected that surface charge has a strong influence onthe processes of inorganic and organic deposition andstructural evolution on the implant material, especiallyin the initial stages of implantation. New HRFSmethodologies can give positionally sensitive measure-ment of nanoscale surface charge variation, which is aninitial step in elucidating electrostatic effects on thebioactivity of HA.

DI Deionized

F2D curves Force vs. tip–sample separation distance curves

HA Hydroxyapatite

HRFS High-resolution force spectroscopy

IS Ionic strength

MFP Molecular force probe

RMS Root mean squared

SAM Self-assembled monolayer

SBF Simulated body fluid

SEM Scanning electron microscopy

TEM Transmission electron microscopy

VDW Van der Waals

WAXD Wide angle X-ray diffraction

XRD X-ray diffraction

XRF X-ray fluorescence spectroscopy

Acknowledgements

The authors thank the laboratories of Prof. MichaelRubner (Department of Materials Science and Engi-neering, MIT) and the MIT Center for Materials Scienceand Engineering for training and use of their equipment,Joonil Seog and Laurel Ng for MFP and AFM training,respectively. Funding was provided by the Cambridge-MIT Institute (CMI) and a Whitaker Foundationgraduate fellowship (DD).

Table 1

Definition and units of parameters

Parameter Name

a Elastic contact radius between probe tip and sur

Acontact Elastic contact area between probe tip and surfa

A Hamaker constant

C0 Bulk concentration of ions

D Probe tip–surface separation distance

Djump-to-contact Separation distance at which the cantilever exhib

E Young’s (elastic) modulus

ew Dielectric permittivity of waterf Faraday constant

F Probe tip–surface force

Fadhesion Maximum attractive force measured on retractio

F=RTIP Force per probe tip end radiusK Reduced modulus for probe tip and surface

kB Boltzmann’s constant

kc Cantilever spring constant

n Number of force vs. distance curves

pKa The pH at which the ionizable compound is 50%

R Universal gas constant

RTIP Probe tip end radius measured experimentally b

T Absolute temperature

Z Direction normal to sample surface

F Electrostatic potentials Surface charge per unit areak�1 Electrical interaction Debye lengthn Poisson’s ratio

Units: C=Coulombs, J=Joules, K=Kelvins, m=meters, N=Newtons, nN

Appendix A

Geometrical effects

Since the HA sample probed is topographicallyheterogeneous, the variance in HRFS curves due togeometrical effects was evaluated. HRFS was approxi-mated as the interaction between a spherical probe tip

Value/units

face nm

ce nm2

J

mol/m3

nm

its an attractive jump to the surface nm

Pa

6.9� 10�10 C/Nm2

96,500C/mol

nN

n nN

mN/m

Pa

1.38� 10�23 J/KN/m

protonated and 50% deprotonated

8.314 J/molK

y SEM nm

K (RT=298)

Unitless

V

C/m2

nm

Unitless

=nanoNewtons, nm=nanometers, Pa=Pascals, and V=Volt.

ARTICLE IN PRESS

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0 5 10 15 20 25

Slope (degrees)

Sur

face

Cha

rge

(C/m

2 )

Fig. 12. Analysis of 3DMFP HRFS data (fitting parameters:

sCOO� ¼ �0:0178C/m2, IS=0.01m, RTIP ¼ 89 nm, pH=5.94) vs.

sample surface slope. Averaged (n ¼ 3) surface charge calculated fromfitting HRFS data at each probe position to the P–B theoretical model

vs. sample surface slope. Hollow data points represent negative slopes.

J. Vandiver et al. / Biomaterials 26 (2005) 271–283282

and a sloped surface (Fig. 11a). Variable D is the tip-surface distance measured by the MFP. However, due tothe possible slope of the surface there are portions of theprobe tip that could be interacting with the surface atdistance D0; which would change how the tip–surfaceinteraction area varied with distance. The change in tipinteraction distance vs. D at various possible surfaceslopes is shown in Fig. 11b. Height profiles via the3DMFP software were taken across the probe locationsas demonstrated in Figs. 8a and 9a, and the slope of theprofile corresponding to probe location was calculated.Absolute values of slopes ranged from 0.34� to 22.64�.The plot of averaged (n ¼ 3) Poisson–Boltzmann fittedsurface charge vs. slope as shown in Fig. 12 demon-strates no significant trend. The R2 value was found tobe 0.0292 while the R2 value needed for statisticalsignificance (p=0.05) is at least 0.532. In conclusion, therange of sample surface slope is not large enough tosignificantly change tip interaction area or force data.This is consistent with geometrical calculations since asample surface slope of 22.64�, the maximum slopeprobed in this experiment, would change the tipinteraction area by less than 8% at 15 nm (5k�1 at0.01m), the approximate maximum range of electro-static interactions at 0.01 IS. Because the geometricalconstraints do not significantly alter the force curves,

Tip

θ

D: Measured Tip-SurfaceDistance from MFP

D’: Real Tip-SurfaceDistance

Slope of Surface

0

750

1500

2250

3000

3750

4500

0 5 10 15 20 25 30

D, Tip-Surface Distance from MFP (nm)

Tip

Inte

ract

ion

Are

a (n

m2 )

d

eter

min

ed b

y D

'

Theta = 0 degTheta = 10 degTheta = 20 degTheta = 30 degTheta = 40 degTheta = 50 degTheta = 60 deg

(b)

(a)

(

Fig. 11. (a) Geometrical considerations to be taken into account when

probing a nonflat surface. (b) Change in interaction area vs. measured

given distance from surface due to slope of sample surface.

trends seen in force curves are likely due to electrostaticdifferences.

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Nanoscale variation in surface charge of synthetic hydroxyapatite detected by chemically and spatially specific high-resolutionIntroductionMaterials and methodsPreparation of hydroxyapatite pelletsGeneral characterizationChemically specific HRFS with SAMsFunctionalization of probe tips with SAMsProbe tip end-radius measurementsAveraged (blind) high-resolution force spectroscopyPositionally specific high-resolution force spectroscopyElectrostatic double layer theory

ResultsGeneral characterization: WAXD, contact angle, ESEM, and AFMChemically specific HRFS: charged SAM probe tips vs. HAAveraged (blind) HRFS with 1DMFPApproachRetract

Positionally specific HRFS with the 3DMFPApproachRetract

DiscussionApproach HRFS dataSpatial heterogeneity of surface charge of hydroxyapatiteRelation of HRFS data to zeta potential measurementRetract HRFS data

ConclusionsAcknowledgementsGeometrical effects

References