Porous materials modeling pore structure

Quantitative, nonempirical models of transport in porous materials require a more sophisticated description of the porous microstructure. For many materials the pore structure is stochastic, consisting of an ensemble of individual pores of random size distributed randomly throughout the material. Useful models of transport in these polymers can be based on percolation descriptions of porous media. Percolation descriptions have been used to describe fluid flow, electrical conduction, and phase transitions in random systems [26, 38]. 

Due to the visualization of a porous medium as an ensemble of large dust molecules in the Dusty G ls Model pore structure properties such as porosity, tortuosity, and pore size distribution are not directly included. All information on pore structure characteristics is contained in the permeability constants Co, Ci, and Ca. Heteroporosity as originating from a wide pore size distribution is not accounted for specifically. On the other hand the Dusty Gas Model has the etdvantage to allow a separation of the influence of pore structure characteristics on the different transport mechanisms. The influence of the adsorbent material pore structure on gas phase mass transport is incorporated through the parameters Co, Ci, and C2 resp. They are determined by flux experiments for the specific adsorbent material (refs. 4, 6). The values for the different trstructural parameters such as representative pore diameter dp, porosity p, and tortuosity factor Tp by the expressions ... 

Abstract A simplified quintuple model for the description of freezing and thawing processes in gas and liquid saturated porous materials is investigated by using a continuum mechanical approach based on the Theory of Porous Media (TPM). The porous solid consists of two phases, namely a granular or structured porous matrix and an ice phase. The liquid phase is divided in bulk water in the macro pores and gel water in the micro pores. In contrast to the bulk water the gel water is substantially affected by the surface of the solid. This phenomenon is already apparent by the fact that this water is frozen by homogeneous nucleation. 

Taking into account the aforementioned effects of ice formation in porous materials, a macroscopic quintuple model within the framework of the Theory of Porous Media (TPM) for the numerical simulation of initial and boundary value problems of freezing and thawing processes in saturated porous materials will be investigated. The porous solid is made up of a granular or structured porous matrix (a = S) and ice (a = I), where it will be assumed that both phases have the same motion. Due to the different freezing points of water in the macro and micro pores, the liquid will be distinguished into bulk water ( a = L) in the macro pores and gel water (a = P, pore solution) in the micro pores. With exception of the gas phase (a = G), all constituents will be considered as incompressible. 

Subsequently, the characterization of the pore structures of the porous materials using gas adsorption method was discussed in detail. The types and characteristics of the adsorption isotherms and the hysteresis loops were introduced. In addition, the BET (Braunauer, Emmett, and Teller) theory92 for the determination of the surface area and various theoretical models for characterization of the pore structures according to the pore size range were summarized based upon the adsorption theory. 

The available transport models are not reliable enough for porous material with a complex pore structure and broad pore size distribution. As a result the values of the model par ameters may depend on the operating conditions. Many authors believe that the value of the effective diffusivity D, as determined in a Wicke-Kallenbach steady-state experiment, need not be equal to the value which characterizes the diffusive flux under reaction conditions. It is generally assumed that transient experiments provide more relevant data. One of the arguments is that dead-end pores, which do not influence steady state transport but which contribute under reaction conditions, are accounted for in dynamic experiments. Experimental data confirming or rejecting this opinion are scarce and contradictory [2]. Nevertheless, transient experiments provide important supplementary information and they are definitely required for bidisperse porous material where diffusion in micro- and macropores is described separately with different effective diffusivities. 

Frequently we define a porous medium as a solid material that contains voids and pores. The notion of pore requires some observations for an accurate description and characterization. If we consider the connection between two faces of a porous body we can have opened and closed or blind pores between these two faces we can have pores which are not interconnected or with simple or multiple connections with respect to other pores placed in their neighborhood. In terms of manufacturing a porous solid, certain pores can be obtained without special preparation of the raw materials whereas designed pores require special material synthesis and processing technology. We frequently characterize a porous structure by simplified models (Darcy s law model for example) where parameters such as volumetric pore fraction, mean pore size or distribution of pore radius are obtained experimentally. Some porous synthetic structures such as zeolites have an apparently random internal arrangement where we can easily identify one or more cavities the connection between these cavities gives a trajectory for the flow inside the porous body (see Fig. 4.30). 

We implement a modified version of the reconstruction method developed in a previous work to model two porous carbons produced by the pyrolysis of saccharose and subsequent heat treatment at two different temperatures. We use the Monte Carlo g(r) method to obtain the pair correlation functions of the two materials. We then use the resulting pair correlation functions as target functions in our reconstruction method. Our models present structural features that are missing in the slit-pore model. Structural analyses of our resulting configurations are useful to characterize the materials that we model. 

Among the structural models of cellular or porous materials those characterized by differently ordered packing of balls or spheres of the same diameters have most widely been used. In this approach either the spheres have been considered as real cells or the cell (pore) models have been derived from an analysis of assumed spacings between the contacting solid spheres. However, no system of packed spheres would adequately describe the properties of any real cellular system which never exhibit a regular packing. It is also impossible to describe the structure of most cellular systems via models assuming spheres of equal size. 

Vycor is a porous silica glass which is widely used as a model structure for the. study of the properties of confined fluids in me.soporous materials. The pores in vycor have an average radius of about 30-35 A (assuming a cylindrical geometry) and are spaced about 200 A apart [2-3]. A literature survey indicates that there are two kinds of (Corning) vycor glasses one type has a specific surface around 100 m /g while the other is characterized by a specific surface around 200 m /g (both values are obtained from N2 adsorption isotherms at 77 K). 

Fig. 4. Fluid-fluid radial distribution functions (right) and paitial structure factors (left) for low and high adsorption in the (a) model porous glass. The low-adsoiption data eoire-spond to 2.82 nimol/g adsorbed density (monolayer regime), and the high-adsorption data to 11.51 mmol/g adsorbed density, in the pore-filling regime. The o.scillations at low r in the g r) data and large k in the S k) data are due to local liquid stmcture, while the long-wavelength fluctuations (large r, small k) arc caused by the porous material.

The industrial application of porous solids is quite widespread. Porous heterogeneous catalysts, adsorbents and membranes are used in chemical industry and in biotechnology, porous materials are common in building engineering, porous eatalysts form the basis of car mufflers, etc. The rates of processes, which take place in pore strueture of these materials, are affected or determined by the transport resistance of the pore structure. Inclusion of transport processes into the description of the whole process is essential when reliable simulations or predictions have to be made. Trends in modem chemical/biochemical reaction engineering point to utilization of more sophisticated, and therefore more reliable, models of proeesses. The basic idea is that the better the description of individual steps of the whole process the better its description and, perhaps, even extrapolation. 

A great number of studies have been published to deal with relation of transport properties to structural characteristics. Pore network models [12,13,14] are engaged in determination of pore network connectivity that is known to have a crucial influence on the transport properties of a porous material. McGreavy and co-workers [15] developed model based on the equivalent pore network conceptualisation to account for diffusion and reaction processes in catalytic pore structures. Percolation models [16,17] are based on the use of percolation theory to analyse sorption hysteresis also the application of the effective medium approximation (EMA) [18,19,20] is widely used. 

The evaluation of the commercial potential of ceramic porous membranes requires improved characterization of the membrane microstructure and a better understanding of the relationship between the microstructural characteristics of the membranes and the mechanisms of separation. To this end, a combination of characterization techniques should be used to obtain the best possible assessment of the pore structure and provide an input for the development of reliable models predicting the optimum conditions for maximum permeability and selectivity. The most established methods of obtaining structural information are based on the interaction of the porous material with fluids, in the static mode (vapor sorption, mercury penetration) or the dynamic mode (fluid flow measurements through the porous membrane). 

These techniques involving the measurement of membrane permeability to a fluid (liquid or gas) lead to a mean pore radius (usually the effective hydraulic radius Th) whose quantitative value is often highly ambiguous. The flux of a fluid through a porous material is sensitive to all structural aspects of the material [129]. Thus, in spite of the simplicity of the method, the interpretation of flux data, even for the simplest case of steady state, is subject to uncertainties and depends on the models and approximations used. 

Characterization of the pore structure of amorphous adsorbents and disordered porous catalysts remains an important chemical engineering research problem. Pore structure characterization requires both an effective experimental probe of the porous solid and an appropriate theoretical or numerical model to interpret the experimental measurement. Gas adsorption porosimetry [1] is the principal experimental technique used to probe the structure of the porous material, although various experimental alternatives have been proposed including immersion calorimetry [2-4], positron... 

Pore structure analysis methods based upon realistic disordered microstructures may be classified into two types. In one approach, the experimental procedures used to fabricate the material are reproduced, to the greatest extent possible, via molecular simulation, and the resulting amorphous material structure is then statistically analyzed to obtain the desired structural information. In the other approach, adsorbent structural data (e.g., smaU-angle neutron scattering) is used to construct a model disordered porous structure that is statistically consistent with the experimental measurements. As in the first approach, molecular simulations can then be carried out using the derived model structure to obtain the structural characteristics of the original adsorbent. 

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