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=Introduction to porous solids= A porous solid is a material whose structure or [microstructure] includes a large density of voids, or pores, and hence a large specific surface area (area per unit volume or weight). These materials include catalysts, adsorbents, oxides, carbons, zeolites, organic polymers, soils, etc. The classification of porous materials can vary widely based on their application or field of study. The purpose of each classification is to organize materials based on characteristics of their pores such as size, geometry, connectivity. Other characteristic properties of porous materials can be structural, compositional, physical, or functional. Porous materials can also be grown or deposited as layers, thin films, membranes, fibers, and particles. The table below describes the pore size categories used in different areas of study.

The distribution of total pore volume with respect to individual pore size (pore size distribution), is important for applications where key physical properties occur at the gas- or liquid- solid interface; such as in catalysts, gas adsorption, filtration, and electrical capacitors.

A large volume of small pores contributes more surface area than the same volume of larger pores. To demonstrate this property, consider the two simple porous structures in the illustration below. Assuming both have the same total porous volume of 1 cubic centimeter (10-6 m3), it can be shown that the total surface area is inversely proportional to the average pore radius.

Typical examples of naturally occuring porous material include zeolites, sponges, limestone. Highly porous synthetic materials include synthetic zeolites, mesoporous silica (such as SBA-15, MCM-23), and nanoporous gold.

=Methods of Characterization=

Adsorption Isotherms
On a macroscopic scale, the total pore volume and surface area in a material can be determined using a method known as isothermal gas adsorption. By measuring the volume of gas adsorbed onto a material at different pressures, and adsorption isotherm plot can be generated and used to infer several key properties of the material. For example, if the surface area per a single adsorbed gas molecule is known, the total surface area can be determined by measuring the total adsorbed gas volume, pressure, or number of gas atoms. The IUPAC classifies adsorption isotherms into six different categories, each one assigned to a specific gas adsorption regime. These adsorption isotherms, I-VI, are illustrated below, along with the adsorption regime.

The first adsorption isotherm, also called Langmuir adsorption indicates the simplest type of gas adsorption. In this regime, gas adsorbs as a single monolayer until the surface is completely covered, at which time the surface saturates and adsorption rate tapers off. Type II adsorption isotherm indicates a mechanism by which the gas forms a monolayer but continues to adsorb, forming layers several atoms thick. Type III adsorption isotherm indicates a mechanism by which the gas adsorbs in thick layers prior to or without first forming a single monolayer. Type IV and V are indications of adsorption and condensation into capillary pores that saturate, or fill with essentially a liquid phase of adsorbant. Type IV indicates an initial monolayer adsorption while Type V indicates direct multilayer adsorption. Type VI indicates irregular isotherm, by which multiple dimensions of pores are present, each reaching saturation incrementally at different total adsorbed volumes, and not having a clear overall saturation level. More information on adsorption isotherms can be found at:
 * Langmuir Isotherm
 * Assumptions
 * Equation
 * BET Theory
 * Assumptions
 * Equation

Pore Size Distribution can also be inferred from the adsorption isotherm assuming a given model of adsorption.
 * Kelvin Equation:(macro/meso) The Kelvin equation describes how the vapor pressure of a liquid changes with a change in the curvature of its surface. A classical approach with simple assumptions of film formation, it does not account for reduction in pore volume due to surface adsorption, hence not applicable for small pore sizes.
 * BJH (Barrett-Joyner-Halenda) Method :(meso/micro) A method for calculating pore size distributions is based on a model of the adsorbent as a collection of cylindrical pores.
 * DFT (Density Functional Theory) Method : (meso/micro) Specific models based on the assumption that the overall isotherm is a weighted average of individual pore adsorption isotherms.  By modeling individual pore geometry isotherms and measuring the total volume of pores, a pore size distribution can be fitted to match the measured overall adsorption isotherm.

To measure the number of molecules adsorbed to a surface, we set up an experiment similar to the one in the figure below. The experimental setup consists of two separate chambers connected by a valve: the first chamber is a known empty volume, and the second one contains the sample. For nitrogen adsorption, the sample must be cooled to liquid nitrogen temperature of 77K. For the adsorption measurements, the following procedure is used : 1. Both chambers are evacuated then isolated from eachother. 2. The first chamber is filled with a certain pressure of gas, then the chamber is isolated and the pressure is recorded. 3. The valve between the first chamber and sample chamber is opened, and the gas is allowed to reach an equilibrium pressure, then recorded. 4. Steps 2 and 3 are repeated, incrementally increasing the pressure, until the sample chamber pressure reaches the equilibrium vapor pressure of nitrogen at 77K, which is 100 kPa or 750 Torr. When using a non-adsorbing gas such as Helium at 77K, the ratio of these pressures will be equal to the ratio of the sample volume to the first chamber volume. Helium is used to measure the sample chamber volume because at 77K it will not adsorb to the sample surfaces. When the procedure is completed using Nitrogen gas, the ratio of the pressures will be greater by the volume of gas adsorbed to the surface. This adsorbed volume is recorded for a number of equilibrium pressures and plotted as the adsorption isotherm.

Valid for low pressures Measures only open, connected porosity (trapped or enclosed pores are not detected)

Microscopic Imaging
Through microscopic imaging techniques, the sizes, shapes, and distribution of pores in a material can be observed and measured directly.
 * Scanning Electron Microscope (SEM) Imaging

=Synthesis and Modification= Synthesis of Bulk porous materials
 * Self-assembly
 * Sol-gel processing
 * Spray Drying Method
 * Aerogels and sol-gel processing
 * Sonochemical preparation methods

Synthesis of Porous films
 * Dealloying
 * Templating
 * Wet Chemical Deposition
 * Electrochemical Deposition
 * Evaporation induced self-assembly
 * Ion bombardment
 * Ultrafast laser bombardment

Synthesis of Porous particles
 * Porous Carbon preparation by ultraasonic spray pyrolysis

=Applications=
 * Catalysts and catalyst supports
 * Hydrogen storage
 * Supercapacitors
 * Sponges
 * Water Purification

=Examples= Metal Organic Framework

=See also=
 * Nanoporous Materials
 * Mesoporous Materials
 * Microporous Materials
 * Macroporous materials
 * Porous Medium
 * Porosity
 * nanopowders
 * Colloidal Solution
 * Surface roughness