Modification of Surface Interactions and Friction by Adsorbed

balance capable of measuring shear as well as normal forces. Normal force measurements indicate that the dendrimers adsorb from dilute toluene solutio...
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Langmuir 2000, 16, 3893-3901

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Modification of Surface Interactions and Friction by Adsorbed Dendrimers: 2. High-Surface-Energy -OH-Terminated Carbosilane Dendrimers Xueyan Zhang,§ Jacob Klein,* Sergei S. Sheiko,† and Aziz M. Muzafarov‡ Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel, Organische Chemie III, Universitat Ulm, 89069 Ulm, Germany, and Institute of Synthetic Polymer Materials of the Russian Academy of Sciences, Profsoyuznaya St. 70, 117393 Moscow, Russia Received March 31, 1999. In Final Form: November 10, 1999 The interactions between two mica surfaces bearing a fourth-generation carbosilane dendrimer (modified to expose -OH groups on its outer surface) were studied across a toluene medium, using a surface force balance capable of measuring shear as well as normal forces. Normal force measurements indicate that the dendrimers adsorb from dilute toluene solution (ca. 5 × 10-4 w/w) as a monolayer on each surface. Two such interacting surfaces experience a longer-ranged van der Waals attraction followed by strong shortrange adhesion (probably of dipolar origin) as the adsorbed dendrimers come into contact. Within the range of our parameters, the dendrimer layers were incompressible normal to the surfaces. Friction versus load profiles were measured at different shear velocities, revealing marked stick-slip sliding, whereas the magnitude of the yield stress increased with longer times of contact and with normal pressure. This suggests that over time scales comparable with the experimental times the interacting layers rearrange to optimize their interfacial shear strength. The behavior of these -OH-exposing carbosilane dendrimers differs qualitatively from that of CH3-exposing poly(propyleneimine) dendrimers studied earlier, a difference attributable to the much more polar nature of the hydroxyl groups.

Introduction Dendrimers, synthetic macromolecules characterized by a regularly branched structure, possess features both of colloidal particles and of polymeric molecules, and have been extensively studied in recent years.1-8 In particular they possess a well-defined nanometer-sized quasispherical shape on one hand, whereas on the other hand their chemistry can be efficiently adjusted to control the nature of the internal structure and of the groups exposed at their outside surfaces. In addition, their size may be adjusted, within limits, via the generation to which they are grown or assembled. These features present intriguing possibilities for the properties of dendrimers in general, and, in particular, at surfaces and interfaces and as modifiers of surface interactions. The behavior of dendrimers at solid-air interfaces and at liquid-air interfaces has been explored in recent years in several studies using a variety of techniques.9-15 These include scanning force * Corresponding author. E-mail: [email protected]. † Universitat Ulm. ‡ Russian Academy of Sciences. § Present address: Department of Materials Science and Engineering, University of Illinois at Urbana-Champagne, UrbanaChampagne, IL. (1) Tomalia, D. A.; Naylor, A.; Goddard, W. Angew. Chem., Int. Ed. Engl. 1990, 29, 138. (2) Tomalia, D. A. Sci. Am. May 1995, 42. (3) Voit, B. I. Acta Polym. 1995, 46, 87. (4) Jansen, J. F. G. A.; de Brabander-van den Berg, E. M. M.; Meijer, E. W. Science 1994, 266, 1226. (5) Astruc, D. C. R. Acad. Sci. Ser II: Mec., Phys., Chim., Astrom. 1996, 322, 757. (6) Wallimann, P.; Seiler, P.; Diederich, F. Helv. Chim. Acta 1996, 79, 779. (7) Kim, Y.; Zimmermann, S. C. Curr. Opin. Chem. Biol. 1998, 2, 733. (8) Wooley, K. L.; Hawker, C. J.; Pochan, J. M.; Frechet, J. M. J. Macromolecules 1993, 26, 1514. (9) Bar, G.; Rubin, S.; Cutts, R. W.; Taylor, T. N.; Zawodzinski, T. Langmuir 1996, 12, 1172.

microscopy (SFM) to study the properties of thin films and droplets of dendrimers on solid substrates; smallangle X-ray scattering (SAXS) to probe dendrimer film structure and thickness; and Langmuir troughs to examine the behavior of spread dendrimer films at a water-air interface. A review of some of these studies has recently appeared.16 These investigations have yielded considerable basic insight into the size, configuration, and lateral compressibility of dendrimers at interfaces. In a recent study17 a surface force balance (SFB) was used to investigate the normal forces between atomically smooth mica sheets bearing layers of a fifth-generation poly(propyleneimine) dendrimer (henceforth PPID) modified by amino acid to expose a dense layer of methyl groups on its outer surface. This dendrimer adsorbed from lowconcentration solution in toluene to form weakly adhering, deformable monolayers on each surface. For layers adsorbed from high solution concentration there was evidence of surface aggregation, resulting in thicker adsorbed layers that exhibited a long-ranged repulsion. The frictional forces between the PPID layers were also characterized: friction between the monolayers was relatively high (friction coefficient µ = 0.2), and resembled that of boundary lubricants in that adhesive contacts were (10) Sheiko, S. S.; Eckert, G.; Ignateva, G.; Muzafarov, A. M.; Spickermann, J.; Rader, H. J.; Mo¨ller, M. Macromol. Rapid Commun. 1996, 17, 283. (11) Tsukruk, V. V.; Rinderspracher, F.; Bliznyuk, V. N. Langmuir 1997, 13, 2171. (12) Sheiko, S. S.; Muzafarov, A. M.; Winkler, R. G.; Getmanova, E. V.; Eckert, G.; Reineker, P. Langmuir 1997, 13, 4172. (13) Sheiko, S. S.; Buzin, A. I.; Muzafarov, A. M.; Rebrov, E. A.; Getmanova, E. G. Am. Chem. Soc. Polym. Abstr. 1998, 215, 195. (14) Hierlemann, A.; Campbell, J. K.; Baker, L. A.; Crooks, R. M.; Ricco, A. J. J. Am. Chem. Soc. 1998, 120, 5323. (15) Saville, P. M.; White, J. W.; Hawker, C. J.; Wooley, K. L.; Fre´chet, J. M. J. J. Phys. Chem. 1995, 99, 8283. (16) Tsukruk, V. V. Adv. Mater. 1998, 10, 253. (17) Zhang, X.; Wilhelm, M.; Klein, J.; Pfaadt, M.; Meijer, E. W. Langmuir 2000, 16, 3884.

10.1021/la9903797 CCC: $19.00 © 2000 American Chemical Society Published on Web 02/04/2000

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Figure 1. Schematic chemical structure of carbosilane dendrimer.

sheared during sliding. The thicker PPID layers, on the other hand, could be compressed and slid past each other with rather low friction coefficients (µ = 0.05). In this paper we extend these studies to the case of a fourthgeneration carbosilane dendrimer exposing -OH groups on its outer surface. Our motivation in the present work was to explore the contrast between the low-energy methyl groups on the PPID surface and the high-energy -OH groups on the carbosilane surface, and its effect on the normal and the frictional forces both in steady state and as a function of time. Experimental Section Materials. The carbosiloxane dendrimer, with hydroxylterminated groups, was synthesized by using the divergent reaction scheme, as has been described in detail earlier.18,19 A carbosiloxane core was synthesized that was subsequently clad with dimethyl-6-hydroxyl-4-oxahexyl silyl groups. A schematic representation of the structure is shown in Figure 1. The molecular weight of the dendrimer was M ) 8923.4 g/mol. At room temperature the pure material is a colorless, transparent liquid of density 970 kg/m3, viscosity h ) 0.7 Pa s, surface tension 29.5 mN/m, and a glass transition temperature Tg ) -65 °C. If one takes the dendrimer molecules in the liquid to be closepacked spheres of uniform density and molecular weight M, their diameter may be evaluated as 3.1 nm. However, several different approaches, including molecular dynamics (MD) simulations, SAXS, Langmuir balances, and SFM, have been used to measure the effective diameter of these dendrimers both in solution and at interfaces;18 the measures of molecular size provided by these will be discussed later. The solvent was hypergrade toluene (99.8%) from Merck (Germany). Toluene is a good solvent for the carbosilane core but a poor solvent for the OH-exposing outer shell.19,20 A stock solution of ca. 10% dendrimer in toluene was prepared, and a small amount of tetrahydrofuran (THF) added to prevent hydrogen bonding between the -OH groups on the outer shells that would otherwise cause the dendrimers to associate and eventually precipitate. The concentration of dendrimer solution used in our experiments was made up to 0.5 mg/mL. The mica used was grade 1 Ruby Clear, supplied by S. & J. Trading Inc., New York. Apparatus and Procedure. The SFB used is a modified version of one that has been described in detail earlier.21,22 It is capable of measuring normal forces Fn(D) between curved mica (18) Sheiko, S. S.; Buzin, A. I.; Muzafarov, A. M.; Rebrov, E. A.; Getmanova, E. V. Langmuir 1998, 14, 7468. (19) Getmanova, E. V.; Chenskaya, T. B.; Gorbatsevitch, O. B.; Rebrov, E. A.; Vasilenko, N. G.; Muzafarov, A. M. React. Polym. 1997, 33, 289. (20) Getmanova, E. V.; Rebrov, E. A.; Vasilenko, N. G.; Muzafarov, A. M. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1998, 39, 581.

Figure 2. Normal force versus distance profiles, Fn/R versus D, between curved mica surfaces (radius of curvature R ≈ 1 cm) a closest distance D apart after incubation in 0.5 mg/mL carbosilane dendrimer solution. Open symbols, approaching profiles; solid symbols, receding profiles. Points J indicate jumps in or out. The inset shows the normal interactions between bare mica surfaces across dendrimer-free toluene, where the broken curve is the expected van der Waals attraction between mica across toluene. The dotted curve in the main figure is identical to the broken curve in the inset. The cartoon shows the schematic configuration of the SFB.22 The top surface is mounted on a piezoelectric tube (PZT) that can provide both normal and lateral motion between the surfaces, whereas the forces between them are monitored via the bending of the two orthogonal springs K1 and K2 on which the lower surface is mounted. surfaces (radius of curvature R ≈ 1 cm) as a function of the distance of closest approach D between them. It can also measure shear forces Fs between the surfaces when one of them is made to move laterally (at velocity vs) with respect to the other. The forces themselves are measured directly by the bending of two orthogonal sets of springs, whereas the motion is provided (both in normal and lateral directions) via a sectored piezoelectric tube (PZT). A brief description appears in the preceding paper;17 a schematic of the essential configuration is given as the cartoon in Figure 2. After the apparatus was assembled and calibrated in air contact, a droplet of the 0.5 mg/mL dendrimer solution was injected between the two mica surfaces and allowed to incubate for some hours before measuring normal and shear forces. At the end of these measurements a droplet of the stock solution (ca. 10 wt % concentration) was added and left for 24-48 h to allow solvent evaporation, leaving nearly bulk liquid between the surfaces, after which measurements were again carried out.

Results Normal Forces. Normal force profiles Fn(D)/R versus D after adsorption of the dendrimer from a 0.5 mg/mL solution are shown in Figure 2. Such normal force profiles were also carried out at different points during an experiment, in particular before and after shear measurements, to control for the integrity of the adsorbed layers. Figure 2 shows the results from several runs of both approaching and receding surfaces; also shown as a broken curve is the normal force profile in pure toluene. The approaching profiles show that no force was detected (21) Klein, J.; Perahia, D.; Warburg, S.; Fetters, L. J. Nature 1991, 352, 143. (22) Klein, J.; Kumacheva, E. J. Chem. Phys. 1998, 108, 6996.

High-Surface-Energy Carbosilane Dendrimers

Figure 3. Fn/R versus D profiles between the curved mica surfaces across nearly bulk dendrimer liquid. Open symbols, approaching profiles; solid symbols, receding profiles.

from far away (>250 nm) down to about 15 nm, after which the surfaces jump (from D ) 15 ( 1 nm) into a contact position at 6.2 ( 0.2 nm; further compression of the surfaces indicated a “hard wall” repulsion, that is, the surface separation did not further decrease within the range of compression studied (J2500 µN/m). On decompressing the surfaces, the separation between two surfaces again remains at D ) 6.2 ( 0.2 nm as Fn decreases from a high repulsion down to zero, then increases slightly (to D ) 7 ( 0.5 nm) on applying negative load to a pull-off value Fp = 2200 µN/m, at which point the surfaces jump out abruptly to ca. 250 nm. Such jumps are expected whenever (∂Fn/∂D) > K2, the spring constant of the normalforce spring on which the lower mica surface is mounted. The range and magnitude of the normal surface forces provide information both about the structure of the adsorbed dendrimer layers and also about the interdendrimer interactions. These will be considered in more detail in the Discussion. Normal force profiles measured in nearly bulk dendrimer liquid differed from the as-adsorbed monolayer behavior of Figure 2, and are shown in Figure 3. On approach of the surfaces a monotonically increasing repulsion is observed from around 60 nm, and is probably attributable to the squeezing-out and compression of the dendrimers loosely associated within the gap. The receding profiles show some hysteresis, and possibly a small attraction on separation (but no jump-out). This suggests that once the thick layers have been compressed, the aggregated material is weakly associated and a weak force is required to break it up and separate the surfaces. Shear Forces. Two kinds of shear responses were noted in our experiments; both required a yield force to initiate sliding between the surfaces: however, in one case the surfaces slid smoothly past each other once sliding had been initiated, whereas in the other a marked stick-slip motion was observed. The smooth sliding appears to be associated with a much weaker shear interaction between the dendrimer layers, as indicated by the much lower effective friction coefficient in this case (see below). At the same time, we observed that after several shear force measurements with smooth sliding, stick-slip behavior gradually set on until it was fully developed. This suggests

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Figure 4. Variation of shear force Fs (lower trace) between the mica surfaces in the smooth-sliding regime, after incubation in 0.5 mg/mL carbosilane dendrimer solution, as the top surface is made to move back and forth at a mean shear velocity vs ) 760 nm/s in each direction (upper trace). The surfaces are slowly approaching, and at point J they jump from D ≈ 15 nm to contact at D ) 6.2 nm.

that the mutual shear interaction between the dendrimer layers is being “massaged” from a weaker to a stronger one, possibly by the optimization of the extent of hydrogen bonding during shear (see Discussion concerning the different possibilities of hydrogen bonding between dendrimers). Additionally, we found that changing contact positions and orientation between the surfaces in a given experiment could result in the behavior reverting from smooth sliding to stick-slip motion. In what follows we describe separately the two modes. Smooth Sliding Mode. Figure 4 shows the shear forces transmitted to the lower dendrimer-bearing surface as a back-and-forth motion at a shear velocity vs is applied to the top surface, and as the two surfaces are slowly made to approach each other. There is no interaction between the surfaces until at the point marked J they jump together from 15 ( 1 nm to contact at D ) 6.2 ( 0.2 nm. The shear force Fs at once rises as the surfaces stick together until it exceeds the frictional force, at which point the surfaces begin to slide past each other. For the sliding velocities shown in Figure 4 (vs ) 760 nm/s), the shear force does not go through a maximum on applying the shear motion, but reverts rather from sticking to sliding. The magnitude of Fs during sliding varies at the noise level of the measurements, but is essentially constant, a signature of smooth sliding. Such measurements were carried out at different applied normal loads and lateral velocities, and the results are summarized in Figure 5. We note that Fs increases roughly linearly with the load Fn, and that there is little systematic variation of Fs with the shear velocity vs in this range of shear velocities, the frictional forces varying over some 20% for an eightfold change in vs (150 nm/s-1220 nm/s). The solid curve running through the data is obtained by applying the Tabor model23 for the shear of boundary lubricants to the case of the dendrimer layers, as discussed in detail later, and indicates an effective friction coefficient µeff ≈ 0.03. We also note that for much slower values of vs, smooth sliding was preceded by a maximum in Fs at the yield point, after which the (23) Tabor, D. In Boundary Lubrication; Georges, J. M., Ed.; Elsevier: New York, 1982; p 651.

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Figure 5. Variation with normal load Fn of the shear force Fs required for steady (smooth) sliding at velocity vs of the two mica surfaces after adsorption of the carbosilane dendrimers from 0.5 mg/mL solution, taken from traces as in Figure 4. Symbols O, 0, ], 4, 3, correspond to mean shear velocities 150, 200, 500, 760, and 1220 nm/s, respectively. The broken curve is the predicted variation from eq 6 with R ) 0, whereas the solid curve through the data is from eq 6 with R ) 0.03, ν ) 0. See text for further details. The data points ! in the inset show the much larger frictional forces encountered at the lower sliding velocity vs ) 18 nm/s; the dotted line corresponds to a slope ∂Fs/∂Fn ) 0.5.

Figure 6. Top trace: shear force Fs between mica surfaces after adsorption of dendrimer from 0.5 mg/mL solution, in response to applied motion of upper surface as shown in lower trace. Mean applied lateral velocity in region I is vs ) 18 nm/s. Normal load Fn/R ) 1950 µN/m. At point B the applied lateral motion is stopped.

shear force relaxed to the value associated with steady sliding. This is seen in Figure 6, where vs ) 18 nm/s. It is important to observe that at this low velocity the frictional resistance to steady (smooth) sliding is much greater than for the range of velocities shown in Figure 5. Although we did not study in detail the effect of such low shear velocities on the frictional force for the smooth

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Figure 7. Variation of shear force Fs (traces b, d) between the mica surfaces in the stick-slip sliding regime, after incubation in 0.5 mg/mL carbosilane dendrimer solution, as the top surface is made to move back and forth at a mean shear velocity vs ) 50 nm/s and 125 nm/s in each direction (traces a, c respectively). The surfaces are slowly approaching, and at point J they jump from D ≈ 15 nm to contact at D ) 6.2 nm.

sliding case, the limited data taken at vs ) 18 nm/s suggest a much higher friction coefficient, µeff ≈ 0.5 (inset to Figure 5). This may be attributed to the fact that, at the much lower shear rates (vs/D) associated with the low vs, the shear interaction between the sliding layers is able to relax to much higher values: the characteristic times for such a process must therefore be comparable with D/vs, of order 0.1-0.3 s. On stopping the applied motion (Figure 6, point B), the shear force relaxes to some finite, very slowly decaying value, which may be viewed as a residual stored stress within the sheared layers. This behavior has characteristics of both a liquid (relaxation) and a solid (residual stress), and resembles the response of the sheared PPID material studied earlier.17 Stick-Slip Sliding Mode. Stick-slip sliding of the surfaces took place after adsorption of dendrimers from solution (the conditions under which stick-slip rather than smooth sliding occurred are discussed above), and also when a nearly bulk liquid was confined between them. Figure 7 shows the shear forces after incubation in a 0.5 mg/mL solution. The surfaces are made to approach each other slowly, while at the same time one of the surfaces is made to move back and forth laterally (traces a and c). At the points J (traces b and d) they jump from about 15 nm to contact at D ) 6.2 ( 0.2 nm, as described earlier (Figure 2); the shear force Fs at once rises as the surfaces stick together until, at some magnitude Fc, it exceeds the frictional force between the surfaces. At this point (A on trace b) the surfaces slip, then stick again (B on trace b), and sliding proceeds via stick-slip motion. Such stick-slip sliding is common, and has been described in many systems;24 it can result from different mechanisms, as discussed later, depending on the nature of the interface being sheared. We do not know what is the origin of the difference between the smooth sliding seen in Figure 4 and the behavior of Figure 7, both of which take place when the surfaces jump from ca. 15 nm to contact at 6.2 ( 0.2 nm. It may be attributable to the different mutual (24) See for example Tabor, D. Friction; Doubleday: New York, 1973; Yoshizawa, H.; Israelachvili, J. J. Phys. Chem. 1993, 97, 11, 300; Kumacheva, E.; Klein, J. J. Chem. Phys. 1998, 108, 7710, and references therein.

High-Surface-Energy Carbosilane Dendrimers

Figure 8. Variation of shear force Fs with normal load Fn once the surfaces have come into contact at D ) 6.2 nm after incubation in dendrimer solution (0.05 mg/mL). Top trace a is back-and-forth lateral motion applied to the top surface, with vs ) 125 nm/s. Curves b, c, and d are the shear forces transmitted to the lower surface at Fn ) 210, 1030, and 4310 µN/m, respectively.

orientation of the interacting dendrimer monolayers in the two cases, though we have no direct evidence for this. The magnitude of the critical shear force Fc at the yield point varied both with normal load Fn and with the applied shear velocity vs. Figure 8 shows typical stick-slip traces for a given vs (125 nm/s) and different Fn for sliding between two dendrimer monolayers (after the spontaneous jump of the surfaces to 6.2 ( 0.2 nm). Fc increases clearly with load, as does the extent of the stick part of the cycle. We note that during the latter part of the stick cycle there is already some slight sliding between the surfaces: the broken straight line in trace c of Figure 8 corresponds to the surfaces moving rigidly together, with no slip, and the deviation of the trace from this broken line is the extent of sliding before the slip from A to B. The slip duration itself, that is, the time taken for the surfaces to slide from A to B, at which point the relative motion abruptly ceases and the sheared material in the gap becomes solidlike (in the sense that it can sustain a shear stress during the next stick motion), has an upper limit of ca. 0.02 s. We note that it is possible to analyze this motion, as done elsewhere,25 to yield an effective shear viscosity ηeff of the confined dendrimer layers during the slip; a more detailed consideration of this is, however, beyond the scope of the present paper. Figure 9 shows the variation of Fc with vs of the top surface, for a range of applied shear velocities at approximately the same normal load. The traces show clearly that, for a constant Fn, Fc decreases with increasing vs, as does the amplitude of the slip part of the stick-slip cycle. Qualitatively, we believe this is due to the shorter times available at the faster shear rates for the dendrimer layers to optimize their adhesive interactions. This is because the duration of the stick part of the cycle, during which the layers are not in mutual motion and can then optimize their interactions, is higher at lower sliding velocities. As noted, a modified stick-slip sliding was observed also when the surfaces were compressed and made to slide across the nearly bulk dendrimer liquid (whose normal (25) Klein, J. J. Non-Cryst. Solids 1998, 235, 422.

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Figure 9. Variation of shear force Fs with applied shear velocity vs once the surfaces have come into contact at D ) 6.2 nm after incubation in dendrimer solution (0.05 mg/mL), at approximately the same load Fn for all cases. In each trace the triangular trace is the back-and-forth motion applied to the top surface, whereas the stick-slip trace is the shear force between the surfaces. Note particularly the higher magnitude of the yield stress Fc and the shorter duration of the stick cycles at the higher vs. Trace a: Fn ) 21.5 µN, vs ) 50 nm/s; trace b: Fn ) 21.6 µN, vs ) 125 nm/s; trace c: Fn ) 21.5 µN, vs ) 245 nm/s; trace d: Fn ) 21.7 µN, vs ) 475 nm/s.

Figure 10. Variation of shear force Fs with normal load Fn between the mica surfaces across nearly bulk dendrimer liquid. Top trace a is back-and-forth lateral motion applied to the top surface, with vs ) 125 nm/s (same as in Figure 9). Curves b, c, and d are the shear forces transmitted to the lower surface at Fn ) 3780, 5050, and 6060 µN/m, respectively.

force versus distance profile characteristics are given in Figure 3), and this was characterized at different normal loads and shear velocities. Figure 10 shows the variation of the shear force at different values of Fn. A clear yield force Fc is indicated, but the slip part of the cycle is much less abrupt than for the stick-slip pattern between sliding dendrimer monolayers, with the characteristic time for slipping being ca. 0.2 s, at least 10 times longer than for monolayer sliding. We attribute this to a higher effective shear viscosity of the confined, nearly bulk dendrimer

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Figure 11. Variation of shear force Fs (lower traces) between mica surfaces bearing dendrimer monolayers (after incubation in 0.5 mg/mL solution) (a) and across nearly bulk dendrimer liquid (b) in response to a lateral motion (top trace) applied to the top surface. Initially the surfaces are at rest; at point A a very low lateral velocity is applied (vs ) 6.7 nm/s), whereas at point B the applied motion is stopped. The lower traces in both cases reveal that little relaxation of the stored shear stress takes place after the stopping of the applied lateral motion.

liquid as the surfaces slide past each other. We note also that the amplitude of the stick-slip decays after some cycles to smooth sliding motion. This suggests qualitatively that a possible higher initial order or layering of the confined molecules before yield, which may have resulted in the initial stick-slip response,22 has degraded upon shear. This trend is in the opposite sense to what was earlier observed with the monolayers, where progressive shear of smoothly sliding surfaces resulted in the onset of stick-slip motion. Finally, we examined the relaxation behavior of the confined dendrimer layers after an applied shear stress. Figure 11 shows the stick-slip response obtained when the surfaces are sheared past each other by applying a very low lateral velocity to the upper mica surface (vs ) 6.7 nm/s, compared with vs ) 125 nm/s for the traces in Figures 8 and 10), and then stopping the applied motion (point B). Both the case of dendrimer monolayers adsorbed from a 0.5 mg/mL solution (Figure 11a) and the case of shear of a nearly bulk dendrimer liquid (Figure 11b) are shown: both show a marked stick-slip response, but once the applied motion ceases, there is no significant relaxation of the shear stress over time scales of at least a few minutes. This indicates a solidlike behavior of the confined layers in the two cases. The absence of relaxation for this stick-slip motion, even at these ultralow sliding velocities, contrasts with the relaxation observed at low vs for the smooth-sliding regime, Figure 6. We also note that at these very low shear velocities the decay of the stick-slip amplitude for the case of nearly bulk liquid is very much weaker than at higher vs (as in Figure 10), probably because of the longer time available for rearrangements of the sheared material. The variation of Fc with Fn and with vs for the cases of sliding of the dendrimer monolayers and for that of nearly bulk liquid are summarized in Figures 12 and 13, respectively. Figure 12 shows the increase in Fc both as Fn increases at a given shear velocity, and also that the rate of increase of Fc with Fn is significantly lower at higher shear velocities. Similar trends are seen also in Figure 13 for the nearly bulk liquid, though as shown by comparison with the monolayer case, they are considerably weaker. These trends are analyzed in detail in the following section.

Figure 12. Variation of yield shear force Fc (from the stickslip sliding regime) with normal load Fn between mica surfaces bearing dendrimer monolayers (after incubation in 0.5 mg/mL solution) at different shear velocities vs. Data sets a, b, c, d correspond to vs ) 50, 125, 250, and 500 nm/s, respectively. The broken curve is the predicted variation from eq 6 with R ) 0, whereas the solid curves through the data are from eq 6 with ν ) -0.5, and R ) 0.7, 0.35, 0.34, 0.33 for curves a-d, respectively. See text for further details.

Discussion In this section we consider our findings both for the carbosilane dendrimer results per se, and also in relation to the low-surface-energy (-CH3 terminated) PPIDs examined earlier.17 As a droplet of the low-concentration (0.5 mg/mL) carbosilane solution is injected between the mica sheets, a layer of the dendrimers, driven by the attraction of the polar -OH groups exposed on the outer dendrimer to the mica substrate, adsorbs on each surface.

High-Surface-Energy Carbosilane Dendrimers

Figure 13. As Figure 12 but for yield shear forces Fc and normal load Fn between mica surfaces across nearly bulk dendrimer liquid. Data sets a and b (filled symbols) are taken from Figure 12 (interaction between dendrimer monolayers) for shear velocities vs ) 50 and 125 nm/s respectively, whereas data sets c and d are for nearly-bulk dendrimer liquid at these same velocities, respectively.

It is of interest that, on the basis of the bulk density of the liquid dendrimer and on its molecular weight, a diameter of some 3.1 nm per molecule in the bulk liquid state may be evaluated. This is precisely half the hardwall repulsion observed as the surfaces approach and jump from D = 15 nm to D ) 6.2 ( 0.2 nm. It is thus tempting to view each adsorbed layer as consisting of a monolayer of the 3.1-nm-diameter spheres, but this is likely to be an oversimplification. Both experimental10,12,18 (SFM and SAXS) and MD simulations26 suggest that the attachment of the -OH groups on the carbosilane to an adsorbing substrate (whether mica or a water surface) in air tends to “squash” the dendrimer, and such compressive distortion has been observed also for other dendrimers. In the presence of a good solvent, MD results indicate27 that some half of the -OH moieties on the carbosilane attach to the substrate, with the others dangling free from the outer dendrimer shell. Langmuir balance experiments on these same carbosilanes18 show that at the water-air interface the attachment of the -OH groups (at the water surface) results in an effective diameter for the dendrimers parallel to the interface of some 3.7 nm. In our experiments adsorption on the mica substrate is also likely to squash the dendrimers, as occurs in other adsorbed dendrimers11 and as also seen in our study of PPID.17 However, the presence of the toluene as a medium (rather than air) weakens that effect by moderating the -OH/mica attraction; in addition, toluene is likely to solvate and swell the dendrimer core,26 thereby opposing any compression. The observed hard-wall layer of thickness 3.1 nm per surface is thus probably due to a combination of compression of the dendrimers due to the -OH attachment to the surfaces, balanced by swelling of the carbosilane core by the toluene. (26) Mazo, M. A.; Zhilin, P. A.; Gusarova, E. B.; Sheiko, S. S.; Balabaev, N. K. Submitted to J Mol. Liq. (27) Mazo, M. A.; Sheiko, S. S.; Perov, N. S.; Gusarova, E. B.; Balabaev, N. K. Izv. Ross. Akad. Nauk 1997, 61, 1728.

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Two further aspects of the normal force profile deserve comment. The jump from some 15 nm to the 6.2-nm hard contact separation is due to a Euler-like instability, and is expected whenever ∂Fn/∂D ) K2, the constant of the normal-forces spring supporting the lower mica surface (cartoon in Figure 2). For the case of the bare mica surfaces across dendrimer-free toluene (inset to Figure 2), such a jump is expected17 at D = 9 nm. For the case of mica covered by PPID the jump occurs from D j 12 nm, and reflects the fact that the Hamaker constant of the PPIDs exposing nonpolar -CH3 groupssis likely to be close to that of the toluene medium. For this reason the overall effective Hamaker constant for the mica-mica interaction with and without the adsorbed PPID layers is likely to be similar. In the present case the inward jump occurs from significantly further out (D J 15 nm). We attribute this to the more polar nature of the -OH-exposing carbosilane dendrimers adsorbed on each surface, which leads to a higher effective value of the overall Hamaker constant characterizing the attraction between the dendrimercoated mica (in the case of the PPID dendrimers, there is the possibility of dipolar interactions due to the presence of amido groups,17 but this appears to be much weaker). The second marked difference relative to the PPID layers examined earlier17 is that the adsorbed carbosilanes appear to be more rigid under compression. Whereas the PPID layers could be compressed from ca. 6.5 to 4.5 nm, the thickness of the confined carbosilane layers appears to remain at 6.2 ( 0.2 nm over the entire range of compression studied (Figure 2). This is a little unexpected, because the fifth-generation PPID molecules have a more crowded outer shell and we would expect them to be more rigid;17 we return to this point below. The slight increase in D just before the pull-off (Figure 2) suggests a slight stretching (and hence flexibility) of the carbosilane dendrimers. For the case of a nearly bulk liquid (Figure 3), the force profiles become softer, but this is likely to be due to a looser aggregate structure within the gap, and not to reflect the rigidity of the individual molecules. Tentatively, we attribute the apparently more rigid nature of the carbosilane monolayers relative to the PPID as follows: the -OH/mica attraction is much stronger than the -CH3/ mica one because of the greater polarity of the hydroxyl group. This distorts the adsorbed dendrimerssas also suggested by the MD studies,26 even in a good solvent mediumsto an extent that further compression (within the range of our parameters) has little additional effect. It is worth observing in this context that at the point of jump-in the large adhesive force (Fp) strongly compresses the dendrimers even in the absence of any applied normal load. Recalling the normal force profile of the adsorbed PPID molecules,17 we note that in that case too no further compression could be observed at normal loads greater than the magnitude of Fp (> 20 µN) in the present case. Once the surfaces jump into contact the strong adhesion between themsreflected by the large pull-off forcesmay be attributed largely to the dipolar (hydrogen-bondinglike) interactions. Two types of H-bonding between the opposing layers may be possible: the -OH‚‚‚HO- interactions, and interactions of -OH groups from one surface with the -O- groups in the outer shell of the dendrimers in the other layer (see Figure 1). In the latter case, a certain (slight) overlapping or interdigitation of the opposing molecules may occur. It is of interest to estimate the magnitude of these interactions. Each of the carbosilane dendrimers exposes 32 -OH groups on its outer shell. Some half of these, as suggested by MD simulations,26 attach to the adsorbing substrate, and of the rest a significant fraction are likely to be interacting with their

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Zhang et al.

adjacent neighbors. Crudely, therefore, we may assume that a number n of order (1-5) -OH groups per dendrimer interact with groups (either -OH or -O-) on the opposing layer. In what follows we further assume that these shortranged dipolar interactions are much larger than the dispersive van der Waals forces, and ignore the latter. From the Johnson-Kendall-Roberts (JKR) model for interaction between adhering curved surfaces,28 the pulloff force Fp relates to the surface energy γ per unit area of each surface as

Fp ) 4πγR

(1)

where R is the radius of the undistorted (crossed cylindrical) surfaces. The interaction energy per unit area between the contacting surfaces is just W ) 2γ. If we attribute the magnitude of γ entirely to the polar -OH interactions, then W ) n/Ad, where  is the magnitude of the attractive dipolar interaction and Ad the area per dendrimer. Taking Fp/R ) 2.2 mN/m (from Figure 2) and the diameter of each adsorbed dendrimer as ca. 4 nm (see earlier discussion), we find  ≈ (6/n) × 10-21 J ≈ (0.3-1.5)kBT for n in the range estimated above. Although this value is smaller than the magnitude of bare dipole-dipole interactions, which is of the order of a few kBT, it is reasonable in the present case as both the presence of the toluene medium and that of the added THF reduce the strength of the bare interactions. Moreover, such a sub-kBT interaction strength is also consistent with the fact that the free dendrimers do not aggregate from solution, as would be the case if the adhesive energy between them greatly exceeded their thermal energy kBT. We consider finally the variation of the shear yield forces with normal load Fn between the surfaces, as appears in Figures 6 (smooth motion) and 13 (stick-slip motion) for the case of the dendrimer monolayers sliding past each other. We note at first the qualitative differences between the Fs versus Fn or Fc versus Fn plots in the two cases. For the case of the smooth sliding, Figure 5, the friction force increases quasi-linearly with load, and at applied lateral velocities vs g 150 nm/s is essentially independent of vs (but see earlier remarks on the increase at very low velocity, inset to Figure 5). For the stick-slip motion, on the other hand, the variation of Fc with Fn has a marked curvature reminiscent of the variation of contact area with load (see later), whereas the yield force for a given load decreases strongly with vs (see also Figure 9). This latter variation suggests that a rearrangement of the layers is taking place over time scales comparable with the period over which the layers are in the stick part of the cycle, as discussed below. Such a slow variation is consistent with infrared (IR) absorption studies of the OH-terminated carbosilane dendrimers.19 These IR measurements show that at high molecular concentrationsscertainly the case within the compressed surface layerssthe -OH branch ends reorient themselves rather slowly to form intermolecular H-bonds. The form of the friction traces, particularly for the case of the stick-slip motion, where a finite yield stress is required to initiate sliding, is reminiscent of frictional behavior with boundary lubricants, as described by Tabor and others.23,29,30 In this model, sliding takes place when adhesive junctions between the compressed boundary lubricant layers are sheared. In the simplest treatment, (28) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London, Ser. A 1971, 324, 301. (29) Briscoe, B. J.; Evans, D. C. B. Proc. R. Soc. London 1982, A380, 389. (30) Tabor, D. Proc. Inst. Mech. Eng. 1991, 205, 365.

the frictional force between sliding surfaces coated with a molecular lubricant layer may be written as

Fs ) SA

(2)

Here S is the yield shear strength of the interface between the dendrimer layers, and A is the contact area between them. For a flat, circular contact between two crossed cylindrical surfaces, as in our experiment, the contact area A is given by the JKR expression28

A ) πa2 ) π

{2KR [F

n

}

+ 2Fp + 2(FnFp + Fp2)1/2]

2/3

(3)

where a is the radius of the area of contact and Fp is as before the pull-off force (at the minimum of the adhesive well, Figure 2). Here K is related to the Youngs modulus of the substrate (mica + glue layer) and has a value estimated22 as K ) (1 ( 0.3) × 109 N/m2. If we write A0 as the contact area at zero applied load (Fn ) 0), then putting (Fn/Fp) ) x, we may rewrite eq 2 as

{ [(

]}

1 x A ) 1 + + (1 + x)1/2 A0 2 2

)

2/3

(4)

In general, the yield stress S in eq 2 may itself depend on the externally applied pressure P () Fn/A) between the sliding surfaces. For the case of clean solid surfaces sliding past each other, there is some indication31 that S is independent of P. However, if we make such an assumption for the dendrimer-coated layers, and insert eq 4 into eq 2, we obtain the variation shown as the broken curves in Figures 5 and 12. Clearly the increase in contact area A alone is not sufficient to explain the increase in the friction with load, and to account for the data there must also be an increase with load of the yield stress S. Indeed, for the case of fatty acid boundary lubricants, Briscoe and Evans29 have measured a yield stress increasing linearly with applied pressure, S ) S0 + RP. Here S0 is the yield stress between the surfaces when there is no externally applied load (and is due to the attraction between them), whereas at large pressures R is equivalent to the effective friction coefficient. In the present case, the mechanism by which the yield stress increases with pressure for the dendrimers used in our study is not known: one may speculate that increased pressure results in a more intimate match between the rubbing layers and thus in a larger number of -OH‚‚‚HO- or -OH‚‚‚-O-interactions. In what follows we shall attempt a semiquantitative analysis of the variation of the yield stress S with applied pressure P, with the aim of obtaining insight into this mechanism. A general form such as:

S ) S0 + RP(P/P0)ν

(5)

allows the yield stress to vary nonlinearly with the applied pressure P. Here the pressure P0 is the effective pressure at Fn ) 0. The thing to note is that, even at Fn ) 0, there is an attractive force between the surfaces equal to the pull-off force Fp, which results in the mean pressure P0 ) (Fp/A0). (We recall that for the case of clean solid surfaces it appears31 that R ) 0, so that the yield stress is independent of pressure, whereas for the fatty acid monolayer boundary lubricants,29,30 ν ) 0, recovering the relation S ) S0 + RP.) Inserting these values for P and P0 into S in eq 4, and substituting in eq 2, we find (after (31) Homola, A. M.; Israelachvili, J. N.; Gee, M. L.; McGuiggan, P. M. J. Tribol. 1989, 111, 675.

High-Surface-Energy Carbosilane Dendrimers

Langmuir, Vol. 16, No. 8, 2000 3901

a little algebra)

{21[(1 + 2x) + (1 + x) ]} + x 1 RF { [(1 + ) + (1 + x) ]} 2 2 1/2

Fs ) Fs0

2/3

1/2

n

-2ν/3

(6)

Fitting eq 6 to the data of Figures 5 and 12 results in the solid curves indicated in these figures. For Figure 5 (corresponding to smooth sliding) we find a good fit to the data (solid curve) for ν ) 0 and R ) 0.03, that is, for a relation S ) S0 + RP similar to that of fatty acid boundary lubricants.30 It is of interest that the magnitude of R (which at high loads is an effective friction coefficient) for the case of the smooth sliding, over the range of parameters covered, is also similar to that of the fatty lubricants, though the interactions in the latter case are predominantly due to van der Waals forces rather than to dipolar interactions. For the data of Figure 12 (corresponding to stick-slip sliding), we find that the four curves, covering an eightfold range of applied lateral velocities, can be fitted well using eq 5 (or 6) by a single value of the parameter ν ) -0.5. This suggests that the yield stress S increases less rapidly with applied pressure (S ) S0 + const.P1/2) than is the case for fatty acid boundary lubrication, for which S ) S0 + const.P). At the same time the magnitude of the prefactor R decreases markedly as vs increases from its lowest value, and we find that R ) 0.7, 0.35, 0.34, 0.33 for the respective velocities. The decrease in this prefactor with vs is a measure of the greater yield stress (for a given P) at the lower velocities. In terms of a molecular mechanism, we attribute this to the longer time available to the dendrimer layers to rearrange and optimize their mutual interactions during the longer stick periods associated with low values of vs (see Figure 9). This consideration was noted also for the smooth motion summarized in Figure 6 and in the traces in Figures 4 and 6, where, for a given applied load, at the lowest shear velocities (18 nm/s) the frictional force was much larger than for vs in the range 150-1220 nm/s, where it was essentially constant. We note here the relation between the prefactor R and the magnitude of the effective friction coefficient µeff at large loads (and pressures). For large P, the shear stress S = RP(P/P0)ν, whereas the frictional force is Fs ) AS. Putting the normal force as Fn ) AP, and µeff ) Fs/Fn, we find µeff = R(P/P0)ν. Since P > P0 and ν < 0, this suggests that at large pressures the effective friction coefficient for these dendrimer monolayers decreases with increasing pressure. We may also try, using the boundary lubricant model, to estimate the friction force resulting from the shear of the interfacial bonds between the compressed dendrimer layers, and compare with the measured values of Fc. Taking a normal force Fn ) 30 µN, say, gives the contact area A ≈ 3 × 10-10 m2. The number of interacting dendrimers in this area is ca. A/d2, where d ≈ 4 nm is the diameter of a carbosilane molecule on the surface; for a bond energy  (estimated at ca. 0.3-1.5 kBT, see above)

the tension needed to break a bond is of the order of /δ, where δ is the stretching required to break the bond and is typically around 1-2 Å. On shearing, the shear stress rises (during the stick part of the stick-slip cycle) to its yield value, at which point the interfacial bonds break, the interface yields, and slip occurs to relax the stress. If all bonds need to break at once, the necessary shear force at yield would be Fc ≈ (A/d2)n(/δ), where n (estimated earlier as in the range 1-5) is the number of -OH‚‚‚HObonds per interaction of one dendrimer with its opposite number on the other surface. This gives Fc ≈ 500 µN. From Figure 13, the measured shear forces at yield for Fn ) 30 µN is about an order of magnitude less, Fc ) ca. 20-25 µN. A weak point in our estimate is probably that not all dipolar bonds between the surfaces need to break simultaneously for yield to occursfor example, a dislocation-like mechanism may operate during the sliding. Such a mechanism would bring the predicted estimate of 500 µN down, closer to the observed values, but at this level of approximation we do not pursue this further. Finally, we emphasize the differences between modification of surface interactions using the OH-exposing carbosilanes in the present investigation and the CH3exposing PPID examined in our previous study.17 Within the parameters of our experiments, the carbosilane layers have characteristics that are much closer to solidlike behavior: they are highly rigid; they undergo stick-slip behavior reminiscent of that between frozen monolayers of confined simple liquids;32 and they undergo little relaxation after shear. We attribute these features, as explained above, to the strong interactions of the polar -OH groups both with the substrate and with each other. In contrast, the CH3-exposing dendrimers appear more deformable, do not exhibit stick-slip sliding under any conditions, and undergo significantsthough partials relaxation of stored stress when they have been sheared. We believe this is due to the much weaker van der Waals forces that dominate the interactions of these molecules both with each other and with the adsorbing substrate. These are first investigations of the way in which dendrimers may modify both normal and frictional forces between surfaces. They point the way to more detailed modifications by suitable tailoring of the chemical groups exposed at the outer dendrimer shell. These include the intriguing possibility of, for example, using dendrimers that are amphiphilic in the sense of exposing blocks of chemically different groups on different regions of their surface. Such blocks could enhance adhesion to a substrate on one hand, while independently providing the desired modification of the surface interactions on the other hand. Acknowledgment. We thank the Deutsches-Israel Program (DIP), the US-Israel Binational Science Foundation, and the Israel Science Foundation for support of this work. S.S.S. thanks the Deutsche Forschungsgemeinschaft (project SH 46/2-1) for financial support. LA9903797 (32) Kumacheva, E.; Klein, J. J. Chem. Phys. 1998, 108, 7010.