Supereritical fluid extraction 27 (5)Aromaticity decreases solubility. This is well demonstrated by the progressive decrease in solubility in the series decalin-tetralin-naphthalene as aromaticity is intro duced into the molecule decalin naphthalene A summary of some of the solubility characteristics of selected classes of compounds in liquid COz is given below (1) Substances with low molecular weight, and low or intermediate polarity are com- pletely miscible. (a) Aliphatic hydrocarbons(CnH2n+2) n<12;(M) (note M= miscible) aromatic structures are less soluble but methyl and branched chain substi tutions increase solubility (b) Alcohols(C,H2n+IOH) n<6;(M) further hydroxylation reduces solubility. c) Carboxylic acids(C,H,n+cOoh (d) Esters( CnH2n+COOCmH2m+1) more soluble than parent acid if m<n (e) Aldehydes(CnH2n+CHO) aromatic aldehydes are insoluble (f) Glycerides. The glycerides illustrate an interesting feature since increasing the extent of esterification of glycerol reduces the polarity but increases the olecular weight. The order of solubility reflects the delicate balance of monoglyceride triglyceride diglyceride (2) Macromolecules or highly polar molecules are essentially insoluble, e.g. salts, glycerol, sugars, proteins, starch
Supercritical fluid extraction 27 (5) Aromaticity decreases solubility. This is well demonstrated by the progressive decrease in solubility in the series decalin-tetralin-naphthalene as aromaticity is introduced into the molecule: a)aa decalin tetralin naphthalene (22%) (1 2%) (2%) A summary of some of the solubility characteristics of selected classes of compounds in liquid C02 is given below: (1) Substances with low molecular weight, and low or intermediate polarity are completely miscible. (a) Aliphatic hydrocarbons (CnH2n+2) n < 12; (M) (note M = miscible) aromatic structures are less soluble but methyl and branched chain substitutions increase solubility. (b) Alcohols (CnH2,+1OH) n < 6; (M) further hydroxylation reduces solubility. (c) Carboxylic acids (C,,H2,+1COOH) n < 9; (M) (4 Esters (C,H2,,+1COOC,H2,+1) more soluble than parent acid if rn < n. (e) Aldehydes (C,,H2,,+1CHO) n < 8; (M) aromatic aldehydes are insoluble. Glycerides. The glycerides illustrate an interesting feature since increasing the extent of esterification of glycerol reduces the polarity but increases the molecular weight. The order of solubility reflects the delicate balance of these opposing effects: (f) monoglyceride < triglyceride < diglyceride (2) Macromolecules or highly polar molecules are essentially insoluble, e.g. salts, glycerol, sugars, proteins, starch
28 D Steytler (3) Surfactants. Recently there has been much interest in the formation and properties of reverse micelles and water-in-oil microemulsions in the ncF alkanes(ethane- butane)( Gale et al., 1987; Eastoe, 1990(a, b)). Moreover, the related Winsor Il systems display a clear dependence of droplet size on pressure which could be portant in the selective separation of enzymes(McFann and Johnston, 1991) However, although some surfactants are soluble in NCF CO2, and may well form reverse micelles therein(Consani and Smith, 1990), it is not an effective medium for stabilising microemulsions Efect of temperature and pressure For liquid solvents with low compressibilities the pressure has very little influence on solubility, A simple explanation of the effect of pressure on solubility in NCFs can be made in terms of the number of solute-solvent interactions which depends upon the ensity of the solvent medium. The overall shapes of solubility isotherms therefore often closely resemble density isotherms of the pure solvent. At very high pressures, restraints of packing can adversely perturb the preferred molecular orientations required for opti mum solvation, and solubilities can then begin to decrease with increasing pressure As heats of solution are more often positive it is generally observed that solt quid solvents increase with temperature at constant pressure. However, with NCFs the situation is more complex since both density and temperature must be considered. A general statement governing the influence of these parameters is that the solubility increases with increasing temperature at constant density. This generality is more universally obeyed than the alternative statement in terms of temperature alone To illustrate these effects the solubility of naphthalene is shown in Fig. 2.6(a)as a unction of temperature and pressure. At constant temperature the solubility increases with pressure in accord with the simple picture of increasing solvation through increasing solvent density. Above about 150 bar the solubility increases with temperature as expected but at lower pressures this 'normal trend is reversed and the solubility then declines with increasing temperature. This behaviour, which appears anomalous at first sight, can be explained in terms of the high thermal expansivity of the SCF in the lower pressure domain. In this highly expansive region the large drop in density on heating(at constant pressure)outweighs the thermal enhancement and the overall solubility declines At higher pressures ermal expansivity of the fluid is much reduced and the solubility then increases with temperature as in liquid solvents. Figure 2.6(b )shows how the solubility dependence can be simplified by replacing the pressure variable with 2.3.2 Theoretical models(equations of state(EOS)) Of all theoretical methods used for the prediction of solubilities in NCFs, the solution of phase equilibrium using equations of state has been most widely applied. The appeal of his approach lies in its simplicity, avoidance of intangible standard states and overall success in correlating the phase behaviour of a wide range of NCF mixtures. To illustrate the general principles involved in the EOS approach, a simple example involving the dissolution of a pure solid(Solute 2)in an NCF(Solvent 1)will be considered as represented schematically in Fig. 2.7(b). Assuming that the NCF does not
28 D. Steytler (3) Surfactants. Recently there has been much interest in the formation and properties of reverse micelles and water-in-oil microemulsions in the NCF alkanes (ethanebutane) (Gale et al., 1987; Eastoe, 1990 (a, b)). Moreover, the related ‘Winsor 11’ systems display a clear dependence of droplet size on pressure which could be important in the selective separation of enzymes (McFann and Johnston, 1991). However, although some surfactants are soluble in NCF COz, and may well form reverse micelles therein (Consani and Smith, 1990), it is not an effective medium for stabilising microemulsions. Effect of temperature and pressure For liquid solvents with low compressibilities the pressure has very little influence on solubility. A simple explanation of the effect of pressure on solubility in NCFs can be made in terms of the number of solute-solvent interactions which depends upon the density of the solvent medium. The overall shapes of solubility isotherms therefore often closely resemble density isotherms of the pure solvent. At very high pressures, restraints of packing can adversely perturb the preferred molecular orientations required for optimum solvation, and solubilities can then begin to decrease with increasing pressure. As heats of solution are more often positive it is generally observed that solubilities in liquid solvents increase with temperature at constant pressure. However, with NCFs the situation is more complex since both density and temperature must be considered. A general statement governing the influence of these parameters is that ‘the solubility increases with increasing temperature at constant density’. This generality is more universally obeyed than the alternative statement in terms of temperature alone. To illustrate these effects the solubility of naphthalene is shown in Fig. 2.6(a) as a function of temperature and pressure. At constant temperature the solubility increases with pressure in accord with the simple picture of increasing solvation through increasing solvent density. Above about 150 bar the solubility increases with temperature as expected but at lower pressures this ‘normal’ trend is reversed and the solubility then declines with increasing temperature. This behaviour, which appears anomalous at first sight, can be explained in terms of the high thermal expansivity of the SCF in the lower pressure domain. In this highly expansive region the large drop in density on heating (at constant pressure) outweighs the thermal enhancement and the overall solubility declines. At higher pressures the thermal expansivity of the fluid is much reduced and the solubility then increases with temperature as in liquid solvents. Figure 2.6(b) shows how the solubility dependence can be simplified by replacing the pressure variable with density. 2.3.2 Theoretical models (equations of state (EOS)) Of all theoretical methods used for the prediction of solubilities in NCFs, the solution of phase equilibrium using equations of state has been most widely applied. The appeal of this approach lies in its simplicity, avoidance of intangible standard states and overall success in correlating the phase behaviour of a wide range of NCF mixtures. To illustrate the general principles involved in the EOS approach, a simple example involving the dissolution of a pure solid (Solute 2) in an NCF (Solvent 1) will be considered as represented schematically in Fig. 2.7(b). Assuming that the NCF does not
Supercritical fluid extraction 29 T=55°C 30 250 T=35c5 T=35c 0350 010020030040050060070080090 Pressure, P(bar ensity p(g/litre Fig. 2.6. Solubility of naphthalene in NCF CO, with (a) pressure and(b) density as variable (reproduced from Brogle, 1982) NCF Fig. 2.7. Relationship between(a)sublimation of a pure solid and( b)dissolution in an NCF dissolve in the solid phase, the system comprises a pure solid phase, represented by () where x=mole fraction of solid in this phase. In this case x2=1. This is in equilibrium with an NCF solution represented by ()with an unknown concentration of solid dis olved in it, i.e. y2=?. The NCF phase is often referred to as the 'gas' phase and the symbol y; accordingly used for mole fraction of component i. The following outlines the procedure for determining y2 The conditions for phase equilibrium are that pressure, temperature and fugacity of each component should be equal in both coexisting phases
Supercritical fluid extraction 29 A 500 - 500 - f 450- - & 400- ;;; 400- C al T=45’C i5 C c - a, 8 100- I 60 100 150 200 250 300 350 0 100 200 300 400 500 600 700 800 900 Density p (ghtre) (4 Pressure, P(bar) (b) Fig 2 6 Solubility 01 naphth‘ilene in NCF COz with (d) pressure and (b) density as variable (reproduced trom Brogle, 1982) Ts Ps TP (4 (b) Fig 2 7 Relationship between (a) sublimation of a pure solid and (b) dissolution In an NCF dissolve in the solid phase, the system comprises a pure solid phase, represented by (’), where x = mole fraction of solid in this phase. In this case x2 = 1. This is in equilibrium with an NCF solution represented by (”) with an unknown concentration of solid dissolved in it, i.e. y;’= ?. The NCF phase is often referred to as the ‘gas’ phase and the symbol y, accordingly used for mole fraction of component 1. The following outlines the procedure for determining y;. The conditions for phase equilibrium are that pressure, temperature and fugacity of each component should be equal in both coexisting phases:
Sterile T=T=T (for all i) If it is assumed that the ncF does not dissolve in the solid the last condition is simplified nce only the fugacity of the solute(2)need be considered f2=f2 For an ideal gas mixture the fugacity of each component is equal to the partial pressure For general application to any system this relationship is modified to include a non ideality term, the fugacity coefficient(oi) f =piyi P The fugacity of the pure solid phase(s)at the system Tand P is given by f2(T, P)=oP2(T) (2.11) To obtain the fugacity at higher pressure it is necessary to introduce a correction term (the Poynting correction) fI(T, P)=p2P(T)exp R(v2/Rr)dP where v2 is the molar volume of the pure solid 2 If it is assumed that the solid is relatively incompressible, then equation (2. 12)can be further simplified fi(T, P)=p2P(T)exp V2(P-P(T)/RT The fugacity of the pure solid phase at the system temperature and pressure can therefore be obtained from sublimation pressure and molar volume data. Using the general form of equation(2. 13) to express the fugacity of the solute in the NCF phase and applying the conditions for phase equilibrium(52=f2), P2P(T)exp V2(P-P(T)/RT(=%2y2P (2.14) arrangement then gives 2=((m)(91p-(r)/r小 (2.15) Poynting ideality correction
30 D. Steytler T' = T" = T p' = p" = p (2.5) (2.6) f.'= 11 f." (for all i) (2.7) If it is assumed that the NCF does not dissolve in the solid the last condition is simplified since only the fugacity of the solute (2) need be considered: fi = fi' (2.8) fi = Yip (2.9) For an ideal gas mixture the fugacity of each component is equal to the partial pressure: For general application to any system this relationship is modified to include a nonideality term, the fugacity coefficient ($ i): fi = GiYiP (2.10) fi(T, P) = $;p2s(T) The fugacity of the pure solid phase(s) at the system T and P is given by (2.1 1) To obtain the fugacity at higher pressure it is necessary to introduce a correction term (the Poynting correction): fifi'(~, P) = $;pi(i,exp{Jls (V~IRT) dp} (2.12) Poynting correction where V2 is the molar volume of the pure solid 2. further simplified: If it is assumed that the solid is relatively incompressible, then equation (2.12) can be ~~(~,P,=QIP:(T)~~~{V,(P- P;(T))/RT} (2.13) The fugacity of the pure solid phase at the system temperature and pressure can therefore be obtained from sublimation pressure and molar volume data. Using the general form of equation (2.13) to express the fugacity of the solute in the NCF phase and applying the conditions for phase equilibrium (fi = f;), $; P; (TI exp{ V, ( P - P; (T))/RT} = $;Y;P (2.14) rearrangement then gives Y;' = (Pf(T)/P) ($;/$;')exP{[V,(P-P;(T))/RT]} (2.15) I I I Perfect Non- Poynting gas ideality correction
Supercritical fluid extraction 31 Since the vapour in equilibrium with a pure solid phase is usually of low density can be considered ideal(o2= 1), equation(2.15)gives the mole fraction of solute in NCF phase explicitly as a function of its sublimation pressure and molar volume. The only unknown quantity is 92. the fugacity coefficient of the solute in an NCF mixture This can be expressed in terms of the volumetric properties of the mixture as given by equation(2. 16), which can be derived from basic thermodynamics(Reid, 1987) In 2=RT Jo 1(am/Pn P/p Solution of equation(2 res an equation of state(EOS)relating the pressure of a mixture to temperature P=F(T, V,xj) Numerical methods can then be applied to solve the system of equations(2. 15)-(2. 17)for One of the most familiar equations of state is that of van der waals(1873) -b)v The equation essentially corrects the ideal gas equation(PV=RT)for molecular olume(b)and introduces a volume-dependent attractive term(a/V"). The constants for the pure components(a; and bi )are obtained from the critical properties Pc and Tc (values for the constants Fa and Fb are given in Table 2.2) Table 2.2. Some equations of state na Equation Fb van der waals (V-b) v Redlich-Kwong v-b)T2v(v+ 0.4275T 0.086 P=(V-b)- 7 2v(V b) 04275F() 0.08664 Peng-Robinson 04572F(o) 0.07780 (V-b) V(V+2b) F()=[1+(0.3764+1.5422600-0.2699202)(1-T/2)32 where(a)=the acentric factor representing
Supercritical fluid extraction 3 1 Since the vapour in equilibrium with a pure solid phase is usually of low density and can be considered ideal ($.j' = l), equation (2.15) gives the mole fraction of solute in the NCF phase explicitly as a function of its sublimation pressure and molar volume. The only unknown quantity is $5, the fugacity coefficient of the solute in an NCF mixture. This can be expressed in terms of the volumetric properties of the mixture as given by equation (2.16), which can be derived from basic thermodynamics (Reid, 1987): ln$~=~,p{[~~ RT 0 2\12 T,p,n2 -~]p (2.16) Solution of equation (2.16) requires an equation of state (EOS) relating the pressure of a mixture to temperature, volume and composition: (2.17) Numerical methods can then be applied to solve the system of equations (2.15)-(2.17) for P = F(T, V, xi) Y5. One of the most familiar equations of state is that of van der Waals (1873): (2.18) RT a p=--- (V-b) V2 The equation essentially corrects the ideal gas equation (PV= RT) for molecular volume (b) and introduces a volume-dependent attractive term (a/V2). The constants for the pure components (ai and 0;) are obtained from the critical properties P, and Tc (values for the constants Fa and F, are given in Table 2.2). Table 2.2. Some equations of state Name Equation Fa Fb van der Waals p=--- 7/64 1 /8 RT a (V-b) v2 0.4275 T 'I2 0.08664 RT a Redlich-Kwong P = ~ - (V-b) T1l2V(V+b) 0.4275 F(w)* 0.08664 RT a Soave p=-- (V - 6) T'I2V(V + b) 0.4572 F(w)* 0.07780 RT a Peng-Robinson p=-- (V - b) V(V + 2b) - b2 * non-sphericity. F(w)* = [I + (0.3764 + 1.54226~- 0.26992~') (1 - T:/*)]' where (w) = the acentric factor representing