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Understanding strength and nature of noncovalent binding to surfaces imposes significant challenge both for computations and experiments. We explored the adsorption of five small nonpolar organic molecules (acetone, acetonitrile, dichloromethane, ethanol, ethyl acetate) to fluorographene and fluorographite using inverse gas chromatography and theoretical calculations, providing new insights into the strength and nature of adsorption of small organic molecules on these surfaces. The measured adsorption enthalpies on fluorographite range from −7 to −13 kcal/mol and are by 1–2 kcal/mol lower than those measured on graphene/graphite, which indicates higher affinity of organic adsorbates to fluorographene than to graphene. The dispersion-corrected functionals performed well, and the nonlocal vdW DFT functionals (particularly optB86b-vdW) achieved the best agreement with the experimental data. Computations show that the adsorption enthalpies are controlled by the interaction energy, which is dominated by London dispersion forces (~70%). The calculations also show that bonding to structural features, like edges and steps, as well as defects does not significantly increase the adsorption enthalpies, which explains a low sensitivity of measured adsorption enthalpies to coverage. The adopted Langmuir model for fitting experimental data enabled determination of adsorption entropies. The adsorption on the fluorographene/fluorographite surface resulted in an entropy loss equal to approximately 40% of the gas phase entropy.
Recently discovered two-dimensional (2D) materials such as graphene, fluorographene, graphene oxide, transition metal dichalcogenides, hexagonal boron nitride, and phosphorene all have very high surface/mass ratios, and many of their potential practical applications rely on their large surface areas. Consequently, there is a need to better understand their surface properties and the way in which their surfaces interact with their surroundings. In particular, there is great interest in the adsorption of molecules on 2D materials because of its technological importance. Small molecule adsorption can be used to tune the electrical properties of 2D materials1 and is important in processes that can be exploited in mass,2 gas,3 and electrochemical4 sensing. All kinds of sensors require a contact between an analyte and an active material to generate a readout, so it is essential to have a good understanding of the strength and nature of the interactions between adsorbed molecules and the sensing surface.5 Fluorographene6−8 (i.e., a fluorographite monolayer), fluorinated graphenes, and fluorographite are all active in electrochemical sensing and have sensing properties that depend on their C/F ratio and topology.9 As such, they could potentially be used to create selective sensors in which specificity is achieved through the interaction of the analyte with an active zone consisting of a suitable fluorinated graphene. In addition to sensing applications, these materials can be used in gas separation and storage.10,11 It has been demonstrated that adsorption to graphene is primarily controlled by London dispersive forces,12 but little is known about adsorption to fluorographene and fluorographite. The few theoretical studies that have explored the adsorption of small molecules to fluorographene have suggested that it may have useful applications in hydrogen storage.10,11,13,14
Adsorption enthalpies on surfaces are usually studied using adsorption calorimetry, temperature-programmed desorption, or equilibrium adsorption isotherms.15 Recently, we witnessed a renaissance of inverse-gas chromatography (iGC) to study the process of adsorption. This technique measures retention characteristics of gas probes injected to a column loaded by analyzed material.16,17 Its main advantage is that it provides results that represent averages over the sample’s surface. In addition, adsorption enthalpies and entropies, and the dependence of these thermodynamic quantities on the surface coverage, can be obtained directly from iGC data.12,18,19 It was shown that iGC provides adsorption enthalpies consistent with other experimental techniques.20
Quantum chemistry and solid-state physics calculations can be used to characterize intermolecular interactions and predict their strengths. However, deciphering the nature and strength of molecule–surface binding by computational means is frequently rather challenging because the binding energies are usually low and involve physical phenomena such as London dispersion forces that are difficult to model reliably;21 physisorption forces are significantly weaker than chemisorption ones.22,23 In finite molecular systems, the electron–electron correlation effects responsible for these noncovalent interactions can be described using the coupled cluster method, with single and double electron excitations being modeled iteratively and triple excitations perturbatively (CCSD(T)), or using the perturbative Møller–Plesset MP2.5 method (in which energies are calculated as the arithmetic mean of the MP2 and MP3 energies).24 Unfortunately, these methods are not available for periodic systems, which are frequently superior to finite models when studying the adsorption of molecules on surfaces.22 Consequently, methods based on density functional theory (DFT) are widely used in such applications. Classical general gradient approximation DFT methods are of semilocal character and thus cannot describe the long-range component of the London forces, which result from nonlocal electron–electron correlation. A range of theoretical methods has been developed to address this deficiency.25 The performance of individual DFT methods is usually benchmarked against CCSD(T) or MP2.5 calculations on finite systems (molecular clusters), in order to identify approaches that accurately describe the system of interest. Both CCSD(T) as well as MP2.5 methods provide highly accurate interaction energies for various types of molecular clusters with errors of less than 2 and 4 relative percent, respectively.24 CCSD(T) can be applied to complexes having up to around 35 heavy atoms, while MP2.5 can handle systems up to twice the size. Unfortunately, however, no reference method of comparable quality is currently available for use with periodic models, with the exception of the stochastic quantum Monte Carlo method,22,26,27 that embody exceeding computational demands.
In this work, we determined isosteric adsorption enthalpies (ΔH) and isosteric adsorption entropies (ΔS) for five organic molecules (acetone, acetonitrile, dichloromethane, ethanol, and ethyl acetate) on fluorographite by iGC. We also performed extensive calculations on finite models of fluorographene to benchmark various DFT methods against CCSD(T) and MP2.5. The application of symmetry-adapted perturbation theory (SAPT)28 to finite model systems allowed us to decipher the nature of the molecular interactions occurring on the fluorographene/fluorographite surfaces. Moreover, DFT calculations on periodic models helped us to clarify the roles of various adsorption sites and surface defects on adsorption to fluorographene, as well as the influence of molecular clustering. We conclude that the enthalpies of adsorption to fluorographene/fluorographite are slightly lower than those for graphene/graphite, i.e., small molecules generally bind more strongly to fluorographene and fluorographite than to their nonfluorinated counterparts.
Using iGC we determined the isosteric adsorption enthalpies of five molecular probes (Table 1) to fluorographite for coverage values ranging from 2 to 20% of the adsorbate monolayer. The isosteric adsorption enthalpies of acetone, acetonitrile, and ethanol decreased as the surface coverage increased, with saturation occurring at a coverage level slightly above 10% (Figure Figure11). The isosteric adsorption enthalpies of ethyl acetate and dichloromethane were rather coverage-independent. The saturated adsorption enthalpies ΔH ± δΔH reported in Table 1 ranged from −6.9 kcal/mol (dichloromethane) to −12.8 kcal/mol (ethanol). The measured enthalpies suggest that the studied molecules adsorb by physisorption.
Isosteric adsorption enthalpies ΔH (top) and entropies ΔS (bottom) for five organic molecules on fluorographite obtained from inverse gas chromatography as a function of surface coverage. The dotted lines are eye-guides.
Saturated Adsorption Enthalpies ΔH (in kcal/mol) and Entropies ΔS (in cal/molK) of Molecules on Fluorographite and Their Respective Confidence Intervals (for a 5% Level of Significance) Obtained by Inverse Gas Chromatography
When explaining coverage dependence of the adsorption enthalpies, one should take into account the fact that the real material surface is really complex containing various structural and chemical features and defects, e.g., edges, steps, cavities, pores, vacancies, or adatoms. Such features may represent sites, where the adsorbate preferentially binds (the high-energy sites19). In addition, some adsorbates may tend to form clusters over the surface.18 As the iGC provides averaged adsorption enthalpies over the surface all these effects are involved. Fortunately, the complexity of the process can be typically deciphered from the plot of adsorption enthalpy vs coverage in combination with atomistic simulations. The decreasing adsorption enthalpies of acetone, acetonitrile, and ethanol with increasing coverage (Figure Figure11) can be explained by the clustering of these molecules over the adsorbent surface, because the same behavior was observed for ethanol adsorption to graphene and was attributed to ethanol clustering over the graphene surface.18 This behavior might occur when the adsorption enthalpy of a single molecule to the surface is greater than the enthalpy of condensation; however, we should note that a tendency of clustering is given by a delicate balance among adsorption enthalpy, enthalpy, and entropy of clustering.18 The rather constant adsorption enthalpies of dichloromethane to the surface (at very low coverage levels; see Figure S1 in the Supporting Information) may indicate that the material used in this work had few high-energy sites or that the enthalpies of adsorption to structural features that typically correspond to high energy sites (e.g., steps, edges, cavities, and defects) are comparable to those for adsorption to a fluorographene/fluorographite surface lacking such features. Computational methods (see below) were used to determine which of these potential explanations was most plausible.
We measured the adsorption enthalpies of the same probe molecules to graphene powder in a previous investigation.12,18,19 On comparing the adsorption enthalpies for fluorographene/fluorographite and graphene/graphite, we found that the enthalpies of adsorption to fluorographite are generally slightly lower than those for graphene/graphite (by 1.2 kcal/mol on average, corresponding to 14% of the ΔH for graphene; see Table 1). This indicates that small organic molecules bind more strongly to fluorographite than to graphite and hence that fluorographene/fluorographite more readily adsorbs guest molecules from its environment.
We used finite systems to benchmark the accuracy of selected DFT methods when applied to the systems of interest and used the best-performing methods in these benchmarking studies to perform further calculations on periodic-boundary models. Two small models of fluorographene/fluorographite surfaces were used in the benchmarking calculations. The smallest model, perfluorohexamethylcyclohexane (C12F24), was small enough to permit the use of the CCSD(T) method, which provides very accurate interaction energies ΔEi for a wide range of complexes. However, because of the small size of this model, it may not constitute an adequate representation of the theoretically infinite fluorographene/fluorographite surface. We therefore also considered a larger model, hexatriacontafluorotetracosahydrocoronene (C24F36), which is more representative and was also used to obtain geometries and enthalpy corrections (see Methods). Because it was computationally unfeasible to perform CCSD(T) calculations on this larger system, we instead performed reference calculations using the MP2.5 method, which is known to approach the quality of CCSD(T) for many noncovalent complexes.29 The use of MP2.5 in this case was validated by comparing the energies calculated with this method for the smaller C12F24 system to those obtained with CCSD(T). Both CCSD(T) and MP2.5 explicitly model the dispersion energy, whereas most DFT methods model it implicitly using some kind of correction.30 This is one of the reasons why the performance of dispersion-corrected DFT techniques must be carefully tested.
The CCSD(T) and MP2.5 interaction energies for the dichloromethane and ethanol complexes of C12F24 were in reasonably good agreement (Table 2), although the CCSD(T) interaction energies are systematically more attractive (by 10% on average) than the MP2.5 energies. This justified the use of the less expensive MP2.5 method as a source of reference data for calculations on the large models. DFT functionals with London dispersion corrections generally provided reasonably accurate energies for the smaller complexes (Table 2, Figure Figure22, Figure S2), but optB86b-vdW and vdW-DF overestimated the interaction energy by over 30% for this model. However, it should be noted that the optB88-vdW functional provided the best agreement with experimental data in a study on the adsorption of small molecules to graphene.12 This may indicate that the individual dispersion-corrected DFT methods do not provide a consistent treatment of dispersion interactions for finite size and periodic systems. Together with the limited amount of available experimental data on such systems, this complicates the assessment of theoretical methods for adsorption studies.
Models of fluorographene (top) and their interaction energies ΔEi with dichloromethane, showing the dependence of the interaction energy on the size of the model system and the computational method used (bottom). Dark gray and green represent C ...
Interaction Energies ΔEi (in kcal/mol) of Five Organic Molecules with Perfluorohexamethylcyclohexane (C12F24)
Table 3 summarizes the interaction energies calculated for complexes of the larger C24F36 system with the five organic molecules using MP2.5 and various DFT functionals. The MP2.5 results suggest that the complexes with the largest and smallest interaction energies are those of ethyl acetate and dichloromethane, respectively, and all of the tested functionals replicated this trend. The optB86b-vdW and vdW-DF functionals again strongly overestimated the absolute interaction energies (by more than 56%), whereas the B97-D3 functional underestimated the interaction energies by more than 25%. Other DFT functionals provided interaction energies that agreed reasonably well with the reference MP2.5 values. The B3LYP-D3 and PBE-D3 functionals gave the most accurate interaction energies with respect to MP2.5 (with deviations below 10%); however, PBE-D2, PBE-TS+SCS, and vdW-DF2 functionals performed also well because the CCSD(T) energies were more negative than the MP2.5 values for the smaller model.
Interaction Energies ΔEi (in kcal/mol) of Five Organic Molecules to Perfluorotetracosahydrocoronene (C24F36)b
To determine how the interaction energy ΔEi depends on the model size, we performed calculations on a larger finite model system - C54F72. We also compared all of the results obtained using finite size models to results for an infinite (periodic) model based on a 5 × 5 fluorographene supercell. This comparison was justified by the fact that the calculated adsorption configurations on fluorographene were similar to those for the finite models (Figure Figure33). Interaction energies for small molecules on all four models of fluorographene (C12F24, C24F36, C54F72, and periodic C50F50; see Figure Figure22) could be computed using DFT methods implemented in the VASP package (see the Methods section), namely the empirically corrected density functionals PBE-D2, PBE-D3, PBE-TS, and PBE-TS-SCS, as well as the nonlocal correlation functionals vdW-DF, vdW-DF2, and optB86b-vdW. We also performed less expensive wave function-based calculations using the MP2/aug-cc-pVDZ method to compare the interaction energies computed in this way for the three finite systems (C12F24, C24F36, and C54F72) to those obtained by DFT.
Adsorption geometries of acetone, acetonitrile, dichloromethane, ethanol, and ethyl acetate (from the top to the bottom, respectively) on perfluorinated tetracosahydrocoronene (left column) and fluorographene (right column). Structures shown in the left ...
Figures Figures22 and S2 present the results of the calculations performed for the adsorption of dichloromethane (and ethanol) on all four fluorographene model systems using various methods. In all cases, the calculated interaction energy decreased as the model size increased, i.e. the small molecules were most strongly bound on periodic fluorographene. The ratio of MP2.5/CBS interaction energies of dichloromethane and ethanol molecules with C24F36 and C12F24 equals to 1.2 and 1.3, respectively. The same ratio of MP2/aug-cc-pVDZ for dichloromethane complexes equals to 1.4, whereas it becomes 1.2 when we consider C54F72 and C24F36 models. It should be noted here that MP2.5 and MP2 describe the dispersion energy explicitly, which means that they model well both pairwise and many-body energy terms31 (however, strictly speaking, MP2 does not provide reliable values for the many-body dispersion term32). This is not necessarily true for DFT methods.33−35 The ratios of the calculated energies of the dichloromethane and ethanol complexes of C24F36 and C12F24 obtained with different DFT methods were generally similar to the MP2.5 values (in the cases of PBE-D2, PBE-D3, vdW-DF2, and optB86b-vdW) or the MP2 values (for PBE-TS, PBE-TS-SCS, and vdW-DF). Moreover, the DFT interaction energy ratios for the C54F72 and C24F36 models were similar to those obtained with MP2. The tested DFT methods thus predict the effects of increasing surface size similarly to MP2.5 and MP2, both of which correctly model many-body terms.
The interaction energies calculated for the largest finite model system, C54F72, were only slightly (0.2–0.8 kcal/mol) higher than those for the infinite periodic surface (Figures Figures22 and S2). This suggests that calculations on C54F72 provide quite good estimates of interaction energies for fluorographene. In addition, the relative ordering of the interaction energies for the studied small molecules on C54F72 matched that for the periodic system.
The calculated interaction energies obtained for the periodic model system with different density functionals decreased in the following order: ΔEiPBE-D3 > ΔEiPBE-D2 > ΔEivdW-DF2 > ΔEiPBE-TS, ΔEiPBE-TS+SCS > ΔEivdW-DF, ΔEioptB86b-vdW (see the interaction curves in Figure S3). The interaction energies provided by the DFT-D3 and optB86b-vdW/vdW-DF functionals thus corresponded to the upper and lower limits of the DFT energy range, which spanned approximately ~3 kcal/mol on average (~5 kcal/mol for ethyl acetate). The DFT energies calculated for the finite C24F36 model were less variable (spanning a range of ~2 kcal/mol for all small molecules other than ethyl acetate; see Table 3), and those for the smallest C12F24 model varied still less, with a range of ~1 kcal/mol (Table 2).
The calculations performed using the DFT functionals with empirical dispersion corrections indicated that dispersion interactions are the most important component of the interaction energy resulting from the binding of small molecules to the fluorographene surface. The pure PBE functional yielded a very shallow potential well for molecular adsorption to fluorographene (<1 kcal/mol, Figure S3), but substantially more negative adsorption energies were obtained using functionals with dispersion corrections. Based on the adsorption energies computed using the many-body D3 dispersion correction, dispersion accounted for 92% of the total binding energy (ΔED3/ΔEPBE-D3) in the case of acetone, 64% for acetonitrile, 69% for dichloromethane, 73% for ethanol, and 83% for ethyl acetate. This trend was confirmed by more rigorous DFT based symmetry adapted perturbation theory (DFT-SAPT)28 calculations on the intermediate finite model C24F36 (see Figure Figure44). The dispersion contribution (calculated as ΔEidisp/(ΔEidisp + ΔEiind + ΔEielst) dominated, accounting for 72%, 70%, 73%, 70%, and 76% of the total attractive interaction energies for acetone, acetonitrile, dichloromethane, ethanol, and ethyl acetate, respectively. The electrostatic term (19–23%) represented the second largest attractive contribution, followed by the induction or polarization term (4–9%); see Figure Figure44. This trend is similar to that observed for the interaction of small molecules with a finite model of graphene (coronene, see Table S1 for a comparison). In the graphene case, the interactions were similarly dominated by dispersion (62–66%), with lesser contributions from electrostatics (26–29%) and induction (8–12%).12 The relative contribution of electrostatics to binding in the case of C24F36 was lower than that for graphene, which is somewhat surprising given that C–F bonds are highly polar (to the extent that they have been labeled “semi-ionic”36), making the distribution of electron density across the fluorographene plane rather inhomogeneous.37
Decomposition of the total attractive energy into dispersion, induction, and electrostatic contributions calculated by DFT-SAPT for the small model system C24F36.
Data for the hexatriacontafluorotetracosahydrocoronene model system (C24F36; see Figure Figure33) were used to estimate the different contributions to the adsorption enthalpies of small molecules12 on fluorographene (Table 4) by applying standard expressions from statistical mechanics under the ideal gas, rigid rotor, and harmonic oscillator approximations. The derived enthalpy/energy differences (ΔH – ΔE) ranged from 1.2 to 1.5 kcal/mol and were used as corrections to derive adsorption enthalpies from the adsorption energies calculated for the periodic model. These adsorption energies ranged from −7.8 to −13.8 kcal/mol (optB86b-vdW functional, Table 5) and dominated the calculated adsorption enthalpies because the correction terms were equal to at most ~19% of the calculated interaction energies. The same trend was previously observed for adsorption to graphene.12
Adsorption Energies (in kcal/mol) and Other Quantitiesa Characterizing the Adsorption of Five Organic Molecules on Perfluorinated Tetracosahydrocoronene
Adsorption Energies and Enthalpies of Five Organic Molecules on Periodic Fluorographene in kcal/mol Calculated with Various Density Functionalsa
We investigated the potential contributions of surface irregularities, defects, and molecular configurations to the adsorption process by studying the roles of (i) multilayers, (ii) surface steps and edges, and (iii) surface defects (Figure Figure55). Specifically, we compared the adsorption of ethanol on monolayer and bilayer fluorographene, because studies on graphene had previously shown that adsorption to multilayer graphene was slightly stronger than that to a graphene monolayer.18,19 Conversely, the energy of adsorption for small molecules on bilayered fluorographene was 1.4 kcal/mol higher than that for a fluorographene monolayer (Table S2, Supporting Information). The addition of a third layer of fluorographene changed the adsorption energy by less than 0.1 kcal/mol relative to that for the bilayer.
Adsorption geometries of an ethanol molecule on multilayer fluorographene and a fluorographene step/edge (top). Adsorption geometries of an ethanol molecule on fluorographene with vacancy defects and a Stone–Wales defect (middle). Clustering of ...
Steps are regarded as high-energy sites in multilayered graphene and graphite because the energy change upon adsorption to steps is up to 2.5 times greater than that for adsorption to a stepless surface. Such effects are easily detected in iGC experiments.18,19 In the case of fluorographene, the calculated adsorption energies on steps were only 10–20% lower than those for the stepless surface (Table 6). Taking into account Boltzmann distribution of probes between the high-energy sites and surface,19 such differences are barely experimentally detectable, as demonstrated by the corresponding iGC data (cf. section 2.1). In addition, the calculated adsorption energies for ethanol on fluorographene edge sites were less favorable (−4.0 and −3.1 kcal/mol) than those for the surface (−8.7 kcal/mol, Figure Figure55).
Adsorption Energies (in kcal/mol) of Five Organic Molecules on Fluorographene Steps and Defect-Free Surfacesa
We also considered four types of defect sites: (i) F vacancies, (ii) C vacancies, (iii) C–F vacancies, and (iv) Stone–Wales (SW) defects, the latter corresponding to lattice reconstructions in which four hexagons were transformed into two pentagons and two heptagons [an SW(55–77) defect] (Figure Figure55). Ethanol bound preferentially to the defect-free surface: its adsorption energies on the defect sites (−6.7 to −7.2 kcal/mol) were less negative than those for the perfect surface (−8.7 kcal/mol).
The experiments indicated that clustering played a significant role in the adsorption of ethanol, acetonitrile, and acetone to fluorographene/fluorographite (cf. section 2.1 and Figure Figure11). To clarify its effects, we explored the binding of ethanol clusters to fluorographene. Our calculations revealed the formation of cyclical planar ethanol clusters lying flat on the fluorographene surface (Figure Figure55). The adsorption energies of ethanol dimers, tetramers, and hexamers on fluorographene were −10.7 kcal/mol, – 11.2 kcal/mol, and −13.1 kcal/mol per molecule, respectively, and were lower than the adsorption energy of single molecules (−8.7 kcal/mol). This strongly suggests that ethanol forms clusters on fluorographene surfaces and that the measured adsorption enthalpies corresponded to the binding of ethanol clusters. Similar analyses were then performed for the binding of ethanol to graphene.18 The adsorption energy of a single ethanol molecule on fluorographene (−8.7 kcal/mol) was lower than on graphene (−7.7 kcal/mol). On the other hand, the adsorption energies of ethanol clusters on fluorographene were higher than on graphene (−11.2 kcal/mol on fluorographene compared to −15.6 kcal/mol for (EtOH)4 on graphene18). This different adsorption behavior of molecules and clusters is probably due to competition between H-bonding in the cyclic ethanol clusters (as occurs on the graphene surface) and possible H-bonding between the OH group of an isolated ethanol molecule and the F atoms of fluorographene: the calculated O–F distance for the O–H···F H-bond was 3.2 Å for a single ethanol molecule positioned on a fluorographene surface such that its −OH moiety was situated in the middle of an F-triangle (Figure Figure55).
The calculations indicate that acetonitrile also formed clusters on the fluorographene surface: the calculated adsorption energy for a single acetonitrile molecule (−7.8 kcal/mol) was substantially less negative than those for acetonitrile dimers (−10.6 kcal/mol per molecule) or trimers (−10.9 kcal/mol per molecule). The flat antiparallel adsorption geometries predicted for acetonitrile clusters on the fluorographene surface (see Figure Figure66 for an image of the trimer) were very similar to those identified for free clusters.38 The C–H···N hydrogen bonding within the acetonitrile clusters appeared to be weak38 given the calculated d(C–N) distance of 3.4 Å, whereas the corresponding d(C–F) distances for the putative C–H···F bonds to the fluorinated surface ranged between 3.2 and 3.5 Å (Figure Figure66).
Top (top) and side (bottom) views of the adsorption geometries of acetonitrile (left) and acetone (right) trimers on fluorographene. Selected weak bonds between molecules in clusters (top) and between molecules and surfaces (bottom) are highlighted by ...
The clustering of acetone on fluorographene appeared to be less favorable than ethanol and acetonitrile because the adsorption energies of the acetone dimer (−10.9 kcal/mol) and trimer (−11.5 kcal/mol) were comparable to that for a single acetone molecule (−10.7 kcal/mol). The planar acetone clusters that were predicted to form on the fluorographene surface (Figure Figure66) do not adopt the typical cyclical structures of free acetone clusters.39 However, the weak intracluster C–H···O=C hydrogen bonding (Figure Figure66, d(O–C) = 3.3 Å) observed on the fluorographene has also been observed in free acetone clusters.39,40
The difference in behavior of the ethanol, acetonitrile, and acetone molecules and other two adsorbates (as indicated by experiment) motivated us to perform additional calculations with ethyl acetate. We performed periodic calculations and evaluated the overall energy balance for the creation and adsorption of selected ethanol and ethyl acetate clusters. The thermodynamic cycle shown in the Scheme 1 explained the different behavior of ethanol and ethyl acetate on the surface, because the energy of clustering ΔE of ethanol molecules over the surface is negative (−2.5 kcal/mol) favoring formation of clusters, while the energy of clustering of ethyl acetate over the surface is close to zero (−0.3 kcal/mol). Typical enthalpy correction ΔH – ΔE for the process of clustering is of order of 1 kcal/mol per molecule (e.g., ΔH – ΔE corrections for ethanol clusters up to pentamer ranged between 0.9–1.4 kcal/mol per molecule18); therefore, enthalpy of clustering of ethyl acetate dimer from monomers on the surface will be positive, i.e., disfavoring formation of surface clusters.
Thermodynamic Cycle for the Creation of an Adsorbed Ethanol Tetramer (Left) and Ethyl Acetate Dimer (Right) on a Fluorographene/Fluorographite Surface Evaluated Using a Periodic Model
The clustering on the fluorographene surface complicates direct comparisons of the measured adsorption enthalpies for the five molecular probes (Table 1) to those obtained from the calculations (Table 5). In fact, direct comparisons are only really justifiable for dichloromethane and ethyl acetate. We therefore corrected the adsorption enthalpies calculated for acetate, acetonitrile, and ethanol to account for the effects of clustering, as discussed in the preceding section. We also corrected the calculated ΔH values for adsorption to fluorographene (Table 5) using the correction terms calculated for fluorographite surface adsorption (Table S2) to enable meaningful comparison of the experimental and calculated quantities. A comparison of the experimental and modified computational results is presented in Figure Figure77.
All of the DFT methods systematically underestimated the strength of molecule/cluster binding to the fluorographite surface, i.e., the calculated ΔH values were always higher than the experimental values. The best accuracy was achieved with the optB86-vdW functional because its ΔH values were closer to the experimental results than those obtained with any other method. For clarity, only results obtained with this functional are shown in Figure Figure77. The inclusion of corrections for clustering always shifted the calculated adsorption enthalpies toward the experimental values. For dichloromethane and ethyl acetate, DFT methods that include dispersion corrections based on nonlocal correlation functional (i.e., optB86b-vdW, vdW-DF, and vdW-DF2) gave adsorption enthalpies that were closer to experiment than those that use corrections based on atom-centered empirical functions (DFT-DX methods). This trend opposes that observed in the benchmark calculations on small fluorographene models. It has many possible causes, ranging from the precise implementations of the empirically corrected DFT methods to the correct inclusion of many-body effects,35,41 and warrants further investigation.
The Langmuir adsorption model enabled enumeration of both the adsorption enthalpies and entropies. The entropies ranged from −19 cal/molK for dichloromethane to −36 cal/molK for ethanol. The overall trends in the adsorption entropies mirrored those for the adsorption enthalpies (Figure Figure11). It has previously been shown that the adsorption entropy of physisorbed molecules is surface-independent, being governed by the temperature and the gas phase entropy of the adsorbate.42,43 This might explain the rather good agreement between the measured adsorption energies and those calculated for the finite fluorographene models (Table 1 and Table 4), although it is important to bear the effects of the experimentally observed clustering. The entropy loss upon adsorption corresponded to around 40% of the total gas phase entropy on average (Table S3 in the Supporting Information), which is consistent with previously published data.42 A restriction of translational and rotational degrees of freedom of the adsorbed molecule was responsible for the entropy loss (Table S3). It should be noted that the discussed mirroring of entropies might indicate that stronger binding leads to larger entropy loss due to larger restriction of the probe conformational freedom on the surface.
We measured adsorption enthalpies of acetone, acetonitrile, dichloromethane, ethanol, and ethyl acetate on fluorographite by inverse gas chromatography at surface coverage levels ranging from 2 (0.2 for dichloromethane) to 20%. Plots of the resulting isosteric adsorption enthalpies revealed that acetone, acetonitrile, and ethanol cluster on the fluorographite/fluorographene surface. The other two molecules exhibited relatively coverage-independent adsorption enthalpies. The calculated saturated adsorption enthalpies on fluorographene ranged from −6.9 kcal/mol for dichloromethane to −12.8 kcal/mol for ethanol and were 1–2 kcal/mol lower than those previously determined for graphene. Computational investigations provided deeper insights into the strength and nature of adsorbate-fluorographene/fluorographite binding. Finite size models amenable to study using reference theoretical methods were a bit too small for reliable estimation of interaction energies but were useful in evaluating the accuracy of the adsorption energies calculated with various DFT methods because they permitted benchmarking against CCSD(T) and MP2.5 results. These benchmarking studies showed that dispersion corrected DFT functionals performed well and can be safely used for relative comparisons of adsorption energies. The finite size models also provided information on enthalpy corrections, which were rather modest, ranging from 1.3 to 1.5 kcal/mol. Despite the good performance of the dispersion-corrected functionals in the benchmarking study, nonlocal vdW DFT functionals (particularly optB86b-vdW) achieved the best agreement with experimental data when using a periodic model of fluorographene. Computational investigations using these functionals revealed that we did not detect binding to high-energy sites in the iGC experiments because binding to these structural features, which is typically very energetically favorable in layered materials, was either only slightly (by 10–20% for steps) more favorable or less favorable (in the case of edges) than binding to the surface. The adsorption enthalpies were largely controlled by the interaction energies, which were dominated by London dispersive forces. The clustering of ethanol, acetonitrile, and acetone on the fluorographene/fluorographite surface was explained by a delicate interplay between intracluster and cluster-surface bonding. Finally, we estimated adsorption entropies for the different adsorbates, which ranged from −19 cal/molK for dichloromethane to −36 cal/molK for ethanol and corresponded to a loss of ~40% of the gas phase entropy upon adsorption. These results indicate that calculations on finite size models are adequate for estimating adsorption entropies on fluorographene surfaces.
All measurements were conducted using an SMS iGC-SEA 2000 instrument (Surface Measurement Systems Ltd., UK) in a silanized column (3 mm diameter and 30 cm long) filled with a 23.9 mg sample of graphite fluoride (Sigma–Aldrich). Before each measurement, the sample was washed at 80 °C using He as the carrier gas at a flow rate of 10 sccm. A detailed characterization of the sample can be found in our previous article.44 The used graphite fluoride crystals have a laminar morphology, and their surfaces are dominated by exposed fluorographene planes with a small proportion of edges and steps. Measurements were carried out with acetone (Merck, LiChrosolv, for HPLC, 99.8%), acetonitrile (Lach:ner, HPLC supergradient, min. 99.9%), dichloromethane (Merck, for LC LiChrosolv, ≥99.9%), ethanol (Merck, gradient grade for LC LiChrosolv, ≥99.9%), and ethyl acetate (Lach:ner, HPLC, min. 99,8%). Primary chromatograms were recorded at temperatures from 303 to 363 K using He as the carrier gas at the flow rate of 10 sccm. The column temperature was controlled by the instrument oven with declared stability of ±0.1 °C. Partial pressures of adsorbates were calculated from the primary chromatograms, i.e., peak maxima, using instrument calibration and Cirrus Plus Software advanced version 188.8.131.52 (Surface Measurement Systems Ltd., UK). The partial pressures of individual adsorbates were measured at the given targeted surface coverage νi as a function of temperature. The measurements were repeated for various target surface coverage νi, which ranged from 2% to 20% of monolayer. The saturated (40 °C) adsorbate vapors were injected into the column, and the injection time was set up to reach the targeted surface coverage. The required injection time was calculated from the targeted surface coverage, known surface area (236.9 m2/g) of the material,44 adsorbate vapor tension at 40 °C, and adsorbate cross sectional area using Cirrus Control Software advanced version 1.3.3 (Surface Measurement Systems Ltd., UK).
The low surface coverage values considered in the experiments permitted application of the Langmuir adsorption model.12,18,19 This assumption leads to the equation18, which we used directly to fit the isosteric enthalpy of adsorption ΔHi ± δΔHi and the entropy of adsorption ΔSi ± δΔSi (Figure S3) for each considered target surface coverage νi. The partial pressure of the adsorbate, the standard pressure of 760 Torr, the universal gas constant, and the column temperature are denoted as p, pø, R, and T, respectively. The saturated adsorption enthalpy ΔH ± δΔH was obtained as the mean value of n particular enthalpies obtained by fitting. The error in the saturated enthalpy, δΔH, was determined as the maximum individual δΔHi value. The same was done for the saturated entropy, ΔS ± δΔS.
The adsorption energy, ΔE, was calculated as the difference between the energy of the most favorable configuration of the complex (comprising one molecule/cluster on fluorographene) and the sum of the energies of the optimized isolated species (fluorographene and the molecule in vacuum). In contrast, the interaction energy, ΔEi, was calculated on the basis of each separated fragment in the geometry of the complex. The enthalpy of adsorption, ΔH, was calculated by adding the zero-point energy (ΔΔE0) and the thermal (ΔΔET) and enthalpic (ΔΔEH) corrections to the adsorption energy, i.e., ΔH = ΔE + ΔΔE0 + ΔΔET + ΔΔEH. The corrections ΔΔE0, ΔΔET, and ΔΔEH were evaluated for the molecule on a finite model of fluorographene, fully fluorinated tetracosahydrocoronene (C24F36), i.e., ΔHfluorographene ≈ ΔEfluorographene + (ΔHC24F36 – ΔEC24F36). For this purpose, geometry optimizations and frequency calculations were performed, and partition functions and thermochemical data (at 313.15 K and 101.325 kPa) were obtained. We used the B97D functional45 and cc-pVTZ basis sets for all elements and the Gaussian09 package46 for calculations on C24F36.
Reference wave function-based calculations of interaction energies ΔEi were performed with a small finite model of fluorographene, perfluorohexamethylcyclohexane (C12F24). Accurate and computationally demanding CCSD(T)/complete basis set limit (CBS) interaction energies were determined using the formula24
Here, the CCSD(T) correction term was determined as the difference between the CCSD(T) and MP2 interaction energies with the 6-31G**(0.25,0.15) basis set. The basis set 6-31G**(0.25,0.15) is a modified version of the 6-31G** basis set in which the exponential parameters of the polarization functions were altered from their original values to 0.25 (C, N, F, O atoms) and 0.15 (H atom). The MP2/CBS interaction energies were determined by summing the Hartree–Fock and MP2 correlation energy components, ΔEi = ΔEiHF + ΔEicorr, both of which were extrapolated from the aug-cc-pVDZ (aDZ) and aug-cc-pVTZ (aTZ) basis sets.24,47,48
Alternative calculations were performed using the MP2-F12 method and the cc-pVDZ-F12 basis set to evaluate interaction energies. In these calculations, the core electrons were frozen, and interaction energies were corrected for the basis set superposition error (BSSE).49
The MP2.5/CBS interaction energies obtained for both the previously mentioned finite models were calculated using the following extrapolation equation24
The MP2.5 correction term was computed as a difference between the MP3 and MP2 interaction energies with the 6-31G**(0.25,0.15) basis set. As an alternative to the CBS limit, explicitly correlated MP2-F12 was used without any extrapolation.24 All reference calculations were performed in TurboMole 6.650 under the Cuby framework51 with the exception of the MP2.5 correction terms, which were calculated in Molcas 8.052
SAPT decomposition allows the interaction energy to be partitioned into physically meaningful components. For this purpose, we used DFT-SAPT28 as implemented by Hesselmann et al.53 in the Molpro program package,54 and we collected SAPT components into four terms corresponding to electrostatics, exchange repulsion, induction, and dispersion:28
We used the LPBE0AC exchange-correlation potential for monomer calculations53 and the cc-pVTZ basis set.
DFT calculations on periodic fluorographene and its finite models were performed using the projector-augmented wave (PAW) method in the Vienna Ab initio Simulation Package (VASP, version 5.3.5).55,56 Empirically corrected density functionals (PBE-D2,45 PBE-D3,57 PBE-TS,58 PBE-TS-SCS59) and nonlocal correlation functionals (vdW-DF,60 vdW-DF2,61 optB86b-vdW62) that approximately account for nonlocal dispersion interactions were employed. The fluorographene sheet was modeled using a 5 × 5 supercell (C50F50···molecule) or 7 × 7 supercell (C98F98···cluster) with a chair structure, which has been shown to be the most stable fluorographene conformer.63 Input geometrical parameters for fluorographene were obtained by PBE optimization from our previous works37,64 and were as follows: lattice constant of a = 2.61 Å, C–C bond length of 1.58 Å, C–F bond length of 1.38 Å, and C–C–C bond angle of 110.9 deg. Multilayer fluorographene structures were modeled by fluorographene sheets with AA stacking;44,65 an interlayer lattice constant of c = 6 Å was used as an input for optimization. For instance, the bilayer step of fluorographene consists of two sheets in a 5 × 10 supercell with the second sheet reduced to a 5 × 5 supercell and terminated by 5 + 5 fluorine atoms (150 carbon and 160 fluorine atoms in total). As periodic boundary conditions were applied in all three dimensions, a periodicity of at least 20 Å in the out-of-plane direction was imposed to minimize (spurious) interactions between adjacent layers. The energy cutoff for the plane-wave (PW) expansion was set to 400 eV, a convergence criterion of 10–6 eV was used in the SCF cycle, and Γ-point calculations were performed. The positions of the atoms were relaxed using the conjugate gradient method until the forces on each atom were below 1 meV/Å. For the final geometries of the 5 × 5 supercells, we recalculated all total energies with the 3 × 3 k-point mesh and an energy cutoff of 500 eV (see Table S4 for the convergence test).
Finally, the interaction energies for the C24F36 complexes were also calculated by DFT using Gaussian orbitals. Several functionals (B97D,45 B3LYP,66,67 and PBE68) and TZVPP69 basis sets were used in conjunction with the empirical D3 dispersion correction;57 the hybrid meta M06-2X70 functional was used with the cc-pVTZ basis set.
The authors gratefully acknowledge support from the Ministry of Education, Youth and Sports of the Czech Republic (LO1305 and CZ.1.05/2.1.00/19.0377) and the Czech Science Foundation (P208/12/G016). Funding from the European Union’s Horizon 2020 research and innovation programme to M.O. under grant agreement No. 683024 (ERC-CoG) is gratefully acknowledged. M.O. thanks Neuron fund for support of science. M. Pitonak was supported by the Slovak Grant Agency VEGA under the contract No. 1/0092/14. M. Pykal was supported by the student project of Palacký University (IGA_PrF_2016_028). This work was part of the Research Project RVO: 61388963 of the Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic.
The authors declare no competing financial interest.