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Ring Formation in Evaporating Porphyrin Derivative Solutions L. Latterini,† R. Blossey,*,‡ J. Hofkens,† P. Vanoppen,† F. C. De Schryver,*,† A. E. Rowan,§ and R. J. M. Nolte§ Department of Chemistry, Katholieke Universiteit Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium, Laboratorium Voor Vaste Stof-Fysica en Magnetisme, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium, and Department of Organic Chemistry, NSR Center, University of Nijmegen, Toernooiveld, NL-6525 ED Nijmegen, The Netherlands Received November 16, 1998. In Final Form: February 19, 1999 The formation of micrometer-size, ring-shaped structures is studied in evaporating solutions of porphyrinbased molecules on glass. Solute concentration, solution and substrate temperature, vapor pressure, and solvent are varied. The molecular arrangements on the substrate are monitored by confocal fluorescence microscopy (CFM), atomic force microscopy (AFM), and near-field scanning optical microscopy (NSOM). From experiment, a nonequilibrium morphology diagram for the observed structures is deduced as a function of solute concentration and evaporation time. The mechanisms involved in ring formation are discussed on the basis of solvent and solute dynamics.
Introduction The formation of “ringlike” or “wheel-like” structures has recently been observed in the evaporation process of organic liquids. When a droplet or film of liquid is evaporated on a substrate, molecular arrangements of dissolved molecules1-3 or dispersed particles4,5 remain on the substrate. Recent experiments on a system consisting of a porphyrin derivative in organic solvents have demonstrated that ring formation can occur after the deposited film has ruptured into an ensemble of droplets.6 While a general understanding of the mechanisms involved in formation of these structures has not yet fully been achieved, it appears clear that the initial driving force for the structure formation process is provided by the solvent, either due to its evaporation or its wetting/nonwetting properties. The complex interplay of evaporation, film rupture instabilities, and hydrodynamics defines a rich class of systems which might become available for molecular assembly governed by nonequilibrium processes rather than equilibrium processes, as, for example, in many phenomena involving molecular self-assembly.7 This motivates the present experimental study of ring formation in a system involving a porphyrin-based molecule (PtP) dissolved in organic liquids (CHCl3, C6H3Cl3) under different experimental conditions of solute concentration, solvent and substrate temperature, pres* To whom correspondence should be addressed. † Department of Chemistry, Katholieke Universiteit Leuven. ‡ Laboratorium Voor Vaste Stof-Fysica en Magnetisme, Katholieke Universiteit Leuven. § University of Nijmegen. (1) Schenning, A. P. H. J.; Benneker, F. B. G.; Geurts, H. P. M.; Liu, X. Y.; Nolte, R. J. M. J. Am. Chem. Soc. 1996, 118, 8549. (2) Hofkens, J.; Latterini, L.; Vanoppen, P.; Faes, H.; Jeuris, K.; De Feyter, S.; Kerimo, J.; Barbara, P. F.; De Schryver, F. C.; Rowan, A. E.; Nolte, R. J. M. J. Phys. Chem. B 1997, 101, 10588. (3) Thiele, U.; Mertig, M.; Pompe, W. Phys. Rev. Lett. 1998, 80, 2869. (4) Ohara, P. C.; Heath, J. R.; Gelbart, W. M. Angew. Chem. 1997, 109, 1120. (5) Ohara, P. C.; Gelbart, W. M. Langmuir 1998, 14, 3418. (6) Latterini, L.; Blossey, R.; Hofkens, J.; Vanoppen, P.; De Schryver, F. C.; Rowan, A. E.; Nolte, R. J. M. Submitted. (7) See, for example: Whitesides, G. M.; Mathias, J. P.; Seto, C. T. Science 1991, 254, 1312.
sure, and solvent evaporation rate. This system was chosen for two reasons. First, porphyrin molecules have a tendency to stack and hence form supramolecular structures. Porphyrin wheels were observed previously in this system and are of interest because of their possible use as models for natural porphyrin structures.1 Second, the optical fluorescence properties of the porphyrin molecule allow the use of modern experimental techniques for the investigation of the structures formed in or from solution. From our experimental observations in this porphyrin/ solvent system, we deduce a tentative nonequilibrium morphology diagram. This concept had previously been used, for example, to characterize structure formation in the growth of crystals by solidification8 or in electrodeposition processes.9 Finally, the mechanisms involved in ring formation are identified as the rupture of the solution film into droplets, contact line fluctuations of these droplets, and enrichment of the solute inside the evaporating droplets, driven by a coupling between evaporation and hydrodynamics. Experimental Setup A porphyrin derivative, bis(21H,23H-5-(4-pyrydyl)-10,15,20tris(4-hexadecyloxyphenyl)porphyrin)platinum dichloride (PtP), was used as solute. Its synthesis has been described elsewhere.1 Chloroform (CHCl3, Biosolve LTD, HPLC grade, bp 61.2 °C, n20D ) 1.446) and 1,2,4-trichlorobenzene (C6H3Cl3, Aldrich, Spectro grade, bp 214 °C, n20D ) 1.571) were used as solvents, both without further purification. Films were prepared by deposition of the solutions in the form of droplets of initially millimeter height on microscope cover glasses (n20D ) 1.523). Film preparation from CHCl3 has been carried out under four different conditions: (i) solvent casting of PtP solutions (10-7 to 10-4 M), in situ and ex situ of the confocal microscope stage (As a control experiment films were prepared from evaporating C6H3Cl3 (10-4 M) at ambient conditions.); (ii) fast evaporation of the solvent obtained by deposition of the solution (8 × 10-6 M) at room temperature on a precooled glass (4 °C); (iii) evaporation of the solvent at 4 °C, after cooling both the solution (8 × 10-6 M) and the glass (8) Brener, E.; Mu¨ller-Krumbhaar, H.; Temkin, D. Phys. Rev. E 1996, 54, 2714. (9) Zeiri, L.; Younes, O.; Efrima, S.; Deutsch, M. Phys. Rev. Lett. 1997, 79, 4685.
10.1021/la981602n CCC: $18.00 © 1999 American Chemical Society Published on Web 04/21/1999
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Langmuir, Vol. 15, No. 10, 1999 3583 Table 1. Ring Measures Taken from Experiment with CHCl3 as Solvent [PtP] (M)
Tamb
Tglass
P
D (µm)
d (µm)
e (nm)
2 × 10-4 2 × 10-5 2 × 10-6 2 × 10-7 8 × 10-6 8 × 10-6 10-5
rt rt rt rt 4K rt rt
rt rt rt rt 4K 4K rt
atm atm atm atm atm atm sat
0.7-1.5 1-4 1-5 3 10-20 10-30 0.5-0.9
0.5 0.5 0.4 0.2-1 0.2-1 0.03-0.05 0.02-0.03
100 100 50-100 30-50 10-20 10-20 30-60
a Abbreviations: rt, room temperature (approx. 20 °C); atm, atmospheric, that is ambient, pressure; sat., controlled pressure in a vapor near-saturated atmosphere.
Figure 1. Topographic (solid curve) and fluorescence (dotted curve) line scans obtained from NSOM imaging on a 10-6 M PtP/CHCl3 sample on glass prepared under ambient conditions. The meaning of the symbols e, D, and d is explained in the text. (Water condensation from the air was prevented by a flow of nitrogen when the samples were exposed to ambient conditions.); (iv) deposition of the solutions (10-5 M) and evaporation of CHCl3 at a constant pressure of a near-saturated vapor atmosphere of CHCl3 at room temperature. To prepare the film at a controlled pressure, the depositions have been carried out in a closed experimental cell. The starting CHCl3 solutions and the glass plates were stored for several hours under the same conditions. Confocal fluorescence images were recorded with a scanning unit (Biorad MRC 600) and an inverted microscope (Nikon Diaphot 300) using a 40×, 0.9 NA objective lens (3 s/frame). The frequency-doubled output of a Ti/sapphire laser (420 nm, Tsunami, Spectra Physics) was used for excitation.10 Atomic force microscopy images have been acquired in noncontact mode by Lumina-AFM (Topometrix) using commercially available lowresonance cantilevers and phase detection. The AFM images have been processed by horizontal leveling. NSOM images have been recorded using a modified commercial instrument (Aurora, Topometrix) described elsewhere.10 The output of an argon ion laser (458 nm, Spectra Physics) was used as excitation source. The experiments were performed with homemade NSOM probes consisting of Al-coated optical fiber probes with a nominally 50 nm aperture at the end. Topographic and fluorescence images were recorded simultaneously.
Results 1. Ex-Situ Depositions. (i) Deposition under Ambient Conditions. For a droplet of PtP/CHCl3 solution deposited on the cover glass at ambient conditions, an evaporation time te of 60 s has been measured. After evaporation of the solvent, ring-shaped structures are observed on the substrate.1,2,6 Figure 1 shows a line scan through a ring structure obtained by NSOM topography and fluorescence imaging on a sample prepared from a PtP/CHCl3 (10-6 M) solution. The radial profile h(r) of the ring structure can, to a good approximation, be described by a Gaussian (r > 0)
h(r) ) e exp(-(r - D/2)2/2d2)
(1)
where e denotes ring height, D is the ring diameter, and d is the width of the rim. An increase of the PtP concentration in solution from 10-7 to 10-4 M leads to a distinct morphological change in the ring shapes:2 the average ring diameter D decreases, from 3 µm to approximately 1 µm, while the ring height e increases by a factor of 2-3. The dimensions of the structures measured by topographic imaging for the (10) Vanoppen, P.; Hofkens, J.; Latterini, L.; Jeuris, K.; Faes, H.; Kerimo, J.; Barbara, P. F.; Rowan, A. E.; Nolte, R. J. M.; De Schryver, F. C. In Applied fluorescence chemistry, biology and medicine; Retting, W., Strehmel, B., Schrader, S., Eds.; Springer: Berlin, in press.
samples prepared under the different experimental conditions are listed in Table 1. A characterization of the structures at room temperature has already been reported.2 In a control experiment, samples have been prepared by deposition of PtP/C6H3Cl3 solutions. In this case, te ≈ 12 h; that is, it is increased by several orders of magnitude as compared to that for CHCl3. Confocal fluorescence imaging of the films obtained by deposition of an approximately 10-4 M PtP/C6H3Cl3 solution showed the presence of only a few large structures with a diameter of D ) 30 µm. No emission has been detected from the inside of these rings. Generally, the substrate is characterized by small structures which show fluorescence (not shown). AFM imaging revealed that the sample is characterized by a continuous layer of material in which small holes are present which have a different topography than that of the rings.6 (ii) Deposition on a Cooled Substrate. When the solution at room temperature is deposited on a cooled glass plate (T ) 4 °C), the measured evaporation time is te ≈ 40 s. The film topography has been investigated by AFM (Figure 2 A). Rings with distorted rims are found over the whole film area. Their average diameter is D ) 10-30 µm. Most of the observed rings are isolated and present a sharp rim of a few tens of nanometers thickness. The big rings are beaded: in every ring a larger deposition of material is observed on one side, presumably a cluster of PtP. Between the big rings smaller rings are observed. This is seen in parts B and C of Figure 2, which show AFM scans acquired by zooming into progressively smaller regions of Figure 2A. The smaller rings maintain a nearly circular shape with a diameter D ) 1-2 µm and a height e ) 10 nm. (iii) Deposition under Cooled Conditions. When the sample has been prepared at 4 °C, te ≈ 70 s. The sample yielded different structures in different areas of the film. Figure 3 presents an AFM image acquired in the central region of the sample. Irregular rings with a diameter of D ) 1-20 µm and tens of nanometers height were present (Table 1). Most of the structures appeared fused together but not closed, since their rim was interrupted. At the edge of the film a higher concentration of material was revealed by the enhanced contrast in the fluorescence imaging. In this area the rings show smaller diameter (not shown). Independently from the solution temperature the samples prepared on a cooled glass show an increase in the average ring diameter D and a decrease in the rim width d compared to those for the sample prepared at room temperature (Table 1). In the samples prepared on the cooled glass the maximum ring height was a few tens of a nanometer, which is about 1 order of magnitude less than that for the samples prepared at ambient conditions. Only the samples prepared by fast evaporation preserve complete “wheel” or ring structures, although they are somewhat distorted.
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Figure 2. Topographic images acquired by AFM on a PtP sample deposited on a cooled glass. The scale bars below the images represents 10 µm for images A and B and 1 µm for image C.
Figure 3. Topographic image acquired by noncontact AFM on a PtP sample on a glass prepared at 4 °C. The scale bar below the image represents 1 µm.
(iv) Deposition under Near-Saturation Conditions. Ring formation is strongly reduced when the samples are prepared in a near-saturated atmosphere, where the average evaporation time is te ≈ 120 s. Confocal fluores-
cence imaging of the samples prepared with 10-5 M solutions at constant pressure reveals the presence of few ringlike structures with a diameter of D ) 10 µm. In general the film is characterized by smaller structures (D ≈ 1 µm) which have a fluorescence intensity higher than the background, produced by a continuous solute layer. The AFM images of this area (Figure 4) show that most of the depositions have a circular shape with a hole in the middle; their outer diameter is always below 1 µm whereas the inner one is between 200 and 400 nm. A line scan through these structures reveals their vulcano-like shape (Figure 5). Furthermore, the spacing among the spots appears quite regular in a 100 × 100 µm2 area. This is indicated in Figure 4, where the structures are connected to their nearest neighbors by straight lines, suggesting an underlying lattice structure. The distance between two holes is approximately 5 µm in both directions in the plane (this estimate is made more precise below). The regularity of this arrangement is disturbed by the presence of depositions which do not have a hole in the middle and present a less regular shape and size. These depositions are presumably PtP agglomerates. The experimental findings in the sets of experiments i-iii can tentatively be arranged in a morphology diagram, as done previously for dendritic structures found in solidification and electrodeposition processes.8,9 In Figure
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Figure 6. Nonequilibrium morphology diagram of substrate structures taken from experiment, in the parameters evaporation time and PtP concentration in solution. Figure 4. Topographic image acquired by AFM on a PtP sample on glass deposited in the presence of a saturated CHCl3 atmosphere. The scale bar below the image represents 10 µm. Volcano-like structures are connected by straight lines as a guide to the eye, indicating their spatial correlation.
of the droplets is shown in Figure 8 A, displaying a sharp maximum at 1.6 µm. After droplet formation, coalescence of the small droplets is observed, which leads to the formation of larger droplets. The large droplets become rapidly pinned to the substrate (Figure 7B). The time between parts A and B of Figure 7 is 2 s. The pinned droplet continues to evaporate and shrinks. Figure 7C presents the structures after drying of the solvent, in which an enhancement of contrast is seen at the rim of the droplet seen in Figure 7B. Discussion
Figure 5. AFM topographic images acquired on a PtP sample prepared in the presence of a saturated CHCl3 atmosphere. The scale bar below the image represents 1 µm. Inset: line scan through image of Figure 5.
6, the evaporation time te and the molar concentration are taken as parameters. At high evaporation rates and for small solute concentrations, the observed rings are big and sometimes distorted or even disconnected. At intermediate concentrations and evaporation rates, the ring shapes are most symmetric; for larger evaporation times and higher concentrations, ring structures are replaced by volcanoes; at very long evaporation times, as for C6H3Cl3, no rings are observed. 2. In-Situ Depositions. Detailed information about the structure formation was obtained by taking in situ images of the dynamics of the evaporation process in PtP/ CHCl3. A camera was used to monitor and record the evaporation process in real time when a droplet of PtP/ CHCl3 (10-5 M) was deposited at T ) 20 °C and p ) patm(air) on a cover glass in the microscope stage. The result of this experiment is shown in parts A-C of Figure 7, which are images extracted from the video taken during the evolution of the film after rupture. Figure 7 A shows small droplets that have appeared immediately after film rupture, 89 s after deposition of the initial droplet. The size distribution
Several hypotheses have been put forward in the literature to explain the formation of rings from evaporating solutions. They have been attributed to gas bubbles in the liquid film1,2 or to solvent convection by the rim of a hole opening in an unstable film.2-5 From the direct observation of ring formation in the in situ experiments, it appears that the ring formation process involves three steps: (1) film rupture after a period of spreading of the initial (macroscopic) droplet and its thinning under evaporation, (2) coalescence of small droplets to bigger droplets until pinning at defects occurs, and (3) final evaporation of the solvent and ring formation. In the following, these processes will be discussed on the basis of an approximate model for the film rupture process which allows semiquantitative estimates of the magnitude of the instability mechanism, and by a more qualitative discussion of the subsequent stages of the ring formation process. 1. Film Rupture. The instability of thin films is commonly described within the lubrication approximation to the Navier-Stokes equation, based on the dynamic interface model11
∂th(x,t) ) (Fν)-1∇[h3(∇p)]
(2)
where h(x,t) is the local height of the liquid over the plane x in time t. In the first term on the right hand side of eq 2, ν is the kinematic viscosity of the liquid (up to a numerical factor), F is the liquid density, and p is the sum of the pressures acting on the film. In general, p contains contributions from hydrostatic, capillary, and disjoining pressures. For an evaporating film, mass loss to the gas phase needs to be included in eq 2, since the liquid is not at its saturation temperature (or pressure). If, for sim(11) See, for example: Oron, A.; Davis, S. H.; Bankoff, S. G. Rev. Mod. Phys. 1997, 69, 931.
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Figure 8. Size distributions of droplets after rupture (A) and of volcanoes (B), and center-to-center distance distribution of volcanoes (C).
a critical thickness below which it can be destabilized by evaporation (vapor recoil) or by molecular forces, if the latter favor a nonwet substrate. Linear stability analysis of a flat, shrinking film shows that both destabilizing effects act in parallel. Perturbing the flat film h ˜ (x,t) ) h(t) + u exp[iq‚x - t/τ], where u is the amplitude of the perturbation with wave vector q and relaxation (or growth) time τ, the dependence of τ on wave vector can be determined. It is found that τ < 0 for wave vectors q with 0 < q < qc; that is, perturbations on sufficiently long length scales λ ) q-1 are unstable and grow in time. The fastest growth mode of the perturbations behaves as
λM ∝ h2/[-6A + (e*ν)2δFh]1/2
Figure 7. Transmission images acquired during in situ preparation of a PtP film on glass, approximately 89 s (A), 90 s (B), and 113 s (C) after deposition of the solution.
plicity, a linear temperature profile across the film is assumed, the right hand side of eq 2 needs to be modified by a term -e*ν/h which accounts for mass loss of the liquid to the gas phase with density Fg. The (dimensionless) evaporation number e* is the ratio of evaporation and hydrodynamic time scales. As discussed by Davis and coworkers,11 evaporation (and additional effects such as e.g. thermocapillarity) can destabilize an evaporating film and lead to film rupture. Particles that leave the film for the gas phase change the momentum balance in the film and lead to a vapor recoil pressure. If mass loss is given as above, vapor recoil is given by pevap ) (e*ν/h)2δF/2, where δ ∝ F/Fg.6,12 On the basis of this extension of eq 2, the film evolution is first characterized by a stabilization of the film by gravity and surface tension. It thins due to mass loss and reaches (12) Burelbach, J. P.; Bankoff, S. G.; Davis, S. H. J. Fluid Mech. 1988, 195, 463.
(3)
where the disjoining pressure is given by pvdW ) -2A/h3 with Hamaker constant A. If A is positive and favors a wet substrate,13 vapor recoil dominates molecular forces for h > hc ≡ 6|A|/[(e*ν)2δF]. Neglecting van der Waals forces for films fulfilling this condition, the dependences λM ∝ (e*)-1 and τM ≡ |τ(qM)| ∝ (e*)-4 follow, where τM is the raising time. For h < hc, van der Waals forces can dominate over vapor recoil instabilities, and if A < 0, spinodal dewetting due to molecular forces becomes possible. In the present system, the van der Waals forces of CHCl3 favor a wet substrate, while C6H3Cl3 favors a nonwet substrate.14 To apply the theory to experiment, the evaporation number is calculated as e* ) h20/2teν, where h0 is the initial film thickness. Due to the highly nonlinear dependence of τM on e*, a quantitative determination of λM and τM requires a precise knowledge of h0 and the viscosity ν, which is not available from experiment at present. By taking the values of F and ν for the pure solvent and the approximately known values of h0 and te, an order of magnitude estimate can be obtained. The vapor recoil instability is then estimated to occur on the experimental time scale for film thicknesses h < 1 µm, with an instability length scale λM of the same order of magnitude. A decrease in e* increases both the instability length scale and the raising time of the instability. Since τM ∝ (e*)-4, the change (13) Israelachvili, J. Intermolecular and Surface Forces, 2nd ed.; Academic Press: New York, 1992. (14) Neglecting retardation effects, the Hamaker constants A of CHCl3 and C6H3Cl3 can approximately be determined from standard expressions involving the dielectric constants and refractive indices of the three phases,13 and one obtains A(CHCl3) ) 3.20 × 10-22 J and A(C6H3Cl3) ) -2.46 × 10-22 J. At still smaller length scales, polar contributions to the interaction forces can also come into play, which we have therefore not considered. The largest linear dimension of a PtP molecule is approximately 7 nm, which is distinctly larger than both CHCl3 (≈0.2 nm) and C6H3Cl6 (≈0.6 nm).
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in e* by a factor of 2 shifts the instability by 1 order of magnitude toward the final stages of the evaporation process. This shift can cause the instability to be preempted by mass loss.15 Parts A and B of Figure 8 show the size distribution of the appearing droplets immediately after rupture, and that of the volcanoes obtained after evaporation in saturated conditions. Both distributions have sharp maxima at D ) 1.5 µm and D ) 0.3 µm, respectively. The average distance between the droplets in Figure 8A is only marginally bigger than their diameter D, while the distance between the volcanoes is around 5 µm, as seen in Figure 8C. Thus, the interstructural distances in Figure 8A and C differ by roughly a factor of 3-4. This is in line with the theoretical argument given for the instability length scale λM, if it can be assumed that the position of the volcanoes is representative of droplets that have appeared immediately after film rupture. This assumption appears justified, as, upon an increase of the evaporation time, film rupture occurs at a later stage of the process, where the film has already lost most of its mass, and smaller droplets and hence smaller structures result. Since in the course of evaporation the solute concentration increases, the viscosity of the solution increases in the later stages of the evaporation process.16 Ring formation thus is inhibited by a slowdown of the hydrodynamics of the system, which causes a less efficient transport of the solute by the solvent and leads to less well-developed structures. These are observed in the experiment also at high initial solute concentrations. The importance of evaporation for the formation of rings is also supported by the results of the control experiment with PtP/C6H3Cl3. Here, the evaporation number e* is several orders of magnitude smaller than that of CHCl3. The shrinking of the film by mass loss occurs therefore much more slowly and hence can allow van der Waals (and possibly polar) forces to intervene. Ring formation is inhibited, but structuring of the substrates by holes occurs. A quantitative estimate of the instability length scale λM (eq 3) based on the parameters for C3H3Cl6 is in accord with the scenario of spinodal dewetting driven by van der Waals forces. However, a definitive conclusion on the underlying physical mechanisms cannot yet be reached, as the film state is affected by the physical properties of the PtP deposit, which at present have not been characterized. 2. Droplet Formation and Coalescence. The shape of the droplets appearing after film rupture is dictated by the surface tensions between the substrate and the liquid and vapor phases, which determine the contact angle of the droplet after relaxation. Therefore, even for an ideally pure system, this regime is dominated by surface forces. In a real system, the situation is more complex due to the presence of disorder: (i) Disorder in the Substrate Surface. After coalescence, the droplets are pinned at substrate defects, which is apparent from the distorted droplet shape in Figure 7B when compared to Figure 7C. As the glass substrate can be “rough”, that is, contain long-range correlations in its surface, it is a possible source of pinning centers.17 Substrate randomness further affects the wetting properties by leading to a local variation of surface tensions and by causing the contact line to wander across the substrate. A balance of substrate pinning forces and contact line elasticity yields an estimate of the maximum random (15) Bonn, D.; Meunier, J. Europhys. Lett. 1997, 39, 341. (16) The observation of incomplete rings in the cooled system iii can also qualitatively be explained by a viscosity increase due to the reduced temperature. (17) de Gennes, P. G. Rev. Mod. Phys. 1985, 57, 827.
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fluctuation amplitude of the contact line on the order of 1 µm, which is in accord with the observed coalescence range of the droplets.18 Therefore, substrate randomness cannot be neglected in a discussion of the droplet (and ring) shapes. (ii) Disorder on Top of the Substrate. As seen in Figure 2A-C, PtP agglomerates are present near the rings. These structures, whose formation had been reported before,2 may have a solubility different from that of PtP. They are a defect in the film when their size is comparable to the film thickness and can cause an “anchoring” of the droplets after film rupture. In some of the in situ observations of the ring formation dynamics, it was observed that bead formation can also result from a secondary rupture of the bulk of the evaporating droplet. In this case, the solvent is found to “heap” solute material up to form an agglomerate. Small agglomerate depositions have been observed under all experimental conditions and deserve further attention, as their presence might influence the structure formation process.19 3. Ring Formation. The comparison of parts B and C of Figure 7 demonstrates that the solute enrichment process occurs inside of an evaporating droplet. It can therefore be assumed to be due to the same mechanism observed recently for macroscopic droplets with dispersed particles.20 An evaporating droplet shrinks under volume reduction, but with a fixed lower surface area due to pinning. It thus must reduce its contact angle.21 The solution of the quasi-static diffusion equation for the solute concentration then shows that the evaporation flux diverges inside the droplet in radial direction at the droplet edges. To accomplish this, liquid flows from the bulk of the three-dimensional droplet to its edge with a velocity v which diverges in space at r ) R, and in time, as the film dries out. From our model, v ∝ (tc - t)-1/2, but for very small film thicknesses, a divergence with exponent -1 is more realistic.11,21 A quantitative measurement of this behavior has not been performed for the present system. Conclusions This paper reported on a study of ring formation in porphyrin derivative solutions. Changes of external and internal system parameters have elucidated that the formation of well-shaped rings requires “optimal” conditions of evaporation rate and solute concentration, as is illustrated by the morphology diagram in Figure 6. The ring formation dynamics has been interpreted as a process involving three stages. Initially, the film ruptures by an evaporation instability, and sub-micrometer droplets are formed. Soon after, coalescence of these droplets occurs. Substrate properties become important by controlling the surface tensions of the droplets and by providing pinning centers for the evaporating droplets. Finally, ring formation by material accumulation at the droplet edges occurs by particle flow inside the droplets. If evaporation is too fast or solute concentration is too low, the ring structures appear poorly developed due to fluctuation effects; if the solute concentration is too high or if evaporation is too slow, the system reaches a regime dominated by viscous (18) This estimate has been obtained by employing eq 2.32 of ref 17. The displacement W of the contact line due to disorder is given by the proportionality W ∼ l1/3ξ2/3, where ξ is the correlation length of the disorder and l is the length of the line. Both lengths are assumed to be comparable. (19) Jacobs, K.; Herminghaus, S.; Mecke, K. R. Langmuir 1998, 14, 965. (20) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827. (21) Parisse, F.; Allain, C. J. Phys. II 1996, 6, 1111.
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effects of the solute hindering ring formation. Thus, the experiments support that an evaporation-driven solute transport mechanism is responsible for ring growth in the PtP/solvent system. It explains the observed efficiency of solute transport, which leads to empty ring interiors, as proved by a lack of fluorescence, and it also accounts for the sharply defined rings of high symmetry (Figure 1), provided they have not been subjected to collisions driven by contact line fluctuations. Only speculations can yet be made on the mechanism leading to the small ring like structures in the vicinity of bigger rings in Figure 2A-C. A possible explanation is that they have originated from the initial rupture instability but have not been able to coalesce to form larger droplets, as the smaller circumference of the droplets permits less fluctuations of the contact line, and thermal fluctuations are reduced due to the reduced temperature in the experiment. The sharp ring boundaries indicate that they result from the same solute enrichment process occurring inside an evaporating droplet that is responsible for the formation of the larger rings.
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Also, the discussed disorder effects need further investigation. In this context it is also noteworthy that the spatial distribution of the volcanoes has two peaks. This can in principle result either from fluctuations in the droplet positions after coalescence or from a distortion of the volcano lattice due to the presence of defects, which are visible in Figure 4. Acknowledgment. F.C.D.S. gratefully acknowledges support by the FWO and DWTC through IUAP-4-11. L.L. thanks the research council of the KU Leuven for a fellowship. J.H. is a postdoctoral fellow of FWO. R.B. gratefully acknowledges support by the FWO under project G.0277.97 “Theory of confinement phenomena in submicron structures”, the Belgian IUAP program, the Flemish Government under (VIS/97/01), and the Schwerpunktprogramm “Strukturbildung und Benetzung an Grenzfla¨chen” of the Deutsche Forschungsgemeinschaft. The EC is thanked for support through TMR SISITOMAS and contract FMRX-CT98-0171. LA981602N
