Density of SCF

Transport Properties Although the densities of SCFs can approach those of conventional liquids, transport properties are more favorable because viscosities remain lower and diffusion coefficients remain higher. Furthermore, CO2 diffuses through condensed-liquid phases (e.g., adsorbents and polymers) faster than do typical solvents which have larger molecular sizes. For example, at 35°C the estimated pyrene diffusion coefficient in polymethylmethacrylate increases by 4 orders of magnitude when the CO2 content is increased from 8 to 17 wt % with pressure [Cao, Johnston, and Webber, Macromolecules, 38(4), 1335-1340 (2005)]. 

Sigman et al.(12) determined n (dipolarity-polarizability) and p (basicity) parameters for supercritical carbon dioxide as a function of density. As the density of SCF CO2 Is decreased, the k values decrease smoothly towards the value obtained in a vacuum. The x parameters were the average values of ten different probes in carbon dioxide, while the n values of HyattOD and Yonker and co-workers(14.15.16.171 were obtained using a single probe. The trends in the n parameters were similar for the various studies, which suggests that the use of a... 

The density of SCFs can be tuned to promote either the liquid-like or gas-like properties with comparatively small pressure changes [14]. The influence of pres-... 

Apart from the direct conformational changes in enzymes, which may occur at very high pressures, pressure affects enzymatic reaction rates in SCFs in two ways. First, the reaction rate constant changes with pressure according to transition stage theory and standard thermodynamics. Theoretically, one can predict the effect of pressure on reaction rate if the reaction mechanism, the activation volumes and the compressibility factors are known. Second, the reaction rates may change with the density of SCFs because physical parameters, such... 

One of the key features of SCFs is their tunability to process operating conditions, which results in higher solvating powers. For example, the density of SCFs is sensitive to pressure. At a constant tanperature, an increase in piessnie lesnlts in an increase in fluid density. The relationship between pressure and doisity is shown in Figure 5.2, where... 

As can be seen from Eq. (14), the solubility of a solid in an SCE depends not only on solid-state parameters, such as sublimation pressure and molar volume V , but additionally on the fiigacity coefficient (]), . The fugacity coefficient is the supercritical analogue to the activity coefficient (5). The fugacity coefficient varies not only with the type of fluid but with temperature and pressure (53). Therefore, solubility of solids can be significantly influenced by changing the density of SCFs on alteration of temperature and/or pressure. The fugacity coefficient is the key variable that explains the different solubility of solids in SCFs compared with ordinary liquids. 

The density of SCF is a function of pressure and temperature. The solvent power can be varied and this can be used for coupling of a reaction with an integrated separation. The first scientists who tried this method were Doddema et al. [91]. They investigated the transesterification of nonanol with ethyl acetate. At the outlet of the reactor they reduced pressure and the solutes separated. Ethyl acetate and ethanol were extracted from the fluid in a column with SCCO2 (7.5 MPa/60 C). In a following step fresh ethyl acetate was added to the remaining mixture then it was pumped into a second enzyme reactor with SCCO2 (20 MPa/60°C). The authors achieved a conversion of over 90% for nonanol, since removal of ethanol avoided a product inhibition. 

Transport Properties Although the densities of supercritical fluids approach those of conventional hquids, their transport properties are closer to those of gases, as shown for a typical SCF such as CO9 in Table 22-12. For example, the viscosity is several orders of magnitude lower than at liquidlike conditions. The self-diffusion coefficient ranges between 10" and 10" em /s, and binaiy-diffusiou coefficients are similar [Liong, Wells, and Foster, J. Supercritical Fluids 4, 91 (1991) Catchpole and King, Ind. Eng. Chem. Research, 33,... 

The stability of SCF solutions for unknown systems should always be tested. Stability considerations apply to and may be tested for in calculations using Density Functional Theory methods as well. 

The use of SCFs as solvents influences the reacting system because it is possible to dramatically change the density of the fluid with small perturbations of temperature and pressure and, in such a way, greatly affect the density-dependent bulk properties such as the dielectric constant, solubility and diffu-sibility of these compressible fluids. 

The physical properties of a SCF are intermediate between those of a typical gas or liquid. For example, the diffusivity of a SCF is intermediate between a liquid and a gas and the viscosity is similar to a gas. The density of a SCF can be changed by varying the applied pressure on the fluid and can range between that exhibited by a gas to liquid-like values when the fluid is compressed... 

Figure 1 3. Contour plot of the electron density of CO, showing the magnitudes and directions of atomic and charge transfer dipoles (arrow length is proportional to magnitude). Arrow heads point to the negative end. The molecular dipole moment is given by the vector sum of charge transfer terms (p.c.t.) and the atomic polarizations ( ra p). Values were obtained at the DFT level using the B3LYP functional and the 6-31 1+G(3df) basis set. The SCF molecular dipole = 0.096 D the computed molecular dipole ( Jtc.t.[0] + Aa.p.[0] + Hc.JC] + Aa.p.[C]) = 0.038 au = 0.096 D, close to the experimental value of 0.1 10 D (15).

In this approach, the electron density of a solvated molecule (p) is calculated using the SCF procedure where the isolated molecule Hamiltonian Hgas is replaced by the solvated molecule Hamiltonian //sol ... 

With traditional solvents, the solvent power of a fluid phase is often related to its polarity. Compressed C02 has a fairly low dielectric constant under all conditions (e = 1.2-1.6), but this measure has increasingly been shown to be insufficiently accurate to define solvent effects in many cases [13], Based on this value however, there is a widespread (yet incorrect ) belief that scC02 behaves just like hexane . The Hildebrand solubility parameter (5) of C02 has been determined as a function of pressure, as demonstrated in Figure 8.3. It has been found that the solvent properties of a supercritical fluid depend most importantly on its bulk density, which depends in turn on the pressure and temperature. In general higher density of the SCF corresponds to stronger solvation power, whereas lower density results in a weaker solvent. 

Characteristic properties of SCFs include variable density, dielectric constant viscosity, and cage strength, local inhomogeneity, high diffusion rate, high miscibility with gaseous substances, and high sensitivity of all properties to added substances. All... 

As a consequence, the presentation of the results will also differ from that in a MD or MC box, where a full set of molecules can be depicted (as snapshots). In an SCF model, all properties will be presented in, for example, (average) numbers of molecules per unit area of the membrane, or equivalent, i.e. the (average) densities of molecules as a function of the z-coordinate. The box thus consists, if one insists, only of one coordinate. For this reason, we can refer to this method as a one-gradient SCF theory or simply 1D-SCF theory. Extensions towards 2D-SCF are available, where lateral inhomogeneities in the bilayer can also be examined [80], There are even implementations of 3D SCF-like models, but here the interpretation is somewhat more delicate [78],... 

Supercritical fluids represent a different type of alternative solvent to the others discussed in this book since they are not in the liquid state. A SCF is defined as a substance above its critical temperature (Tc) and pressure (Pc)1, but below the pressure required for condensation to a solid, see Figure 6.1 [1], The last requirement is often omitted since the pressure needed for condensation to occur is usually unpractically high. The critical point represents the highest temperature and pressure at which the substance can exist as a vapour and liquid in equilibrium. Hence, in a closed system, as the boiling point curve is ascended, increasing both temperature and pressure, the liquid becomes less dense due to thermal expansion and the gas becomes denser as the pressure rises. The densities of both phases thus converge until they become identical at the critical point. At this point, the two phases become indistinguishable and a SCF is obtained. 

The density of a SCF is typically less than half that of the liquid state, but two orders of magnitude greater than that of a gas. Viscosity and diffusivity are also temperature and pressure dependent. 

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