Adsorption of calf serum organic matter from a phosphate-buffered solution was studied using the electrochemical quartz crystal microbalance with additional dissipation measurements. Two types of crystal surfaces were used: one rough with micrometer-range surface features and one with roughness in the low nanometer range. The results showed that the adsorption of the organic material was about 1.5 orders of magnitude larger on the rough surface and almost independent of serum concentration in the electrolyte. The adsorption rates were found to increase with increasing serum concentration. For rough crystals, the adsorption kinetics were interpreted with the Johnson–Mehl–Avrami–Kolmogorov model, indicating an initial growth phase according to the tn-law, followed by a slower growth as the nucleation sites fill up. This study suggests that specific surface sites are critical to promote adsorption of proteins on a titanium surface.

The interaction between a passive metal surface and corporal fluids is interesting from many aspects: improving the in-growth of fixed parts in a prosthesis, understanding wear phenomena in articulating parts in hip joints, or avoiding inflammatory reaction and possibly rejections of materials implanted in the body. In the scientific literature, one can find a number of ideas on how the proteins may interact with a metal surface, many of which start off with a Langmuir isotherm and then add modifications to accommodate effects of rotating the protein, concentration, and serum composition. In this study, we investigate the properties of the metal surface with particular focus on how roughness influences protein adsorption. To accomplish this, we introduce a calibration concept for the electrochemical quartz crystal microbalance with dissipation technique (EQCM-D) that quantifies the mass and viscous loading response into real-time replacement and viscous loss curves. The resulting curves are explained by a concept focusing on nucleation.

Protein interaction with metal surfaces is a highly complex phenomenon. It has been reviewed by Rabe et al.1 and more recently by Talha et al.2 Rabe et al. list the important parameters for protein adsorption, starting with pH. If it is close to the isoelectric point, the protein is neutral. If the pH is lower, the protein is charged positively, whereas it carries negative charge at higher values. The maximum mass load is normally obtained near the isoelectric point. A charge difference between the protein and the substrate also has a significant influence on the protein adsorption rate. Ions known to restrain protein adsorption include ClO4, SCN, and NH4+, whereas SO42−, F, Mg2+, and Ca2+ act in favor. On the solid side of the liquid/surface interface, the important parameters include surface energy, polarity, charge, and morphology. Protein orientation effects can be used to explain overshoot phenomena during adsorption. Recently, the interaction between bovine serum albumin and biomedical alloys has been reviewed by Klok et al.3 For CoCrMo alloys and stainless steels, protein adsorption was potential dependent.

From an experimental standpoint, one of the more common tools for studies of protein adsorption is fluorescence detection. Other useful tools include infrared absorption, ellipsometry, optical waveguides, or techniques based on neutron absorption, all of which are discussed in the review by Rabe et al.1 One powerful technique for an in situ analysis of small weight changes is EQCM-D. In addition to mass sensing, the dissipation provides information of the viscous damping of the liquid environment, which gives information on the rigidity of adsorbates. For small changes in mass, there is a linear relation in the resonance frequency. To maintain the linear relation between mass and frequency, changes have to be small, which limits the EQCM technique to thin film deposits. The sensing coatings can be plated from a liquid phase or made with techniques such as physical vapor deposition (PVD). The thin film requirement limits the freedom of experimental design, including factors such as roughness, chemistry, and layer thickness. The use of EQCM-D technique has been used extensively by Rodahl and Kasemo. One example is an article by Höök et al. who used ellipsometry, EQCM-D, and optical waveguide lightmode spectroscopy to quantify the adsorption of proteins on a titanium surface.4 They interpreted the data with a geometrical formalism called “random parking isotherm.”

For adsorption studies in liquids, it is necessary to consider the viscous load on the quartz surface. This was first suggested by Kanazawa and Gordon.5 Later, Rodahl et al. developed and commercialized the technique to allow for measuring the damping of the oscillations—the energy dissipation—and applied this technique to protein interaction with titanium surfaces.6 Access to energy dissipation and frequency changes for a set of harmonics makes it possible to construct a depth-resolved model of the interaction between the quartz surface and the liquid.7 More recently, Jia et al. used this technique to investigate the orientation dependence of proteins adsorbing on different types of surfaces.8 It is also possible to compare the response to protein exposure of bulk and QCM samples, as discussed by Liamas et al.9 

The surface roughness of the quartz crystal has a significant influence on the response of the QCM to a mass change. For an ideally smooth surface, the flow can be considered laminar, which leads to a viscous load proportional to ρlηl. Surface roughness might lead to a turbulent flow between the quartz surface and the electrolyte. For moderately rough surfaces, this can be modeled using perturbation theory. For rougher surfaces, the response will be determined by two characteristic length scales: that of the surface roughness and the interaction volume between the surface and the solution, which is strongly dependent on the measurement frequency. If these lengths are close to equal, there is no roughness dependence, as shown by Urbakh and Daikin.10 The interaction between proteins on a rough quartz surface could be expected to be more complex, as the length scale of the proteins need also to be considered. Studies of protein adsorption on titanium surfaces have been carried out by Rockwell et al., who used sputter-deposited titanium samples with roughness at different length scales. By ex situ electron probe x-ray microanalysis measurements of carbon contents on the surface, they found that the adsorption of fibrinogen and albumin increased with roughness. They mention curvature as one important parameter affecting the adsorption mode, where a high curvature (smaller features) favor end-on protein binding and, thus, more adsorbed protein per available surface.11,12 The importance of the surface roughness over different scales has also been illustrated by Chauvy et al., who produced nano- and microscale roughness and studied the proliferation of osteoblasts on the surface.13 In this article, we study the interaction between calf serum and two different titanium surfaces with lateral dimensions of the rough surface in the 5–10 μm range. It illustrates the importance of the surface condition to the adsorption of proteins.

Crystals with a titanium PVD coating were purchased from QuartzPro (Järfälla, Sweden) in two conditions: a smooth surface and a rough surface. The smooth surface had an Ra value of 34 nm, whereas the rough surface, Ra = 340 nm, showed grooves in the micrometer range, see Fig. 1. The crystals were 5 MHz with 14 mm diameter. The rough surface only oscillated at the base frequency. For the smooth surface, the titanium coating was about 50 nm to allow for recording of all available harmonics. The working electrode side was covered with a circular deposit covering the top side, and the oscillating electrode on the back side was of a keyhole design placing the mass sensing area at the center of the quartz. The areas of the rough quartz crystals were for the working electrode AWE = 1.36 cm2 and the mass sensing area AOsc = 0.33 cm2, and for the smooth quartz crystals, AWE = 1.12 cm2/AOsc = 0.25 cm2.

FIG. 1.

Scanning electron micrographs from smooth (a) and rough (b) surfaces together with a 3D-rendering of the rough surface (c). The smooth surface was very flat, whereas the rough surface contained grooves in both nanometer and micrometer ranges.

FIG. 1.

Scanning electron micrographs from smooth (a) and rough (b) surfaces together with a 3D-rendering of the rough surface (c). The smooth surface was very flat, whereas the rough surface contained grooves in both nanometer and micrometer ranges.

Close modal

The electrochemical quartz crystal microbalance was an X1 system from Advanced Wave Sensors (AWS) S.L. Paterna-ES. It has an operating range from 4 to 160 MHz with a maximum frequency resolution of 0.1 Hz. The number of harmonics is limited by the crystal quality. For smooth crystals, they were acquired up to no. 13, but for rough crystals, only the ground tone was available. The specified resolution in mass sensitivity in liquid is 0.6 ng cm−2, and the normal dissipation sensitivity in liquid is 3.5 × 10−8, specified at 25 °C. For all experiments, the temperature control unit X1-TCU was set to 37.0 °C. All solutions were preheated before being injected into the cell, which accommodated a total volume of about 10 ml. The electrochemical cell used was of the quick lock type, applied in combination with a preheated electrolyte. No stirring was performed during the experiment. Data were acquired using the AWS suite Mirage 4.0.7.3.

The potentiostat for the experiments was a Biologic SP200, connected to the microbalance in the working electrode-to-ground mode. It was set up as a three-electrode measurement using a platinum spiral wire as counter and an Ag/AgCl reference electrode (0.222 VSHE at 25 °C). The experiment was controlled through aws software. Electrochemical experiments were performed for at least 1800 s. They consisted of polarization curves and following of the potential at an open circuit. All measurements were performed at 37 °C. During the experiment, conventional electrochemical parameters—current and potential—were recorded together with oscillating frequency and energy dissipation. Due to the limited adhesion of the deposits, the potential sweeps were made from −0.5 to +0.5 VAg/AgCl.

It is possible to separate the mass and viscous loading by recording the frequency shift in a series of water–glycerol mixtures with different viscosities. This was performed at 37 °C in a set of four solutions with glycerol concentrations: [0 0.95 1.50 3.35] wt. %. The frequency shifts were recorded as 5 min averages after temperature stabilization. All solutions were preheated to 37 °C for an hour prior to the experiment. For the base harmonic, the frequency shift compensated for viscous load is obtained from Δfvisc = Δfmeas − 2.51 ΔD, where the dissipation difference ΔD is in ppm.

The mass to frequency conversion constant (Sauerbrey) was determined using a copper sulfate electrolyte, plating at 1 mA for 5 min at close to 100% yield: 0.5M CuSO4 + 0.5M H2SO4 + 1.1M EtOH at 37 °C.14 The calibration was made on smooth gold crystals with a working electrode area of 1.14 cm2, and a mass sensing area of 0.26 cm2. The frequency shift was compensated for change in viscous load before comparing with the Faradaic mass. These values were recalculated to Sauerbrey constants using nominal working electrode and oscillating areas for the rough and smooth titanium coated crystals, giving a Sauerbrey factor of Cs = 38.6 ng/Hz for the rough and Cs = 29.2 ng/Hz for the smooth variant. It is important to note that these constants are obtained at 37 °C and should not be compared with literature values determined at 25 °C.

There is no need to record the absolute viscosity for the electrolytes, as microbalance data are normally differential values. The frequency to mass conversion was made using the following equation:

Δm=Cs{ΔfmeaskviscΔD}.
(1)

The base electrolyte was a phosphate-buffered solution (PBS) made from de-ionized water to which was added 0.14M NaCl + 0.1M KH2PO4 + 3mM KCl + 10mM Na2HPO4. To this was added newborn calf serum of type HyClone, triple 0.1 μm sterile filtered from Thermo Scientific, having a protein concentration of 51 g/l. Before the measurement, the crystals were cleaned in Deconex 12PA-x/de-ionized water mixture and ultrasound for 5 min at room temperature. The electrochemical cell and the electrolytes were preheated to the target temperature of 37 °C before adding liquid to the cell, which was filled with 10 ml of solution immediately before the experiment starts. Before starting acquisition, equivalent circuit parameters were established by software. The data acquisition was then started within 30 s after adding liquid to the electrochemical cell.

The Auger electron spectrometer was a PHI 680 scanning Auger microprobe, manufactured by ULVAC-PHI, Eden Prairie, MN, USA. It was equipped with a field emission electron gun, an argon ion sputter gun, and a concentric mirror analyzer for the detection of Auger electrons. For sputter depth profiling, the ion gun was operated at 1 kV using a 1 × 1 mm2 raster, resulting in a sputter rate of 0.6 nm/min on an anodized TiO2 oxide. For 2 kV, the sputter rate was 1.9 nm/min. The quantification was performed using sensitivity factors, as listed in the PHI Auger Handbook.15 

Two different quartz surfaces were used: a rougher, designed for thickness measurement in PVD systems, and a smoother, designed for use in EQCM applications requiring a set of harmonics. Secondary electron micrographs of smooth and rough surfaces can be found in Fig. 1. The smooth surface [Fig. 1(a)] is almost atomically flat with an Sa value of 34 nm and showed no height extension in an interferometer providing nanometer resolution. The rougher surface with an Sa value of 350 nm [Fig. 1(b)] revealed a comparatively coarse-grained structure characterized by grooves with length dimensions in the micrometer range. The presence of grooves larger in size is clearer in the low magnification 3D rendering of the surface given in Fig. 1(c). A large fraction of the surface is undulating-flat, but there are also sharp features with nanometer-extension creating micrometer-range grooves and plateaus.

Auger sputter depth profiles were recorded before and after exposure of rough and smooth surfaces. Compared to surface oxide already present on the as-delivered surfaces, there was no detectable change in surface chemistry after immersion into PBS solutions. Figure 2 shows sputter depth profiles after exposure to PBS + 32 g/l calf serum for 1 h at 37 °C. The samples were rinsed in de-ionized water before being introduced into ultrahigh vacuum. For the smooth surface, the interfaces were sharp, and there were only low levels of oxygen and carbon within the titanium PVD film. After about 10 min of sputtering, the underlying gold layer was reached. For the rough surface, there was a marked carbon signal also in the titanium film, even though the analysis spot was small and placed on a flat surface region. After 1 h of sputtering, the oxygen signal did not descend below 25 at. %. Part of this is explained by surface roughness; and it is also likely that bulk titanium contained higher amounts of interstitial oxygen on the rough samples.

FIG. 2.

Auger sputter depth profiles for a smooth (top) and rough (bottom) quartz surface after exposure to 32g/l calf serum in PBS for 1 h at 37 °C. The titanium coating on the rough surface is considerably thicker. In addition, there are remaining carbon and oxygen signals even after 1 h (at least 200nm) of sputtering.

FIG. 2.

Auger sputter depth profiles for a smooth (top) and rough (bottom) quartz surface after exposure to 32g/l calf serum in PBS for 1 h at 37 °C. The titanium coating on the rough surface is considerably thicker. In addition, there are remaining carbon and oxygen signals even after 1 h (at least 200nm) of sputtering.

Close modal

Polarization curves from −0.5 to + 0.5 VAg/AgCl were recorded for both the rough and smooth surfaces, see Fig. 3. The electrolyte was PBS with an addition of 32 g/l of calf serum. There is a difference in cross-over potential between the two electrolytes. The frequency (b) and dissipation signals (c) are indicating a mass increase together with an increased dissipation, which shows no apparent correlation to the potential sweep. For the rough surface, there is an initial strong increase in dissipation, but toward the end of the sweep, the dissipation signals of the two crystal types align. When studying the frequency signal, the mass change is constantly higher on the rough surface, whereas viscous coupling stabilizes after an initial increase. This is normal as viscous coupling reflects the interaction between the surface and the solution, which should change with the nature of the adhering layer but not necessarily with its thickness. The higher current levels on the anodic side could in part be explained by the larger active surface area of the rough electrode.

FIG. 3.

Polarization curves for rough and smooth titanium PVD coatings. Sweep rate: 20mV/min; temperature: 37 °C. In both cases, there was an increase in mass (decrease in frequency) and an increase in dissipation, but these changes appear not to be linked to the applied potential.

FIG. 3.

Polarization curves for rough and smooth titanium PVD coatings. Sweep rate: 20mV/min; temperature: 37 °C. In both cases, there was an increase in mass (decrease in frequency) and an increase in dissipation, but these changes appear not to be linked to the applied potential.

Close modal

The experimental investigations were continued by acquiring frequency and dissipation as a function of time at the open circuit potential (OCP) for a set of different concentrations of calf serum in PBS. This experiment series was carried out on both smooth (Fig. 4) and rough (Fig. 5) surfaces. For the plain PBS electrolyte, the mass and dissipation curves on both surface types remain essentially flat. When protein is added, there is an adsorption process, which is more pronounced for the highest concentration of 32 g/l. On the smooth surface (Fig. 4), an adsorption peak can be seen for the highest calf serum concentration. This is also reflected in the dissipation signal. The rough surface, see Fig. 5, did not show these types of variations, indicating a stronger adhesion of the proteins to the surface. For the smooth surface, the open circuit potential shows an initial excursion in the cathodic direction, possibly indicating a change in the titanium oxide film during an initial period up to 200 s. In the long term, all three surfaces gave similar OCP values.

FIG. 4.

PBS and calf serum at two different concentrations adsorbed on a smooth quartz surface. The reference curve for the PBS solution with no serum added showed no significant change during the experiment.

FIG. 4.

PBS and calf serum at two different concentrations adsorbed on a smooth quartz surface. The reference curve for the PBS solution with no serum added showed no significant change during the experiment.

Close modal
FIG. 5.

Experiment series with different concentrations of calf serum on a rough quartz surface. The figure shows acquired frequency, dissipation, and the open circuit potential as a function of time.

FIG. 5.

Experiment series with different concentrations of calf serum on a rough quartz surface. The figure shows acquired frequency, dissipation, and the open circuit potential as a function of time.

Close modal

As can be seen in Fig. 5, the behavior on the rough surface was markedly different. The adsorption was at least 1.5 orders of magnitude higher, and the kinetics were faster albeit with a longer time before adsorption start. For the curves with calf serum added, there was an initial dissipation decrease during the first 100 s followed by an increase. This indicates an initial desorption process during the first 100 s followed by stronger adsorption. This nucleation period was present for all concentrations. The most interesting observations on the rough surface were the absence of dependence on concentrations, in terms of both the amount of adsorbed material and the time scale. The higher concentrations showed somewhat higher rates.

Figure 6 shows the adsorption curves for smooth and rough surfaces after compensation for viscous load and calibration into mass units. Note that the scale between smooth (a) and rough (b) surfaces differs by more than a magnitude. The smooth surface shows an initial adsorption for both solutions with serum added, although the measured frequency changes were different. It appears that the adsorption is independent of concentration and that a significant part of the frequency shift is induced by the change in viscosity observed at higher concentrations.

FIG. 6.

Mass change compensated for viscous load for smooth and rough surfaces.

FIG. 6.

Mass change compensated for viscous load for smooth and rough surfaces.

Close modal

For the rough surface in Fig. 6(b), the mass showed an initial slow increase up to about 200 s after contact with the solution, followed by a higher growth rate during some 100 s. The fastest adsorption is seen for the highest concentration, 32 g/l. The pure PBS solution shows initial desorption during the first 30 s and then a stable line. After 20 min in contact with the solution, the adsorption for all samples was about 80 μg/cm2.

It is also interesting to study the adsorption kinetics directly. This is the differential of the mass signal on the rough surface, which is displayed in Fig. 7. The highest adsorption rates are found for the highest concentrations. For all concentrations, the major part of the adsorption occurred within 10 min after immersion.

FIG. 7.

Adsorption kinetics calculated as the differential of mass change with respect to time for a titanium surface immersed in PBS + calf serum.

FIG. 7.

Adsorption kinetics calculated as the differential of mass change with respect to time for a titanium surface immersed in PBS + calf serum.

Close modal

The literature on the adsorption of proteins on solid surfaces is vast.1 To simplify the discussion, three main factors governing the adsorption were identified:

  • Solution chemistry: pH, protein concentration, concentrations of other species in the electrolyte, ionic strength, and other relevant parameters.

  • Surface chemistry, including surface oxides, their electronic band structure and potential differences at oxide/metal and oxide/electrolyte interfaces.

  • Surface roughness, which describes the surface geometry on a relevant scale, typically 100 μm and below. It is typically mirror-smooth on a nano-level in many studies but can also involve roughness tailored to fit a typical protein dimension. A relevant scale ranges from submicrometer to tens of micrometers.

In this article, a phosphate-buffer solution was used with different concentrations of calf serum. The amount of calf serum was varied over one order of magnitude in the electrolyte, but after about half an hour in contact with the titanium surfaces, all concentrations of calf serum gave a similar response in terms of adsorbed weight. Assuming water replacement at the surface and a protein density of 136 ng nm−1 cm−2,16 the adsorption on the rough surface represented more than 50 monolayers of adsorbate. In this study, a comparatively large variation in protein concentration had no marked effect on the amount of adsorbed protein. It does, however, appear to influence the adsorption kinetics with higher concentrations giving faster adsorption. Changes in pH and other critical parameters could alter this behavior.

To somewhat account for differences in surface chemistry between the samples studied, Auger sputter depth profiles were recorded before and after adsorption experiments. The smooth surface had a thinner deposit to allow for acquiring a wider range of harmonics. The deposit was also cleaner in the sense that the rough surface had higher oxygen contents dissolved in the titanium metal, which can take as much as 30% in its metallic state. For most practical applications, the titanium is in its passive state, covered by an anodic oxide film. For the passive state, the oxygen content in the underlying titanium metal should have only a minor influence on the interaction with proteins. The present set of exposures did not leave any trace of change in oxide chemistry following exposure at open circuit potential for an hour.

In the present context, the surface chemistry of the Ti/TiO2 system corresponds to variations in stoichiometry, crystal structure, and oxide film thickness. Titanium is a valve metal. During anodic potential sweeps, it forms an anodic film that grows with the applied potential. Titanium belongs to a subclass of valve metals that allows for growing anodic films with thicknesses up to several tens of nanometers (e.g., Al, Ti, Nb, Zr, and Hf), whereas other valve metals (e.g., Fe, Cr, and Co) only allow for growing films in the ranges of 1–3 nm. One condition for film formation is that the oxide has low or no solubility in the electrolyte. As there is a linear relation between potential and film thickness, the potential at the oxide/electrolyte interface remains quasiconstant during the forward sweep—the major part of the applied potential is accommodated as an electric field within the film. The potential distribution across a titanium oxide/electrolyte interface was studied by Vergé et al. using a rotating ring disk EQCM, which allowed for investigating potential distributions and side reactions.17 For this study, mass and dissipation changes were monitored during a potential sweep, see Fig. 3. The curves were recorded from −0.5 to +0.5 VAg/AgCl. Wider scans occasionally led to deposit decohesion. Within this potential region, no correlation between the applied potential and protein adsorption was observed.

Literature data on protein adsorption on metal surfaces with anodic films show some divergence. It is possible to obtain differences in surface chemistry by preoxidizing, using either electrochemical methods or thermal oxidation. Kusakawa et al. compared the response of ZrO2 and TiO2 surfaces to exposure of albumin and fibronectin.18 They used 27 MHz as base frequency and observed a frequency decrease of about −600 Hz for the fibronectin on TiO2 and −400 Hz for the same protein on ZrO2. The time scale of about half an hour matches the rates observed in this article. The frequency shifts would correspond to about 14 Hz on a 5 MHz crystal, which is in the same magnitude as observed for smooth quartz crystals, keeping in mind that the experiments in this study were performed at 37 °C, as opposed to 25 °C for the Kusakawa study. The difference in frequency shift between ZrO2 and TiO2 was about a factor of two, i.e., one order of magnitude smaller than the shift between the two types of surfaces in the present study.

The limited dependence on surface chemistry is also in accordance with what has already been reported by van de Keere et al., who studied adsorption of lysozymes on thermally evaporated titanium which they tested in a PBS solution. They did not find any influence of the applied potential on adsorption.19 Their protein adsorption amplitudes were in the same magnitude as those observed for the smooth quartz surface in this study, although their experiments were performed at 22 °C. When studying albumin in lower-conducting electrolytes, Brusatori et al. did find a potential dependence on adsorption using optical waveguide lightmode spectroscopy with a two-electrode system at ambient temperature.20 For the other protein studied—horse heart cytochrome c—there was no apparent correlation between the applied potential and adsorption during an initial phase. The adsorption of albumin was less pronounced in electrolytes with higher conductivity, as used in the present study. A higher ionic strength in the solution is one important factor that reduces migration by screening of electrostatic interactions.

The surfaces used in this study were titanium deposited on quartz crystals, which were either atomically smooth or with roughness features in the micrometer range. This is rougher than most surfaces used in EQCM studies. The difference between the two surfaces was striking, with some 80 μg cm−2 of adsorbed matter on the rough surface compared to 4 μg cm−2 for the smooth surface, see Fig. 6. It appears that the final amount of organic matter adsorbed is independent of calf serum concentration in the solution. From the graph in Fig. 7, the most rapid adsorption is found for the highest concentration. The base line in PBS with no calf serum added is a flat line, indicating a stable experiment. The adsorption kinetics appear to be rather complex, as already outlined in the review by Rabe et al.1 

Many types of models for protein adsorption are based on the Langmuir isotherm. In this study, the amount of adsorbed matter is more than one order of magnitude thicker than a monolayer before adsorption abates. This observation rules out most adsorption isotherms. Instead, a possible interpretation of the present experiment could be that proteins start adsorbing at nucleation sites, which are not present on the smooth surface. In Fig. 1, there are local regions with considerably smoother appearance on rough samples. If this region is found in a groove, this could be a site for nucleation. As it is a surface process, it will grow by order r2 until the disks start to touch. Once all nucleation sites are filled, the adsorption process follows a slower growth law. A model that accounts for these basic assumptions is the model first introduced by Kolmogorov in 1937.21 It is also known as Johnson–Mehl–Avrami–Kolmogorov (JMAK) following independent development in North America some years later. It has been reviewed by Fanfoni and Tomellini, who also discussed its application to thin films.22 

For precipitation kinetics on a 2D surface, the projection of the overlayer on the substrate can be considered 2D transformation. In this case, the growth of the adhered proteins is considered three-dimensional, whereas the limiting surface is two-dimensional. As parallel to the three-dimensional case, it corresponds to assembling all nucleation sites on one wall of the volume to be transformed. When they are large enough to interact, the overall growth rate abates.

When precipitates are growing independently of each other in three dimensions, the extended fraction of adsorbed substance (index β),

VβeV=π3Nt[rt]3t4,
(2)

where N is the number of nucleation sites and size of the precipitate and V is a volume near the interface with an arbitrary thickness. A full list of parameters with explanations can be found in Tables I. For short times, the number of nuclei grows as Nt, and the radius of each precipitate as (∂r/∂t)⋅t; hence the volume grows as t3, and the total volume fraction will grow as t4. As the phase cannot nucleate in areas where adsorption has already taken place, it is useful to adjust the extended volume estimate to get the real volume,

dVβ=dVβe[1VβV].
(3)

Rewriting and introducing Y = Vβ/V gives a total differential expression,

V1YdY=dVβe,
(4)

which, applying the boundary condition that the radii are 0 at t = 0, can be integrated into

ln(1Y)=VβeV=π3Nt[rt]3tn.
(5)

The right-hand side in Eq. (5) comes from Eq. (2).

It is frequently of interest to define the n-value from a linear fit according to

ln(ln[1Y])=lnK+nlnt,
(6)

where Yβ is the volume fraction of phase β and n is the order of the reaction, t4, for free growing particles in three dimensions.

In the present case, Vβ is replaced by mass fraction m/mmax, where the corresponding plot for the highest serum concentration can be found in Fig. 8. In this analysis, it was chosen to ignore the initial phase during the first 100 s of the experiment. Different growth modes can be distinguished; two of which are marked by dashed lines. The n-values for the adsorption process were calculated for all concentrations, and their respective values can be found in Tables II. For an ideally flat surface with a two-dimensional adsorption process, the n-value is 3. For a three-dimensional process, n = 4. There is a difference between the lower concentrations (0.5 and 2 g/l) and the higher levels (8 and 32 g/l). The steepest slopes, i.e., the highest adsorption rates, were concentration dependent, as also seen in the differential adsorption plot in Fig. 7.

FIG. 8.

Plots to find slopes for the Kolmogorov model for different calf serum concentrations. As the attachment sites of proteins become scarce, the kinetics slow down to a slope with n < 1.

FIG. 8.

Plots to find slopes for the Kolmogorov model for different calf serum concentrations. As the attachment sites of proteins become scarce, the kinetics slow down to a slope with n < 1.

Close modal
TABLE II.

n-values from Eq. (3) calculated as indicated in Fig. 8 for the rough sample. Two different growth phases were distinguished, a faster around 200 s (ln t ≈ 5–5.5) abating to a slower regime (ln t > 6).

Addition to PBS
g/l
n
ln t ≈ 5–5.5ln t ≈ 6.5
0.5 3.1 0.7 
2.3 1.1 
3.6 1.1 
32 4.5 0.7 
Addition to PBS
g/l
n
ln t ≈ 5–5.5ln t ≈ 6.5
0.5 3.1 0.7 
2.3 1.1 
3.6 1.1 
32 4.5 0.7 
TABLE I.

List of parameters.

Latin
AWE Area of the working electrode-to-ground cm2 
AOsc Oscillating (mass sensing) area cm2 
Cs 38.6 (rough) and 29.2 (smooth) values for nominal surfaces ng Hz−1 
ΔD Energy dissipation difference ppm 
Δfmeas Measured frequency shift, Δf(t = 0) = 0 Hz 
Δfvisc Frequency shift corrected for viscous load Hz 
kvisc 2.51 Hz ppm−1 
K Linear fit parameter, see Eq. (6) m3 s−4 
Δm Mass change, calculated from the Sauerbrey equation Ng 
N Number of nucleation sites — 
n Linear fit parameter, see Eq. (6) — 
Sa Surface roughness parameter 
R Radius of the nucleated particles 
T Time 
Veβ Extended volume of the β matter — 
V Total volume where the β is growing m3 
Y Vβ/V, volume fraction of β — 
Greek 
β Precipitating (growing/adsorbing) phase — 
ηl Viscosity of the liquid N s cm−2 
ρl Density of the liquid g cm−3 
Latin
AWE Area of the working electrode-to-ground cm2 
AOsc Oscillating (mass sensing) area cm2 
Cs 38.6 (rough) and 29.2 (smooth) values for nominal surfaces ng Hz−1 
ΔD Energy dissipation difference ppm 
Δfmeas Measured frequency shift, Δf(t = 0) = 0 Hz 
Δfvisc Frequency shift corrected for viscous load Hz 
kvisc 2.51 Hz ppm−1 
K Linear fit parameter, see Eq. (6) m3 s−4 
Δm Mass change, calculated from the Sauerbrey equation Ng 
N Number of nucleation sites — 
n Linear fit parameter, see Eq. (6) — 
Sa Surface roughness parameter 
R Radius of the nucleated particles 
T Time 
Veβ Extended volume of the β matter — 
V Total volume where the β is growing m3 
Y Vβ/V, volume fraction of β — 
Greek 
β Precipitating (growing/adsorbing) phase — 
ηl Viscosity of the liquid N s cm−2 
ρl Density of the liquid g cm−3 

The highest n-value measured was 4.5, which could be understood as a fast filling of all available nucleation sites where growth would occur as half-spheres placed on a rough surface with an effective surface area considerably larger than its nominal value. For lower concentrations, the nucleation sites would fill slower. After the initial growth phase, when the nucleation sites are occupied, the growth abates to a slower mode.

The adsorption data appear consistent with a model based on growth limitation by the number of nucleation sites. In this context, the lower adsorption on the smooth surface would be explained by the absence of nucleation sites. The proteins also appear to have weaker bonds to the smooth surface, as indicated by Figs. 4(a) and 4(b), where desorption became dominating after some 1200 s.

Figure 7 indicates different stages of adsorption, disregarding the initial incubation phase. As the calf serum contains different proteins, this is consistent with the Vroman effect.23 The calf serum contains both albumin and gamma globulin. This makes a replacement reaction possible where the albumin would be expected to adsorb first. The different concentrations of the proteins in calf serum would contribute to variations in adsorption rates.

The present study has shown the importance of the surface condition for protein adsorption. This has practical implications for the interaction of biomaterials with corporal liquids. The roughness scale on the rough quartz crystal is of the same scale as the surface finish of an implant in the human body. Surface defects in the micrometer range would have a strong impact on the adsorption of organic matter. It also illustrates the difficulty in comparing results from different studies, as it is cumbersome to maintain equal surface conditions between different laboratories. Nevertheless, the EQCM remains a powerful tool for studying adsorption phenomena related to proteins and metal surfaces.

In this EQCM investigation, titanium surfaces with different roughnesses, Sa = 34/350 nm, were studied during the first half hour of immersion. It was shown as follows:

  • Surface roughness was found to be a crucial factor for adsorption kinetics. Taking the nominal surface area into account, the rough surface adsorbed 15 times more matter.

  • Increasing serum concentrations do not influence the amount of adsorbed material but do lead to higher adsorption rates.

  • The adsorption was interpreted using a Kolmogorov (JMAK) model for nucleation. Two stages were distinguished: an initial phase where the growth is limited by the number of nucleation sites, and a secondary, slower phase where all nucleation sites are occupied, and the growing regions start interacting.

Valuable comments on the script were made by Dr. Yann Chevolot, Ecole Centrale de Lyon. Funding was provided by Fonds National Suisse under Grant No. 200021-184851/1 “Mesynic.”

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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