J. Phys. Chem. B 2008, 112, 7267–7272
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Deposition at Glancing Angle, Surface Roughness, and Protein Adsorption: Monte Carlo Simulations Vladimir P. Zhdanov,*,†,‡ Kristian Rechendorff,† Mads B. Hovgaard,† and Flemming Besenbacher† Interdisciplinary Nanoscience Center (i NANO) and Department of Physics and Astronomy, UniVersity of Aarhus, DK-8000 Aarhus C, Denmark, and BoreskoV Institute of Catalysis, Russian Academy of Sciences, NoVosibirsk 630090, Russia ReceiVed: October 8, 2007; ReVised Manuscript ReceiVed: January 28, 2008
To generate rough surfaces in Monte Carlo simulations, we use the 2 + 1 solid-on-solid model of deposition with rapid transient diffusion of newly arrived atoms supplied at glancing angle. The surfaces generated are employed to scrutinize the effect of surface roughness on adsorption of globular and anisotropic rodlike proteins. The obtained results are compared with the available experimental data for Ta deposition at glancing angle and for the bovine serum albumin and fibrinogen uptake on the corresponding Ta films. Introduction
Deposition at Glancing Angle
In nature, experiments, and industrial applications, solid surfaces are often rough.1 Physical, chemical, and biological rate processes (e.g., surface diffusion2 or catalytic reactions3) occurring on such surfaces may be dramatically influenced by surface roughness. To simulate such processes, it is desirable to have models allowing one to easily generate rough surfaces and to systematically change their properties. Following this line, we first present below Monte Carlo (MC) simulations of deposition in the framework of the 2 + 1 solid-on-solid model with rapid transient diffusion of newly arrived atoms supplied at glancing angle. This part of our work was motivated by the experiments indicating that the metal deposition at glancing angle results in the formation of surfaces with well-controlled roughness or nanometer-sized structures (see e.g. the data without4 or with substrate rotation;5–9 for recent trends in this field, see also ref 10). Illustrating the use of the results obtained in the first part of this work, we then scrutinize the effect of surface roughness on adsorption of globular and anisotropic rodlike proteins. The latter part of our work was motivated by measurements11 of the influence of roughness of Ta films on the uptake of bovine serum albumin (BSA) and fibrinogen. Concerning this subject, it is appropriate to note that experimental and theoretical studies of protein adsorption on rough surfaces are just beginning (for a brief review, see ref 12). Adsorption of BSA and fibrinogen on such surfaces is especially interesting because these two proteins are good examples of spherically shaped and strongly anisotropic proteins. In addition, these proteins are abundant in the blood. In particular, the former one is one of the main components of the blood transport system13 while the latter one plays an important role in blood coagulation,14,15 and both of these proteins can influence cellular adhesion to the implanted biomaterials.16 * To whom correspondence should be addressed. E-mail: zhdanov@ catalysis.ru. † University of Aarhus. ‡ Russian Academy of Sciences.
Earlier theoretical studies of ballistic deposition at oblique incidence include MC simulations in the absence of surface diffusion.17 More recent MC and analytical treatments9,18 are focused on the regimes with substrate rotation (for a general review of theoretical approaches used in this field, see ref 19). In our MC simulations of deposition at glancing angle without substrate rotation, we employ the conventional 2 + 1 solid-onsolid model.20 Metal atoms are considered to occupy sites on a cubic lattice. Each lattice site is either vacant or occupied by one atom. The occupation of a site is allowed only if the site located below it is already occupied. This means that no overhangs are permitted. With this restriction, the atoms form columns. To mark atoms in columns, we use the coordinates along (x and y) and perpendicular (z) to the surface. During ballistic deposition, a newly arriving atom is considered to move toward the surface and simultaneously in the x direction so that the latter coordinate decreases. As soon as the atom touches at least one of the already arrived atoms, the ballistic motion is terminated. Depending on the type of contacts [we take into account contacts with atoms located in nearestneighbor (nn) and next-nearest-neighbor (nnn) sites], three situations can occur: (i) If the newly arrived atom contacts an atom located in the nn site below and simultaneously at least one atom located in the lateral nn site, the position of the newly arrived atom is fixed. (ii) If the newly arrived atom contacts an atom located in the nn site below and has no lateral nn contacts, it is allowed to perform Ndif diffusion jumps on top of nn columns. This transient diffusion is terminated and the atom location is fixed if the atom reaches a site, allowing the formation of two or more nn contacts, or after Ndif diffusion jumps. (iii) If the contact is lateral, the newly arrived atom may form an overhang just after arrival. If this is the case, it is shifted down and located on top of the corresponding column. (After this shift, the atom forms two or more nn contacts with other atoms.) For each deposition trial, the deposition angle, that is, the angle between the atom trajectory (in the x-z plane) and the surface, is chosen at random in the range θ ( δθ, where θ is
10.1021/jp709806k CCC: $40.75 2008 American Chemical Society Published on Web 05/27/2008
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Figure 1. Results of simulations with Ndif ) 5: interface width (a) as a function of time (MCS) for L ) L0 ) 512 and (b) as a function of L for t ) 32 MCS and (c) surface area (ML) as a function of time (MCS).
Figure 3. Lattice height, h - 〈h〉, as a function of (a) x and (b) y for Ndif ) 5, L0 ) 512, and t ) 32 MCS.
Figure 2. Growth exponents, R and β, as a function of the deposition angle. The former exponent has been calculated by using the data (Figure 1b) for L < 10. The latter exponent has been obtained by employing the data (Figure 1a) for t g 16.
the average angle, and δθ ) 1° is the distribution half width. This angle distribution, introduced to mimic the experiment, is
rather narrow. The results were found to be nearly independent of whether we take it into account or just use δθ ) 0. Diffusion of already arrived atoms is not allowed in our model. The algorithm of our simulations includes sequential trials of deposition as described above. To measure time, we use MC steps (MCS). One MC step is identified with L0 × L0 deposition trials, where L0 is the lattice size. All of the results presented in this section were obtained for L0 ) 512 and Ndif ) 5 and 100. To generate rough surfaces related to the experiments mentioned in the introduction, the duration of MC runs was 32 and 256 MCS for Ndif ) 5 and 100, respectively. In reality, deposition is often performed at room temperature. In this case, an atom forming a small number of bonds (in our
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Figure 4. Snapshot of a 200 × 200 fragment of the 512 × 512 lattice in the end (at t ) 32 MCS) of one of the MC runs with θ ) 5° and Ndif ) 5. The black colour correspond to the regions with h g 〈h〉. This figure shows that the regions are nearly isotropic despite the anisotropy of deposition (the arriving atom moves along the x direction).
model, this corresponds to one nn contact) may still diffuse rapidly. Such atoms are primarily generated immediately after deposition. A few first jumps after deposition are expected to occur because of the energy released in this process, and then the jumps are thermally activated. Atoms forming a small number of bonds can also be generated because of thermal jumps of earlier deposited atoms. We take the former channel into account and neglect the latter channel. Our experience indicates that, if diffusion is absent, the surface is too rough and/or is of the sawlike shape not observed in experiment with Ta.4 For diffusion with Ndif g 5, the surface roughness generated in the simulations is found to be in reasonable qualitative agreement with the experiment. In particular, the model allows one to generate surfaces with appropriate ratio of the vertical and horizontal scales of the surface roughness. To characterize the time and length dependence of the surface roughness, we use the interface width, defined as the meansquare surface-height difference,
w(L, t) ) 〈 (∑[h(r, t) - 〈h 〉 ]2/L2)1/2 〉,
(1)
where h(r, t) is the column height, and the summation is performed on the sublattices of size L (L e L0). Usually (since the mid-1980s21), the interface width is believed to behave as1
w(L, t) ∝
{
tβ ,
if L . Lc
L , if L , Lc R
(2)
where R and β are the growth exponents, and Lc is the crossover length corresponding to the transition from one dependence to another. The crossover length is comparable with the correlation length, defined as the position of the first zero of the height correlation function. Bearing adsorption in mind (see the following section), we have also calculated the adsorption capacity, S, of the surfaces generated. To characterize the adsorption capacity, one can use the surface area. It can be defined either as the geometric area per unit support area or as the ratio of the number of vacant
Figure 5. Results of simulations with Ndif ) 100: interface width (a) as a function of time (MCS) for L ) L0 ) 512 and (b) as a function of L for t ) 256 MCS and (c) surface area (ML) as as a function of time (MCS).
sites contacting the occupied sites to the number of sites in a plane layer. In this work, we used the latter definition, representing the adsorption capacity in monolayers (ML), because it is more natural for adsorption. The results of our simulations for Ndif ) 5 are presented in Figures 1 through 4. In particular, Figure 1 shows the dependence of w on t and L and the dependence of S on t. The surface roughness is seen to rapidly increase with decreasing deposition angle. Quantitatively, this effect is characterized by calculating the growth exponents (Figure 2). Typical lattice snapshots, obtained at different angles in the end of MC runs, are exhibited in Figures 3 and 4. The corresponding results for Ndif ) 100 are shown in Figures 5 through 9. Comparing Figures 2 and 6 exhibiting the angle dependence of the growth exponents for Ndif ) 5 and 100, one can see that, in both cases, as expected, the exponents decrease with increasing angle. For Ndif ) 100, the drop is however somewhat faster.
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Figure 6. Growth exponents, R and β, as a function of the deposition angle. The former exponent has been calculated by using the data (Figure 5b) for L < 10. The latter exponent has been obtained by exmploying the data (Figure 5a) for t > 100.
While our model obviously does not take into account all of the aspects of real deposition, it is of interest to compare the results of simulations with experiment. For the Ta films, the AFM measurements4 of surface roughness show that, with increasing deposition angle from 5° to 40°, the growth exponent R decreases from 0.92 to 0.75. In the simulations, the corresponding drop is from 0.57 to 0.37 for Ndif ) 5 (Figure 2) and 0.52 to 0.33 for Ndif ) 100 (Figure 2). Thus, the decrements of the measured and calculated exponents are in reasonable agreement. The absolute value of the calculated exponent is however lower than that in the experiment. Although the latter seems to indicate that as expected the model is not fully adequate compared with the reality (e.g., due to the prohibition of overhangs), one should also note that in the experiments the lowest values of L were comparable with the AFM tip size, and accordingly, the corresponding values of the interface width might be somewhat underestimated. In turn, the exponent R might be overestimated. Thus, the fit of the reality is expected to actually be somewhat better than it appears. Protein Adsorption Adsorption of BSA and fibrinogen on the rough Ta films, grown by oblique incidence deposition without substrate rotation4 (due to subsequent exposition to ambient conditions, the films contained a thin 2-5 nm oxide layer), was studied11 by using quartz crystal microbalance. For fibrinogen, additional experimental data were obtained by employing the ellipsometry technique. The interface width was varied from 2 to 33 nm. With increasing roughness, the increase in the saturation uptake was found to be about 25% for BSA and 75% for fibrinogen. This appreciable difference seems to be related to the features of the protein shape (see the discussion in ref 11). Here, it is appropriate to recall that BSA is a globular protein with a molecular weight of 65 kDa and a radius of roughly 6 nm. Fibrinogen is an extracellular protein with mass 340 kD and an elongated shape with dimensions 45nm × 9nm × 6nm. To explicitly illustrate the effect of surface roughness on the adsorption of such proteins (the conventional models of protein adsorption23 ignore this effect), we have performed coarsegrained MC simulations. Taking into account the specifics of the shape of the proteins under consideration, we represent BSA and fibrinogen as a monomer and a linear pentamer, respectively. In the case of BSA, the monomer size is considered to be 12 nm (this is the
Figure 7. Lattice height, h - 〈h〉, as a function of (a) x and (b) y for Ndif ) 100, L0 ) 512, and t ) 256 MCS.
BSA diameter). For fibrinogen, the monomer size is assumed to be 7.5 nm (this is the average value of 9 and 6 nm). To mimic the rough Ta films, we use the lattice structures generated as described in the preceding section. To keep the model as simple as possible, we identify lattice sites with sites for adsorption of monomers representing protein. In this case, the dimensionless interface width, which should correspond to the experiment, can be obtained by dividing the experimentally measured roughness by the monomer size. This means that the interface width should be varied from 0 to 2.75 in simulations of BSA (the latter value is obtained by dividing 33 nm by 12 nm). For fibrinogen, the interface width should be varied from 0 to 4.4 (4.4 ) 33/7.5),
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Figure 10. Snapshots of a fragment of the lattice after adsorption of petramers up to saturation. The filled and open circles represent the surface (with w ) 0 (a) and 4.4 (b)) and monomers composing petramers, respectively.
Figure 8. Lattice height, h - 〈h〉, as a function of (a) x and (b) y for Ndif ) 100, L0 ) 512, θ ) 5°, and t ) 32 MCS. In this case, the surface roughness is 3.2. (This figure can be compared with Figure 3 which also represents the results for t ) 32 MCS.)
Figure 9. Saturation uptake of pentamers as a function of surface roughness. The uptake is normalized to 1 ML of monomers (on the flat surface).
respectively. The dimensionless correlation length, which should correspond to the experiment, can also be obtained by dividing the measured length by the monomer size. In the simulations, the correlation length can be varied by changing θ and Ndif. Our analysis performed following this line indicated that the model reasonably mimics the real films provided that θ ) 5° and Ndif ) 5. These values were used to generate rough surfaces for simulation of BSA and fibrinogen adsorption. With the specification above, the saturation BSA uptake, normalized per ML, coincides with the adsorption capacity introduced in the previous section. When the surface roughness is increased from 0 to 2.75, the increase in the saturation uptake is predicted (Figure 1c) to be about 60%. This value is significantly higher than the experimentally measured increase of 25%. This difference between the simulations and experiment seems to indicate that BSA relaxes during adsorption, and its size becomes larger than that in the solution. Thereby, the scaled surface roughness would be lower, and the predicted increase of the uptake would also be lower. In particular, the experiment can be reproduced by increasing the BSA diameter from 12 nm to about 20 nm and respectively by decreasing the dimensionless interface width. This conjecture is in line with the results of kinetic experiments,22 indicating that the BSA uptake on flat surfaces can be reduced by a factor of 2 because of denaturation. For adsorption of linear pentamers representing fibrinogen, one of the sites contacting the substrate from top or laterally was chosen at random. If the site was vacant, an adsorption trial of a pentamer was performed so that one of its end monomers was located at this site. Then, the steric constraints for adsorption were inspected for all of the possible directions of the pentamer orientation. If
adsorption of at least one of the other four monomers was impossible because of the constraints, the adsorption trial was rejected. If adsorption was possible, the orientation of a pentamer was selected at random among the orientations with the lowest energy of the protein-surface interaction (the interaction included nearest-neighbor contacts in all of the possible directions). Surface diffusion of pentamers was neglected (this corresponds to the experiment24), and reorientation of pentamers after adsorption was neglected as well. The lattice size was 256 × 256. When the scaled interface width is increased from 0 to 4.4, the increase in the saturation uptake for pentamers is predicted to be 70% as shown in Figure 9 (this figure was earlier presented in our Letter11). Simultaneously, the fraction of pentamers contacting the substrate via all five monomers decreases from 32% to 14% (for typical lattice snapshots, see Figure 10). Thus, the simulations taking only roughness and protein anisotropy into account reproduce the experimental findings for fibrinogen quite well. Conclusion We have performed MC simulations of deposition at glancing angle by using the conventional 2 + 1 solid-on-solid model with transient diffusion of newly arrived atoms. Specifically, we have studied the influence of deposition angle and the rate of diffusion on surface roughness. Although the growth exponents are not found to be in perfect agreement with experiment, the model is proved to be convenient for generating rough surfaces with realistic topology (cf. the surfaces topologies shown in Figures 3 and 4 with those shown in Figure 1 in ref 4). Because of its flexibility, the model can be used in various applications, for example, for simulations of adsorption, surface diffusion, and chemical reactions on rough surfaces. In particular, we have shown that the model can be employed to clarify some aspects of adsorption of globular and anisotropic rodlike proteins on such surfaces. Acknowledgment. One of the authors (V.P.Zh.) is grateful for the Guest Professorship at the i NANO center at the University of Aarhus. References and Notes (1) Barabasi, A.-L.; Stanley, H. E. Fractal Concepts in Surface Growth; Cambridge University Press: Cambridge, 1995. (2) Zgrablich, G. In Equilibria and Dynamics of Gas Adsorption on Heterogeneous Surfsces; Rudzinski, W.; Steele, W. A.; Zgrablich, G. Eds.; Elsevier: Amsterdam, 1997. (3) Dooling, D. J.; Rekoske, J. E.; Broadbelt, L. J. Langmuir 1999, 15, 5846. (4) Rechendorff, K.; Hovgaard, M. B.; Chevallier, J.; Foss, M.; Besenbacher, F. Appl. Phys. Lett. 2005, 87, 073105.
7272 J. Phys. Chem. B, Vol. 112, No. 24, 2008 (5) Dick, B.; Brett, M. J.; Smy, T. J. Vac. Sci. Technol. B 2003, 21, 23. (6) Dick, B.; Brett, M. J.; Smy, T. J. Vac. Sci. Technol. B 2003, 21, 2569. (7) Alouach, H.; Mankey, G. J. Appl. Phys. Lett. 2005, 86, 123114. (8) Jensen, M. O.; Brett, M. J. Appl. Phys. A: Mater. Sci. Proc. 2005, 80, 763. (9) Singh, J. P.; Karabacak, T.; Ye, D. X.; Liu, D. L.; Picu, C.; Lu, T. M.; Wang, G. C. J. Vac. Sci. Technol. B 2005, 23, 2114. (10) Pfeiffer, L. N.; West, K. W.; Willett, R. L.; Akiyama, H.; Rokhinson, L. P. BELL Labs Technol. J. 2005, 10, 151. (11) Rechendorff, K.; Hovgaard, M. B.; Foss, M.; Zhdanov, V. P.; Besenbacher, F. Langmuir 2006, 22, 10885. (12) Song, W.; Chen, H. Chin. Sci. Bull. 2007, 52, 3169. (13) Ho¨o¨k, F.; Vo¨ro¨s, J.; Rodahl, M.; Kurrat, R.; Boni, P.; Ramsden, J. J.; Textor, M.; Spencer, N. D.; Tengvall, P.; Gold, J.; Kasemo, B. Coll. Surf. B: Biointerf. 2002, 24, 155.
Zhdanov et al. (14) Horbett, T. A.; Cheng, C. M.; Ratner, B. D.; Hoffman, A. S.; Hansonand, S. R. J. Biomed. Mater. Res. 1986, 20, 739. (15) Kiaei, D.; Hoffman, A. S.; Horbett, T. A.; Lew, K. R. J. Biomed. Mater. Res. 1995, 29, 729. (16) Tang, L.; Eaton, J. W. Am. J. Clin. Pathol. 1995, 103, 466. (17) Meakin, P.; Krug, J. Phys. ReV. A 1992, 46, 3390. (18) Main, E.; Karabacak, T.; Lu, T. M. J. Appl. Phys. 2004, 95, 4346. (19) Vvedensky, D. D. J. Phys.: Condens. Matter 2004, 16, R1537. (20) Zangwill, A. Physics at Surfaces; Cambridge University Press, Cambridge, 1988. (21) Family, F.; Vicsek, T. J. Phys. A 1985, 18, L75. (22) Wertz, C. F.; Santore, M. M. Langmuir 2001, 17, 3006. (23) Ramsden, J. J. In Biopolymers at Interfaces, 2nd ed.; Malmsten, M., Ed.; Marcel Dekker: New York, 2003; p 199. (24) Tilton, R. A. In Biopolymers at Interfaces, 2nd ed.; Malmsten, M. Ed.; Marcel Dekker: New York, 2003; p 250.
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