Quantitative Probing in Atomic Force Microscopy of ... - ACS Publications

Chapter 15

Quantitative Probing in Atomic Force Microscopy of polymer Surfaces 1

Downloaded by UNIV LAVAL on July 16, 2014 | http://pubs.acs.org Publication Date: July 7, 1998 | doi: 10.1021/bk-1998-0694.ch015

Valery N. Bliznyuk, John L. Hazel, John Wu, and Vladimir V. Tsukruk

College of Egineering and Applied Sciences, Western Michigan University, Kalmazoo, MI 49008

Quantitative measurements of friction, elastic, and shearing behavior on a sub-micron scale and "multidimensional" characterization of surface properties are crucial for studying multicomponent polymer systems. We discuss the latest developments in quantitative characterization of local surface properties by scanning probe microscopy. First, we analyze calibration of cantilever spring constants. Second, we focus on approaches for estimation of tip/surface contact area that is vital for calculation of specific parameters such as surface energy and elastic compliance. Third, we discuss a chemical modification of the tips for chemical force microscopy. Recent endeavors have resulted in substantial progress in all these fields. We are moving towards a new level of surface nanoprobing when a poorly characterized tool with unknown shape, mechanical parameters, and surface chemistry will be replaced by a well defined nanoprobe that allows quantitative nanoprobing of surface properties.

Quantitative measurements of friction, elastic, and shearing behavior on a sub-micron scale is crucial for studying surface properties of multicomponent polymers systems (1-3). Promising results have been recently obtained using combined atomic force (AFM), chemical force (CFM), and friction force (FFM) microscopy techniques. A major advantage of these methods is the possibility of local testing of the surface physical properties in relation to the surface's topography and chemical composition. Apparently, the focus of SPM studies on polymer surfaces is gradually changing towards quantification of the surface measurements and a "multidimensional" characterization of surfaces. Just a few years ago, almost all publications in this field discussed polymer surface topography and microstructure. In contrast, now, more 1Corresponding authors. Fax: 616-387-6517; e-mail: [email protected].

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©1998 American Chemical Society

In Scanning Probe Microscopy of Polymers; Ratner, B., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1998.


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and more papers discuss surface topography in conjunction with friction properties, elastic behavior, adhesion, chemical composition, viscoelastic properties, conductive state, and thermal transformations. Such "multidimensional" collection of experimental data opens exciting opportunities for readdressing the traditional task of "structure-property relationships" of polymer surfaces on the molecular/submicron levels. An example of "multidimensional mapping" of surface properties (topography, friction, adhesion, and compliance) is demonstrated for a composite polymer molecular layer in Figure 1 (4). Langmuir film of polynaphtJioylene benzemidazole/stearic acid complexes deposited on silicon wafer shows domain morphology with clearly visible polymer domains of 2 nm thick separated by interdomain boundaries (silicon oxide) on topographical mode (Figure la). Other scanning modes reveal lower friction properties, lower stiffness, and lower adhesion for the domains as compared to the silicon surface (Figure lb -Id). Such concurrent information is invaluable for intelligent design of molecular films with controlled micromechanical properties (4). Currently, researchers use the third generation of scanning probe microscopes (SPM) with sophisticated modes and options which were not available on preceding versions. A general scheme of any S P M apparatus includes several major blocks which provide various functions: precise 3D movements of either a sample or a cantilever (piezoelements); S P M tip deflection (detection scheme); microfabricated probe (cantilever/tip); control of scanning parameters (electronic feedback); on-line and off-line analysis of 3D images (analyzing software) (Figure 2). Various aspects of reliable collection of experimental data are critical for quantitative measurements of surface properties: calibration, non-linearity, and creep of piezoelements; flexibility of tunneling, optical, and electric detection schemes; different designs of cantilevers (parallel beam, V-shaped) and tips (growth, aspect ratio, sharpness); different versions of electronic feedback/detection schemes (constant height, constant deflection, amplitude, phase) and modes of operation (contact, dynamic, lateral); on-line corrections (filters, gains, scanning parameters) and off-line analysis (sections, roughness, FFT, autocorrelation). Detailed recent reviews on these subjects can be found in the literature (5-10). In the present communication, we focus on one crucial part of this complex SPM scheme: the cantilever with integrated nanoprobe for correct measurements of surface responses (Figure 2). We review the current level of understanding of this critical component of the S P M instrument and some of the latest developments in quantitative characterization of local surface properties with emphasis on composite polymer molecular films. First, we analyze different approaches in calibration of cantilever spring constants that are used to convert tip deflections to a force scale. Second, we focus on estimation of contact area tip/surface that is vital for calculation of specific parameters such as surface energy or elastic compliance. This is especially important for compliant polymer surfaces where elastic deformation can be very substantial. Third, we discuss chemical modification of the tip surface and study of interactions between well defined surface chemical groups. Experimental results are illustrated by several examples of such studies undertaken in our research group. Calibration of cantilever spring parameters Knowledge of spring constants of the SPM cantilevers is critical for determination of absolute values of vertical and torsional forces acting on a tip. In linear approximation, conversion of cantilever deflections, Ax, to a force scale, F = 1^ A x , requires knowledge of with a high precision. However, due to uncertain spring



254

Figure 1. Multidimensional approach in SPM representing concurrent imaging of composite monolayer of ladder polymer/stearic acid in different scanning regimes: by atomic force (a), friction force (b), force modulation (c), and adhesive force (d) modes (4).



255

Figure 2. A general scheme of SPM technique and designated focus of this paper.



256 parameters, forces resulting from the tip deflections are not so easily determined and, therefore, quantitative force measurements are still challenging. The absolute values of normal and lateral forces might be within ± 100% of nominal values quoted by a manufacturer (11, 12). The V-shaped cantilevers are the most popular in S P M because of stable scanning (Figure 3). Simple "diving board" cantilevers (Figure 3) are also available which allows use of standard analytical solutions (12). However, this type of cantilever does not provide stable scanning for variety of surfaces. Several experimental, analytical, and computational approaches were recendy explored for estimation of normal ( k j spring constants of the S P M cantilevers but only a few papers considered estimations of torsional (kj) spring constants. The first approach for calibration of the V-shaped cantilevers is a direct experimental measurement of a variation of resonant frequency for a cantilever loaded by microspheres (12). Heavy microspheres (e.g., tungsten) are attached to the end of the cantilever and resonant frequency is measured as a function of applied mass. Extrapolation to a zero mass gives "effective mass" of the cantilever that can be used for evaluation of spring constants. Measurement of resonant frequency for unloaded cantilevers provides means for estimation of actual spring constants if calibration curves are available (13). However, accumulation of various uncertainties like the errors in microsphere weight or position might lead to a possible error of at least 50% in 1^. Alternative determination of the vertical spring constant by measurement of deflections between a cantilever and a wire or a pendulum results in large uncertainty as well (14). Moreover, these approaches do not solve the problem completely. In fact, to calculate kj from known one has to use some analytical approximation anyway. Second approach is an analytical one that uses simple theoretical equations (such as those derived from a parallel beam approximation (PBA)) for estimation of both 1^ and 1^ (15). This scheme works nicely for simple parallel beam cantilevers where an exact solution for the spring constant exists (10). However, analytical estimates for a "workhorse", V-shaped cantilevers, may vary widely due to different treatments of the models (e. g., replacement of the complicated V-shaped beam by a parallel beam) and are rarely confirmed by independent measurements. In addition, all analytical approaches use a "best guess" for material properties of microfabricated ceramic cantilevers. This raises additional concerns because the properties of ceramic materials with thickness below 1 pm (such as Young's modulus, E,) can be greatly influenced by surface effects and stoichiometry rendering bulk values grossly in error (16). On the other hand, important geometrical dimensions of the microfabricated cantilevers (typical length of 100 - 200 pm, width of 10 - 30 pm, and thickness below 1 um) are taken frequently from a manual despite possible variations of geometrical sizes within ± 5% from set to set. Third, the most recent approach, relies on computer modeling of the S P M cantilever actual geometry by a finite element analysis (FEA) and numerical calculation of mechanical parameters for the V-shaped beams (17). This approach can provide reliable values of spring constants for the S P M cantilevers. However, past FEA studies have not adequately modeled the composite nature of the S P M cantilevers (ceramics/gold) although they have a gold coating that significantly changes the mass and stiffness of the cantilever. In addition, exr^rimental verification of material properties such as Young's modulus has not been implemented. We briefly summarize our version of the later approach that helps to produce the most reliable solution. A complete description of the FEA calculation results can be found elsewhere (11). Tip dimensions were measured by high magnification optical microscopy, and cantilever thickness, gold film thickness, and tip location and height were obtained from scanning electron microscopic and S P M images. Geometrical dimensions measured on several cantilevers randomly selected within the


257 same wafer have been shown to be quite uniform. Cantilevers in our particular wafer have an overall thickness, t, of 0.60 ± 0.01 pm and a gold coating thickness of 47 ± 7 nm. The change in stiffness due to the Au overlay was determined by analysis of the equivalent transformed section (19). Then, we measured the lowest resonant frequency of real cantilevers and then adjusted the equivalent Young's modulus for the homogeneous plate elements so that the F E A model had a calculated resonant frequency matching the actual values. Our results for different types of cantilevers gave a Young's modulus for S i N of 215 - 245 GPa for density of 3.2 g/cm (185 215 GPa for density of 3.0 g/cm ). These values are within the range of 135 to 305 GPa reported for different stoichiometry of Si N ( 16). After the value of Young's modulus had been found, the spring constant 1^ was determined by F E A simulations with loads applied at the tip of the cantilever model. The torsional spring constant 1^ was calculated from inclinations of the tip base plane caused by application of lateral forces to the end of the tip. We compared FEAdetermined spring constants for parallel beam, ideal triangular, and real V-shaped (Digital Instruments, DI) cantilevers (Figure 3) to test the validity of various simplifications of the actual cantilever geometry. We also tested our FEA modeling against the exact analytical solution for the P B A (diving board) model. The F E A model gave vertical spring constant 0.279 N/m (for density of 3.2 g/cm ) that was fairly close to the exact solution (12) k„ = E r V / L = 0.275 N/m (see Figure 3 for designations). Two analytical parallel beam approximations (15, 20) used for evaluation of triangular cantilevers gave of 0.220 and 0.189 N/m that is on 6% 25% below FEA results for either ideal triangular or real V-shaped cantilevers. Estimation of a torsion spring constant k, according to an analytical approach proposed in Ref. 21 gave ratio k^/k^ = 4.0 x 10" that underestimates the torsion constant by about 45%. Modification of this approach that includes the supporting beam's connection at the tip resulted in different mode of bending deformation gave a new expression for k ^ (for detailed discussion see Ref. 11): k_ 4 3

3

4 3


3

4

3

3

9

J

=

2

2

k 3 [ c o s 0 + 2(l + v)sin 0] that is close to the exact FEA solution (within 10%). n

E x a m p l e . Large differences in the friction force were observed between the Langmuir monolayers of fatty acids and underlying silicon oxide in several reports (22-24). All results here and below were obtained on the Nanoscope HI microscope (Digital Instruments). To quantify this difference we measured a friction loop, measured loading curves, and calculated friction coefficients using vertical and torsional spring constants discussed above for silicon wafers, stearic acid monolayer, and cadmium salt of stearic acid monolayers (Figure 3) (23). As is clear from these data, the friction forces increase almost linearly with load and are much higher for silicon surface than for Langmuir monolayers. In addition, cadmium salt Langmuir monolayer possesses the lowest friction coefficient. Friction coefficient p for the Langmuir monolayer is in the range 0.01 - 0.05 but reaches 0.2 for silicon oxide surface (23). Contact area and mechanical parameters Knowledge of the tip end shape is critical for recognition of imaging artifacts that are produced by broken, asymmetric, blunt, or double S P M tips. On the other hand, estimation of tip radius is required for calculation of surface compliance, J, and surface energy, E , through work of adhesion, W, (8). Importance of this information can be


258 illustrated by variation of a formula for work of adhesion derived from pull-off forces, AF, according to: W = k A F / S n R ^ J , 26). Numerical coefficient k in this equation varies from 0 to 2 depending upon the type of physical contact. For three major mechanical contacts, namely, Hertzian, J K R , and DMT, the values of k are presented in Figure 4 (8, 25, 26). Different scenarios of mechanical contact can take place depending upon parameters of interacting surfaces (tip and substrate in SPM experiment) such as tip radius, adhesive forces, and elastic modulus. Hertzian behavior is valid for high loads and low surface forces. The JKR approach works well for high adhesive forces, large radii, and soft materials. Finally, DMT theory is a good approximation for hard surfaces, low adhesion, and small radii (8, 25, 26). Because it is not clear what situation corresponds to a particular mating pair, a proof of applicability of one of the approaches should be provided. It can be done by studying variation of friction response, F , or contact area, A , versus normal load, F : a d

f

n


n

F (F ) or A (F ) (8, 25). Variation of F

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