Ind. Eng. Chem. Res. 2005, 44, 4435-4441
4435
Effect of Nonidealities in Perfume Mixtures Using the Perfumery Ternary Diagrams (PTD) Concept Vera G. Mata,* Paula B. Gomes, and Alı´rio E. Rodrigues Laboratory of Separation and Reaction Engineering, Departamento de Engenharia Quı´mica, Faculdade de Engenharia da Universidade do Porto, 4200-465 Porto, Portugal
This work shows a methodology to help flavorists and perfumers in the prediction of the headspace odor value for a ternary perfume mixture diluted in ethanol, based on the concept of perfumery ternary diagrams (PTD). In particular, this work takes into account the effect of liquid nonidealities in PTD, on the basis of the calculation of activity coefficients for all components in the liquid phase using the universal quasichemical functional group activity coefficients method. Using the chemical properties of the odorants and their odor threshold values in air, this technique allows a fast evaluation of all combinations of the three fragrant components for a fixed amount of solvent, and it eliminates some trial and error work usually done to choose a liquid mixture with a desired odor. Three examples of test mixtures representative of perfumes were used to illustrate these differences in PTD when considering the liquid as either an ideal mixture or a nonideal mixture. These systems are (1) benzaldehyde, phenylethanol, eugenol, and ethanol; (2) R-pinene, linalool, vanillin, and ethanol; and (3) limonene, geraniol, tonalide, and ethanol. The effect of the ethanol content in each ternary system was also studied. Introduction Perfumes are complex mixtures of odorant materials, generally essential oils or chemicals, that belong to one of three categories (or notes), depending on their volatility and behavior in the air above the liquid perfumes the headspace.1-3 These categories are top notes (the more volatiles, like citrus oils), middle notes (middle volatiles, like flower oils), and base notes (the less volatiles, like musks or vanillin; they act like fixatives of the others).4,5 Perfume design is a good example of product engineering. The main goal when developing perfumes is to translate consumer wishes and consumer-perceived product properties into physical and chemical product properties.6 Some valuable attempts to create systematic methods related to product engineering have been made lately.7-9 In perfume design, one important objective is to quantify the intensity of an odorant in the headspace over a certain liquid perfume. Many approaches use the odor value, OV, which is the ratio between the concentration of that odorant component in the headspace and its odor threshold.10 It is known that not all of the fragrant compounds that occur in a liquid or solid flavor or fragrance contribute to its aroma or scent, respectively. New techniques have been developed in order to identify the compounds with higher OVs for the preparation of synthetic mixtures, called aroma models, resembling natural products,11,12 like coffee brew,13 basil,14 apple and orange juice,15 or wine.12,16 Progress in instrumental analyses, like gas chromatography/ olfactometry (GC/O) and gas chromatography/mass spectrometry (GC-MS), has shown that the volatile fraction of a flavor or fragrance consists of a multiplicity of compounds. In the 1980s, a new strategy of instrumental and sensory analysis was developed toward * To whom correspondence should be addressed. Tel.: +351225081669. Fax: +351225081674. E-mail:
[email protected].
orientation of the identification experiments on those volatiles that contribute mainly to food flavors. In this new concept, the analysis of a flavor is started with a screening of the potent odorants either by complex hazardous air release model (CHARM) analysis17 or by aroma extract dilution analysis (AEDA).18 In both experimental procedures, an extract obtained from the food is evaluated by GC/O,19 then the extract is diluted, usually as a series of 1:1 or 1:2 dilutions, and each dilution is analyzed again by GC/O. In the case of AEDA, the result obtained for each odor-active volatile compound is expressed as the flavor dilution (FD) factor, reflecting the ratio of the concentration of the odorant in the initial extract to its concentration in the most dilute extract in which an odorant was detected by GC/ O. Consequently, the FD factor is a relative measure of odor potency.12 To indicate which of the compounds revealed by these techniques actually contribute to the aroma, quantification of the odorants is the next step in the analytical procedure.18 On the basis of these results, the ratio of concentrations to odor thresholds, the so-called odor activity values (OAVs), or commonly OVs can be calculated. Often, it is considered that only volatiles showing an OV higher than 1 are assumed to contribute to the odor. The existing classifications for single flavors and fragrances are made in terms of their volatilities. However, the behavior of one fragrant chemical or essential oil, and consequently its OV, depends largely on the medium or solvent and on the remaining fragrant components present in the perfume mixture. This is due to molecular size and in great extent to physical interactions at the molecular level, like polarity forces (ion-dipole, dipole-dipole, London forces, and hydrogenbonding forces). Generally, the affinity of a molecule for its surrounding medium is measured using the concept of an activity coefficient, γ. A high value of γ implies an increased tendency for a given substance to be “pushed out” of the mixture. On the other hand, a low value of
10.1021/ie048760w CCC: $30.25 © 2005 American Chemical Society Published on Web 05/07/2005
4436
Ind. Eng. Chem. Res., Vol. 44, No. 12, 2005
γ implies a low concentration in the headspace and a higher longevity of that substance on the liquid mixture because of the higher affinity to the medium.20 As an example, one work shows the value of γ for benzyl acetate (A), heptan-2-ol (B), and limonene (C) in three different media, water (high polarity), an aqueous surfactant, and diethyl phthalate (DEP; moderate polar solvent).21 It was concluded that all compounds had low values of γ in the DEP solution (γA ) 0.3; γB ) 2.2; γC ) 2.3), moderate values in the aqueous surfactant (γA ) 75; γB ) 57; γC ) 732), and high values in water (γA ) 1750; γB ) 2770; γC > 70 000). The very high value of limonene in water means that the nonpolar molecules of limonene do not participate in any polar forces with the water, tending, this way, to quickly leave the solution. As a result, this system will have a high intensity of limonene in its headspace. This means that a smell can change if diluted in different solvents because the volatility of the single compound and its OV will be affected in different ways. This is very important in perfume formulations because the quantity of alcohol, water, or other solvent/cosmetic base can largely influence the headspace above the liquid that is smelled. In this work, a new theoretical methodology was developed to help perfumers in the prediction of the headspace OV for a ternary perfume mixture diluted in ethanol. This technique allows a fast headspace evaluation of all combinations of the three fragrant components and for a fixed amount of solvent. The effect of nonidealities in the liquid perfume phase due to intermolecular interactions is studied and compared to the ideal liquid perfume mixture assumption.
universal quasichemical functional group activity coefficients (UNIFAC) method, which is based on molecular group contribution.23 This method takes into account the contribution due to differences in molecular size and shapescombinatorial partsand the contribution due to molecular interactionssresidual part. Once it is considered that the headspace is an ideal solution, the concentration of component i in the headspace, cig, is given by
cig )
fig ) fil
(1)
where fi is the fugacity of component i and superscripts g and l are the gas and liquid phases, respectively. For a mixture of ideal gases, the fugacity value for the gas phases is equal to
fig ) yiP
(2)
where yi is the gas-phase molar fraction of component i and P is the total gas-phase pressure. The fugacity of component i in the liquid phase is related to the composition of that phase through the activity coefficient, γi. For subcritical conditions,
fil ) γixiPisat
(3)
where xi is the liquid-phase molar fraction of component i in equilibrium with the headspace gas molar fraction, yi, and Pisat is the saturated vapor pressure of component i. Substituting eqs 2 and 3 into eq 1 results in sat
yi )
γixiPi P
(4)
In this work, values of γi were calculated using the
(5)
where Mi is the molecular weight of i, R is the ideal gas constant, and T is the absolute temperature (Kelvin). The intensity of a fragrant compound i can be expressed in terms of its OV as OVi, which is defined as10
OVi )
cig Thri
(6)
where Thri is the threshold concentration of i in air. This value of threshold is commonly measured using a human panelist and an olfactometer that registers the minimum concentration that the panelist’s nose can detect and recognize. Extensive compilations of Thri values obtained experimentally can be found in the literature.24-26 Substituting eqs 4 and 5 into eq 6 gives
( )( )
PisatMi 1 OVi ) γixi Thri RT
Methodology A perfume system consists of a complex fragrant liquid mixture and a corresponding air phase above it, the headspace. In this work, it is considered that for every component i in the mixture, the condition of thermodynamic equilibrium is given by22
yiMiP RT
(7)
This equation relates the liquid perfume composition to the human sensory response of the evaporated perfume. In this work, it is considered that a component, i, present in a liquid mixture of N fragrant components, is perceived strongly by a human nose when its OVi in the headspace above the liquid is higher than those of the other components. Perfumery Ternary Diagrams Consider a ternary liquid mixture, A + B + C, constituted by three chemical compounds having different volatilities, each one belonging to one type of fragrant note; that is, A represents a top note, B a middle note, and C a base note. It is also considered that a certain amount of solvent, S, in this case ethanol, is added to the mixture, resulting, this way, in a quaternary mixture that will be called test perfume. The quantity of each component in the test perfume is given by its molar fraction: xA, xB, xC, and xS. To simplify, this quaternary system is transformed into a ternary system27 by recalculating the molar fractions for A, B, and C on a solvent-free basis, resulting in the new fractions.
x A′ )
xA xB , x B′ ) , and xC′ ) xA + xB + xC xA + x B + x C xC xA + xB + xC
Ind. Eng. Chem. Res., Vol. 44, No. 12, 2005 4437 Table 2. Number of UNIFAC Groups and Subgroups Present in the Molecules of Systems 1-3
molecule (i) benzaldehyde
Figure 1. Scheme of a PTD and a representation of ternary mixture compositions. Table 1. Physical Properties for Systems 1-3 system 1
A B C 2 A B C 3 A B C solvent S a
name
Pisat (Pa)a
Thri (g/m3)a Mi (g/mol)
benzaldehyde phenylethanol eugenol R-pinene linalool vanillin limonene geraniol tonalide ethanol
1.06 × 4.8 1.3 3.9 × 102 3.1 × 101 1.6 × 10-2 2.1 × 102 2.7 6.7 × 10-5 7.3 × 103
1.99 × 10-4 9.27 × 10-5 8.06 × 10-5 4.20 × 10-3 3.72 × 10-4 1.87 × 10-7 2.45 × 10-3 2.48 × 10-5 1.82 × 10-5 5.53 × 10-2
102
106.2 122.2 164.2 136.2 154.3 152.2 136.2 154.3 258.4 46.0
From Calkin and Jellinek.10
These three quantities are then represented in a ternary diagram,27 as it is shown in Figure 1. Considering a general liquid mixture, in which the composition is represented by point X′, the composition (solvent-free basis) of component A, xA′, is given by the distance X′A′; the composition of B, xB′, is given by the distance X′B′; and the composition of C, xC′, is given by the distance X′C′. It is considered that the mole fraction of the solvent, xS, is known and constant for each ternary diagram. As it can be seen, the ternary diagram represents all compositions that could be made experimentally using different quantities of A, B, and C, for a given quantity of ethanol, S. Now, for each liquid perfume mixture, X′ (i.e., each point in the ternary diagram), the OV of each component in that mixture, OVi, is calculated using eq 7. After the calculation of all of the individual OVs for a given mixture X′ (represented in the ternary diagram), the maximum OV, OVmax, is determined:
OVmax ) max (OVA, OVB, OVC, OVS) for point X′ (8) Then, we consider that for each mixture X, we strongly smell the component that has the maximum OV. After the determination of the component that has the OVmax for a large number of points of the ternary diagram, we obtain, as a result, a perfumery ternary diagram (PTD). However, it is important to notice that we consider that when compound A has a maximum odor value, OVmax ) OVA, it will be stronger perceived than the others that coexist in the mixture, but it does not mean that all of the solutions where OVmax ) OVA have the same smell.
subgroup
ACH AC CHO phenylethanol ACH ACCH2 CH2 OH eugenol ACOH ACH ACCH2 CH ) CH2 CH3O R-pinene CH3 CH2 CH CH ) C C linalool CH3 CH2 C CH ) C CH2 ) CH OH vanillin ACH AC ACOH CHO CH3O limonene CH3 CH2 CH CH ) C CH2 ) C geraniol CH3 CH2 CH ) C OH tonalide CH3 CH C CH ) C C)C CH3 ) CO ethanol CH3 CH2 OH
number of UNIFAC UNIFAC group subgroups subgroup 22 22 number in molecule i number 10 11 21 10 13 2 15 18 10 13 5 25 1 2 3 8 4 1 2 4 8 5 15 10 11 18 21 25 1 2 3 8 7 1 2 8 15 1 3 4 8 9 19 1 2 15
3 3 10 3 4 1 5 8 3 4 2 13 1 1 1 2 1 1 1 1 2 2 5 3 3 8 10 13 1 1 1 2 2 1 1 2 5 1 1 1 2 2 9 1 1 5
5 1 1 5 1 1 1 1 3 1 1 1 3 2 2 1 1 3 2 1 1 1 1 3 2 1 1 1 2 3 1 1 1 4 2 2 1 6 1 2 2 1 1 1 1 1
Figure 1 shows an example of a PTD. In this diagram, three different areas can be distinguished, highlighting some of the following typical composition points: Pt: OVmax ) OVA (dark shaded area) Pm: OVmax ) OVB (light shaded area) Pb: OVmax ) OVC (dotted area). There can also exist points where OVmax ) OVS. These points are referred to as Ps. This situation generally happens for mixtures having a high content of solvent, as it will be seen below. Effect of Nonidealities in the Liquid Phase The activity coefficient of a component i in a mixture, γi, provides a useful way of accessing the affinity of this odorant for the surrounding medium.20 The reasons are as follows: With γi > 1, the partial pressure of component i is in excess of that predicted if we consider the liquid an ideal solution, indicating that this volatile will be “pushed out” of the liquid system. γi < 1 implies lower partial pressures of component i, less material in the
4438
Ind. Eng. Chem. Res., Vol. 44, No. 12, 2005
Figure 2. Effect of ethanol for System 1: benzaldehyde (gray square), phenylethanol (black triangle), eugenol (open circle), and ethanol (gray circle) using (i) an ideal liquid solution and (ii) a nonideal liquid solution. The mole percent of ethanol is equal to (a) 50%, (b) 70%, and (c) 90%.
gas phase than expected if we consider the liquid an ideal solution, and increased duration in the liquid. As a consequence, the OV can change using different solvents or different quantities of each fragrant chemical for a specific multicomponent mixture. So, the perfumer needs to know how to increase the performance of selected materials for a given application by choosing the right composition. The developed PTD theory was tested using three types of systems: • System 1: benzaldehyde + phenylethanol + eugenol + ethanol • System 2: R-pinene + linalool + vanillin + ethanol • System 3: limonene + geraniol + tonalide + ethanol Each system consists of a four-component mixture, representing one typical perfume: one top note, one middle note, one base note, and one solvent (ethanol). The physical constants at 25 °C for individual chemicals in System 1, System 2, and System 3 are shown in Table 1. The physical constants are molecular weight, Mi; saturated vapor pressure, Pisat; and odor threshold in air, Thri. Table 2 shows the list of UNIFAC groups and subgroups22 and their respective numbers existing in each molecule used in this work.
Figures 2-4 show the effect of ethanol in the PTD for System 1, System 2, and System 3, respectively. In all of the PTDs shown, the mole percent of ethanol is constant and equal to (a) 30%, (b) 50%, and (d) 70%. In the same figures, the effect of the ethanol content is shown together with the effect of the nonidealities in the liquid mixture. So, for the construction of the PTD, the values of OVi (eq 7) were calculated assuming that (i; left side) the liquid solution is ideal (γi ) 1) and (ii; right side) the liquid solution is nonideal (γi * 1). The effect of ethanol is important for two reasons: First, if we look at these figures from top to bottom (i.e., a-c), we are simulating the addition of ethanol in the final part of the perfume composition. For a given composition of components A, B, and C, we can determine the maximum quantity of ethanol that can be added in order to have the component that we want with the desired OVmax, for example, when sniffing a perfume bottle (generally, the top note). And second, if we look from bottom to top (c-a), we are simulating the fast evaporation of ethanol, some seconds after application. Looking to Figure 2, which represents System 1 [A (benzaldehyde), B (phenylethanol), C (eugenol), and S (ethanol)], it can be seen for each composition (represented by one point in a PTD) what the compound is
Ind. Eng. Chem. Res., Vol. 44, No. 12, 2005 4439
Figure 3. Effect of ethanol for System 2: R-pinene (gray square), linalool (black triangle), vanillin (open circle), and ethanol (gray circle) using (i) an ideal liquid solution and (ii) a nonideal liquid solution. The mole percent of ethanol is equal to (a) 50%, (b) 70%, and (c) 90%.
where OVi ) OVmax. In all of the PTD represented, there is a high percentage of compositions where OVmax ) OVA. This happens because benzaldehyde has a high value of saturated vapor pressure, Pisat. However, when the left side (i) and right side (ii) of Figure 2a (xS ) 0.3) are compared, we can see that, if we consider nonideal liquid mixtures (right side), there is a region of compositions that results in mixtures where the odor value maximum is that of ethanol, OVmax ) OVS. This fact means that if we choose such a composition based on a PTD calculated using the simplification of ideal liquid mixtures, we could have, as a result, a perfume smelling strongly of ethanol and not the expected top, middle, or base odor. The area of compositions where OVmax ) OVS increases as the molar fraction of ethanol in the liquid also increases. When xS ) 0.5 (Figure 2b), it can be seen that the area with compositions where OVmax ) OVC was substituted by compositions where OVmax ) OVS and the area with compositions where OVmax ) OVB is also much smaller or null. Both effects are due to an increase in the OV of ethanol. Finally, when the liquid mixture has xS ) 0.7 (Figure 2c), almost half of the PTD is represented by compositions where OVmax ) OVS. Figure 3 represents the same study for System 2 [A (R-Pinene), B (linalool), C (vanillin), and S (ethanol)].
Looking, for example, to Figure 3c (left and right sides), the reason for the difference in the number of points where OVmax ) OVA, where A is R-pinene, is its low polarity. If we consider nonideal liquid mixtures, increasing the quantity of the highly polar solvent, ethanol, will “push out” the nonpolar component A more than would be expected when no molecular interaction is assumed in the ideal model. Figure 4, represents the effect of ethanol on System 3 [A (limonene), B (geraniol), C (tonalide), and S (ethanol)]. In this case, there are no mixtures where OVmax ) OVC, because the saturated vapor pressure of C is much smaller than that of the other compounds. It can also be noticed that, in this case, it is possible to choose a composition where OVmax ) OVA, even when the molar fraction of ethanol is high (xS ) 0.7). However, this behavior is only possible to preview if we consider the nonideal liquid mixture. This information can be taken directly from the PTD, avoiding a long trial-and-error procedure to find the optimal mixture. Conclusions A methodology to predict the behavior of nonideal ternary perfume mixtures in a given solvent was developed, using the concept of PTD. This method allows
4440
Ind. Eng. Chem. Res., Vol. 44, No. 12, 2005
Figure 4. Effect of ethanol for System 3: limonene (gray square), geraniol (black triangle), tonalide (open circle), and ethanol (gray circle) using (i) an ideal liquid solution and (ii) a nonideal liquid solution. The mole percent of ethanol is equal to (a) 50%, (b) 70%, and (c) 90%.
the prediction of the characteristic smell in the headspace above a ternary perfume mixture in a solvent, described as the odor value, OV, for any combination of ternary fragrant mixtures in that solvent. The liquid is considered to be nonideal, and the nonidealities due to molecular interactions are accounted for by the activity coefficients for each component in the mixture, calculated by the UNIFAC method. It is shown that in cases where molecular interactions are neglected,2 a large deviation can occur in the prediction of the headspace odor. As an illustration, three systems were studied: (1) benzaldehyde, phenylethanol, eugenol, and ethanol; (2) R-pinene, linalool, vanillin, and ethanol; and (3) limonene, geraniol, tonalide, and ethanol. The deviations when considering the liquid ideal and nonideal were shown using PTDs for each system, and the effect of ethanol content was also studied. It was concluded that these diagrams are important tools for perfumers in making important decisions, such as how to control the intensity of the top note; how to automatically find which compositions will have an intense smell to the top, middle or base note; and how to find the maximum quantity of ethanol for a given mixture.
Acknowledgment We gratefully acknowledge the financial support of Fundac¸ a˜o para a Cieˆncia e Tecnologia (FCT) and FEDER (Project Grant POCTI/EQU/39990/2002, Post Doctoral Grant SFRH/BPD/1576/2000, and PhD Grant SFRH/BD/968/2000). We also thank Dr. Sima˜o P. Pinho for his contributions to the calculation of the activity coefficients using the UNIFAC method. Nomenclature cig ) concentration of component i in the headspace (mg/ m3) g,l fi ) fugacity of component i in the gas phase (g) or liquid phase (l) (Pa) R ) ideal gas constant (Pa m3/mol/K) Mi ) molecular weight of i (g/mol) OVi ) odor value of i P ) total pressure (Pa) Pisat ) saturated vapor pressure of component i (Pa) PTD ) perfumery ternary diagram T ) absolute temperature (K) Thri ) odor threshold value of i (mg/m3) xi ) liquid-phase molar fraction of i xi′ ) liquid-phase molar fraction of i on a solvent-free basis
Ind. Eng. Chem. Res., Vol. 44, No. 12, 2005 4441 yi ) gas-phase molar fraction of component i γi ) activity coefficient of component i
Literature Cited (1) Mata, V. G.; Gomes, P. B.; Rodrigues, A. E. The Science Behind Perfume Design, 2nd European Conference on Product Technology (Product Design and Engineering), Groningen, The Netherlands, 2004. (2) Mata, V. G.; Gomes, P. B.; Rodrigues, A. E. Perfumery Ternary Diagram (PTD): a new concept applied to the optimization of perfume compositions. Flavour Fragrance J. 2005, in press. (3) Mata, V. G.; Gomes, P. B.; Rodrigues, A. E. Engineering Perfumes. AIChE J. 2005, accepted for publication. (4) Poucher, W. A. A classification of odors and its uses. Am. Perf. Essent. Oil Rev. 1955, 66. (5) Carles, J. A method of creation in perfumery. Soap Perfum. Cosm. 1962, 35, 328. (6) Bruin, S. Product-Driven Process Engineering: the eternal triangle. Molecules, product, process, inaugural lecture at Eindhoven University of Technology, Eindhoven, The Netherlands, 2004. (7) Cussler, E. L.; Moggridge, G. D. Chemical Product Design; Cambridge University Press: New York, 2001. (8) Wesselingh, J. A.; Janssen, L. P. B. M. Product Processing, lecture notes; University of Groningen: Groningen, The Netherlands, 2001. (9) Wesselingh, J. A. Bio and Chemical Product Innovation, course notes; Technical University of Denmark: Denmark, 2004. http://www.kt.dtu.dk/education/index.php?p)produktudvikling. (10) Calkin, R. R.; Jellinek, J. S. Perfumery: Practice and Principles; John Wiley and Sons: New York, 1994. (11) Czerny, M.; Grosch, W. Potent odorants of raw arabica coffee. J. Agric. Food Chem. 2000, 48, 868. (12) Grosch, W. Evaluation of key odorants of foods by dilution experiments, aroma models and omission. Chem. Senses 2001, 26, 533. (13) Semmelroch, P.; Grosch, W. Studies on character impact odorants of coffee brews. J. Agric. Food Chem. 1996, 44, 537. (14) Guth, H. Quantitation and sensory studies of character impact odorants of different white wine varieties. J. Agric. Food Chem. 1997, 45, 3027.
(15) Durr, P.; Schobinger, U. The contribution of some volatiles to the sensory quality of apple and orange juice odor. In Flavour '81; Schreier, P., Ed.; Walter de Gruyter: Berlin, 1981; pp 179193. (16) Guth, H.; Murgoci, A. M. Identification of the key odorants of basil (Ocimum basilicum L.)seffect of different drying procedures on the overall flavour. In Flavour PerceptionsAroma Evaluation. Kruse, H. P., Rothe, M., Eds.; Eigenverlag Universitat Potsdam: Potsdam, Germany, 1997; pp 233-242. (17) Acree, T. E.; Barnard, J.; Cunningham, D. G. A procedure for the sensory analysis of gas chromatographic effluents. Food Chem. 1984, 14, 273. (18) Grosch, W. Determination of potent odorants in foods by aroma extract dilution analysis (AEDA) and calculation of odor activity values (OAVs). Flavour Fragrance J. 1994, 9, 147. (19) Acree, T. E. GC/Olfactometry. Anal. Chem. 1997, 69, 170A. (20) Pybus, D. H.; Sell, C. The chemistry of fragrances; RSC: Cambridge, U. K., 1999. (21) Behan, J. M.; Perring, K. D. Perfume interactions with sodium dodecylsulphate solutions. Int. J. Cosmet. Sci. 1987, 9, 261. (22) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987. (23) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. GroupContribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J. 1975, 21 (6), 1086-1099. (24) Devos, M.; Patte, F.; Rouault, J.; Laffort, P.; van Gemert, L. J. Standardized Human Olfactory Thresholds; IRL Press: Oxford, U. K., 1990. (25) van Gemert, L. J. Compilation of Odor Threshold Values in Air and Water; TNO Nutrition and Food Research Institute, BACIS: Zeist, The Netherlands, 1999. (26) Leffingwell, D.; Leffingwell, J. C. Odor & Flavor Detection Thresholds in Water (In Parts per Billion). http://www.leffingwell.com/odorthre.htm (2004). (27) Ruthven, D. M. Encyclopedia of Separation Technology; John Wiley and Sons: New York, 1997; Vol. 1.
Received for review December 22, 2004 Revised manuscript received March 28, 2005 Accepted April 18, 2005 IE048760W
