Gas-solid Virial Coefficients Research Articles

Comparison of gas–solid chromatography and MM2 force field molecular binding energies for greenhouse gases on a carbonaceous surface

Gas–solid chromatography was used to determine B 2s (gas–solid virial coefficient) values for eight molecular adsorbates interacting with a carbon powder (Carbopack B, Supelco). B 2s values were determined by multiple size variant injections within the temperature range of 313–553 K. The molecular adsorbates included: carbon dioxide (CO 2); tetrafluoromethane (CF 4); hexafluoroethane (C 2F 6); 1,1-difluoroethane (C 2H 4F 2); 1-chloro-1,1-difluoroethane (C 2H 3ClF 2); dichlorodifluoromethane (CCl 2F 2); trichlorofluoromethane (CCl 3F); and 1,1,1-trichloroethane (C 2H 3Cl 3). Two of these molecules are of special interest because they are “super greenhouse gases”. The global warming potential, GWP, for CF 4 is 6500 and for C 2F 6 is 9200 relative to the reference value of 1 for CO 2. The GWP index considers both radiative blocking and molecular lifetime. For these and other industrial greenhouse gases, adsorptive trapping on a carbonaceous solid, which depends on molecule–surface binding energy, could avoid atmospheric release. The temperature variations of the gas–solid virial coefficients in conjunction with van’t Hoff plots were used to find the experimental adsorption energy or binding energy values ( E *) for each adsorbate. A molecular mechanics based, rough-surface model was used to calculate the molecule–surface binding energy (Ecal *) using augmented MM2 parameters. The surface model consisted of parallel graphene layers with two separated nanostructures each containing 17 benzene rings arranged in linear strips. The separation of the parallel nanostructures had been optimized in a prior study to appropriately represent molecule–surface interactions for Carbopack B. Linear regressions of E * versus Ecal * for the current data set of eight molecules and the same surface model gave E * = 0.926Ecal * and r 2=0.956. A combined set of the current and prior Carbopack B adsorbates studied (linear alkanes, branched alkanes, cyclic alkanes, ethers, and halogenated hydrocarbons) gave a data set with 33 molecules and a regression of E * = 0.991Ecal * and r 2=0.968. These results indicated a good correlation between the experimental and the MM2 computed molecule–surface binding energies.

Binding energies for alkane molecules on a carbon surface from gas–solid chromatography and molecular mechanics

Gas–solid chromatography was used to determine B 2 s (gas–solid virial coefficient) values for 12 alkanes (10 branched and 2 cyclic) interacting with a carbon powder (Carbopack B, Supelco). B 2 s values were determined by multiple size variant injections within the temperature range of 393 to 623 K with each alkane measured at 5 or 6 different temperatures. The temperature variations of the gas–solid virial coefficients were used to find the experimental adsorption energy or binding energy values ( E ∗ ) for each alkane. A molecular mechanics based, rough-surface model was used to calculate the molecule–surface binding energy ( E cal ∗ ) using augmented MM2 parameters. The surface model consisted of three parallel graphene layers with each layer containing 127 interconnected benzene rings and two separated nanostructures each containing 17 benzene rings arranged in a linear strip. As the parallel nanostructures are moved closer together, the surface roughness increases and molecule–surface interactions are enhanced. A comparison of the experimental and calculated binding energies showed excellent agreement with an average difference of 3.8%. Linear regressions of E ∗ versus E cal ∗ for the current data set and a combined current and prior alkane data set both gave excellent correlations. For the combined data set with 18 linear, branched and cyclic alkanes; a linear regression of E ∗ = 0.9848 E cal ∗ and r 2 = 0.976 was obtained. The results indicate that alkane-surface binding energies may be calculated from MM2 parameters for some gas–solid systems.

Determining molecule–carbon surface adsorption energies using molecular mechanics and graphene nanostructures

Five model surfaces were developed using molecular mechanics with MM2 parameters. A smooth, flat model surface was constructed of three parallel graphene layers where each graphene layer contained 127 interconnected benzene rings. Four rough surfaces were constructed by varying the separation between a pair of graphene nanostructures placed on the topmost layer of graphene. Each nanostructure contained 17 benzene rings arranged in a linear strip. The parallel nanostructures were moved closer together to increase the surface roughness and to enhance the molecule–surface interaction. Experimental adsorption energy values from the temperature variation of second gas–solid virial coefficients values were available for 16 different alkanes, haloalkanes, and ether molecules adsorbed on Carbopack B (Supelco, 100 m 2/g). For each of the five different surface models, sets of 16 calculated adsorption energies, E cal ∗ , were determined and compared to the available experimental adsorption energies, E ∗ . The best linear regression correlation between E ∗ and E cal ∗ was found for a 1.20 nm internuclei separation of the surface nanostructures, and for this surface model the calculated gas–solid interaction energies closely matched the experimental values ( E ∗ = 1.018 E cal ∗ , r 2 = 0.964 ).

Adsorption energies for a nanoporous carbon from gas–solid chromatography and molecular mechanics

Gas–solid chromatography was used to obtain second gas–solid virial coefficients, B 2 s , in the temperature range 342–613 K for methane, ethane, propane, butane, 2-methylpropane, chloromethane, chlorodifluoromethane, dichloromethane, and dichlorodifluoromethane. The adsorbent used was Carbosieve S-III (Supelco), a carbon powder with fairly uniform, predominately 0.55 nm slit width pores and a N 2 BET surface area of 995 m 2/g. The temperature dependence of B 2 s was used to determine experimental values of the gas–solid interaction energy, E ∗ , for each of these molecular adsorbates. MM2 and MM3 molecular mechanics calculations were used to determine the gas–solid interaction energy, E cal ∗ , for each of the molecules on various flat and nanoporous model surfaces. The flat model consisted of three parallel graphene layers with each graphene layer containing 127 interconnected benzene rings. The nanoporous model consisted of two sets of three parallel graphene layers adjacent to one another but separated to represent the pore diameter. A variety of calculated adsorption energies, E cal ∗ , were compared and correlated to the experimental E ∗ values. It was determined that simple molecular mechanics could be used to calculate an attraction energy parameter between an adsorbed molecule and the carbon surface. The best correlation between the E cal ∗ and E ∗ values was provided by a 0.50 nm nanoporous model using MM2 parameters.

Predicting second gas–solid virial coefficients using calculated molecular properties on various carbon surfaces

Gas–solid chromatography was used to obtain values of the second gas–solid virial coefficient, B 2 s , in the temperature range from 343 to 493 K for seven adsorbate gases: methane, ethane, propane, chloromethane, chlorodifluoromethane, dimethyl ether, and sulfur hexafluoride. Carboxen-1000, a 1200 m 2/g carbon molecular sieve (Supelco Inc.), was used as the adsorbent. These data were combined with earlier work to make a combined data set of 36 different adsorbate gases variously interacting with from one to four different carbon surfaces. All B 2 s values were extrapolated to 403 K to create a set of 65 different gas–solid B 2 s values at a fixed temperature. The B 2 s value for a given gas–solid system can be converted to a chromatographic retention time at any desired flow rate and can be converted to the amount of gas adsorbed at any pressure in the low-coverage, Henry's law region. Beginning with a theoretical equation for the second gas–solid virial coefficient, various quantitative structure retention relations (QSRR) were developed and used to correlate the ln B 2 s values for different gas adsorbates with different carbon surfaces. Two calculated adsorbate molecular parameters (molar refractivity and connectivity index), when combined with two adsorbent parameters (surface area and a surface energy contribution to the gas–solid interaction), provided an effective correlation ( r 2=0.952) of the 65 different ln B 2 s values. The two surface parameters provided a simple yet useful representation of the structure and energy of the carbon surfaces and thus our correlations considered variation in both the adsorbate gas and the adsorbent solid.

Molar Refractivity and Connectivity Index Correlations for Henry's Law Virial Coefficients of Odorous Sulfur Compounds on Carbon and for Gas-Chromatographic Retention Indices

Gas–solid chromatography was used to obtain values of the second gas–solid virial coefficient, B2s, in the temperature range from 392 to 511 K for 10 volatile, malodorous organic sulfur compounds; ethanethiol, 1-propanethiol, methyl sulfide, 2-propanethiol, 1-methyl-1-propanethiol, 2-methyl-1-propanethiol, 2-methyl-2-propanethiol, ethyl sulfide, ethyl methyl sulfide, and tert-butyl methyl sulfide. Carbopack C (Supelco Inc.), a graphitized carbon black powder, was used as the adsorbent. Beginning with a theoretical equation for the second gas–solid virial coefficient, it was shown how a quantitative structure–retention relation (QSRR) could be developed to correlate ln B2s and hence chromatographic retention times with calculated molar refractivity and connectivity index values for the thiols and thioethers. It was found that both the gas–solid interaction energies and the ln B2s values could be correlated with calculated adsorbate molar refractivity (r2=0.951) and (r2=0.961), respectively. Connectivity index and molar refractivity together provide a r2=0.989 correlation of the ten ln B2s values at 403 K. A set of 373 organic compounds with retention indices taken from the literature was used to further test our approach. The 373 molecules were divided into 10 structural subgroups and molar refractivities and connectivity indices were calculated and used to correlate their retention index values. An overall correlation of r2=0.982 for the retention indices of the 373 molecules was found.

Correlations of Henry's Law Gas–Solid Virial Coefficients and Chromatographic Retention Times for Hydrocarbons and Halocarbons Adsorbed on Carbopack C Carbon

Second gas–solid virial coefficients were determined at 403.5 ± 0.5 K for 6 adsorbates, including butane, chloroform, trichlorofluoromethane (Freon 11), bromochloromethane, 1-chloro-2-methylpropane, and dibromodifluoromethane. For another 11 adsorbates, including dichlorodifluoromethane (Freon 12), chlorodifluoromethane (Freon 22), methyl chloride, methylene chloride, propane, n-pentane, n-hexane, carbon tetrachloride, 1,2-dichloropropane, butyl chloride, and cyclohexane, B2s was measured over a range of temperatures between 308 and 494 K. These values were found using gas–solid chromatography with Carbopack C (Supelco Inc.), a graphitized carbon black powder, as the adsorbent. We find that both the ln B2s values and the gas–solid interaction energies are effectively correlated with adsorbate-calculated molar refractivity, r2 = 0.947 and r2 = 0.964, respectively. Dipole moment alone provides a nearly random correlation of ln B2s and, if used with molar refractivity, gives r2 = 0.970 for the 17 hydrocarbon and alkyl halide (halocarbon) adsorbates. A theoretical equation was developed that predicts a quantitative structure retention relationship (QSRR) used to correlate ln B2s values with molar refractivity. B2s values are directly proportional to the retention times of the adsorbates. Using one-surface and two-surface models, a calculation of the surface area of the Carbopack C for each of the 17 adsorbates provided a check on the consistency of the analysis as the adsorbate was varied.

Two-Surface Virial Analysis of Alkane Adsorption on Carbopack C with and without Hydrogen Treatment

Second gas–solid virial coefficients for propane, butane, pentane, and hexane were found for Carbopack C and Carbopack C-HT (Supelco Inc.) within the temperature range of 323 to 471 K using gas–solid chromatography in the Henry's law region of adsorption. Carbopack C and Carbopack C-HT are both graphitized carbon black powders. Treatment of Carbopack C with hydrogen at 1273 K converts it to Carbopack C-HT and is believed to remove certain high energy sites or “hot spots” from the carbon surface. These two surfaces provide appropriate model systems to test a two-surface virial analysis. Surface areas for both powders were calculated using a uniform single-surface model and a two-surface model. Only the two-surface virial model which is based on gas–solid interaction parameters determined by an iterative process and numerical integration gave reasonable areas for the two surfaces: 13.2 and 13.9 m2/g for Carbopack C and Carbopack C-HT, respectively. The percentage of high energy sites on the Carbopack C was found to be 2.6% and for Carbopack C-HT was found to be 1.5%. The gas–solid interaction energy for the high energy sites was found to be 1.80 times greater than the corresponding value for the low energy portion of the surface. In addition, the gas–solid adsorption energies for the four alkane adsorbates were found to have a linear correlation with their boiling points and with the ratio of their critical temperatures divided by the square root of their critical pressures.

Henry's Law Gas-Solid Chromatography and Correlations of Virial Coefficients for Hydrocarbons, Chlorofluorocarbons, Ethers, and Sulfur Hexafluoride Adsorbed onto Carbon

Gas-solid chromatography was used to determine the Henry's law second gas-solid virial coefficients within the temperature range of 314-615 K for ethane, propane, butane, isobutane, pentane, hexane, heptane, chloromethane, dichloromethane, trichloromethane, tetrachloromethane, trichlorofluoromethane (Freon 11), chlorodifluoromethane (Freon 22), dichlorodifluoromethane (Freon 12), methyl ether, ethyl ether, and sulfur hexafluoride with Carbopack B, a microporous carbon adsorbent. The temperature dependence of the second gas-solid virial coefficients of these adsorbates was used in conjunction with analyses based on a graphical method, a single-surface numeric integration method, a single-surface analytic expression method, and a two-surface analytic expression method to determine the gas-solid interaction energies and other parameters. The interaction energies were correlated with a ratio of the critical temperature divided by the square root of the critical pressure. The four methods were compared in their abilities to successfully calculate second gas-solid virial coefficient values.

Correlation of Henry's Law, Virial Coefficients for the Adsorption of Hydrocarbons and Chlorofluorocarbons on Microporous Solids

Correlations were developed and used to calculate gas-solid interaction energy parameters which in turn were used to calculate Henry's law constants for the adsorption of a series of hydrocarbons and chlorofluorocarbons on either a 13X zeolite or a microporous carbon, SuperSorb. The adsorption energetic parameter was correlated with the boiling point, critical constant ratio (critical temperature divided by the square root of the critical pressure), number of carbon atoms, and molecular structure or atomic structure of the adsorbate molecule. These correlations were used to calculate gas-solid interaction energies and, with a selection of the gas-solid interaction potential parameters, were used in an integral expression to calculate the gas-solid virial coefficients. The critical constant ratio was found to provide the best means of predicting the gas-solid interaction energy and the corresponding second gas-solid virial coefficient. This approach could be used to predict the extent adsorption in the Henry's law region using only adsorbate molecular properties where energy correlations have been previously established for a series of adsorbate molecules.

A Comparison of Flat, Parallel Plate, and Cavity Virial Models for Henry's Law Argon-Solid Adsorption

Seven sets of second gas-solid virial coefficients for argon adsorbed onto seven different surfaces (two graphitic carbons, three microporous carbons, and two zeolites) were analyzed with three different virial models. Flat, parallel plate, and cavity virial models were used to describe the interactions between the adsorbate molecule and each type of adsorbent surface, over a range of temperatures, in the Henry's law region. In calculating theoretical B2s values, parameters which gave the most consistent structural results for a given solid over a range of temperature were selected. Surface areas and effective pore volumes were then calculated from the chosen parameters. The objective of this research was to test the surface specificity of the three virial adsorption models and to compare the energetic and structural parameters obtained from these models.

A comparison of two surface virial analyses of monatomic gases on graphite and boron nitride

By examining monatomic gases (argon, krypton, and xenon) adsorbed on P33 graphite and hexagonal boron nitride, a two-surface model to represent gas-solid interaction systems was developed. Second gas-solid virial coefficients were used in conjunction with a Lennard-Jones (16,3) potential to determine the gas-solid interaction energy, the surface area, and the percentage area of the higher energy surface for both gas-P33 and gas-boron nitride systems. The analyses indicated that P33 graphite is best characterized as a single-surface solid, while boron nitride is best characterized as a two-surface solid. This two-surface virial approach was able to clearly distinguish the two types of surfaces using the temperature dependence of Henry's law adsorption data, but without any specific prior assumptions of differences in surface structures.

Gas—solid chromatography and virial analysis of chlorofluorocarbon adsorption on a microporous carbon

Gas-solid chromatography was used to determine the second gas-solid virial coefficients in the temperature range 373–512 K for ethane, propane, chloromethane, dichloromethane, fluoromethane, chlorodifluoromethane (Freon 22), and dichlorodifluoromethane (Freon 12), with Super Sorb, a microporous carbon adsorbent. The temperature dependence of the second gas-solid virial coefficients of these adsorbates was used in conjunction with a Lennard-Jones and Devonshire cell model to determine the effective structural parameters of cavity radius and number of cavities per gram of adsorbent, as well as gas-cavity interaction energies. The interaction energies were correlated with adsorbate boiling points and energetic additivity rules based on molecular structure including the number of atoms of different types in the molecule and the dipole moment of the molecule.

Influence of an energetically heterogeneous surface on the second gas-solid virial coefficient

A new equation is derived for the second gas-solid virial coefficient on a heterogeneous surface characterized by a gamma distribution of adsorption energies. Analysis of this equation shows that the influence of the adsorbent energetic heterogeneity on the second virial coefficient is significant, especially in the region of low temperatures.

Gas—solid chromatography and virial analysis of hydrocarbon adsorption on 13X zeolite

Gas-solid chromatography was used to determine the second gas-solid virial coefficients in the temperature range 343–597 K for ethane, propane, n-butane, 2-methylpropane, n-pentane, 2-methylbutane, 2,2-dimethylpropane, n-hexane, 2,2-dimethylbutane, and cyclohexane with 13X zeolite. The temperature dependence of the second gas-solid virial coefficients of these 10 hydrocarbons along with the available methane data was used in conjunction with a Lennard-Jones and Devonshire cell model to determine the 13X zeolite structural parameters of cavity radius and number of cavities per gram of adsorbent, as well as gas-cavity interaction energies. The 13X structural parameters were compared to X-ray crystallographic values. The interaction energies were found to be linearly dependent on the number of carbon atoms in the adsorbate hydrocarbon with the more highly branched molecules having somewhat lower energies. The interaction energies were correlated with hydrocarbon boiling points and energetic additivity rules on the basis of molecular structure.

The gas-solid Joule-Thomson effect

Abstract

Investigation of the gas-solid Joule-Thomson effect for argon-, nitrogen-, and carbon dioxide-carbon powder aerosol systems

An apparatus was constructed to disperse a fine powder in a flowing gas and measure the thermal changes associated with a pressure drop across a glass orifice. The gas-solid Joule-Thomson effect was examined for 12 different gas-solids systems at a temperature of 302 K, a downstream pressure of 120 kPa, pressure drops across the orifice from 5 to 45 kPa, flow rates from 2 to 14 mmol/s, and aerosol concentrations from 0 to 16 g of powder/mol of gas. The gaseous component included either argon, nitrogen, or carbon dioxide and the particulate component included either Mexican Graphite (26 m/sup 2//g), Nuchar S-C (903 m/sup 2//g), Nuchar S-A (1661 m/sup 2//g), or Super Sorb (3169 m/sup 2//g) carbon powder. A significant enhancement of the Joule-Thomson cooling effect was found for gas-porous carbon systems relative to a pure gas. The dependence of the magnitude of this effect on the gas-gas and gas-solid interactions was predicted from a virial equation of state based on statistical thermodynamic considerations. Gas-solid virial coefficients and their temperature derivatives were used in conjunction with the theoretical model as modified by heat-transport effects to assess the reliability of theory in predicting the experimentally determined gas-solid Joule-Thomson coefficients.

Statistical thermodynamics of aerosols and the gas–solid Joule–Thomson effect

Due to the adsorption of a gas by a solid, it is expected that an aerosol created by dispersing a fine powder in a gas would have unique thermodynamic properties not found in pure or mixed gases. The virial equation of state associated with an aerosol dusty gas is obtained from statistical thermodynamic considerations. In the theoretical model presented here, the aerosol is considered to be a two component fluid made up of solid particles and gas molecules. The aerosol virial equation of state is used to derive an expression for the Joule–Thomson effect associated with a gas–solid dispersion. The magnitude of the gas–solid Joule–Thomson effect is expressed in terms of gas and gas–solid virial coefficients. Previous adsorption data for an argon–porous carbon system is used to obtain gas–solid virial coefficients and to predict the magnitude of the gas–solid Joule–Thomson effect. A significant enhancement of the Joule–Thomson effect is predicted for gas–solid systems which display a strong interaction. For example, at a temperature of 300 K an argon–Saran 746 porous carbon aerosol system at a concentration of (0.4 g of powder/ℓ of gas) is predicted to have a gas–solid Joule–Thomson coefficient of 3.6 K/atm which is ten times greater than the effect for pure argon.

High-temperature physical adsorption of argon, krypton, and xenon on hexagonal boron nitride

The interaction of argon, krypton, and xenon with hexagonal boron nitride was examined utilizing a two-surface gas—solid virial analysis. A precision volumetric apparatus was used to obtain 10 adsorption isotherms in the temperature range 273–368°K. The low coverage, Henry's law isotherm data were used to obtain values for the second gas—solid virial coefficients for ArBN, KrBN, and XeBN. The boron nitride adsorbent consists of higher energy edge sites and basal plane sites. A two-surface virial coefficient treatment was coupled with a graphical fitting technique to separate the effects of the two surface sites. Values of the inert gas-edge and inert gas-basal plane interaction energy are reported for each of the three adsorbates. Also, the surface area for the two surfaces and fraction of edge sites are reported. The results are compared with previous studies for these systems.

Analytical expressions for the retention volume in gas adsorption chromatography

It has been shown that the experimentally obtained function — retention volume VN vs pressure p — approximates the exponential higher degree polynomial very well. The possibilities of utilizing this approximation in the determination of energetic heterogeneity of adsorbents, in calculating adsorption isotherms and the gas-solid virial coefficients are shown. The experimentally obtained functions VN(p) for the adsorption of n-hexane and 1-hexene on controlled porosity glass serve to illustrate theoretical considerations.