Characterization And Diffusion In Pore Structure Of Micro/Mesoporous Media Based On Reconstructed Model

Micro/mesoporous matierals with disordered pore structures which areapplied as carriers, catalysts, or adsorbents have many applications in thefields of petroleum, chemical engineering, energy sources, and environmentalprotection. Undoutedly, in these applications, transport properties of gaseswithin the pore structure are of great importance. However, the understandingon the features and transport properties of porous media are incompletelyknown due to the complexity of the disordered pore structure. For instance,the tortuosity factor which was used to characterize the macroscopic featuresof the pore structure and to correlate with the effective diffusion coefficientcannot be applied to characterize the microscopic features of the pore structure.In addition, the transport properties of porous media obtained from the fractalmodel are in somewhat disagreement with the experimental results due to thelimitation in scale of fractal region. Moreover, when the porosity is at and nearthe threshold of the porous media, a significant change of the transportproperties of gas or mass will be emerged in the porous media due to a verysmall change of the pore structure, which was ascribed to a percolationbehavior. It is known that the percolation theory was proposed based on amodel where clusters are randomly distributed. Yet, many natural and artificialsystems are not completely random and actually have spatial correlations intheir internal structure. Untill now many percolation behaviors of correlatedporous media are still poorly understood. Therefore, the more investigations inthe features of the pore structure and the diffusion properties are needed. Andthey have been investigated in our work based on a reconstructed model ofporous media, which will provide some new theories for design, preparation,and performances prediction of porous material, and are of great theoreticalsignificance and application prospects.In the work, the polyethylene BCE catalysts and Debye model were studied.The Debye model which can be characterized by an exponential correlationfunction is used to describe one of the homogeneous materials in which holesof varying and undermined shape are randomly distributed. The chief contentof the paper could be concluded as three parts. The first part contains thecharacterization and reconstruction of BCE catalysts based on the small-angle X-ray scattering, the simulation of effective diffusion coefficient of BCEcatalysts, and the correlation between the physical performances and theactivity of catalysts. The estimates of static and dynamic exponents ofuncorrelated and correlated percolation both at and near the threshold arepresented in the second part. When the porosity is far more than the thresholdof correlated porous media, the relations between the features of the porestructure and normal diffusion coefficients are given in the last part.Main results of this work are as follows:(1) Characterization and reconstruction of BCE catalysts based on small-angleX-ray scattering (SAXS) and diffusion in the reconstructed catalyst model.Pore structures of10BCE catalysts were characterized by the SAXSmethod. First, qualitative analysis of the scattering curve was performed. Ithas been found that the intensity was scattered from two parts: the envelope ofcatalyst grains and the inner pores of the grains. The intensity due to theenvelope of grains complied with the Porod law. However, the intensity fromthe inner pores of the grains abided by the Guinier law at the low scatteringangle and performed the mass or surface fractal properties at the highscattering angle.The calculated scatter intensity of inner pores was obtained by subtractingthe intensity due to the envelope of the grains from original data and wasanalyzed by Guinier law, Porod law, Debye law, and fractal method,respectively.In terms of the Guinier law applied at the small angle we have found thatthe structure of pores of most catalysts behaved as a monodisperse phase. Inaddition, the specific surfaces of catalysts were calculated from the Debye andPorod analysis. The results of Porod analysis were more reasonable and werecloser to BET consequences. Moreover, some values of specific surface werelarger than the results from BET because closed pores were also measured.According to the Debye analysis, the scattering intensity of inner pores at thelow and intermediate angle indicated that the pores were random distributed,and the pore shapes were undetermined at these scales. However, the intensityat the large angle deviated from the Debye model but could be fitted by fractalmodel. In terms of the analysis from the fractal model, we have found that thepores spatial distribution was surface fractal model or mass fractal model.Moreover, it has been found that the larger the Porod exponent was, the betterthe morphology of catalyst was.Three-dimensional model of BCE catalyst was reconstructed by stochasticmethods based on an autocorrelation function of the catalyst evaluated from the SAXS method and a porosity of the catalyst estimated from the BETmethod. The single-level correlated Gaussian field method and the simulatedannealing method were compared in our work. It has been found that thereconstructed models from both methods had the same porosity and the sameautocorrelation function as the original catalyst. At last, the Gaussian fieldmethod was chosen to reconstruct the3D model because the less time wascost.Ethylene molecules were performed in the reconstructed catalyst models bya molecular trajectory algorithm, and effective diffusion coefficients werecalculated. It has been found that if an accurate value of the effective diffusioncoefficient wanted to be obtained, the computations must be repeated for alarge number of molecules with sufficient travel time. In particular,homogeneous regions of models must be reached by the molecules. We havefound the order of magnitude of the effective diffusion coefficient was10-8and the tortuosity factor of BCE catalyst was between4and7.In addition, we have found that the activity of catalysts increases with theincrease in the effective diffusion coefficient De, and the mean chord length lav,and the autocorrelation R(u) at short range scales, but decreases with theincrease of tortuosity factorτ lavof catalysts.(2) Dynamic exponents of random (uncorrelated) percolation.Diffusion on random systems in two and three dimensions was carried outby the molecular trajectory algorithm and an ant-in-the-labyrinth method(ANT) respectively. The fractal dimension of the random walk was evaluatedby the simulations on the incipient infinite cluster, and on all clusters at thethreshold not subject to the infinite restriction, respectively.The conductivity exponent was estimated from the diffusion on randomsystems both above and at their percolation threshold. The simulations on thecritical random system, in which the analysis of corrections to scaling wascarried out, were more accurate than the simulations above the threshold inwhich only a log-log relation was considered.In sum, the simulations in two dimensions deviated somewhat from theAlexander-Orbach[154]rule but were close to the former results[157-164]calculated from other methods. However, the results in three dimensions fromthe molecular trajectory algorithm were in agreement with the predictions ofAlexander-Orbach.In addition, the correlation length exponent of three-dimensionalpercolation was estimated as ν=0.879±0.012for the molecular trajectory rules and ν=0.826±0.012for the ant-in-the-labyrinth method. However, onlythe value from the molecular trajectory algorithm is close to the referenceresult[165].Moreover, it has been found from all simulations that the moleculartrajectory method showed the faster convergence than the ant-in-the-labyrinthmethod.(3) Critical exponents of correlated percolation clusters.The critical exponents of the Debye model and the BCE catalyst (c13) intwo dimensions were calculated.The percolation threshold pcand the correlation-length exponent ν wereevaluated by the finite-size scaling method. It has been found that thedependence of the percolation threshold for Debye models on the correlationlength w was fitted by an exponential functionpc=pc∞+(p0c p∞c) exp(α w),wherep0candp∞care the threshold when w=0and∞, respectively. However,the correlation-length exponents of Debye models and the catalyst c13wereindependent of the correlation length w and had the same value as in pure(uncorrelated) percolation.The mass fractal dimension of correlated percolation at criticality wascalculated in terms of the two-point correlation function of models. We foundthat the results of Debye models and the catalyst c13were also independent ofthe correlation length w and had the same value as in pure (uncorrelated)percolation.The random walk dimension exponentsd wand k, and the spectrumdimension dsfor these correlated models at the threshold were estimated bythe simple lattice random walk. It has been found that the values ofd wand k,and the pectrum dimension calculated from the equation ds/2＝df/dwwereclose to the results in pure (uncorrelated) percolation. However, the results ofspectrum dimension from method proposed by Rammal and Toulouse[141]deviated apparently from the value in pure (uncorrelated) percolation.In conclusion, the two-dimensional correlated percolation such as theDebye random media and the catalyst c13model belonged in the sameuniversality class as the uncorrelated percolation.(4) Relations between features of pore structures and the norm diffusioncoefficient of porous media.In the work, the model was reconstructed by the Gaussian filed method, andeffective diffusion coefficients were calculated by the molecular trajectory algorithm. At the same porosity, the effective diffusion coefficient of catalystsincreases with the increase in the mean chord length lav, and theautocorrelation R(u) at one unit length of the model, and the lacunarity indexat the small scale. It should be noted that the small scale is relative to theresolution of the modelMoreover, we have found the mean chord length of the two-andthree-dimensional porous media could be related to the porosity ε andautocorrelation in one unit, RZ (a e), of the model by the relation:is zero for uncorrelated percolation systems.In addition, the dependence of the norm diffusion coefficient D＝d<R2>/dtof the two-and three-dimensional Debye model on the porosity ε and thecorrelation length w could be fitted by a function:where aeis the resolution of the model, lavis the mean chord length of themodelpcthe threshold of the model, and a, b,and k are the parameters which vary with the condition of diffusion.