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Transient Surface Roughening of Thin Films of Phase Separating Polymer Mixtures† Klaus D. Jandt,*,‡ Jakob Heier,‡ Frank S. Bates,§ and Edward J. Kramer*,‡ Department of Materials Science and Engineering and the Materials Science Center, Cornell University, Ithaca, New York 14853-1501, Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455 Received September 11, 1995X The surface morphology of thin molten films of phase separating mixtures of poly(ethylenepropylene) (PEP) and perdeuterated poly(ethylenepropylene) (dPEP) of the critical composition were investigated using scanning force microscopy. Volume fraction versus depth profiles were also obtained using timeof-flight forward recoil spectrometry (TOF-FRES). The free surface of a film with a nominal thickness of about d ) 200 nm is initially smooth but develops a regular roughness pattern, with a wavelength about 500 nm and an amplitude about 2.5 nm, after a certain annealing time, which corresponds to the transition from a four-layer (dPEP/PEP/dPEP/PEP) to a two-layer (dPEP/PEP) phase-separated domain structure in the direction normal to the film thickness. At much longer times the two-layer films become smooth again. We attribute these fine surface patterns to transient pressure differences accompanying mass transport by hydrodynamic flow, where this transport occurs though perforations in the PEP-rich layered domain just below the dPEP-rich surface layer. This flow is driven by the pressure beneath the highly curved lateral interfaces of the intermediate layers. In keeping with this hypothesis, thicker films (d > 280 nm), which do not develop breaks in the PEP-rich layered domain and for which diffusional transport is necessary for coarsening of the layer structure to occur, do not show this transient roughening.
Introduction Polymer mixtures (blends) are of special interest for both technological applications and fundamental investigations of phase transitions.1,2 The technological interest is focused on the production of polymer blends with specific properties and thus on controlling the phase composition and morphology which develops as a result of phase separation. This technological interest motivates many fundamental studies of morphological control of phase separating polymer mixtures. In addition polymer mixtures provide excellent model systems for studying the fundamentals of phase separation by spinodal decomposition (SD). Unlike phase separation by the more familiar nucleation and growth, in phase separation by SD even small amplitude composition fluctuations of long enough wavelength lead to a decrease in free energy. The amplitude of these composition fluctuations initially grows exponentially with time as a result of up-gradient diffusion (the diffusion coefficient is negative). In the bulk, these fluctuations can be characterized as composition waves with randomly oriented wave vector whose magnitude q (q ) 2π/λ, where λ is the spatial period of the wave) is close to that, qm, of the fastest growing wave. At longer times however the phase separating structure coarsens and the magnitude of the dominant wave vector qm decreases. The SD of bulk binary polymer mixtures has been extensively investigated, both theoretically and experimentally.3-8 Mixtures of isotopically labeled polymers, e.g., a protio-polymer and its deuterio-counterpart, * To whom correspondence should be addressed. e-mail: jandt@ msc.cornell.edu,
[email protected]. † MSC Report No. 7917. ‡ Cornell University. § University of Minnesota. X Abstract published in Advance ACS Abstracts, July 1, 1996. (1) Hashimoto, T. In Structure of Polymer Blends. Materials Science and Technology; Thomas, E. L., Ed.; VCH: Weinheim, Germany, 1993; Vol 12, Chapter 6, p 251. (2) Gunton, J. D.; San Miguel, M.; Sahini P. S. In Phase Transitions and Critical Phenomena; Domb, C., Lebowitz, J. L., Eds.; Academic Press: London, 1983; Vol. 8. (3) de Gennes, P. G. Rev. Mod. Phys. 1985, 57, 827.
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have proved to be very useful as model systems for these experiments.4,5 These may be investigated by both light scattering and small angle neutron scattering experiments and such scattering experiments demonstrate the isotropic nature of the domain structure at all stages. In thin films of such polymer mixtures the situation is qualitatively different.9 The composition of such films can be profiled in a direction (z) normal to the film plane using methods such as forward recoil spectrometry10 or its time of flight version,11 secondary ion mass spectrometry,12 or neutron reflectometry.13 These methods have shown that in the one-phase region the mixture-vacuum interface and the mixture-substrate interface are typically enriched in one of the components. In all cases where the chains are of approximately equal length, the deuterio component was found to be enriched near the mixturevacuum interface.14 When the polymer mixture is quenched into the unstable two-phase region (inside the spinodals), the presence of the two interfaces (and their preference for one of the components) leads to a strongly varying composition profile as a function of the zcoordinate perpendicular to the substrate surface (surface directed spinodal decomposition).15-17 In thick films the laterally-averaged volume fraction of the deuterio com(4) Bates, F. S.; Wiltzius, P.; Heffner, W. R. Phys. Rev. Lett. 1988, 60, 1538. (5) Bates, F. S.; Wiltzius, P. J. Chem. Phys. 1990, 91, 3258. (6) de Gennes, P. G. J. Chem. Phys. 1980, 72, 4756. (7) Pincus, P. J. Chem. Phys. 1981, 75, 1986. (8) Binder, K. J. Chem. Phys. 1983, 79, 6387. (9) Krausch, G. Mater. Sci. Eng. Rep. 1995, R14, 1. (10) Jones, R. A. L.; Kramer, E. J.; Rafailovich, M. H.; Sokolov, J.; Schwarz, S. A. Phys. Rev. Lett. 1989, 62, 280. (11) Sokolov, J.; Rafailovich, M. H.; Jones, R. A. L.; Kramer, E. J. Appl. Phys. Lett. 1989, 54, 590. (12) Zhao, X.; Zhao, W.; Sokolov, J.; Rafailovich, M. H.; Schwarz, S. A.; Wilkens, B. J.; Jones, R. A. L.; Kramer, E. J. Macromolecules 1991, 24, 5991. (13) Jones, R. A. L.; Norton, L. J.; Kramer, E. J.; Composto, R. J.; Stein, R. S.; Russell, T. P.; Mansour, A.; Karim, A.; Felcher, G. P.; Rafailovich, M. H.; Sokolov, J.; Zhao, X.; Schwarz, S. A. Europhys. Lett. 1990, 12, 41. (14) Kumar, S. K.; Russell, T. P. Macromolecules 1991, 24, 3816. (15) Ball, R. C.; Essery, R. L. H. J. Phys. Condens. Matter 1990, 2, 10303.
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ponent could be interpreted as a damped spinodal wave originating from the mixture-vacuum interface.16 The earliest experiments were done using a binary poly(ethylene propylene) and perdeuterated poly(ethylene propylene) (PEP-dPEP) mixture that has an upper critical solution temperature (UCST), but experiments on mixtures of the chemically different polymers, deuterated polystyrene (dPS) and partially brominated polystyrene (UCST)18 and dPS and tetramethylbisphenolApolycarbonate (lower critical solution temperature),19 show that surface-directed spinodal decomposition is a general phenomenon. Using time-of-flight forward recoil spectrometry (TOFFRES) the composition and the phase separation behavior of thin films of dPEP-PEP mixtures on silicon substrates from which the oxide had been stripped were measured.20-22 These investigations focused on the study of the time,20 thickness,21 and composition dependence22 of the spinodal decomposition of the mixture. The laterally averaged compositions of dPEP-PEP samples can be modeled by two distinct spinodal waves, one originating from the surface, producing a dPEP-rich surface layer and a PEP-rich layer immediately below it, and one generated from the silicon, producing a PEP-rich layer at the silicon interface and a dPEP-rich layer immediately above it. Layers with smaller enrichments form below (above) the pair of layers, i.e., in the sequence surface/ dPEP-rich/PEP-rich/partially-dPEP-rich... (...partiallyPEP-rich/dPEP-rich/PEP-rich/silicon). Cell-dynamical simulations21 suggest that these partially enriched layers consist of, for example, dPEP-rich domains that are not continuous but contain small perforations consisting of PEP-rich phase. Further than three layers from either the surface or the interface the “layers” become an equiaxed domain structure of dPEP-rich and PEP-rich domains whose laterally averaged composition matches that of the film as a whole; the structure of this equiaxed domain structure is thought to be similar to that of the bulk. As the film becomes thinner than about six layer thicknesses, interference between the two spinodal waves is observed, with layers in the center of the film being either driven toward larger departures from the average composition or toward smaller departures depending on whether the interference is constructive or destructive. In the thin dPEP/PEP films on stripped silicon these layers coarsen with time. For thick films of the critical composition the thickness of the dPEP-rich outer layer increased as t1/3, where t was the annealing time of the sample.20 This result is exactly that expected for growth of the surface dPEP-rich layer by diffusion of dPEP though a continuous PEP-rich underlayer and is in excellent agreement with predictions based on cell dynamic simulations21-23 and scaling arguments24 based on diffusional transport. However, if the composition of the blend was richer in dPEP than the critical composition (but still within the spinodal) the thickness of the dPEP outer layer was found to grow not as t1/3 but as t1, significantly faster.22 The faster growth was attributed to the transport of dPEP to the outer layer by hydrody(16) Jones, R. A. L.; Norton, L. J.; Kramer, E. J.; Bates, F. S.; Wiltzius, P. Phys. Rev. Lett. 1991, 66, 1326. (17) Puri, S.; Binder, K. Phys. Rev. A 1992, 46, R4487. (18) Bruder, F.; Brenn, R. Phys. Rev. Lett. 1992, 69, 624. (19) Kim, E.; Krausch, G.; Kramer, E. J.; Osby, J. O. Macromolecules 1994, 27, 5927. (20) Krausch, G.; Dai, C.-A.; Kramer, E. J.; Bates, F. S. Phys. Rev. Lett. 1993, 22, 3669. (21) Krausch, G.; Dai, C.-A.; Kramer, E. J.; Marko, J. F.; Bates, F. S. Macromolecules 1993, 26, 5566. (22) Krausch, G.; Kramer, E. J.; Bates, F. S.; Marko, J. F.; Brown, G.; Chakrabarti, A. Macromolecules 1994, 27, 6768. (23) Brown, G.; Chakrabarti, A. Phys. Rev. A 1992, 46, 4829. (24) Marko, J. F. Phys. Rev. E 1993, 48, 2861.
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namic flow through perforations in the PEP-rich domains in the underlying PEP-rich layer, which is less PEP-rich than is the case for films of the critical composition. Eventually in all cases a bilayer morphology is achieved in thin enough films consisting of a dPEP-rich phase layer at the film-vacuum interface and a PEP-rich phase layer at the substrate.25 For films of the critical composition thinner than about 280 nm, however, the coarsening of the phase structure was found to be severely altered.21 For these samples (annealed for 5.5 h at 321 K) the characteristic wave vector in the bulk was estimated to be qm ) 3.6 × 10-2 nm-1 corresponding to a spinodal wavelength λm(t)0) ) 174 nm.21 Since the substrate surface is covered by a PEPrich layer in contrast to the film-vacuum interface, a minimal film thickness of dmin ) 1.5λm ) 261 nm is required in order to realize a composition wave with qm,bulk. For thinner films the system may be forced to decompose with a larger characteristic wave vector determined by the thickness of film. Interesting effects are expected for the phase structures of these ultrathin film systems. In the present study we have investigated the surface structures of thin PEP-dPEP films with scanning force microscopy (SFM). Distinct lateral surface patterns of these samples were found. These measurements are complemented by corresponding TOF-FRES measurements of the (laterally averaged) composition versus depth profiles of the films. Experimental Section Poly(ethylene propylene) (PEP) and perdeuterated poly(ethylene propylene) (dPEP) with nearly identical polymerization indices (NH ) 2360, ND ) 2140)26 were used to prepare a symmetric binary mixture. As a result of the difference in C-H and C-D bond length and polarizability,27,28 the interaction parameter χ of the PEP-dPEP mixture is positive, leading to an upper critical solution temperature Tc ) 365 K well above the glass transition temperature of PEP, 217 K. To make thin films the PEP/dPEP was dissolved in toluene (2.35% w/w). Subsequently PEP/dPEP films of nearly critical composition (Φ ) Φc ≈ 0.5) were produced by spin casting the solution on Si wafers. Prior to the spin casting process the Si wafers were exposed to aqueous HF.29 This procedure (stripping) removes the native SiO2 layers from the wafers and results in a hydrogen-terminated silicon surface. The film thicknesses were measured with ellipsometry and the samples were annealed under high vacuum conditions at the required temperatures. Time-of-flight forward recoil spectrometry (TOF-FRES)11 was used to measure the volume fraction versus depth profiles of the PEP and the dPEP components of the mixture perpendicular to the substrate surface. The resolution of TOF-FRES along the z-coordinate of the sample is about 25 nm. (The lateral resolution of this method is limited to 3 mm by the size of the beam spot. The ion beam technique averages laterally over the entire size of the beam spot.) The ion beam also cross-links the polymer mixture resulting in a structure, after a typical fluence of 4 × 1015 He2+/cm2 (∼40 µC charge collected on the sample), that is effectively “frozen”, both in composition vs depth and in surface morphology. The subsequent scanning force microscopy was performed on the cross-linked samples. Cross-linking the film makes it possible to store the film at room temperature without the structure changing and does not introduce any artifacts.30 A Nanoscope III SFM31 was used for the scanning force microscopy. Experiments using the constant force mode of (25) Heier, J.; Krausch, G.; Kramer, E. J.; Bates F. S. In preparation. (26) Bates, F. S.; Rosedale, J. H.; Bair, H. E.; Russell, T. P. Macromolecules 1988, 21, 86. (27) Bates, F. S.; Wignall, G. D.; Koehler, W. C. Phys. Rev. Lett. 1985, 55, 2425. (28) Gehlsen, M. D.; Rosedale, J. H.; Bates, F. S.; Wignall, G. D.; Hansen, L.; Almdal, K. Phys. Rev. Lett. 1992, 68, 2452. (29) Hagashi, G. S.; Chabal, Y. J.; Trucks, G. W.; Raghavachri, K. Appl. Phys. Lett. 1990, 56, 656. (30) Jandt, K. D.; Heier, J.; Kramer, E. J. Unpublished results. (31) Digital Instruments, Santa Barbara, CA.
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Figure 1. (a) SFM image of 200 nm thick dPEP/PEP film annealed for 2.2 h at 322 K. The surface of this sample is smooth. Randomly distributed small spots (bright) of a few nanometers in height are visible. (b) TOF-FRES spectrum of the sample shown in Figure 1a. Shown is the distribution of dPEP volume fraction along the z-coordinate (film normal). The depths of 0 and 200 nm represent the free film surface (vacuum surface) and the film-substrate interface. Two dPEP-rich layers can be seen: one near the free surface and one about 110 nm beneath the free surface. Two PEP-rich layers can also be seen; one about 55 nm beneath the free surface and one adjacent to the silicon substrate (c) SFM image of 200 nm thick dPEP/PEP film annealed for 7.5 h at 322 K. The surface of this sample shows a distinct surface pattern composed of interconnected peaks and valleys. The height difference between the peaks (bright) and the valleys (dark) is 5 nm. The surface peak structure can be interpreted as reflecting a twodimensional pattern of perforations in the PEP-rich second layer. (d) TOF-FRES spectrum of the sample shown in Figure 1c. Note the extraordinarily wide interface between the dPEP-rich layer at the surface and the PEP-rich layer adjacent to the substrate. operation, where the cantilever Si3N4 tip is in permanent contact with the sample surface, were carried out under ambient conditions. The cantilevers used were supplied by the microscope manufacturer, and had a nominal force constant of 0.06 N m-1. The forces applied with the SFM tip were e10-9 N. The imaging force was adjusted to be just above the pull-off point of the cantilever as soon as possible after the first contact in order to reduce the applied force to the minimum possible for stable imaging. From time to time we checked that the set point was stable and still at the same location of the force curve. No filtering was applied to the feedback signal or the images. All structures shown in the SFM images were reproducible independent of scanning frequency, scanning direction, and x-y range.
Results and Discussion Parts a and c of Figure 1 show SFM images of 200 nm thick dPEP/PEP films annealed at 322 K for 2.2 h and 7.5 h, respectively. Parts b and d of Figure 1 show the corresponding depth profiles of ΦdPEP, the volume fraction
of dPEP obtained from the TOF-FRES spectra of the samples. The surface structure of the sample shown in Figure 1a is more or less homogeneous and smooth with a peak-to-valley roughness of 2 ( 1 nm. The corresponding TOF-FRES spectrum (Figure 1b) shows that there are two dPEP-rich layers, one near the mixture-vacuum interface (free surface) and one starting about 110 nm beneath that interface. The volume fraction of the dPEPrich layer near the free surface of the film is approximately 0.65. From the combined SFM and TOF-FRES data of this sample, we conclude that the dPEP-rich phase has formed a more or less smooth and continuous layer at the free surface of the sample. The deep layer at 110 nm has a lower average volume fraction and may not be continuous (see the cell dynamical simulations in ref 21). A different situation obtains after the sample is annealed a longer time (7.5 h) as shown in parts c and d of Figure 1. The surface of the sample shown in Figure 1c exhibits
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Figure 2. (a) SFM image of the sample shown in Figure 1c at a higher magnification revealing the fine structure of the peaks and valleys. (b) Section profile analysis of a peak region. The dark arrows indicate the edges of a peak and the bright arrow indicates the vertex point (highest point of the peak). The thickness of this typical peak was measured to be 390 nm. The vertical distance from the valley to the peak was measured to be 3.9 nm. (c) The larger SFM scan area of the surface shows the random lateral distribution of the peaks. This is confirmed by the homogeneous ring in the Fourier transformation of the sample roughness, inserted in the upper right corner of Figure 2c.
a highly structured lateral pattern which may be characterized as an interconnecting set of meandering “peaks” and “valleys”. The lateral average peak to peak distance was measured to be about 500 ( 100 nm. The peak to valley height differences are remarkably uniform at 5 ( 1 nm. This height difference is much smaller than the spinodal wavelength λm of dPEP/PEP even at zero time,32 and thus it cannot be due to formation of “islands” (or “holes”) corresponding to extra (fewer) dPEP-rich or PEPrich layers. SFM images of the surface pattern at high and low magnifications, a corresponding Fourier transformation of the pattern and a typical cross-section profile of the surface are shown in Figure 2. The corresponding TOFFRES spectrum (Figure 1d) shows only one dPEP-rich layer near the free surface of the film and one PEP-rich layer near the substrate, but the laterally averaged depth profile shows the interface between them to be very broad. From the high volume fraction (0.85) of the dPEP-rich phase at the free surface, one would expect an even more homogeneous and smooth structure of the outermost layer than of the sample annealed for only a short time; the corresponding SFM micrograph however shows the opposite. The observed height differences may be explained in the following way: For earlier times an oscillatory (32) Kedrowski, C.; Bates, F. S.; Wiltzius, P. Macromolecules 1993, 26, 3448.
composition profile is observed leading to a lamellar structure shown schematically in Figure 3a. A dPEPrich phase wetting the film-vacuum interface is followed by three more layers with a PEP-rich phase wetting the silicon-substrate. We assume that the second and third layer are not continuous, the second layer consisting of mainly PEP-rich phase with perforations of dPEP-rich phase forming channels connecting the top and third layer. The third layer is assumed to consist of mainly dPEP-rich phase with corresponding perforations of PEP-rich phase. This picture agrees with the TOF-FRES depth profile, which shows that the PEP content of the second layer (and the dPEP content of the third layer) is less than that in the corresponding layer (assumed to be continuous) in thicker films.21 The evolution of this four-layer structure into the final equilibrium bilayer could occur, in principle, by two mechanisms, by diffusion or by hydrodynamic flow. Diffusion would be the only possible mechanism if the second and third layers were continuous. Under these circumstances, which seem to prevail in the thicker films of critical composition judging from the observed t1/3 dependence of the dPEP layer growth, we would not expect a roughening of the surface and we do not observe one. On the other hand, perforations in the PEP-rich second layer would allow the system to evolve by hydrodynamic flow, which is a “faster” mechanism, with the dPEP surface layer thickness growing as t1. The strong curvature of
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Figure 3. Schematic sketch showing the formation of the observed surface patterns in the dPEP-PEP film. Shown are cross sections of the film. The total film thickness (200 nm) as well as the peaks and valleys at its surface are drawn to scale. The horizontal scale corresponds to 1400 nm. (a) A four-layer structure is established after 2.2 h of annealing. A dPEP-rich phase completely wets the vacuum interface; a PEP-rich phase wets the silicon substrate. Layers two and three have perforations in the PEP-rich and dPEP-rich layers, respectively. The strong curvature of the boundary between the phases within each layer leads to a strong driving force for hydrodynamic flow. (b) Nonequilibrium bilayer structure established after 7.5 h of annealing. The surface is slightly elevated over the positions of the perforations in the PEP-rich second layer (see Figure 2a) though which dPEP-rich polymer from the third layer was transported to the surface layer by hydrodynamic flow.
the phase boundaries between the dPEP-rich and PEPrich phases inside the second and third layers drives the system toward another intermediate structure,33 in which a bilayer is established but for which the z-position of the interface varies with the coordinates x and y in the plane of the film as shown in Figure 3b. This structure would account for the enormous apparent width of the “interface” seen in the TOF-FRES depth profile in Figure 1d. The surface pattern of peaks and valleys, drawn to scale on Figure 3b, then can be understood very simply. It results from pressure exerted on the surface by the flowing dPEP phase; i.e., the peaks are expected to map onto the perforations in the PEP-rich layer. As soon as the phase boundary flattens out, the surface structure flattens out as well. This result is indeed what we observe at longer times. Investigations of the surface structure of thicker (d > 240 nm) dPEP-PEP films are in progress and will be published elsewhere.33 However, it should be noted here that for the thicker samples no 2-D surface roughening patterns are found. The transient 2-D surface roughening patterns in the 200 nm thick films probably derive ultimately from the thinness of the PEP-rich second layer and dPEP-rich third layers in such films. These layers are thin due to the fact that the wavelength of the surfacedirected spinodal decomposition waves is forced in this case to be less than the natural spinodal wavelength in order that there be a dPEP-rich layer at the surface and a PEP-rich layer against the silicon substrate. The thinness of these layers leads to their perforation and the possibility for growth of the dPEP-rich surface layer by hydrodynamic flow, rather than by diffusion. If these ideas are correct, similar surface roughness patterns should also be observed for even thick films with dPEP-rich (off-critical) compositions such that the surface dPEP-rich layer grows linearly with t, the kinetics expected for growth by hydrodynamic flow through perforations in the second PEP-rich layer. Figure 4 shows the SFM image (33) Jandt, K. D.; Heier, J.; Bates, F. S.; Kramer, E. J. In preparation.
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Figure 4. SFM image of a dPEP-PEP film of off-critical composition (62% dPEP) approximately 1 µm thick. The films have been annealed for 17.25 h at 322 K. These conditions have been shown previously (ref 22) to result in the surface dPEPrich layer growing linearly with t, the kinetics expected for growth by hydrodynamic flow through perforations in the second PEP-rich layer.
of just such a sample, a film consisting of 62% dPEP and 38% PEP approximately 1 µm thick that had been annealed at 322 K for just over 17 h. A two-dimensional pattern of surface roughness is observed whose peak to valley height difference is nearly 80 nm and whose lateral wavelength is about 800 nm. Clearly these expectations are confirmed. Conclusions 1. Scanning force microscopy of surfaces of thin films (200 nm) of spinodally decomposed dPEP-PEP binary mixtures reveals regular patterns of roughness of amplitude ∼2.5 nm and period 500 nm after intermediate annealing times. The films are smooth both before and after these intermediate times. This transient roughening is not observed in films thicker than ∼240 nm. 2. We believe that the patterns observed are formed by pressure differences accompanying the growth of the dPEP-rich surface layer by hydrodynamic flow through perforations in the PEP-rich second layer, perforations that develop because of the thinness of the PEP-rich and dPEP-rich second and third layers enforced by the overall thinness of the polymer film. Acknowledgment. Primary funding for this research from the National Science Foundation Polymers Program NSF-DMR Grant Number 92-23099, with additional support for FSB on NSF-DMR Grant 94-05101, is gratefully acknowledged. K. D. Jandt is grateful for partial financial support in the form of a Feodor-Lynen Fellowship of the Alexander von Humboldt Foundation, Bonn, Germany. The use of the Central Facilities of the Cornell Materials Science Center (funded by the NSF-DMRMRSEC program) for ion beam analysis and scanning force microscopy is greatly appreciated. The authors thank J. Marko and S. Kumar for helpful discussions. LA950753C
