Literature DB >> 33403262

Peering into the Formation of Template-Free Hierarchical Flowerlike Nanostructures of SrTiO3.

Anderson Thesing1, Eduardo J Damiani2, Lara F Loguercio3, Pedro G Demingos4, André R Muniz4, Neftali L V Carreño5, Sherdil Khan6, Marcos J L Santos2, Alexandre G Brolo7, Jacqueline F L Santos2.   

Abstract

The development of efficient advanced functional materials is highly dependent on properties such as morphology, crystallinity, and surface functionality. In this work, hierarchical flowerlike nanostructures of SrTiO3 have been synthesized by a simple template-free solvothermal method involving poly(vinylpyrrolidone) (PVP). Molecular dynamics simulations supported by structural characterization have shown that PVP preferentially adsorbs on {110} facets, thereby promoting the {100} facet growth. This interaction results in the formation of hierarchical flowerlike nanostructures with assembled nanosheets. The petal morphology is strongly dependent on the presence of PVP, and the piling up of nanosheets, leading to nanocubes, is observed when PVP is removed at high temperatures. This work contributes to a better understanding of how to control the morphological properties of SrTiO3, which is fundamental to the synthesis of perovskite-type materials with tailored properties.
© 2020 American Chemical Society.

Entities:  

Year:  2020        PMID: 33403262      PMCID: PMC7774077          DOI: 10.1021/acsomega.0c04343

Source DB:  PubMed          Journal:  ACS Omega        ISSN: 2470-1343


Introduction

According to Landolt–Boernstein,[1] the generic structure of perovskite-type oxides ABO3 can accommodate 30 different elements on the A site and half of the periodic table on the B site. This versatility in terms of structure and chemical composition is hardly found in any other class of materials and provides an exceptional opportunity to tailored properties and functionalities for different applications.[2−7] Among the ABO3 perovskites, strontium titanate (SrTiO3) exhibits an ideal cubic perovskite-type structure with the space group Pm3m in a corner-sharing network of BO6 octahedral in a wide range of temperature ranging from −160 to 2080 °C, providing a high thermodynamic stability.[8] In addition, it has been reported to be an important n-type semiconductor widely used in different applications, such as photocatalysts for water splitting, electron-transport layers in perovskite solar cells, gas sensors, energy storage devices, and multitasking cost-effective catalysts for condensation, hydrogenation, and amination reactions.[5,7,9−11] Solvothermal synthesis is certainly one of the most interesting and simple ways to easily obtain SrTiO3 nanostructures with a controlled morphology, crystallinity, chemical composition, and size. The solvothermal approach allows the synthesis to be carried out in a wide range of temperatures (40–250 °C) and using different soluble strontium precursors, such as nitrates, chlorates, acetates, and hydroxides.[12−15] In addition, the use of titanium precursors, such as butoxides, isopropoxides, and chlorides, in solvothermal processes allows a certain degree of control over the rate of hydrolysis by the modulation of nucleation and growth rates, resulting in a drastic selection of morphologies.[16,17] In most of the materials, the growth rate of a crystal is kinetically controlled, as specific facets grow faster to decrease the total surface free energy of the particle. Hence, a lot of efforts have been devoted to the understanding and control of the facets;[18−21] for instance, the predominant formation of desirable surfaces was achieved by adjusting the synthetic route.[22−24] Several efforts have been made to synthesize different SrTiO3 morphologies.[12,25] In particular, SrTiO3 hierarchical nanostructures are potential candidates for energy applications with improved performances relative to their counterparts.[26] Previously, such structures have been synthesized through template-assisted methods,[27−29] which involve complex steps and are not cost effective. On the other hand, a few attempts of template-free synthesis have been described in the literature.[30−32] In any case, there is still plenty of room for the development of simple methodologies to obtain hierarchical nanostructured perovskite nanomaterials. Surface chemistry plays a crucial role in tuning the properties of solid-state materials, mainly in the nanoscale regime with large surface-to-volume ratios.[33] The (100) plane presents the lowest surface energy in SrTiO3; hence, the most suitable and stable morphology of a particle is a cube bounded by the (100) facets.[34−36] Facet control during synthesis is then required to drive noncubic morphologies. As an example, Xu et al. used the solvothermal method and ethylene glycol (EG), which adsorbs onto (110) facets, to produce SrTiO3 nanosheets; however, a complete formation of regular hierarchical nanostructures was not achieved.[37] Previous studies have shown that poly(vinylpyrrolidone) (PVP) can easily bind to metal oxide surfaces[38−40] to affect surface energy and influence crystal nucleation and growth. The Yang group used PVP with templating microspheres of TiO2 to obtain litchilike SrTiO3 structures in a hydrothermal setup.[41] After synthesizing SrTiO3 by the solvothermal method, Zhao et al. produced an SrTiO3PVP thin film in which PVP acted as trapping centers for memory devices. The observed strong interaction between PVP and SrTiO3 in thin films allowed promising results in device performance.[42] In this work, the hierarchical nanostructures of SrTiO3 were synthesized using PVP in a template-free solvothermal process. The morphological, structural, and crystalline control of SrTiO3 hierarchical nanostructures is presented. The PVP interactions with different SrTiO3 facets were investigated experimentally, and the findings were supported through molecular dynamics simulations. The conversion of the resulting petal structures from nanosheets to nanocubes by thermal treatment while preserving the hierarchical morphology was demonstrated. The mechanism of morphological and crystal growth was comprehensively elucidated by a variety of characterization techniques.

Results and Discussion

Figure compares the morphology of the as-prepared samples with and without PVP during a 12 h solvothermal synthesis. The presence of PVP (Figure a1–a3) has a tremendous effect on the morphology. Clearly, a hierarchical flowerlike morphology surrounded by nanosheets, named here as “petals,” is obtained with PVP; otherwise, nanosheets-like structures are observed in the absence of PVP (Figure b1– b3). The morphology obtained in the PVP-free synthesis corroborates previous reports.[37,43] The average size of the flowerlike structures was 1.1 ± 0.2 μm, and the average thickness of the petals was ca. 15.3 ± 5.1 nm. On the other hand, the nanostructures observed in the PVP-free synthesis were ca. 13.8 ± 4.1 nm in size.
Figure 1

(a) SEM (a1) and TEM (a2–a3) images of the as-synthesized samples obtained after the solvothermal reaction for 12 h in the presence of PVP. (b) TEM images (b1–b3) of the as-synthesized samples obtained under the same conditions as those in (a) but without PVP.

(a) SEM (a1) and TEM (a2–a3) images of the as-synthesized samples obtained after the solvothermal reaction for 12 h in the presence of PVP. (b) TEM images (b1–b3) of the as-synthesized samples obtained under the same conditions as those in (a) but without PVP. The results in Figure strongly suggest that PVP is key to the production of a hierarchical flowerlike morphology, even in the absence of templates.[27−29] The synthesis can be made more cost effective by decreasing the solvothermal reaction time. Figure displays the SEM and TEM images of the as-prepared samples after 6 and 3 h of the solvothermal reaction. The morphology observed in Figure does not differ much from Figure a1–a3. The average size and petal thickness of the samples shown in Figure a1–a3 and Figure highlight that the morphology is not reaction time dependent. The XRD patterns of the as-synthesized samples were acquired as a function of reaction time (Figure S1), once it may have affected the crystal structure.[44] SrTiO3 (JCPDS No. 35-0734) and SrCO3 (JCPDS No. 05-0418) related to unreacted Sr(OH)2 are observed. One can observe that the amount of SrTiO3 increased with reaction time relative to the amount of SrCO3. Therefore, reaction time shorter than 3 h was not attempted in this study, and we have chosen the sample prepared in the 3 h solvothermal reaction for further characterization.
Figure 2

SEM (1) and TEM (2, 3) images of SrTiO3 samples after the solvothermal reaction of (a) 6 h and (b) 3 h.

SEM (1) and TEM (2, 3) images of SrTiO3 samples after the solvothermal reaction of (a) 6 h and (b) 3 h. Molecular dynamics simulations were carried out to elucidate the formation of hierarchical flowerlike nanostructures in the presence of PVP. The likelihood of PVP adsorption on either the {100} or the {110} facets of the flowerlike nanostructures was compared. PVP oligomers were placed in contact with different SrTiO3 surfaces in equilibrium at 160 °C, as described in the Experimental Section. Figure presents the PMF profiles computed to assess the relative affinity of PVP with the different surfaces. A higher adsorption energy (ΔEads) was found for the {110} (−9.5 kJ.mol–1) and {100} (−9.2 kJ.mol–1) facets for TiO2-terminated surfaces when compared to the {100} facet in contact with the SrO-terminated surface (−7.2 kJ·mol–1) (Figure ). The energy difference is justified by the lower partial charge of strontium ions on the {100} SrO surface compared to titanium, which weakens the interaction with the polar groups of the oligomers. However, the differences between the adsorption energies on the {110} and {100} facets of TiO2 are not significant. Interestingly, Figure shows that the adsorption/desorption activation energy (Eb) is significantly higher for the {110} facet (21.1 kJ.mol–1) in TiO2 relative to both the {100} facet in TiO2 (17.6 kJ.mol–1) and the {100} facet in SrO (11.7 kJ.mol–1). These results lead to the conclusion that the adsorbed PVP molecules are more labile on the {100} surfaces than on the {110} facets, stabilizing the latter from a kinetic point of view. This effect might favor the crystal growth along the {100} facets, which is, in fact, the lowest surface energy facet in SrTiO3.[45] This assumption is strongly supported by the XRD patterns of the samples obtained after the solvothermal reaction for 12 h in the presence and absence of PVP (Figure S6), where the ratio I(110)/I(100) was found to increase from 3.3 to 6.7, respectively. Therefore, during the solvothermal process, PVP strongly adsorbs onto the {110} facet and acts as a self-assembly nucleation guide for the formation of hierarchical flowerlike structures.
Figure 3

PMF computed from molecular dynamics simulations of the interfacial interaction of vinylpyrrolidone trimers on SrTiO3 facets. Inset: structure of surface crystal terminations (green: Sr2+; gray: Ti4+; and red: O2–).

PMF computed from molecular dynamics simulations of the interfacial interaction of vinylpyrrolidone trimers on SrTiO3 facets. Inset: structure of surface crystal terminations (green: Sr2+; gray: Ti4+; and red: O2–). The as-prepared samples were heat treated at 300, 400, 500, 750, and 1000 °C. In addition to show that the SrTiO3 (JCPDS No. 35-0734) peaks turn sharper and intense as the temperature was increased from 300 to 1000 °C, Figure indicates a decrease in the SrCO3 at temperatures higher than 500 °C. The reason for SrCO3 phase depletion with increasing temperature is still unclear. We believe that the SrCO3 reacts directly with the titanium species to yield the SrTiO3 phase, as observed before.[46] The intensity ratios of the (110) characteristic peak to the (100) peak, i.e., I(110)/I(100), presented an exceptional temperature dependency, as indicated in Figure d. This ratio increases up to 750 °C and becomes nearly invariant for higher temperatures, strongly suggesting a favored growth of the {110} facets (Figure d). The lattice parameter (a0) and the crystallite size (Dhkl) were calculated using Bragg’s law and the Scherrer equation (see the Supplementary Information) from the highest intensity peak, i.e., (110) direction and are also displayed in Figure d. The lattice parameter a0 decreased up to 750 °C, resulting in the unit cell volume contraction; hence, a crystal structure with shorter bond lengths is formed. On the other hand, the calculated a0 at 750 °C (a0 = 3.8998 Å) and higher temperatures is closer to the ideal cubic structure (a0 = 3.9050 Å, from JCPDS No. 350734).
Figure 4

(a) XRD patterns of SrTiO3 hierarchical nanostructures after thermal treatment from 300 to 1000 °C; (b) enlarged version of the regions containing the (100) and (c) the (110) characteristic peaks; and (d) Dhkl, a0 cell parameters, and intensity ratios as a function of the post-heat treatment.

(a) XRD patterns of SrTiO3 hierarchical nanostructures after thermal treatment from 300 to 1000 °C; (b) enlarged version of the regions containing the (100) and (c) the (110) characteristic peaks; and (d) Dhkl, a0 cell parameters, and intensity ratios as a function of the post-heat treatment. Figure d shows that the average crystallite size increases linearly from 6 to 40 nm. These results indicate that the post-heat treatment has a profound effect on the overall crystal growth, which leads to morphological changes. The SEM and TEM images of the thermally treated samples are compared in Figure , and the morphological parameter distributions are displayed in Figure S2. Nearly no change in the size and morphology is observed in Figure for 300 and 400 °C; however, significant changes started to be observed at 500 °C. The average size of the flowerlike nanostructure decreased from ca. 1.15 ± 0.2 μm at 300 °C to ca. 0.78 ± 0.1 μm at 1000 °C. The hierarchical structure was preserved at even higher temperatures, but the petal format changed from the lamellar nanosheets to nanocubes. As seen in Figure , these nanocubes are thicker and denser compared to the samples thermally treated below 500 °C. These results clearly corroborate the XRD analyses in Figure d that presented a decrease in the lattice parameter a0 to a value close to an ideal cubic structure at a higher temperature (Figure d). The same general behavior was observed for samples prepared using either 6 or 12 h of solvothermal reaction and subjected to post-heat treatment (see Figures S3 and S4), indicating that the initial amount of SrTiO3 relative to SrCO3 does not affect the morphology after post-heat treatment.
Figure 5

SEM (1) and TEM (2, 3) images of SrTiO3 hierarchical flowerlike nanostructures after thermal treatment at (a) 300, (b) 400, (c) 500, (d) 750, and (e) 1000 °C.

SEM (1) and TEM (2, 3) images of SrTiO3 hierarchical flowerlike nanostructures after thermal treatment at (a) 300, (b) 400, (c) 500, (d) 750, and (e) 1000 °C. Several syntheses of SrTiO3 that led to the formation of conventional nanocubes have been described.[34,47,48] The key to the formation of hierarchical nanostructures and their morphological control in Figure lies in the presence of EG and PVP, which undergo adsorption on metal oxides.[37] PVP drives the self-assembly of SrTiO3 nanocrystalline nanosheets, and they undergo a crystallization process during the solvothermal reaction, leading to the hierarchical nanostructure formation.[37] The post-heat treatment clearly demonstrates control over the petal morphology, since it is possible to obtain hierarchical flowerlike structures with either lamellar nanosheets or nanocubes. Figure displays the HRTEM image of nanocubic petals prepared after 3 h of solvothermal reaction and 1000 °C post-heat treatment. The interplanar distances of 0.290 and 0.389 nm correspond to the (110) and the (100) crystallographic planes, respectively. The angle between these planes was 45.15°. The selected area electron diffraction pattern of the petal (inset Figure b) shows single spots, suggesting that the perovskite-type oxides have grown and self-orientated to assume single-crystal behavior and exhibit a high order of crystallinity. Figure agrees with the XRD analyses in which the largest crystallite size was observed for this sample, and the a0-value was closer to the ideal cubic structure (Figure d).
Figure 6

(a) STEM (a secondary electron image), (b) HRTEM image, and (c) FFT of the HRTEM image of the SrTiO3 hierarchical flowerlike nanostructure after thermal treatment of 1000 °C. Inset of (b): selected area electron diffraction pattern.

(a) STEM (a secondary electron image), (b) HRTEM image, and (c) FFT of the HRTEM image of the SrTiO3 hierarchical flowerlike nanostructure after thermal treatment of 1000 °C. Inset of (b): selected area electron diffraction pattern. The effect of post-heat treatment on the chemical composition was investigated by FTIR and Raman spectroscopy. The IR features shown in Figure a display the vibration bands at 1084 and 1030 cm–1, related to the C–C–O vibration of surface-adsorbed EG.[49,50] The bands at 1650 and 1460 cm–1 are related to the C=O and pyrrolidinyl groups from the PVP chains.[51] A low intensity band can also be observed for all samples at 856 cm–1. This band can be assigned to the CO3–2 vibration of SrCO3.[52] The broad band within 650–545 cm–1 is associated with the perovskite structure of the TiO6 octahedron stretching vibration mode.[16] This band becomes sharper and shifts to a lower wavenumber with an increase in temperature. This is in accordance with the XRD measurements (Figure ), where higher temperatures result in a lower a0 value and a larger crystallite size (Dhkl). The inset in Figure a shows the changes in the intensity of PVP (ca. 1460 cm–1) and EG (ca. 1084 cm–1) vibration modes against temperature. EG is not observed for temperatures higher than 300 °C;49,50 meanwhile, PVP only disappears at temperatures above 500 °C. Interestingly, this is the same temperature where the most significant change from nanosheets to the cubic morphology was observed (Figure ).
Figure 7

(a) FTIR and (b) Raman spectra of the as-synthetized SrTiO3 hierarchical nanostructures and after thermal treatment from 300 to 1000 °C. The inset in (a) shows the change in the intensity of PVP and EG modes vs post-heat treatment temperature.

(a) FTIR and (b) Raman spectra of the as-synthetized SrTiO3 hierarchical nanostructures and after thermal treatment from 300 to 1000 °C. The inset in (a) shows the change in the intensity of PVP and EG modes vs post-heat treatment temperature. It is possible to identify a series of first-order scattering broad bands at ca. of 180, 288, 544, 727, and 793 cm–1 in the Raman spectra in Figure b, corresponding to the TO2, TO3, TO4, TO and LO4 modes, respectively (Figure b).[12,16,53] UV–vis spectroscopy shows no change in the band gap (Figure S5).[2,12,15] The formation of titanate-based structures was described by a simplified three-stage mechanism.[54,55] In the first stage, the alcohol chains replace the Ti atoms from titanium butoxide, making the hydrolysis of titanium species slower. In the second stage, the hydrolysis leads to the formation of Ti(OH)4 nuclei, which are randomly distributed in the liquid phase. At this point, the strontium ions start to react with titanium species to decrease the formation energy of the final structure. In the third stage, condensation reactions lead to the formation of a network system from the original basic units with stable Ti–O–Ti and Sr–O–Sr bonds, forming SrTiO3 species.[16] Once the nucleation step is completed, like previously observed for EG,[37] we suggest that the PVP also starts to interact with the metal oxide surface. This surface interaction affects the crystal growth, driving the formation of the lamellar nanostructure. After heat treatment, as PVP is removed at temperatures higher than 500 °C, the coarsening and ripening process driven by thermal energy enables the nanosheets to form SrTiO3 nanocubes. Under the experimental conditions explored in this work, this process can explain the temperature-dependent morphological evolution, in which thermodynamically less-stable small particles (nanosheets) transform into large particles (nanocubes) via kinetic pathways, such as surface diffusion. As a result, there is the formation of highly oriented nanocubes.[36,56] PVP-free solvothermal synthesis resulted in the formation of nanosheets (Figure ), corroborating previous work where the synthesis was performed using only EG.[37,42] Both EG and PVP adsorbed onto SrTiO3 drive the formation of hierarchical flowerlike structures surrounded by nanosheet petals during solvothermal synthesis. Therefore, their integrated presence plays a vital role in the formation of hierarchical nanostructures. Since EG is easily removed during the post-heat treatment (Figure a), the results suggest that the most important interaction leading to the preservation of nanosheets in hierarchy is PVP. Once PVP is removed at high temperatures (above 500 °C), a surface reconstruction is initiated to decrease the surface energy, resulting in the more thermodynamically stable cube morphology.[34−36] Crystallographically, the surface interaction of PVP is dominated predominantly with the {110} plane, as confirmed by molecular dynamics simulations. Therefore, the morphology evolves toward a surface energy minimization at high temperatures, guiding the lamellar nanosheets to grow along {100} facets; thereby, the petal structures change from nanosheets into nanocubes. The results suggest that a comprehensive control of the petal morphology can be achieved by tuning the PVP amount in hierarchical nanostructures. A schematic representation of the template-free formation mechanism introduced here is given in Scheme .
Scheme 1

Morphology Evolution through Thermal Treatment

Conclusions

The formation of the hierarchical flowerlike SrTiO3 nanostructure is strongly dependent on the presence of EG and PVP during the solvothermal reaction. The organic species interact preferentially with the {110} facets, decreasing the surface energy and inducing the {100} facet growth. The solvothermal reaction time has little effect on the morphology of the hierarchical nanostructures; however, decreasing the reaction time increases the SrCO3 content. Upon high temperature, the morphology evolves toward a surface energy minimization, i.e., structural reorganization densifies the nanoflowers, decreasing their size and transforming the petals into nanocubes. This study has shown a simple, cost-effective, and template-free strategy to achieve a fine control over SrTiO3 morphology and crystallinity. The potential for the fine-tuning morphology of SrTiO3 introduced here can be applied to other perovskite nanostructures that are widely used in energy applications.

Experimental Section

Materials

Titanium butoxide (Sigma-Aldrich, ≥97%), strontium hydroxide octahydrate (Sigma-Aldrich, 95%), ammonium hydroxide (Sigma-Aldrich, 28–30%), ethylene glycol (Química Moderna, 99.5%), poly(vinylpyrrolidone) (Vetec, average mol. wt 40,000), ethanol (Synth, 99.5%), and isopropyl alcohol (Synth, 99.5%) were used as received.

Synthesis of Hierarchical Flowerlike SrTiO3 Nanostructures

Hierarchical flowerlike SrTiO3 nanostructures were synthesized by controlling the hydrolysis of titanium butoxide with EG and PVP. Strontium hydroxide (4.25 g), PVP (0.74 g), ammonium hydroxide (8.0 mL), and EG (40.0 mL) were added to a single-neck glass flask under constant stirring for 30 min. Titanium butoxide (5.44 g) was then added to the solution, and the constant stirring was maintained for another 30 min. After this, the solution was placed in a 170 mL removable Teflon cup in stainless-steel body and heated to 160 °C at a rate of 5 °C.min–1 (ventilated electrical heating oven, Marconi) during 12, 6, and 3 h to enable the solvothermal reaction. The samples were rinsed by 5 cycles of centrifugation with ethanol for 5 min each at 2500 rpm.

Heat Treatment – Petal Morphological Control from Nanosheets to Nanocubes

The samples obtained after 3 h of solvothermal synthesis were heat treated for 300, 400, 500, 750, and 1000 °C during 4 h, with a heating and cooling rate of 4 °C·min–1. The resulting samples were labeled as SrTiO3-T, where T indicates the temperature of the heat treatment.

Characterization

Transmission electron microscopy (TEM) images were obtained on a Jeol JEM 1200 EXll with an acceleration voltage of 80 kV. The selected area electron diffraction (SAED) and high-resolution transmission electron microscopy (HRTEM) images were obtained with a Hitachi HF-3300 V STEHM, at an acceleration voltage of 300 kV. A dispersion of the samples in isopropyl alcohol was deposited by drop casting onto a carbon-coated copper grid of 200 mesh. Scanning electron microscopy (SEM) images were obtained on a Zeiss Auriga with an acceleration voltage of 2 kV. Particle size distributions were evaluated using ImageJ software from SEM images (Figure S2). X-ray diffraction patterns were obtained on a Siemens D500 diffractometer with a Cu Kα radiation (λ = 1.54 Å, at 40 kV and 17 mA) in the 2 theta range of 10–80°, with an increment of 0.05°. UV–vis spectroscopy was carried out on a Shimadzu UV-2450PC spectrometer using an integrating sphere at the range of 300–800 nm. Infrared spectroscopy was performed on an FTIR-ATR Bruker Alpha-P within 1750–500 cm–1. Raman spectroscopy was performed using a Renishaw Raman confocal microscope, equipped with a 20× microscope objective (Leyca Microsystems) and a 633 nm laser (He–Ne, Melles Griot).

Classical Molecular Dynamics Simulations

Molecular dynamics simulations were carried out in LAMMPS[57] to study the PVP adsorption on two different SrTiO3 surfaces of interest: {110} and {100} with two different terminations, namely, {100} TiO2 and {100} SrO. The {110} surface had its strontium atoms removed for stabilization, as suggested before.[58] Slabs, of about 45 × 45 Å2 (periodic along the x and y directions) and a thickness along z (perpendicular to the surface) that is enough for the bulk density far from the surface to reach a constant value, were put in contact with vinylpyrrolidone trimers with density corresponding to its bulk under the relevant conditions, at 433 K (synthesis temperature of 160 °C for solvothermal reaction) for 10 ns (long enough for system equilibration), as performed in similar works.[59] The Nosé–Hoover thermostat was used for temperature control. The atomic positions of the crystal were kept fixed during the simulations. Atomic charges and Lennard-Jones parameters for SrTiO3 surfaces were taken from previous works on the adsorption of organic molecules,[58] and the interatomic interactions for PVP molecules were described using the CHARMM General Force Field,[60] with specific parameters for PVP.[61] The PPPM method was used to compute long-range electrostatic interactions. The LAMMPS initialization files were prepared with the aid of the ChemStruct Python package (https://pypi.org/project/chemstruct/). The bulk density for vinylpyrrolidone was previously determined at 1.0 atm for the force field parameters, showing good agreement with experimental values. Atomic positions were saved every 50 ps to compute the density as a function of position ρ(z),[58] by counting carbonyl oxygen atoms on a fine mesh of domain slices along the z axis (perpendicular to the exposed surface). This density was then used to compute potential of mean force (PMF) profiles along z, using eq as in previous works:[58]where R is the gas constant, T is the temperature, and ρ0 is the bulk density (far from the surface). Therefore, the shown PMF is given as energy per mol of repeating unit. PMF profiles are then used to estimate relative adsorption energies ΔEads (computed as the difference between the PMF of the bulk phase and the PMF at its lowest value, near the surface) and activation energy barriers for adsorption/desorption Eb (computed as the difference between maximum and minimum PMF values along the z direction) for the three investigated surfaces.
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