The effect of nano confinement on the C-h activation and its corresponding structure-activity relationship.

The C-H activation of methane, ethane, and t-butane on inner and outer surfaces of nitrogen-doped carbon nanotube (NCNTs) are investigated using density functional theory. It includes NCNTs with different diameters, different N and O concentrations, and different types (armchair and zigzag). A universal structure-reactivity relationship is proposed to characterize the C-H activation occurring both on the inner and outer surfaces of the nano channel. The C-O bond distance, spin density and charge carried by active oxygen are found to be highly related to the C-H activation barriers. Based on these theoretical results, some useful strategies are suggested to guide the rational design of more effective catalysts by nano channel confinement.

Reactions or molecule structures n class="Chemical">confined in nano channels are quite different from those outside of channels. Such confinement effects widely exist in carbon nanotubes (CNTs), zeolites, and other mesoporous materials123456. The confinement provides a potential method to control the reactivity of catalysts dramatically.

It was found from a variety of experiments that confinement efn class="Chemical">fects could accelerate the reaction on the inner surface of channels789101112131415, such as hydrogenation of CO to ethanol7, Fischer-Tropsch chemistry8, hydrolytic and kinetic resolution of epoxides9, asymmetric hydrogenation10, sulfoxidation11, solvent-free esterifications12, hydrogenation1314, photocatalytic reaction15, and so on. Confinement can influence both the active phase and the reactants inside the CNTs. As a result, the reactions in channel are more effective1216.

Some experimental technologies (such as IR1718, in situ XRD8, and neutron scattering19) have been successfully developed to investigate the chemical phenomena happening in nano channels. Because experimental measurements can only reflect an integration over multiple effects20, theoretical calculations are still useful and important methods for understanding the origin of the stn class="Chemical">ructure and reaction inside the nano channels2122.

The confinement efn class="Chemical">fects have been observed theoretically in many reaction processes, such as D + H2 → HD + H in CNTs23, ethylene oligomerization in zeolitic mesopores24, propene metathesis reaction in zeolites25, syngas reaction in CNTs26, ethylene dimerization in zeolites27, O2 dissociation between two Pt (111)28, H2 dissociation in CNTs29, and acetone tautomerization in zeolite30. Why does confinement influence the reaction in channels? Theoretical researches have revealed that confinement can change the interactions between reactant and catalyst31323334353637. Confinement can also influence the electronic structure of catalyst in channel2324252627282930. In addition, confinement effect can even induce the variation of hydrophilic-hydrophobic property38 and dynamical behavior39 of the compounds in the nano channel.

It is believed that the reactions in the channel are influenced by the confinement whereas there is no such efn class="Chemical">fect on the outer surface of channel12345678910111213141516232425262728293031323334353637. It is important, though quite difficult, to describe the reaction both on the inner and outer surfaces of nano tube using the same model. If we can find a unified structure-reactivity relationship, it will build a bridge between reactions inside and outside of the nano tube.

Results

Modeling

The model used here is the C–H activation of methane by n class="Chemical">oxygen adsorbed on the inner and outer surfaces of nitrogen-doped carbon nanotubes (NCNTs). The model of NCNTs with adsorbed oxygen has been shown previously40. We also have discussed the adsorption and activation of oxygen on NCNTs4142, and the oxidation of methane on the surface of NCNTs by the adsorbed oxygen in previous papers43. In the oxidative dehydrogenation of ethane, the NCNT is also an effective catalyst44. The ability of these adsorbed oxygen in the oxidation reactions have also been proved by experiments454647. NCNTs used here are armchair nanotubes with delocalized σ electrons and terminated with C–H bonds, in which a nitrogen atom was placed substitutionally in the middle of a pure carbon nanotube40. The O atom is located on the surface of NCNTs with an optimized C–O bond length based on previous research of oxygen adsorption on NCNTs404143. There are two ways to generate the active oxygen atom on the surface of NCNT: (1) O2 dissociate on carbon atoms neighboring a nitrogen dopant of NCNT with a small dissociation barrier4849. In this case, both of the oxygens are active50; (2) A hydrocarbon can be oxidized by the terminal oxygen of O2 adsorbed on the surface of NCNT, and the remainder oxygen atom is active43. They are abbreviated as NCNT (N, N) (N = 5, 7, 9, and 10, the corresponding optimized diameters are 7.0, 9.8, 12.5, and 13.9 Å, respectively). For NCNT (7, 7), different N concentrations are taken into consideration (0.82% and 2.45% for C139NH28 (N0.82CNT (7, 7)) and C137N3H28 (N2.45CNT (7, 7)), respectively, see Supplementary information for the structure details). Correspondingly, NCNT with different O concentrations are investigated (0.93% and 2.72% for C139NOH28 and C137N3O3H28 respectively). The length of all NCNTs is 12.9 Å if not mentioned. Both reactions inside and outside of NCNT were taken into consideration. The following abbreviations are used: NCNT (N,N)in-hydrocarbon or NCNT (N,N)out-hydrocarbon means that the C–H activation of hydrocarbon is inside or outside of NCNT (N, N), respectively.

Confinement effects on catalysts and C–H activation

First, the influences of confinement on the electronic and geometric characteristic of the adsorbed n class="Chemical">oxygen were investigated. Four parameters are taken into account, the spin density (SDO) and charge (QO) carried by the active oxygen, the C–O bond length (RC-O), and the gap between the lowest unoccupied and highest occupied molecular orbital (LUMO-HOMO) (Figure 1). It is obvious that the values in the inside of the NCNTs are quite different from those of outside, especially when the diameter of the channel is small. The SDO, QO, RC-O, and LUMO-HOMO gap obtained on outer surface of NCNTs show a monotonic increase or decrease with the increasing tube diameter. However, for the SDO, QO, and RC-O values obtained inside NCNTs, there exists a inflection point for NCNT (5, 5) (diameter = 7.0 Å) that is induced by extreme confinement. To understand why the SDO value of NCNT(5, 5)in is different from others, the spin density distributions of NCNTs with active oxygen inside and outside are presented in Figure 2. The spin density of NCNT(5, 5)out, NCNT(7, 7)in, NCNT(9, 9) and NCNT(10, 10) are mainly located around the active oxygen, whereas that of NCNT(5, 5)in is dispersed on the whole tube. As result, the SDO value of NCNT(5, 5)in is far smaller than others.

Figure 1

The influences of NCNT diameter on the SDO, QO, RC-O, and LUMO-HOMO values with oxygen in (black square) and outside (red circle) of nano channel.

Figure 2

The spin density distributions of NCNTs with active oxygen in and outside of the channel.

When the diameter is larger than 7.0 Å, the curves become regular. The difn class="Chemical">ference between the electronic and geometric parameters obtained inside or outside becomes smaller and smaller as the tube diameter increases, implying that the confinement effect becomes weaker and weaker. One can image that when the diameter of the tube is large enough, the inside and outside can be considered as two parallel sides of a plane. In this case, the confinement effect should disappear.

The oxidation of hydrocarbons includes two steps, C–H activation and C–O rebound43515253. The C–H activation is the rate-determining step in reactions catalyzed by NCNT43 and other catalysts515253. Herein, we focus on the C–H activation of methane, ethane, and t-butane on the inner or outer surfaces of NCNTs with different diameters. The imaginary frequencies of the transition state for the C–H activation are −1448.7, −1464.5, −1452.5 and −1442.8 in NCNT(5,5)in–CH4, NCNT(5,5)out–CH4, NCNT(7,7)in–CH4, and NCNT(7,7)out–CH4 respectively. These transition states have only one imaginary frequency and the values are big enough to show the corresponding structures are real transition states. The motion described by the eigenvector associated with these imaginary frequencies corresponds to the proton transfer from carbon to oxygen.

In all cases, the C–H activation barriers obtained inside are lower than those on the outside for the same substrate and NCn class="Chemical">NT (Table 1). Taking the reaction occuring on the inner and outer surface of NCNT(7,7) as example, B3LYP/6-31G structure optimization and energy calculation show that the methane C–H activation barrier obtained in channel is 8.8 kJ/mol lower than that obtained outside. A MP2/6-31G single point energy calculation shows that the barrier obtained inside is 26.1 kJ/mol lower than that obtained outside. Correspondingly, the H–CCH4 bond distances of the transition states obtained outside are larger than those obtained inside for the same NCNT (Figure 3). The order of the H–CCH4 bond distances is: NCNT(5,5)in–CH4 < NCNT(7,7)in–CH4 < NCNT(9,9)in–CH4 < NCNT(10,10)in–CH4 < NCNT(5,5)out–CH4 < NCNT(7,7)out–CH4 < NCNT(9,9)out–CH4 < NCNT(10,10)out–CH4. It suggests that confinement can shorten the proton transfer distance from reactant to transition states, which is beneficial for reducing the reaction barrier. Being consistent with the influence on electronic and structural parameters, a small diameter brings larger difference in C–H activation barrier (Figure 4). Even so, for the largest tube NCNT(10,10) investigated here, the energy difference of 4.1 kJ/mol will bring about 5 times enhancement of the reaction rate according to the transition state theory. These findings agree well with experimental results. Till now, most of the experiments have shown that the reactions performed in the inside of channel are faster than those of outside789101112131415.

Table 1

The C–H activation barrier (E≠) and substrate binding energy (BE) in or outside of different NCNTs[a]

	BE (in)	E≠ (in)	BE (out)	E≠ (out)
NCNT(5,5)–CH4	32.2	66.4	−6.0	76.4
NCNT(7,7)–CH4	−3.4	65.4	−6.6	74.2
NCNT(7,7)–C2H6	−2.8	46.4	−0.4	50.2
NCNT(7,7)–C4H10	5.0	34.4	−7.1	39.0
N2.45CNT(7,7)–CH4	−10.4	54.7	−7.0	73.6
NCNT(9,9)–CH4	−5.2	70.3	−7.4	75.1
NCNT(10,10)–CH4	−3.3	69.9	−4.9	74.0
NCNT(11,0)–CH4	−9.4	125.6	-	-

[a]All energies are given in kJ/mol. ‘In' means reaction in the channel and ‘out' represents reaction outside of the channel.

Figure 3

The optimized transition states of methane C–H activation.

The shown values are CNCNT–O, O–HCH4 and H–CCH4 distances in Å.

Figure 4

The barrier difference of methane C–H activation in the inside and outside of the NCNT.

Previous researches using the model with only one N atom doping have revealed that the origin of catalytic activity of NCNTs is that the N-doping can induce electron-deficient carbon around the doped N atom4041. When three N atoms are doped in the nano tube, each N atom on the NCNT shows almost the same negative charge, and the carbon atoms around the nitrogen show similar positive charge comparing with the NCNT with only one N atom doping (Figure S1 in Supplementary information). It is interesting to find that each N–C part can be regarded as a new active center for the activation of oxygen. The O atom binding with any N–C part carries similar charge and spin density compared with the NCNT with only one N atom doping (Figure 5). As results, these O atoms are quite reactive for the C–H bond activation. The barriers of methane C–H activation on the inner and outer surface of N2.45CNT (7,7) are 54.7 and 73.6 kJ/mol respectively. Though the barrier of C–H activation on different N–C part may have a little difference induced by the variation of SDO and QO values in different region, these barrier heights are low enough to indicate the high reactivity of each N–C part. In this case, it is reasonable to believe that NCNTs doped with more N atoms will provide more active centers to adsorb and activate oxygen, which will make the NCNTs more powerful catalyst. In fact, experimental results have revealed that NCNT doped with 2.6% N atom is more active than that doped with 1.2% N atom54.

Figure 5

The QO and SDO values carried by N2.45CNT(7,7) (upper) and the optimized transition state (lower).

Values out and in parentheses are QO and SDO values respectively. The italic data are bond distances in Å.

Armchair and zigzag CNTs are two typical stn class="Chemical">ructures of nanotubes. A zigzag NCNT with diameter of 8.6 Å [NCNT (11,0)] was fully optimized and compared with the armchair NCNTs with similar diameter [NCNT (7, 7)] (Figure 6). It was found that the O atom in the inside of NCNT (11,0) is quite different from that of NCNT (7, 7). The QO value of NCNT (11,0)in is more negative compared with all armchair NCNTs investigated here, and the SDO value of NCNT (11,0)in is also smaller than those of all other armchair NCNTs. As a result, the methane C–H activation barrier obtained in the inside of NCNT (11,0) is quite high (125.5 kJ/mol).

Figure 6

The QO and SDO values carried by zigzag NCNT(11,0) (left) and the optimized transition state (right).

Values out and in parentheses are QO and SDO values, respectively. The italic data are bond distances in Å.

Discussion

Structure-activity relationship

As we know, molecular structures and reactions occurring inside of the channel are influenced by n class="Chemical">confinement, whereas there has no such effect on the outer surface of channel123456789101112131415161718192021222324252627282930313233343536373839. It seems that it is quite difficult to describe the reaction in and outside of the channel by the same model. Does there exist a universal structure-reactivity relationship to predict the reactions occurring both inside and outside of channel?

The well-known BEP relations have revealed that the reactivity of catalysts is related to the binding strength of the reactant5556. Herein, the C–H activation barrier is used as the y-axis to plot against the binding energy between methane and NCNTs in which only one oxygen binds with methane (Figure 7). If all structures are taken into consideration, there has no any relationship between reaction barrier and binding energy (R2 = 0.101). It seems that the BEP relation does not work for NCNTs systems. The electronic and geometric parameters of NCNT(5, 5)in is abnormal due to the extreme confinement (Figure 1). The diameter of NCNT(5, 5) is so small (7.0 Å) that methane is hindered to enter the tube (Table 1). If the point belonging to NCNT(5, 5)in is not included in the data fitting, the correlation coefficient increases to 0.586. In this case, the activity of NCNTs are correlated with the binding energy of the reactant to some extent (R2 = 0.586). Adsorption of reactant with small binding energy corresponds to low activation energy. This is similar to the case of ethylene hydrogenation on the surface of Pd/Au(111), Pd(111), Pd/Ru(0001) and Pd/Re(0001)55. For the nano confinement space, if the channel is too small, the adsorption of key reactant will be highly unfavorable. In this case, the reaction may be inhibited in confined space5758. The activation of methane in NCNT(5, 5) and t-butyl in NCNT(7, 7) are two typical examples (Table 1).

Figure 7

The relationships between the reaction barrier and binding energy of methane.

To find out a more reasonable structure-activity relationship for nano n class="Chemical">confinement systems, the reaction barrier is used as the y-axis to plot against SDO, QO, RC-O or LUMO-HOMO values, respectively (Figure 8). Similarly, the point belongs to NCNT(5, 5)in is not included in the data fitting due to the extreme confinement. It is interesting to note that SDO, QO, and RC-O are highly related to the C–H activation barrier, no matter whether the reaction happens inside or outside of the surface. The correlation coefficients are 0.992, 0.990, and 0.846 for SDO, QO, and RC-O respectively. Designing more powerful catalyst becomes much easier with these linear structure-reactivity relationships. Modification that leads to larger SDO or RC-O will give a more powerful catalyst. According to the results presented in Figure 1, if the catalytic active center is inside of the channel, we should adopt small tube diameter to increase its reactivity. Indeed, this idea has been achieved in some experiments123456. The challenges are how small the tube diameter can be and whether the substrate can enter the tube smoothly when the tube is too small.

Figure 8

The relationships between the reaction barrier and SDO, QO, RC-O or LUMO-HOMO values.

Though the HOMO-LUMO gap has been widely used to predict the reactivity of catalysts in homogeneous systems59, it seems that this common method does not work in predicting the influence of n class="Chemical">confinement (Figure 8). There is no relationship between the LUMO-HOMO gap and reaction barrier obtained on the inner or outer surface of the channel. Though the electronic structure of O atom inside of zigzag NCNT is quite different from those of armchair NCNT, the structure-activity relationship revealed here can predict the C–H activation barrier on the surface of both armchair and zigzag NCNTs.

It should be noticed that the results obtained here are based on finite carbon nanotubes. Theoretical calculations that have adopted this method have achieved many successes in previous researches27283740414243536061626364656667, including the prediction on the reactivity of NCNT4143 which has been proven by experiment454647. Methods taking the periodic boundary condition into consideration may further improve these theoretical results. Though the influence of periodic boundary is not taken into consideration, theoretical researches using finite CNT and NCNT have revealed that the properties of carbon nanotubes exhibit a periodic behavior with increase in tube length426869. For the systems investigated here, a periodic oscillation is also observed as the tube length increases (Figure 9). In order to investigate the influence of boundary, NCNT(7, 7)out with different lengths and terminals were calculated (Figure S2 in Supplementary information). Though the SDO, QO and RC-O values of different NCNT(7, 7)out are various, their C–H activation barriers can be ascertained by the structure-activity relationship summarized in Figure 8.

Figure 9

The HOMO–LUMO gap of NCNTs with different tube length.

In conclusion, based on a systematic DFT investigation on the C–H activation of n class="Chemical">methane, ethane, and t-butane on the inner and outer surface of NCNTs with different diameters, different N and O concentrations, and varying types (armchair and zigzag), the following can be stated: (1) The C–H activation processes investigated here perform more effectively inside of NCNTs due to the confinement effect. This effect is weakened as the tube diameter increases; (2) A universal structure-reactivity relationship was found for reactions occurring both on the inner and outer surface of nano channel. No matter whether the reactions occur inside or outside of the channel, SDO, QO, or RC-O can be used to predict the C–H activation barrier. It gives a clear connection between reactions in and outside of nanotubes.

Methods

As a good compromise between n class="Chemical">computational efficiency and reasonable results, the density functional theory (DFT) based method is widely used for the calculation of nanotube27283740414243536061626364656667 and small molecular activation using nanomaterial as catalysts4041424364. Among these DFT based calculations, the B3LYP method is a good choice for nanotube and it has been shown to be in excellent agreement with the experimental data273740414243474849505152606162636465. When B3LYP method is applied for NCNT systems, using different basis sets (6-31G, 6-311G, and aug-cc-pvdz) gave similar C–H activation barrier43. Hence, all the structures were optimized at the B3LYP/6-31G level of theory using the Gaussian 03 program.

The computed stationary points have been characterized as minima or transition states by diagonalizing the Hessian matrix and analyzing the vibrational normal modes. In this way, the stationary points can be classified as minima if no imaginary frequencies are shown or as transition states if only one imaginary frequency is obtained. The particular nature of the transition states has been determined by analyzing the motion described by the eigenvector associated with the imaginary frequency.

Author Contributions

X.B.H. and Y.T.W. proposed the idea, analyzed the data and wrote the paper. J.S. and L.H.Y. performed the calculations. Z.B.Z. participated in the discussion and revised the manuscript. All authors reviewed the manuscript.