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The scanning force microscope as a tool for the detection of local mechanical properties within the interphase of fibre reinforced polymers
Composites Part A 29A (1998) 1251–1259 1359-835X/98/$ - see front matter q 1998 Elsevier Science Ltd. All rights reserved
PII: S1359-835X(98)00077-3
The scanning force microscope as a tool for the detection of local mechanical properties within the interphase of fibre reinforced polymers M. Munz a, H. Sturm a,*, E. Schulz a and G. Hinrichsen b a
Federal Institute for Materials Research and Testing, Lab. VI.21, Unter den Eichen 87, D-12205 Berlin, Germany b Technical University of Berlin, Institute for Nonmetallic Materials, Englische Straße 20, D-10587 Berlin, Germany
Scanning force microscopy (SFM) has been used to assess the local mechanical properties of fibre-reinforced polymers. Using a sinusoidal displacement modulation (DM) and lock-in technique the method allows to characterize local viscoelastic properties with a high lateral resolution. The simultaneous measurement of the local electrical conductivity is proposed which facilitates the interpretation of the mechanical data. The investigation of cross-sections perpendicular to the axis of carbon fibres embedded in PPS delivers some information about the change in local stiffness within the interfacial region. As a first approach, assuming a singleexponential decrease in local stiffness along a radial line from fibre to polymer we find characteristic decay lengths which are distributed in a range between 20 and 80 nm. Further, a modified DM-mode is proposed which is expected to provide a contrast enhancement of the signal which is related to local stiffness. This can be achieved by installing an additional feedback loop which keeps constant the amplitude of dynamic indentation (CDI-mode). q 1998 Elsevier Science Ltd. All rights reserved (Keywords: A. polymer–matrix composites (PMCs); B. interface/interphase; SFM/AFM; B. surface properties; D. nondestructive testing)
INTRODUCTION It is widely accepted that the mechanical properties, the environmental stability and the failure mechanisms of fibrereinforced polymers are strongly influenced by the interfacial zone which is formed when the constituents are combined into a composite. The interfacial region can be considered as a third phase, the interphase, which possesses neither the properties of the reinforcing phase nor those of the matrix. Moving along a radial line from the centre of a fibre towards a point within a plain polymer, the change in physical properties from fibre to bulk polymer (which is expected to occur within the interphase) causes some gradient. In thermoplastic systems a loss of long-range chain flexibility and mobility of the polymer molecules, entropically driven segregation of molecules according to their molecular weight, and strongly influenced crystallization behaviour are observed in the vicinity of the filler surface1. In thermosetting systems the cross-linking chemistry in the matrix adjacent to the surface is modified2. Focussing on a certain attribute, e.g. on local mechanical stiffness, the respective size of the interphase may be defined by the width of the region of interfacial gradient. The size of the interphase can range from nanometres to * Corresponding author.
micrometres2. A lot of work has been done to get some corresponding information3, but until the invention of scanning force microscopy (SFM) there was no microscopic method available which allows one to investigate local mechanical properties4. Both a monotonic decrease in local stiffness when moving from fibre to polymer5 and a dip in the stiffness line profile1 have been proposed. SFM in contact mode offers different techniques for investigating not only the topography but also local physical and chemical properties. Simultaneously measured contrasts of static and dynamic friction6, local elastic and viscoelastic properties7 or ohmic and capacitive conductivity8 open a wide range of applications in materials research. In SFM a micromachined cantilever with a small tip is scanned across the surface under investigation. Typically, the radius of curvature of the tip lies between 10 and 70 nm. The forces between tip and sample produce a bending of the cantilever (the force constant of SFM cantilevers usually ranges from 0.001 to 10 N m ¹1 9), which is detected via a laser beam and a segmented photodiode. When working in contact mode the repulsive forces between tip and sample are kept constant via a feedback loop (so-called equiforce mode or constant height mode). Part of the feedback loop is a piezo element which retracts the sample or the cantilever when an ascent on the scanned surface produces a change in
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Scanning force microscopy: M. Munz et al. the bending of the cantilever. In this way the force between tip and sample is kept constant and the output of the feedback loop is used for writing a topography image. SFM has been applied for investigations of both thin films10 and cross-sections of bulk samples11. For example, when studying phase-separating polymer mixtures12 or film formation processes13 a lot of information can be taken from the topography signal. As the topography of cross-sections of bulk samples is mainly influenced by the preparation procedure there is a strong need for some additional contrasts, reflecting physical or chemical properties of the material. In the following we will focus on the measurement of local stiffness.
SFM WITH DISPLACEMENT MODULATION (DM) In this SFM mode, while scanning, the normal position of sample or cantilever is modulated sinusoidally over a small distance of some nanometres14. As a consequence there is a modulation of the load exerted by the tip and a modulation of the bending of the cantilever depending on local mechanical sample properties. Thus the DM entails a modulation of the normal load and is often referred as force modulation14. However, DM should be distinguished from the more direct magnetic force modulation where a timedependent magnetic field is acting on a small magnetic particle15 or a magnetic layer16 deposited on the upper side and close to the free (tip-sided) end of the cantilever. The resulting ac part of the detection signal can be fed to a lock-in amplifier which is driven at the excitation frequency (Figure 1). The lock-in amplifier delivers an amplitude and a phase signal. The amplitude signal is related to the local stiffness (see below) and the phase signal reflects deviations from perfect elastic behaviour, which is important, e.g. when studying viscoelastic materials like polymers. However, due to the fact that only two external channels are at our disposal, only the amplitude of the electrical ac current
Figure 1 Experimental setup of a SFM in displacement modulation (DM) mode. The grey box shows the additional feedback which is installed for keeping constant the amplitude of the dynamic deformation within contact zone (CDI-mode)
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signal (see following section) and the amplitude of the mechanical ac signal have been recorded. Therefore, the phase shift between the mechanical excitation z dyn and the dynamical cantilever bending b dyn will not be discussed in the following. The relationship between the excitation and the corresponding dynamic indentation and dynamic cantilever bending is explained in Figure 2. On soft sites the indentation depth of the sample surface by the tip is higher than on harder sites. When working below the resonance frequency of the cantilever the modulation amplitude z dyn can be exactly decomposed into the amplitude d dyn of dynamic contact deformation and the shift of the tip in normal direction b dyn which is detected as an appropriate amount of cantilever bending. For the sake of clarity only the indentation amplitude j dyn is shown. When investigating polymers the deformation of the tip, which is usually made from stiff Si or Si 3N 4, is known to be negligible 17. The ratio of d dyn and b dyn is given by the ratio of k c, the spring constant of the cantilever, and k ts, the stiffness of the tip–sample contact. Hence, on soft sites the modulation amplitude decomposes into a high indentation amplitude j dyn and a low bending amplitude b dyn. Figure 3(a) shows the topographic image of a crosssection, prepared from a E-glass fibre (Bayer AG, Germany) with a rather thick polypropylene (PP)-sizing (PCD Polymere, Linz, Austria), embedded in a commercial epoxy (resin L180 and curing agent 181; mgs Kunstharzprodukte GmbH, Stuttgart, Germany). The sample was cut perpendicular to the fibre axis by using a diamond saw. Great care was taken to prepare a rather flat cross-section. Emery paper with coarseness 4000 was used and final polishing was done with a 0.05 mm alumina suspension. Finally, the surface was cleaned in a 1:1 water/2-propanol solvent mixture in an ultrasonic bath for 10 min. The cantilever which was used is I-shaped and has a typical force constant of 2.8 N/m (LOT-Oriel, Darmstadt, Germany). The modulation frequency was 50 kHz. The measurements were performed using a stand-alone SFM microscope (Model
Figure 2 Schematic representation of dynamic cantilever bending amplitude b dyn and dynamic indentation amplitude j dyn during a DM measurement. For a given modulation amplitude z dyn the magnitudes of b dyn and j dyn depend on local sample stiffness
Scanning force microscopy: M. Munz et al.
Figure 3 Topography (a) and mechanical amplitude contrast (b) of an E glass fibre with PP sizing, embedded in epoxy. The sample was prepared as a crosssection perpendicular to the fibre axis. Topography grey scale: 0 (dark)…873 (bright) nm; amplitude grey scale in a.u.: soft (dark)…stiff (bright)
steps and comparing topographic features, in particular near the rim of the fibres. When the direction of cutting or polishing was not changed, that part of the fibre where the abrasive forces move the polymeric material away in direction to the matrix should be preferred for scanning. Smearing is expected to be reduced by cutting with a cryogenic microtome. However, as our experiments have shown, at low temperatures the tendency to delamination between fibres and polymer is a major hindrance for the application of such techniques. When investigating composites with carbon fibres as the reinforcing phase, an advantage can be taken from the fact that carbon fibres are electrically conductive. Thus, when scanning from fibre to polymer the pronounced decrease in electrical conductivity can be used as a criterion to decide if the tip is in contact with polymeric material or not. Figure 4 SEM micrograph from the tip which was used for simultaneous mechanical and electrical measurements. The inset shows a magnification of the apex of the tip (image contrast inverted)
Explorer; TopoMetrix Inc., Santa Clara, USA) and a lock-in amplifier (Model SR830; Stanford Research, Sunnyvale, USA). The topography (Figure 3(a)) reflects the tremendous differences in mechanical properties between glass fibre and polymer. The fibre is much less abraded by the preparation process than the epoxy matrix and thus its surface is higher (bright) than those of the epoxy. The amplitude signal (Figure 3(b)) indicates a high amplitude (bright) of the dynamic cantilever bending and thus a high local stiffness in the region of the fibre. In contrast the PP phase shows the lowest amplitude. The lack of definition in the amplitude contrast at the steep right edge of the fibre is produced by the feedback loop. This is obvious from the image of the static cantilever bending which reflects deviations from the chosen feedback setpoint (image not given here). The finite time constant of the feedback loop (as a result of the chosen feedback parameters and the cut-off frequency of the analog-to-digital converter) prevents an instantaneous adjustment of the tip height when scanning such steep features. Some polymeric material might be smeared during the preparation of the cross-section and cover the interfacial zone or even some area of the fibre surface. The occurrence of such effects can be studied by scanning the surface immediately after the cutting process and several polishing
DISPLACEMENT MODULATION WITH SIMULTANEOUSLY PERFORMED AC CURRENT MEASUREMENTS The instrumentation to measure simultaneously topography and an ac current collected by a conductive tip is given in detail elsewhere18. The used ac voltage was 0.32 V at 42.605 kHz superimposed to a þ 0.2 V dc offset. The current collected by the tip was amplified with a gain of 10 5 and the resulting voltage was fed to a second lock-in amplifier (Model SR830; Stanford Research). The used cantilever has a conducting W-coated silicon tip (specific resistance about 50 mQ cm, tip height 7 mm, angle between axis and pyramid edge less than 108, Figure 4) and a force constant between 2.5 and 4.5 N m ¹1 according to the manufacturer (NT-MDT, Moscow, Russia). The measurement of the force constant by the software option of the microscope (Model Discoverer; TopoMetrix Inc., Santa Clara, USA) delivers 5.7 N m ¹1. Using this value the chosen static contact force was estimated to lie between 60 and 90 nN in all cases. The measurement of the response to the mechanical excitation was done in a similar manner to that in the previous section. For technical reasons, the alternative way of modulating the position of the cantilever base was used instead of modulating the sample position. The mechanism for contrasting different local stiffnesses is the same for both cases. The frequency for the displacement modulation of the cantilever base was 74.89 kHz, the
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Figure 5 Topography (a), electrical conductivity (b) and mechanical amplitude contrast (c) of a carbon fibre/PPS prepreg. The scan shows a part of the fibre– polymer borderline. Current amplitude grey scale in a.u., low current (dark)…high current (bright); mechanical amplitude grey scale in a.u., soft (dark)…stiff (bright). The bright areas in the upper right part of the images (b) and (c) indicate fibrous material. In (b) the upper section of the bright part is scaled logarithmically, whereas the lower section is in binary scale. The white lines drawn in (a) and (c) correspond to the fibre–matrix borderline as detected from the current image (b). The curves below the images are the respective cross-sections which were averaged from 10 neighboured pixel lines within the indicated rectangular area AB
modulation amplitude can be estimated to be in the nm range. The sample under investigation was prepared by cutting and polishing a carbon fibre/polyphenylenesulfide (PPS) prepreg (HM-type carbon fibre; Toray, Japan; PPS; Fortron, Hoechst, Germany). The direction of sawing was perpendicular to the surface. As a connection for an ac voltage source the bottom side of the sample is glued on a metal plate using an epoxy which contains silver. After additional fixing with insulating epoxy, the top side was polished manually with emery (coarseness 4000), a diamond lapping film (coarseness 0.1 mm) (3M, St. Paul, USA) and a 0.05 mm alumina suspension. The resulting surface was cleaned in a 1:1 water/2-propanol solvent mixture in an ultrasonic bath for 10 min. Several flat sites of the carbon fibre/PPS interface have been investigated. In Figure 5 the topography image (Figure 5(a)), the current image (Figure 5(b)) and the DM image (Figure 5(c)) of a 500 3 500 nm scan are shown. From the current and the DM image the upper half can be attributed to the electrical conductive and stiff polymer (compared to the fibre). In Figure 5(b) the upper section of the bright part is scaled logarithmically, whereas the lower section is in binary scale. In logarithmic scale the variations of lower currents are pronounced. Thus, distinctive lateral features become visible which indicate inhomogeneities of the scanned fibre. The images of Figure 5(a,c) are linearly scaled. The white lines drawn in Figure 5(a,c) correspond to the fibre–matrix borderline as detected from the current image (see below). The curves below the images of Figure 5 are the respective cross-sections which were averaged from 10
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neighboured pixel lines within the indicated rectangular area AB in order to increase the S/N ratio. The width and the length of the rectangles are 16.6 and 287 nm, respectively. The corrugation of the image cross-sections was checked concerning the problem of tip shape convolution. The tip shape was determined from the SEM micrographs (Figure 4), scaled anisotropically in the same manner as the corresponding topography cross-section and indented 5 nm, according to the static load including the contribution from the adhesion (see below). The resulting contact radius is 11 nm. Obviously, the measured line profile is smooth compared to the contour of the tip. Therefore the flattening of the measured topography compared to the true topography (as an effect of the convolution between corrugation and tip shape) seems to be neglectable. Using the fact that the electrical conductivity of the carbon fibre is much higher than those of the insulating polymer 19 we observe a pronounced increase in the ac current when the tip is scanned from polymer to fibre. Considering the steepness of the jump in the current profile, the lateral position accuracy for this procedure can be estimated as two image pixels, i.e. 3.32 nm. The crosssection of the DM image (Figure 5(c)) reflects an increase in local stiffness some tens of nanometres before the conductivity indicates the carbon fibre edge. This region can be considered to be part of the interfacial polymer zone where an interaction between the two components is expected. On the one hand, precondition for a stable feedback loop is a smooth, step-less topography. On the other hand, a more-or-less featureless topography renders the identification of the fibre edge rather difficult. Also, deducing the
Scanning force microscopy: M. Munz et al. fibre edge from the stiffness image alone can be misleading as the stiffness values vary over the fibre cross-section (Figure 5(c)). The mean values of the local stiffness and the corresponding rms deviations were determined by averaging rectangular areas containing at least 12 780 datapoints for both fibre and bulk polymer. For the bulk polymer value the scattering lies within the diameter of the drawn black point. The stronger scattering of our mechanical data over the fibre cross-section is consistent with the variations in local conductivity (Figure 5(b)). This variation might originate from the structure of the carbon fibres and was also observed by other groups20. Nevertheless the drop in the current signal at the fibre edge is generally rather pronounced. Hence, the breakdown in the measured current is used as a criterion for defining a fibre–matrix borderline. This borderline as defined by the drop in the measured current (apparent edge Z) is identical with the true edge D of the fibre only in the case of a vanishing dead zone (Figure 6). The dead zone (DZ) may result from both currents between the flank of the tip and the fibre edge when the apex of the tip is already in contact with polymeric material. Figure 6 depicts the two extremes of an ideal flat (Figure 6(b)) and of a step-like (Figure 6(c)) fibre–matrix edge. Point C denotes a mechanical and current-carrying contact between fibre and tip-flank, point T represents the location of a possible tunneling current. The width d of the dead zone DZ depends from the opening angle of the tip, the height difference between fibre and matrix and the steepness of this transition. Assuming a situation as demonstrated in Figure 6(c) with a total opening angle of 208 (this corresponds to the opening angle of our tip, approximately) and a step of about 50 nm the width d of the dead zone will be less than 20 nm (tunneling currents are expected only over distances shorter than 2 nm21). Defining the fibre–matrix borderline by the current-based criterion, that part of the data within the dead zone will be truncated and not taken into account for further analysis. Thus, for cases where the local stiffness adjusts from the mean fibre value to the bulk polymer value, the existence of a 20 nm wide dead zone would render the detection of the interphase impossible. But, even in the case of a perfectly flat fibre–matrix transition and an exactly known true fibre edge D (if it would be exactly detectable), the respective mechanical data in the very near of the true fibre edge should be interpreted with great care. As rather schematically shown in Figure 6(a), an anisotropically deformed tip apex is to be expected, corresponding to the enormous differences in local stiffness when the tip contacts both fibrous and polymeric material. Further, also when the tip has just lost contact with the fibre, the (mechanical) measurement should be influenced by the near fibre, as the sub-surface distribution of the mechanical stresses will be deformed by such a heterogeneous surface. Following the calculations of Ref. 22 for a homogeneous surface the lateral extension of the sub-surface stresses will be on the order of the contact radius. Using the Johnson–Kendall–Roberts (JKR) theory for adhesive contacts23, the value of the contact radius of our tip with PPS was estimated to be about
11 nm (radius of curvature 6.7 nm as determined from the SEM micrograph (Figure 4), external load 90 nN, Young’s modulus of PPS about 3.31. 10 9 N m ¹2 24, Poisson’s ratio about 0.36, adhesion energy about 30 mJ m ¹2 (typical value for polymers25)). This means that our mechanical data within a zone of about 11 nm from the true fibre edge should be omitted for the evaluation. The width of this zone, as defined by mechanical restrictions, is comparable to the width d of the dead zone DZ as defined by the electrical criterion. Thus, the usage of the apparent (current-based) borderline will, generally, also lead to the truncation of doubtful datapoints. Following this selection procedure for the fibre edge 25 stiffness profiles were taken into account. Eight stiffness profiles are given in the following figures, plotted in a way that only the stiffness values of the non-conducting surface is shown. The position of the first pixel with low conductivity value is set to 0 nm. In Figure 7(a) four examples of datasets are shown which where omitted in the further analysis, either because the S/N ratio is too low or because the curve exhibits some strong superimposed oscillations. However, most of the line profiles are modified only by weak oscillations. This deviations from perfect monotonic behaviour might be produced by oscillations of the feedback loop. But as the images of the static cantilever bending signal do not show some corresponding features, the feedback loop as a source of oscillations can be ruled out. However, PPS is a thermoplastic, semicrystalline material. Thus, we expect some variations in s bp due to stiffness differences between crystalline and ‘amorphous’ regions. In the case of a monotonic decrease in local stiffness (Figure 6(d)) and under the precondition that the width of
Figure 6 Schematic representation of the contact situation near the fibre edge. (a) The situation when the apex of the tip is in mechanical contact with both fibre and matrix material. Due to the resulting asymmetric pressure profile the apex of the tip is expected to be strongly deformed. (b,c) Two extremes of an ideally flat and a step-like fibre–matrix transition. The width d of the dead zone DZ depends from the geometrical conditions and the drop of currents via conductive junctions C and tunneling currents T. (d) Sketch of the procedure of data evaluation. The characteristic length l c of the stiffness decay is determined by fitting the truncated stiffness profile
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Figure 7 (a) Four examples of datasets, which are not taken into account for the fits. The straight lines serve as a guide to the eye. (b) Some typical patterns of the stiffness related amplitude signal. The lateral position is rescaled to give a distance of 0 nm for the edge Z, as defined by the drop in electrical current
the interphase is at least some tens of nm, the characteristic parameters of the stiffness profile can be determined by a fitting procedure. In a first approach we have assumed a single-exponential profile and fitted the remaining 19 datasets using the following formula: s(x) ¼ sbp þ sw ·exp( ¹ x=lc )
(1)
x denotes the distance from the fibre edge and s(x) the respective value of the stiffness related signal (a.u.), i.e. s(x) denotes the amplitude of the dynamic and in general complex signal b dyn as detected by the lock-in amplifier in amplitude-phase mode. The fitting parameters are the asymptotic value of s (s bp), the weight factor s w and the characteristic length l c (nm) (Figure 6(d)). s bp reflects the stiffness of the bulk polymer material. Four of the fits are shown in Figure 7(b). It can be seen, that within of 75–150 nm the average value for the bulk polymer stiffness s bp is reached. The fits deliver values of
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the characteristic length l c which range from 15 to 84 nm (Figure 8). Although a tip shape convolution problem is not expected, the lateral resolution is clearly affected by the characteristic linear extension of the contact area which was assessed to be about 22 nm. This is similar to the smallest values of the characteristic length l c. In Figure 8 the distributions of the three parameters s w, s bp and l c are shown as determined by fitting the stiffness profiles according to eqn (1). The strong scatter in s bp between 55 and 84 a.u. underpins the above supposition that the mechanical data are influenced by the expected stiffness variations according to the semicrystalline nature of PPS. When sorting the three distributions with ascending characteristic length l c as an index, a distinct correlation between s w, s bp and l c is not perceptible, but a tendency to decreasing values of s bp with increasing values of l c cannot be ruled out. To get clarity in this points we have to extend the analysis to a broader statistic base.
Scanning force microscopy: M. Munz et al. DISPLACEMENT MODULATION WITH CONTROLLED DYNAMIC INDENTATION (CDIMODE) As already stated the area of the contact between tip and surface has an influence on the stiffness-related signal. Following the results of Kendall and Tabor26 the contact stiffness k ts is proportional to the contact radius a (assuming a circular contact area): kts ¼ paEts
(2)
The prefactor p is a constant between 1.9 and 2.4. In the case of the Hertz model it is equal to 2.027. E ts denotes the reduced modulus of the tip–sample contact: 1=Ets ¼ (1 ¹ n2t )=Et þ (1 ¹ n2s )=Es
(3)
The contact radius a is growing with increasing indentation depth and consequently larger for more compliant sites of the surface under investigation. This means that the stiffness dependence of a pretends a contact stiffness k ts too high compared to less compliant sites. But, as already mentioned, the ratio of contact stiffness k ts and force constant k c of the cantilever defines the ratio of the detected bending of the cantilever and the contact deformation. Thus, the stiffness contrast is expected to be reduced as an effect of the variations in the magnitude of a. Indeed, contrast reversal has been observed which was attributed to the increase of a within compliant regions28. On the other hand, a high stiffness sensitivity is desired in order to detect slight differences in local compliance. In the special case of extremely inhomogeneous samples, the stiffness resolution within compliant regions (interphase and bulk polymer)
should be similar to those within stiff regions (fibre). This can be achieved by matching the modulation amplitude z dyn to the local stiffness in a way that the amplitude of the periodical variation of the contact radius is kept constant. The modulation amplitude z dyn has to be reduced on soft sites. However, the amplitude of contact deformation d dyn in direction normal to the sample surface is given as the difference between z dyn and the shift b dyn resulting from the cantilever bending. Assuming that the contact radius a is proportional to this contact deformation d dyn, a can be kept constant by a second feedback loop (CDI-mode). Thus, the input of this additional feedback would be a signal proportional to d dyn and its output a dc voltage which can be used for adapting the amplitude z dyn of the displacement modulation to the local stiffness. The appropriate experimental setup is shown in Figure 129. Conventionally the amplitude z dyn of displacement modulation is fixed and both the detected amplitude of cantilever bending b dyn and the amplitude of dynamic indentation j dyn change with local stiffness (Figure 2). On soft sites b dyn is smaller and j dyn is larger compared to stiffer sites. When switching on the CDIM control the modulation amplitude z dyn is reduced on soft sites in a way that j dyn is kept constant. As a result, the difference in the response b dyn between soft and hard sites is increased. In other words we get an improved stiffness contrast and thus a better sensitivity for small variations in local stiffness. Beyond the lateral resolution for the mechanical measurement is the same on compliant and stiff regions, provided that the corresponding changes in the static part of the contact radius a can be neglected compared to the dynamic variations in a. Furthermore, the risk of detrimental effects on the surface under investigation as a consequence of the measurement procedure is reduced. Compliant phases which are expected to be more delicate are knocked with adapted forces.
DISCUSSION AND CONCLUSIONS
Figure 8 The distributions of the three parameters s w, s bp and l c as a result of fitting the stiffness decays according to eqn (1)
SFM measurements with displacement modulation have been shown to give valuable information about local compliance. The method was applied to both a singleglass-fibre sample and a multi-carbon-fibre sample. Crosssections were prepared perpendicular to the fibre axis. From the measurements, some information about the variations of local mechanical stiffness within interphase are obtained. In order to get a well-defined reference signal for the definition of a fibre borderline the fact that the carbon fibres are electrically conductive was used. Applying an ac voltage to the carbon fibres and scanning with a conductive tip we get a distinct electrical contrast between fibres and the matrix polymer PPS. Drawing this borderline in the stiffness contrast we get a criterion for omitting datapoints which clearly do not represent polymeric material. Following this criterion, if there still exists a currentcarrying contact between the edge of the fibre and a sidewall of the tip when its apex already has lost contact with the fibre, the beginning of the interfacial zone will be truncated. Such a situation might occur, especially in the case of a step
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Scanning force microscopy: M. Munz et al. between fibre and polymer with a height comparable to the length of the tip. In the worst case, the width d of the dead zone, meaning the region near the edge of the fibre that cannot be touched by the tip as a consequence of the fibrepolymer-step and the finite aspect ratio of the tip, is as large as the ‘width’ of the interfacial region. That is why great care was taken in order to prepare rather flat surfaces, in particular without abrupt height differences and delaminations between fibre and polymer. In the case of step-like features the electrical reference may be influenced by sidewall contacts and the true topography is blurred by the convolution effect. Then a deconvolution algorithm might be applied30, but this needs some knowledge about tip shape and radius of curvature. Especially the determination of the latter is a difficult and time-consuming task31. On the other hand, in the case of a smooth topography with only slight differences in the height level between fibre and polymer, the topography image will not generally provide welldefined features indicating the edge of the fibre. In the ideal case of a vanishing fibre-polymer-step only some differences in mean roughness between fibre and matrix would indicate the edge of the fibre. Despite only having mechanical and electrical contact with polymeric material, the vicinity of the stiff fibre might have some influence on the mechanical measurement when the interaction volume is affected by the adjacent fibre surface. Following the Hertzian theory27, the normal load exerted by the tip is transferred to a club-shaped volume element underneath the contact area. As a rule of thumb, the effective volume probed by the tip is about 10 times deeper than the indentation depth32. Thus, irregularities of the cylindrical fibre shape, a peculiar rough fibre surface or the lateral extent of the tension club might result in an increase of the stiffness-related amplitude signal, also some nanometres away from the fibre edge (as detected on the sample surface). In principle, the instrumental response function for a given radius of curvature of the tip might be determined by scanning a surface, characterized by a step-like profile of Young’s modulus (meaning a hard–soft transition with an infinitely thin boundary) and a rather smooth topography. However, such a type of surface is difficult to prepare. Prerequisite to the experiment are both the missing of an interphase and a sufficient adhesion between the soft and the hard phases. In the case of reduced adhesion forces, and under the influence of shearing forces, the formation of a gap along the borderline is expected, thus damaging the condition of a flat topography (on the nanometre scale). Alternatively, the response to an ideal modulus step can be determined by theoretical calculations (to be published elsewhere). Concluding, the combination of smooth topography and the simultaneous analysis of topography, current and the stiffness-related contrast seem to be the right key for a serious analysis of mechanical properties within the interfacial region. As a first approach, assuming a single-exponential decrease in local stiffness along a section from fibre to polymer we find characteristic decay lengths which are
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distributed in a range between 20 and 80 nm. The observation of small oscillations superimposed to the exponential line profile is not clear. In order to decide if this is a systematic effect and to get a more solid statistical base an extended study has to be performed. Furthermore, considering the influence of the contact radius on the stiffness signal a DM-mode with controlled dynamic indentation (CDI-mode) is proposed. In this mode via an additional feedback loop the variations in the amplitude of the dynamic part of the contact radius are eliminated. As a result both an improved stiffness contrast and a constant lateral resolution are expected. This might be rather useful, especially when studying interphases of reinforced polymers, as the amplitude of modulation is adapted to the different stiffness values of matrix and filler.
ACKNOWLEDGEMENTS M.M. would like to thank the German National Science Foundation (DFG) and the Technical University of Berlin for financial support in form of a scholarship (Graduiertenkolleg ‘Polymer Materials’). The authors also wish to thank R. Sernow and M. Bistritz for technical support.
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Jandt, K.D., Heier, J., Bates, F.S. and Kramer, E.J., Transient surface roughening of thin films of phase separating polymer mixtures. Langmuir, 1996, 12, 3716–3720. Seyama, H., Maki, K. and Yamazaki, N., Atomic Force microscopic observation at initial growth stage of vacuumdeposited thin film of polyvinylidenefluoride. J. Vac. Sci. Technol. B, 1997, 15(2), 192. Maivald, P., Butt, H.J., Gould, S.A.C., Prater, C.B., Drake, B., Gurley, J.A., Elings, V.B. and Hansma, P.K., Using force modulation to image surface elasticities with the atomic force microscope. Nanotechnology, 1991, 2, 103–106. Florin, E.-L., Radmacher, M., Fleck, B. and Gaub, H.E., Atomic force microscopy with magnetic force modulation. Rev. Sci. Instrum., 1994, 65(3), 639–643. O’Shea, S.J., Welland, M.E. and Pethica, J.B., Atomic force microscopy of local compliance at solid-liquid interphases. Chem. Physics Letters, 1994, 223, 336–340. Heuberger, M., Dietler, G. and Schlapbach, L., Elastic deformations of tip and sample during atomic force microscope measurements. J. Vac. Sci. Technol. B, 1996, 14(2), 1250–1254. Sturm, H. and Schulz, E., Local AC current contrast on carbon fibre surfaces imaged by Scanning Force Microscopy. Acta Polymer, 1995, 46, 379–384. Sturm, H. and Schulz, E., Atomic force microscopy with simultaneous AC conductivity contrast for the analysis of carbon fibre surfaces. Composites Part A, 1996, 27(9), 677– 684. Peebles, L.H. Jr., Carbon fibres: Structure and mechanical properties. Internat. Mater. Reviews, 1994, 39(2), 75–92.
21. 22. 23. 24. 25. 26. 27. 28.
29. 30. 31. 32.
Gomez-Herrero, J., Gomez-Rodriguez, J.M., Garcia, R. and Baro, A.M., High F values in scanning tunneling microscopy: Field emission and tunnel regimes. J. Vac. Sci. Technol. A, 1990, 8(1), 445–449. Landman, U., Luedtke, W.D., Burnham, N.A. and Colton, R.J., Atomistic mechanisms and dynamics of adhesion, nanoindentation and fracture. Science, 1990, 248, 454–461. Johnson, K.L., Kendall, K. and Roberts, A.D., Surface energy and the contact of elastic solids. Proc. R. Soc. London A, 1971, 324, 301–313. Mark, J.E. (ed.), Physical Properties of Polymers Handbook. Am. Inst. of Physics, Woodbury, New York, 1996. Cherry, B.W., Polymer Surfaces. Cambridge University Press, Cambridge, 1981. Kendall, K. and Tabor, D., Proc. R. Soc. A, 1971, 323, 321. Johnson, K.L., Contact Mechanics. Cambridge University Press, Cambridge, 1987. Bar, G., Rubin, S., Parikh, A.N., Swanson, B.I., Zawodzinski, T.A. and Whangbo, M.H., Scanning Force Microscopy study of patterned monolayers of alkanethiols on gold. Importance of tipsample contact area in interpreting force modulation and friction force microscopy images. Langmuir, 1997, 13(3), 373–377. German patent pending (reference 197 28 357.8-33). Keller, D., Reconstruction of STM and AFM images distorted by finite-size tips. Surface Science, 1991, 253, 353–364. Umehara, Y., Ogiso, Y., Chihara, K., Mukasa, K. and Russell, P.E., Method for evaluating sharpness of tip apex of a cantilever for the atomic force microscope. Rev. Sci. Instrum., 1995, 66(1), 269–270. Burnham, N. A., Kulik, A. J. and Gremaud, G., Tip surface interactions. In Procedures in Scanning Probe Microscopy. ed. R. J. Colton et al., John Wiley and Sons, NY, 1996.
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PII: S1359-835X(98)00077-3
The scanning force microscope as a tool for the detection of local mechanical properties within the interphase of fibre reinforced polymers M. Munz a, H. Sturm a,*, E. Schulz a and G. Hinrichsen b a
Federal Institute for Materials Research and Testing, Lab. VI.21, Unter den Eichen 87, D-12205 Berlin, Germany b Technical University of Berlin, Institute for Nonmetallic Materials, Englische Straße 20, D-10587 Berlin, Germany
Scanning force microscopy (SFM) has been used to assess the local mechanical properties of fibre-reinforced polymers. Using a sinusoidal displacement modulation (DM) and lock-in technique the method allows to characterize local viscoelastic properties with a high lateral resolution. The simultaneous measurement of the local electrical conductivity is proposed which facilitates the interpretation of the mechanical data. The investigation of cross-sections perpendicular to the axis of carbon fibres embedded in PPS delivers some information about the change in local stiffness within the interfacial region. As a first approach, assuming a singleexponential decrease in local stiffness along a radial line from fibre to polymer we find characteristic decay lengths which are distributed in a range between 20 and 80 nm. Further, a modified DM-mode is proposed which is expected to provide a contrast enhancement of the signal which is related to local stiffness. This can be achieved by installing an additional feedback loop which keeps constant the amplitude of dynamic indentation (CDI-mode). q 1998 Elsevier Science Ltd. All rights reserved (Keywords: A. polymer–matrix composites (PMCs); B. interface/interphase; SFM/AFM; B. surface properties; D. nondestructive testing)
INTRODUCTION It is widely accepted that the mechanical properties, the environmental stability and the failure mechanisms of fibrereinforced polymers are strongly influenced by the interfacial zone which is formed when the constituents are combined into a composite. The interfacial region can be considered as a third phase, the interphase, which possesses neither the properties of the reinforcing phase nor those of the matrix. Moving along a radial line from the centre of a fibre towards a point within a plain polymer, the change in physical properties from fibre to bulk polymer (which is expected to occur within the interphase) causes some gradient. In thermoplastic systems a loss of long-range chain flexibility and mobility of the polymer molecules, entropically driven segregation of molecules according to their molecular weight, and strongly influenced crystallization behaviour are observed in the vicinity of the filler surface1. In thermosetting systems the cross-linking chemistry in the matrix adjacent to the surface is modified2. Focussing on a certain attribute, e.g. on local mechanical stiffness, the respective size of the interphase may be defined by the width of the region of interfacial gradient. The size of the interphase can range from nanometres to * Corresponding author.
micrometres2. A lot of work has been done to get some corresponding information3, but until the invention of scanning force microscopy (SFM) there was no microscopic method available which allows one to investigate local mechanical properties4. Both a monotonic decrease in local stiffness when moving from fibre to polymer5 and a dip in the stiffness line profile1 have been proposed. SFM in contact mode offers different techniques for investigating not only the topography but also local physical and chemical properties. Simultaneously measured contrasts of static and dynamic friction6, local elastic and viscoelastic properties7 or ohmic and capacitive conductivity8 open a wide range of applications in materials research. In SFM a micromachined cantilever with a small tip is scanned across the surface under investigation. Typically, the radius of curvature of the tip lies between 10 and 70 nm. The forces between tip and sample produce a bending of the cantilever (the force constant of SFM cantilevers usually ranges from 0.001 to 10 N m ¹1 9), which is detected via a laser beam and a segmented photodiode. When working in contact mode the repulsive forces between tip and sample are kept constant via a feedback loop (so-called equiforce mode or constant height mode). Part of the feedback loop is a piezo element which retracts the sample or the cantilever when an ascent on the scanned surface produces a change in
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Scanning force microscopy: M. Munz et al. the bending of the cantilever. In this way the force between tip and sample is kept constant and the output of the feedback loop is used for writing a topography image. SFM has been applied for investigations of both thin films10 and cross-sections of bulk samples11. For example, when studying phase-separating polymer mixtures12 or film formation processes13 a lot of information can be taken from the topography signal. As the topography of cross-sections of bulk samples is mainly influenced by the preparation procedure there is a strong need for some additional contrasts, reflecting physical or chemical properties of the material. In the following we will focus on the measurement of local stiffness.
SFM WITH DISPLACEMENT MODULATION (DM) In this SFM mode, while scanning, the normal position of sample or cantilever is modulated sinusoidally over a small distance of some nanometres14. As a consequence there is a modulation of the load exerted by the tip and a modulation of the bending of the cantilever depending on local mechanical sample properties. Thus the DM entails a modulation of the normal load and is often referred as force modulation14. However, DM should be distinguished from the more direct magnetic force modulation where a timedependent magnetic field is acting on a small magnetic particle15 or a magnetic layer16 deposited on the upper side and close to the free (tip-sided) end of the cantilever. The resulting ac part of the detection signal can be fed to a lock-in amplifier which is driven at the excitation frequency (Figure 1). The lock-in amplifier delivers an amplitude and a phase signal. The amplitude signal is related to the local stiffness (see below) and the phase signal reflects deviations from perfect elastic behaviour, which is important, e.g. when studying viscoelastic materials like polymers. However, due to the fact that only two external channels are at our disposal, only the amplitude of the electrical ac current
Figure 1 Experimental setup of a SFM in displacement modulation (DM) mode. The grey box shows the additional feedback which is installed for keeping constant the amplitude of the dynamic deformation within contact zone (CDI-mode)
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signal (see following section) and the amplitude of the mechanical ac signal have been recorded. Therefore, the phase shift between the mechanical excitation z dyn and the dynamical cantilever bending b dyn will not be discussed in the following. The relationship between the excitation and the corresponding dynamic indentation and dynamic cantilever bending is explained in Figure 2. On soft sites the indentation depth of the sample surface by the tip is higher than on harder sites. When working below the resonance frequency of the cantilever the modulation amplitude z dyn can be exactly decomposed into the amplitude d dyn of dynamic contact deformation and the shift of the tip in normal direction b dyn which is detected as an appropriate amount of cantilever bending. For the sake of clarity only the indentation amplitude j dyn is shown. When investigating polymers the deformation of the tip, which is usually made from stiff Si or Si 3N 4, is known to be negligible 17. The ratio of d dyn and b dyn is given by the ratio of k c, the spring constant of the cantilever, and k ts, the stiffness of the tip–sample contact. Hence, on soft sites the modulation amplitude decomposes into a high indentation amplitude j dyn and a low bending amplitude b dyn. Figure 3(a) shows the topographic image of a crosssection, prepared from a E-glass fibre (Bayer AG, Germany) with a rather thick polypropylene (PP)-sizing (PCD Polymere, Linz, Austria), embedded in a commercial epoxy (resin L180 and curing agent 181; mgs Kunstharzprodukte GmbH, Stuttgart, Germany). The sample was cut perpendicular to the fibre axis by using a diamond saw. Great care was taken to prepare a rather flat cross-section. Emery paper with coarseness 4000 was used and final polishing was done with a 0.05 mm alumina suspension. Finally, the surface was cleaned in a 1:1 water/2-propanol solvent mixture in an ultrasonic bath for 10 min. The cantilever which was used is I-shaped and has a typical force constant of 2.8 N/m (LOT-Oriel, Darmstadt, Germany). The modulation frequency was 50 kHz. The measurements were performed using a stand-alone SFM microscope (Model
Figure 2 Schematic representation of dynamic cantilever bending amplitude b dyn and dynamic indentation amplitude j dyn during a DM measurement. For a given modulation amplitude z dyn the magnitudes of b dyn and j dyn depend on local sample stiffness
Scanning force microscopy: M. Munz et al.
Figure 3 Topography (a) and mechanical amplitude contrast (b) of an E glass fibre with PP sizing, embedded in epoxy. The sample was prepared as a crosssection perpendicular to the fibre axis. Topography grey scale: 0 (dark)…873 (bright) nm; amplitude grey scale in a.u.: soft (dark)…stiff (bright)
steps and comparing topographic features, in particular near the rim of the fibres. When the direction of cutting or polishing was not changed, that part of the fibre where the abrasive forces move the polymeric material away in direction to the matrix should be preferred for scanning. Smearing is expected to be reduced by cutting with a cryogenic microtome. However, as our experiments have shown, at low temperatures the tendency to delamination between fibres and polymer is a major hindrance for the application of such techniques. When investigating composites with carbon fibres as the reinforcing phase, an advantage can be taken from the fact that carbon fibres are electrically conductive. Thus, when scanning from fibre to polymer the pronounced decrease in electrical conductivity can be used as a criterion to decide if the tip is in contact with polymeric material or not. Figure 4 SEM micrograph from the tip which was used for simultaneous mechanical and electrical measurements. The inset shows a magnification of the apex of the tip (image contrast inverted)
Explorer; TopoMetrix Inc., Santa Clara, USA) and a lock-in amplifier (Model SR830; Stanford Research, Sunnyvale, USA). The topography (Figure 3(a)) reflects the tremendous differences in mechanical properties between glass fibre and polymer. The fibre is much less abraded by the preparation process than the epoxy matrix and thus its surface is higher (bright) than those of the epoxy. The amplitude signal (Figure 3(b)) indicates a high amplitude (bright) of the dynamic cantilever bending and thus a high local stiffness in the region of the fibre. In contrast the PP phase shows the lowest amplitude. The lack of definition in the amplitude contrast at the steep right edge of the fibre is produced by the feedback loop. This is obvious from the image of the static cantilever bending which reflects deviations from the chosen feedback setpoint (image not given here). The finite time constant of the feedback loop (as a result of the chosen feedback parameters and the cut-off frequency of the analog-to-digital converter) prevents an instantaneous adjustment of the tip height when scanning such steep features. Some polymeric material might be smeared during the preparation of the cross-section and cover the interfacial zone or even some area of the fibre surface. The occurrence of such effects can be studied by scanning the surface immediately after the cutting process and several polishing
DISPLACEMENT MODULATION WITH SIMULTANEOUSLY PERFORMED AC CURRENT MEASUREMENTS The instrumentation to measure simultaneously topography and an ac current collected by a conductive tip is given in detail elsewhere18. The used ac voltage was 0.32 V at 42.605 kHz superimposed to a þ 0.2 V dc offset. The current collected by the tip was amplified with a gain of 10 5 and the resulting voltage was fed to a second lock-in amplifier (Model SR830; Stanford Research). The used cantilever has a conducting W-coated silicon tip (specific resistance about 50 mQ cm, tip height 7 mm, angle between axis and pyramid edge less than 108, Figure 4) and a force constant between 2.5 and 4.5 N m ¹1 according to the manufacturer (NT-MDT, Moscow, Russia). The measurement of the force constant by the software option of the microscope (Model Discoverer; TopoMetrix Inc., Santa Clara, USA) delivers 5.7 N m ¹1. Using this value the chosen static contact force was estimated to lie between 60 and 90 nN in all cases. The measurement of the response to the mechanical excitation was done in a similar manner to that in the previous section. For technical reasons, the alternative way of modulating the position of the cantilever base was used instead of modulating the sample position. The mechanism for contrasting different local stiffnesses is the same for both cases. The frequency for the displacement modulation of the cantilever base was 74.89 kHz, the
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Figure 5 Topography (a), electrical conductivity (b) and mechanical amplitude contrast (c) of a carbon fibre/PPS prepreg. The scan shows a part of the fibre– polymer borderline. Current amplitude grey scale in a.u., low current (dark)…high current (bright); mechanical amplitude grey scale in a.u., soft (dark)…stiff (bright). The bright areas in the upper right part of the images (b) and (c) indicate fibrous material. In (b) the upper section of the bright part is scaled logarithmically, whereas the lower section is in binary scale. The white lines drawn in (a) and (c) correspond to the fibre–matrix borderline as detected from the current image (b). The curves below the images are the respective cross-sections which were averaged from 10 neighboured pixel lines within the indicated rectangular area AB
modulation amplitude can be estimated to be in the nm range. The sample under investigation was prepared by cutting and polishing a carbon fibre/polyphenylenesulfide (PPS) prepreg (HM-type carbon fibre; Toray, Japan; PPS; Fortron, Hoechst, Germany). The direction of sawing was perpendicular to the surface. As a connection for an ac voltage source the bottom side of the sample is glued on a metal plate using an epoxy which contains silver. After additional fixing with insulating epoxy, the top side was polished manually with emery (coarseness 4000), a diamond lapping film (coarseness 0.1 mm) (3M, St. Paul, USA) and a 0.05 mm alumina suspension. The resulting surface was cleaned in a 1:1 water/2-propanol solvent mixture in an ultrasonic bath for 10 min. Several flat sites of the carbon fibre/PPS interface have been investigated. In Figure 5 the topography image (Figure 5(a)), the current image (Figure 5(b)) and the DM image (Figure 5(c)) of a 500 3 500 nm scan are shown. From the current and the DM image the upper half can be attributed to the electrical conductive and stiff polymer (compared to the fibre). In Figure 5(b) the upper section of the bright part is scaled logarithmically, whereas the lower section is in binary scale. In logarithmic scale the variations of lower currents are pronounced. Thus, distinctive lateral features become visible which indicate inhomogeneities of the scanned fibre. The images of Figure 5(a,c) are linearly scaled. The white lines drawn in Figure 5(a,c) correspond to the fibre–matrix borderline as detected from the current image (see below). The curves below the images of Figure 5 are the respective cross-sections which were averaged from 10
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neighboured pixel lines within the indicated rectangular area AB in order to increase the S/N ratio. The width and the length of the rectangles are 16.6 and 287 nm, respectively. The corrugation of the image cross-sections was checked concerning the problem of tip shape convolution. The tip shape was determined from the SEM micrographs (Figure 4), scaled anisotropically in the same manner as the corresponding topography cross-section and indented 5 nm, according to the static load including the contribution from the adhesion (see below). The resulting contact radius is 11 nm. Obviously, the measured line profile is smooth compared to the contour of the tip. Therefore the flattening of the measured topography compared to the true topography (as an effect of the convolution between corrugation and tip shape) seems to be neglectable. Using the fact that the electrical conductivity of the carbon fibre is much higher than those of the insulating polymer 19 we observe a pronounced increase in the ac current when the tip is scanned from polymer to fibre. Considering the steepness of the jump in the current profile, the lateral position accuracy for this procedure can be estimated as two image pixels, i.e. 3.32 nm. The crosssection of the DM image (Figure 5(c)) reflects an increase in local stiffness some tens of nanometres before the conductivity indicates the carbon fibre edge. This region can be considered to be part of the interfacial polymer zone where an interaction between the two components is expected. On the one hand, precondition for a stable feedback loop is a smooth, step-less topography. On the other hand, a more-or-less featureless topography renders the identification of the fibre edge rather difficult. Also, deducing the
Scanning force microscopy: M. Munz et al. fibre edge from the stiffness image alone can be misleading as the stiffness values vary over the fibre cross-section (Figure 5(c)). The mean values of the local stiffness and the corresponding rms deviations were determined by averaging rectangular areas containing at least 12 780 datapoints for both fibre and bulk polymer. For the bulk polymer value the scattering lies within the diameter of the drawn black point. The stronger scattering of our mechanical data over the fibre cross-section is consistent with the variations in local conductivity (Figure 5(b)). This variation might originate from the structure of the carbon fibres and was also observed by other groups20. Nevertheless the drop in the current signal at the fibre edge is generally rather pronounced. Hence, the breakdown in the measured current is used as a criterion for defining a fibre–matrix borderline. This borderline as defined by the drop in the measured current (apparent edge Z) is identical with the true edge D of the fibre only in the case of a vanishing dead zone (Figure 6). The dead zone (DZ) may result from both currents between the flank of the tip and the fibre edge when the apex of the tip is already in contact with polymeric material. Figure 6 depicts the two extremes of an ideal flat (Figure 6(b)) and of a step-like (Figure 6(c)) fibre–matrix edge. Point C denotes a mechanical and current-carrying contact between fibre and tip-flank, point T represents the location of a possible tunneling current. The width d of the dead zone DZ depends from the opening angle of the tip, the height difference between fibre and matrix and the steepness of this transition. Assuming a situation as demonstrated in Figure 6(c) with a total opening angle of 208 (this corresponds to the opening angle of our tip, approximately) and a step of about 50 nm the width d of the dead zone will be less than 20 nm (tunneling currents are expected only over distances shorter than 2 nm21). Defining the fibre–matrix borderline by the current-based criterion, that part of the data within the dead zone will be truncated and not taken into account for further analysis. Thus, for cases where the local stiffness adjusts from the mean fibre value to the bulk polymer value, the existence of a 20 nm wide dead zone would render the detection of the interphase impossible. But, even in the case of a perfectly flat fibre–matrix transition and an exactly known true fibre edge D (if it would be exactly detectable), the respective mechanical data in the very near of the true fibre edge should be interpreted with great care. As rather schematically shown in Figure 6(a), an anisotropically deformed tip apex is to be expected, corresponding to the enormous differences in local stiffness when the tip contacts both fibrous and polymeric material. Further, also when the tip has just lost contact with the fibre, the (mechanical) measurement should be influenced by the near fibre, as the sub-surface distribution of the mechanical stresses will be deformed by such a heterogeneous surface. Following the calculations of Ref. 22 for a homogeneous surface the lateral extension of the sub-surface stresses will be on the order of the contact radius. Using the Johnson–Kendall–Roberts (JKR) theory for adhesive contacts23, the value of the contact radius of our tip with PPS was estimated to be about
11 nm (radius of curvature 6.7 nm as determined from the SEM micrograph (Figure 4), external load 90 nN, Young’s modulus of PPS about 3.31. 10 9 N m ¹2 24, Poisson’s ratio about 0.36, adhesion energy about 30 mJ m ¹2 (typical value for polymers25)). This means that our mechanical data within a zone of about 11 nm from the true fibre edge should be omitted for the evaluation. The width of this zone, as defined by mechanical restrictions, is comparable to the width d of the dead zone DZ as defined by the electrical criterion. Thus, the usage of the apparent (current-based) borderline will, generally, also lead to the truncation of doubtful datapoints. Following this selection procedure for the fibre edge 25 stiffness profiles were taken into account. Eight stiffness profiles are given in the following figures, plotted in a way that only the stiffness values of the non-conducting surface is shown. The position of the first pixel with low conductivity value is set to 0 nm. In Figure 7(a) four examples of datasets are shown which where omitted in the further analysis, either because the S/N ratio is too low or because the curve exhibits some strong superimposed oscillations. However, most of the line profiles are modified only by weak oscillations. This deviations from perfect monotonic behaviour might be produced by oscillations of the feedback loop. But as the images of the static cantilever bending signal do not show some corresponding features, the feedback loop as a source of oscillations can be ruled out. However, PPS is a thermoplastic, semicrystalline material. Thus, we expect some variations in s bp due to stiffness differences between crystalline and ‘amorphous’ regions. In the case of a monotonic decrease in local stiffness (Figure 6(d)) and under the precondition that the width of
Figure 6 Schematic representation of the contact situation near the fibre edge. (a) The situation when the apex of the tip is in mechanical contact with both fibre and matrix material. Due to the resulting asymmetric pressure profile the apex of the tip is expected to be strongly deformed. (b,c) Two extremes of an ideally flat and a step-like fibre–matrix transition. The width d of the dead zone DZ depends from the geometrical conditions and the drop of currents via conductive junctions C and tunneling currents T. (d) Sketch of the procedure of data evaluation. The characteristic length l c of the stiffness decay is determined by fitting the truncated stiffness profile
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Figure 7 (a) Four examples of datasets, which are not taken into account for the fits. The straight lines serve as a guide to the eye. (b) Some typical patterns of the stiffness related amplitude signal. The lateral position is rescaled to give a distance of 0 nm for the edge Z, as defined by the drop in electrical current
the interphase is at least some tens of nm, the characteristic parameters of the stiffness profile can be determined by a fitting procedure. In a first approach we have assumed a single-exponential profile and fitted the remaining 19 datasets using the following formula: s(x) ¼ sbp þ sw ·exp( ¹ x=lc )
(1)
x denotes the distance from the fibre edge and s(x) the respective value of the stiffness related signal (a.u.), i.e. s(x) denotes the amplitude of the dynamic and in general complex signal b dyn as detected by the lock-in amplifier in amplitude-phase mode. The fitting parameters are the asymptotic value of s (s bp), the weight factor s w and the characteristic length l c (nm) (Figure 6(d)). s bp reflects the stiffness of the bulk polymer material. Four of the fits are shown in Figure 7(b). It can be seen, that within of 75–150 nm the average value for the bulk polymer stiffness s bp is reached. The fits deliver values of
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the characteristic length l c which range from 15 to 84 nm (Figure 8). Although a tip shape convolution problem is not expected, the lateral resolution is clearly affected by the characteristic linear extension of the contact area which was assessed to be about 22 nm. This is similar to the smallest values of the characteristic length l c. In Figure 8 the distributions of the three parameters s w, s bp and l c are shown as determined by fitting the stiffness profiles according to eqn (1). The strong scatter in s bp between 55 and 84 a.u. underpins the above supposition that the mechanical data are influenced by the expected stiffness variations according to the semicrystalline nature of PPS. When sorting the three distributions with ascending characteristic length l c as an index, a distinct correlation between s w, s bp and l c is not perceptible, but a tendency to decreasing values of s bp with increasing values of l c cannot be ruled out. To get clarity in this points we have to extend the analysis to a broader statistic base.
Scanning force microscopy: M. Munz et al. DISPLACEMENT MODULATION WITH CONTROLLED DYNAMIC INDENTATION (CDIMODE) As already stated the area of the contact between tip and surface has an influence on the stiffness-related signal. Following the results of Kendall and Tabor26 the contact stiffness k ts is proportional to the contact radius a (assuming a circular contact area): kts ¼ paEts
(2)
The prefactor p is a constant between 1.9 and 2.4. In the case of the Hertz model it is equal to 2.027. E ts denotes the reduced modulus of the tip–sample contact: 1=Ets ¼ (1 ¹ n2t )=Et þ (1 ¹ n2s )=Es
(3)
The contact radius a is growing with increasing indentation depth and consequently larger for more compliant sites of the surface under investigation. This means that the stiffness dependence of a pretends a contact stiffness k ts too high compared to less compliant sites. But, as already mentioned, the ratio of contact stiffness k ts and force constant k c of the cantilever defines the ratio of the detected bending of the cantilever and the contact deformation. Thus, the stiffness contrast is expected to be reduced as an effect of the variations in the magnitude of a. Indeed, contrast reversal has been observed which was attributed to the increase of a within compliant regions28. On the other hand, a high stiffness sensitivity is desired in order to detect slight differences in local compliance. In the special case of extremely inhomogeneous samples, the stiffness resolution within compliant regions (interphase and bulk polymer)
should be similar to those within stiff regions (fibre). This can be achieved by matching the modulation amplitude z dyn to the local stiffness in a way that the amplitude of the periodical variation of the contact radius is kept constant. The modulation amplitude z dyn has to be reduced on soft sites. However, the amplitude of contact deformation d dyn in direction normal to the sample surface is given as the difference between z dyn and the shift b dyn resulting from the cantilever bending. Assuming that the contact radius a is proportional to this contact deformation d dyn, a can be kept constant by a second feedback loop (CDI-mode). Thus, the input of this additional feedback would be a signal proportional to d dyn and its output a dc voltage which can be used for adapting the amplitude z dyn of the displacement modulation to the local stiffness. The appropriate experimental setup is shown in Figure 129. Conventionally the amplitude z dyn of displacement modulation is fixed and both the detected amplitude of cantilever bending b dyn and the amplitude of dynamic indentation j dyn change with local stiffness (Figure 2). On soft sites b dyn is smaller and j dyn is larger compared to stiffer sites. When switching on the CDIM control the modulation amplitude z dyn is reduced on soft sites in a way that j dyn is kept constant. As a result, the difference in the response b dyn between soft and hard sites is increased. In other words we get an improved stiffness contrast and thus a better sensitivity for small variations in local stiffness. Beyond the lateral resolution for the mechanical measurement is the same on compliant and stiff regions, provided that the corresponding changes in the static part of the contact radius a can be neglected compared to the dynamic variations in a. Furthermore, the risk of detrimental effects on the surface under investigation as a consequence of the measurement procedure is reduced. Compliant phases which are expected to be more delicate are knocked with adapted forces.
DISCUSSION AND CONCLUSIONS
Figure 8 The distributions of the three parameters s w, s bp and l c as a result of fitting the stiffness decays according to eqn (1)
SFM measurements with displacement modulation have been shown to give valuable information about local compliance. The method was applied to both a singleglass-fibre sample and a multi-carbon-fibre sample. Crosssections were prepared perpendicular to the fibre axis. From the measurements, some information about the variations of local mechanical stiffness within interphase are obtained. In order to get a well-defined reference signal for the definition of a fibre borderline the fact that the carbon fibres are electrically conductive was used. Applying an ac voltage to the carbon fibres and scanning with a conductive tip we get a distinct electrical contrast between fibres and the matrix polymer PPS. Drawing this borderline in the stiffness contrast we get a criterion for omitting datapoints which clearly do not represent polymeric material. Following this criterion, if there still exists a currentcarrying contact between the edge of the fibre and a sidewall of the tip when its apex already has lost contact with the fibre, the beginning of the interfacial zone will be truncated. Such a situation might occur, especially in the case of a step
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Scanning force microscopy: M. Munz et al. between fibre and polymer with a height comparable to the length of the tip. In the worst case, the width d of the dead zone, meaning the region near the edge of the fibre that cannot be touched by the tip as a consequence of the fibrepolymer-step and the finite aspect ratio of the tip, is as large as the ‘width’ of the interfacial region. That is why great care was taken in order to prepare rather flat surfaces, in particular without abrupt height differences and delaminations between fibre and polymer. In the case of step-like features the electrical reference may be influenced by sidewall contacts and the true topography is blurred by the convolution effect. Then a deconvolution algorithm might be applied30, but this needs some knowledge about tip shape and radius of curvature. Especially the determination of the latter is a difficult and time-consuming task31. On the other hand, in the case of a smooth topography with only slight differences in the height level between fibre and polymer, the topography image will not generally provide welldefined features indicating the edge of the fibre. In the ideal case of a vanishing fibre-polymer-step only some differences in mean roughness between fibre and matrix would indicate the edge of the fibre. Despite only having mechanical and electrical contact with polymeric material, the vicinity of the stiff fibre might have some influence on the mechanical measurement when the interaction volume is affected by the adjacent fibre surface. Following the Hertzian theory27, the normal load exerted by the tip is transferred to a club-shaped volume element underneath the contact area. As a rule of thumb, the effective volume probed by the tip is about 10 times deeper than the indentation depth32. Thus, irregularities of the cylindrical fibre shape, a peculiar rough fibre surface or the lateral extent of the tension club might result in an increase of the stiffness-related amplitude signal, also some nanometres away from the fibre edge (as detected on the sample surface). In principle, the instrumental response function for a given radius of curvature of the tip might be determined by scanning a surface, characterized by a step-like profile of Young’s modulus (meaning a hard–soft transition with an infinitely thin boundary) and a rather smooth topography. However, such a type of surface is difficult to prepare. Prerequisite to the experiment are both the missing of an interphase and a sufficient adhesion between the soft and the hard phases. In the case of reduced adhesion forces, and under the influence of shearing forces, the formation of a gap along the borderline is expected, thus damaging the condition of a flat topography (on the nanometre scale). Alternatively, the response to an ideal modulus step can be determined by theoretical calculations (to be published elsewhere). Concluding, the combination of smooth topography and the simultaneous analysis of topography, current and the stiffness-related contrast seem to be the right key for a serious analysis of mechanical properties within the interfacial region. As a first approach, assuming a single-exponential decrease in local stiffness along a section from fibre to polymer we find characteristic decay lengths which are
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distributed in a range between 20 and 80 nm. The observation of small oscillations superimposed to the exponential line profile is not clear. In order to decide if this is a systematic effect and to get a more solid statistical base an extended study has to be performed. Furthermore, considering the influence of the contact radius on the stiffness signal a DM-mode with controlled dynamic indentation (CDI-mode) is proposed. In this mode via an additional feedback loop the variations in the amplitude of the dynamic part of the contact radius are eliminated. As a result both an improved stiffness contrast and a constant lateral resolution are expected. This might be rather useful, especially when studying interphases of reinforced polymers, as the amplitude of modulation is adapted to the different stiffness values of matrix and filler.
ACKNOWLEDGEMENTS M.M. would like to thank the German National Science Foundation (DFG) and the Technical University of Berlin for financial support in form of a scholarship (Graduiertenkolleg ‘Polymer Materials’). The authors also wish to thank R. Sernow and M. Bistritz for technical support.
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