Synthesis and Characterization of Nano-Aerogels

1.5. Supercritical Fluids and Supercritical Carbon Dioxide

1.5.1. Supercritical Fluids (SCFs)

By definition, a supercritical fluid (SCF) is a single phase when its temperature is above the critical temperature (T_c) and its pressure is above the critical pressure (P_c), as shown in a typical pressure-temperature (P-T) phase diagram (Figure 1.1). In the P-T phase diagram of a pure substance, the phase boundary lines divide the diagram into solid, liquid and gas regions. However, the boundary between the liquid and the gas disappears when the pressure is higher than the critical pressure, and the temperature is higher than the critical temperature.



Figure 1.1. Schematic: the phase diagram of a typical material.

A SCF has a density comparable with a liquid, which enables it to function as a solvent, and a viscosity similar to a gas, which provides superior mass and heat transfer compared with a conventional solvent. Also, due to the zero surface tension, SCFs have been extensively used for supercritical drying to maintain high surface areas of the materials.^54 As a result of these favorable properties as a solvent, extensive research and development on SCFs for chemical reactions and extractions have been conducted in recent decades.^55-57

By definition, viscosity is a measure of the resistance of a fluid to deform under shear stress.^58 Using CO₂ as an example, the viscosities and densities of vapor, liquid and supercritical CO₂ under selected conditions are listed in Table 1.1.^59 From this table, it can be observed that the viscosity and density of supercritical fluid are a function of temperature and pressure. By tuning temperature and/or pressure, a desired physical property of the SCF such as viscosity and density can be achieved.
Table 1.1. The selected viscosities and densities of CO₂ in vapor, liquid and supercritical phases.^{59, 60}

Temperature (K)	Pressure (psia.)	Phase	Viscosity (10^-6 Pa·S)	Density (mol/L)
313	1000	Vapor	19.1	4.4
303	3000	Liquid	90.5	20.4
323	2000	Supercritical	52.5	15.2
333	2000	Supercritical	41.3	12.6
333	5000	Supercritical	82.8	19.5

Surface tension is caused by the molecules of the liquid at the surface that are subject to an inward force of molecular attraction.^61 The surface tension of the saturated liquid CO₂ as a function of pressure/temperature is plotted in Figure 1.2.^{60, 62} In the saturated liquid region, the surface tension decreases as the pressure/temperature increases. In the supercritical region, the surface tension is zero due to the disappearance of the interface between the liquid and vapor phases.

Figure 1.2. Surface tension of saturation liquid CO₂ vs. pressure. The data points were labeled with the corresponding saturation temperatures at the specific pressures. In the supercritical region, the surface tension is zero.^60

Different substances have their own critical properties. Table 1.2 shows the T_c, P_c and ρ_c (the density at the critical point) of selected substances that have been used as SCFs for material processing and chemical reactions.^57 Generally speaking, low T_c and P_c of a substance are desirable due to economic issues. Practically, the safety and environmental issues for using a flammable organic compound and the solvent power of the substance have to be considered when one selects a SCF. Among the candidates of SCFs, CO₂ is an outstanding one, because of its relative low T_c and P_c, low cost, abundance, and the fact that it is environmentally benign. Usage of scCO₂ instead of water or organic solvent can reduce the water pollution and emission of VOCs. The industrial sources of CO₂ include the flue gas from power stations, as well as CO₂ being a by-product of existing processes such as ethanol, ammonia and hydrogen production.

Table 1.2. Critical properties for selected supercritical fluids in chemical reactions^57



1.5.2. Particle Formation in SCFs

SCFs offer many opportunities to form particles with improved properties. From the processing aspect, producing particles by SCFs can be classified into several major processes such as gas antisolvent (GAS), rapid expansion of supercritical solution (RESS), precipitation from gas saturated solutions (PGSS), etc.^{63, 64}

RESS Process. In 1984, Krukonis first reported using the RESS process for the preparation of small particles and fibers of polypropylene and soybean lecithin.^65 After this report, extensive studies were made on the formation of a variety of materials by means of the RESS process. For example, silica particles with a diameter of 100 ~ 500 nm were prepared by the rapid expansion of supercritical water solution at 470 C.^66 It was found that the pre-expansion solution temperature had the most significant impact on product morphology among the RESS parameters, while the polymer-solution concentration had only a minor effect.^{66, 67} The RESS process can be considered to consist of four steps:

1. 
   Preparation of the supercritical solution, typically by dissolution of the solute in the supercritical solvent.
   
2. 
   Setting of the pre-expansion conditions upstream of the expansion device.
   
3. 
   Rapid expansion of the supercritical solution from the pre-expansion conditions to ambient conditions through a device such as a micro-orifice or capillary.
   

4. Recovery of the product in an expansion chamber.^57

When a SCF containing a dissolved solute goes through a micro-orifice, the density and solvation power of the fluid decreases dramatically in a very short time, resulting in supersaturation and subsequent precipitation of solute particles.^57

GAS Process. In the Gas-Antisolvent (GAS) method, the solute is soluble in an organic solvent but insoluble in a SCF. If the SCF is added into the organic solvent, the solubility of the solute decreases, hence causing precipitation. The resulting particle size and size distribution depend on the selection of the solution/antisolvent system, the solution concentration, the relative solution and antisolvent quantities, the rate of the antisolvent addition, and the degree of mixing.^68

1.5.3. Chemical Reactions in SCFs

The usage of SCFs as an alternative to conventional solvents has been the subject of increasing investigation over the last two decades due to the solvation and transport properties that can be varied appreciably.^57 Specifically, CO₂ has been used for polymerization,^69-73 catalytic oxidation,^74 catalytic hydrogenation,^75 enzymatic reactions,^76 and sol-gel reactions.^{53, 77-79}

Temperature and pressure are fundamental physical properties that affect various thermodynamic and kinetic parameters, especially for chemical reactions carried out in a SCF using a relatively high operating pressure.^80 The Arrhenius equation can be used to estimate the temperature effect on the reaction rate constants:

(1.1)

where k = the reaction rate constant, k₀ = the frequency factor, E_a = the activation energy in J/mol, R = universal gas constant = 8.314 J/(mol·K), T = temperature in K.

The pressure effect can be evaluated using transition state theory.^{81, 82} This theory assumes a chemical equilibrium between the reactants and an activated transition state species, with the latter proceeding directly to products. The rate of the chemical reaction is governed by the rate constant k:

A + B ⇌ M^‡ products (1.2)

where A and B denote the reactants, M^‡ is the transition state complex, and k is the rate constant.

The pressure effect on the reaction rate is given by:

(1.3)

where = bimolecular rate constant (mol/L·min), = _M^‡ -_A-_B = activation volume (the difference between the partial molar volume of the transition state species and that of the reactants), _i = partial molar volume of component i at reaction conditions, = mixture isothermal compressibility (this term is not included if the rate constant is expressed in a pressure-independent form, such as molar fraction or molarity), R = universal gas constant, and n = the sum of the stoichiometric coefficients of the reactants.^83 The partial molar volume, _i, and isothermal compressibility of the reaction mixture, , can be estimated from an equation of state.^{57, 82, 84} According to Equation 1.3, when =0 and is negative, an increased pressure will result in a higher rate constant.

The density variation in a SCF also influences the chemical potential of solutes and, thus, reaction equilibrium constants.^85

The clustering phenomenon is also important for consideration of chemical transformations in SCF media.^57 It was widely recognized that the solvent density in the region around a solute molecule will be higher than the bulk density, and this deviation is often 50 to 300 % and influences the kinetics of the reaction.^86 For instance, in their study on the pressure’s effect on the esterification of phthalic anhydride in supercritical CO₂, Ellington et al. attributed the reaction rate deviation from Equation 1.3 to the clustering effect.^87

1.5.4. Commercial Implementation of SCFs

Commercial implementation of SCF extraction applications include coffee and tea decaffeination, cholesterol and fat removal from eggs, acetone removal from antibiotics, and organic removal from water.^57 The early commercial implementation of SCF technology for conducting chemical reactions include ammonia synthesis (1913), methanol synthesis (1923), oxidation of light alkanes (1920) and the synthesis of low-density polyethylene (1940).^55 In 1985, SCF butene was used for 2-butanol production from 1- and 2-butene.^57 In 2002, DuPont commercialized the synthesis of fluoropolymers in scCO₂.^88

1.5.5. ScCO₂

Of the supercritical fluids, the most exciting potential is provided by the environmentally friendly solvent, supercritical carbon dioxide (scCO₂). The utilization of scCO₂ as a substitute for conventional organic solvents for the processing of materials has been widely reported.^89-92 The reasons are due to scCO₂ being non-toxic, non-flammable, inexpensive, naturally abundant, and environmentally benign. With a critical temperature of 31.1 C and a critical pressure of 1070 psig, the critical conditions of scCO₂ are easy to be achieved so that a lower capital cost is required for the autoclave materials and a lower operation cost is achieved due to lower energy consumption. The properties of scCO₂ can be easily tuned by changes of total pressure and/or temperature, hence changing the solubility of various compounds as desired.^{93, 94} In addition, removal of scCO₂ can be easily achieved by venting, hence no evaporation or drying processes are required. Particularly, supercritical drying extinguishes the liquid surface tension that causes the shrinkage of the solid, hence the microstructure of the aerogel is maintained after the drying process.^95 As a result, scCO₂ has been widely employed for aerogel processes.^96-99 A recent study shows that large pore sizes were obtained when using scCO₂ as a solvent for synthesizing mesoporous silica, in which silicon alkoxide was the precursor and a block copolymer was used as the template.^100

The first study on homogeneous catalysis in scCO₂ started in 1991 when Rathke and Klingler reported their work on hydroformylation of propylene catalyzed by HCo(CO)₄ in scCO_2.^101 The advantages of homogeneous catalysis in scCO₂ include higher solubility of the gaseous reactant in the SCF compared to conventional organic solvents,^102 higher mass transfer than that of heterogeneous catalysis, and easy ability to scale-up. A major drawback of homogeneous catalysis lies in the difficulty of catalyst recovery and recycling.^57