Solution-growth kinetics and thermodynamics of nanoporous self-assembled molecular monolayersAmandine Bellec, Claire Arrigoni, Guillaume Schull, Ludovic Douillard, Céline Fiorini-Debuisschert et al. Citation: J. Chem. Phys. 134, 124702 (2011); doi: 10.1063/1.3569132 View online: http://dx.doi.org/10.1063/1.3569132 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v134/i12 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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THE JOURNAL OF CHEMICAL PHYSICS 134, 124702 (2011)

Solution-growth kinetics and thermodynamics of nanoporousself-assembled molecular monolayers

Amandine Bellec,1 Claire Arrigoni,1,2 Guillaume Schull,1,a) Ludovic Douillard,1

Céline Fiorini-Debuisschert,1 Fabrice Mathevet,2 David Kreher,2 André-Jean Attias,2

and Fabrice Charra1,b)

1Laboratoire de Nanophotonique, Service de Physique et Chimie des Surfaces et Interfaces, IRAMIS, CEA,F-91191 Gif-sur-Yvette Cedex, France2Laboratoire de Chimie des Polymères — UMR7610, Université Pierre et Marie Curie, 4 place Jussieu,case 185, F-75252 Paris Cedex 05, France

(Received 24 November 2010; accepted 1 March 2011; published online 23 March 2011)

The temperature and concentration dependences of the self-assembly onto graphite from solutionof a series of molecular building blocks able to form nanoporous structures are analyzed experi-mentally by in situ scanning tunneling microscopy. It is shown that the commonly observed coexis-tence of dense and nanoporous domains results from kinetic blockades rather than a thermodynamicequilibrium. The ripening can be favored by high densities of domain boundaries, which can be ob-tained by cooling the substrate before the nucleation and growth. Then ripening at higher-temperatureyields large defect-free domains of a single structure. This thermodynamically stable structure canbe either the dense or the nanoporous one, depending on the tecton concentration in the supernatantsolution. A sharp phase transition from dense to honeycomb structures is observed at a critical con-centration. This collective phenomenon is explained by introducing interactions between adsorbedmolecules in the thermodynamic description of the whole system. © 2011 American Institute ofPhysics. [doi:10.1063/1.3569132]

Self-assembled networks of adsorbed monomolecularlayers on atomically flat surfaces are focusing growing inter-est as model nanostructures resulting from a bottom-up fab-rication. The thermodynamic equilibrium structure of a self-assembled monolayer corresponds to a minimum of its Gibbsfree energy and thus results from a balance between inter-action energies and entropic effects.1 However, the structurewhich is actually formed may substantially differ from theequilibrium one because of kinetic limitations.2 The design ofthe molecular building blocks (the so-called tectons) sponta-neously forming specific predetermined arrangements as wellas their deposition conditions must thus account for all thesephenomena.

Organizations in the form of alveolate networks areof particular interest for possible applications.3 These so-called nanoporous networks expose well-defined voids whichconstitute supramolecular embeddings able to precisely im-mobilize and confine third-party molecules into highlyhomogeneous environments,4 to force their arrangement asunconventional clusters,5 or to adjust itself to its guest.6, 7

This yields new material concepts for organic electronics8

or nanolithography.9 Moreover, such assemblies enable theaddressing of individual host and guest molecules in scan-ning tunneling microscopy (STM).10 These studies permittedto evidence intriguing dynamic behaviors, including lateral

a)Present address: Institut de Physique et de Chimie de Strasbourg, Univer-sité Louis Pasteur, CNRS UMR 7504, 23 rue du Loess, 67034 Strasbourg,France.

b)Author to whom correspondence should be addressed. Electronic mail:fabrice.charra@cea.fr.

or rotational11 mobility inside a cavity and diffusion throughcavity-to-cavity hopping12 that strongly depends on the na-ture of the host and the guest. This paves the way towardfunctional surfaces acting as molecular sieves,13 chemical re-actors, catalysts, or artificial molecular receptors. For practi-cal applications of such processes, the systems need to be incontact with a solution and thus to operate at the liquid–solidinterface.

Yet nanoporous monolayers are inherently thermody-namically less stable than the dense ones: first, despite afew remarkable cases,14 weak supramolecular noncovalentbonds generally favor the aggregation into dense domains.Second, at the liquid–solid interface, where the solution be-haves as a reservoir of tectons, the adsorption energy fur-ther promotes denser packing. It has been revealed recentlythat tecton concentration in the solution affects the stabilityof nanoporous organizations, denser structures being prefer-entially formed at high concentrations, whereas dilution fa-vors porous structures.15–17 A theory based on the thermody-namic equilibrium between independent molecules has beenproposed.16 It predicts the systematic coexistence of denseand honeycomb domains in proportions which follow a lawof mass action. Although this theory explains the trends of thedependence in concentration,17 recent observations of transi-tions between structures of different surface densities showthat collective behaviors,18 entropic,19 and kinetic limitations2

may also play major roles.In this paper, we analyze experimentally the tempera-

ture and concentration dependences of the solution growthof a nanoporous monolayer for a coherent series of tec-tons. We demonstrate that the coexistence of dense and

0021-9606/2011/134(12)/124702/7/$30.00 © 2011 American Institute of Physics134, 124702-1

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124702-2 Bellec et al. J. Chem. Phys. 134, 124702 (2011)

FIG. 1. Current-mode (i.e., constant-height) STM images of a self-assembled monolayer of TSB3,5-C12 deposited at room temperature from asolution of concentration (3.0 ± 0.3) × 10−5 mol L−1 (30 × 16 nm2, samplebias: VS = –970 mV, average current: 〈IT〉 = 14 pA). The white dotted lineemphasizes the border between a dense and a porous domain. The molecularstructure of TSB3,5-Cn is shown on the lower right corner (R represents analkyl substituent, –CnH2n+1). The models for both domains are superimposedon the image together with the common directions of the 〈100〉 directions ofthe HOPG substrate. The alkyl chains of both models (red in the model) arearranged in registry with HOPG according to the Groszek model, i.e., alignedon a 〈100〉 direction.

nanoporous domains results from a kinetic blockade, whereasthe thermodynamically stable assemblies present abruptphase transitions from dense to honeycomb homogeneousstructures.

Molecules of 1,3,5-tristyrylbenzene substituted byalkoxy peripheral chains presenting n = 6, 8, 10, 12, or 14carbon atoms (TSB3,5-Cn, see Fig. 1) have been observed toform a series of honeycomb structures on highly oriented py-rolytic graphite (HOPG) at the liquid–solid interface.20 Be-cause of the energy cost associated with areas left uncov-ered, for the longer alkoxy chains, a dense network can beformed instead of the expected nanoporous one. Similar toanalogous porous/dense transitions the increased density isobtained through the release of some alkoxy chains from thesubstrate16, 21 to form a structure which is equivalent to theone obtained with molecules deprived from these specificchains,7 as shown in Fig. 1. Notice that porous and dense net-works exhibit different symmetry elements. For each alkoxychain length, the exact lattice parameters of dense and porousnetworks relative to HOPG can be determined by a carefulanalysis of the angles between domains.20, 22 This accuratestructural knowledge together with the possibility of varyingdense-to-honeycomb relative density through alkoxy chainlengths makes this family of molecules perfectly suited forthe present study. In what follows, we focus on the molecules

with n = 10, 12, or 14 carbon atoms (TSB3,5-C10, TSB3,5-C12, TSB3,5-C14) deposited on HOPG. Their structural dataare summarized in Table I.

STM experiments were conducted at the interface be-tween HOPG and a solution of TSB3,5-Cn in 1-phenyloctane(98%, Aldrich). This solvent is well suited for in situ STMbecause of its hydrophobic, highly insulating, and poorlyvolatile nature. Moreover, it doesn’t present any specific inter-actions with TSB3,5-Cn which would interfere with the self-assembly.23 A concentrated reference solution has been madefor each molecule by completing with solvent a weightedamount of product up to a known volume. The concentra-tions were then varied by dilution from the reference solutionand confirmed by transmission optical spectrometry, applyingthe Beer–Lambert law (molar extinction coefficient of TSB3,5-Cn at the maximum of the π–π* absorption: ε = 4.9 × 104

L mol−1 cm−1 at 310 nm).The substrate was a freshly cleaved 0.5 × 0.5 cm2 HOPG

sample (Goodfellow). The adsorbed monolayers were imme-diately formed following the application of a 3-μl droplet ofthe solution using a micropipette on the HOPG substrate andwere then imaged by STM.

In order to vary the sample temperature, the substrate waspressed on a Peltier element (Melcor, CP0.81706L) fitted intothe adapted sample compartment of the STM. Temperaturevariations ranging from 0 ◦C (273 K) to +65 ◦C (338 K) wereattainable simultaneously with the STM operation. The tem-perature was monitored in situ using a miniature temperaturesensor (Pt100, Correge).

The tips used for STM imaging were mechanicallyformed in a 250-μm Pt–Ir wire (Pt80/Ir20, Goodfellow). TheSTM was a home-made fully digital system. The images re-ported here were obtained either in the current mode (i.e.,constant-height) or in the height mode (i.e., constant-current),at a sample bias VS≈ –1000 mV and tunnel-current (IT) setpoints in the range 3–17 pA. The scan angle was adjusted insuch a way as to keep the fast-scan axis nearly perpendicu-lar to the sample slope. Images acquired simultaneously inforward and backward fast-scan directions are systematicallyrecorded and compared.

The structures of the monolayers can be characterized notonly by the ratio of the total surface covered with dense andnanoporous structures, but also by the number and averagesize of domains occupied by each type of molecular organi-zation. The influence of the sample temperature and of thetecton concentration in the solution on these characteristicshas been pointed out in the literature. Our first observation

TABLE I. Network parameters of dense and honeycomb molecular monolayers. Unit cell dimensions (a;b) are given asa function of the HOPG lattice parameter aHOPG = 0.246 nm. Aα (α = [dense, porous]) are the HOPG area per moleculein each structure. m = Aporous/Adense is the relative density of the dense structure to that of the honeycomb structure.

Dense Porous

n a;b (aHOPG) ab (◦) Adense (nm2) a;b (aHOPG) ab (◦) Aporous (nm2) m

10√

84;√

337 80.2 5,00√

241;√

241 60 6,29 1,2612

√84;

√403 80.0 5,46

√289;

√289 60 7,55 1,38

14√

84;√

475 79.9 5,93√

343;√

343 60 8,96 1,51

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124702-3 Nanoporous self-assemblies J. Chem. Phys. 134, 124702 (2011)

FIG. 2. STM current images of a TSB3,5-C12 solution with a concentrationof (4.1 ± 1.0) × 10−4 mol L−1. The images (b) and (c), taken at the sametemperature and concentration, show different reconstructions depending onthe sample history: in the first experiment, the droplet of TSB3,5-C12 is de-posited on a cold substrate (12 ◦C). (a) is the STM current-image recordedjust after the deposition. Then the sample is heated at 60 ◦C for 1 h and (b)corresponds to the STM current-image obtained at this temperature. In thesecond experiment, the droplet is deposited on a substrate at 60 ◦C leadingto the formation of huge nanoporous domains. (c) The STM images recordedjust after the deposition and 1 h later are similar in this case. (a) 91 × 91 nm2,sample bias: VS = –890 mV, average current: 〈IT〉 = 16 pA, sample temper-ature: 12 ◦C; (b) 94 × 94 nm2, VS = −890 mV, 〈IT〉 = 16 pA, sample tem-perature: 60 ◦C; (c) 201 × 205 nm2, VS = –890 mV, 〈IT〉 = 16 pA, sampletemperature: 60 ◦C; insert: higher-resolution image of 18 × 18 nm2 showingthe alveolate structure.

is that, even at a given final temperature and concentration,the characteristics of the adsorbed monolayer strongly de-pend on its growth history, that is, on the detailed sequenceof temperatures applied during and after the solution dropletdeposition. One of the most striking results in this respect isreported in Fig. 2. The STM images presented in Figs. 2(b)and 2(c) were acquired at 60 ◦C for samples realized from thesame TSB3,5-C12 solution but with different growth histo-ries: in a first experiment, the initial substrate temperature ap-plied during the droplet application, was slightly below theambient. The typical STM image obtained just after the de-position [Fig. 2(a)] presents no specific molecular organiza-tion at this stage. Then, the system was allowed to ripen at

60 ◦C for at least 1 h before further STM observation. Thisfirst method leads to a monolayer formed exclusively withlarge domains of dense structure as seen in Fig. 2(b). In a sec-ond experiment, the initial substrate temperature was 60 ◦Cand was maintained unchanged for 1 h. In this case, the ob-tained molecular structure [Fig. 2(c)] didn’t evolve with time(similar images are observed right after the deposition and1 h later). More importantly, unlike the first method, thesecond one yields exclusively porous assemblies, with evenlarger domains, often extended over entire HOPG terraces.

The above result demonstrates unambiguously the exis-tence, even at relatively high temperatures, of kinetic block-ades in at least one of the above situations. Hence, anyreliable study of thermodynamics of the monolayer in con-tact with the solution requires knowledge of the nature ofthose kinetic blockades and of a way to overcome them inorder to attain thermodynamic equilibrium, for each givenconcentration. To this aim, a first set of experiments werecarried out to identify the kinetic processes taking place dur-ing the two stages of the monolayer formation, namely: (i)The nucleation of adsorbed molecules and the subsequentdomain growth, which take place concomitantly, right afterthe initial contact between the solution and the substrate; (ii)The ripening process which starts when the substrate is fullycovered.

To understand the nucleation-and-growth stage, dropletsof TSB3,5-C12 solutions of specific concentrations were de-posited successively on substrates heated at various temper-atures and observed immediately, at the same temperature.Figure 3 presents a STM topography obtained just after thedeposition of the droplet on a substrate at 21 ◦C. Both denseand honeycomb domains are coexisting and their numberare similar (four and five, respectively, in this example im-age). Nevertheless, the honeycomb domains are larger than

FIG. 3. STM topography of a TSB3,5-C12 solution [concentration c = (6.1± 0.6) × 10−5 mol L−1] just after the deposition of the droplet on a HOPGsubstrate at 21 ◦C. 107 × 107 nm2, VS = +935 mV, set-point IT = 17 pA.

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124702-4 Bellec et al. J. Chem. Phys. 134, 124702 (2011)

FIG. 4. (a–d) Succession of STM topographies showing the evolution of thereconstruction for a TSB3,5-C12 solution. 45 × 45 nm2, c = (6.1 ± 0.6)× 10−5 mol L−1, VS = 1180 mV, IT = 10 pA, acquisition rate: 84 s perimage, room temperature.

the dense ones. If we neglect the effects of ripening in suchimages taken almost immediately after deposition, then thenumber of domains directly reflects the number of nuclei ofeach type formed before the substrate is fully covered. Here,the nucleation rates are thus comparable for both types ofstructures. Next, the average size of the domains attainedafter the same amount of time reflects the relative growthrate of each type of structure. Then, the comparison betweenthe two deposition methods illustrated in Fig. 2 indicatesthat the honeycomb structure is kinetically favored over thedense one during the initial growth of domains after nucle-ation. Qualitatively, we observed that an increase of the initialsubstrate temperature induces simultaneously a decrease ofboth number of domains and an increase of the size of hon-eycomb domains relative to the dense ones. This shows thathigher deposition temperatures favor the growth of honey-comb domains and explains the above-mentioned observation[Fig. 2(c)] of large domains exclusively of honeycomb typefor our highest deposition temperatures (60 ◦C). Conversely,at below-ambient deposition temperatures, small domains areformed with an increased proportion of dense structure.

The ripening of the sample can be studied in realtime by successively imaging the same area. During thisstage, the system evolves irreversibly toward its thermody-namic equilibrium, i.e., decreasing its Gibbs free energy.24

Figure 4 presents four STM topographies obtained succes-sively at a rate of 84 s per frame. On the first STM topography[Fig. 4(a)], one honeycomb domain is imaged between twodense domains which have different orientations. As illus-trated in the typical sequence from Figs. 4(b) to 4(d), the hon-eycomb domain progressively shrinks in favor of its denseneighbors. In turn, it is worth noticing that in both kinds ofdomain the molecules acquire a definite chiral conformation,

which yields a number of different types of domain bound-ary, with possibly different kinetics of evolution.25 We neverobserved the spontaneous appearance of a porous nucleus in-side a larger dense domain or the reverse. This blockade ofmolecular configurations in the bulk of a domain is consis-tent with the observed stability of atomically labeled ana-logues of these molecules inside self-assembled domains.26

Ostwald ripening studies carried out on other kinds ofalkylated systems27 or even on H-bonded networks28 alsoconducted to a predominance of 2D processes over those in-volving the supernatant solution. The difference between thereactivity of border and inner molecules has been consistentlyquantified through molecular mechanics simulations, in thecase of H-bonded networks.28 The motion of domain bound-aries is the most important mechanism of ripening. It proceedsin the direction which increases the area of the thermodynam-ically most stable structure, which was the dense one in theconditions of Fig. 2 [TSB3,5-C12 solution with a concentra-tion of (6.1 ± 0.6) × 10−5mol L−1 imaged at room tempera-ture]. The prominent role of domain boundaries in the evo-lution toward thermodynamic equilibrium explains that theinitial formation of large domains during high-temperaturenucleation and growth decreases the kinetics of the ripening,and may even lead to metastable situations, as illustrated inFig. 2(c) for the largest honeycomb domains. Conversely,the large number of small domains—and thus of domainboundaries—formed during low-temperature deposition fa-vors subsequent ripening and thus the ability to reach ther-modynamic equilibrium.

In the following, we study the thermodynamic equilib-rium as a function of tecton concentration in the solution. Tothis aim, we need to overcome the kinetic barriers so as tolet the system evolve toward minimization of the Gibb’s freeenergy. According to the kinetic analysis developed above,we proceeded as follows. We deposited the droplet on a coldsubstrate (12 ◦C) to favor the formation of a large density ofdomain boundaries. The sample was then heated to 55 ◦C tofurther accelerate the ripening. STM observations were per-formed at room temperature. This method is applied for thedifferent solutions of TSB3,5-Cn (n = 10, 12, and 14) withvarious concentrations.

Once the thermodynamic equilibrium between adsorbedand solvated tectons is reached, we measured the fraction ofthe substrate covered by the honeycomb network. For eachsolution, this measurement was done over at least six 100× 100 nm2 images after quenching at room temperature toavoid further evolution of the sample. The experimental re-sults are presented in Fig. 5(a) for the TSB3,5-C12 (red trian-gles) and the TSB3,5-C14 (black squares) as a function of thesolution concentration c. A sharp transition is observed at acritical concentration (C0), below which only the honeycombstructure is observed [Fig. 5(b)], and above which only thedense structure is present [Fig. 5(c)]. Moreover, the value ofC0 depends on the length of the alkoxy side-chains. Indeed,the critical concentration is one order of magnitude higherfor TSB3,5-C12 than for TSB3,5-C14 [C0 = (5.0 ± 2.0)× 10−5 mol L−1 and (4.0 ± 1.5) × 10−6 mol L−1, respec-tively] and it is never reached up to saturation for TSB3,5-C10, which always form the honeycomb structures.

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124702-5 Nanoporous self-assemblies J. Chem. Phys. 134, 124702 (2011)

FIG. 5. (a) Fraction of the surface covered by the honeycomb structure(Yporous) as a function of the solution concentration c. The red triangles andthe black squares correspond to the experimental measurements for TSB3,5-C12 and TSB3,5-C14, respectively. For each solution, this statistic was ob-tained after quenching at room temperature to avoid further evolution of thesample while examining several locations. Experimentally, the critical con-centrations C0 at which Ydense = Yporous = 0.5 are C0 = (5.0 ± 2.0) × 10−5

mol L−1 for TSB3,5-C12 and C0 = (4.0 ± 1.5) × 10−6 mol L−1 for TSB3,5-C14. The solid lines correspond to the model proposed by Lei et al. (Ref.16) (red and black lines for TSB3,5-C12 and TSB3,5-C14, respectively), inwhich the equilibrium constant K is determined with the experimental valueof C0 (see text). (b) and (c) STM topographies of both reconstruction forTSB-C14 solutions. (b) Nanoporous structure: 38 × 38 nm2, VS = 1260 mV,IT = 13pA. (c) Dense structure: 38 × 38 nm2, VS = 970 mV, IT = 4 pA.

To interpret our results, we first applied directly to oursystem the theory of thermodynamic equilibrium between in-dependent molecules proposed by Lei et al. for their simi-lar system.16 The TSB3,5-Cn molecules in the solution are inequilibrium with both, those adsorbed in the dense domainsand those in the nanoporous domains:

{TSBdense ↔ TSBsolution + AdenseSTSBporous ↔ TSBsolution + AporousS

, (1)

where S represents a unit area of the free surface and Aα(α= [dense, porous]) is the area of the substrate surface occu-pied by one adsorbed molecule in each structure, given inTable I. At equilibrium, the Gibb’s free energy change as-sociated with each reaction in Eq. (1) is zero. Since the ex-pression of the chemical potential of adsorption sites is heremuch more involved than in the single-component Langmuirmodel and we are merely interested in relative proportionsof dense and porous structures, we consider the Gibb’s freeenergy change associated with a transformation at a constantoverall surface coverage, obtained by combining reactions (1)as

mTSBdense ↔ TSBporous + (m − 1)TSBsolution, (2)

where m = Aporous/Adense is the relative density of the densestructure to that of the honeycomb one, given in Table I.By assuming a chemical potential of noninteracting adsorbedmolecules in the form μα = μ0

α + kB T ln Yα ,16 whereYαarethe fractions of the surface area covered by either the denseor the porous structure, respectively, and μS = μ0

S + kB T ln cfor the solution, the equilibrium constant K for reaction (2)can be expressed as

K = exp

(mμ0

dense − μ0porous − (m − 1)μ0

S

kB T

)= Yporous cm−1

Ymdense

.

(3)

The maximum number of tectons present on the 5 mm× 5 mm surface can be estimated from the molecular area inTable I and the number of molecules initially present in the3-μl solution can be deduced from the concentration. For allthe situations observed here, the number of tectons present inthe solution is much larger than the number of adsorbed ones(a factor of 4 in the worst observed case, TSB3,5-C14 at thecritical concentration). In other words the solution can be con-sidered as an infinite reservoir of solute molecules. Hence, forquantitative analysis of the experimental data, we assume that(i) we can neglect concentration depletion through adsorptionand (ii) most of the surface area is covered (Ydense + Yporous

= 1). The equilibrium constant K can then be evalu-ated with the help of the experimental value of thecritical concentration C0 at which Ydense = Yporous = 0.5and for which Eq. (3) gives K = (2C0)m−1. The de-pendence Yα(c) obtained for TSB3,5-C12 and TSB3,5-C14 is reproduced in Fig. 5 (red and black lines, respec-tively). In both cases these curves fail to reproduce the abruptchange around concentration C0.

We attribute this discrepancy to the fact that Eq. (3) hasbeen obtained by considering adsorbed molecules as inde-pendent from one another. This means that any molecule,even if it is located in the bulk of a domain, was supposedto have an equal probability to change from one type (denseor honeycomb) to the other. However, if this was the case,we should observe a completely random distribution of indi-vidual molecules in dense and honeycomblike conformationsrather than the experimentally observed domains of moleculeswith identical conformation. The formation of domains con-siderably reduces the entropy of the adsorbed monolayer. Inthe picture of kinetically driven equilibrium, this translatesinto the fact that the dense-porous transformations take placeexclusively at the boundaries of the domains, as observedexperimentally, e.g., in Fig. 4. Hence, only a reduced num-ber of molecules, those at domain bordering, are to be takeninto account in the kinetics of reaction (2) rather than all themolecules in the domain.

The tectons studied here have been shown topresent strong domain cohesion through alkoxy chaininterdigitation.7 Hence, we refined the above model toaccount for such interactions between adsorbed molecules,which lead to the formation of large domains. To this aim, wenow consider an equilibrium between dense domains Ddense

and honeycomb domains Dporous rather than the previousequilibrium between independent molecules. To make the

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124702-6 Bellec et al. J. Chem. Phys. 134, 124702 (2011)

analysis simpler, we assume that each domain, whatever itstype, contains strictly N molecules. Although this clearlyconstitutes a crude approximation in view of the wide distri-bution of domain sizes, we will see below that it still retainsmost of the physics of the thermodynamic equilibrium. Undersuch assumption, the chemical equation of the equilibrium(2) now writes

m

NDdense ↔ 1

NDporous + (m − 1) TSBsolution. (4)

The introduction of N accounts for the interactions be-tween molecules, which impose the formation of domains,while the molecules are still independent in the solution. Thechemical potential of domains can be obtained from the the-ory developed for surface-micelle isotherms which expressesthe chemical potential of molecules in 2D aggregates of ag-gregation number N as29

μα,N = μ0α,N + kB T

Nln

(1

Aα,Aggr

), (5)

where 1Aα,Aggr

is the 2D number density of domains of type α,which is linked to Yα through N and Aα inside either dense orporous domains by 1

Aα,Aggr= Yα

N Aα. Thus, Eq. (5) becomes

μα,N = μ0α,N − kB T

Nln (NAα) + kB T

Nln (Yα)

= μ0α,N + kB T

Nln (Yα) , (6)

where μ0α,N = μ0

α,N − kB TN ln (NAα), N and Aα being con-

stants. The factor 1N in the second term of the chemical poten-

tial is the only mathematical change compared with the theoryof independent molecules presented previously. It merely re-flects the drastic reduction of entropy of the monolayer, whichresults from the constraint of forming domains of N moleculesadsorbed in the same conformation rather than a completelyrandom spatial distribution of independent molecules in eitherconformation. For large N, the chemical potential becomesindependent of Yα . Then, for concentrations c above (below)C0, only the dense (porous) structure is thermodynamicallystable. This corresponds to a phase transition. As a conse-quence, for concentrations other than C0, the coexistence ofboth structures is an out-of-equilibrium situation which canonly result from a kinetic blockade. Keeping a finite value ofN, the equilibrium constant then becomes

KN = exp

⎛⎜⎝

m

Nμ0

dense,N − 1

Nμ0

porous,N − (m − 1)μ0S

kB T

⎞⎟⎠

= Y1N

porouscm−1

YmN

dense

. (7)

Again, KN can be evaluated from Eq. (7) with the helpof C0 as KN = (2

1N C0)m−1. Figure 6 presents the different

curves Yα(c) obtained in the example of TSB3,5-C12 by vary-ing the number N of molecules in each domain. As expected,the case N = 1 (red curve), which corresponds to fully inde-

FIG. 6. Model of the chemical equilibrium between domains containing Nmolecules. The fraction of the surface covered by the honeycomb structureis presented as a function of the solution concentration for TSB3,5-C12. Thelines correspond to the model with different values of N (from 1 to 100)compared to the experimental data (red triangles). The equilibrium constantKN is determined, for each N, thanks to the experimental value of C0 at whichYdense = Yporous = 0.5 (see text).

pendent molecules, is equivalent to the previous model. ForN = 10, which corresponds to 2 cavities of the honeycombnetwork [see Fig. 5(b)], the curve already present a markedinflection point around C0. For N = 100 and above, the sharptransition is well reproduced. In all our experimental obser-vations, after ripening, the average number N is much largerthan 103 (domains with a size larger than 100 × 100 nm2).The energetic cost of domain boundaries is known to leadto an increase of domain sizes during ripening, as observedby many previous studies.24, 25 Since the ripening becomesslower and slower with increasing domain sizes, this numberis very probably still limited by kinetics, the thermodynami-cally stable value of N being much larger.

The entropy of the molecules in solution strongly domi-nates over those of adsorbed molecules.30 Hence, at the crit-ical concentration C0, the gain of entropy given by the re-lease of m − 1 molecule into the solution in reaction (4),(m − 1)(S0 + kB ln C0), exactly counterbalances in the freeenergy the energy cost of the desorption of those moleculesfrom the dense phase, (m − 1)Hdense, and of the change ofone molecule from the dense to the porous structure, (Hdense

− Hporous). This yields an approximate expression for C0:

C0 = e− S0kB e

− 1kB T

(Hdense− Hporous−Hdense

m−1

). (8)

It immediately follows from Eq. (8) that a porous phasebetween the dense adsorbed phase and the completely sol-vated molecules only exists if the porous structure has ahigher stabilization energy, that is, if Hporous < Hdense. It isthe case here because the transformation from a porous to adense structure requires the breaking of the interdigitation oftwo alkoxy chains per molecules and their desorption fromHOPG (see models in Fig. 1). These noncovalent bondingsbetween neighboring adsorbed tectons, estimated to ∼0.7 eV7

is larger than kBT, which justifies the formation of large do-mains rather than a random distribution of tectons in either

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124702-7 Nanoporous self-assemblies J. Chem. Phys. 134, 124702 (2011)

dense or porous configuration. When Hporous < Hdense, an in-creased value of the relative density (m) reduces the range ofconcentrations compatible with the existence of the porousphase at equilibrium. This is consistent with the experimen-tal evolution of C0 when increasing the alkoxy chain lengthfrom 10 methylenes (m = 1.26) to 12 (m = 1.38) and thento 14 (m = 1.51). Recent experiments carried out on guest–host self-assembled systems31 suggest that C0 should also de-pend quantitatively on the nature of the solvent. Finally, thestriking difference between the abrupt variation of Yα(c) ob-served here and the progressive ones observed by Lei et al.16

may be explained either by a reduced energy of interdigita-tion, smaller than kBT, due to a mismatch of the interchainlateral distance with HOPG, or simply by kinetic blockades.

In conclusion, the experimental analysis of the tempera-ture and concentration dependences of TSB3,5-C10, TSB3,5-C12, and TSB3,5-C14 self-assemblies at the solution–HOPGinterface shows that the coexistence of dense and nanoporousdomains results from a kinetic blockade. The kinetic bar-rier can be overcome by playing on the temperature of thesample during the nucleation–growth process and the ripen-ing stage. Lower temperatures during the solution depositionlead to an increase of the density of domain boundaries dueto the formation of small domains. Then, moving to highertemperatures enables the system to ripen toward the thermo-dynamically stable structure, which depends on the solutionconcentration in the form of a sharp phase transition fromdense to honeycomb homogeneous structures. By combiningthe kinetic and thermodynamic control of the solution growth,very large defect-free self-organized area with either dense ornanoporous structure (up to 200 × 200 nm2) can be formed ina highly reproducible way. This possibility widens the oppor-tunities for applications of self-assembled nanoporous molec-ular networks, for example, as surface molecular sieves.

This work has been partially supported by the French Na-tional Agency (ANR) in the framework of its nanosciencesand nanotechnologies program “PNANO.” (Project NO-MAD, n◦ANR-08-NANO-013), by the Region Ile-de-Francein the framework of C’Nano IdF, the nanoscience competencecenter of Paris Region, supported by CNRS, Commissariat al’ Energie Atomique (CEA), Ministere de l’ Enseignment Su-perieur et de le Recherche (MESR), and Region Ile-de-France(Project PANAME) and by a PhD cofunding from CEA andCNRS (CA).

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