Probing Properties, Stability, and Performances of HierarchicalMesoporous Materials with Nanoscale InterfacesGianguido Baldinozzi,‡ Guillaume Muller,† Christel Laberty-Robert,*,† Dominique Gosset,‡
David Simeone,‡ and Clement Sanchez†
†Laboratoire de Chimie de la Matiere Condensee de Paris, UMR 7574 UPMC-CNRS-College de France, site College de France 11Place Marcelin Berthelot, 75005 Paris, France‡SPMS, MFE, CNRS-Ecole Centrale Paris & CEA, DEN, DMN, 91191 Gif-sur-Yvette, France
*S Supporting Information
ABSTRACT: Nanocrystals growth mechanism embedded into mesoporous thinfilms has been determined directly from grazing incidence X-ray diffraction data.We have shown, for the first time, that surface capillary forces control the growthmechanism of nanocrystals into these nanoarchitectures. Moreover, these dataallow an estimation of the surface tension of the nanocrystals organized into a 3-D nanoarchitecture. The analysis of the variations in the strain field of thesenanocrystals gives information on the evolution of the microstructure of thesemesoporous films, that is, the contacts among nanocrystals. This work representsthe first application of grazing incidence X-ray for understanding stability andperformances of mesoporous thin films. This approach can be used to understandthe structural stability of these nanoarchitectures at high temperature.
1. INTRODUCTIONMesoporous materials have received considerable attention inrecent years, not only for their structural and physicochemicalproperties but also because they can be used in manyapplications ranging from fuel cells to catalysis, membranes,and coatings.1−4 Better understanding of the formation ofmesoporous films is crucial to further improve their functionalproperties. For example, having particles in the nanometerrange arranged into a 3-D architecture is a prerequisite to usethese mesoporous thin films as electrodes for electrochemicaldevices.5 Knowing the conditions where the coalescence ofparticles occurs is also very important as it determines theirstability domains.Despite noticeable progress achieved in recent years, many
aspects of the formation of these mesoporous thin films remainunsolved. To explain the formation of the 3-D nano-architectures, extrapolations from known systems at completelydifferent length scales and microstructures (dense versusporous) have often been used. However, none of them relatesthe evolution of the interfaces during the formation of the films.Thus, they cannot predict, for example, the collapse of the 3-Darchitecture in their working environment. To describe theinterface stability, knowing the surface tension is crucial as it is akey parameter of many important properties such as reactivity,stability, particle growth, aging, etc. Few experimental data onsurface tension of nanocrystals arranged into a 3-D nano-architecture are available due to the difficulty inherent to suchmeasurements. Most of surface tensions available in theliterature come from calorimetric studies obtained onagglomerated powders.6 It is therefore necessary to developexperimental methods to study the energetic of well-defined
surfaces and interfaces. Estimating the surface tension in adirect manner will be an excellent tool to better predict theformation and stability of the 3-D nanoarchitectures in variousconditions.Laboratory “in-situ” X-ray diffraction tools and computa-
tional modeling can provide surface tension information tounderstand the formation and the stability of these mesoporouslayers. This Article details this approach on a simple andrealistic system, a ceria-based anodic material (50 vol %Ce0.9Gd0.1O2−x−50 vol % NiO, noted as CGO−NiO), whichhas efficient interface properties in solid oxide fuel cells. We (i)determine the nanocrystal growth mechanism, (ii) estimate thesurface tension, and (iii) describe the mechanical properties ofthese mesoporous layers from X-ray diffraction data. This is thefirst time in the literature that X-ray diffraction data have beenused to understand the mechanical properties of mesoporousthin films. This gives rise to very promising opportunities tofurther develop functional mesoporous nanocrystalline materi-als for broad applications, including advanced energy devices.
2. EXPERIMENTAL SECTIONSynthesis. The mesoporous oxide films consisting of pure
CGO (=Ce0.9Gd0.1O2−x) and composite films made of CGO−NiO (50% vol CGO−50% vol NiO) synthesized in this workwere produced using evaporation-induced self-assemblyapproach. For the pure CGO films, an ethanolic solutioncontaining inorganic precursor in the adequate proportion (0.9
Received: December 9, 2011Revised: March 18, 2012Published: March 21, 2012
mol of CeCl3,7H2O; 0.1 mol of GdCl3,7H2O) was mixed with asolution that was THF-based containing the structure-directingagent (100 mg of PS-b-PEO; polystyrene(40 000)-b-polyethylene(49 000) oxide (Polymer Sources Inc.)). Thefinal solution is dip-coated onto a silicon substrate with awithdrawal speed of 3−6 mm s−1. On evaporation of solvent,the system co-assembles to form an inorganic−organiccomposite film. Upon heating at 500 °C during 1 h in air,this composite develops a unique pore-solid architecture withnanocrystalline pore wall. The films exhibit a thickness of ∼150nm (estimated from FE-SEM images) and an overall porosityof the films of 30% in vol. (estimated from porosimetryellipsometry experiments using alcohol as solvent, alreadydetailed elsewhere5). Different heat-treatments (at 1073, 973,873, and 773 K for CGO and at 1073, 1023, 973, 923, 873, 823,and 773 K for CGO−NiO) were performed to obtain differentnanocrystals sizes.Characterization. The microstructure of the films obtained
after different heat treatments was observed by field emissiongun scanning electron microscopy (FE-SEM, Zeiss Ultra 55)and high-resolution transmission electronic microscopy (HR-TEM; JEOL JEM 2011). For HR-TEM analyses, mesoporousfilms were scratched from the substrates, and the obtainedpowders were deposited on coated carbon−copper grids.The CGO−NiO and CGO mesoporous film structures were
measured using a Bruker D8 Advance X-ray diffractometerequipped with a Gobel mirror producing a parallel Cu Kalphabeam (40 kV, 40 mA). The beam cross section was 0.1 × 6mm2, producing an almost perfectly square 6 × 6 mm2 beamfootprint on the sample at incidence 1°. The diffracted signalwas measured using a Vantec position sensitive detector. Thegrazing incidence diffraction patterns (10° < 2θ < 140°, α = 1°,3718 step scans corresponding to an average step size of0.0349°) were refined using the Rietveld software XND (ftp://ftp.grenoble.cnrs.fr/xnd).
3. RESULTSCeria-based films were chosen because mesoporous CGO andcomposite CGO−NiO films made of nanocrystals have beensynthesized with well-defined morphologies and orderedporosity.5 The meso-structure in these films is defined by thearrangement of the nanocrystal in a 3-D dimension. There isstrong technological interest for the ceria-based system for solidoxide fuel cells and water−gas shift applications.7−9 In theliterature, it has been shown that structural defects influence thediffusion and growth mechanisms of ceria nanoparticles.10 Thisshould affect the stability of these 3-D architectures at hightemperature. In this study, X-ray diffraction and high-resolutiontransmission electron microscopy (HR-TEM) were used (i) tostudy the grain growth and (ii) to assess the structural andmicrostructural changes after isothermal annealing at severaltemperatures. The methodology developed in this work wasapplied to samples corresponding to the isothermal annealingtemperatures between 773 and 1023 K for CGO samples andfor similar composite CGO−NiO samples made of 50% volCGO and 50% vol NiO. Nanoparticles of CGO are spherical, asshown in a typical high-resolution transmission electronmicroscopy image (Figure 1). HR-TEM images show thatCGO films annealed at 500 °C during 30 min in airflow consistof spherical nanoparticles with a diameter of ∼10−15 nm.Complete diffraction patterns (10° < 2θ < 140°) (Figure 2)
were measured using a grazing incidence setup to enhance thecontribution of the mesoporous layer to the total diffracted
intensity. The best compromise between sensitivity todiffraction in the mesoporous layer and good instrumentalresolution was achieved for a grazing angle of 1°. Rietveldrefinements (see Supporting Information, Figure S1) wereperformed on all of the measured diffraction patterns, and theyconfirm the formation of the fluorite phase. No change of the Ostoichiometry was observed.
3.1. Nanocrystal Growth Mechanism in MesoporousArchitectures. Controlling the organization and the size of thenanocrystals into the 3-D architecture is very important as awide range of technological properties, including mechanical
Figure 1. HR-TEM image of Ce0.9Gd0.1O2−x nanoparticles.
Figure 2. (a) Grazing incidence diffraction pattern measured with abeam impinging angle α = 1° on nanocrystalline mesoporousCe0.9Gd0.1O2−δ layers at different annealing temperatures. (b) Grazingincidence diffraction pattern measured with a beam impinging angle α= 1° on composite layers made of equal volumes of nanocrystallinemesoporous Ce0.9Gd0.1O2−δ and nanocrystalline NiO, as a function ofthe annealing temperature.
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strength, toughness, atomic transport, and electrical con-ductivity, will be affected. During grain growth, a decrease inGibbs free energy is observed at the crystal interface regions.Better understanding of the grain growth mechanism istherefore of fundamental importance not only, per se, butalso for its technological significance (stability of themesostructure, nanocrystals size, etc.). In this study, wedemonstrate using X-ray diffraction that the mechanism ofparticle growth differs from the one observed in dense filmswith nanoparticles of the same size.10 This emphasizes the factthat an extrapolation of the mechanism observed in the densenanocrystalline system is not possible.From a fundamental point of view, the grain growth is
governed by the intrinsic grain boundary mobility that is afunction of several parameters, including temperature anddefect concentrations. Because these parameters do not dependon the grain size, a single growth mechanism is generallyexpected at all length scales.11 This behavior has been observedin conventional polycrystalline samples. Yet for small metalnanoparticles, different mechanisms are expected: during theearly stages of metal nanocrystals growth, spatially inhomoge-neous concentration of vacancies12,13 must be redistributed inthe nanocrystal bulk. The excess energy of these defectscontributes to the total energy of the system, and a self-diffusion mechanism actually governs the growth mechanismduring these early stages. Usually, it will slow the rate of growthbelow a critical particle size. However, this effect might berelevant in metallic systems where point defects are neutral.To measure the nanocrystal growth mechanism in these
mesoporous thin films, grazing incidence X-ray diffraction hasbeen performed. The analysis of the peak intensities and of theprofile line shape14 of these diffraction patterns providesquantitative information on the size of the nanocrystals and onthe strain field as a function of the annealing temperature. HR-TEM and FE-SEM studies also confirm the nanocrystal sizedistribution remains very narrow. To explain the evolution ofthe average nanocrystal size as a function of the annealingtemperature, we assume that the atomic transport at theinterface is due to the surface curvature.15 The interfaceboundary tends to migrate toward its center of curvature as itreduces the interface area. We consider that (i) the surfacetension16 γ is independent of grain size, (ii) the radius ofcurvature R is proportional to the mean grain size d (i.e., d =2R), (iii) the rate of variation of the radius of curvature isinversely proportional to the nanocrystal radius (parabolicgrowth), and (iv) the only forces acting on the crystal are thoserelated to the surface curvature. These different assumptionsare summarized by eq 1:
=Rt
k TR
dd
( )(1)
where R is the radius of the particle, t is time, and k(T) is atemperature-dependent Arrhenius constant.Grain growth mechanism is usually characterized by the
knowledge of the value of the activation energy for theboundary migration, Qm. The rate of crystal growth istemperature dependent, and the constant k(T) can beexpressed17,18 in a modified Arrhenius-type equation (eq 2):
= −⎛⎝⎜
⎞⎠⎟k T
kT
Qk T
( ) exp0 m
B (2)
Note that the constant, k(T), depends on both the grain-boundary mobility and the interfacial energy γ, T is thetemperature, and kB is the Boltzmann constant.In Figure 3, the Arrhenius plot of the experimental data for
CGO nanocrystals of the CGO−NiO composite films follows
this equation, confirming that the nanocrystal growth is onlydue to the surface curvature effect. From this linear regression,the values for both the size of the initial nuclei, d0 at t = 0 s, andthe activation energy, Qm = 1.42(3) eV, are determined. Thissimple trend definitely rules out the existence of twomechanisms for grain growth, such as segregation andsecondary phases. A single parabolic law holds for all lengthscales. The value of the effective activation energy for interfacemigration already measured in dense CGO films,10 Qm = 1.3(1)eV, is consistent with our result, but the self-limited graingrowth observed in dense films is radically different as it is notgoverned by the interface curvature. This result confirms thatan extrapolation of the behavior of dense nanocrystalline filmsis not possible for describing nanocrystals growth into themesoporous architecture.Note that the values observed for pure CGO films heat-
treated at various temperatures are not on the same trend linealthough they obey the same equation. This behavior provesthat the CGO nanocrystals growth in pure CGO mesoporousfilms is still driven by the interface curvature but with differentmobility and initial grain sizes. This result is not shown in thefigure.
3.2. The Surface Tension of Nanocrystals in Meso-porous Architecture. Properties in functionalized materialsdepend on their structures and microstructures at differentlength scales. Previously, we have demonstrated that the forceassociated with surface curvature controls the way particlesgrow in these mesoporous layers. Here, we analyze the effectsof these surfaces and nanocrystal interfaces on the strain withinthe nanoparticles. From the evaluation of the strain, weestimate, for the first time, the surface tension of nanocrystalsembedded into a mesoporous films. The analysis of the latticeparameter measured by grazing incidence X-ray diffractionallows the estimation of the variation of the lattice parameter as
Figure 3. Modified Arrhenius plot for the mesoporous films. Theestimated value of the effective activation energy for interfacemigration of CGO nanocrystals in the mesoporous CGO−NiO films(e.g., the driving force for diffusion) is Qm = 1.42(3) eV = 137(3) kJmol−1 with an initial grain size d0 = 1.7 nm.
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a function of the nanocrystal size. The nanocrystal size has beenobtained by measuring the finite size broadening component ofthe diffraction peaks.The lack of anisotropy of the finite size component to the
peak broadening in all of the studied samples and the HR-TEMpictures of mesoporous films (Figure 1) suggests that theassumption of spherical nanocrystals is acceptable. The latticeparameter exhibits a linear variation as a function of the inverseof the nanocrystal size (Figure 4). This behavior is actually
predicted by the Young Laplace equation that describes thecapillary pressure difference due to the phenomenon of surfacetension. In this equation (eq 3), the interface stress σ0 of aspherical object is directly related to the interface curvature viaγ, the surface tension. R is the radius of the curvature.
σ = γR2
0 (3)
This result establishes that (i) the nanocrystals in themesoporous layer exhibit an elastic behavior and (ii) the surfacetension is constant.Using the extrapolated lattice parameter for the bulk system
(a∞ = 5.4355(9) Å), it is possible to convert the latticevariation into strain (ε). Taking the bulk modulus19 of ceria as200 GPa, the measured surface tension for the nanocrystal inthe mesoporous thin films is 3.98(19) N m−1. This value ofsurface tension is generally about double the surface freeenergy.16 This result agrees with the typical surface freeenergies obtained from calorimetric experiments20 on agglom-erated oxide nanopowders. The variation of strain as a functionof the inverse of the particle size is reported in Figure 5, whereall measurements on CGO nanocrystals, both in pure CGOfilms and in the composite CGO−NiO films, follow the samelinear trend. This suggests that the CGO interfaces in pureCGO and in the composite CGO−NiO actually behave in thesame way: the presence of NiO does not modify the elasticproperties of the CGO nanocrystals. Therefore, this analysisallows, for the first time, the estimation of the surface tension ofthe nanoparticles arranged in a complex mesoporous 3-D nano-architecture.3.3. Predicting the Collapse of the Mesoporous
Architecture. In a hierarchical multiscale system, key
information is needed at both (i) the mesoporous scale and(ii) at the nanocrystals scale. In the assembly of nanocrystalsthat form the mesoporous layer, contacts among nanocrystalsare very important as they will define, in fine, the stability of thenanoarchitecture. It is reasonable to suppose that theseinterfaces actually influence the mechanical properties of thesystem via a modification of the strain field in the nanocrystals.Grazing incidence X-ray diffraction provides specific informa-tion on these effects. The analysis of the variance of the strain isdirectly related to the measure of the microstrain broadeningcomponent (W) in the diffraction pattern (see the SupportingInformation).Previously, we have demonstrated that the nanocrystals
behave as an elastic medium and follow the Young Laplaceequation. This result may seem surprising because thenanocrystals in these layers are not isolated but interconnected(see, for instance, the field emission gun scanning electronmicroscopy pictures, Figure 6). However, because the sample isuntextured, these contact anisotropies exhibit isotropicprobability distributions.21 Therefore, these mesoporous filmscan be modeled as a set of spherical grains undergoing atorsionless axisymmetric load. Following the approach22 byLur’E, the displacement field of these elastic spherical crystals iscalculated. At the crystal interface, the radial stress σr isexpressed using Legendre’s polynomials.
∑σ = σ θ=
∞P (cos )
nn nr
0 (4)
In this relation, the first term of the expansion, σ0, correspondsto the stress acting on an isolated nanocrystal, and it is actuallyidentified with the result of the Young−Laplace equation (eq3). The next term, σ1, disappears for a self−-equilibrated load.The other terms σ2,...,σn depend on the topology of thecontacts. If we consider the strain effect generated by twosymmetric contacts (as in a pillar), the leading term of thedevelopment is σ2. This stress component represents a solid−solid interface, and the value of its modulus could range from−σ0 for a flat interface (perfect continuity of the lattices of the
Figure 4. The lattice parameter of CGO nanocrystals in pure CGOand in composite CGO−NiO mesoporous films is a linear function ofthe inverse of the average nanocrystal size, as predicted for a sphericalparticle subject to the capillary effect due to the surface curvature.
Figure 5. Evidence of the elastic behavior of the nanocrystals in CGOand CGO−NiO mesoporous layers. Strain (ε = 1 − a/a∞) is a linearfunction of the inverse of the particle size.
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two nanocrystals) to 0 (no modification of the surface stress fora vanishing contact). The calculation of the diagonalcomponents of the strain tensor ε at any point inside thenanocrystal is then straightforward. The trace of the straintensor is evaluated and integrated on the nanocrystal volume todefine the average strain ⟨ε⟩ in the nanocrystal. The calculationshows that the average strain is still proportional to the inverseof the particle size and thus in agreement with the X-raydiffraction results already discussed in the previous section(Figure 5).The average of the variance on the nanocrystal volume gives
a constant, proportional to σ2. Therefore, if the topology of thecontact does not change during the particle growth, the productof the particle size and the microstrain component of thebroadening of the diffraction peaks is a constant. Figure 6shows that the product of the measured microstrain broadeningand the particle size as a function of the inverse of the particlesize is actually a constant function between 823 and 973 K. Thisresult suggests that the topology of the mesoporous layerremains unchanged in this temperature range. The mesoporousstructure is stable although the nanocrystal size is changing.Below 823 K, the mesoporous layer is not well crystallized yet,and a significant amount of glassy phase might be still present.The small value of the microstrain below 823 K seems relatedto a poor quality of the contacts between nanocrystals. Above973 K, the mesoporous structure becomes increasingly unstableas is also displayed in the SEM pictures in Figure 6.The increase of the microstrains above 973 K suggests an
emerging instability possibly related to the development ofextended imperfect attachments between nanocrystals and theappearance of significant dislocations densities23 to accom-modate the excess of energy. These observations can be usedeither to follow the aging of the mesoporous layer or to designthe mesoporous architecture.
4. CONCLUSIONSUnderstanding the nanocrystal growth mechanisms and thestability of mesoporous films is essential to design relevant
synthesis approaches and to improve the performances of thesesystems in a variety of industrial and environmental conditions.Traditional models for the nanocrystal growth often assume acrossover of different mechanisms and generally neglectparticle−particle interactions imposed by the mesoporousarchitecture. Using high-resolution X-ray diffraction, we havedemonstrated CGO nanocrystals in a mesoporous film grow viaa parabolic mechanism driven by the capillary forces related tothe curvature of the surface of the nanograins. We havemeasured the surface tension γ of these nanocrystals and shownthat it is not dependent upon the nanocrystal size as long as themesoporous architecture is preserved. During the growthprocess, the mesoporous architecture is maintained. Thecollapse of this mesoporous architecture is then monitoredthrough the determination of the particle−particle contacts viathe measurement of the microstrains into these mesoporouslayers. These results are both of fundamental and oftechnological importance as they demonstrate that by using asimple technique, grazing X-ray diffraction, it is possible topredict nanocrystal growth and the conditions where thecollapse of the mesostructure occurs.
■ ASSOCIATED CONTENT*S Supporting InformationAdditional equations and figure. This material is available freeof charge via the Internet at http://pubs.acs.org.
NotesThe authors declare no competing financial interest.
■ ACKNOWLEDGMENTSWe gratefully acknowledge the financial support of C’nano IDF(Solnac project.)
Figure 6. Product of the particle size and the microstrain broadening component (W, the microstrain component to the peak broadening in radians,is proportional to ⟨ε2 − ⟨ε2⟩⟩1/2) as a function of the inverse of the nanoparticles size in these mesoporous films.
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