Atomic force microscopy of local compliance at solid—liquid interfaces

24 June 1994

ELSEVIER

CHEMICAL PHYSICS LETTERS

Chemical Physics Letters 223 (1994) 336-340

Atomic force microscopy of local compliance at solid-liquid interfaces S.J. O’Shea ‘, M.E. Welland ‘, J.B. Pethica b aDepartment OfEngineering, Cambridge University, Cambridge CB2 lPZ, UK b Department OfMaterials, University of Oxford, Oxford OXI 3PH, UK

Received 25 April 1994

Abstract A modified atomic force microscope ( AFM ) is used to directly measure the local compliance of ordered liquid layers at solidliquid interfaces. Measurements of the compliance of the solvation structure for octamethylcyclotetrasiloxane and n-dodecanol near graphite and mica surfaces are presented. We show that reasonable correlation decay lengths, molecular sixes, and material rigidities can be determined. The new method is based on a force modulation technique and can be more sensitive to weak longer range interactions compared with the more direct measurement of forces using the static deflection of the AFM cantilever.

The mechanical response of materials at the nanometer length scale can be very different from that of the bulk. A good example of such local response is provided by the ordering of liquids near solid surfaces since the region of a liquid immediately adjacent to a solid surface undergoes some molecular ordering due to the constraint provided by the solid wall. This structuring, originally suggested by Hardy (for a review of early work, see ref. [ 1] ), is particularly marked when the liquid is between two closely spaced solid surfaces. It has important consequences for a wide range of phenomena including adsorption, friction and adhesion, particularly in polymeric or colloidal and biological systems [ 2,3 1. Direct evidence of the mechanical consequences of these highly structured short-range forces in liquids (solvation forces) was originally provided by Israelachvili and co-workers [ 4,5 ] using the surface force apparatus ( SFA ) . In SFA experiments two flat mica surfaces are brought together with a liquid in the gap. The force between the surfaces is observed to oscillate with a period determined by the liquid molecular size and with an in-

creasing amplitude as the mica surfaces approach mutual contact. The range and magnitude of the solvation force shows a strong dependence on molecular shape and conformation [ 3 1. Furthermore the fiictional force between the surfaces may also depend on the discrete number of molecular layers in the gap and may show solid-like shear resistance [ 6 1. These phenomena are of considerable importance in the operation of the atomic force microscope (AFM) both in liquids and in ambient since in the latter case adsorbed water is usually present on the surface [ 71. In this Letter, we demonstrate that a modified form of AFM can be used to directly observe solvation structures in liquids at surface separations of six or seven molecule dimensions, comparable to SFA sensitivity. We show that reasonable correlation decay lengths, molecular sizes, and material rigidities can be determined. This brings the advantages of high spatial resolution to solvation force studies, with the spatial scales involved being directly relevant to the scale of colloidal particles. Furthermore there is some evidence that spatial varia-

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S.J. O’Shea et al. /Chemical Physics Letters 223 (1994) 336-340

tions of forces across a surface can be highly significant [ 8,9]. An additional aspect of AFM in comparison with the SFA is that it allows for a very wide choice of solid substrates and geometries, and the possibility of the simultaneous measurement of other physical properties at a molecular scale using related scanning microscopy techniques. Our previous work on the measurement of structural forces in liquids [lo] was constrained by the necessity of having a moderately blunt AFM tip (radius of curvature > x 10 nm) in order to clearly observe the solvation force oscillations. Here we present new, direct measurements of the compliance (or stiffness) of the solvation structure. A large tip radius does not appear to be such a severe requirement in the new technique, which measures local stiffness rather than the force. The key modification we make to AFM operation is the direct application of a force to the tip, rather than the usual application of a displacement between the tip and the surface. This gives the direct determination of junction stiffness without possible complications from the interaction of the comparable cantilever and junction stiffnesses [ 111. Specifically, if the tip is driven with an oscillatory force of constant amplitude then the junction stiffness (S) is givenby [ll] S=k

$1 (

, )

(1)

where k is the spring constant of the cantilever, x the amplitude of the lever oscillation as a result of the applied oscillatory force and x0 the lever amplitude far from the surface. The dynamic aspects of the lever response can be ignored for the present experiments because the system is heavily damped and the driving frequencies ( 10 Hz to 1 kHz) are much less than the lever resonance frequencies (26 to 60 kHz). An important corollary of this technique is that in principal the mechanical contact area of the junction can be found since, for an elastic contact [ 111, S%2E*a, where E+ is a modified Young’s modulus and a is the radius of the contact zone. A measurement of the junction contact area is of considerable importance in understanding many aspects of AFM, such as the basis of the imaging contrast mechanism or the shear forces acting between the tip and the sample.

331

The force modulation technique is implemented in the AFM by coating the AFM tip with a magnetic material, in our case a 17 nm cobalt thin film, and applying an external magnetic field to produce a force modulation normal to the sample surface. To minimise unwanted deflection signals arising from the flexing of the lever in the magnetic field the lever is masked from the evaporation source so that only the region at the end of the lever, around the tip, is coated. The deflection of the lever is monitored using an optical beam deflection type AIM [ 121 and the oscillatory component of the signal arising from the force modulation is measured using a lockin amplifier. A stainless steel liquid cell encloses the sample and the cantilever and a coil is wound around the cell to produce a field which is approximately normal to the sample surface. The maximum field strength is x 10e3 T and the maximum force we can apply to the tip is z 1 nN. Freshly cleaved mica and graphite surfaces are used as substrates. Two liquids are investigated, namely octamethylcyclotetrasiloxane (OMCTS ), a large almost spherical molecule, and n-dodecanol (C, ,H,,CH,OH), a linear molecule with a polar head group. Silicon AIM cantilevers were used with spring constants ranging from 0.5 to 1.1 N/m #‘. The applied force acting on the tip is given by k AZ, where AZis the change in displacement of the tip normal to the surface. The applied force is defined as zero far from the surface. In a typical experiment the applied force and stiffness are measured as the tip-sample separation distance is varied by linearly ramping the voltage applied to the appropriate piezoelectric. Fig. 1 gives an example of the raw data obtained at the dodecanol/ graphite interface. Periodic changes in the amplitude of the lever oscillation due to the solvation force can be seen. These also occur when the tip withdraws from the surface as the dodecanol is strongly layered at the interface. To allow for the possible influence of hydrodynamic forces (which are less likely in AFM than SFA because of the small tip radius) we varied both the approach speeds and the modulating force frequency by an order of magnitude or more. These changes had no discernible effect on oscillation period until thermal drift became a significant problem w1Nanosensors GmbH, Aidlingen, Germany.

S.J. O’Sheaet al. /Chemical PhysicsLetters 223 (1994)336-340

338

B : 0.3 5 s ‘ij m ; 0fJ 0.2 @I L A 0.1 -4

-2 0 Sample Displacement

2 (nm)

4

Fig. 1. The variation in the force acting on the tip (heavy line) and the cantilever oscillation (which is driven by the force modulation and is related to the compliance of the tip-sample junction) as the tip approaches and retreats from a graphite surface immersed in n-dodecanol. The tip-sample distance is varied by ramping the piezoelectric tubescanner a known distance normal to the surface. In the above case the tip approaches the surface from +5 nm. At an arbitrary distance of 0 nm the ramp is reversed and the tip is pulled back off the surface to - 5 nm. The tip approach speed is 1 rim/s and the lever is oscillated at 335 Hz.

at very low approach speeds ( x 0.1 nm/s). The lever oscillation decreases to zero as the tip drives into the surface because of the increasing stiffness of the material within the junction. In these experiments the maximum stiffness which can be measured is z 5 N/ m. This is set by the signal/noise level in the amplitude ratio x0/x and by the spring constant k, as seen in Eq. ( 1). To investigate more solid-like contacts, such as the repulsion between neighbouring atoms, requires the measurement of stiffnesses of x 50 N/m [ 13 1. This appears feasible if we note that, (i) x0/x is measured using a modulation technique so long integration times can be used to reduce the noise level, provided that any drift in the tip-sample distance is reasonable, and (ii) stiffer cantilevers can be used, provided that a stronger magnetic force can be applied to the tip to give a reasonable value of x0. The solvation structure can be seen out to long ranges, up to x 7 shells for both the OMCTS/graphite and dodecanol/graphite systems. This is comparable with the sensitivity achieved by the SFA apparatus [ 31. The oscillations in the lever amplitude (the stiffness signal) are more readily observed than the corresponding changes in the applied force, where a significant material stiffness is required to cause a

measurable static lever deflection. The data for the dodecanol/mica system, which is shown in Fig. 2, differs in that only one solvation shell is observed in the stiffness signal on tip approach. In this case the polar head group is oriented towards the hydrophilic mica surface and the flexible hydrocarbon chain lies perpendicular to the substrate. It is the flexible nature of the molecule so oriented which leads to the shorter-range solvation forces [ 3 1. In all three systems studied we often find that one or two solvation jumps are seen in the applied force curve after the lever oscillation signal has decayed to zero. That is, the compliance of the solvation layers nearest the surface can be relatively high ( > 3 N/m). The data can be replotted to give the material stiffness as a function of the tip-sample distance, as shown in Fig. 3 for OMCTS/graphite. As the tip-sample distance (D) is varied the force curves show a discontinuous jump between successive solvation shells whenever dF/dD > k, where F is the total force acting on the tip. Prior to the onset of the lever instabilities the stiffness oscillations are smooth. We can model this behaviour by expressing the solvation forces acting per unit area cf) between two flat surfaces as [ 3 ] f(z)=

-k,Tpcos(2nz/a)

e+/‘,

(2)

where z is the distance normal to the planar surface, kB is the Boltzmann constant, Tis the temperature, p I

“5”‘s..

/..

,I

0.6

3

3 b E =

0.4

s ‘Z m .E P ;

0.2

t J

0.0 -2 0 Sample Displacement

2 (nm)

4

Fig. 2. The variation in the force acting on the tip (heavy line) and the cantilever oscillation as the tip approaches a mica surface immersed in ndodecanol. The sample displacement has been defined as zero where the applied force becomes repulsive. Positive values of displacement correspond to the tip being off the surface. The tip approach speed is 0.7 rim/s and the lever is oscillated at 380 Hz.

S.J. O’Shea et al. /Chemical Physics Letters 223 (1994) 336-340

(W

Tip-Sample

Distance

(nm)

Fig. 3. The simultaneous measurement of the force acting on the tip (a) and the junction stiffness (b) as the tip approaches a graphite surface immersed in OMCTS. Dashed lines show the occurrence of tip instability jumps. To obtain the tip-sample displacement the measured piezoelectric movement of the sample is corrected for any displacement of the cantilever. The tip-sample has been defmed as zero where the applied force begins to increase monotonically. The tip approach speed is 0.9 rim/s and the cantilever is oscillated at 0.09 nm peak-peak and 380 Hz.

is the number density of molecules in the bulk liquid, ‘Iis a decay length and CJis the molecular diameter of the spherical liquid molecules. Summing f(z) over the surface elements of the tip (the Derjaguin approximation [ 31) as it approaches a planar surface gives

F(D) = 7 2nvf(z)

dv ,

(3)

D

where y is the distance along the surface plane and the tip-sample distance (D) is the distance between the tip apex and the surface, which is set at y= 0. For a parabolic tip shape (z=D+y2/2R) we find wcos(y

F(D)=-

S(D)=

g

=k,Tp(2xR)cos

+,>emDir,

(4a) (4b)

339

where R is the tip radius of curvature and tan 6= 2n, i.e. S= 8 1”. For simplicity the decay length has been equated to Qin the pre-factor terms. The above expressions are necessarily simplistic and the Derjaguin approximation is poor for R < x 100. Nevertheless the important trends of Eq. (4), namely the oscillatory nature of the profiles, the exponential decay of the amplitude and the phase difference between F(D) and S(D), are observed in the experimental data. We find a phase difference between F(D) and S(D) of !z 20” to %70” for the OMCTS/graphite and dodecanol/graphite systems. The large range of phase angle is a consequence of noise, particularly in the applied force data. The amplitude of the stiffness signal envelope decreases exponentially as the surfaces retreat from each other with a decay length of = 0.8 nm for OMCTS/graphite and x0.6 nm for dodecanollgraphite. There is some error in measuring the envelope amplitude wherever tip instabilities occur because it is not certain that the force minima is being sampled. This difficulty can be overcome to some extent by sampling the force profile as the tip retreats but before it has come into adhesive contact with the substrate. The measured oscillation period for dodecanol/graphite is 0.37 Z!I0.07 nm which is consistent with the molecule lying parallel to the substrate. The periodicity for the OMCTS/graphite data (0.5 f 0.1 nm) is reasonable but somewhat smaller than the values measured using the SFA ( x 0.8 nm) for OMCTS on mica [ 41. This difference may arise from water contamination of the liquid in our experiments which can strongly influence the surface forces acting [ 31. The significant van der Waals component to the applied force curve suggests that water may indeed be present in the tip-sample gap. While water contamination does not alter the solvation jump distances for large radii surfaces [ 41 the effect on a very local scale around the AFM tip is not known. By fitting Eq. (4b) to the OMCTS/graphite stiffness data of Fig. 3b we find that the pre-exponential term A0( = 2nRk,Tp) is x 10 N/m and hence R x 200 nm. Another estimation of R can be found by comparing the force data of Fig. 3a with SFA data for OMCTS on mica [ 41 which yields Rz 35 nm. The similarity of the estimates of R give further contidence that the essential features of the model are reasonable even for tip radii of high curvature. This is

340

S,J. O’Shea et al. /Chemical PhysicsLetters223 (I 994) 336-340

particularly so when we consider that the pre-exponential term of Eq. (2) has been fixed such that the force at D= 0 is equal to the continuum van der Waals adhesive force (kJp) which may not be strictly true in our experiments. A straightforward interpretation of the pre-exponent A0 is somewhat difftcult as the high tip curvature clearly implies that the measured compliance is not one-dimensional as suggested by the model but must also involve the lateral movement or shear of a considerable proportion of material within the tipsample gap. That is, A0 cannot be related to the simple compression of an individual molecule but is strongly influenced by all the molecules in the local environment. In this regard it is important to stress that the tip geometry is not known. Molecular scale roughness and tip shape can be expected to influence the measured solvation force or compliance and differences in the magnitude of the force oscillations were indeed observed using different tips under identical experimental conditions. Molecular dynamics simulations would appear to offer the best means for a deeper understanding of such problems in AFM [ 141. At a simpler level however we can view A0 as an elastic constant for the entire assembly of molecules in the tip-sample gap. For example if we take the effective tip-sample contact area to be 2rrRa [ 3,141 then using Sk:2E*u we find that the elastic modulus E*z& e-“/m, where n is the number of liquid layers in the gap. Hence we can estimate that E*x0.15 GPa for n= 1 and E*zO.04 GPa for n=2. These values are, not surprisingly, smaller than the bulk compressibility of the liquid ( x 1.5 GPa ) . In conclusion, we have shown that direct observation of both local compliance and solvation forces to several molecular diameters is possible using a modified form of AFM. This opens up the possibility of

high spatial resolution studies of the influence of surface structure on adjacent liquid. Equally importantly AFM allows the use of a much wider range of solid substrates than used hitherto in SFA. Reasonably quantitative statements can be made about the decay lengths for ordering and the compliance of the material in the tip-sample gap under the influence of the short-range structuring forces. We would like to thank Hugh Hunt, Ruth LyndenBell and Lev Gelb for many useful discussions. This work has been supported by Imperial Chemical Industries (ICI) plc. References [ I] J.C. Henniker, Rev. Mod. Phys. 2 1 ( 1949) 322. [2] J.N. Israelachvili, Surf. Sci. Rept. 14 (1991) 109. Intermolecular and surface forces (Academic Press, New York, 1992). [4] R.G. Horn and J.N. Israelachvili, J. Chem. Phys. 75 (1981) 1400. [ 51J.N. Israelachvili and R.M. Pashley, Nature 300 ( 1982) 341. [ 61 M.L. Gee, P.M. Mcguiggan, J.N. Israelachvili and A.M. Homola, J. Chem. Phys. 93 (1990) 1895. [ 71 R. Erlandsson, G.M. McClelland, C.M. Mate and S. Chiang, J. Vacuum Sci. Technol. A 6 ( 1988) 266. [ 81 Y.-H. Tsao, D.F. Evans and H. Wennerstrom, Science 262 (1993) 547. [9] N.A. Bumham, R.J. Colton and H.M. Pollock, Phys. Rev. Letters 69 (1992) 144. [lo] S.J. O’Shea, M.E. Welland and T. Rayment, Appl. Phys. Letters 60 (1992) 2356. [ 111 J.B. Pethica and W.C. Oliver, Physica Scripta T 19 ( 1987)

[ 31 J.N. Israelachvili,

[ 121 Z’Meyer and N.M. Amer, Appl. Phys. Letters 53 (1988) 1054.

[ 13 ] S.P. Jarvis, A. Oral, T.P. Weihs and J.B. Pethica, Rev. Sci. Instr., in press.

[ 141 L.D. Gelb and R.M. Lynden-Bell, Phys. Rev. B, accepted for publication.