Microtribological behaviour of monodisperse polystyrene

Microtribological behaviour of monodisperse polystyrene

Transient Processes in Tribology G. Dalmaz et al. (Editors) 9 2004 Elsevier B.V. All rights reserved 507 Microtribological behaviour of monodisperse...

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Transient Processes in Tribology G. Dalmaz et al. (Editors) 9 2004 Elsevier B.V. All rights reserved

507

Microtribological behaviour of monodisperse polystyrene R.P. Schaake ,bc, W.P. Vellinga bc and H.E.H. Meijer bo a Dept. of Surface Engineering / Tribology, TNO Industrial Technology, P.O. Box 6235, 5600 HE, Eindhoven, The Netherlands, E-mail: [email protected] b Materials Technology, Dept. of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, E-mail: [email protected] c Dutch Polymer Institute, P.O. Box 902, 5600 AX Eindhoven, The Netherlands Single asperity friction measurements in the mN-#m range were performed on monodisperse polystyrenes of different molecular weight. The experiments were performed according to a "slidehold-slide" protocol, measuring indentation creep, peak friction after hold and steady sliding friction. Indentation creep, peak friction after hold and steady sliding friction were found to be equivalent at high molecular weight, but not for low molecular weight. It was found that ~:, a characteristic time appearing in the description of indentation creep, was dependent on molecular weight, and on initial contact age. For low molecular weight steady sliding friction forces were higher than for high molecular weight, while the contact area was of similar size, indicating that different dissipative mechanisms were active.

Keywords: Polystyrene, Friction dynamics, LFA, Creep 1. INTRODUCTION

Polymers are frequently used for sliding applications because of their ability to slide without lubrication. This has generated scientific interest in the structure-tribology relations of polymers. We have investigated the microscopic sliding of a single asperity on monodisperse polystyrenes of different molecular weight in "slide-hold-slide" experiments, a protocol that has already proven successful in macroscopic, multi-asperity contacts. Using these experiments Dieterich was able to establish the relation between socalled "static" friction (friction after hold) and "dynamic" friction (friction during steady sliding) and propose a unifying description in rate and state models [1].

Macroscopic contacts consist of many micro contacts between roughness peaks. The processes between these asperities determine the friction and wear behaviour [2]. In multiasperity situations the contact area and friction force are usually proportional to load [2]. This proportionality between contact area and friction force has been experimentally verified for velocity weakening contacts [1], in which the friction force decreases with increasing velocity. 1.1. Velocity, contact creep and friction

Dieterich [1,3] has explained the dynamics of sliding at different velocities from contact age, i.e. the time it takes to refresh the real contact area. Contacts have different ages and, consequently, different sizes. Dieterich and Kilgore have performed experiments in which

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contact growth during hold, peak friction and friction during steady sliding were measured. With these measurements they experimentally verified, for a wide range of materials, that velocity dependence of friction force is controlled by creep [1]. Baumberger and coworkers [4-6] have performed slide-hold-slide experiments on amorphous polymers. They experimentally verified that, in velocity weakening, both peak and steady sliding friction force, F,... and F F respectively, can be described in the general form [3]: Fz(t h) - Fz(0) + ,6 InCt. )

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(5)

where y is a contact geometry dependent factor of order unity, o-. is the yield stress and e is the strain. o o

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with Fr..x the peak friction force upon the start of sliding and r a characteristic time related to an effective strain rate through a stress aided Eyring equation [5]. Assuming a proportionality between contact area, Az, and friction force, as shown by Dieterich and Kilgore [1], the geometric relation: D~=2z(t.)R with R the radius of the spherical asperity, and D the contact diameter, can be used to show that indentation z(t.), is proportional to A~ and, therefore, to F L. So in a stationary contact friction and indentation develop in time as:

Fm,x(t~____))= z(t~___))=1 + me~ In(1 + th/r) F~,x(0) z(0)

,

(1)

with FL the lateral force F~x or F~, ,fl an empirical parameter and tc the contact time. The description of the peak friction force, Fm.~, upon resuming the motion, as a function of contact age, th, can be more specifically described as [5]:

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z(O).

509 The effect of creep on contact area can be used to explain the velocity weakening part of Dieterich's dynamic equation [1]:

examine the wear and friction of polystyrene at a nanometre and micronewton scale [8,9,13]. 1.3. Intrinsic mechanical behaviour

(6)

where x is the displacement in the sliding direction, FF the steady state friction force and Vo and r are normalising constants which can be chosen as a reference velocity and a matching contact time respectively, so that ~o=Do/Vowith Do the sliding distance required to obtain steady sliding when accelerating from

v=Oto V=Vo. The state term with r is a velocity weakening term, analogous to static ageing of the contact and the other logarithmic term is a rate term, which is a velocity strengthening term. Both terms are weighed using the empirical parameters B and A respectively. Dieterich and Kilgore have determined that the length Do is equal to the sliding distance required to refresh all contacts [1], so Do~D. Sliding dynamics can be described with a dynamic system using an evolution law for r

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(7)

Both Dieterich and Baumberger [1,3-6] have verified these equations using so-called slidehold-slide experiments on macroscopic multiasperity contacts of various materials, including glassy amorphous thermoplastics. 1.2.

Single asperity contacts

In single-asperity contacts the contact geometry can be controlled, and consequently the stress and strain distribution can be calculated relatively easy [7]. This implies that single asperity measurements are very useful for studying structure-tribology relations [8-20]. One of the most popular single-asperity techniques is Friction Force Microscopy (FFM). FFM has been used by several authors to

The effect of the number of entanglements on the intrinsic mechanical behaviour of an amorphous polymer can be seen in figure 3 which displays a typical true stress - true strain curve. With increasing molecular weight, the number of entanglements will increase, which will result in an increase in the strain at failure, Er [21]. Other material properties, like the yield stress and E-modulus, are independent of molecular weight [21]. Van Melick et al. were successful in studying the intrinsic material behaviour using indentation experiments. They found that a hydrostatic stress of 40 MPa is required to initiate crazing in polystyrene at room temperature [22].

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age~

Figure 3. Intrinsic behaviour of amorphous polymers. Molecular weight affects only the true strain at failure. 1.4. Molecular weight

Molecular weight dependent wear mechanisms at the nanometre scale have been reported [8]. However, the wear was only measured in very low molecular weight materials. Keeping in mind that PS has an entanglement molecular weight, Me, of around 19k [23], the materials showing wear in Aoike et al.'s experiments [8] had at most 3 entanglements. According to Tervoort et al. the wear rate of polymers with less than 4 entanglements is indeed strongly dependent on molecular weight [24]. Tervoort et al. [24] found a relation between the macroscopic wear rate and the number average molecular weight, MN',

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of the chains with more than a critical number of entanglements. While relations with molecular weight averages of the complete distribution show a weak correlation to wear, this corrected molecular weight, MN', shows a very strong correlation [24].

1.5. Glass transition

Besides wear mechanisms, glass transitions are also widely studied using single-asperity techniques. Near the glass transition of a polymer the loss modulus shows a peak, indicating that more energy is dissipated near the glass transition when the polymer is deformed. As a consequence, behaviour controlled by dissipative mechanisms, is affected. This can be observed as an increase of the friction force around the glass transition Several authors have observed that Tg was reduced at the polymer-air interface [14,16,18,25,26]. Using deuterated end groups, Kajiyama et al. showed an increased presence of chain ends at the surface, as well as an increased loss modulus [18]. Using Monte Carlo simulations, Jain and De Pablo [25] showed that chains possess loops at the surface that have a higher mobility than chain segments in the bulk. Furthermore, they showed that chain relaxation times decrease towards the centre of the chain and that, for linear chains, the most mobile sites are mostly the chain ends. 1.6. Objective

The objective of the research described in this paper was to study the relation between creep and friction for polystyrene at the ~m and mN level, performing three independent measurements (indentation creep, peak friction after hold and steady sliding friction) with a single hard asperity. Effects of molecular weight on creep and friction are investigated and discussed.

2. EXPERIMENTAL 2.1. Material Two different molecular weight materials were used. Low molecular weight (PS56k), M~= 56 kDa, M,/MN=1.05 and high molecular weight (PS1M), M~ 966 k O a , M,/M,,,=1.15, polystyrene were supplied by John Gearing Scientific. The material was first pressed into 0.5 mm thick plates at 180~ for 10 minutes under a load of 300 kN and subsequently cooled at 15~ and pressed under a load of 100 kN. Samples were cut from these plates and subsequently embossed with a silicon wafer at a temperature above Tg to obtain a smooth surface. The silicon wafer was coated with crosslin ked (tridecafluoro-1,1,2,2tetrahydrooctyl)trichlorosilane to ease release, without polluting the sample's surface. These samples were subsequently stored at ambient conditions for at least a week. 2.2. Method

Slide-hold-slide experiments were performed using a Lateral Force Apparatus (LFA). An LFA is a single asperity measurement device that allows independent measurement of lateral and normal forces. A detailed description can be found elsewhere [27]. This single asperity measurement device has been upgraded to facilitate measurements at sliding velocities from 25 nm/s to 1 mm/s and can be programmed to change velocities during sliding. A diamond tip with R= 10 pm was mounted onto a cantilever of normal stiffness, k,,,=1716 N/m and lateral stiffness, kL=541 N/m with a cross talk between normal and lateral measurement of 5%. The cantilever was stiff enough to ascertain steady sliding. A typical experiment is shown in figure 4. All signals are acquired simultaneously. After applying the normal load, FN, of 10 mN the contact was first refreshed at a certain approach velocity, vo, in steady sliding, this way a reproducible starting situation was created. The motion was then halted for a certain hold time, th, after which it was resumed at sliding velocity v. During th, the creep, ,dz was

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t(s) Figure 4. Slide-indent-slide experiment. T o p velocity vs. time. A fresh contact is created by sliding at velocity Vo, after which motion is halted for th and motion is resumed at velocity v, in the current experiment V=Vo. Middle - Both the dynamic fiction, FF(v), and the friction peak value, Fm~x(t,), are measured. B o t t o m - during the time the motion is halted creep, Az(th, Vo), is measured. measured as a function of Vo and t,. An extensive study of the creep was performed at Vo=2.5 pm/s. The development of the friction peak, Fmax, as a function of t, was measured atVo-2.5 pm/s and th= 1, 10, 100 and 1000 s. The steady state friction force, FF, was measured at different sliding velocities, v. All experiments were performed with Vo=V, so

FF(e) = FF(D o/V)=Fm,x( t,) . 3. RESULTS AND DISCUSSION 3.1. Results

The creep measurements showed a difference between the high and low MN material, as can be seen in figure 5. The fits with equation (4) are very good. At the same approach velocity, Vo, 9 was smaller for the low molecular weight material, compared to the high molecular weight material, Tps,,,=O.24s and

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~ps,M=3.0s The long term creep rate, z(O)m,~, however, was equal. Creep, Az, and F,,a, are both displayed in figure 6 according to equation (3). Figure 6 clearly shows that creep and peak friction force showed a similar behaviour in time. To obtain the fitted lines in figure 6 the value of m,, and zwere taken the same for equations (2) and (4), but different for both materials. This shows the assumption of proportionality between Fr,,x and Az was valid.

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Fmax, measured on both materials cannot be explained by differences in the contact area alone, different dissipative mechanisms must have been active. Since the contact area was velocity dependent over the whole velocity range, the levelling off of the friction at high velocities on the 1MDa material must be due to a velocity strengthening effect rather than creep related effects.

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Fm,,(t~): PS56k (O)/PS1M (D) and FF(Do/V): PS56k (e)/PS1M (m). The lines are fits of F~,~(th) with equation (2). Figure 7 shows the peak and steady state friction force at different contact times. Fitting the peak friction force with equation (2) resulted in good fits. On PS1M F~,~(t,) corresponded well to FF(Do/V). On PS56k F~,,(t,)was larger than FF(Do/v). Apparently, Do/V was not equivalent to thin the case of PS56k. Fitting the creep and friction data, the contact diameter Do, was found for Vo=2.5 #m/s: 12 ~m for PS1M and 18 ~m for PS56k. However, AFM measurements of the plastic groove left after the experiments, showed little difference in the distance between the pile-up ridges. Finite element simulations of indentation showed that the edge of the original contact area becomes the summit of the pile up left after the experiments [28]. Using AFM the contact diameter of the tracks from sliding at different velocities was measured on both materials. At 1 mm/s it was 7 #m, and at 25 nm/s it was 9 pm. Since there was hardly any dependence of the contact diameter during sliding on MN, there was hardly a difference in indentation at th=O between the two materials. Since the differences in FF and

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y (l~m) Figure 8. Cross section of plastic deformation measured with AFM. The distance between the summits of the pile up is the diameter of the original contact area. The cross section was obtained by averaging 32 scans To determine whether material failure played a role, (polarised) light microscopy and AFM were used. These did not reveal any signs of material failure. The AFM results from the bottom of the sliding track are displayed in figure 9. Although a pattern perpendicular to the sliding direction was observed, this did not reveal any crazes. The groove had a continuous wavy surface, while in the case of crazes sharp cracks should be observable. Finite element indentation simulations according to [22] indicated that in our experiments the hydrostatic stress was indeed not high enough to cause crazing. However, the AFM images do show that the nature of the deformation was different for both materials.

Figure 9. AFM images of the bottom of the sliding track.

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Figure 10. Master creep curve for PS1 M. 10a: From the AFM data the initial value of z at different approach velocities, v, is determined. The creep curves plotted from this value eventually reach the same slope at t,>>~. 10b: Creep curves of all velocities could be shifted to start and end on a master creep curve.

3.2. Discussion: Interpretation of r Figure10 shows the effect of approach velocity on creep for PS1 M. Figurel0a shows that ~: is smaller at increasing v o and that all curves eventually obtain the same creep rate. It was possible to

shift the curves along the z axis, so the curves coincide at high th. This could be done by taking the indentations measured with AFM for different v and taking these as z(O). Shifting the indentation creep curves by ~: along the time axis, they all ended up on the master creep curve (figure l0b). When the

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motion was halted, the material had already been creeping during sliding according to the master creep curve. It was calculated that for the high molecular weight material the master creep curve would intersect with the surface, z=O pm, at a time of the order 10"s, a much shorter time than any v measured by fitting the data. The cut-off time, T, depends on the deformation history before motion is halted. However, ~: is not equal to Do/Vo, but it is proportional, which is in agreement with observations by Berthoud et al. [5]. For PS56k such a master curve could not be constructed. 3.3. Discussion: Molecular weight effects Since there were no significant differences in the size of the contact area at equal v between both materials, the difference between low and high molecular weight friction must have been caused by differences in the dissipative mechanisms. Current knowledge of the macroscopic mechanical behaviour of glassy amorphous polymers associates molecular weight only to the strain at failure [21]. The surface inside the grooves did reveal that the deformation had not been the same for both materials. Patterns perpendicular to the sliding direction started appearing at much Iower velocitiesonthe PS56ksurface. While we measured a different creep behaviour between both materials, macroscopic creep experiments show no effect of molecular weight [21]. This might be explained by the fact that, in macroscopic experiments, the creep is not yet measured at the short times we measured in these slide-hold-slide experiments, The origin of the difference in r probably lies in the deformation history. The molecular weight effects measured could not be explained from the results of the experiments described here. The possible effects of chain ends have not been explored experimentally.

4. CONCLUSION Measurements of indentation creep, peak friction force after hold and friction force during steady sliding, during a single slide-hold-slide experiment, were successfully performed for hard single asperities on monodisperse polystyrenes, in the mN-l~m regime. For 1MDa PS, indentation creep, peak friction force after hold and friction force during steady sliding appeared to be equivalent. However, AFM examination of the plastic deformation showed that the contact area was different for short times and high velocities. For 56kDa PS, it was shown that creep indentation was proportional to peak friction after hold. The steady sliding friction forces were also shown to be dependent on the growth of the contact area in time, however, the dependence was different from static creep for similar contact times. For 1MDa PS it was shown that the characteristic time r depends on the history of the contact. At constant approach velocity, v was found to be smaller for the 56kDa PS than for the 1MDa PS. ACKNOWLEDGEMENTS The authors would like to acknowledge Cees Bastiaansen and David Trimbach for their useful advise regarding the embossing of polymers; Kees Hendriks, Erwin Dekkers, Rinus Janssen and Simon Plukker for the existence of a working LFA and Christophe Pelletier and Leon Govaert for sharing their expertise on the finite element modelling of indentation on amorphous polymers. The continuing development of the LFA was partly financed under EET grant EETk99029. REFERENCES 1. J. H. Dieterich and B. D. Kiigore, PAGEOPH 143 (1994) 283 2. F. P. Bowden and D. Tabor The Friction And Lubrication Of Solids (Clarendon Press, Oxford, 1964) 3. J.H. Dieterich, PAGEOPH 116 (1978) 790

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