Three-dimensional pore structure of chromatographic adsorbents from electron tomography

The pore structure of chromatographic adsorbents directly influences macromolecular partitioning and transport in chromatography. Quantitative structural characterization of chromatographic media has generally been performed in terms of the mean pore size or, at best, the pore size distribution (PSD), but more detailed information on, e.g., connectivity has been lacking. We have applied electron tomography, a 3D TEM technique that views a sample from multiple perspectives and allows reconstruction of the volumetric structure, to capture the internal details of microporous chromatographic media with nanometer-scale resolution. Visualization of reconstructions of three adsorbents, Toyopearl SP-650 C, SP-550 C, and CM Sepharose FF, provides thorough and direct information on the geometry and the interconnectivity of the pore network. The structures are qualitatively consistent with in situ AFM images, and quantitative data for the porosities and PSDs from the analysis of tomographic data agree reasonably well with inverse size-exclusion chromatography results. For a more straightforward representation of the networking and size features of the disordered pore space, a 3D thinning algorithm was used to derive pore skeletons and consequently quantitative data on distributions of local path lengths, widths, tortuosities, and connectivities. Such enriched structural information can be instrumental in more discriminate structural evaluation and construction of engineered pore models for the study of solute intraparticle transport.     

Evaluation of methods for determining the pore size distribution and pore-network connectivity of porous carbons

The pore size distribution (PSD) and the pore-network connectivity of a porous material determine its properties in applications such as gas storage, adsorptive separations, and catalysis. Methods for the characterization of the pore structure of porous carbons are widely used, but the relationship between the structural parameters measured and the real structure of the material is not yet clear. We have evaluated two widely used and powerful characterization methods based on adsorption measurements by applying the methods to a model carbon which captures the essential characteristics of real carbons but (unlike a real material) has a structure that is completely known. We used three species (CH4, CF4, and SF6) as adsorptives and analyzed the results using an intersecting capillaries model (ICM) which was modeled using a combination of Monte Carlo simulation and percolation theory to obtain the PSD and the pore-network connectivity. There was broad agreement between the PSDs measured using the ICM and the geometric PSD of the model carbon, as well as some systematic differences which are interpreted in terms of the pore structure of the carbon. The measured PSD and connectivity are shown to be able to predict adsorption in the model carbon, supporting the use of the ICM to characterize real porous carbons.     

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 ofgraphitized 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.     

How realistic is the pore size distribution calculated from adsorption isotherms if activated carbon is composed of fullerene-like fragments?

A plausible model for the structure of non-graphitizing carbon is one which consists of curved, fullerene-like fragments grouped together in a random arrangement. Although this model was proposed several years ago, there have been no attempts to calculate the properties of such a structure. Here, we determine the density, pore size distribution and adsorption properties of a model porous carbon constructed from fullerene-like elements. Using the method proposed recently by Bhattacharya and Gubbins (BG), which was tested in this study for ideal and defective carbon slits, the pore size distributions (PSDs) of the initial model and two related carbon models are calculated. The obtained PSD curves show that two structures are micro-mesoporous (with different ratio of micro/mesopores) and the third is strictly microporous. Using the grand canonical Monte Carlo (GCMC) method, adsorption isotherms of Ar (87 K) are simulated for all the structures. Finally PSD curves are calculated using the Horvath-Kawazoe, non-local density functional theory (NLDFT), Nguyen and Do, and Barrett-Joyner-Halenda (BJH) approaches, and compared with those predicted by the BG method. This is the first study in which different methods of calculation of PSDs for carbons from adsorption data can be really verified, since absolute (i.e. true) PSDs are obtained using the BG method. This is also the first study reporting the results of computer simulations of adsorption on fullerene-like carbon models.     

密度泛函与分子模拟计算介孔孔径分布比较

用巨正则系综Monte Carlo模拟(GCMC)方法和密度泛函理论（ DFT）结合统计积分方程（SIE）计算了介孔材料的孔径分布.为比较这两种方法,以77 K氮气在介孔活性碳微球中的吸附数据为依据,求出其孔径分布.在GCMC模拟和DFT计算中,流体分子模型化为单点的Lerrnard-Jones球;流体分子与吸附剂材料之间的作用采用平均场理论中的10-4-3模型.在DFT方法中,自由能采用Tarazona 提出的加权近似密度泛函方法(weighted density approximation,WDA)求解.结果表明,对于孔径大于1.125 nm的介孔材料,GCMC和DFT两种方法都可以用来研究介孔材料的孔径分布;对于小于1.125 nm的介孔材料,不能用DFT方法计算孔径分布（DFT方法本身的近似产生了误差）,只能用分子模拟方法.     

Determination of particle size distribution by gravitational field-flow fractionation: Dimensional characterization of silica particles

Summary Gravitational field-flow fractionation (GFFF) is the simplest and cheapest of field-flow fractionation (FFF) techniques, although it is still at an early development stage. The application of GFFF to the determination of particle size distribution (PSD) of silica particles used as chromatographic supports is described. The accuracy of the method is evaluated by comparing PSDs obtained by GFFF with those obtained by laser diffraction, a non-separative technique widely applied to particle characterization. It is ultimately demonstrated that a low-cost GFFF channel can simply replace the column of a standard HPLC system, allowing laboratories that are not specialized in size analysis to perform accurate PSD studies with standard HPLC expertise.     

Evaluating the bioavailability of explosive metabolites, hexahydro-1-nitroso-3,5-dinitro-1,3,5-triazine (MNX) and hexahydro-1,3,5-trinitroso-1,3,5-triazine (TNX), in soils using passive sampling devices

The uptake kinetics of two major RDX (hexahydro-1,3,5-trinitro-1,3,5-triazacyclohexane) metabolites, hexahydro-1-nitroso-3,5-dinitro-1,3,5-triazine (MNX) and hexahydro-1,3,5-trinitroso-1,3,5-triazine (TNX), into passive sampling devices (PSDs), and the ability of PSDs to serve as surrogates for evaluating bioavailability of MNX and TNX were investigated in laboratory sand and two soil types. The results indicate that MNX and TNX absorption into PSDs was best fitted with a polynomial curve model: y = ax2 + bx + c (y: amount of MNX or TNX absorbed into PSD; x: incubation time of PSDs in soil), with an excellent correlation coefficient (>0.95) for each type of soil amended with 10 mg/kg MNX or TNX. TNX was more readily absorbed by PSDs than MNX. Soil conditions, especially organic matter content, affected MNX and TNX uptake into PSDs. A relatively good correlation between MNX and TNX uptake into PSDs and uptake into earthworms was obtained in two types of natural soils (a silt loam soil from Nebraska and a sandy loam soil from Texas) and laboratory sand. A linear relationship between PSD uptake and earthworm uptake was observed. The correlation coefficients (r2) were > or = 0.82 for all test soils spiked with MNX or TNX. Organic matter content is one soil factor that affected the ratio of MNX or TNX uptake into earthworms versus uptake into PSDs. These data indicate that C18 PSDs may be used as a surrogate for soil organisms such as earthworms and provide a simple and easy chemical test for assessing the bioavailability of contaminants in soils.     

几种植物基活性炭材料的孔结构与吸附性能比较——(I)孔结构表征

测定了3种植物基活性炭材料:椰壳活性炭 (CAC4)、剑麻茎基活性炭 (SSAC) 和剑麻基活性碳纤维 (SACF) 的氮吸附等温线,并用不同的理论方法对其孔结构进行了分析和表征。结果表明:CAC4为微孔型,孔径分布集中且大部分是0.7nm以下的极微孔;在相同条件下制备的SSAC和SACF孔分布较为相似,都呈多分散性,结构中除微孔外,还含有丰富的中孔,中孔率均超过50%以上。两者相比,SACF的中孔量和平均孔径更大。3个样品的形态特征和孔结构虽然不同,但其吸附过程都可以用微孔多段填充机理来解析。     

The Structure of Adsorbed CO(2) in Slitlike Micropores at Low and High Temperature and the Resulting Micropore Size Distribution Based on GCMC Simulations

The Monte Carlo method is used in its grand ensemble variant in combination with CO(2) experimental isotherm data at low (195.5 K) and high temperatures (at 298 and 308 K, i.e., slightly below and above the CO(2) critical temperature, respectively) to characterize microporous carbons and obtain the corresponding pore size distribution (PSD). Specifically, the CO(2) density inside a single, slit-shaped, graphitic pore of given width is found on the basis of grand canonical Monte Carlo (GCMC) simulations for a predefined temperature and different relative pressures. The simulation results provide useful insights concerning the densification process in the micropores and the structure of the CO(2) molecules packing in the individual pores as the temperature or pressure changes from 195.5 K to ambient or from very low to 70 bar, respectively. Effects of temperature, pore size, quadrupole interactions, and molecule elongation on the local density profile within the pore are examined and discussed. In an additional step, we determine the optimal PSD for which the best match is obtained between computed and measured CO(2) isotherms. Comparisons are made between the PSDs found for the same carbon sample at low and high temperatures and conclusions are drawn concerning the applicability of the method and the reliability of the resulting micropore size distributions. Copyright 2000 Academic Press.     

Latex Particle Size Distribution by Dynamic Light Scattering: Computer Evaluation of Two Alternative Calculation Paths

Two calculation paths for estimating the particle size distribution (PSD) of a polymer latex from single-angle dynamic light scattering (DLS) measurements are evaluated on the basis of a numerical example. In the more common "double-step method," two calculation steps are applied, with the intermediate estimation of the particle light intensity distribution (PLID). In the "single-step method," the calculation is performed in one operation. From the specification of several PSDs, a mathematical model is used to produce the synthetic measurements. An iterative procedure was applied for determining the diameter range and the number of PSD points. The inversion operations were carried out using a regularization technique. For narrow distributions with diameters in the range 100-1000 nm, the PSD and the PLID are similar in shape, and both calculation paths produce similar results. For broad PSDs in the range 100-1000 nm, and for arbitrary PSDs in the range 10-100 nm (i.e., in the Rayleigh region), the single-step method proved preferable. Copyright 2000 Academic Press.     

Effect of the pore geometry in the characterization of the pore size distribution of activated carbons

In this work, the characterization of Activated Carbons (AC) by using the independent pore models is discussed, with special emphasis on the issue of how the assumed pore geometry can affect the resulting Pore Size Distribution (rPSD) and on the problem of the unicity of the PSD when different probe molecules are used in adsorption experiments. A theoretical test was performed using virtual solids based in the so-called Mixed Geometry Model (MGM) (Azevedo et al. 2010). The MGM uses a kernel of adsorption isotherms generated by GCMC for different pore sizes and two pore geometries: slit and triangular. The adsorption isotherms of a virtual MGM solid were fitted with both the traditional Slit Geometry Model (SGM) and the Mixed Geometry Model (MGM). It is demonstrated that, by assuming a different pore geometry model from that of the real sample, different PSDs may be obtained by fitting adsorption isotherms of different probe gases. Finally, experimental results are shown which both point toward the MGM as an acceptable extension of the SGM and confirm that the MGM is a closer representation of the actual porous structure of most activated carbons.     

微孔椰壳焦孔结构表征

为了更深入地了解微孔生物质焦的孔隙结构特征,在水蒸气气氛下制备椰壳焦（CSCs）,并且采用了不同分子探针、计算模型和校准步骤对其进行表征。结果表明,椰壳焦有较高的碳含量和比较丰富的孔隙度,适合进一步活化以制备活性炭。表征椰壳焦较为合适的方法是：以Ar为分子探针,并采用非定域密度泛函（NLDFT）模型。当校准步骤优先进行时,以N₂和Ar为分子探针的吸附测试结果如孔径分布（PSD）和吸附等温线会受到孔隙阻塞的影响,从而错误地描述椰壳焦的孔隙结构。实验结果还表明,273 K下仪器的真空处理可以去除绝大部分残留的He,降低孔隙阻塞的影响。     

Comparison of heterogeneous pore models QSDFT and 2D-NLDFT and computer programs ASiQwin and SAIEUS for calculation of pore size distribution

The pore size distributions (PSD) of selected carbons were calculated from their nitrogen adsorption isotherms using both the QSDFT model implemented in ASiQwin version 3.0 software (Quantachrome Instruments) and 2D-NLDFT model implemented in SAIEUS software (Micromeritics). The results showed that both the QSDFT and the 2D-NLDFT methods give similar PSDs despite the different methods for accounting for the heterogeneity of the carbon adsorbent. The characteristic features of the methods and software were discussed and possible improvements were proposed.     

Nitrogen adsorption on silica surfaces of nonporous and mesoporous materials

We present an accurate comparative analysis of N 2 adsorption at 77 K on nonporous silica and the pore wall surface of MCM-41 materials. The analysis shows that in the low-pressure region of N 2 adsorption obeys a peculiar mechanism governed by short-ranged forces, which makes the surface curvature effect on the N 2 adsorption in mesopores nearly negligible. We used this observation to define more exactly compared to the BET technique the specific surface area of the reference adsorption isotherm on nonporous silica basing on XRD data and linear sections of t-plots. Calculation of the capillary evaporation and condensation pressures seems to confirm our previous finding that the capillary condensation pressure corresponds to the equilibrium transition rather than spinodal condensation at least for pore sizes less than 7 nm. It allowed us to provide more reliable pore size distribution (PSD) analysis of mesoporous silica materials. For example, the PSDs of MCM-41 samples do not show artificial peaks in the micropore range that we obtained in our earlier publications.     

Monte carlo simulation and pore-size distribution analysis of the isosteric heat of adsorption of methane in activated carbon

The isosteric heat of adsorption of methane in an activated carbon adsorbent has been modeled by Monte Carlo simulation, using a pore-size distribution (PSD) to relate simulation results for pores of different sizes to the experimental adsorbent. Excellent fits were obtained between experimental and simulated isosteric heats of adsorption of methane in BPL activated carbon. The PSD was then used to predict the adsorption of methane and ethane in the same carbon adsorbent, with good results. The PSD derived from isosteric heat data was shown to be richer in information than PSDs obtained by the more conventional method of fitting to isotherm data.     

Estimating the pore size distribution of activated carbons from adsorption data of different adsorbates by various methods

Experimental adsorption isotherms of four adsorbates (N2, Ar, C6H6, and CCl4) as well as adsorption enthalpy (C6H6 and CCl4) measured on two strictly microporous carbons are used to evaluate the porosity of adsorbents (i.e., pore size distributions (PSDs) and average pore diameter ( Lav )). The influence of the diameter of adsorbates ( dA) as well as of the temperature ( T ) is analyzed in order to explain the differences or similarities between the above-mentioned quantities for all systems. Proposed previously, the general relationships between the parameters of the Dubinin-Astakhov (DA) isotherm equation (the characteristic energy of adsorption ( E0 ) and the exponent of this equation ( n )) and the average slit-width of carbon micropores are investigated. Moreover, the thermodynamic verification of the Horvath-Kawazoe (HK) theory and the ND model is presented based on data of the adsorption and enthalpy of adsorption of benzene and carbon tetrachloride on two carbons. Finally, the pore diameters calculated from calorimetry data using the Everett and Powl method and those calculated applying the recently developed equations are compared. In our opinion the change of apparent PSD should be monitored by performing a series of isotherm measurements from high (equal and higher than room temperature) to low temperatures (ca. 77.5 K) as was presented in the current study. Moreover, the analysis of the experimental data leads to the conclusion that the entropy of C6H6 and CCl4 can approach to the values characteristic of quasi-solid (a partially ordered structure). Therefore, this behavior of the adsorbate should be taken into consideration in the theoretical assumptions of model and its thermodynamic verification.     

Quantitative information on pore size distribution from the tangents of comparison plots

The comparison plot obtained from the nitrogen adsorption data has a similar shape to that of the curve of accumulating pore volume of a solid. The intrinsic nature of this relation is discussed. It is known that the derivatives of the accumulating pore volume with respect to the pore size are the pore size distribution (PSD) of the solid. Thus, the tangent curve of the comparison plot can display, at least qualitatively, the PSD of a solid, over a wide range of pore sizes (from approximately 1 to 50 nm) because the comparison plot is applicable to both micropores and mesopores. Quantitative pore structure information can be derived from the comparison plots by establishing a relationship between the t value and the pore size from the samples with uniform pore structure and known pore sizes, such as MCM-41 and alumina pillared clay samples. A calculation procedure to derive quantitative PSD from the comparison plots is suggested, giving reasonable results. This study proposes concise and reliable methods based on the comparison plots to derive information on pore structure in porous solids.     

锆基色谱填料的制备方法和物理化学性质

氧化锆基质色谱填料适合于碱性物质,特别是生物大分子的分离,因而具有良好的应用前景。它的制备方法对其物理化学性质有很大的影响,从而影响填料的色谱性能。该文对氧化锆微球的制备方法及其物理化学性质进行了综述。分析表明,目前氧化锆基质色谱填料的制备方法存在着难以克服的缺点,要制备理想的锆基色谱填料需要新的思路。