The initial wear in nanometer scale contacts between Si₃N₄ tips with 20 nm nominal radius and polystyrene surfaces was studied in air using a scanning force microscope (SFM). Polystyrene films had molecular weights (MW) 24k and 210k and were cast from toluene solution and dried in vacuum. Film thicknesses were greater than 0.5 µm to avoid film-substrate interfacial effects. The starting surfaces were smooth (roughness of 0.8 nm root-mean-square over 4 µm x 4 µm areas) except for a few small pits ( 80 nm wide and 10 nm deep) at low molecular weight which had no apparent influence on the abrasion process. Wear was produced on 4 µm x 4 µm areas by raster scanning the Si₃N₄ tip under applied loads of 10-210 nN at speeds in the range 80-320 m/s. The abraded area develops characteristic parallel ridges oriented perpendicular to the scan direction. For 24k MW polystyrene, the roughness of the abraded areas increases with the number of abrasion cycles and, at constant load, the ridge spacing is proportional to scan speed. 210k MW polystyrene is more resistant to wear and has smaller ridge spacing than 24k MW polystyrene. Some samples were also heated at about 25 K above the glass transition temperature. After cooling, heated samples of both molecular weights show enhanced resistance to wear. The qualitative features of the observed wear correlate with the MW dependence of the tensile, flexure, and impact strengths of polystyrene.

The processes that result in wear of polymer surfaces are not well understood. This is particularly true of the processes involved in the onset of wear. In this paper, we describe the effects of molecular weight (MW) and thermal processing on the initial wear caused by a single asperity sliding on a polystyrene surface. The asperity is the silicon nitride tip of a Scanning Force Microscope (SFM).

There have been two previous studies of wear on polystyrene using the SFM. Leung and Goh [1] studied 1 µm thick films cast from solution in benzene, toluene, and chloroform onto freshly cleaved mica and then dried in air. They used pyramidal Si₃N₄ tips and applied loads estimated to be about 10^-7 N. Surface deformation was induced by raster scanning the tip over 2 µm x 2 µm areas at a speed of about 17 µm/s. The deformation consisted of irregular ridges approximately 50 nm wide with orientation roughly perpendicular to the scan direction. Ridges broadened and deepened with additional scans. They report no obvious changes for MWs between 32,000 and 573,000. The entanglement MW for polystyrene is about 19k [2]. Leung and Goh also report evidence for gradual transfer of polystyrene to the tip. They did not discuss possible mechanisms for the deformations.

Similar ridge structures on polystyrene were also studied by Meyer, DeKoven and Seitz (here after MDS) [3] for MWs 13k to 1000k. They used films at least 2 µm thick prepared by spin coating 2-12 wt% solution in toluene onto UV ozone treated Si wafers and air drying at room temperature. Si₃N₄ tips were used at loads of about 1.5x10^-8 N. The same tip was used for all studies and contact pressures were estimated to be larger than 40 MPa, which is comparable to the tensile strength of polystyrene (30-100 MPa) [4,5]. Tips were raster scanned over 1µm x 1µm areas at 4.8 µm/s. During the initial 15 min, the root-mean-square roughness increased monotonically with larger increases for larger MW. For higher MW samples, little additional change in root-mean-square roughness occurs after longer times. However, root-mean-square roughness continues to increase for low MW (13k to 35k) material. For example, it increased from an initial value less than 1 nm to 5.6 nm for 24k MW after 45 min. The roughness is in the form of ridges oriented approximately at right angles to the scan direction with mean spacing l in the range 50-100 nm. Simultaneously, a high ridge of material builds up at one edge of the image indicating that true wear has occurred. The modification appears to be completed after about 60 min for MW above 100k. Below 100k, the ridge structure becomes more broken up. MDS [3] assume a power law relationship between load and ridge spacing in an attempt to correlate their results with previous macroscopic studies of elastomers by Schallamach [6] obtained at loads 5 orders of magnitude larger than used by MDS. Based on this extrapolation, which they do not justify on physical grounds, they suggest that the surface of polystyrene is elastomer like. We show in this paper that the relationship between load and ridge spacing is not power law.

2. EXPERIMENTAL

2.1. Polystrurene Films

The polystyrene films used were cast out of a 2% solids by weight toluene solution onto clean glass slides. The glass was cleaned with a chromic and sulfuric acid solution in an ultrasonic bath for 20 min, followed by rinsing in distilled water, and then baking in an oven at 150 C for 1 hour. The polystyrenes were of two different molecular weights, 24k and 210k as measured by manufacturer (Aldrich Chemical Company) using size exclusion chromatography. These two molecular weights were chosen so that we could compare to the two different regimes studied by MDS [3]. 4 l drops of the toluene solution were deposited onto the glass by micropipette. The solvent was allowed to evaporate in air and the samples were then placed in a vacuum desiccator and evacuated to a few hundred mtorr for 20 minutes or longer. Cast films had thickness values ranging from 0.6 to 1.0 m as measured by contact profilometry. Some samples were also taken from the desiccator and annealed in an oven at 130 C for 1 hour.

2.2. Scanning Force Microscope

A Universal SFM (Park Scientific Instruments) was used in these experiments. The SFM (also called an atomic force microscope) is a well established technique to image nonconducting materials with nanometer resolution [7]. It has also been used to cause wear on polymer surfaces [1,3,8,9].

In the Universal SFM used for these experiments, the sample is mounted on a piezoelectric tube scanner and the sample position is controlled with respect to the tip by voltages applied to electrodes on the tube scanner. Typically, a sharp tip is placed into contact with the sample at a predetermined load and the sample is scanned under the tip. During scanning, a feedback loop adjusts the sample position to maintain constant load. If the load is very small, typically a few nN, the SFM functions as an imaging profilometer. If the load is large enough, the tip can deform the sample surface and cause wear. Lateral forces could not be measured on this instrument.

The Si₃N₄ tips were approximately conical in shape with an apex angle of about 20 and a nominal end radius of 20 nm. The axis of the tip was inclined about 15 from the normal to the substrate surface as shown in Figure 1. Each tip was mounted near the end of a triangular cantilever beam force sensor (see Fig. 1). Cantilevers (Park Scientific Instruments) with nominal force constants of 0.03 N/m and 0.10 N/m were used. The load applied to the tip was calculated from the measured cantilever deflection and the nominal force constants using Hooke's Law.

2.3 Initiating wear on the polystyrene films

Prior to each wear experiment, the surface of the as-prepared polystyrene film was imaged at low load (10^-9 N) and scan speed (8 m/s) with the SFM.

Each wear experiment consisted of a fixed number of abrasion cycles. Each abrasion cycle was carried out in the raster pattern illustrated in the top view in Fig. 1. The tip was scanned 4 micron in the +x direction at constant speed and load. Loads used were in the range 10 to 210 nN and the maximum speed was 320 micron/s. This speed is substantially larger than the 20 mmicron/s used in previous studies [1,3]. The direction was reversed at the end of the scan and the initial path was retraced to its starting point at the same speed and load. The tip was then displaced 15.6 nm in the +y direction. This cycle was repeated 256 times until the entire 4 micron by 4 micron area had been covered. This constituted one abrasion cycle. Additional abrasion cycles were carried out by returning the tip to the origin and repeating the cycle. During a multi-cycle wear experiment, the origin of the first few abrasion cycles are displaced slightly because of hysteresis, creep, and coupling between the x, y, and z motions of the piezoelectric tube scanner.

At the conclusion of each wear experiment the load and scan speed were returned to 10^-9 N and 8 micron/s and the damaged surface was imaged over a 6.5 micron by 6.5 micron area so that the edges of the abraded area were included.

Each wear experiment was carried out on a fresh surface and not on top of a previously damaged region. Since the tip shape and cantilever force constant vary slightly from one cantilever/tip assembly to another, we always used the same tip within each set of experiments. All experiments were done under ambient conditions at room temperature ( 25 C) and approximately 40% relative humidity.

3. EXPERIMENTAL RESULTS

3.1. Characterization of the initial polystyrene surfaces

Before the induction of wear all samples were imaged across a 4 micron by 4 micron area under loads 10^-9 N and a scan speed of 8 micron/s to characterize the surface of the as-prepared film. Typical images can be seen in Figure 2. As-prepared surfaces for the 24k MW polystyrene (Fig. 2a) were the least smooth of the samples studied with a root-mean-square roughness of 0.5 nm over a 1 micron² area. These surfaces had two characteristic structural features: pits and hillocks. The pits had dimensions on the order of 80 nm in width and 10 nm in depth. The hillocks were low (10 - 50 nm) and wide (0.4 - 1.5 micron). The mechanisms responsible for the formation of these structures are not understood. Annealed 24k MW samples (Fig. 2b) had slightly smaller root-mean-square roughness values, but surface pits were absent and the hillocks were barely discernible. 210k MW samples, both as cast (Fig. 2c) and annealed (Fig. 2d.), had root-mean-square roughness values in the range of 0.3 nm - 0.4 nm without hillocks or pits. The as-prepared surfaces were not usually damaged by the tip during acquisition of these images but occasionally, even at these gentle imaging conditions, there was damage to the unheated 24k MW surfaces.

3.2. Evolution of wear patterns on 24k MW polystyrene

Figure 3 shows 6.5 micron by 6.5 micron images of typical wear patterns created on unannealed 24k MW polystyrene surfaces using a load of 210 nN and a scan speed of 160 micron/s. The abraded regions in Fig. 3 have several characteristic features. The most prominent of these are the parallel ridges oriented perpendicular to the scan direction. Ridge structures have been reported previously on polystyrene [1,3] but their orientation perpendicular to the scan direction was not as strong as observed in the data presented here. Another feature is the accumulation of material at the top, and to a lesser extent at the bottom, of the abraded areas. This transport of material demonstrates that wear has occurred as opposed to the localized plastic deformation typically observed in microploughing on polymers [8,9,10]. Similar accumulations were observed on polyimides by Jin and Unertl [8] but were not reported in the previous studies of polystyrene [1,3]. More detailed studies are required to determine wear rate. Material does not accumulate at the pattern edges where the scan direction changes, this is also similar to what is seen on polyimides [8].

The parallel ridges have a characteristic spacing that is independent of applied load and number of wear cycles for the range of conditions described here. The amplitude of the ridges does increase with the number of abrasion cycles as also reported before [3]. This is demonstrated in Fig. 4a where we have used the root-mean-square roughness as a measure of the amplitude. The root-mean-square roughness values for an applied load of 210 nN goes from 1.9 nm to 2.8 , 4.7, and 6.2 nm for 4, 7, 14, and 21 cycles respectively. This is in comparison to a starting root-mean-square roughness of about 0.5 nm. The pit and hill structures seen on the 24k MW starting surfaces do not effect the development of the parallel ridges.

The spacing of the parallel ridges was dependent on the scan speed used during the wear process. Figure 5 shows typical images for the case of wear patterns induced with the same tip on a 24k MW surface after 4 abrasion cycles with an applied load of 210 nN at varying scan speeds. Figure 4b plots the ridge spacing as a function of scan speed. At a scan speed of 80 micron/s ridges were not well enough formed to define a unique ridge spacing. At higher speeds the spacing increased approximately linearly with scan speed. Upon closer inspection the patterns formed at lower scan speeds appear very similar to the patterns seen in the experiments by Leung and Goh [1] and MDS [3]. Ridge patterns formed at lower applied loads are also not as regularly spaced. One spin coated 24k MW sample was also abraded and formed patterns consistent with those found on the cast samples.

3.3. 210k MW abrasion

Development of abrasion patterns on the 210k MW surfaces were carried out under similar conditions to those described above. The 210k MW surfaces developed a pattern with a smaller ridge spacing than was seen on the 24k MW surface. An example of this pattern for an unannealed 210k MW film is shown in Fig. 6. For this example six abrasion cycles were carried out at an applied load of 148 nN and a speed of 160 micron/s. The initial 210k MW surface root-mean-square roughness was 0.4 nm and increased to 1.0 nm after abrasion. The resulting abrasion pattern shows well developed ridges likes those formed on 24k MW films. One difference is apparent near the top and bottom of the abraded region shown in Fig. 6. Near these edges there are only half as many ridges as in the rest of the abraded area. This bifurcation was not seen on the 24k MW samples and the mechanism by which it forms is not currently understood.

The 210k MW samples were generally slightly more resistant to wear than the 24k MW samples for similar abrasion conditions. This result is in disagreement with the previous work done by Leung and Goh [1], but appears to agree with MDS [3] who report less roughening on high molecular weight polystyrene for long abrasion times.

3.4. Effects of annealing

The annealed 24k and 210k MW samples also developed abrasion patterns that were similar to those formed on the unannealed samples except that a higher applied load was required to obtain similar ridge heights. Clearly, annealing at 130 C increases the resistance of polystyrene surfaces to wear under the room temperature conditions of our wear experiments. Figure 7 compares the case of two 24k MW samples, one as cast (Fig. 7a) and one annealed (Fig. 7b), for which wear patterns were formed with the same tip under an applied load of 41 nN and a scan speed of 160 micron/s. Twenty abrasion cycles were carried out on each specimen. The initial root-mean-square roughness value of the annealed sample was 0.5 nm and increased to about 0.7 nm after abrasion where as, initial and final root-mean-square roughness for the as cast samples were 0.5 nm and 0.8 nm, respectively.

4. RESULTS AND DISCUSSION

Our experimental observations follow the same general trends with MW as observed for the tensile, flexure, and impact strengths of bulk polystyrene. For example, the tensile strength of polystyrene is a strong function of MW [4]. Below 80k MW, the tensile strength of bulk polystyrene is low; i.e. less than 2 MPa. Above 80k MW, it increases rapidly, reaching a saturation value of 35-40 MPa by about 160k MW. In contrast, the hardness and modulus of elasticity are independent of MW for bulk samples [4,5].

The applied loads above which plastic deformation is expected to occur can be estimated from bulk mechanical properties using contact mechanics. In the case of an elastic Hertzian contact between an undeformable sphere of radius R and a soft planar surface with modulus E and Poisson ratio [11,12], the radius a of the contact and the average pressure P are given by:

and

respectively, where F is the applied load. For the present experiment R=20 nm, E=3.5 GPa [4,5], and v = 0.333 [4,5]. Using Eqn. 1, the Hertzian contact radius can be calculated assuming bulk mechanical parameters; e. g., for R = 20 nm, a varies from 1.6 nm for F = 10 nN up to 9.3 nm for F = 210 nN. However, the actual contact areas are larger in most cases studied because plastic deformation occurs at these loads because P, Eqn. 2, exceeds the yield strength of polystyrene. P is plotted in Fig. 8 for the case R = 20 nm. Also shown as horizontal lines in the figure are the pressures at which the bulk is expected to become fully plastic based on the criterion that plasticity occurs at about three times the yield stress [12]. The upper line is for MWs above 160k and the lower line is for MWs below 80k. This Hertzian analysis suggests that both 24k and 210k MW polystyrene should be fully plastic under all of the conditions of the experiments described here.

The effects of interfacial adhesion between the tip and the substrate can be important but are not included in the Hertzian analysis. According to the JKR theory of adhesive contacts [13]

and

where 2g is the work of adhesion between the tip and polystyrene. Clearly, a_JKR > a. This increase in contact area results in a decrease in average pressure for a given applied load; i.e., the load for which plastic deformation will occur is underestimated by Eqns. 1 and2. In JKR theory, g is related to the pull-off force, F_p, by

where F_p is defined as the force required to separate the tip from the substrate. Experimentally, we find that |F_p| for our tip-substrate combination was always less than 20 nN. Thus, for a tip with R = 20 nm, a_JKR is as large as 2.15a = 3.4 nm for F = 10 nN and 1.23a = 11.4 nm for F =210 nN. The contact pressure P_JKR, Eqn. 4, calculated using F_p = -20 nN is shown in Fig. 8. Both JKR and Hertzian theories show that the 24k MW polystyrene is expected to be fully plastic for all loads above a few nN. However, the JKR analysis predicts that the 210k MW polystyrene does not reach the fully plastic regime until the load exceeds 20 nN. This correlates surprisingly well with our observations considering the simplicity of this model compared to the experimental case of sliding contact. However, the results do suggest that adhesive interactions between the tip and substrate are an important component in a more detailed model of the wear of polystyrene.

MDS [3] speculate that ridge formation on polystyrene may be due to a Schallamach abrasion mechanism [6,14]. Specifically, by comparison of their data with previously published results obtained above 4 mN, they attempt to show that the applied load has a power law dependence on ridge spacing; i.e., F l^m where l is the ridge spacing. MDS give no physical motivation for a power law relationship between F and l. From Fig. 5 in MDS, we estimate that 0.7 < m < 2.5. Based on this power law extrapolation, MDS suggest that the surface of polystyrene is more elastomer like than bulk polystyrene. Our measurements show that l and F are independent and rule out a power relationship for loads in the range 10 nN - 210 nN which includes the 15 nN load used by MDS.

5. CONCLUSIONS

We have used a scanning force microscope to study the initial stages of wear on polystyrene films with molecular weights of 24k and 210k. The films were cast from toluene solution and dried in vacuum. Wear was induced by multiple cycles of raster scanning the SFM tip over the surface at loads in the range 10 nN to 210 nN.

In general, we find that high molecular weight films are more resistant to wear than low molecular weight films. We also find that wear occurs more easily on the as-cast films and that heating the films to 130 C increases their wear resistance at room temperature. The mechanism for this is not understood at present. However, there are at least two possible sources of this increased abrasion resistance. One is that toluene trapped in the as-prepared film is removed by annealing. The other is that the configuration of polymer chains changes upon annealing above T_g. Additional experiments are required to understand this phenomenon.

In agreement with previous studies [1,3], we find that SFM induced abrasion of polystyrene is characterized by the formation of parallel ridges oriented perpendicular to the direction of motion of the SFM tips. However, we show explicitly that the ridge spacing is independent of the applied load. This result casts doubt on the conjecture by MDS [3] that a Schallamach mechanism is responsible for the ridges and that the surface of polystyrene is more elastomer like than bulk polystyrene.

ACKNOWLEDGMENTS

This work was supported in part by the Department of Energy, the Maine Science and Technology Foundation, and the industrial sponsors of the Paper Surface Science Program at the University of Maine.

REFERENCES

1. O. M. Leung and M. C. Goh, Science 255 (1992) 64.

2. J. D. Ferry, Viscoelastic Properties of Polymers, John Wiley & Sons, New York, 1980).

3. G. F. Meyers, B. M. DeKoven and J. T. Seitz, Langmuir 8 (1992) 2330.

4. Goodfellows Catalog 1995/96 (Goodfellows Corp., Cambridge, UK).

5. Moore, E. R., Encyclopedia of Polymer Science and Engineering, Vol. 16, John Wiley & Sons, New York, 1989. TP1087 .E46 1985

6. A. Schallamach, Wear 17 (1971) 301.

7. N. A. Burnham and R. J. Colton in Scanning Tunneling Microscopy and Spectroscopy, edited by D. A. Bonnell (VCH Publishers Inc, New York, 1993) p. 191.

8. X. Jin and W. N. Unertl, Appl. Phys. Lett. 61 (1992) 657.

9. J. A. Lin and W. N. Unertl, J. Adhesion Sci. Technol. 8 (1994) 913.

10. K. Li, B. Y. Ni, and J. C. M. Li, J. Mater. Res. 11 (1996) 1574.

11. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd Edition (Pergamon Press, Oxford, 1986).

12. K. L. Johnson, Contact Mechanics (Cambridge University Press, Cambridge, 1985).

1. K. L. Johnson, K. Kendall, and A. D. Roberts, Proc. R. Soc . London Ser. A, 324 (1971) 301.

2. B. J. Briscoe and D. Tabor, Polymer Surfaces, D. T. Clark and W. J. Feast, Eds. (Wiley, Chichester, UK, 1978).