Experimental and Molecular Simulation Study for the Preparation of Ordered Mesoporous Carbons

In recent years a number of mechanisms for the preparation of ordered mesoporous carbons (OMCs) have been proposed for different systems. However, the exact preparation mechanism for the soft template method remains unclear, which seriously inhibits the further design and development of OMC materials on the molecular level, as well as better understanding of the related structure-activity relationship and their wider application. To clarify the mechanisms involved in the preparation of OMCs via the soft-template method, experimental and molecular simulation studies were performed in this work. First, OMCs were prepared using a triblock copolymer Pluronic F127 as the template and phenolic resin as the carbon source. These OMCs were characterized using X-ray diffraction (XRD), N2 adsorption-desorption and transmission electron microscopy (TEM), and the results show that the OMCs have well-ordered 2D-hexagonal structures and narrow pore size distributions. Additionally, the dissipative particle dynamics (DPD) method was carried out to investigate the phase behavior and self-assembly process of the F127/phenolic resin/ethanol system. The simulation results show that F127 could self-assemble a series of stable micellar structures at different concentrations, such as spherical, cylindrical, lamellar, body-centered cubic and cubic perforative ones. These micellar structures, similar to the template used in the experiment, controlled the structure of phenolic resin in ethanol solution, while the introduction of phenolic resin did not affect the selfassembled structure of F127. An investigation of the dynamic formation process involved in production of the cylindrical micelles indicates that the system transformed from a homogeneous state into the typical stable micellar structures due to their amphiphilic properties, which explains why cylindrical and uniform mesopores of OMCs were experimentally obtained. This work deepens our understanding of the mechanisms involved in the preparation of OMCs on a mesoscopic level. It also demonstrates that the DPD method is effective for studying the self-assembly of polymer systems, and provides useful guidance for the fabrication of novel materials.

One challenge in the synthesis of OMCs is in controlling their mesopore sizes and the pore sizes distributions, which are not typically uniform for the catalytic activation, polymer blending carbonization and organic aerogel carbonization methods (Tamon et al., 1998;Kyotani, 2000;Kim and Pinnavaia, 2001).The hard template method is a multistep, high-cost and time-consuming process (Zhang et al., 2006), which likely makes it unfeasible for the large-scale preparation of OMCs.The soft template method, however, is a relatively straightforward, inexpensive, and reproducible route for the preparation of OMCs (Sterka et al., 2012), which escapes from a fussy hard template process.As a result, the soft template method has been of great interest for the synthesis of OMCs.
Up to now, researchers have proposed many mechanisms for the preparation of OMCs, including the liquid crystal template mechanism (Beck et al., 1992), the cooperative formation mechanism (Huo et al., 1994;Wan et al., 2007), the charge density matching mechanism (Monnier et al., 1993;Schmidt et al., 2000), the generalized liquid crystal template mechanism (Huo et al., 1994;Firouzi et al., 1997), the silicate layer puckering mechanism (Inagaki et al., 1993;Göltner et al., 1998) and the silicate rod assembling mechanism (Chen et al., 1993).The exact preparation mechanism of OMCs for soft template method, however, is still ambiguous and not clear fully now, which inhibits seriously the further development of OMCs materials design on molecular level, structure-activity relationship and their wider application.
Based on precise theoretical models for accurate theoretical calculation, the molecular simulation technique could be helpful for tackling the problem mentioned above.Dissipative particle dynamics (DPD) simulation, a mesoscopic method developed by Hoogerbrugge and Koelman (1992), appears to be suitable for the simulation of systems that contain millions of atoms in a wider range of time and length scales, as compared with molecular dynamics or Monte Carlo techniques (Groot and Warren, 1997;Groot and Madden, 1998).Also, the DPD method can be used to simulate soft particles interacting through a simple-wise potential and thermally equilibrate through hydro-dynamics (Huang et al., 2003).In DPD, one treats simulated elements on a coarse-grained level by grouping atoms as a single bead, rather than as individual atoms.The beads experience a simple soft pair-wise interaction potential that allows for large time-scale simulations.Time evolution of the system is found by solving Newton's equations of motion.In the past decade, the DPD method has been applied successfully to numerous complex systems, such as self-assembly of amphiphilics (Rekvig et al., 2004;Qian et al., 2005;Yang et al., 2006), biological membranes (Allen, 2000;Kranenburg et al., 2003;Li et al., 2004), interfacial phenomena (Clark et al., 2000;Malfreyt and Tildesley, 2000;Kong and Yang, 2006), and polymeric vesicles (Laradji and Kumar, 2004;Ortiz et al., 2005;Shillcock and Lipowsky, 2005).
For better understanding regarding the preparation process of OMCs which were prepared by soft template method, experimental and molecular simulation study were performed in this work.Firstly, we prepared the OMCs using F127 as a template and phenolic resin as a carbon source, and then these OMCs were characterized using XRD, N 2 adsorptiondesorption and TEM.Additionally, the DPD method was performed to investigate the phase behavior and self-assembly process of the F127/Phenolic resin/Ethanol system.First, the mesoscale phase behavior of F127 in ethanol solution was investigated in detail under different concentrations and simulation time scales.Then, the true system of F127/Phenolic resin/Ethanol solution was simulated to investigate the preparation mechanism of OMCs.To the best of our knowledge, this is the first attempt to simulate the self-assembly process of OMCs using the DPD method.This study could offer a new way for the investigation of mechanisms on self-assembly for polymer systems on the mesoscopic level, and the results could be helpful for guiding the experimental synthesis of OMCs with desired properties efficiently.

Preparation Method of OMCs
OMCs were synthesized using F127 (PEO 106 -PPO 70 -PEO 106 , M w = 12600) as the template and phenolic resin as the carbon source.The soluble phenolic resin was prepared from phenol and formaldehyde according procedures reported by Meng et al. (2005Meng et al. ( , 2006)).The molar ratios of the synthesis compositions were Phenol:Formaldehyde:NaOH:F127 = 1: 2:0.1:0.015, and the final product was dissolved in ethanol to remove the NaCl precipitates which yielded a 20wt.%phenolic resin solution.
The typical process for synthesizing OMCs is described (Meng et al., 2005(Meng et al., , 2006;;Lin et al., 2006) as follows: 5 g F127 was dissolved in 40 mL ethanol, then 25 g of 20 wt.% phenolic resin solution was added with stirring for 20 min at room temperature.Next, the mixture was formed by evaporating the ethanol at 100°C for 24 h.Afterwards, the solid product was ground into powder and calcined in a tubular furnace at 450°C for 2 h, and then at 900°C for 3 h under N 2 flow.The heating rates were 1 °C/min below 450°C and 5 °C/min above 450°C.

Material Characterization
The X-ray powder diffraction patterns of OMCs were measured using a D8 diffractometer (Bruker, Germany) with Ni-filtered Cu-Ka radiation between 0.6° and 6° for small-angle X-ray diffraction and between 10° and 90° for wide-angle X-ray diffraction (Chang et al., 2012;Grigoriu et al., 2012).The N 2 adsorption-desorption isotherms were measured using a ASAP2010 (Micromeritics, USA) system, and the pore size distribution curves were determined from the adsorption branch of the isotherm.Morphologies of the OMCs were observed by transmission electron microscopy (TEM) using a JEM-2010HR (Jeol, Japan) instrument operated at 200 kV (Kim et al., 2011).

Simulation Method
The DPD method is a particle-based mesoscale simulation technology, which can be used to study the hydrodynamics behavior of complex fluids over long length and time scales by dividing them up into small interacting fluid packages.This method is based on the dynamics of a set of soft beads of a given mass and size, which interact with other beads via pairwise forces, leading to a correct hydrodynamic description (Hoogerbrugge and Koelman, 1992).
In this work, the DPD model used is based on that Groot and Warren (1997) and Groot and Madden (1998).Molecules in the system are divided into soft beads, and the evolution of the positions and impulses of all interacting beads over time is governed by Newton's equations: where r i , v i and f i are the position, velocity and total force vectors on the ith bead, respectively.The total force exerted on bead i contains three pairwise forces: the conservative force F C , dissipative force F D , and random force F R , respectively.Therefore, f i is composed of: (2) Beads interact with others only within a certain cut-off radius r c .When r c = 1, they are given, respectively, by where a ij is the repulsion parameter between particle i and σ defines the fluctuation amplitude, and θ ij is a randomly fluctuating variable with Gaussian statistics.Groot and Warren (1997) showed that F ij D and F ij R obey a fluctuation-dissipation theorem, where γ and σ are related by where γ and σ are the two multiplicative constants that are related by the absolute temperature T, and the Boltzmann constant, k B .The ω D (r ij ) and ω R (r ij ) can be taken simply as Groot and Warren (1997) also established the relationship between repulsive a ij and the Flory-Huggins χ-parameter: where ρ is the density, a ii is the repulsion parameter between the same type of particles, and a ij is the repulsion parameter between different types of particles.

Simulation System and Parameters
In this work, the simulation system is comprised of F127 (PEO 106 -PPO 70 -PEO 106 ), phenolic resin and ethanol.In a DPD simulation, the PEO-PPO-PEO block copolymer is treated as a coarse-grained chain, which describes the real molecular structure at the characteristic ratio statistical segment level, where the atomistic details are ignored.The molecular structure of F127 is separated into two types of beads (E, P), where seven EO segments and four PO segments represent one E bead and one P bead, respectively.According to previous studies on the partial volumes of EO groups and PO groups (Vlimmeren et al., 1999;Guo et al., 2002), it ensures that the EO and PO beads have comparable sizes of 450 Å 3 .Therefore, the nominal formula and coarsegained chains of F127 used in this study are shown in Fig. 1(a).Low-molecular-weight phenolic resin is composed of numerous repeated units [C 6 H 2 (OH)CH 3/2 ], and three of them are considered as an R bead to ensure that its volume is comparable with an E or P bead in the simulations.So, the typical structure of phenolic resin could be represented as R1R1[R1]R1 in Fig. 1(b).Accordingly, a small cluster with five ethanol molecules was taken together and grouped into a T bead in Fig. 1(c), whose size is approximately equal to the E, P or R bead mentioned above.
To simulate a system, a set of interaction parameters between beads must be determined.In this work, the bead density ρ was set to be 3 and the T-T, E-E, P-P, and R-R maximum repulsive parameters (a ii ) to be 25 in Eq. ( 10).The values of all the interaction parameters employed in this study are shown in Table 1.In the simulated system, the total volume V = V F + V P + V E , and the volume of F127, phenolic resins and ethanol are V F , V P and V E , respectively.So the concentration of F127 and phenolic resin were defined as C F = V F /V, C P = V P /V and C E = V P /V, respectively.A cubic simulation box of size 20 (nm) × 20 (nm) × 20 (nm) with periodic boundary conditions used in each direction was adopted, and the simulation box is large enough after testing.The number of beads in this box is 3.0 × 10 4 , and the integration time step Δt is taken as 0.05.All the simulations are performed with the commercial software package Materials Studio 4.4 from Accelrys Inc.

XRD, N 2 Adsorption and TEM
The small-angle XRD pattern of OMCs is shown in Fig. 2(A).The pattern reveals three distinct peaks that are   indexable as (100), ( 110) and ( 200) reflections, which are the characteristic diffraction peaks of a space group P6mm hexagonal structure (Liu et al., 2006).The interplaner spacings d are 8.8 nm, 5.1 nm and 4.4 nm, respectively.Their ratios corresponded with 1: ( 1/ 3 ): (l/2), which indicates that the OMCs have well ordered 2D-hexagonal structure.The wide-angle XRD pattern of OMCs is illustrated in Fig. 2(B).It shows a broad peak at 24° and a less intense peak at 44° in the pattern, which could be attributed to the (002) and ( 100) diffraction peaks of carbon material (Ting et al., 2012).
The nitrogen adsorption-desorption isotherms and pore size distribution for the OMCs are shown in Fig. 3(A).As shown in the figure, the nitrogen adsorption-desorption isotherms of OMCs are of a typical type IV with a clear H1-type hysteresis loop, which is characteristic of highly ordered mesoporous materials with high pore size uniformity.A very sharp step at P/P 0 = 0.4-0.8,corresponding to the capillary of nitrogen inside the mesopore, reveals the narrow pore size distribution of the obtained carbon material.From the pore size distribution curve (Fig. 3(B)), a narrow pore distribution centralized at 3.6 nm can also be obtained.
The high-resolution TEM images of OMCs show a highly ordered degree of periodicity, viewed along the (100) and ( 110) directions (Fig. 4), further confirming the 2-D hexagonal p6mm arrangement of the pores with uniform sizes and well-aligned channels.The pore diameter estimated   from the TEM image is 3.7 nm, which is consistent with the nitrogen adsorption result.In addition, no other mesophases can be observed, implying that the ordered 2-D hexagonal mesostructure is a pure phase.

Simulation Time Scale
Fig. 5 shows the evolution of the diffusion coefficient of each bead type (T, E, P and R) in the simulated system with the simulation time.It is shown that, in the early stage (up to 5000 DPD time steps), the diffusion coefficients of F127, phenolic resin, and ethanol are all fluctuant and distinct from each other, which indicates the existence of metastable aggregates during self-assembly.After about 15,000 DPD time steps, the diffusion coefficient of each type of bead does not change, which indicates the system has achieved equilibrium.The motion velocities of the R bead are a little higher than those of the E and P beads, while the E and P beads become equal but obviously different from that of T bead.It indicates that the F127 and phenolic resin assemble together into stable colloids in ethanol solution.It also indicates that it is reasonable to use 20,000 DPD time steps (t = 1 ms) per simulation to attain sufficient simulation quality with a reasonable computation time cost.

Phase Behavior of F127/Ethanol Two-Component System
For an amphiphilic block copolymer, such as F127, one of its remarkable properties is it can assemble into a series of ordered structures via the process of phase separation (Tanaka et al., 2005;Qian et al., 2011).The F127 concentration has a significant influence on the micelle stability of F127/Phenolic resin/Ethanol system.The effect of F127 concentration on the mesostructure has been investigated and the results are shown in Fig. 6, which displays a rich variety of typical and stable micellar structures of the F127 aggregates formed with the increasing of C F at the end of 20,000 DPD time steps.When C F is 0.15, the micelles are spherical (Fig. 6(a)).Then, cylindrical micelles are formed when C F is 0.30 (Fig. 6(b)).With a further increasing of C F , the lamellar micelles, the body-centered cubic micelles and cubic perforative micelles are formed subsequently (Fig. 6(c)-(e)).Generally, the micellar structures transform from simple to complicated in the simulated system with the increase of C F .In addition, it is clear that hydrophobic P segments form the inner core of the micelles due to the repulsive interaction with ethanol, and the core is wrapped by the hydrophilic E segments and set up a shell between the core and ethanol for all micellar structures mentioned above, which is consistent with results from previous research (Alexandridis et al., 1994a, b;Wanka et al., 1994;Alexandridis et al., 1995;Cau and Lacelle, 1996).Theoretically, the phase separation process of F127 is driven by thermodynamic properties such as enthalpy and entropy.The entropy is related to the conformation, configuration and translation of different block chains, and it is regulated by the degree of polymerization and composition.(Soto-Figueroa et al., 2007, 2008).The enthalpy is associated with the Flory-Huggins interaction parameter, which involves the repulsive interaction between different components due to their chemical incompatibility.Therefore, the enthalpicentropic balance dominates the self-assembly process via phase separation and it has been applied successfully in dynamics simulations (Leibler, 1980).
According to one previous experimental study (Wang et    al., 2012), we concluded that F127 is a structure-directing agent during the preparation of OMCs, and that the type of mesoporous channel is cylindrical and well-aligned from TEM observation.So the formation of cylindrical micelles for F127/Ethanol system is the basis of mesopore-forming of OMCs.Therefore, we selected the concentration C F = 0.3 for the further simulation investigation regarding the preparation of OMCs.

Phase Behavior of F127/ Phenolic Resin/Ethanol Three-Component System
To simulate OMCs preparation, phenolic resin was introduced into the F127/Ethanol system.A series of simulations were performed at a constant concentration (C p = 0.1) to investigate the influence of phenolic resin on the self-assembly process of F127 (Fig. 7).This figure presents the equilibrium morphologies formed at the end of 20000 DPD time steps.When C F = 0.15, spherical micelles start to form (Fig. 7(a)).At C F = 0.30, the system assembles into cylinder (Fig. 7(b)).With a further increase of C F from 0.45 to 0.60, lamellar (Fig. 7(c)) and body-centered cubic micelle (Fig. 7(d)) structures are observed, respectively.Finally, the micelles are cubic perforative (Fig. 7(e)) when C F = 0.75.The structures obtained above could be compared with those achieved from experimental results in the amphiphilic triblock copolymer-phenolic resin synthesis (Wanka et al., 1994;Meng et al., 2005Meng et al., , 2006;;Wan et al., 2007).Generally, the micellar structures transform from spherical micelles, cylindrical micelles, lamellar micelles, body-centered cubic micelles to cubic perforative micelles in the simulated system with the increase of C F .Obviously, the typical micellar structures are in good agreement with those in F127/Ethanol system at the same C F , respectively.The simulation results mean the introduction of phenolic resin did not affect the self-assembly process of F127 in ethanol solution.
Also, it is clear that all the typical micelles in Fig. 7 correspond to a three-layer core-shell structure, with hydrophobic P beads forming the inner core, then E and R beads forming a shell between the core and ethanol, and finally with phenolic resin beads forming the outer layer of the shell.The structure is consistent with previous results of research (Alexandridis et al., 1994a, b;Wanka et al., 1994;Alexandridis et al., 1995;Cau and Lacelle et al., 1996).It is well known that micelles start to form when the amphiphilic copolymer concentration in ethanol is higher than the critical micellization concentration.The self-assembly process is driven by the phase separation thermodynamics due to the repulsive interaction of chemically dissimilar components (Soto-Figueroa et al., 2007), which illustrates the mechanism of phase formation.On the other hand, the interaction between the hydrogen bonds of F127 and the phenolic resin has a significant impact on phase transformation.This interaction could cause a change in the ratio of hydrophilic to hydrophobic segments in the phenolic resin-F127 mesophase and induce a curvature at the PEO/PPO interface.The volume ratio of hydrophilic/hydrophobic changed with the increasing of C F , which makes it unable to support the original interfacial curvature and a new balance is needed.Consequently, the phase transformation occurred.
The formation of the cylindrical three-layer core-shell micellar structures for F127/Phenolic resin/Ethanol system is the basis of OMCs preparation, so we take the cylindrical micelle structure (Fig. 7(b)) as an example for investigating the dynamic process of micelle formation.,The evolution of cylindrical structures as a function of simulation time is shown in Fig. 8.In order to see the simulated snapshots more clearly in the complicated system, the isosurface of density fields for the snapshots is shown and the ethanol molecules (blue beads) are not shown in the Fig. 8.The simulation starts from a homogeneous state in the simulated cell (Fig. 8(a)).With the increase of DPD time steps, the chains of F127 molecules rapidly form small clusters due to their amphiphilic properties.When the DPD time steps approaches 2,000 (Fig. 8(c)), the F127 molecules form the initial cylindrical micellar structure, and are wrapped by the phenolic resin partly after a period of fluctuation.Then, the micellar structures changed from out-of-order state into a regular cylinder with the further increasing of DPD time steps from 2,000 to 6,000 (Fig. 8(c)-(e)).When the DPD time steps exceed 6,000, the cylindrical micelles changed little, which indicates that the system has achieved equilibrium.One stable mesophase is formed at 20,000 DPD time steps (Fig. 8(f)).We can see clearly from Fig. 8 that the equilibrium morphology obtained is a three-layer core-shell structure, and the structure indicates the repulsion force of ethanol with phenolic resin beads is more than R-E and R-P, which corresponds to the interaction parameters value in Table 1.Also, the F127 provides a stable framework for the phenolic resin to form a cylindrical mesoporous structure, showing its great influence on morphology in the phase separation process (Wanka et al., 1994;Meng et al., 2006).

Preparation Mechanism of OMCs for F127/Phenolic Resin/Ethanol System
Through investigating the phase behavior and self-assembly process of the preparation of OMCs using a simulation method, the preparation mechanism of on the molecular level could be summarized in Fig. 9. Firstly, C F = 0.3 is selected because the formation of cylindrical micelles for F127 is the basis of mesopore-forming of OMCs.At beginning of the simulation, E, P, R and T beads are distributed uniformly in the simulated system (Fig. 9(a)).Then, the micellar structure Fig. 8. Dynamics process of forming cylinder micelles for the F127/Phenolic resin /Ethanol system (Green, Magenta and Cyan represents the P beads, E beads and R beads, respectively.)Fig. 9.The preparation mechanism of OMCs for the F127/Phenolic resin/Ethanol system (Green, Magenta, Blue and Cyan represents the P beads, E beads, T beads and R beads, respectively.) is changed from an out-of-order state into regular and stable cylinders with the increasing of DPD time steps to 20,000 (Fig. 9(b)).It is clear that the cylinders exhibit a three-layer core-shell structure by the isosurface of density fields, with hydrophobic P beads forming the inner core (Fig. 9(c)), E beads forming a shell between the core and ethanol (Fig. 9(d)), and finally the phenolic resin beads being adsorbed on the surface of hydrophilic E beads to form the outer layer of the shell (Fig. 9(e)).In this system, the structure of phenolic resin is controlled by F127, which indicates that the F127 acts as a structure template.Finally, the three-layer cylindrical structure is kept with the evaporation of ethanol during the thermal polymerization, so that the OMCs are prepared successfully after the calcinations (Fig. 9(f)).During the calcinations, F127 is completely eliminated to form mesopore and the phenolic resins are eSntirely carbonized to form the framework of OMCs.Additionally, the OMCs obtained in simulation exhibit well ordered 2D-hexagonal structures.The structures observed from parallel and vertical direction of channel are similar with the images viewed along the ( 110) and (100) directions by TEM (Fig. 9(g)-(h)) respectively, which suggests that the results are in good agreement with the experimental results (Wang et al., 2012).

CONCLUSIONS
In present study, we have successfully prepared the OMCs using a soft template method, and utilized the DPD simulation method to investigate the phase behavior and self-assembly process of F127/Phenolic resin/Ethanol system for better understanding the preparation mechanism of OMCs on mesoscopic level.Some conclusions were drawn as follows: (1) OMCs with an ordered 2-D hexagonal mesostructure were successfully prepared by the soft-template method.
(2) For the F127/Phenolic resin/Ethanol system, a series of typical and stable micellar structures were shown at different F127 concentrations, such as spherical, cylindrical, lamella, body-centered cubic and cubic perforative.The ordered mesostructure formed is mainly controlled by the self-assembly of F127, and the introduction of phenolic resin did not affect the selfassembly process.Additionally, the enthalpic-entropic balance dominates the self-assembly process via phase separation during all simulations.(3) The dynamic process of forming cylindrical micelles shows that the micellar structures changed from a homogeneous state into an equilibrium state and one stable mesophase is formed finally due to their amphiphilic properties, which explains why the cylindrical and uniform mesopores of OMCs were experimentally obtained.In addition, the three-layer core-shell structure is formed with phenolic resin forming the outer layer of the shell, which means that the ordered mesostructure formed is mainly controlled by the self-assembly of F127 that acts as a structuredirecting agent.This conclusion is in agreement with the results from experiments.(4) This constitutes the first attempt to simulate the selfassembly process of OMCs with DPD method and has deepened the understanding of preparation mechanism on a mesoscopic level.This work has demonstrated that the DPD method is effective for studying the selfassembly of polymer systems and gives useful guidance on the fabrication of novel materials.

Fig. 5 .
Fig. 5. Evolution of the diffusion coefficient of DPD beads in the simulated system with the simulation time.

Table 1 .
Bead-bead interaction parameters a ij in DPD simulation.