Thermosolutal Self-Organization of Supramolecular Polymers into

Jan 21, 2011 - Tomas Marangoni,‡ Stefano A. Mezzasalma,*,‡ Anna Llanes-Pallas,‡ K. .... (25) Mohnani, S.; Llanes-Pallas, A.; Bonifazi, D. Pure A...
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Thermosolutal Self-Organization of Supramolecular Polymers into Nanocraters† )

Tomas Marangoni,‡ Stefano A. Mezzasalma,*,‡ Anna Llanes-Pallas,‡ K. Yoosaf,§ Nicola Armaroli,*,§ and Davide Bonifazi*,‡, ‡

)

Dipartimento di Scienze Farmaceutiche and UdR INSTM, Universit a di Trieste, Piazzale Europa 1, 34127 Trieste, Italy, §Molecular Photoscience Group, Istituto per la Sintesi Organica e la Fotoreattivit a, Consiglio Nazionale delle Ricerche (CNR-ISOF) Via Gobetti 101, 40129 Bologna, Italy, and Department of Chemistry, University of Namur, Rue de Bruxelles 61, 5000 Namur, Belgium Received October 29, 2010. Revised Manuscript Received December 21, 2010 The ability of two complementary molecular modules bearing H-bonding uracilic and 2,6-(diacetylamino)pyridyl moieties to self-assemble and self-organize into submicrometer morphologies has been investigated by means of spectroscopic, thermogravimetric, and microscopic methods. Using uracilic 3N-BOC-protected modules, it has been possible to thermally trigger the self-assembly/self-organization process of the two molecular modules, inducing the formation of objects on a mica surface that exhibit crater-like morphology and a very homogeneous size distribution. Confirmation of the presence of the hydrogen-bonding-driven self-assembly/self-organization process in solution was obtained by variable-temperature (VT) steady-state UV-vis absorption and emission measurements. The variation of the geometric and spatial features of the morphologies was monitored at different T by means of atomic force microscopy (AFM) and was interpreted by a nonequilibrium diffusion model for two chemical species in solution. The formation of nanostructures turned out to be affected by the solid substrate (molecular interactions at a solid-liquid interface), by the matter-momentum transport in solution (solute diffusivity D0 and solvent kinematic viscosity ν), and the thermally dependent cleavage reaction of the BOC functions (T-dependent differential weight loss, θ = θ(Τ)) in a T interval extrapolated to ∼60 K. A scaling function, f = f (νD0, ν/D0, θ), relying on the onset condition of a concentration-driven thermosolutal instability has been established to simulate the T-dependent behavior of the structural dimension (i.e., height and radius) of the self-organized nanostructures as Æhæ ≈ f (T) and Æræ ≈ 1/f (T).

Introduction In the last few decades, materials possessing well-defined structural properties on the nanoscale and microscale have shown to be extremely promising for applications in several fields such as microelectronics,1-3 biology,4 and solar cells fabrication.5 This is due to the fact that the manufacture of organic-based devices, for any kind of application, requires the development of reproducible protocols to engineer materials featuring precise structural properties. To improve control on the nanoscale level, both bottom-up and top-down approaches have been intensively exploited to date.6,7 Although nowadays the second is still predominant at applicative levels, Moore’s law foresees its final limit in a few years.8 Among the various bottom-up approaches, † Part of the Supramolecular Chemistry at Interfaces special issue. *Corresponding authors. E-mail: [email protected], armaroli@isof. cnr.it, [email protected].

(1) Coropceanu, V.; Cornil, J.; da Silva Filho, D. A.; Olivier, Y.; Silbey, R.; Bredas, J. L. Chem. Rev. 2007, 107, 926. (2) Kim, D. H.; Lee, B.-L.; Moon, H.; Kang, H. M.; Jeong, E. J; Park, J.; Han, K.-M.; Lee, S.; Yoo, B. W.; Koo, B. W.; Kim, J. Y.; Lee, W. H.; Cho, K.; Becerril, H. A.; Bao, Z. J. Am. Chem. Soc. 2009, 131, 6124. (3) Forrest, S. R. Nature 2004, 428, 911. (4) Sarikaya, M.; Tamerler, C.; Jen, A. K. Y.; Schulten, K.; Baneyx, F. Nat. Mater. 2003, 2, 577. (5) G€unes, S.; Neugebauer, H.; Sariciftci, N. S. Chem. Rev. 2007, 107, 1324. (6) Balzani, V.; Credi, A.; Venturi, M. Chem.;Eur. J. 2002, 8, 5524. (7) Smay, J. E.; Gratson, G.; Shepperd, R. Adv. Mater. 2002, 14, 1279. (8) Moore, G. Electronics 1965, 38, 114. (9) Bleger, D.; Kreher, D.; Mathevet, F.; Attias, A. J.; Schull, G.; Huard, A.; Douillard, L.; Fiorini-Debuischert, C.; Charra, F. Angew. Chem., Int. Ed. 2007, 46, 7404. (10) Kudernac, T.; Lei, S.; Elemans, J. A. A. W.; De Feyter, S. Chem. Soc. Rev. 2009, 38, 402.

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the exploitation of non-covalent interactions,9-11 capable of inducing the selective and controlled association of molecular components leading to aggregates of defined structural properties, has turned out to be extremely promising. In this field, the key concepts of molecular recognition through noncovalent interactions (i.e., supramolecular chemistry) have been very effective tools for the preparation of nanostructured organic materials.12-27 The exploitation of highly directional noncovalent interactions such as hydrogen bonds has been employed to induce (11) Puigmartı´ -Luis, J.; Minoia, A.; Ujii, H.; Rovira, C.; Cornil, J.; De Feyter, S.; Lazzaroni, R.; Amabilino, D. B. J. Am. Chem. Soc. 2006, 128, 12602. (12) Lehn, J. M. Supramolecular Chemistry: Concepts and Perspectives; WileyVCH: Weinheim, Germany, 1995. (13) Hoeben, F. J. M.; Jonkheijm, P.; Meijer, E. W.; Schenning, A. Chem. Rev. 2005, 105, 1491. (14) Davis, J.; Spada, G. Chem. Soc. Rev. 2007, 36, 296. (15) Ajayaghosh, A.; Praveen, V. K. Acc. Chem. Res. 2007, 40, 644. (16) Ajayaghosh, A.; Praveen, V. K.; Vijayakumar, C. Chem. Soc. Rev. 2008, 37, 109. (17) Palermo, V.; Samori, P. Angew. Chem., Int. Ed. 2007, 46, 4428. (18) Palermo, V.; Schwartz, E.; Finlayson, C. E.; Liscio, A.; Otten, M. B. J.; Trapani, S.; Mullen, K.; Beljonne, D.; Friend, R. H.; Nolte, R. J. M.; Rowan, A. E.; Samori, P. Adv. Mater. 2010, E81. (19) Elemans, J. A. A. W.; Hameren, R. v.; Nolte, R. J. M.; Rowan, A. E. Adv. Mater. 2006, 1251. (20) Elemans, J. A. A. W.; Rowan, A. E.; Nolte, R. J. M. J. Mater. Chem. 2003, 2661. (21) Nakanishi, T. Chem. Commun. 2010, 20, 3425. (22) Asanuma, T.; Li, H.; Nakanishi, T.; Moehwald, H. Chem.;Eur. J. 2010, 16, 9330. (23) Guldi, D. M.; Zerbetto, F.; Georgakilas, V.; Prato, M. Acc. Chem. Res. 2005, 38, 871. (24) Bonifazi, D.; Mohnani, S.; Llanes-Pallas, A. Chem.;Eur. J. 2009, 15, 7004. (25) Mohnani, S.; Llanes-Pallas, A.; Bonifazi, D. Pure Appl. Chem. 2010, 10, 917.

Published on Web 01/21/2011

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Marangoni et al. Scheme 1. Schematic Representation of the Thermally Induced Self-Assembly Process on the Molecular Levela

a After the thermally activated cleavage of the BOC groups, tetratopic uracyl-bearing molecular module 1a undergoes self-assembly with ditopic linear module 2, giving rise to H-bonded assemblies [1a 3 2]n.

the formation of supramolecular polymers, macromolecular structures in which single monomers are held together through reversible noncovalent interactions.28-30 Our work on selfassembled and self-organized microstructures started with the preparation of vesicular nanostructures under temperature and solvent polarity control (i.e., through solvophobic/solvophilic interactions that are established in binary or ternary supramolecular adducts) by means of supramolecular ensembles formed through the recognition of complementary31-33 monouracyl and bis-2,6-di(acetylamino)pyridyl H-bonding moieties.34 Along these lines, we also prepared a library of nine chromophoric acetylenic scaffolds also peripherally equipped with 2,6-di(acetylamino)pyridine or uracyl-type terminal fragments that, by taking advantage of self-assembly and self-organization, drove the formation of nanostructures of different shapes and sizes such as nanoparticles, nanovesicles, nanofibers, and nanorods, also with helicoidal or circular variants.34 In parallel, a thermally activated cleavage reaction leading to self-assembly has also been exploited with newly (26) Yagai, S.; Manesh, S.; Kikkawa, Y.; Unoike, K.; Karatsu, T.; Kitamura, A.; Ajayaghosh, A. Angew. Chem., Int. Ed. 2008, 47, 4691. (27) Yagai, S.; Kubota, S.; Saito, H.; Unoike, K.; Karatsu, T.; Kitamura, A.; Ajayaghosh, A.; Kanesato, M.; Kikkawa, Y. J. Am. Chem. Soc. 2009, 131, 5408. (28) Brunsveld, L.; Folmer, B. J. B.; Meijer, E. W.; Sijbesma, R. P. Chem. Rev. 2001, 101, 4071. (29) de Greef, T. F. A.; Meijer, E. W. Nature 2008, 453, 171. (30) Wang, F.; Han, C.; He, C.; Zhou, Q.; Zhang, J.; Wang, C.; Li, N.; Huang, F. J. Am. Chem. Soc. 2008, 130, 11254. Wang, F.; Zhang, J. Q.; Ding, X.; Dong, S. Y.; Liu, M.; Zheng, B.; Li, S. J.; Wu, L.; Yu, Y. H.; Gibson, H. W.; Huang, F. H. Angew. Chem., Int. Ed. 2010, 49, 1090 . (31) Prins, L. J.; Reinhoudt, D. N.; Timmerman, P. Angew. Chem., Int. Ed. 2001, 40, 2382. (32) Brienne, M. J.; Gabard, J.; Lehn, J. M.; Stibor, I. J. Chem. Soc., Chem. Commun. 1989, 1868. (33) Shi, X.; Barkigia, K. M.; Fajer, J.; Drain, C. M. J. Org. Chem. 2001, 66, 6513. (34) Yoosaf, K.; Belbakra, A.; Armaroli, N.; Llanes-Pallas, A.; Marangoni, T.; Marega, R.; Botek, E.; Champagne, B.; Bonifazi, D. Chem.;Eur. J. 2011, DOI: 10.1002/chem.201002103.

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synthesized molecular modules exhibiting uracyl recognition sites protected with a tert-butyloxycarbonyl (BOC) group.34 This strategy allowed us to obtain further control of the self-assembly/ self-organization process, obtaining ordered linear nanostructures or hollowed circular nanoobjects, by temperature control. In fact, the BOC group was easily and quantitatively removed upon heating35 and the molecules became more soluble and thus easier to process in organic solvents, which would otherwise be impossible for molecules with multiple uracyl residues. This was the starting point for the preparation as well as the spectroscopic and microscopic characterization of the thermally activated self-assembly/self-organization of novel BOC-protected tetratopic pyrene 1 and linear di(acetylamino)pyridine 2 reported in this work. Upon thermal heating,35 the four hydrogen-bonding-based recognition sites in the uracilic moieties of molecule 1 would be deprotected to yield 1a, which is capable of establishing complementary triple hydrogen-bonding interactions with the 2,6-(diacetylamino)pyridine (donor-acceptor-donor, DAD) sites (Scheme 1), thus seeding the controlled hierarchical organization of 1a and 2. In this way, the geometrically constrained association of the singlemolecular module produced nanostructures31-33 of extremely precise geometry, which resemble the shape of a crater. From a mechanistic point of view, the morphologies resulting from the self-assembly and self-organization processes at the molecular level on a substrate from colloidal, polymeric, surfactant or nanoparticle solutions can be a complex combination of a number of heterogeneous variables. When macromolecular systems are processed, the final patterns are generally influenced by several phenomena such as solvent dewetting and evaporation,36-38 (35) Rawal, V. H.; Cava, M. P. Tetrahedron Lett. 1985, 26, 6141. (36) Thiele, U.; Vancea, I.; Archer, A. J.; Robbins, M. J.; Frastia, L.; Stannard, A.; Pauliac-Vaujour, E.; Martin, C. P.; Blunt, M. O.; Moriarty, P. J. J. Phys.: Condens. Matter 2009, 21, 1. (37) Li, M.; Xu, S.; Kumacheva, E. Macromolecules 2000, 33, 4972. (38) Carvalho, A. J. F.; Pereira-da-Silva, M. A.; Faria, R. M. Eur. Phys. J. E 2006, 20, 309.

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Figure 1. Optimized geometrical structure of molecular modules 1 and 2 performed with semiempirical PM3 method as implemented within Spartan.

Rayleigh-Benard instabilities,39-41 Marangoni effects,41-43 and phase separations.44,45 Joint control of even a few of these variables remains a difficult task, especially at the nanoscale level. Thus, determining the actual experimental domain where defining and investigating their effects can raise discussions and debates.46,47 However, if some approximations are made, then there is room to gain novel theoretical insight into these mechanistic aspects. In this respect, de Gennes has recently described new instability mechanisms for evaporating polymer solutions.48,49 He concluded that, under certain conditions (e.g., for nonglassy polymeric films with low viscosity and no polymer adsorption at the free surface of the solution phase), concentration-gradient effects (e.g., surface or substrate forces) should predominate over Benard-Marangoni effects. The supramolecular assembly of functional organic molecules is a younger discipline with respect to covalent classical organic chemistry, but over the years, it has opened a substantial number of experimental and theoretical questions.50 One of the relevant issues to be tackled in the preparation of supramolecular nanomaterials is the establishment of quantitative criteria capable of combining the influences of chemical structures and spatialtemporal scales. Accordingly, formulating new theoretical models that would interpret and predict the protocol conditions at which specific structural and physical properties can be generated would be of utmost importance. Herein, we report a diffusive-like model where the geometrical properties of the thus-formed nanostructures turned out to be dependent on the concentration-driven instability. In particular, the proposed mechanism shows how the BOC-cleavage kinetics are intimately connected with the physical and chemical properties of both solutions and interfaces as the H-bonded polymer is formed.

Bayville Chemical Supply Company and cleaved immediately before use. TGA Analysis. Thermogravimetric analyses were carried out on a TGA Q500 series V6.3 Build 189 produced by TA Instruments. The relative data were elaborated using Universal Analysis V4.1D software. Procedure for Compound 1. To perform the TGA analysis, 0.42 mg of compound were analyzed on a platinum pan under nitrogen flow at 60 mL/min using the protocol here reported: (a) equilibration of the sample at 35 C for 10 min, (b) temperature ramp of 2.00 C/min until reaching 300 C, and (c) equilibration of the sample at 50 C. Procedure for Compound 1a. To perform the TGA analysis, 1.47 mg of the compound were analyzed on a platinum pan under nitrogen flow at 60 mL/min using the protocol reported here: (a) equilibration of the sample at 45 C for 10 min, b) temperature ramp of 5.00 C/min until reaching 300 C, and (d) equilibration of the sample at 50 C. UV-Vis Absorption and Emission Measurements. The solutions for spectroscopic studies were prepared by injecting certain microliter quantities of 1 in ortho-dichlorobenzene (oDCB) and 2 in THF into 2.0 mL of an o-DCB solution. Electronic absorption and emission measurements were carried out, respectively, on a Lambda 950 UV/vis/NIR spectrophotometer (Perkin-Elmer) and on an Edinburgh FLS920 spectrofluorimeter (continuous 450 W Xe lamp) equipped with a Peltier-cooled Hamamatsu R928 photomultiplier tube (185850 nm). The temperature of the solutions was varied with a HAAKE F3-C digital heated/refrigerated silicone oil bath (Haake Mess-Technik GmbH u.Co., Germany), which can be manually connected to a cuvette holder and controlled externally. All of the solvents (THF and o-DCB) are spectrophotometric-grade Carlo Erba (99.8%) and were used as received. Tapping-Mode (TM) AFM Measurements. TM-AFM of the mica substrates was carried out on air at 298 K using a Nanoscope V (Digital Instruments Metrology Group, model MMAFMLN). The tips used in all measurements were phosphorus-doped silicon cantilevers (T = 20-80 mm, L = 115-135 mm, fo = 200-400 kHz, k = 20-80 N m-1, Veeco) at a resonance frequency of ca. 300 kHz. The collected images were then analyzed with WsXm 4.0 software (Nanotec Electronica S. L.) and with Gwyddion (free and open source software as downloaded from http://gwyddion.net/) to acquire the cross-sectional values of nanoassemblies and processed 3D images. Preparation of the Samples for AFM Analysis. Twenty microliters of a solution of molecules 1 and 2 (1:1) in CH2Cl2/ o-xylene (9:1) at a concentration of 0.014 mM were drop cast onto freshly cleaved mica surfaces and heated at the respective temperature (Supporting Information S5) for 15 min under an Ar atmosphere. Then the samples were dried under vacuum for 10 min to ensure the complete removal of the residual solvent.

Experimental Section General Materials. Chemicals were purchased from Aldrich, Fluka, and Riedel and used as received. Mica was purchased from (39) Reiter, G. Phys. Rev. Lett. 1992, 68, 75. (40) Maeda, H. Langmuir 2000, 16, 9977. (41) Gonuguntla, M.; Sharma, A. Langmuir 2004, 20, 3456. (42) Weh, I. J. Colloid Interface Sci. 2001, 235, 210. (43) Karthaus, O.; Grasjo, I.; Maruyama, N.; Shimomura, M. Thin Solid Films 1998, 327, 829. (44) Van Dijk, M. A.; Van der Berg, R. Macromolecules 1998, 28, 6773. (45) Kim, G.; Libera, M. Macromolecules 1998, 31, 2569. (46) Bormashenko, E.; Balter, S.; Pogreb, R.; Bormashenko, Y.; Gendelman, O.; Aurbach, D. J. Colloid Interface Sci. 2010, 343, 602. (47) Tsui, O. K. C.; Wang, Y. J.; Zhao, H.; Du, B. Eur. Phys. J. E 2003, 12, 417. (48) de Gennes, P. G. Eur. Phys. J. E 2001, 6, 421. (49) de Gennes, P. G. Eur. Phys. J. E 2002, 7, 31. (50) Gomar-Nadal, E.; Puigmartı´ -Luis, J.; Amabilino, D. B. Chem. Soc. Rev. 2008, 37, 490.

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Results and Discussion Synthesis and Spectroscopic and Microscopic Characterizations. The synthesis of molecules 1 and 2 is reported in the Supporting Information following the experimental protocols previously developed by us.34,51 To characterize the thermal deprotection process needed for the self-assembly of molecular modules 1 and 2, thermogravimetric analysis (TGA) of module 1 was carried out first (Figure 2a, black curve). In a typical experiment, a known amount of compound was exposed, under inert N2 flow, to a variation of T ranging from 50 to 300 C. The total weight loss (23.8%) was in good agreement (51) Llanes-Pallas, A.; Palma, C. A.; Piot, L.; Belbakra, A.; Listorti, A.; Prato, M.; Samori, P.; Armaroli, N.; Bonifazi, D. J. Am. Chem. Soc. 2009, 131, 509.

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Figure 2. TGA profiles. (a) Combined T-dependent weight-loss profile for molecules 1 (black curve) and 1a (red curve). (b) Combined derivatives of the weight-loss curves for molecules 1 and 1a (black and red curves, respectively) showing a maximum peak centered at 130.8 C and no meaningful variations for 1a.

with the theoretical one calculated for the loss of all four BOC groups (27.0%). From the weight loss of molecule 1, it was possible to elaborate the first derivative curve presenting a maximum peak at 130.8 C (Figure 2b, black curve); this can be considered to be the average T at which the pyrolysis of the BOC group occurs at the highest speed. To obtain information about the effective T range over which self-assembly can occur without destroying the deprotected pyrenyl module, TGA analysis of molecule 1a was also performed over the same T interval. The TGA plot (Figure 2a, red curve) first showed a “plateau” region (from 50 to 180 C) in which the module can be considered to be thermally stable because of the absence of any significant change in its weight (weight loss 0. We remind the reader that the values of Rc for mechanically rigid-free and rigid-rigid boundaries would simply increase by a proportionality factors of roughly ∼2 and ∼3, respectively. In deriving eq 12, we used Dh , D0, implying that δh ≈ - vQ/D0 < 0. In spite of being emphasized here, this approximation conforms to the experimental observations for which the cleavage of the BOC group was revealed to alter the chemical and diffusion properties of pyrenyl module 1 radically. In our view, whenever a solute molecule differentiates into phase h and takes part in the self-assembly dynamics, it will obviously reduce its contribution to the molecular diffusion in solution.48 Note again that for the instability onset to be reached we need a distribution of solute molecules to be settled away from a chemically affine substrate, or Æbæσ < 0. This constraint will always hold here, where Æfzæ < 0 and Æbæ < 0, but would also apply to a reverted experimental setting (for instance, the dropwise addition of the solution onto the substrate surface). Naturally, a thorough analysis of instability dynamics or conditions falls outside the scope of this article. A numerical check of the orders of magnitude implied by eq 12 is reported in Appendix III. We derive now an equation interpreting a rescaled experimental behavior such as Æhæ versus T, where the reduced quantity h ≈ hm/ÆHmæ ≈ hM/ÆHMæ accounts for the two heights rescaled to their maxima (ÆHMæ = 0.93 and 0.33 nm). The issue to be verified is to let the characteristic lengths in eq 12 scale correspondingly [hd3/ h∈ ≈ Æhæ2  vD0/(1 þ (vQ/D0)) where h∈ is the interaction length scale, see Appendix III] and deal with the T dependence implied Langmuir 2011, 27(4), 1513–1523

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by the Q-concentration ratio, the diffusion constant, and the kinematic viscosity. To avoid useless formal complications in the final results, we will use the simplest possible phenomenological trends, particularly ηD0  T (Stokes-Einstein) and thus ν/D0  T/D02, with D0  T exp(-ÆEDæ/kBT) where ÆEDæ denotes an apparent activation barrier. To deal with the last term, we have rewritten it as if it were driven by T fluctuations around each experimental value, Q = Δch/Δc ≈ (dch/dT)/(dc/dT). A thorough thermodynamic analysis of a macromolecular solution comprising both diffusible and nondiffusible components in a medium of negligible volume fluctuations is long since available. The equilibrium concentration, chemical potential, and T fluctuations would clearly depend on the second derivatives of the thermodynamic potential (for state variables T, V, and ck). Nonetheless, the cleavage reaction of the BOC protecting group arguably identifies an out-of-equilibrium process. At any rate, the Q numerator is still inaccessible by our measurements, but it can be settled to be a negative semiheuristic coefficient, rescaling the differential concentration (or weight) loss at the denominator. Accordingly, we will be allowed to use the TGA data for the BOC cleavage reaction in a best-fit form such as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi νD0 hhi  1 þ ½ν=ðD0 θÞ

ð13Þ

where θ(T) ≈ 1/Q reproduces the positively valued profile in Figure 2 and the overbar indicates that the viscosity and diffusivity were rescaled by two coefficients for their product (Λ) and their ratio (χ). The previous equation expresses in this way a convenient change of units. At first sight, imagining the variables on the right of eq 13 to be changed independently, any positive variation of them would increase the assembly’s efficiency. This still agrees with previous theoretical predictions, where the critical nanometer thickness turned out to increase by increasing cooperative diffusivity in polymer solutions. On examining Table 1 and taking into consideration eq 13, the dominant effect seems to be ascribed to the BOC-cleavage effect. We thus performed two interpolations, one devoid of Æhæ ≈ [Λ0 /(1 þ (χ0 /θ))]1/2 and another one provided with the correction originating from transport coefficients (eq 13). To exploit in the model equation the as-measured TGA data (Figure 1), it was necessary to avoid the usual spurious negative fluctuations that would compromise the square root definition in eq 13. We thereby gave in Figure 6 a representation of Æhæ2 = ÆΣæ versus T, where all numerical details are reported in the caption. As may be seen from the theoretical curves, the agreement is rather satisfactory, especially in the second case, where the T dependence of the phenomenological coefficients was known. The improved convergence toward the experimental behavior yields reasonable proof that, as the BOC-cleaving reaction starts (Scheme 1 and dashed line in Figure 6), the formation of the nanostructure turns out to be assisted by diffusive-like transport phenomena (solid line) in the solution. From a more quantitative point of view, reasonable extrapolations from eq 13 are Tm ≈ 91.7 C, TM ≈ 151.3 C, and a shift by only ∼1-2 C of the optimum value pointed out by the TGA profile (T* ≈ 133.5 C). Formally, this temperature fulfills the relation hv0 /vh2 = -(Dθh)/(Dθh), getting back to the maximum in Figure 2 upon hv0 = Dh0 = 0 (where the prime denotes the first T derivative). Analysis of the Average Radius. Turning our attention to the craters’ radius distribution, a useful remark must be considered. A simple phenomenological interplay, giving the first explanation for the generation of the hierarchized nanocraters, lies in the competition between the space and time scales of the self-assembled Langmuir 2011, 27(4), 1513–1523

molecular adduct 1a þ 2 in the bulk phase (from which the selfassembly arises) and at the solid-liquid interface (where it terminates). For a finitely extended hierarchical aggregate to form, it is necessary to make certain that the establishment of hydrogen-bonded recognition motifs will not indefinitely advance in the liquid phase and that the solute molecules will not have to collapse quickly onto the substrate. The occurrence of these limiting regimes should be carefully evaluated case by case, but in general, it always results from the balance between bulk and surface interactions, which ensures the growth of a nanostructure and the corresponding completion at the end of the process. The former scaling analysis is thus helpful in putting these considerations into a formula. We should simply start from eq 12 and express it through the relevant characteristic times that it involves. In fact, Rayleigh’s number can be rewritten as |Rhσ| = τvτd/τs2, where τv ≈ h2/v, τv ≈ h2/D0, and τs2 ≈ h/(γσ|ΔC|) indicate the viscous, diffusive, and interaction time scales. This means that the former stability criterion can be rearranged to   τv τd τd ð14Þ τs 2  0 1 þ Q τv Λ The viscosity and diffusivity in eq 13 are mapped to their characteristic times. Accordingly, because we reasonably expect ÆRæ  τs, the scaling relation to be adopted now reduces to hri 

1 hhi

ð15Þ

where r = R/ÆRmæ is rescaled to the minimum value found in the experiments (ÆRmæ = 14.8 nm). Equations 13 and 15 point out a joint geometric description of the mean (x, y) and z dimensions. Best fits for the radius, in fact, were built directly upon those for the height, and the final approximations were very satisfactory (Figure 7). Notably, the lowermost and uppermost temperatures correspond, in this model, to an infinite organization for Æræ f þ¥. Outside this region, for T e Tm or T g TM, Æræ would not be properly defined. Alternatives to this interpretation might be provided, for instance, by a bimodal radius distribution or an onset of nanostructure formation with a finite (x, y) size and zero height. Although the latter does not seem to be a sound theoretical hypothesis, the former is, to our experimental knowledge, even more implausible.63 To take a better look at this point, it is instructive to use eq 14 as the product of an intrinsic solution time ((τvτd)1/2) times a scale dilation factor, accounting for the available hydrogen bond sites.64 Nonetheless, a possibility remains that the dilation factor and diffusion time may increase together, with their effects overlapping to a certain extent. In principle, this might occur at T g TM, where a large number of BOC-cleavage reactions could lead to a chain distribution of large and less diffusible molecular weights (Mk) in solution (from polymer scaling theory,65 D0 ≈ ÆMæ-β with β > 0). If this were the case, then the (63) More reasonable candidates for a joint best fit could be Æhæ ≈ const þ f(T) and Æræ ≈ 1/(const’ þ f(T)), but there is no reason at present to modify either equations accordingly. (64) Understanding the limit behaviors pointed out by these quantities would require an analysis of the infinitesimal orders and orders of infinity in T. However, physically sufficient conditions for the process to be infinitely slow (Æræ f þ¥) are Q≈ 1/θ f þ¥(τd 6¼ 0þ), τd f þ¥(τd 6¼ 0þ and Q 6¼ 0þ), τd f þ¥(τd 6¼ 0þ), but it would be infinitely fast (Æræ f 0þ) for τd f 0þ(Q 6¼ ¥ or τv 6¼ ¥). Despite the fact that the last two conditions are hardly applicable here (v f 0þ, D0 f þ ¥), nanostructures should not form or be detectable under each of these circumstances. Between the first two conditions, we expect the left and right regions, outside the T width, to be mainly characterized by the term Q ≈ 1/θ (65) Mezzasalma, S. A. Macromolecules in Solution and Brownian Relativity; Elsevier/Academic Press: Amsterdam, 2008.

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characteristic (diffusion) time would be too long for the incipient molecules to organize into larger nanostructures.

Conclusions Two complementary molecular modules 1 and 2 have been synthesized, and their ability to self-assemble and self-organize upon thermal activation through the selective cleavage of the BOC protecting groups (as shown by TGA analysis) has been proven in solution and on surfaces through UV-vis spectroscopy and AFM microscopy. Specifically, AFM investigations showed the formation of hierarchical objects on mica surfaces that exhibit crater-like morphology and a very homogeneous size distribution. The general trend in the self-assembly/self-organization processes is ruled by the BOC cleavage reaction, the physical chemistry of which is likely to be fundamental at any level. In fact, the cleavage temperature, also indicated as T*, was revealed to affect other phenomena responsible for the formation of the unique hierarchical crater-like structures. The variation of the geometrical and spatial features of the morphologies as monitored by AFM imaging at different temperatures allowed us to elaborate on a theoretical thermodynamic model. In particular, it has been shown that the formation of nanostructures turned out to be affected by the matter-momentum transport in solution (solute diffusivity D0 and solvent kinematic viscosity ν) and the thermal-dependent cleavage reaction of the BOC functions (T-dependent differential weight loss, θ = θ(Τ)) in a T interval extrapolated to ∼60 K. A scaling function, f = f (νD0, ν/D0, θ), relying on the onset condition of a concentration-driven thermosolutal instability, has been very well established to simulate the T-dependent behaviors of the structural dimensions (i.e., height and radius) of the selforganized nanostructures as Æhæ ≈ f and Æræ ≈ 1/f (eqs 13 and 15). In general, the work reported here represents one of first efforts to interconnect experimental and theoretical prospects, the physics of macromolecular solutions, and the chemistry of supramolecular assemblies. Linking current macroscopic measurements to a chemical and physical analysis of hierarchical mechanisms on the nano- and microscale levels will allow the discovery of new paradigms for establishing the necessary experimental conditions for the programmable and controllable engineering of organic soft materials. Acknowledgment. This work was supported by the European Union through Marie-Curie Research Training Network “PRAIRIES” (contract MRTN-CT-2006-035810), Marie-Curie Initial Training Network “FINELUMEN” (grant agreement PITNGA-2008-215399), CNR (commessa PM.P04.010, MACOL), INSTM, the Belgian National Research Foundation (through FRFC contract nos. 2.4.625.08, 2.4.550.09, and 2.4.617.07.F and MIS no. F.4.505.10.F), the Loterie Nationale, Region Wallonne through the SOLWATT program (contract no. 850551), the TINTIN ARC project from the Belgian French Community (contract no. 09/14-023), and the University of Namur and the University of Trieste.

Appendix I Radius values in Table 1 originate from those first derived from AFM images that were then modified by an excluded volume correction. We modeled the tip as being spherical, of average radius ÆRtæ, and coming in contact with a rectangular nanopattern of mean height Æhsæ and apparent radius ÆRaæ. The actual value, ÆRæ, can be written accordingly as = -(2/-1)1/2. The overall error in it propagates by three sources of uncertainty, two of which were obtained as standard 1522 DOI: 10.1021/la104276y

deviations for hs and Ra and the third obtained as the maximum uncertainty (Rt = 20.5 ( 9.5 nm). In Table 1, the most severe evaluation |ΔR| e |ΔRa| þ ((2ÆRaæ/Æhsæ) - 1)1/2|Δhs| þ |ΔRt|((2ÆRaæ/Æhsæ) - 1)-1/2((|ΔRt|/ÆRtæ) þ (|Δhs|/Æhsæ)) was reported for each ÆRæ value. Systematic error sources, such as those related to the specific chemical system (mica and/or molecular assemblies), tapping technique, and tip-sample geometries, may clearly come into play.

Appendix II62 The equation system comprising eqs 9-11 is completed by the last vorticity relation ! Dr2 u ¼ νr4 u - γσrðzÞ 2 u Dt 

Dδch Dt

 ¼ hbh iu þ Dh r2 δch

  Dδc ¼ hbiu þ D0 r2 δc þ δDr2 δch Dt   Dwz ¼ νr2 wz Dt which comes from projecting the Navier-Stokes equation onto the z axis (wB = rot νB). This system should be solved with the boundary conditions of free and conductive surfaces (z = 0, hd): !   D2 u Dwz ¼ ¼ 0, δc ¼ δch ¼ 0 2 Dz Dz In a normal-mode analysis along the substrate plane, each perturbation is expanded in Fourier’s (x, y) double series with wave vector kB =(kx, ky) and angular frequency ωBk∈ C u kB ðrB, tÞ ¼ U kB ðzÞeiðkx xþky yÞþω Bk t δc kB ðrB, tÞ ¼ C kB ðzÞeiðkx xþky yÞþω Bk t δch Bk ðrB, tÞ ¼ Ch Bk ðzÞeiðkx xþky yÞþω Bk t wz Bk ðrB, tÞ ¼ Wz Bk ðzÞeiðkx xþky yÞþω Bk t in terms of which the starting system is recast into (kB indexes will be omitted for brevity) ωCh ¼ hbh iU þ Dh

ωC ¼ hbiU þ D0

! d2 2 - K Ch dz2

! ! d2 d2 2 2 - K C þ δD - K Ch dz2 dz2

! !2 d2 d2 2 2 ω -K U ¼ ν -K U þ σγK 2 C dz2 dz2 Langmuir 2011, 27(4), 1513–1523

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Article

! d2 2 ωWz ¼ ν - K Wz dz2

ðδh - 1Þ Rσ
/ |Æbhæ| = Æbæ/|Æbæ| = -1), boundary conditions Uh = (d2U)/ (dZ2) = 0, Ch = Ch= 0 (Z = 0, 1), and cross term δh = (δD)(Ph/Ph)(Δch/Δc)  νQ(δD)/D02, where Q  Δch/Δc. Note that, as being independent from the other equations, the vorticity relationship is henceforth omitted. It will be mandatory whenever a complete characterization of the solution is needed. In brief, by writing Uhn, Chn, and Chhn  sin(nπZ), with n integer number it turns out that U n  sinðnπZÞ C n  ðan, R 2 þPh sÞ - 1 ½1 - an, R 2 δh ðan, R 2 þPh sÞ - 1 sinðnπZÞ C hn  ðan, R 2 þPh sÞ - 1 sinðnπZÞ with an,R2  n2π2 þ R2 and the characteristic third-order polynomial (s∈C) "   1 þ Ph 1 1 1 1 2 2 an, R s þ an, R 4 þ þ þ s þ Ph Ph Ph Ph Ph Ph 

3

þ

 1 2 1 R Rσ an, R - 2 s þ fan, R 6 þ R2 Rσ ð1 - δh Þg ¼ 0 Ph Ph Ph

The application of Hurwitz’s criterion predicts that the system is asymptotically stable if and only if the conditions

Langmuir 2011, 27(4), 1513–1523

! a16, R Ph 2 P h δh - 1 Rσ < 2 R ð1 þ Ph ÞðPh þ Ph Þ Ph 1 þ Ph are fulfilled with -Rhσ > 0 (positive concentration gradient) and -δh > 0 (Q > 0 and δD < 0). Formally, they can be seen as the projection of the locus point of marginal stability for a thermosolutal problem with a zero temperature gradient (and a cross term in the matter flux). Here, min{a1,R6/R2} = 27π4/4 Rc (at Rc=π/(2)1/2) is the critical Rayleigh number and Ph, Ph .1, so we get -

d - R2 - P h s C h ¼ U dZ 2

a1, R 6 R2

Rσ j minfð1 - δh Þ - 1 , ðPh þ Ph ÞðPh - δh Þ - 1 g Rc

A simple rearrangement of the terms in parentheses shows the one on the left to be the smaller of the two because 1 < Phþ (1- (1/ δh))Ph, leading to the stability criterion in eq 12. A thorough analysis of the complete thermosolutal convection related to the present case can be found in ref 62 for a rarefied binary fluid undergoing nonlinear instabilities of the Soret type.

Appendix III A point to check is the consistency of the numerical orders of magnitude related to eq 12. To provide a reasonably simple estimation above the threshold, we develop it a little further upon neglecting D0 e 10-2v, which is typically valid for a liquid, and setting Q ≈ 1. In the semiheuristic relation h∈ = czM ∈ hd3/(RcF0D20), cz should approximate the interaction length scale introduced by the average energy per unit mass in σ ≈ ∈/h∈. We use the identity Æbæhd4 = Δc0hd3 and take |γΔc| ≈ csM/F0, where M (= M1 þ M2 = 2351.26 g/mol) is the sum of the molar weights of the two molecular modules. Finally, referring to triple hydrogen bond contacts (∈ ≈ 3EH/M) as the most stable interactions directing the molecular self-assembly in these nanostructures and using typical orders of magnitude of D0 ≈ 2  10-9 m2/s,66-68 hd ≈ 10 nm,49 F0 ≈ 1 g/cm3, and EH ≈ 15 kcal/mol69 would return exactly h∈ ≈ 1 nm. Height measurements in Table 1 range from ∼0.2 to 1.0 nm, fairly agreeing with this estimation. Supporting Information Available: Synthesis procedures, selected 1H and 13C NMR spectra, UV-vis measurements, TGA analysis, and TM-AFM measurements. This material is available free of charge via the Internet at http://pubs.acs.org. (66) Bird, R. B.; Stewart, W. E., Lightfoot, E. N., Transport Phenomena, 2nd ed.; John Wiley & Sons: New York, 2007. (67) Umesi, N. O.; Danner, R. P. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 662. (68) Pickup, S.; Blum, F. D.; Ford, W. T. J. Polym. Sci.: Polym. Chem. Ed. 1990, 28, 931. (69) Gilli, G.; Gilli, P. The Nature of the Hydrogen Bond: Outline of a Comprehensive Hydrogen Bond Theory; Oxford University Press: Oxford, U.K., 2009.

DOI: 10.1021/la104276y

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