Supra-aggregates of Fiber-Forming Anisotropic Molecules - The

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J. Phys. Chem. B 2006, 110, 2116-2124

Supra-aggregates of Fiber-Forming Anisotropic Molecules Antonio Raudino*,† and Bruno Pignataro*,‡ Dipartimento di Scienze Chimiche, UniVersita` di Catania, Viale A. Doria 6-95125, Catania, Italy, and Dipartimento di Chimica Fisica “F. Accascina”, UniVersita` di Palermo, V.le delle Scienze Parco D’Orleans II, 90128 Palermo, Italy ReceiVed: October 28, 2005; In Final Form: December 7, 2005

In this paper, the self-organization of fiber-forming anisotropic molecules is inspected both theoretically and experimentally. In the first part, a theoretical model which extends the de Gennes theory of thin films to assemblies of strongly anisotropic molecules is reported. The model predicts that solid supported thin films made up of fiber-forming discotic molecules can grow with both tangential and radial arrangement of the fibers, respectively leading to the formation of compact and holed supra-aggregates. These last systems form according to the following picture. The tangential growth minimizes the number of unfavorable free ends but introduces elastic strain especially in the central region of the aggregate. To reduce the elastic strain, some molecules are displaced from the central region toward the periphery of the growing aggregate, producing a localized well. In the second part of the paper, we experimentally face the above issue by depositing a strongly anisotropic disk-shaped molecule (rhodamine 123) onto different solid substrates through a spin coating procedure. By employing scanning force microscopy (SFM), the formation of thermodynamically favored fiberlike supramolecules as well as of compact and holed submicron-sized supra-aggregates has been demonstrated. The observed phenomena have been found to depend on the interplay of different parameters such as molecular concentration, evaporation time, and substrate composition. As main features, both theory and experiments show that holed supra-aggregates are more stable beyond a critical aggregation size and that the formation of holes is favored at high supersaturation. The theory seems valuable in extending previous dewetting models developed for fluid films with isotropic interaction forces.

Introduction The organization of organic and biological molecules at solid surfaces has stimulated in the last two decades the interest of a broad part of researchers either for the fundamental aspects of self-assembly or for their implication in different applications. It has been found that molecules can organize in mono-,1 bi-,1-3 and three-dimensional4 supramolecules as well as in larger superstructures made up of ordered arrays of supramolecular assemblies.5,6 The shape of the organized assemblies is of fundamental importance in view of the peculiar application in which they would be involved.7 Thus, for instance, rodlike systems are of interest as wires for the engineering of electronic devices,8 spheroids and planelike assemblies can be used as biomimetic supports or as an active layer in sensors,9 and laterally ordered 2D assemblies are of relevant interest for dimensional scaling in electronics and nanopatterning.7 Furthermore, it is well-known that 1D protein fibrils are fundamental for the onset of different pathological processes, for instance, Alzheimer and prion-related diseases. To design a given supra- or supermolecular structure at a solid surface, the choice of the experimental conditions together with the specific sequence of operations during the preparation is crucial. Indeed, these factors determine the interplay of the * To whom correspondence should be addressed. E-mail: [email protected] (A.R.); [email protected] (B.P.). † Universita ` di Catania. ‡ Universita ` di Palermo.

different competing forces involved and the mechanism responsible for the formation of the structures. Unlikely the organization of molecules in molecularly thin films is very hardly to be interpreted, even more than the self-assembly of molecules in liquid. This is mainly due to the complexity of the system that involves at least three different partners (the surface, the solvent, and the molecule) and to the bidimensional restrictions which have to be considered. More effort has to be spent to understand the basic physics that governs these complex phenomena from both the experimental and theoretical point of views. Among the large number of solid supported organized systems, in this paper, we focus on supra-aggregates consisting of fiber-forming anisotropic molecules. The assembly processes of this kind of systems are indeed of increasing interest in different fields, for instance, in molecular electronics where the development of molecular or supramolecular extensive (at least some tens of nanometers) wires with intrinsic electrical properties and prominent stiffness is required.10 Our study has been performed both theoretically and experimentally. In particular, here, we report at first on an original theoretical model which extends the de Gennes theory11 of thin films to assemblies of strongly anisotropic molecules. The model enables one to predict the possible different shapes of supra-aggregates arising from the assembly of fiber-forming anisotropic molecules. Experimentally, we studied by scanning force microscopy the structures resulting from the growth on solid supports of rhodamine 123 (R123; see Scheme 1). This molecule has been intentionally chosen, since it is a strongly anisotropic molecule, which due to its shape is expected to assemble through π-π interactions in thermodynamically favored fiberlike supramolecules. The

10.1021/jp0562227 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/19/2006

Supra-aggregates of Fiber-Forming Molecules

J. Phys. Chem. B, Vol. 110, No. 5, 2006 2117

SCHEME 1: Molecular Structure of Rhodamine 123

relevant experimental features agree with the theoretical predictions of the model developed here. Experimental Section Chemicals and Deposition Procedure. Rhodamine 123 (R123; Scheme 1) was purchased in the hydrate form from Aldrich. R123 was dissolved in a mixture of ethanol (Fluka, 99.8%) and dichloromethane (Aldrich, 99.9%) in a ratio of 40/ 60 at concentrations ranging from 8.4 × 10-3 to 8.4 × 10-5 M. A 10 µL portion of these solutions was spin coated onto sheets, 1 cm2 in size, of mica (Metafix), highly oriented pyrolitic graphite (HOPG), and silicon. The spin coating process was performed for 30 s at rotation speeds ranging from 500 to 4000 rounds per minute (rpm) and with a ramp acceleration of 1000 rpm/s. Before the transfer, mica and HOPG were freshly cleaved, while the silicon surfaces were treated for about 30 s by a HF/ H2O (1/20) solution, leading to hydrogenated silicon substrates. Scanning Force Microscopy. The samples were immediately observed after the spin coating deposition by scanning force microscopy (SFM). SFM was carried out in air by using a Multimode/Nanoscope IIIa instrument equipped with an extender electronics module (Digital Instruments) in tapping mode. Commercially available tapping etched silicon probes (Digital) having a pyramidal-shaped tip with a nominal curvature of 1020 nm and a nominal internal angle of 35° were used. During the analysis, the cantilever, about 125 µm long, with a nominal spring constant of 20-100 N/m, oscillated at its resonance frequency (∼300 kHz). Height and phase images were recorded contemporaneously by collecting 512 × 512 points for each scan and maintaining the scan rate below 1 Hz. During the experiments, the laboratory temperature and humidity were about 20 °C and 40%, respectively. Theory Self-Assembly of Strongly Anisotropic Molecules. Consider self-assembling molecules with strong anisotropic interactions (such as the discotic ones). The strong face-to-face interactions favor the formation of long linear aggregates, while favorable but weaker lateral interactions favor the formation of compact supra-aggregates made up of fiber bunches. The possible structures of such supra-aggregates, which form upon drying dilute solutions spread over a flat surface, are schematically shown in Figures 1 and 2. Figure 1 schematically shows a cartoon of the top (a) and side (b) views of a disk of self-assembled fibers which grow radially with favorable fiberfiber lateral interactions. This kind of supra-aggregate has a considerable number of energetically unfavorable dead ends and bifurcations. The enlarged portion of the figure shows the structure of a single fiber, which is supposed to consist of faceto-face interacting discotic molecules. Another possible accretion mechanism is shown in Figure 2, where we hypothesize a tangential growth (viewed from the top (part a) and from the side (part b)). The number of dead

Figure 1. Schematic top (a) and side (b) view of a radial growth of the fibers. The enlarged portion of the figure shows the structure of a single fiber. This kind of supra-aggregate has a considerable number of energetically unfavorable dead ends and bifurcations.

Figure 2. Schematic top (a) and side (b) view of a tangential growth of the fibers. The number of dead ends is much smaller than that given in Figure 1, but the inner fibers of the supra-aggregate are strongly bent. To partially reduce the energy cost due to the elastic bending energy, the number of fibers near the center of the disk decreases. The result is the formation of a deep well in the central region.

ends is much smaller than that found for radial growth, but the fibers lying in the interior part of the supra-aggregate are strongly bent. To partially reduce the energy cost due to the elastic bending deformation, the number of fibers in the central region of the growing disk decreases. The competition among lateral interactions, fibers bending, solvent-aggregate and substrate-aggregate interface tensions leads to the formation of a deep well in the central region of the disk (Figure 2b). The modeling for such different kinds of growth is reported below. Consider a thick film growing onto a flat substrate, as sketched in Figure 2. The total free energy of the film can be partitioned into different contributions. The first contribution arises from the interfacial tension between the dilute solution and the solid film growing over a flat substrate11

∫0Rx1 + (∂h/∂r)2r dr ≈ R (Γ - Γ′)πR2 + πΓ∫0 (∂h/∂r)2r dr

GTENSION ) -πR2Γ′ + 2πΓ

(1)

where Γ and Γ′ are the film-solvent and substrate-solution interfacial tensions (erg‚cm-2), h ≡ h(r) is the local height of the film, and R is the film radius.

2118 J. Phys. Chem. B, Vol. 110, No. 5, 2006

Raudino and Pignataro

The second contribution accounts for the interaction between a substrate of infinite thickness and a fluid film of local height h. This term can be conveniently described by

∫0

1 GINTERACTION ) -2π 2 a

(

)

1 A 1 r dr ≈ 12π l2 (h + l)2 A R1 -Γ′′πR2 + 2 0 2r dr (2) 6a h

R

∫

Here, l ≈ a , h is the shortest film-substrate distance (of the order of the molecular size a), A is the Hamaker constant proportional to the strength of the intermolecular interactions,12 and Γ′′ ≡ A/12πa4. When the closely packed fibers grow in a tangential (Figure 2) rather than in a radial (Figure 1) arrangement, the unfavorable energy of the dangling ends is minimized but the elastic energy is nonzero. The fiber’s bending energy per unit volume is related to the local curvature radius r by (1/2)KM/r2, where KM is the bending elasticity modulus (erg‚cm2). The total elastic energy is obtained by integrating the above expression over the whole volume of the film: dV ) 2πhr dr. Then,

∫0Rhr12r dr

1 2π GELASTIC ) KM 3 2 a

This formula shows a spurious singularity at r f 0. In real systems, the smallest curvature radius is of the order of the molecule size a. A reasonable formula for the elastic energy thus reads

GELASTIC )

π Ea 12

∫0Rhr2r+dra2

(3)

where we related the bending elasticity modulus and the Young modulus E for a fiber of cross section a:13 KM ) (1/12)Ea4. Obviously, nonvanishing E values occur when the monomermonomer interactions within a single fiber are stronger than the lateral interfiber interactions. For molecules interacting through isotropic forces, the elastic term vanishes. Adding together the different energy contributions gives

GTOT ) GTENSION + GINTERACTION + GELASTIC ) -γπR2 + 2π

[

∫0R 21Γ(∂h ∂r )

2

]

h a2 1 + Γ′′ 2 + Ea 2 r dr (4a) 24 h r + a2

with γ ≡ -Γ + Γ′ + Γ′′. Minimization of the free energy functional (eq 4a) must satisfy the mass conservation constraint

V ) 2π

∫0Rhr dr

(4b)

In the absence of elastic energy (E ) 0) and for strong filmsubstrate interactions, the film takes the so-called “pancake” shape: it is essentially flat everywhere (h ) hh0, ∂h/∂r ≈ 0), unless near the pancake rim r f R where the film thickness suddenly drops to zero. In that limit, eq 4a becomes G°TOT ) -γπR2 + Γ′′(a2/hh02)πR2 + 2πΓhh0R, while the mass conservation constraint (eq 4b) reduces to V ) πhh0R2. Solving for R and combining with the previous equation yields

( )

hh0 1 γ a2 G°TOT ) - + Γ′′ 3 + 2Γ π V hh0 V hh 0

1/2

(5)

The optimum film thickness arises when ∂G°TOT/∂hh0 ) 0, and minimization of eq 5 leads to

(

hh0 ≈ hhMAX 1 -

1/2 Γ 3/2 π hh + ... 2γ MAX V

()

)

(6)

where hhMAX ≡ a(3Γ′′/γ)1/2. It is evident that the film edge has a little effect on the film thickness, with edge effects vanishing for large films as O(V -1/2). When the edge effects are neglected, we recover the de Gennes formula:11 hh0 ≡ a(3Γ′′/γ)1/2. Let us consider the case where elastic forces are present (E * 0). Looking at eq 4a, one may suppose that their influence is particularly strong in the region near r ≈ 0. Then, it is reasonable to assume

h ) hh + η(r)

(7)

where hh is the mean film thickness and η(r) describes the local deviation from planarity. η(r) is a strongly peaked function at r ) 0, rapidly falling to zero as r approaches the film periphery. Mass conservation imposes that η(r) must satisfy the constraint

∫0Rη(r)r dr ) 0

(8)

Inserting eq 7 into the free energy functional, expanding h-2 in a power series of η/hh, and eliminating linear terms in η by eq 8, one obtains after straightforward algebra

a2 π GTOT ≈ -γπR2 + Γ′′ 2πR2 + 2πΓhhR + Eahh log(R/a) + 12 hh 1 η 2π R 1 ∂η 2 1 + B(hh)η2 + Ea 2 r dr (9) Γ V 0 2 ∂r 2 24 r + a2

∫

[ ()

]

with B(hh) ≡ 6Γ′′a2/hh4. Minimization of the free energy functional (eq 9) leads to

∂GTOT ∂hh

)0

(10a)

∂GTOT ∂ ∂GTOT )0 ∂η ∂r ∂(∂η/∂r)

(10b)

Introducing the new variable X ) (B(hh)/Γ)1/2r ≡ λr, we obtain from eq 10b

C ∂2η 1 ∂η -η) 2 + 2 X ∂X ∂X X + Λ2

(11)

where Λ ≡ λa and C ≡ (1/24)(Ea/Γ). The solution to the above differential equation (eq 11) is

[

η ) A1I0(X) + A2K0(X) + C I0(X)

∫0XK0(x)x2x+dxΛ2 -

K0(X)

]

∫0XI0(x)x2x+dxΛ2

(12)

I0(X) and K0(X) are Bessel functions of the second kind,14 while A1 and A2 are two integration constants to be determined by applying the proper boundary conditions. Since K0(X) diverges when X f 0, one must set in eq 12 A2 ) 0. Moreover, on approaching the disk border (r f R), the elastic deformation, which is mainly localized at the disk center, vanishes:

lim η ) 0

XfλR

With the aid of these boundary conditions, we obtain from eq 12



[

K0(λR)

I0(X)

∫XλRK0(x)x2x+dxΛ2 - K0(X)∫0XI0(x)x2x+dxΛ2

η ) C I0(X)

∫λRI (x) x dx I (λR) 0 0 x2 + Λ2

]

0

(13)

Equation 13 describes the deformation profile of a thin film with anisotropic interactions. A compact and transparent approximation to eq 13 has been obtained in Appendix A

η(r) ≈ -

R2 r2 + β 2

(14)

where R2 ≡ (π2/96)(1 - π/4)-1(Ea3/ΓΛ3) and β2 ≡ π(1 π/4)-1(a2/Λ2). Equation 14 shows that the depth of the deformation is nearly Lorentian, with a minimum near the pancake center r ) 0. It linearly increases with the elastic bending modulus E of the film-forming fibers, as shown in Figure 3a. Expressing R as a function of V by the relationship V ) πhhR2, inserting the analytical equation for the deformation profile η(r) (eq 14) into the energy functional (eq 9), and integrating over r (all of the integrals are analytical), eventually we obtain the optimized energy of the pancake

( )

γ hh 1 a2 GTOT ≈ - + Γ′′ 3 + 2Γ π V hh V hh

[ ( )

1/2

+

( ( ) )] (15)

π Ea Ehh4 V Γ′′ a 4 hh log σ log 2 3 24 V σΓ hh πhha Γ′′a

with σ ≡ (π/6)(1 - π/4) - 1. This expression differs from that of a film of isotropic molecules (eq 5) for a term proportional to the bending elasticity E. Minimizing the energy (eq 15) with respect to hh enables one to calculate the mean thickness hh. As expected, hh is almost independent of the elastic term, whose main effect is a localized depression of the thickness near the film center, as described by eq 14. For large films, the elasticityrelated contribution to the mean thickness decreases as V-1, so without an appreciable error, we can employ for hh the simple formula given by eq 6. Insertion of the optimized thickness hh into the free energy (eq 15) enables us to calculate the minimum energy of a deformed aggregate. This result is of interest in calculating the phase diagram among different shapes, as shown in the next section. Equilibrium between Compact and Holed Supraaggregates. Let us calculate the energy of a thin compact aggregate made up of radially growing fibers (Figure 1), and let us compare the calculated energy with that of tangential growing fibers (Figure 2). In the case of radial growth, the elastic energy is zero because the fibers are not bent. On the other hand, to achieve a compact structure where the number of lateral interactions is maximum, one must introduce a number of Y-shaped bifurcations along the fiber, as shown in Figure 1. The number of bifurcations is greater in the regions of higher curvature. An estimate of the energy penalty paid for the formation of Y-shaped defects is as follows. Consider a circular film of radius R formed by radial fibers, and let a be the size of a fiber-forming molecule. We consider a corona of thickness 2a and radius r (0 < r < R), as shown in Figure 4. The number of linear nI and bifurcated nY fibers in the range r and r + 2a are related by nISI + nYSY ) SCORONA, where SI ) 2a2 and SY ) 3a2 are the areas of a linear and bifurcated fiber portion, respectively, within the corona. Elementary geometry yields SCORONA(r) ) π(r + 2a)2 - πr2 and nI + nY

) 2πr/a. From the above equations, we easily calculated the concentration C(r) of the Y-shaped defects, C(r) ) nY/ SCORONA(r) ) (1/a)(r + a)-1, which shows that the number of defects is greater in the interior of the disk. The associated energy GDEFECT is obtained by integrating the local energy density over the whole volume of the aggregate in the range 0 < r < R:

hh GDEFECT ) 2π a

∫0RC(r)r dr

where is the energy cost required to form a single defect. Upon integration,

a log R 98 2πhhR GDEFECT ) 2πhhR2 (1 - R a ) R/a.1 a a2

(16)

namely, the bifurcation energy linearly increases with the film radius R (at least for large R). In other words, the bifurcation energy is accounted for by increasing the effective surface tension at the disk edge. The above estimate of the defect energy must be augmented by considering the unfavorable energy associated with the free ends of the fibers (see Figure 1). Once again, this energy contribution is linear in the aggregate radius R. Adding the two above energies, we find that the energy of a radially growing aggregate made up of anisotropic interacting molecules differs from an isotropic film (eq 5) by the presence of a new term: GDEFECT ≈ 2π∆ΓhhR. By relating R and V by V ) πhhR2, eventually we get a compact expression for the total energy

γ hh 1/2 1 a2 GTOT ≈ - + Γ′′ 3 + 2(Γ + ∆Γ) π V hh V hh

( )

(17)

The main effect of the anisotropic interactions is then a rescaling of the edge tension from Γ to Γ + ∆Γ. It is worth noting that this term vanishes (∆Γ ) 0) for isotropically interacting molecules. To calculate the phase diagram, we need the chemical potential of flat (µ) and holed (µ′) aggregates. Let n be the number of molecules and a3 their volume, and using the relationship µ ) ∂GTOT/∂n ) a3∂GTOT/∂V, we get from eqs 15 and 17

1 µ ) -A + σ(Γ + ∆Γ) xV

(18a)

1 1 + EEL µ′ ) -A + σΓ V xV

(18b)

where A ≡ [2γ3/2/a(27Γ′′)1/2], σ ≡ (πa)1/2(3Γ′′/γ)1/4, and EEL ≡ (π/24)Ea2(3Γ′′/γ)1/2. The general behavior of the chemical potential against the volume V is plotted in Figure 3b. The two shapes are in equilibrium when µ ) µ′. From eqs 18a and b, we immediately obtain the critical size at which the shape transition occurs, Vcrit ) const‚(E/∆Γ)2, showing that the critical size increases with the fiber rigidity E. This result means that, for small disks, V < Vcrit, a flat aggregate shape is favored, while, when V > Vcrit, a perforated disk is more stable. The above conclusions are based on thermodynamic reasoning alone. Inclusion of nonequilibrium effects may strongly affect our conclusions, and a few of these effects are being investigated in the next section. Nonequilibrium Effects. Consider a growing disk made up of self-assembling molecules with strong lateral interactions. The growth takes place when the energy gain due to disk formation overcomes the energy of the free molecules. We have



Figure 3. (a) Deformation profile of a perforated film around the origin r ) 0. We used the dimensionless radial coordinate r/a, with a being the averaged molecular radius. The curves have been calculated for different values of the dimensionless parameter E/Γ, where E is the bending elastic modulus of the aggregate-forming fibers and Γ is the aggregate-solution interfacial tension. From the bottom to the top, E/Γ ) 1.0, 0.5, and 0.25. (b) Chemical potential for the radially (straight line) and tangentially (dashed line) growing disk described in Figures 1 and 2. The chemical potential is reported as a function of the scaled disk volume V/a3. The curves meet at a critical point which defines the stability domains of compact and perforated disks.

(b) Compact structures are energetically favored when their size is small. Holed aggregates are more stable when their size grows beyond a critical value which depends on a few parameters such as the fiber’s bending rigidity and interfacial tension. (c) The nucleation of holed aggregates depends in a complex way on the supersaturation. The number of holed aggregates becomes significant only at high supersaturation. Figure 4. Schematic picture of a radially growing aggregate (top view). For simplicity, we followed the fate of a single fiber and counted only the bifurcations contained in the corona comprised between r and r + 2a, with a being the mean size of a single molecule.

shown in the previous section that flat aggregates are preferred when the disks are small. Our system however is more complex because it contains two characteristic volumes (or lengths): the critical volume Vcrit for the flat f hole transition previously defined and the aggregate maximum volume VMAX which depends on the nucleation and growth rate processes. VMAX depends on the instantaneous supersaturation S of the solution, while Vcrit is independent of S. At this stage, two different scenarios can be envisaged, and we shall discuss them separately. (a) Vcrit < VMAX. In this case, the flat f hole transition occurs before the growing aggregate reaches its maximum size: the flat f hole transition is likely to occur. (b) Vcrit > VMAX. In this region, no perforated aggregates are allowed. In principle, the above regimes can be studied by varying the concentration of the solution at constant evaporation rate which affects VMAX leaving unchanged Vcrit. At low supersaturation, the nucleation rate is small (roughly ≈Exp(-Const/log S), as shown in Appendix B). The limited amount of molecules in solution, however, limits the further growth of the formed nuclei. On the contrary, at high supersaturation, the nuclei concentration is high but the large amount of molecules in solution enables the formation of bigger aggregates. Summary of the Theoretical Findings. A brief list of the main theoretical predictions of the model is as follows. (a) Solid supported thin films built up by fiber-forming anisotropic molecules may show pancakelike supra-aggregates with a depression (hole) in the central region. The hole depth is linearly related to the fiber bending rigidity E, which, in turn, is proportional to the monomer-monomer stacking energy inside the fiber.

Experiments To experimentally investigate the supra-aggregation phenomena of a model fiber-forming anisotropic molecule, we chose the disc-shaped R123, since it has been found to self-assemble in thermodynamically favored fiberlike structures. As follows, a SFM study of R123 thin films deposited by spin coating is reported. Scanning Force Microscopy of R123 Thin Films. The SFM investigation of R123 spin coated thin films showed that their topology strongly depends on the mechanism of formation which, in turn, depends on the interplay of several factors including speed transfer, molecular concentration in solution, and substrate physicochemical properties. First, we observed that high concentrations and low speeds lead, as expected, to increased film roughness and thickness. A submonolayer coverage is typically observed for concentrations e8.4 × 10-4 M. We confine the discussion to this last condition, since it enables the early aggregation stages where individual supra-aggregates are distinguishable to be investigated. Let us first report on experiments performed at the highest growth speed which corresponds to a rounding spin coating plate speed of 4000 rpm (rounds per minutes). By using a concentration in solution of 8.4 × 10-5 M, the SFM data showed that R123 can aggregate both under globular and fiberlike structures. Figure 5 compares the topography of R123 onto three different substrates: mica (a), HOPG (b), and SiH (c). Globular and fiberlike structures are present on mica. The height and lateral dimension of the fibers in direct contact with the substrate measure about 1 nm and 15-20 nm, respectively. The coexistence of bumps and elongated structures is observed on graphite and SiH, as well. In the case of SiH substrates, very large elongated aggregates consisting of the helical coil of individual long fibers are observed. These aggregates extend up to several micrometers. By increasing the concentration up to 8.4 × 10-4 M at constant speed, R123 was found to form a submonolayer system including broad regions with the characteristic shape of a cellular network.



Figure 5. SFM images of R123 transferred by spin coating at 4000 rpm and at a concentration in solution of 8.4 × 10-5 M on (a) mica, (b) HOPG, and (c) hydrogenated silicon.

Figure 7. SFM image of R123 transferred on mica by spin coating at 500 rpm and at a concentration in solution of 8.4 × 10-4 M.

Figure 6. SFM image taken after a slight thermal annealing of R123 transferred on mica by spin coating at 4000 rpm and at a concentration in solution of 8.4 × 10-4 M.

Figure 6 shows the above sample after a slight thermal annealing process (80 °C for 30 min). This process allows for the formation of a more defined network. Note that the network may be represented as being formed by adjacent polygonal features having nanoscopic fibers as sides. The average height of the network sides is about 1 nm. Let us now focus on the film features observed at lower speeds (500 rpm). As in the case reported above, R123 concentrations of 8.4 × 10-5 M generally lead to fiberlike and globular aggregates of nanoscopic dimension. By increasing the R123 concentration in solution up to 8.4 × 10-4 M, a large amount of 3D aggregates (pancakes) were obtained (Figure 7). About 20% of the whole aggregates show a characteristic hole in the central region. The average diameter of these last structures measures 333 ( 67 nm, whereas the average diameter of the holes is 96 ( 58 nm. Moreover, the average rim height of the holed structures is of the order of some R123 diameter (4.4 ( 0.7 nm). As the compact bumps are concerned, they are smaller, with the average height and diameter being 5.7 ( 1.4 and 183 ( 45 nm, respectively. It is also possible to observe a few individual globular and elongated structures of molecular thickness (≈1 nm) still attached to the edge of the larger aggregates. Figure 8 compares two restricted regions showing aggregates formed respectively at concentrations of 8.4 × 10-5 and 8.4 × 10-4 M. At the lowest concentration, a number of systems consist of a few wrapping-up elongated structures, showing an empty space in the central region (Figure 8a). On the other side, the image obtained at the highest concentration (Figure 8b) shows two compact bumps together with a holed aggregate. On

the right-hand side of Figure 8, the section analyses obtained along the lines marked in the images are reported. The effect of molecular saturation at constant speed (500 rpm) is summarized in the state diagram of Figure 9 where we report the percentage of holed supra-aggregates as a function of R123 concentration in solution. This diagram shows that in order to find net holed structures the R123 concentration has to be chosen in the range 10-4-10-3 M. Concentrations exceeding 10-3 M typically lead to thick films where the eventual holed structures can no longer be probed. This could be due to the fact that in thick films the empty spaces are likely filled in by incoming molecules. Discussion The SFM investigation of R123 spin coated thin films showed a rich class of morphological structures, with their shape being connected to the experimental conditions used. As an important feature, it has been observed that R123 may form thermodynamically favored fiberlike structures. The observed dimensional data of the fibers are in agreement with a picture in which the discotic R123 molecules linearly stack with each other, as sketched in the pictorial enlargement of Figure 1. Indeed, the observed height of the fibers (about 1 nm) closely corresponds to the theoretical height of a R123 molecule (see Scheme 1) with its plane orthogonal with respect to the surface. The lateral size of the fibers (15-20 nm) appears larger than the diameter of a single R123 molecule, but it is still in agreement with the above structural model as far as one considers the well-known tip-broadening artifact in SFM. Indeed, according to current models,15 the measured lateral size of R123 fibers is consistent with a broadening induced by a SFM tip of 10-20 nm radius rolling over a real cylindrical fiber 1 nm in diameter. By guessing an intermolecular distance of about 3-4 Å typical for π-π conjugated disklike systems,16 our experiments showed that the aggregation, at least on SiH, can be so extensive (the fiber length was on the micrometric scale) to involve thousands of molecules. On mica and HOPG, linear aggregation has been observed on a smaller length scale (typically on the nanometric scale), but it still would be so extensive to involve hundreds of molecules. In the absence of any fiber-fiber interaction, the length of the aggregates mainly reflects the strength of the intermolecular interactions within the fiber.17



Figure 8. SFM images of restricted regions of R123 transferred on mica by spin coating at 500 rpm (solution concentrations of (a) 8.4 × 10-5 M and (b) 8.4 × 10-4 M). On the right-hand side, we report section analyses along the lines marked in parts a and b, respectively.

Figure 9. Percentage of ring-shaped aggregates vs R123 molar concentration: in region A, there are essentially bumps and fiberlike structures (Figure 5); compact and holed aggregates coexist in region B (Figure 7); in region C, a 3D thick film grows.

In addition to fiberlike systems, SFM showed that R123 under submonolayer conditions gives rise to aggregation patterns which depend on the growth speed. Thus, at the highest speed, the film grows from globular structures at low concentrations (8.4 × 10-5 M) to cellular networks at higher concentrations (8.4 × 10-4 M). This behavior evokes processes induced by spinodal dewetting.18-21 In contrast, at the lowest speed (Figure 7), the first stages of the film growth are mainly characterized by individual compact and holed supra-aggregates with any interconnection. The above findings indicate that the growth speed is a critical problem in defining the mechanism of accretion. As a consequence, a balance between thermodynamically and kinetically controlled processes has to be considered. The model proposed in this paper can be generally applied to such a fiber-forming system, allowing for a prediction of supra-aggregate shapes also under out-of-equilibrium conditions. Experimentally, other systems already reported in the literature showed features similar to those observed for R123. Thus, holed supra-aggregates have been obtained in monolayers by the assembly of supra-molecular fibers of quercetin-palmitate tangentially wrapped in disklike systems (as sketched in Figure 2a) rather than in compact structures.22 Another interesting surface showing a rich class of ring-shaped structures (rings,

wheels, volcano-like) was observed by using a different anisotropic molecule (a Pt-porphyrin derivative).23,24 The formation of holed systems was explained by these authors according to the following scenario: Under evaporation, the film thickness decreases and becomes unstable (spinodal dewetting). This process leads to the formation of droplets at the substrate surface which further reduce their size because of the steady solvent evaporation. Droplets are pinned by surface defects shrinking under volume reduction with a fixed droplet-substrate surface area. The curvaturedependent evaporation flux increases in the radial direction toward the droplet edges where it diverges. To accomplish this, liquid flows from the center of the 3D droplet to its edge with a velocity diverging at the edge. This kind of radial mass transfer from the center to the droplet periphery eventually leads to holed structures after complete solvent evaporation.25,26 At variance with the above picture, the theory presented here does not require any defect induced pinning of the droplets. This is more consistent with our experiments that were mostly performed on freshly cleaved mica consisting of a uniform atomically flat oxygen surface layer. In addition, our theory points out the anisotropic nature of the interactions among nonsymmetrical (discotic) molecules which lead to fibers. We believe that these factors can more likely justify a nanoscale structuring of strongly anisotropic molecules than a hydrodynamics-based model23-26 which should be more consistent with micrometric features. Several features of our theory are reproduced by SFM observations on R123 molecularly thin films: (a) The theory predicts that discotic molecules first aggregate in fiberlike structures which then may tangentially grow to form perforated nuclei (see Figure 2a). SFM investigation of samples prepared at low R123 concentration and low evaporation speed (Figure 8a) show the formation of perforated nuclei consisting of a few wrapping-up fiberlike systems. Once the nuclei are formed, they act as a template for the growth of holed supraaggregates. These may grow either from tangential assembly



of preformed fibers (as sketched in Figure 2a) or from monomers sticking on the existing nucleus. (b) As predicted by the theory (Figure 3b), our SFM data confirm that compact structures are favored for small aggregates while holed structures are likely for the larger ones (Figure 7). Compact structures would result from a radial fiber growth with strong fiber-fiber attractive forces. (c) Holed supra-aggregates are mainly observed at high concentration (Figure 9) where the aggregate growth is faster.

On the other hand, at large distances from the center, the film deformation behaves as

η9 80 X.1 Therefore, a good expression for η valid over the whole range of X is obtained by matching the formulas found at X , 1 and X . 1 through the interpolation function

η≈-

Conclusions Molecules with anisotropic lateral interactions may aggregate in thermodynamically favored fibers. Once fibers are formed, the topology of the growing film made up of interacting fibers depends on the fibers elastic properties in addition to the solvent-film and substrate-film interfacial free energies. The interplay between the above contributions may lead to differently shaped supra-aggregates such as the compact (radial growth mechanism) or the holed (tangential growth) ones. The application of this model to R123 can explain several experimental findings and gives some important insights on the modulation of the film features. Other fiber-forming systems already studied in the literature showed similar features. The above concept is proposed as an alternative to conventional dewetting models as far as one considers the organization of 1D supramolecular systems at interfaces. Acknowledgment. Consorzio Catania Ricerche is acknowledged for the hospitality in its laboratory and for the use of the surface preparation and characterization tools. Giuseppe Francesco Indelli is acknowledged for technical assistance. Both authors are grateful to MIUR (fondi di Ateneo, ex 60%) for partial financial support.

8 π 1 - π 2 + O(Λ-4)) ∫0∞K0(X)X2X+dXΛ2 9 Λ.1 4Λ2( 6Λ 2

eventually we obtain the approximate eq 14 of the main text. Appendix B The nonequilibrium energy of a solution in contact with a growing pancake of volume V is proportional to the difference between the chemical potentials in solution and in the growing film: ∆G ) (µ - µ0)V. The chemical potential µ is given by eq 18a, while in solution it is proportional to the concentration c through the standard relationship: µ0 ) µ0° + kT log c. It is useful to introduce the saturation concentration c∞ defined as the concentration at which the macroscopic aggregate is in equilibrium with the solution. Such a concentration is calculated by setting V f ∞ in eq 18a. Simple rearrangement enables us to write ∆G ) (µ - µ0)V ) -V(kT log S) + V1/2σ(Γ + ∆Γ), where we introduced the supersaturation S ≡ c/c∞. It is trivial to see that the energy ∆G has a maximum at

and of the asymptotic formulas14

()

eX I0(X) 9 8 8 , K0(X) 9 X.1 x2πX X.1 yields

1 η ≈ -B1 + B2X2 2 where up to O(e-λR)

∫0∞K0(X)X2X+dXΛ2

and

(

x

π -X ‚e 2X

(A1)

Xf0

1 1 B2 ≡ C 2 4 Λ

π 3Γ′′ 1/2 Γ + ∆Γ 2 1 4a γ kT log2 S

( )(

)

The energy at V ) V* yields the nucleation barrier:

π 3Γ′′ 1/2Γ + ∆Γ 1 4 γ kT log S

( )

Therefore, the associated nucleation rate behaves as ≈exp(∆G*/kT). It is worth mentioning that these formulas are valid for quite large volumes V*; for small volumes, they give only a rough estimate.

1 1 8 1 + X2, K0(X) 9 8 -log X , I0(X) 9 Xf0 Xf0 4 2

B1 ≡ C

V ) V* )

∆G* )

∂I0(X) ∂K0(X) 1 K0(X) I (X) ) ∂X ∂X 0 X

(A2)

where P2 ) 2B12/B2 and Q2 ) 2B1/B2. Using the asymptotic formula

Appendix A The maximum deformation of a thin film surface occurs near r ≈ 0. Power series expansion of the deformation profile η(X) given by eq 13 near X ) λr ≈ 0 together with the use of the identity14

P2 Q + X2 2

)

∫0∞K0(X)X2X+dXΛ2

References and Notes (1) Niemeyer, C.; Adler, M.; Pignataro, B.; Lenhert, S.; Gao, S.; Chi, L. F.; Fuchs, H.; Blohm, D. Nucleic Acids Res. 1999, 27, 4553. (2) Schwartz, D. H. Surf. Sci. Rep. 1997, 27, 241. (3) Zhongcheng, Mu; Zhiqiang, W.; Xi, Z.; Kaiqi, Y.; Yue, W. J. Phys. Chem. B 2004, 108, 19955. (4) Pignataro, B.; Janshoff, A.; Steinem, C.; Fuchs, H. Biophys. J. 2000, 78, 487. (5) Gleiche, M.; Chi, L. F.; Fuchs, H. Nature 2000, 403, 173. (6) Chi, L. F.; Jacobi, S.; Anczykowski, B.; Overs, M.; Sha¨ferand, H. J.; Fuchs, H. AdV. Mater. 2000, 12, 25. (7) Science_special_issue, in ‘Supramolecular chemistry and selfassembly’, 2002. (8) Hoeben, F. J. M.; Jonkheijm, P.; Meijer, E. W.; Schenning, A. P. Chem. ReV. 2005, 105, 1491. (9) Sortino, S.; Petralia, S.; Pignataro, B.; Marletta, G.; Conoci, S.; Valli, L. New J. Chem. 2003, 27, 615. (10) Nitzan, A.; Ratner, M. A. Science 2003, 300, 1384. (11) De Gennes, P. G. ReV. Mod. Phys. 1985, 57, 827. (12) Mahanty, J.; Ninham, B. W. Dispersion Forces; Academic Press: London, 1976.

2124 J. Phys. Chem. B, Vol. 110, No. 5, 2006 (13) Landau, L. D.; Lifsits, E. M. Theory of Elasticity; Pergamon Press: New York, 1985. (14) Gradshteyn, I. S.; Ryzhik, I. M. Table of Integrals, Series and Products; Academic Press: London, 1980. (15) Garcia, V. J.; Martinez, L.; Briceno-Valero, J. M.; Shilling, C. M. Probe Microsc. 1997, 1. (16) Simpson, C. D.; Wu, J. S.; Watson, M. D.; Mu¨llen, V. J. Mater. Chem. 2004, 14, 494. (17) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: San Diego, CA, 1995. (18) Gu, X.; Raghavan, D.; Douglas, J. F.; Karim, A. J. Polym. Sci., Part B: Polym. Phys. 2002, 40, 2825.

Raudino and Pignataro (19) Rabani, E.; Reichman, D. R.; Geissler, P. L.; Brus, L. E. Nature 2003, 426, 271. (20) Herminghaus, S.; Jacobs, K.; Mecke, K.; Bischof, J.; Fery, A.; IbnElhaj, M.; Schlagowski, S. Science 1998, 282, 916. (21) Kargupta, K.; Konnur, R.; Sharma, A. Langmuir 2001, 17, 1294. (22) Pignataro, B.; Sardone, L.; Marletta, G. Langmuir 2003, 19, 5912. (23) Latterini, L.; Blossey, R.; Hofkens, J.; Vanoppen, P.; De Schryver, F. C.; Rowan, A. E.; Nolte, R. J. M. Langmuir 1999, 15, 3582. (24) Blossey, R.; Lorke, A. Phys. ReV. E 2002, 65, 021603/1. (25) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827. (26) Parisse, F.; Allain, C. J. Phys. II 1996, 6, 1111.

Supra-aggregates of Fiber-Forming Anisotropic Molecules - The

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