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Measurement of interaction forces between individual powder particles using an atomic force microscope
Powder Technology 117 Ž2001. 247–254 www.elsevier.comrlocaterpowtec
Measurement of interaction forces between individual powder particles using an atomic force microscope U. Sindel, I. Zimmermann) Institute of Pharmacy and Food Chemistry, Pharmaceutical Technology, UniÕersity of Wurzburg, 97074 Wurzburg, Germany ¨ ¨ Received 1 May 1999; received in revised form 1 August 2000; accepted 6 September 2000 Prof. Dr. B. Lippold on the occasion of his 60th birthday.
Abstract The atomic force microscope ŽAFM. was used to investigate the interaction forces between individual particles qualitatively as well as quantitatively. Lactose as a typical excipient for solid drugs was chosen as model substance. The interaction forces were determined between a single particle of crystalline lactose and a tablet of lactose. Their surface topography was characterized by AFM and scanning electron microscopy ŽSEM. in order to allow a quantitative assessment of the surface roughness and its influence on the measured forces. To analyze the representative surface segments, the minimum and maximum surface roughness of the lactose tablet is determined in dependence of the segment size. The contact area between the tablet and the particle of lactose was quantified by the tip estimation of Villarrubia. Interparticle forces were measured with force volume scans. They allow the determination of the three-dimensional surface structure and, simultaneously, a defined number of force curves in regular distances is taken. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Atomic force microscopy; Interparticle forces; Lactose; Surface roughness; Force volume scan
1. Introduction The properties of bulk solids are of great importance in the pharmaceutical development and production of solid dosage forms. Many processes are rendered difficult due to poor flow properties of the bulk. These flow properties are determined by the forces acting between individual powder particles, like van der Waals, capillary and electrostatic forces. To improve flow properties in a straightforward way, it is necessary to comprehend interparticle forces qualitatively as well as quantitatively and to have methods available to measure them. The methods applied hitherto for the characterization of the flowability of powders and the underlying interparticle forces are restricted to measurements on bigger sample quantities Že.g., Refs. w1–3x.. Therefore, inferences on )
Corresponding author. Tel.: q49-931-888-5471; fax: q49-931-8884608. E-mail address: [email protected] ŽI. Zimmermann..
individual interactions turn out to be very difficult and become misleading. With the development of scanning probe microscopes w4x, new instruments have become available having the precision and sensitivity to probe surfaces with molecular resolution. In addition to the normal topographical imaging, scanning probe microscopes can also record fundamental properties of sample surfaces, e.g., local adhesive or elastic properties. By affixing a particle to the cantilever of an atomic force microscope ŽAFM., the interaction between this particle and a substrate can be investigated as a function of variables like particle diameter, particle–substrate separation and ambient conditions. Recently, the measurement of the force required to remove an individual micrometer-size polystyrene sphere from a silicon substrate using this technique w5x has been reported. Similar experiments have been carried out using the pharmaceutical excipient lactose. For the sake of simplicity and in order to approximate the sphere–surface interaction, an individual particle of lactose was attached to the can-
0032-5910r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 0 . 0 0 3 7 3 - 9
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U. Sindel, I. Zimmermannr Powder Technology 117 (2001) 247–254
Fig. 1. SEM image of an AFM cantilever modified by affixing a lactose particle.
tilever and used as a probe on a flat lactose tablet. Adhesion forces were determined by measuring the lift-off forces necessary for separating probe and substrate. The measured forces were analyzed quantitatively as well as qualitatively. As Rietema w6x points out, the interparticle forces depend strongly on the area of contact and, therefore, are heavily influenced by the roughness of probe and substrate. The topographical structure of the lactose tablet was quantified by the roughness of the defined surface segments. According to Kiely and Bonnell w7x, surface structures possess a minimum and a maximum roughness depending on the size of the segment being analyzed. If the size of a segment is between these two limits, its roughness is proportional to its size. For the measurement of interparticle forces, representative surface segments were chosen showing either the minimum or the maximum surface roughness. The surface structure of the adhering particle and the resulting contact area between probe and substrate is of great importance for the interpretation of the measured interaction forces. Pictures taken by scanning electron microscopy ŽSEM. show the size, orientation and surface structure of the fixed lactose particle ŽFig. 1.. However, they do not allow an estimation of the contact area. More detailed information could be obtained with Villarrubia’s w8x tip estimation based on a blind algorithm. The interparticle forces were measured with a special scanning technique. By means of so-called force volume scans, the three-dimensional surface structure of the substrate is determined. Simultaneously, a defined number of force curves are recorded in regular distances. 2. Experimental 2.1. Materials Crystalline a-lactose monohydrate ŽGranuLac 200, Meggle, Wasserburg, Germany. was used in the form of
single particles attached to the cantilever of an AFM or in the form of pure lactose tablets. These tablets were manufactured on a hydraulic press ŽPW 10, Paul Weber Maschinen-und Apparatebau, Stuttgart, Germany. with pressures of 0.4, 0.6 and 0.9 GPa. The technique in fixing a particle to a cantilever is described elsewhere in detail w9x. Small particles adhering to the probes and substrates were removed with compressed air. The tip apex radius of the lactose particle was estimated by means of the blind algorithm of Villarrubia Žsee Section 2.2.1.6.. After finishing a certain series of experiments, the cantilever with the adhering particle was analyzed by means of a scanning electron microscope ŽZeiss DSM 962, Carl Zeiss, Oberkochen, Germany, Fig. 1.. 2.2. Methods 2.2.1. Atomic force microscope The AFM measurements were performed using a NanoScope Ee ŽDigital Instruments, Santa Barbara, USA.. The scans were analyzed with the NanoScopee software version 4.22. Three basic types of measurement can be performed: determination of the interaction force at a given point, scans of surface topography and force volume scans. 2.2.1.1. Determination of the interaction force at a giÕen point. A force sensor is the core element of an AFM. Roughly speaking, it consists of a cantilever with a sharp tip acting as a probe and of a piezo displacement unit which carries the substrate ŽFig. 2.. While the basis of the cantilever is kept in a fixed position, the substrate can be moved up- and downward by means of the piezo displacement unit ŽFig. 2a.. As soon as the substrate interacts with the probe, the cantilever is deflected from its normal horizontal position. The tip jumps into contact with the substrate surface ŽFig. 2b.. The piezo unit continues its upward movement until a pre-set value of the z-coordinate Ž z scan size. is reached ŽFig. 2c.. Then, it reverses its direction of movement. As soon as the restoring force F of the cantilever equals the interaction force of the cantilever, the tip separates from the surface of the substrate ŽFig. 2d–e.. By means of the reflection angle of a laser beam reflected at the surface of the cantilever, the extent z of the cantilever deflection can be measured. According to the Hooke law, F s ykz Ž 1. the restoring force of the cantilever and the interaction force F, respectively, are given by the cantilever deflection z at the moment of separation multiplied by its spring constant k. The force curve is described in detail in Ref. w10x. To quantify the adhesion forces acting between lactose particles, the forces acting between a modified cantilever and the surface of a lactose tablet were recorded.
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Fig. 2. Force–distance-plot of the atomic force microscope. Ža. Non-contact range; Žb. jump-into-contact between probe and substrate; Žc. maximum position of substrate; Žd. maximum interaction force; Že. abrupt separation probe–substrate.
The accuracy of the force measurements depends upon the knowledge of the spring constant of the cantilever that probes these forces. There are several methods for its determination w11–13x. One is to calibrate the spring constant by applying the principle of thermal fluctuations w14x. This method, which was used in this work, is described in detail in Ref. w15x. 2.2.1.2. Scans of surface topography. To acquire topographic images of a sample, the substrate is moved upwards by the piezo displacement unit until the tip of the cantilever jumps into contact with the sample surface. Then, the piezo displacement unit adjusts its vertical position Ž z-value. in such a way that the force acting on the cantilever corresponds to a pre-set load. This z-value is recorded as a function of its horizontal position. With the tip of the cantilever remaining in contact with the sample surface, the piezo displacement unit moves the sample into the next horizontal position. The load acting on the cantilever is adjusted to the pre-set load by adapting the vertical position. Again, the corresponding z-value is recorded as a function of its horizontal position. In this way, a defined surface area is scanned. The step-widths in the x- and y-directions have to be defined before each scan. The surface topography is then given by the set of z-values over the scanned x, y-planes. 2.2.1.3. Force Õolume scans. A force volume scan consists of a series of adhesion force determinations at the various points on the substrate surface. In general, the topography of the surface has been scanned before. As a result, a complete force curve is stored in addition to the x-, y-, z-coordinates of each point of a substrate surface range. A force volume scan shows the distribution of adhesion over a given surface area as well as the three-dimensional structure of this area. By interpreting the force curve
qualitatively as well as quantitatively, characteristics of certain surface structures can be described. Therefore, force volume scans offer the opportunity to correlate the measured adhesion forces with the surface structure. 2.2.1.4. Surface characterization. To characterize the surface of lactose particles as well as of lactose tablets, scans of areas of 9 mm2 were made by means of the NanoScope Ee in contact mode. From these scans the z range, which gives the difference between the highest and the lowest point of the scanned area, is determined. Furthermore, the standard deviations sŽ z . of all z values were compared. The sample with the smoothest surface was chosen for the force measurements. 2.2.1.5. Quantification of the topographic structure. To quantify the surface structure of the substrate, a roughness analysis was carried out. Any surface has some distribution of heights. According to Kiely and Bonnell w7x, this is best described by the variational root-mean-square roughness sŽ z .. However, when imaged locally, only a fraction of the surface height distribution appears in the image height distribution. In consequence, sŽ z . increases with the area over which it is measured. It becomes scale-independent when the measurement area is greater than the largest characteristic area A) of the surface. Analogous to A) , there is a minimum characteristic area at which sŽ z . again becomes scale-independent at small scales which occurs at fractions of the tip radius. Between these two extremes, the area dependence of sŽ z . is a function of the distribution of feature heights and widths. This distribution is described by the slope of the variational sŽ z .. Slope changes accordingly identify feature dimensions. As a first step in the quantification of the surface structure of a substrate, the overall size of the image was defined. Then this area was subdivided into segments of
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Fig. 3. Influence of the shape of the probe on the resulting surface scan. ŽThe thick line shows the probe scanning a very steep part of the substrate. The broken line represents the result of the scan, showing one half of the mirrowed shape of the probe..
The blind algorithm of Villarrubia w8x searches the scan for the surface structure with the steepest slope which is then used as an approach to the real shape of the probe. To get a reliable estimation of the probe shape, it is necessary to analyze a big number of suitable surface scans showing sharp asperities. A calibration standard with a surface of low-, 180 nm, ŽApitsB . and high areas, which are separated vertically by 5 mm ŽDigital Instruments, Santa Barbara, USA. and a lactose tablet Žpressure: 0.9 GPa., was used for the estimation of the probe shape. In order to find surface areas suited for the tip estimation by means of the Villarrubia algorithm, both substrates were first scanned with a normal siliciumnitride cantilever before characterizing the modified cantilever.
3. Results different edge lengths over which sŽ z . was measured to identify the smallest and largest feature dimensions of the surface. 2.2.1.6. Estimation of the tip apex radius and of the shape of the probe. An extensive interpretation of the measured adhesion is only possible by determining the contact area between the probe and the substrate. The portion of the contact area arising from the lactose tablet can be characterized by analyzing a surface scan. But how about the shape and the surface morphology of the adhering particle of lactose acting as probe? The analysis of surface scans offers an opportunity to gain some information on the structure of the probe. It is based on the fact that by scanning the surface with a given cantilever, no asperity sharper than the probe itself can be recorded. Instead, sharper asperities result in surface structures corresponding to the turned shape of the probe ŽFig. 3.. This means that a scan of a surface with isolated, sharp asperities will only represent reality when the scanning probe is sharper than the sharpest surface asperity. Otherwise, this asperity will show the mirrowed shape of the probe. This is due to the fact that in case of a surface structure sharper than the probe, their roles are changed. The surface asperity acts as a probe and images the shape of the real probe. Therefore, by scanning a surface that shows sharp asperities, the sharpest peaks of this scan will represent the structure of the probe of the cantilever.
3.1. Characteristics of lactose surfaces In order to simplify the interpretation of the measured interaction forces, areas on lactose surfaces being as smooth as possible have been chosen. For this purpose, the surface roughness of individual lactose particles and of lactose tablets manufactured with different pressures was analyzed with the AFM. The results in Table 1 demonstrate clearly that lactose particles possess very structured surfaces with remarkable differences in height. In contrast to lactose particles, the surface structure of the lactose tablets is very regular ŽFig. 4. and shows no features like jumps, trenches or adhering small particles. As expected, all lactose tablets have surfaces smoother than the original substrate. The tablet pressed at 0.9 GPa exhibits the surface with the lowest differences in height. Within an area of 9 mm2 , the standard deviation of all z-values is 2.7 nm. 3.2. Quantification of the surface structure For the determination of the minimum and the maximum roughness on the surface of the lactose tablet Ž0.9 GPa., scans were taken at typical sites of the substrate surface. Three representative areas were chosen: the first one being relatively smooth, the second one regularly rough and the third one, fissured. The scan sizes covered 1,
Table 1 Surface characteristics of lactose samples measured by the AFM Ž3 = 3 mm. Surface characteristics
Particle of lactose
Tablet of lactose Ž0.4 GPa.
Tablet of lactose Ž0.6 GPa.
Tablet of lactose Ž0.9 GPa.
z range wnmxa sŽz. wnmxa
1073 154.8
53.5 5.2
45.5 5.3
27.1 2.7
a
All results are averages of three scans.
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flattening, were of first order w7,16x. In addition, there exist scan artifacts which have to be eliminated manually. 3.3. Estimation of the shape of the probe
Fig. 4. AFM scan of the surface of a lactose tablet Žpressure: 0.9 GPa..
25, 100, 2500 and 10 000 mm2 . For the analysis, the scans were divided in segments of equal size. The roughness of each segment was determined by calculating the standard deviation of the z values. Fig. 5 shows the average standard deviation sŽ z . in dependence of the size of the segments. The minimum and the maximum surface roughness of the lactose tablet is given by the plateaus. In scans of surface areas smaller than 1 mm2 , a roughness of 8 nm can be measured, whereas over scan sizes of more than 2500 mm2 , height differences of 80 nm can be identified. Reliable conclusions from force measurements can only be drawn if the scan size corresponds either to the minimum or the maximum roughness of the lactose tablet. With regard to the roughness analysis of surface scans, it is important to consider the sources of error which have to be eliminated in post-acquisition modification procedures. Often, there is a tilt of the surface due to a slanting attachment of the substrate. To eliminate such a tilt carefully, in a first step, a plane in the x direction has to be removed. It is determined by a last square fit to the average to all rows of data Žplane-fitting.. The same is done in the y direction. Eventually, each line of the image is raised or lowered until the mean average of each line was at the same height Žflattening.. Plane-fitting, as well as
Fig. 5. Surface roughness sŽ z . of the lactose tablet Ž0.9 GPa. in dependence of the segment size; plateaus are found over segments of 0.5–1 mm and 50–100 mm edge length.
The tip estimation, according to Villarrubia w8x, was used to estimate the contact area of the adhering particle of the modified cantilever as well as the tip apex of the normal cantilever. In order to find the suitable surface structure for this method, the calibration standard as well as the surface of a lactose tablet were first scanned with a normal siliciumnitride cantilever ŽDigital Instruments. with nominal tip radius of 10–22 nm Ždistance from the apex: 10 nm.. The evaluation of several surface scans of the calibration standard results in estimated tip radii of 116–154 nm. This is in clear contrast to reality. Therefore, the surface structure of the calibration standard is not suited for the algorithm-based tip estimation. As requested by the theory w8x, this surface possesses areas with steep elevations, however, their one-sidedness falsifies the results of the algorithm. The evaluation of 19 surface scans of the lactose tablet Žpressure: 0.9 GPa. resulted in tip radii being in agreement with their real structure. For the normal, non-modified, cantilever, a tip radius of 25.1 nm at a distance of 10 nm from the apex was estimated by means of the algorithm. This finding, being in agreement with the reality, proves the suitability of the surface of the lactose tablet for the tip qualification using the Villarrubia algorithm. On the basis of 24 scans made with a modified cantilever for the lactose particle, an apparent tip radius of 15.3 nm at a distance of 10 nm from the apex was determined. This means that only an asperity of these dimensions on the surface of the lactose particle interacted with the surface of the lactose tablet. Surprisingly, this asperity is sharper than the tip of the normal cantilever.
Fig. 6. Calculated radius of the tip apex of the normal and the modified cantilever.
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Fig. 8. Surface scan Ž1 mm2 . of the lactose tablet Ž0.9 GPa.. Fig. 7. Zoomed presentation of the calculated tip apexes.
With respect to the tip qualification, it becomes obvious that a large number of scans has to be analyzed. The evaluation of only about 30% of all scans resulted in tip radii being smaller than 30 nm. The shapes of the normal and the modified cantilever, estimated by means of the Villarrubia algorithm, are shown in Fig. 6 and a zoomed diagram in Fig. 7. The fact that the lactose particle affixed on the cantilever interacts with the tablet surface only via the asperity means that the contact area of the adhering lactose particle with the substrate is as small as with a good siliciumnitride cantilever. Therefore, it cannot be compared with the contact area of an ideal sphere of the same volume as the particle.
Fig. 9. Surface scan Ž2500 mm2 . of the lactose tablet Ž0.9 GPa..
3.4. Force Õolume scans After a careful post-acquisition analysis of the data, force volume scans as a combination of surface scan and force measurement give information on the surface topography of the substrate as well as on a direct relation between adhesion and surface structure. In dependence of the scan size in Section 3.2, it was possible to identify two different lengths of 8 and 80 nm, respectively, characterizing surface asperities Žsee Section 3.2.. Therefore, force volume scans have been performed with the minimum Ž1 mm2 . and the maximum Ž2500 mm2 . scan size in order to allow the probe to interact with asperities of both characteristic lengths. In all cases, a
Fig. 10. Relative frequency of the measured adhesion Žscan area: 1 mm2 ..
Table 2 Evaluation of the force volume scans made with the modified cantilever Scan size wmm2 x sŽz.-range wnmx Adhesion wnNx Standard deviation wnNx Min. adhesion wnNx Max. adhesion wnNx
1 7.7 4.3 2.05 0.42 9.89
2500 53.7 5.0 3.06 0.53 11.23
Fig. 11. Relative frequency of the adhesion determined over scan areas of 2500 mm2 .
U. Sindel, I. Zimmermannr Powder Technology 117 (2001) 247–254
Fig. 12. Force curve measured on the top of an asperity.
modified cantilever Žspring constant: 0.228 Nrm. was used. In the post-acquisition analysis, plane-fitting and flattening were again of first order. In the following, only one force volume scan is discussed in detail. The results of the evaluation of the data are summarized in Table 2. The surface over the small scan area ŽFig. 8. is characterized by an average roughness of 7.7 nm. The corresponding length over the larger area ŽFig. 9. is given by 53.7 nm. The average adhesion between the lactose particle and the tablet surface determined over scan areas of both sizes is almost the same, 4.3 and 5.0 nN, respectively. The difference is statistically not significant. Each scan comprised 1024 force curves. The distribution of the measured forces was evaluated with a force program ŽS. Vinzelberg, Digital Instruments, Mannheim, Germany.. The results are shown in Figs. 10 and 11. Over the small scan areas, forces ranging from 0.4 to 12 nN were determined. Over the larger scan areas maximum forces of up to 14 nN were observed. Generally, the interaction forces measured over a representative surface area are expected to follow a normal distribution. However, the tests on a Gaussian distribution reject this assumption. In force volume scans, the measured force curves can be related directly to the structure of the interacting surfaces. Therefore, conclusions about the extent of the adhesion in dependence of the surface structure can be made. The force curves measured on the top of the asperities are
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characterized by a sharp rupture of the interaction contact ŽFig. 12.. The adhesion between the particle and curved surface structures or valleys, however, is characterized by a step-wise separation ŽFig. 13.. In addition, the interaction forces measured over these structures are bigger than those observed on the top of the asperities. A closer look at the measured force curves reveals some irregularities. First of all, there is the wavy ascent in the non-contact area. This is caused by interferences in the optical detection system. They have no influence on the force measurement itself. The slope of the force curve right behind the jumpinto-contact region ŽFig. 2b. is smaller than expected from theory. The corresponding smaller vertical deflection of the cantilever can be caused by elastic or plastic deformations of the probe or of the substrate. Since this peculiarity is observed even after repeated measurements at the same point it can be assumed that the deformation is elastic. When measured in surface valleys the force curves ŽFig. 13. show another peculiarity. The shape before the rupture of contact indicates not a sharp but a stepwise separation of the particle from the tablet surface. This can be explained by the assumption of several contact points between probe and substrate which are separated one by one. 3.5. Comparison with other methods The interparticle forces as determined with an AFM were compared with the corresponding values obtained from measurements performed with a Jenike shear cell and the tensile strength tester w17,18x. For all measurements, lactose GranuLac 200 was used as substrate ŽTable 3.. It becomes obvious that the interaction energies measured by the different methods cannot be compared directly. An AFM allows the determination of the interaction energy in a single contact point. With the other two methods, however, only averages from multiple contacts can be measured. It seems that the average adhesion determined by these methods increases with the number of contacts between the individual particles and the overall number of particles involved in the separation step. This number is highest in the case of the Jenike shear cell. The results highlight the difficulties arising when forces determined from a bulk of powder are transformed into forces acting between individual particles as this is achieved only under the assumption of ideal material properties w2x.
Table 3 Comparison of the results obtained with different methods
Fig. 13. Force curve measured in a valley.
Apparatus
Porosity w%x
Average adhesion per particle wnNx
Shear cell Tensile strength tester Atomic force microscope
58 58 –
85 21 5
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4. Discussion Our results show that AFM is suited for the determination of surface forces acting between lactose substrates. We especially studied the interaction between an individual lactose particle and the surface of a lactose tablet made at a pressure of 0.9 GPa. AFM scans of the tablet surface allowed a detailed qualitative and quantitative description of the substrate surface. By analyzing the roughness of surface segments of different sizes, a minimum and a maximum roughness of the lactose tablet could be found. A characteristic length of 8 nm is observed for the smallest roughness at scan sizes smaller than 1 mm2 . The corresponding value for the largest roughness is given by 54 nm. It can be measured at scan sizes larger than 2500 mm2 . For an analysis of a surface being representative for the tablet surface, scans of these two sizes have to be performed. The contact area between probe and substrate is another important factor influencing the size of the measured forces. Based on the analysis of a large number of surface scans, the size as well as the shape of the contacting asperity of the lactose particle affixed on the cantilever was approximated. The regular surface of a calibration standard proved to be unsuited for a tip calibration. Scans of the lactose tablet, however, gave good results. It was shown that the contact area of the adhering lactose particle was almost of the same size as the one of a commercial cantilever. Force volume scans over representative surface segments allowed a direct relation between surface structures and the shape of force curves. Forces measured on the top of the asperities are smaller than those determined in valleys. A sharp interruption of the corresponding contact was observed in the case of the asperity. In the case of the valleys, however, a stepwise interruption of obviously multiple contacts was observed. Further peculiarities in the shape of the force curves could be related to the material properties of lactose. It was shown that most probably lactose undergoes elastic deformations during the force measurements. The measured interparticle forces between the probe and the lactose substrate ranged from 0.4 to 14 nN. Depending on the characteristic roughness of the surface structure, average adhesions of 4.34 and 4.98 nN, respectively, were determined. A comparison of the adhesion forces determined by different methods, e.g., the AFM, the Jenike shear cell and the tensile strength tester, showed the difficulties arising when calculating the properties of individual particles from bulk properties.
Acknowledgements The authors wish to thank Meggle ŽWasserburg, Germany. for the donation of the substances.
References w1x A.W. Jenike, P.J. Elsey, R.H. Wooley, Flow properties of bulk solids, Proc., Am. Soc. Test. Mater. 60 Ž1960. 1168–1181. w2x K. Rietema, Application of mechanical stress theory to fluidization, Proc. Int. Symp. Fluid., Eindhoven Ž1967. 258–265. w3x H. Fukuzawa, S. Kimura, Cohesion of particulate solids: I. Measuring method for cohesive forces, Yakugaku Zasshi 92 Ž1972. 42–50. w4x G. Binnig, C. Quate, Atomic force microscope, Phys. Rev. Lett. 56 Ž1986. 930–933. w5x D.M. Schaefer, M. Carpenter, R. Reifenberger, L.P. Demejo, D.S. Rimai, Surface force interactions between micrometer-size polystyrene spheres and silicon substrates using atomic force techniques, J. Adhes. Sci. Technol. 8 Ž1994. 197–210. w6x K. Rietema, The Dynamics of Fine Powders, Elsevier, London, 1994, 71. w7x J.D. Kiely, D.A. Bonnell, Quantification of topographic structure by scanning probe microscopy, J. Vac. Sci. Technol., B 15 Ž4. Ž1997. 1483–1493. w8x J.S. Villarrubia, Morphological estimation of tip geometry for scanned probe microscopy, Surf. Sci. 321 Ž1994. 287–300. w9x U. Sindel, I. Zimmermann, D. Schaefer, R. Reifenberger, Direct measurement of interparticle forces in particulate solids using an atomic force microscope, Proc. World Congr. Part. Technol., Brighton vol. 3, 1998, no. 68. w10x U. Sindel, I. Zimmermann, D. Schaefer, R. Reifenberger, Direct measurement of interaction forces between individual particles using an atomic force microscope,Preprints for the 1st European Symposium of Process Technology in Pharmaceutical and Nutritional Sciences, PARTEC 98, Nurnberg, 1998, pp. 37–46. ¨ w11x C.T. Gibson, G.S. Watson, S. Myhra, Determination of the spring constants of probes for force microscopyrspectroscopy, Nanotechnology 7 Ž1996. 259–262. w12x J.P. Cleveland, S. Manne, D. Bocek, P.K. Hansma, A nondestructive method for determining the spring constant of cantilevers for AFM, Rev. Sci. Instrum. 64 Ž1993. 403–405. w13x E.-L. Florin, M. Rief, H. Lehmann, M. Ludwig, C. Dornmair, V.T. Moy, H.E. Gaub, Sensing specific molecular interactions with the atomic force microscope, Biosens. Bioelectron. 10 Ž1995. 895–901. w14x J.L. Hutter, J. Bechhoefer, Calibration of atomic-force microscope tips, Rev. Sci. Instrum. 64 Ž1993. 1868–1873. w15x U. Sindel, Messung interpartikularer ¨ Haftkrafte ¨ mittels Rasterkraftmikroskopie, thesis, University of Wurzburg, 1999. ¨ w16x Scanning Probe Microscope Instruction Manual, Digital Instruments, Version 4.20, 1996. w17x A. Schweiger, I. Zimmermann, A new approach for the measurement of the tensile strength of powders, Powder Technol. 101 Ž1999. 7–15. w18x A. Schweiger, Untersuchungen zum Fließverhalten feinkorniger ¨ Schuttguter, 1998. ¨ ¨ thesis, University of Wurzburg, ¨
Measurement of interaction forces between individual powder particles using an atomic force microscope U. Sindel, I. Zimmermann) Institute of Pharmacy and Food Chemistry, Pharmaceutical Technology, UniÕersity of Wurzburg, 97074 Wurzburg, Germany ¨ ¨ Received 1 May 1999; received in revised form 1 August 2000; accepted 6 September 2000 Prof. Dr. B. Lippold on the occasion of his 60th birthday.
Abstract The atomic force microscope ŽAFM. was used to investigate the interaction forces between individual particles qualitatively as well as quantitatively. Lactose as a typical excipient for solid drugs was chosen as model substance. The interaction forces were determined between a single particle of crystalline lactose and a tablet of lactose. Their surface topography was characterized by AFM and scanning electron microscopy ŽSEM. in order to allow a quantitative assessment of the surface roughness and its influence on the measured forces. To analyze the representative surface segments, the minimum and maximum surface roughness of the lactose tablet is determined in dependence of the segment size. The contact area between the tablet and the particle of lactose was quantified by the tip estimation of Villarrubia. Interparticle forces were measured with force volume scans. They allow the determination of the three-dimensional surface structure and, simultaneously, a defined number of force curves in regular distances is taken. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Atomic force microscopy; Interparticle forces; Lactose; Surface roughness; Force volume scan
1. Introduction The properties of bulk solids are of great importance in the pharmaceutical development and production of solid dosage forms. Many processes are rendered difficult due to poor flow properties of the bulk. These flow properties are determined by the forces acting between individual powder particles, like van der Waals, capillary and electrostatic forces. To improve flow properties in a straightforward way, it is necessary to comprehend interparticle forces qualitatively as well as quantitatively and to have methods available to measure them. The methods applied hitherto for the characterization of the flowability of powders and the underlying interparticle forces are restricted to measurements on bigger sample quantities Že.g., Refs. w1–3x.. Therefore, inferences on )
Corresponding author. Tel.: q49-931-888-5471; fax: q49-931-8884608. E-mail address: [email protected] ŽI. Zimmermann..
individual interactions turn out to be very difficult and become misleading. With the development of scanning probe microscopes w4x, new instruments have become available having the precision and sensitivity to probe surfaces with molecular resolution. In addition to the normal topographical imaging, scanning probe microscopes can also record fundamental properties of sample surfaces, e.g., local adhesive or elastic properties. By affixing a particle to the cantilever of an atomic force microscope ŽAFM., the interaction between this particle and a substrate can be investigated as a function of variables like particle diameter, particle–substrate separation and ambient conditions. Recently, the measurement of the force required to remove an individual micrometer-size polystyrene sphere from a silicon substrate using this technique w5x has been reported. Similar experiments have been carried out using the pharmaceutical excipient lactose. For the sake of simplicity and in order to approximate the sphere–surface interaction, an individual particle of lactose was attached to the can-
0032-5910r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 Ž 0 0 . 0 0 3 7 3 - 9
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Fig. 1. SEM image of an AFM cantilever modified by affixing a lactose particle.
tilever and used as a probe on a flat lactose tablet. Adhesion forces were determined by measuring the lift-off forces necessary for separating probe and substrate. The measured forces were analyzed quantitatively as well as qualitatively. As Rietema w6x points out, the interparticle forces depend strongly on the area of contact and, therefore, are heavily influenced by the roughness of probe and substrate. The topographical structure of the lactose tablet was quantified by the roughness of the defined surface segments. According to Kiely and Bonnell w7x, surface structures possess a minimum and a maximum roughness depending on the size of the segment being analyzed. If the size of a segment is between these two limits, its roughness is proportional to its size. For the measurement of interparticle forces, representative surface segments were chosen showing either the minimum or the maximum surface roughness. The surface structure of the adhering particle and the resulting contact area between probe and substrate is of great importance for the interpretation of the measured interaction forces. Pictures taken by scanning electron microscopy ŽSEM. show the size, orientation and surface structure of the fixed lactose particle ŽFig. 1.. However, they do not allow an estimation of the contact area. More detailed information could be obtained with Villarrubia’s w8x tip estimation based on a blind algorithm. The interparticle forces were measured with a special scanning technique. By means of so-called force volume scans, the three-dimensional surface structure of the substrate is determined. Simultaneously, a defined number of force curves are recorded in regular distances. 2. Experimental 2.1. Materials Crystalline a-lactose monohydrate ŽGranuLac 200, Meggle, Wasserburg, Germany. was used in the form of
single particles attached to the cantilever of an AFM or in the form of pure lactose tablets. These tablets were manufactured on a hydraulic press ŽPW 10, Paul Weber Maschinen-und Apparatebau, Stuttgart, Germany. with pressures of 0.4, 0.6 and 0.9 GPa. The technique in fixing a particle to a cantilever is described elsewhere in detail w9x. Small particles adhering to the probes and substrates were removed with compressed air. The tip apex radius of the lactose particle was estimated by means of the blind algorithm of Villarrubia Žsee Section 2.2.1.6.. After finishing a certain series of experiments, the cantilever with the adhering particle was analyzed by means of a scanning electron microscope ŽZeiss DSM 962, Carl Zeiss, Oberkochen, Germany, Fig. 1.. 2.2. Methods 2.2.1. Atomic force microscope The AFM measurements were performed using a NanoScope Ee ŽDigital Instruments, Santa Barbara, USA.. The scans were analyzed with the NanoScopee software version 4.22. Three basic types of measurement can be performed: determination of the interaction force at a given point, scans of surface topography and force volume scans. 2.2.1.1. Determination of the interaction force at a giÕen point. A force sensor is the core element of an AFM. Roughly speaking, it consists of a cantilever with a sharp tip acting as a probe and of a piezo displacement unit which carries the substrate ŽFig. 2.. While the basis of the cantilever is kept in a fixed position, the substrate can be moved up- and downward by means of the piezo displacement unit ŽFig. 2a.. As soon as the substrate interacts with the probe, the cantilever is deflected from its normal horizontal position. The tip jumps into contact with the substrate surface ŽFig. 2b.. The piezo unit continues its upward movement until a pre-set value of the z-coordinate Ž z scan size. is reached ŽFig. 2c.. Then, it reverses its direction of movement. As soon as the restoring force F of the cantilever equals the interaction force of the cantilever, the tip separates from the surface of the substrate ŽFig. 2d–e.. By means of the reflection angle of a laser beam reflected at the surface of the cantilever, the extent z of the cantilever deflection can be measured. According to the Hooke law, F s ykz Ž 1. the restoring force of the cantilever and the interaction force F, respectively, are given by the cantilever deflection z at the moment of separation multiplied by its spring constant k. The force curve is described in detail in Ref. w10x. To quantify the adhesion forces acting between lactose particles, the forces acting between a modified cantilever and the surface of a lactose tablet were recorded.
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Fig. 2. Force–distance-plot of the atomic force microscope. Ža. Non-contact range; Žb. jump-into-contact between probe and substrate; Žc. maximum position of substrate; Žd. maximum interaction force; Že. abrupt separation probe–substrate.
The accuracy of the force measurements depends upon the knowledge of the spring constant of the cantilever that probes these forces. There are several methods for its determination w11–13x. One is to calibrate the spring constant by applying the principle of thermal fluctuations w14x. This method, which was used in this work, is described in detail in Ref. w15x. 2.2.1.2. Scans of surface topography. To acquire topographic images of a sample, the substrate is moved upwards by the piezo displacement unit until the tip of the cantilever jumps into contact with the sample surface. Then, the piezo displacement unit adjusts its vertical position Ž z-value. in such a way that the force acting on the cantilever corresponds to a pre-set load. This z-value is recorded as a function of its horizontal position. With the tip of the cantilever remaining in contact with the sample surface, the piezo displacement unit moves the sample into the next horizontal position. The load acting on the cantilever is adjusted to the pre-set load by adapting the vertical position. Again, the corresponding z-value is recorded as a function of its horizontal position. In this way, a defined surface area is scanned. The step-widths in the x- and y-directions have to be defined before each scan. The surface topography is then given by the set of z-values over the scanned x, y-planes. 2.2.1.3. Force Õolume scans. A force volume scan consists of a series of adhesion force determinations at the various points on the substrate surface. In general, the topography of the surface has been scanned before. As a result, a complete force curve is stored in addition to the x-, y-, z-coordinates of each point of a substrate surface range. A force volume scan shows the distribution of adhesion over a given surface area as well as the three-dimensional structure of this area. By interpreting the force curve
qualitatively as well as quantitatively, characteristics of certain surface structures can be described. Therefore, force volume scans offer the opportunity to correlate the measured adhesion forces with the surface structure. 2.2.1.4. Surface characterization. To characterize the surface of lactose particles as well as of lactose tablets, scans of areas of 9 mm2 were made by means of the NanoScope Ee in contact mode. From these scans the z range, which gives the difference between the highest and the lowest point of the scanned area, is determined. Furthermore, the standard deviations sŽ z . of all z values were compared. The sample with the smoothest surface was chosen for the force measurements. 2.2.1.5. Quantification of the topographic structure. To quantify the surface structure of the substrate, a roughness analysis was carried out. Any surface has some distribution of heights. According to Kiely and Bonnell w7x, this is best described by the variational root-mean-square roughness sŽ z .. However, when imaged locally, only a fraction of the surface height distribution appears in the image height distribution. In consequence, sŽ z . increases with the area over which it is measured. It becomes scale-independent when the measurement area is greater than the largest characteristic area A) of the surface. Analogous to A) , there is a minimum characteristic area at which sŽ z . again becomes scale-independent at small scales which occurs at fractions of the tip radius. Between these two extremes, the area dependence of sŽ z . is a function of the distribution of feature heights and widths. This distribution is described by the slope of the variational sŽ z .. Slope changes accordingly identify feature dimensions. As a first step in the quantification of the surface structure of a substrate, the overall size of the image was defined. Then this area was subdivided into segments of
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Fig. 3. Influence of the shape of the probe on the resulting surface scan. ŽThe thick line shows the probe scanning a very steep part of the substrate. The broken line represents the result of the scan, showing one half of the mirrowed shape of the probe..
The blind algorithm of Villarrubia w8x searches the scan for the surface structure with the steepest slope which is then used as an approach to the real shape of the probe. To get a reliable estimation of the probe shape, it is necessary to analyze a big number of suitable surface scans showing sharp asperities. A calibration standard with a surface of low-, 180 nm, ŽApitsB . and high areas, which are separated vertically by 5 mm ŽDigital Instruments, Santa Barbara, USA. and a lactose tablet Žpressure: 0.9 GPa., was used for the estimation of the probe shape. In order to find surface areas suited for the tip estimation by means of the Villarrubia algorithm, both substrates were first scanned with a normal siliciumnitride cantilever before characterizing the modified cantilever.
3. Results different edge lengths over which sŽ z . was measured to identify the smallest and largest feature dimensions of the surface. 2.2.1.6. Estimation of the tip apex radius and of the shape of the probe. An extensive interpretation of the measured adhesion is only possible by determining the contact area between the probe and the substrate. The portion of the contact area arising from the lactose tablet can be characterized by analyzing a surface scan. But how about the shape and the surface morphology of the adhering particle of lactose acting as probe? The analysis of surface scans offers an opportunity to gain some information on the structure of the probe. It is based on the fact that by scanning the surface with a given cantilever, no asperity sharper than the probe itself can be recorded. Instead, sharper asperities result in surface structures corresponding to the turned shape of the probe ŽFig. 3.. This means that a scan of a surface with isolated, sharp asperities will only represent reality when the scanning probe is sharper than the sharpest surface asperity. Otherwise, this asperity will show the mirrowed shape of the probe. This is due to the fact that in case of a surface structure sharper than the probe, their roles are changed. The surface asperity acts as a probe and images the shape of the real probe. Therefore, by scanning a surface that shows sharp asperities, the sharpest peaks of this scan will represent the structure of the probe of the cantilever.
3.1. Characteristics of lactose surfaces In order to simplify the interpretation of the measured interaction forces, areas on lactose surfaces being as smooth as possible have been chosen. For this purpose, the surface roughness of individual lactose particles and of lactose tablets manufactured with different pressures was analyzed with the AFM. The results in Table 1 demonstrate clearly that lactose particles possess very structured surfaces with remarkable differences in height. In contrast to lactose particles, the surface structure of the lactose tablets is very regular ŽFig. 4. and shows no features like jumps, trenches or adhering small particles. As expected, all lactose tablets have surfaces smoother than the original substrate. The tablet pressed at 0.9 GPa exhibits the surface with the lowest differences in height. Within an area of 9 mm2 , the standard deviation of all z-values is 2.7 nm. 3.2. Quantification of the surface structure For the determination of the minimum and the maximum roughness on the surface of the lactose tablet Ž0.9 GPa., scans were taken at typical sites of the substrate surface. Three representative areas were chosen: the first one being relatively smooth, the second one regularly rough and the third one, fissured. The scan sizes covered 1,
Table 1 Surface characteristics of lactose samples measured by the AFM Ž3 = 3 mm. Surface characteristics
Particle of lactose
Tablet of lactose Ž0.4 GPa.
Tablet of lactose Ž0.6 GPa.
Tablet of lactose Ž0.9 GPa.
z range wnmxa sŽz. wnmxa
1073 154.8
53.5 5.2
45.5 5.3
27.1 2.7
a
All results are averages of three scans.
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flattening, were of first order w7,16x. In addition, there exist scan artifacts which have to be eliminated manually. 3.3. Estimation of the shape of the probe
Fig. 4. AFM scan of the surface of a lactose tablet Žpressure: 0.9 GPa..
25, 100, 2500 and 10 000 mm2 . For the analysis, the scans were divided in segments of equal size. The roughness of each segment was determined by calculating the standard deviation of the z values. Fig. 5 shows the average standard deviation sŽ z . in dependence of the size of the segments. The minimum and the maximum surface roughness of the lactose tablet is given by the plateaus. In scans of surface areas smaller than 1 mm2 , a roughness of 8 nm can be measured, whereas over scan sizes of more than 2500 mm2 , height differences of 80 nm can be identified. Reliable conclusions from force measurements can only be drawn if the scan size corresponds either to the minimum or the maximum roughness of the lactose tablet. With regard to the roughness analysis of surface scans, it is important to consider the sources of error which have to be eliminated in post-acquisition modification procedures. Often, there is a tilt of the surface due to a slanting attachment of the substrate. To eliminate such a tilt carefully, in a first step, a plane in the x direction has to be removed. It is determined by a last square fit to the average to all rows of data Žplane-fitting.. The same is done in the y direction. Eventually, each line of the image is raised or lowered until the mean average of each line was at the same height Žflattening.. Plane-fitting, as well as
Fig. 5. Surface roughness sŽ z . of the lactose tablet Ž0.9 GPa. in dependence of the segment size; plateaus are found over segments of 0.5–1 mm and 50–100 mm edge length.
The tip estimation, according to Villarrubia w8x, was used to estimate the contact area of the adhering particle of the modified cantilever as well as the tip apex of the normal cantilever. In order to find the suitable surface structure for this method, the calibration standard as well as the surface of a lactose tablet were first scanned with a normal siliciumnitride cantilever ŽDigital Instruments. with nominal tip radius of 10–22 nm Ždistance from the apex: 10 nm.. The evaluation of several surface scans of the calibration standard results in estimated tip radii of 116–154 nm. This is in clear contrast to reality. Therefore, the surface structure of the calibration standard is not suited for the algorithm-based tip estimation. As requested by the theory w8x, this surface possesses areas with steep elevations, however, their one-sidedness falsifies the results of the algorithm. The evaluation of 19 surface scans of the lactose tablet Žpressure: 0.9 GPa. resulted in tip radii being in agreement with their real structure. For the normal, non-modified, cantilever, a tip radius of 25.1 nm at a distance of 10 nm from the apex was estimated by means of the algorithm. This finding, being in agreement with the reality, proves the suitability of the surface of the lactose tablet for the tip qualification using the Villarrubia algorithm. On the basis of 24 scans made with a modified cantilever for the lactose particle, an apparent tip radius of 15.3 nm at a distance of 10 nm from the apex was determined. This means that only an asperity of these dimensions on the surface of the lactose particle interacted with the surface of the lactose tablet. Surprisingly, this asperity is sharper than the tip of the normal cantilever.
Fig. 6. Calculated radius of the tip apex of the normal and the modified cantilever.
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Fig. 8. Surface scan Ž1 mm2 . of the lactose tablet Ž0.9 GPa.. Fig. 7. Zoomed presentation of the calculated tip apexes.
With respect to the tip qualification, it becomes obvious that a large number of scans has to be analyzed. The evaluation of only about 30% of all scans resulted in tip radii being smaller than 30 nm. The shapes of the normal and the modified cantilever, estimated by means of the Villarrubia algorithm, are shown in Fig. 6 and a zoomed diagram in Fig. 7. The fact that the lactose particle affixed on the cantilever interacts with the tablet surface only via the asperity means that the contact area of the adhering lactose particle with the substrate is as small as with a good siliciumnitride cantilever. Therefore, it cannot be compared with the contact area of an ideal sphere of the same volume as the particle.
Fig. 9. Surface scan Ž2500 mm2 . of the lactose tablet Ž0.9 GPa..
3.4. Force Õolume scans After a careful post-acquisition analysis of the data, force volume scans as a combination of surface scan and force measurement give information on the surface topography of the substrate as well as on a direct relation between adhesion and surface structure. In dependence of the scan size in Section 3.2, it was possible to identify two different lengths of 8 and 80 nm, respectively, characterizing surface asperities Žsee Section 3.2.. Therefore, force volume scans have been performed with the minimum Ž1 mm2 . and the maximum Ž2500 mm2 . scan size in order to allow the probe to interact with asperities of both characteristic lengths. In all cases, a
Fig. 10. Relative frequency of the measured adhesion Žscan area: 1 mm2 ..
Table 2 Evaluation of the force volume scans made with the modified cantilever Scan size wmm2 x sŽz.-range wnmx Adhesion wnNx Standard deviation wnNx Min. adhesion wnNx Max. adhesion wnNx
1 7.7 4.3 2.05 0.42 9.89
2500 53.7 5.0 3.06 0.53 11.23
Fig. 11. Relative frequency of the adhesion determined over scan areas of 2500 mm2 .
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Fig. 12. Force curve measured on the top of an asperity.
modified cantilever Žspring constant: 0.228 Nrm. was used. In the post-acquisition analysis, plane-fitting and flattening were again of first order. In the following, only one force volume scan is discussed in detail. The results of the evaluation of the data are summarized in Table 2. The surface over the small scan area ŽFig. 8. is characterized by an average roughness of 7.7 nm. The corresponding length over the larger area ŽFig. 9. is given by 53.7 nm. The average adhesion between the lactose particle and the tablet surface determined over scan areas of both sizes is almost the same, 4.3 and 5.0 nN, respectively. The difference is statistically not significant. Each scan comprised 1024 force curves. The distribution of the measured forces was evaluated with a force program ŽS. Vinzelberg, Digital Instruments, Mannheim, Germany.. The results are shown in Figs. 10 and 11. Over the small scan areas, forces ranging from 0.4 to 12 nN were determined. Over the larger scan areas maximum forces of up to 14 nN were observed. Generally, the interaction forces measured over a representative surface area are expected to follow a normal distribution. However, the tests on a Gaussian distribution reject this assumption. In force volume scans, the measured force curves can be related directly to the structure of the interacting surfaces. Therefore, conclusions about the extent of the adhesion in dependence of the surface structure can be made. The force curves measured on the top of the asperities are
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characterized by a sharp rupture of the interaction contact ŽFig. 12.. The adhesion between the particle and curved surface structures or valleys, however, is characterized by a step-wise separation ŽFig. 13.. In addition, the interaction forces measured over these structures are bigger than those observed on the top of the asperities. A closer look at the measured force curves reveals some irregularities. First of all, there is the wavy ascent in the non-contact area. This is caused by interferences in the optical detection system. They have no influence on the force measurement itself. The slope of the force curve right behind the jumpinto-contact region ŽFig. 2b. is smaller than expected from theory. The corresponding smaller vertical deflection of the cantilever can be caused by elastic or plastic deformations of the probe or of the substrate. Since this peculiarity is observed even after repeated measurements at the same point it can be assumed that the deformation is elastic. When measured in surface valleys the force curves ŽFig. 13. show another peculiarity. The shape before the rupture of contact indicates not a sharp but a stepwise separation of the particle from the tablet surface. This can be explained by the assumption of several contact points between probe and substrate which are separated one by one. 3.5. Comparison with other methods The interparticle forces as determined with an AFM were compared with the corresponding values obtained from measurements performed with a Jenike shear cell and the tensile strength tester w17,18x. For all measurements, lactose GranuLac 200 was used as substrate ŽTable 3.. It becomes obvious that the interaction energies measured by the different methods cannot be compared directly. An AFM allows the determination of the interaction energy in a single contact point. With the other two methods, however, only averages from multiple contacts can be measured. It seems that the average adhesion determined by these methods increases with the number of contacts between the individual particles and the overall number of particles involved in the separation step. This number is highest in the case of the Jenike shear cell. The results highlight the difficulties arising when forces determined from a bulk of powder are transformed into forces acting between individual particles as this is achieved only under the assumption of ideal material properties w2x.
Table 3 Comparison of the results obtained with different methods
Fig. 13. Force curve measured in a valley.
Apparatus
Porosity w%x
Average adhesion per particle wnNx
Shear cell Tensile strength tester Atomic force microscope
58 58 –
85 21 5
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4. Discussion Our results show that AFM is suited for the determination of surface forces acting between lactose substrates. We especially studied the interaction between an individual lactose particle and the surface of a lactose tablet made at a pressure of 0.9 GPa. AFM scans of the tablet surface allowed a detailed qualitative and quantitative description of the substrate surface. By analyzing the roughness of surface segments of different sizes, a minimum and a maximum roughness of the lactose tablet could be found. A characteristic length of 8 nm is observed for the smallest roughness at scan sizes smaller than 1 mm2 . The corresponding value for the largest roughness is given by 54 nm. It can be measured at scan sizes larger than 2500 mm2 . For an analysis of a surface being representative for the tablet surface, scans of these two sizes have to be performed. The contact area between probe and substrate is another important factor influencing the size of the measured forces. Based on the analysis of a large number of surface scans, the size as well as the shape of the contacting asperity of the lactose particle affixed on the cantilever was approximated. The regular surface of a calibration standard proved to be unsuited for a tip calibration. Scans of the lactose tablet, however, gave good results. It was shown that the contact area of the adhering lactose particle was almost of the same size as the one of a commercial cantilever. Force volume scans over representative surface segments allowed a direct relation between surface structures and the shape of force curves. Forces measured on the top of the asperities are smaller than those determined in valleys. A sharp interruption of the corresponding contact was observed in the case of the asperity. In the case of the valleys, however, a stepwise interruption of obviously multiple contacts was observed. Further peculiarities in the shape of the force curves could be related to the material properties of lactose. It was shown that most probably lactose undergoes elastic deformations during the force measurements. The measured interparticle forces between the probe and the lactose substrate ranged from 0.4 to 14 nN. Depending on the characteristic roughness of the surface structure, average adhesions of 4.34 and 4.98 nN, respectively, were determined. A comparison of the adhesion forces determined by different methods, e.g., the AFM, the Jenike shear cell and the tensile strength tester, showed the difficulties arising when calculating the properties of individual particles from bulk properties.
Acknowledgements The authors wish to thank Meggle ŽWasserburg, Germany. for the donation of the substances.
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