Supplementary material:
Development of a protocol for supercritical carbon dioxide extraction of ubiquinone-10 from dried biomass of Pseudomonas diminuta
Mahesh V. Bule a,b
(
 ) ∙ Rekha S. Singhal a a
Food Engineering and Technology Department, Institute of Chemical Technology, Mumbai –
400 019, India b Bioproduct and Bioprocess Engineering Laboratory, Biological System Engineering
Department, Washington State University, Pullman, Washington-99163, USA e-mail: mahesh.uict@gmail.com
Supplementary method:
Estimation of solubility parameters for CoQ10, CO
2
, co-solvents and a mixture consisting of
CO
2
and a co-solvent
One of the ways to have a detailed insight into the solubility of a solute in supercritical fluid is the estimation of its solubility parameter [1, 2]. The solubility parameter estimation provides a semi-quantitative evaluation of experimental conditions to be selected for optimized extraction conditions. The solubility parameter, δ, of a supercritical fluid can be estimated by using the following equation (1) [3].

3 1/2
(cal/cm )

1.25
P c

 r.SF
r.L

0.47
 r.SF
P c
(1) where, P c is the critical pressure (bar), ρ r:SF is the reduced density (g/cm 3 ) of the supercritical fluid, and
ρ r:L
is the reduced density of liquid state. This equation reflects the variation of the solvent power of the supercritical fluid as a function of density. For a mixture

consisting of CO
2
and a co-solvent, the solubility parameter, δ, for the mixed fluid is determined as follows [4].

3 1/2
(cal/cm )
  
CO
2

CO
2
  entrainer
  entrainer
Here,

CO
2
 x
CO
2

V
CO
2
( x
CO
2

V
CO
2
 x entrainer

V entrainer
)
 entrainer
(volume fraction of entrainer)
 x entrainer

V entrainer
( x

V
CO
2
CO
2
 x entrainer

V entrainer
)
(2) where, χ is mole fraction and V is the molar volume. Mole fraction of co-solvents was determined by considering change in density with respect to temperature and pressure. The density of used co-solvent was calculated theoretically by equation (3):

1

[

0
/{1
 
( t
1
 t
0

P
1

P
0
) / E ] (3)
Where,
ρ
1
final density (kg/m
3
);
ρ
0
initial density (kg/m
3
);
β
volumetric temperature expansion coefficient (m 3 /m 3 / o C); t
1
final temperature ( o C); t
0
initial temperature ( o C); E bulk modulus fluid elasticity (N/m
2
); P
1 final pressure (N/m
2
) and P
0
initial pressure (N/m
2
).
Solubility parameter of a given solute can be estimated by using the Fedors group contribution method when the solute molecular structure is known [5]. Table 1 illustrates the procedure to estimate the solubility parameter of CoQ10 by using the Fedors method. The solubility parameter of CoQ10,
δ
CoQ10
, was calculated using equation (4):

3 1/2
(cal/cm )


 i i
(

E ) v i
(
 v ) i
(4) where, ∑(∆E v
) i
is the summation of cohesive energies (cal/mol) and ∑(∆v) i
is the summation of molar volumes (cm
3
/mol).

Using the above equation,
δ
CoQ10
for CoQ10 at 25 o
C was found to be 9.628 (cal/cm
3
)
1/2
or
19.68 MPa
½
.
The δ
CoQ10 values for CoQ10 at other temperatures are shown in Table 2. The critical temperature of CoQ10 was calculated using the equation: T c
= 535 log∑∆T i
, where ∆T i is the summation of the critical temperatures of the contributing groups.
The Fedors method was found to be useful for estimating the extraction potential of complex molecules using supercritical fluids [6]. Table 1 lists solubility parameter contributions of CoQ10 molecule. The solubility of CoQ10 in SC-CO
2
as a function of temperature can be described as follows [7].

3 1/2
(cal/cm )
 
1


V
V
2
1


1.13
 
1




2
1


1.13



T c

T
2
T c

T
1
 0.33
(5) where, δ
2 and δ
1
are the solubility parameter of the solute at temperature T
2
and T
1
, and
T c
is the critical temperature estimated by a group contribution method [8]. Hildebrand [9] proposed the square root of the cohesive energy density as a numerical value indicating the solvency behavior of a specific solvent. The solubility parameter of methanol, δ, at different temperatures and pressures was calculated using equation (6):

3 1/2
(cal/cm )




E vap
V
 1/ 2




H vap
V

RT
 1/ 2
(6)
The compressibility factor for methanol at varying pressure and temperature conditions obtained from Reid and Sherwood [8] was used to calculate ∆H vap
under different conditions.
Results and discussion:
Use of solubility parameter studies for evaluation of experimental conditions
In order to select appropriate experimental conditions for optimization of SCE protocol, the solubility parameter calculations were done. The solubility parameters of CoQ10, CO
2
, co-

solvents, CO
2
+ methanol and CO
2
+ ethanol mixture were calculated. Fig. 1a and 1b shows the dependence of solubility parameter of CoQ10, CO
2
(150 bar) and co-solvents ethanol (150 bar) and methanol (150 bar), respectively. It is evident that the solubility parameter of CoQ10 depends on temperature. With an increase in operating temperature, the solubility parameters of
CoQ10, CO
2
, co-solvents and mixtures of CO
2
+ methanol and CO
2
+ ethanol decreased. This could be due to decrease in the density of SC-CO
2
with increase in temperature. These results are in accordance with Matias et al. [10] who reported solubility values to increase with a decrease in temperature. Also, the solubility parameters of CO
2
+ ethanol (19.91 MPa
1/2
) and CO
2
+ methanol (19.82 MPa
1/2
) as co-solvents were slightly different at temperature of 40

C and pressure 150 bar. Hence, the practical feasibility of CoQ10 extraction with initial conditions
(temperature 40

C, pressure 150 bar and run time of 60 min) were validated with the experimental data.
References:
1.
Kim WJ, Kim JD, Kim J, Oh SG, Lee YW (2008) Selective caffeine removal from green tea using supercritical carbon dioxide extraction. J Food Eng 89:303-309
2.
King JW (1989) Fundamentals and applications of supercritical fluid extraction. J
Chromatogr Sci 27:355-364
3.
Castro MDL, Valcárcel M, Tena MT (1994) Analytical Supercritical Fluid Extraction,
Springer-Verlag, Germany, pp 100-108
4.
Fedors RF (1974) A method for estimating both the solubility parameters and the molar volumes of liquids. Polym Eng Sci 14:147-154
5.
King JW, Friedrich JP (1990) Quantitative correlations between solute molecular structure and solubility in supercritical fluids. J Chromatogr A 517:449-458

6.
Galia A, Argentino A, Scialdone O, Filardo G (2002) A new simple static method for the determination of solubilities of condensed compounds in supercritical fluids. J Supercrit
Fluids 24:7-17
7.
Reid RC, Sherwood TK (1966) Pressure-volume-temperature relationships of pure gases and liquids. In: The properties of gases and liquids, Their estimation and correlation,
McGraw Hill Book Co., 2 edn. New York, pp 45-113
8.
Hildebrand JH (1936) The solubility of non-electrolytes, New York, Reinhold.
9.
Matias AA, Nunes AVM, Casimiro T, Duarte CMM (2004) Solubility of coenzyme Q10 in supercritical carbon dioxide. J Supercrit Fluids 28:201-206
Nomenclature
∆E v
or ∆E vap
Pc
Tc
V
∆v
χ
ρ r.SF
ρ r.L
δ
1
δ
2
Φ
CO2
Φ entrainer summation of all cohesive energy (cal/mol) critical pressure (bar) critical temperature (ºC) molar volume summation of all molar volume (cm
3
/mol) mole fraction reduced density of the supercritical fluid (g/cm
3
) reduced density of liquid state (g/cm
3
) solubility parameter of solute at temperature T
1
(cal/cm
3
)
1/2 solubility parameter of solute at temperature T
2
(cal/cm
3
)
1/2 volume fraction of CO
2 volume fraction of entrainer

∆H vap
R
E heat of vaporization of solvent gas constant = 1.987 cal/mol ºK, 8.314 J/mol ºK, 0.08205 L atm/ºK mol bulk modulus fluid elasticity (N/m
2
)

Table 1 Solubility parameter contributions of CoQ10
Groups Quantity
∆E i
(cal/mole)
∆v i
(cm 3 /mole)
-CH
3
-CH2-
-CH=
=C<
>C=O
-O-CH3
6 membered rings
Conjugated double bonds
Ortho substitution
∑
2
1
2
2
12
19
10
16
2
800
250
400
-
73650
1125
1180
1030
1030
4150
3.8
16
-2.2
-
324
33.5
16.1
13.5
-5.5
10.8
∆T i
1.56
2.68
0.13
1.16
66.79
1.79
1.34
1.4
0.89
1.59

Table 2 δ values (MPa ½
) for CoQ10 at different temperatures (ºC)
Temperature ( o C) Solubility parameter (δ)
55
60
65
40
45
50
70
19.55
19.50
19.46
19.41
19.37
19.32
19.28

Supplementary Figure captions:
Fig. 1. Solubility parameters of CoQ10, CO
2
, (a) CO
2 with ethanol and (b) CO
2 with methanol as co-solvent