Determination of domain sizes in blends of poly(ethylene) and poly(styrene) formed in the presence of supercritical carbon dioxide

Well-mixed blends of poly(ethylene) and poly(styrene) have been synthesized using supercritical carbon dioxide as a solvent. The morphology of the blends has been conclusively characterized using differential scanning calorimetry (DSC), small-angle X-ray scattering (SAXS), Raman microprobe microscopy, and C-13 solid-state cross-polarization magic angle spinning NMR (C-13 CPMAS NMR). DSC measurements demonstrate that poly(styrene) in the blends resides solely in the amorphous regions of the poly(ethylene) matrix; however, corroborative evidence from the SAXS experiments shows that poly(styrene) resides within the interlamellar spaces. The existence of nanometer-sized domains of poly(styrene) was shown within a blend of poly(styrene) and poly(ethylene) when formed in supercritical carbon dioxide using Raman microprobe microscopy and C-13 CPMAS NMR spectroscopy coupled with a spin diffusion model. This contrasts with blends formed at ambient pressure in the absence of solvent, in which domains of poly(styrene) in the micrometer size range are formed. This apparent improved miscibility of the two components was attributed to better penetration of the monomer prior to polymerization and increased swelling of the polymer substrate by the supercritical carbon dioxide solvent.

High-pressure adsorption capacity and structure of CO2 in carbon slit pores: Theory and simulation

We present new simulation results for the packing of single-center and three-center models of carbon dioxide at high pressure in carbon slit pores. The former shows a series of packing transitions that are well described by our density functional theory model developed earlier. In contrast, these transitions are absent for the three-center model. Analysis of the simulation results shows that alternations of flat-lying molecules and rotated molecules can occur as the pore width is increased. The presence or absence of quadrupoles has negligible effect on these high-density structures.

Effects of potential models on the adsorption of ethane and ethylene on graphitized thermal carbon black. Study of two-dimensional critical temperature and isosteric heat versus loading

Adsorption of ethylene and ethane on graphitized thermal carbon black and in slit pores whose walls are composed of graphene layers is studied in detail to investigate the packing efficiency, the two-dimensional critical temperature, and the variation of the isosteric heat of adsorption with loading and temperature. Here we used a Monte Carlo simulation method with a grand canonical Monte Carlo ensemble. A number of two-center Lennard-Jones (LJ) potential models are investigated to study the impact of the choice of potential models in the description of adsorption behavior. We chose two 2C-LJ potential models in our investigation of the (i) UA-TraPPE-LJ model of Martin and Siepmann (J. Phys. Chem. B 1998,102, 25692577) for ethane and Wick et al. (J. Phys. Chem. B 2000,104, 8008-8016) for ethylene and (ii) AUA4-LJ model of Ungerer et al. (J. Chem. Phys. 2000,112, 5499-5510) for ethane and Bourasseau et al. (J. Chem. Phys. 2003, 118, 3020-3034) for ethylene. These models are used to study the adsorption of ethane and ethylene on graphitized thermal carbon black. It is found that the solid-fluid binary interaction parameter is a function of adsorbate and temperature, and the adsorption isotherms and heat of adsorption are well described by both the UA-TraPPE and AUA models, although the UA-TraPPE model performs slightly better. However, the local distributions predicted by these two models are slightly different. These two models are used to explore the two-dimensional condensation for the graphitized thermal carbon black, and these values are 110 K for ethylene and 120 K for ethane.

Adsorption of ethylene on graphitized thermal carbon black and in slit pores: A computer simulation study

In this paper, we studied vapor-liquid equilibria (VLE) and adsorption of ethylene on graphitized thermal carbon black and in slit pores whose walls are composed of graphene layers. Simple models of a one-center Lennard-Jones (LJ) potential and a two-center united atom (UA)-LJ potential are investigated to study the impact of the choice of potential models in the description of VLE and adsorption behavior. Here, we used a Monte Carlo simulation method with grand canonical Monte Carlo (GCMC) and Gibbs ensemble Monte Carlo ensembles. The one-center potential model cannot describe adequately the VLE over the practical range of temperature from the triple point to the critical point. On the other hand, the two-center potential model (Wick et al. J. Phys. Chem. B 2000, 104, 8008-8016) performs well in the description of VLE (saturated vapor and liquid densities and vapor pressure) over the wide range of temperature. This UA-LJ model is then used in the study of adsorption of ethylene on graphitized thermal carbon black and in slit pores. Agreement between the GCMC simulation results and the experimental data on graphitized thermal carbon black for moderate temperatures is excellent, demonstrating that the potential of the GCMC method and the proper choice of potential model are essential to investigate adsorption. For slit pores of various sizes, we have found that the behavior of ethylene exhibits a number of features that are not manifested in the study of spherical LJ particles. In particular, the singlet density distribution versus distance across the pore and the angle between the molecular axis and the z direction provide rich information about the way molecules arrange themselves when the pore width is varied. Such an arrangement has been found to be very sensitive to the pore width.

Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons

A new approach based on the nonlocal density functional theory to determine pore size distribution (PSD) of activated carbons and energetic heterogeneity of the pore wall is proposed. The energetic heterogeneity is modeled with an energy distribution function (EDF), describing the distribution of solid-fluid potential well depth (this distribution is a Dirac delta function for an energetic homogeneous surface). The approach allows simultaneous determining of the PSD (assuming slit shape) and EDF from nitrogen or argon isotherms at their respective boiling points by using a set of local isotherms calculated for a range of pore widths and solid-fluid potential well depths. It is found that the structure of the pore wall surface significantly differs from that of graphitized carbon black. This could be attributed to defects in the crystalline structure of the surface, active oxide centers, finite size of the pore walls (in either wall thickness or pore length), and so forth. Those factors depend on the precursor and the process of carbonization and activation and hence provide a fingerprint for each adsorbent. The approach allows very accurate correlation of the experimental adsorption isotherm and leads to PSDs that are simpler and more realistic than those obtained with the original nonlocal density functional theory.

Comparisons of diffusive and viscous contributions to transport coefficients of light gases in single-walled carbon nanotubes

We examine here the relative importance of different contributions to transport of light gases in single walled carbon nanotubes, using methane and hydrogen as examples. Transport coefficients at 298 K are determined using molecular dynamics simulation with atomistic models of the nanotube wall, from which the diffusive and viscous contributions are resolved using a recent approach that provides an explicit expression for the latter. We also exploit an exact theory for the transport of Lennard-Jones fluids at low density considering diffuse reflection at the tube wall, thereby permitting the estimation of Maxwell coefficients for the wall reflection. It is found that reflection from the carbon nanotube wall is nearly specular, as a result of which slip flow dominates, and the viscous contribution is small in comparison, even for a tube as large as 8.1 nm in diameter. The reflection coefficient for hydrogen is 3-6 times as large as that for methane in tubes of 1.36 nm diameter, indicating less specular reflection for hydrogen and greater sensitivity to atomic detail of the surface. This reconciles results showing that transport coefficients for hydrogen and methane, obtained in simulation, are comparable in tubes of this size. With increase in adsorbate density, the reflection coefficient increases, suggesting that adsorbate interactions near the wall serve to roughen the local potential energy landscape perceived by fluid molecules.

Prediction of high-pressure adsorption equilibrium of supercritical gases using density functional theory

In this paper, we present the results of the prediction of the high-pressure adsorption equilibrium of supercritical. gases (Ar, N-2, CH4, and CO2) on various activated carbons (BPL, PCB, and Norit R1 extra) at various temperatures using a density-functional-theory-based finite wall thickness (FWT) model. Pore size distribution results of the carbons are taken from our recent previous work 1,2 using this approach for characterization. To validate the model, isotherms calculated from the density functional theory (DFT) approach are comprehensively verified against those determined by grand canonical Monte Carlo (GCMC) simulation, before the theoretical adsorption isotherms of these investigated carbons calculated by the model are compared with the experimental adsorption measurements of the carbons. We illustrate the accuracy and consistency of the FWT model for the prediction of adsorption isotherms of the all investigated gases. The pore network connectivity problem occurring in the examined carbons is also discussed, and on the basis of the success of the predictions assuming a similar pore size distribution for accessible and inaccessible regions, it is suggested that this is largely related to the disordered nature of the carbon.

Characterization of activated carbon fibers using argon adsorption

In this paper, we present results of the internal structure (pore size and pore wall thickness distributions) of a series of activated carbon fibers with different degrees of burn-off, determined from interpretation of argon adsorption data at 87 K using infinite and finite wall thickness models. The latter approach has recently been developed in our laboratory. The results show that while the low bun-off samples have nearly uniform pore size (

Application of density functional theory to equilibrium adsorption of argon and nitrogen on amorphous silica surface

We present a new version of non-local density functional theory (NL-DFT) adapted to description of vapor adsorption isotherms on amorphous materials like non-porous silica. The novel feature of this approach is that it accounts for the roughness of adsorbent surface. The solid–fluid interaction is described in the same framework as in the case of fluid–fluid interactions, using the Weeks–Chandler–Andersen (WCA) scheme and the Carnahan–Starling (CS) equation for attractive and repulsive parts of the Helmholtz free energy, respectively. Application to nitrogen and argon adsorption isotherms on non-porous silica LiChrospher Si-1000 at their boiling points, recently published by Jaroniec and co-workers, has shown an excellent correlative ability of our approach over the complete range of pressures, which suggests that the surface roughness is mostly the reason for the observed behavior of adsorption isotherms. From the analysis of these data, we found that in the case of nitrogen adsorption short-range interactions between oxygen atoms on the silica surface and quadrupole of nitrogen molecules play an important role. The approach presented in this paper may be further used in quantitative analysis of adsorption and desorption isotherms in cylindrical pores such as MCM-41 and carbon nanotubes.

Van der Waals-corrected density functional theory: benchmarking for hydrogen-nanotube and nanotube-nanotube interactions

Density functional theory (DFT) is a powerful approach to electronic structure calculations in extended systems, but suffers currently from inadequate incorporation of long-range dispersion, or Van der Waals (VdW) interactions. VdW-corrected DFT is tested for interactions involving molecular hydrogen, graphite, single-walled carbon nanotubes (SWCNTs), and SWCNT bundles. The energy correction, based on an empirical London dispersion term with a damping function at short range, allows a reasonable physisorption energy and equilibrium distance to be obtained for H-2 on a model graphite surface. The VdW-corrected DFT calculation for an (8, 8) nanotube bundle reproduces accurately the experimental lattice constant. For H-2 inside or outside an (8, 8) SWCNT, we find the binding energies are respectively higher and lower than that on a graphite surface, correctly predicting the well known curvature effect. We conclude that the VdW correction is a very effective method for implementing DFT calculations, allowing a reliable description of both short-range chemical bonding and long-range dispersive interactions. The method will find powerful applications in areas of SWCNT research where empirical potential functions either have not been developed, or do not capture the necessary range of both dispersion and bonding interactions.

Adsorption of N-2, Ar, acetone, chloroform and acetone-chloroform mixture on carbon black in the framework of molecular layer structure theory (MLST)

Adsorption of pure nitrogen, argon, acetone, chloroform and acetone-chloroform mixture on graphitized thermal carbon black is considered at sub-critical conditions by means of molecular layer structure theory (MLST). In the present version of the MLST an adsorbed fluid is considered as a sequence of 2D molecular layers, whose Helmholtz free energies are obtained directly from the analysis of experimental adsorption isotherm of pure components. The interaction of the nearest layers is accounted for in the framework of mean field approximation. This approach allows quantitative correlating of experimental nitrogen and argon adsorption isotherm both in the monolayer region and in the range of multi-layer coverage up to 10 molecular layers. In the case of acetone and chloroform the approach also leads to excellent quantitative correlation of adsorption isotherms, while molecular approaches such as the non-local density functional theory (NLDFT) fail to describe those isotherms. We extend our new method to calculate the Helmholtz free energy of an adsorbed mixture using a simple mixing rule, and this allows us to predict mixture adsorption isotherms from pure component adsorption isotherms. The approach, which accounts for the difference in composition in different molecular layers, is tested against the experimental data of acetone-chloroform mixture (non-ideal mixture) adsorption on graphitized thermal carbon black at 50 degrees C. (C) 2005 Elsevier Ltd. All rights reserved.

Adsorption of argon from sub- to supercritical conditions on graphitized thermal carbon black and in graphitic slit pores: A grand canonical Monte Carlo simulation study

In this paper we consider the adsorption of argon on the surface of graphitized thermal carbon black and in slit pores at temperatures ranging from subcritical to supercritical conditions by the method of grand canonical Monte Carlo simulation. Attention is paid to the variation of the adsorbed density when the temperature crosses the critical point. The behavior of the adsorbed density versus pressure (bulk density) shows interesting behavior at temperatures in the vicinity of and those above the critical point and also at extremely high pressures. Isotherms at temperatures greater than the critical temperature exhibit a clear maximum, and near the critical temperature this maximum is a very sharp spike. Under the supercritical conditions and very high pressure the excess of adsorbed density decreases towards zero value for a graphite surface, while for slit pores negative excess density is possible at extremely high pressures. For imperfect pores (defined as pores that cannot accommodate an integral number of parallel layers under moderate conditions) the pressure at which the excess pore density becomes negative is less than that for perfect pores, and this is due to the packing effect in those imperfect pores. However, at extremely high pressure molecules can be packed in parallel layers once chemical potential is great enough to overcome the repulsions among adsorbed molecules. (c) 2005 American Institute of Physics.

Cooperative and competitive adsorption of ethylene, ethane, nitrogen and argon on graphitized carbon black and in slit pores

In this paper we investigate the mixture adsorption of ethylene, ethane, nitrogen and argon on graphitized thermal carbon black and in slit pores by means of the Grand Canonical Monte Carlo simulations. Pure component adsorption isotherms on graphitized thermal carbon black are first characterized with the GCMC method, and then mixture simulations are carried out over a wide range of pore width, temperature, pressure and composition to investigate the cooperative and competitive adsorption of all species in the mixture. Results of mixture simulations are compared with the experimental data of ethylene and ethane (Friederich and Mullins, 1972) on Sterling FTG-D5 (homogeneous carbon black having a BET surface area of 13 m(2)/g) at 298 K and a pressure range of 1.3-93 kPa. Because of the co-operative effect, the Henry constant determined by the traditional chromatography method is always greater than that obtained from the volumetric method.

Fractal effects on the measurement of the specific surface areas of single-walled carbon nanotubes

The specific surface area (SSA) of single-walled carbon nanotubes (SWNTs) has been measured by different groups. Fujiwara et al. measured the SSA of SWNT bundles by using nitrogen and oxygen as adsorbates, and found that the SSA from O2-adsorption was 6.6% larger than that from N2-adsorption for the same SWNT sample [1]. Also Wei et al. [2] measured the SSA of HiPco SWNTs by using O2, N2 and Ar, and found that, for the same samples, Vm(Ar) > Vm(O2) > Vm(N2), here Vm is the monolayer adsorption capacity at the standard conditions of temperature and pressure (STP). Those research results indicate that, for the same SWNT sample, its measured surface area depends on the employed adsorbate.

Adsorption of argon on homogeneous graphitized thermal carbon black and heterogeneous carbon surface

In this paper we investigate the effects of surface mediation on the adsorption behavior of argon at different temperatures on homogeneous graphitized thermal carbon black and on heterogeneous nongraphitized carbon black surface. The grand canonical Monte Carlo (GCMC) simulation is used to study the adsorption, and its performance is tested against a number of experimental data on graphitized thermal carbon black (which is known to be highly homogeneous) that are available in the literature. The surface-mediation effect is shown to be essential in the correct description of the adsorption isotherm because without accounting for that effect the GCMC simulation results are always greater than the experimental data in the region where the monolayer is being completed. This is due to the overestimation of the fluid–fluid interaction between particles in the first layer close to the solid surface. It is the surface mediation that reduces this fluid–fluid interaction in the adsorbed layers, and therefore the GCMC simulation results accounting for this surface mediation that are presented in this paper result in a better description of the data. This surface mediation having been determined, the surface excess of argon on heterogeneous carbon surfaces having solid–fluid interaction energies different from the graphite can be readily obtained. Since the real heterogeneous carbon surface is not the same as the homogeneous graphite surface, it can be described by an area distribution in terms of the well depth of the solid–fluid energy. Assuming a patchwise topology of the surface with patches of uniform well depth of solid–fluid interaction, the adsorption on a real carbon surface can be determined as an integral of the local surface excess of each patch with respect to the differential area. When this is matched against the experimental data of a carbon surface, we can derive the area distribution versus energy and hence the geometrical surface area. This new approach will be illustrated with the adsorption of argon on a nongraphitized carbon at 87.3 and 77 K, and it is found that the GCMC surface area is different from the BET surface area by about 7%. Furthermore, the description of the isotherm in the region of BET validity of 0.06 to 0.2 is much better with our method than with the BET equation.