ARTICLE pubs.acs.org/IECR
Evaluation of Group-Contribution Methods To Predict VLE and Odor Intensity of Fragrances Miguel A. Teixeira, Oscar Rodríguez, Fatima L. Mota, Eugenia A. Macedo, and Alírio E. Rodrigues* Laboratory of Separation and Reaction Engineering (LSRE), Associate Laboratory LSRE/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
bS Supporting Information ABSTRACT: Several predictive GE methods based on the group-contribution concept have been tested for prediction of multicomponent vaporliquid equilibria (VLE) of fragrance mixtures. The evaluation covered 24 binary, 20 ternary, and 21 quaternary mixtures combining six different fragrances typically used in perfume formulation and ethanol as the solvent. The selected predictive methods are the original UNIFAC (updated to the last revision), the UNIFAC-Dortmund, the ASOG, and the A-UNIFAC. The equilibrium compositions were experimentally measured at 23 C by headspace gas chromatography (HS-GC). For each liquid composition, the corresponding experimental and predicted vapor compositions were compared. This study confirmed that the UNIFAC method is the best predictive model for prediction of VLE, while the A-UNIFAC performed poorer than other evaluated methods for the mixtures studied in this work. Moreover, from the vapor composition the odor intensity and character of the fragrance mixtures was calculated using a previous developed model which considers the Stevens’ power law for the olfaction intensity scale and the stronger component model for quality perception. In this way, the odor intensity and character of fragrance mixtures was predicted and compared to experimental and sensorial evaluations. From this work it can be concluded that the UNIFAC and UNIFAC-Dortmund methods allow obtaining optimal predictions of the character of the fragrance mixtures with an agreement of 95.4% when compared to experimental measurements.
’ INTRODUCTION Fragrances are important sensory attributes that companies of consumer goods have been using, more and more often, to differentiate their products from others.14 Consequently, they are willing to increase the appreciation that consumers have for their products and thus increase their market share, distancing themselves from their nearest competitors. Accordingly, fragrances are known to be appellative and appreciated by consumers, so that their incorporation in a wide variety of products brings with it an increase in products’ value. However, the formulation of fragranced products (either fine fragrances or functional perfumes like soaps, household cleaners, detergents, and so on) is a complex and lengthy process often developed by experts in the art of odor perception, called perfumers.2 Considering the number of available fragrances (on the order of several thousands), the possible combinations of fragrance ingredients for a perfumer are endless. For that reason, it involves a long and costly trial-and-error process for testing the perceived odor of hundreds of different samples. Moreover, when a perfume is incorporated into a product (e.g., liquid soap, detergent, or bath oil) it is usual to observe a variation in the headspace composition which results in a different perception of fragrance intensity and character. For that, molecular interactions within a product play an important role in the evaporation of fragrance ingredients, especially in liquid solutions.5 With an eye toward this goal comes the so-called product engineering, which congregates different scientific fields together with materials and processes for a common end: product development.69 As for perfumes and fragranced products, evaporation of the ingredients used in their formulation is a critical issue for product r 2011 American Chemical Society
design. Recently, Friberg and co-workers have been developing a significant work on the release of fragrance chemicals from emulsion systems, combining phase diagrams with algebraic calculations to withdraw information from ternary diagrams. Their methodology allows one to predict the evaporation path of fragrances in water/oil and three-phase emulsions and the effect of different parameters on their evaporation rate (e.g., relative humidity, surfactant concentration, growth, and reduction of phase volumes at nonequilibrium conditions).1013 Continuing a series of studies devoted to product engineering applied to perfumes,1417 the purpose of this work is to evaluate several thermodynamic models for prediction of the vapor liquid equilibrium (VLE) compositions of fragrance mixtures. It is intended to validate the use of group-contribution methods to model the VLE, in terms of both the composition in the gas phase as well as olfactory perception. Toward this purpose, several fragrance mixtures were formulated, their headspace was evaluated by gas chromatography and by olfactory analysis, and, finally, the experimental results were compared with those predicted from the VLE models. Methodology for Odor Perception. In previous studies, the authors have divided the process for the perception of scents released from a perfume mixture into four steps: (i) it starts with a liquid mixture of fragrance ingredients and solvents with known molar compositions (xi) that customers spray on the skin or Received: February 10, 2011 Accepted: June 7, 2011 Revised: May 30, 2011 Published: June 07, 2011 9390
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to explain the quality perception of odorants in mixtures, although none has yet imposed universally over the others.2933 The stronger component model is the simplest, but it has also proved to consistently give better results when all these models are compared.29,31 It states that in a mixture of N odorants, the one with the highest odor intensity is the most strongly perceived, as mathematically expressed by eq 2 Ψmax ¼ maxðΨi Þ, " i ¼ 1, :::, N
Figure 1. Schematic representation of the steps involved in the odor perception model for fragrance mixtures.
clothes; (ii) then, this liquid mixture begins to evaporate into the air at ambient conditions, accompanied by a change in the gasphase (yi) and the liquid-phase compositions (xi); (iii) subsequently, the vapors of the fragrant components diffuse through the surrounding air; (iv) finally, some of the fragrance molecules will eventually reach the nose of the customer or other people around, who will perceive the odors with a certain intensity and character. As aforementioned, this process encompasses different scientific fields including thermodynamics, transport phenomena, and psychophysics, as schematically depicted in Figure 1. From a product engineering point of view, it is of prime interest to obtain a reliable model for this process, so that the olfactory effect of a given formulation can be identified. Moreover, if the mathematical model is predictive, these effects can be known in advance and it can be used to obtain suitable preliminary formulations for the perfume. Consequently, this is expected to reduce the number of trial-and-error experiments and decrease the consumption of raw materials (some of which are quite expensive), thus improving the development process of the final product. Nevertheless, from the stepwise process shown in Figure 1, a mathematical model is needed to establish the relationship between the odorant concentration and its odor perception. For that purpose there are several models within olfactory perception that are used to relate odor intensity as a function of the odorant concentration in air. The Stevens psychological law (also known as the power law) set forth that the sensation (Ψ) is proportional to the stimulus (S) raised to an exponent (n)1821 Ci n Ψi ¼ ð1Þ ODTi where the subscript i refers to a given odorant and Ψi, Ci, ODTi, and n are its odor intensity, concentration in air, odor detection threshold, and olfactory power law exponent, respectively. Both Ci and ODTi should have the same units (e.g., mg/m3). The odor threshold represents the minimum concentration in the gas phase for an odorant so that it can be detected (detection threshold, ODT) or recognized (recognition threshold) by humans.2,17,22 Odor detection threshold concentrations and exponents for the power law can be obtained in the open literature from compilations of hundreds of odorant species.2,2326 Equation 1 relates the odor intensity of a given component to its concentration in air, which can be measured by analytical methods. However, when more components are present in the air the perception of that mixture will be a blend of odorants. The perception of a mixture of odorants is a complex process, far from been completely understood.27,28 Hitherto, several models have been proposed
ð2Þ
This model has been used by several authors in the past showing good results,17,31 and so it will be used in this work to account for the odor character of mixtures. Combining eqs 1 and 2, the dominant odor in a mixture can be found from their compositions in air. However, perfumes are liquid mixtures, and so before these equations may be of any help in the perfume formulation process, the odorant concentration in air, Ci, must be calculated from that in the liquid phase (the composition of the perfume mixture). In order to do so, the vaporliquid equilibrium compositions can be calculated using a modified Raoult’s law34 yi 3 P ¼ xi 3 γi 3 Pisat
ð3Þ
where yi and xi are the mole fractions of component i in the gas and liquid phases, respectively. P is the total pressure, Psat i is the vapor pressure of component i, and γi is its activity coefficient in the liquid phase. Nonidealities in the gas phase can be neglected, since we are dealing with atmospheric pressure and temperature conditions so that odorants will be highly diluted in air. In this way, combining eqs 1 and 3, the odor intensity of an odorant i can be calculated as follows !n xi 3 γi 3 Pisat 3 Mi ð4Þ Ψi ¼ R 3 T 3 ODTi where Mi is the molecular weight of component i, R is the universal gas constant, T is the absolute temperature, and all other variables have been previously defined. It is important to highlight that variables in eq 4 involve the experimental conditions (temperature, T), physicochemical properties of the components used in the perfume formulation (vapor pressure, Psat i , molecular weight, Mi, odor detection threshold, ODTi, and olfactory power law exponent, n), the molar compositions used for that formulation (xi), and, finally, the activity coefficient of each component in the liquid phase (γi). All these variables are known in advance except for the activity coefficients. These must be calculated from experimental data or predicted using suitable models. It is evident that for preliminary results, predictions of activity coefficients may provide sufficient information. The predictions can be used a priori to give estimates of perfume formulations (namely, in the preformulation step), thus reducing the trial-and-error experiments commonly used in the development of fragranced products. Prediction of Activity Coefficients. The activity coefficients of chemicals in a liquid mixture can be calculated using a range of thermodynamic models. Among them, the excess Gibbs energy (GE) models based on the group-contribution approach34,35 present relevant advantages. The group-contribution concept considers the system as a mixture of functional groups, rather than molecules. The interaction parameters are obtained from experimental data involving molecules containing those functional groups (but not necessarily the same molecules). As these 9391
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parameters are available in the literature, the model can be used to predict activity coefficients of any molecule involving the same functional groups. It is important to note here that the only information needed to calculate the activity coefficients of each component in a liquid mixture is just the composition. Then, the molecules of each component have to be divided into the appropriate functional groups to obtain their number and type. All structural and interaction parameters for the groups needed in the calculations should be found in the literature. In this work, four thermodynamic models have been selected to predict and compare the VLE compositions with experimental data: UNIFAC, UNIFAC-Dortmund, A-UNIFAC, and ASOG.3643 In general, these methods consider the activity coefficient as the sum of two contributions, one accounting for conformational effects (C, also referred to as the combinatorial or entropic contribution) and the other for group interactions (R, referred to as the residual or enthalpic contribution). The A-UNIFAC introduces a third term for associative interactions (A). In the liquid phase, the nonideal behavior can be described using any of these methods as the summation of these two or three contributions ln γi ¼ ln γCi + ln γRi + ðln γAi Þ
ð5Þ
The ASOG (analytical solution of groups) method was the first to be developed, combining the FloryHuggins theory and the Wilson equation for the entropic and enthalpic contributions of the activity coefficient, respectively.35,41 The selected parameters for the ASOG method were obtained from the literature.41 In a similar way, the UNIFAC (UNIversal Functional Activity Coefficient) method uses the UNIQUAC equation (which contains per se the summation of the entropic and enthalpic contributions) for the activity coefficient of the functional groups.36,37,44,45 Over the years, the original UNIFAC method has gone through expansions in the number and parameters of its interaction groups, thus improving the performance of the model. Its predictive capability has been enhanced by including more experimental data in the parameter regression, thus filling the gaps (not available parameters) in the group parameter matrix and also including new groups on it. The parameters used in this work were taken from the most recent available versions.34,36,37 Besides, several modifications of the UNIFAC method have been proposed and can be found in the literature.34,46 Two of these modifications were also selected for this work. The UNIFAC-Dortmund (UNIFAC-D) introduces changes in the volume parameter, ri, and extends the interaction parameters as quadratic functions of temperature.38,39 It should be noted that the UNIFAC-Dortmund method presents a more detailed group division and so has more interaction parameters than the other models. The parameters for the UNIFAC-D method have also suffered several revisions, and the latest was used in this work.39 The A-UNIFAC method, instead, introduces a new term in the activity coefficient calculation (see eq 5) to account for associative interactions. This introduction requires the estimation of new association parameters (energy and volume) and also a reparameterization of the group-interaction parameters since association is now explicitly taken into account. This correction is pertinent when dealing with mixtures that have functional groups (e.g., hydroxyl, acid, ether, ester) which participate in such interactions. These groups are frequently found in fragrant molecules. The combinatorial and residual contributions are kept as in the original UNIFAC method, and a new association
Figure 2. Iterative procedure for calculation of the vaporliquid compositions.
contribution based on Wertheim’s theory for fluids with highly directed attractive forces is introduced.40,43 The group-interaction parameters for the A-UNIFAC method were obtained from the literature.40,43,47,48 The parametrization procedure involves the correlation of equilibrium data (vaporliquid and liquidliquid equilibrium and infinite dilution data) of representative (associative) molecules. As the data set for parametrization is much smaller than in other methods (namely, UNIFAC), the number of interaction parameters is also more limited but affects groups that do not participate in the association term. In particular, there are no parameters for the following groups: double-bonded hydrocarbons (group 2, CdC), aldehyde (group 10, CHO), or ether (group 13, CH2O). Whenever there is interaction between two nonassociating groups whose group-interaction parameters are not in the A-UNIFAC table, the UNIFAC parameters were used. These parameters, as well as the association energy and volume, have been tabulated for some functional groups showing self- and/or cross-association (like carboxyl, hydroxyl, ester, aromatic rings, and water), and we have used the latest available data in the literature.40,47,48 As already indicated above, the only requirements to calculate activity coefficients using the referred methods are the compositions of all components involved in the liquid phase and the availability of the interaction parameters involved. That may be a problem when dealing with fragrances, as these molecules may have several functional groups (hydroxyl, carbonyl, ether, ester, aromatic rings, and double bonds) in the same molecule. Thus, it is necessary that interaction parameters among all these functional groups exist in the database. All methods presented above, at least to some extent, obey this premise. That is especially true for the UNIFAC and UNIFAC-Dortmund models for which the parameter table is very extensive. 9392
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Table 1. Properties of the Components Obtained from the Literature, Molecular Formula, Molecular Weight (MW), Vapor Pressure at 296 K (Psat), Boiling Point (Tb), Odor Detection Threshold (ODT), and Olfactory Power Law Exponent (n) fragrance chemicals limonene (Lim)
mol. formula C10H16
MW (g 3 mol1)
Psat (Pa)a
Tb (C)
ODT (g 3 m3)e
nf
136.2
1.96 102b
178.0
6.84 104
0.37
2b
R-pinene (Pin) linalool (LOH)
C10H16 C10H18O
136.2 154.3
5.13 10 2.21 101c
155.5 198.5
5.44 104 1.26 105
0.49 0.35
geraniol (Ger)
C10H18O
154.3
4.00 100c 7.05 10
46.0
225.0
1.63 105
0.36
3b
78.2
1.21 101
0.58
ethanol (EtOH)
C2H6O
linalyl acetate (Lin. ac.)
C12H20O2
196.3
1.48 101c
220.0
2.65 104
0.35
vanillin (Van)
C8H8O3
152.2
2.44 102d
282.6
8.35 108
0.31
a
Vapor pressures for pure components were obtained at 296 K. b From DIPPR 801 Database. c From Chemspider Database of Chemical Structures and Property Predictions, Royal Society of Chemistry; http://www.chemspider.com/Default.aspx (Accessed Feb 2011). d From Mackay, D.; Shiu, W. Y.; Ma, K.-C.; Lee, S. C. Handbook of Physical-Chemical Properties and Environmental Fate for Organic Chemicals; CRC Press and Taylor and Francis Group: Boca Raton, FL, 2006; Vols. IIV. e From van Gemert, L. J. Compilations of odor threshold values in air, water and other media; Oliemans Punter and Partners BV: The Netherlands, 2003. f n is the olfactory power law exponent as expressed in eq 1, and literature data was obtained from Devos, M.; Rouault, J.; Laffort, P. Standardized olfactory power law exponents; Editions Universitaires-Sciences: Dijon, France, 2002.
The compositions of the odorant mixture in the gas phase were experimentally measured in this work by headspace gas chromatography (HS-GC) in a closed environment, as will be presented in detail ahead. A flash calculation was performed to compute the vapor compositions in equilibrium with the liquid perfume. The iterative procedure for the resolution of the equilibrium equations using the group contribution methods is schematically presented in Figure 2. The UNIFAC, ASOG, and UNIFAC-Dortmund methods were implemented in the MATLAB software17,21,49 while the A-UNIFAC method was developed in FORTRAN language.40 In terms of experimental evaluations, different fragrance systems (24 binary, 20 ternary, and 21 quaternary systems) were analyzed through headspace gas chromatography (HS-GC), comprising a total of six fragrant compounds: R-(+)-limonene (LIM), ()-R-pinene (PIN), geraniol (Ger), (()-linalool (LOH), linalyl acetate (Lin. ac.), and vanillin (Van), plus ethanol (EtOH) as solvent. A comparison was performed between the experimentally measured gas-phase compositions and those predicted by the group-contribution models. Moreover, olfactory evaluations of selected mixtures were also performed. Finally, a previously developed model (see eqs 14 and further details in previous articles17,21) was used to predict the odor character or the dominant smell of these perfume mixtures, and results were compared with those measured by gas chromatography and by the olfactory panel.
’ EXPERIMENTAL SECTION Materials. R-(+)-Limonene (CAS no. 5989-27-5, >97%, >98% ee) and geraniol (CAS no. 106-24-1, >98%) were obtained from Sigma-Aldrich. (()-Linalool (CAS no. 78-70-6, >97% GC) and ()-R-pinene (CAS no. 7785-26-4, >98%, purum) were obtained from Fluka. Linalyl acetate (CAS no. 115-95-7, >97%, FCC) and vanillin (CAS no. 121-33-5, >97%, FCC) were supplied by Aldrich. Ethanol (Absolute GR for analysis, >99.9%) was supplied by Merck. All reagents were used as received without further purification. All chemicals together with the values for the properties used throughout this work are presented in Table 1. Sample Preparation and Analysis of the Vapor Phase. First, liquid mixtures of fragrances, with or without ethanol, were prepared gravimetrically using an Adam Equipment balance model AAA250L with a precision of (0.2 mg. Four replicates
of each mixture (1 mL) were placed on 20 mL closed-cap headspace vials and allowed to equilibrate for at least 24 h. In order to significantly reduce evaporation losses of the volatile fragrant ingredients during weighing, syringes were used to collect pure fragrance components and place them into headspace vials that were previously cap sealed. From the resulting mixture, four aliquots of 1 mL were pipetted and each one was placed in sealed 20 mL vials, constituting the four replicates. The required time for equilibration proved to be enough in preliminary experiments considering the volume of liquid and vials used in the experiments. The temperature at which the experiments were performed (including equilibration and analysis) was controlled in the lab through an air-conditioning system to 23 ( 1 C. The composition in the gas phase was assessed by headspace gas chromatography (HS-GC) using a Varian CP-3800 equipped with a split/splitless injector, FID detector, and a capillary column Chrompack CP-Wax 52 CB, 50 m length, 0.25 mm i.d., and 0.2 μm film thickness. The oven temperature was programmed isothermal at 60 C for 7 min, heated up to 100 C at a heating rate of 20 C/min, held isothermal for 3 min, then heated up to 220 C at a heating rate of 20 C/min, and finally held isothermal for 5 min. The injector and detector ports were set at 240 and 250 C, respectively. Injection volume for the gas phase was 0.5 mL with a split ratio of 1:25. Injection was performed using a gastight syringe from SGE and a headspace auto sampler HT250D by HTA SrL. The carrier gas was helium (He N60) with a constant flow rate of 1 mL/min. Calibration lines were obtained for the pure fragrant components of each system using liquid samples and analyzed in triplicate. The GC was operated with the same temperature program for the analysis of liquid samples as for the headspace samples, although the injection volume used was 0.1 μL and the split ratio was set at 1:150. Olfactory Analysis. Some selected perfumery systems studied in this work were subjected to an experimental olfactory analysis. Two nontrained male panelists (26 and 35 years old), nonsmokers with normal olfactory function, were chosen. The olfactory evaluations were performed during 3 days in a temperaturecontrolled environment (23 ( 1 C), were not intensive, and were carried out at the same time of the day per mixture stimulus and subject. The testing protocol allowed the panelists to be aware of what fragrances composed the system under evaluation (e.g., for a binary mixture the two components were known) and to smell each pure fragrance compound prior to evaluation of the 9393
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Industrial & Engineering Chemistry Research Table 2. Fragrance Systems Studied in This Work Comprising Binary, Ternary, and Quaternary Mixtures components FS1
R-pinene + linalool
FS2
limonene + linalool
FS3
R-pinene + limonene
FS4 FS5
R-pinene + limonene + linalool R-pinene + geraniol
FS6
R-pinene + limonene + geraniol
FS7
R-pinene + linalool + geraniol
FS8
linalool + geraniol
FS9
limonene + geraniol
FS10
limonene + linalool + geraniol
FS11
R-pinene + limonene + linalool + geraniol
FS12 FS13
R-pinene + linalyl acetate limonene + linalyl acetate
FS14
R-pinene + limonene + linalyl acetate
FS15
limonene + linalool + geraniol + ethanol
FS16
limonene + geraniol + vanillin + ethanol
samples. Throughout that test, subjects were given time to make meaningful associations that would help them remember the odor of the pure fragrances. Each system was evaluated separately from the others, and the samples were presented randomly, so panelists did not know the composition of each one. Overall, 31 different samples (with four replicates each) were evaluated by each panelist, including binary, ternary, and quaternary mixtures. For each replicate panelists had to choose the strongest perceived odor, and whenever the same intensity was perceived for two fragrance ingredients both were assigned to that mixture.
’ RESULTS AND DISCUSSION First, it should be said that the selection of the fragrant species obeys the typical formulation and composition of perfumery products. These are normally constituted by three types of notes (top, middle, and base notes, according to their volatility and sensorial properties) and one or more solvents (ethanol and water, though they may also include other chemicals such as stabilizers). Top notes (e.g., limonene or R-pinene) comprise those chemicals that are most volatile and so tend to have an impact in the first seconds or minutes after applying the mixture; then, as their smell starts to fade, the scent of the middle or heart notes (e.g., geraniol or linalool) becomes more noticeable and can be perceived for hours; finally, the odor would evolve to the scent given by the base notes (e.g., vanillin), which often have the lowest volatility and so remain longer, persisting for several hours or even days. In this way there is a large range of volatilities among the fragrant components used throughout this work (see Table 1). At a glance, this traditional view holds that perfumes can be viewed as blends, composed of top, middle, and base notes together with solvents. However, in terms of its human perception, this analysis is clearly an oversimplification because all fragrant species evaporate simultaneously, though at different rates (which depend on volatility, composition, molecular structure, and molecular interactions) from the time the perfume is applied.16 The group assignment for the UNIFAC-based methods and the ASOG method was performed for all components studied in
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this work according to the definitions of each method. In Table 2 are presented all the binary, ternary, and quaternary systems studied, while in Table 3 the experimental results obtained for the molar compositions in the liquid and vapor phases of all these systems at 296 K are shown. Evaluation of Vapor Compositions. The comparison of group-contribution methods and experimental data is presented graphically in Figures 36. The quaternary system FS11, composed of the two top notes (limonene and R-pinene), a middle note (linalool), and a middle-to-base note (geraniol) is presented first. The molar compositions for the liquid and vapor phases (experimental and predicted with different models) of the corresponding binary and ternary subsystems (FS1FS10) are shown graphically in Figure 3, while the behavior of the quaternary mixture (FS11) is shown in a tetrahedric diagram in Figure 4. Figure 5 shows the ternary diagram with the liquid and predicted vapor compositions for the ternary system FS14, composed by two top notes (limonene and R-pinene) and a middle note (linalyl acetate). In order to bring us closer to a real perfume formulation, two quaternary systems were evaluated, consisting of top, middle, and base notes plus a solvent (ethanol). The tetrahedric representations for quaternary systems of limonene + geraniol + linalool + ethanol (FS15) and limonene + geraniol + vanillin + ethanol (FS16) are presented in Figure 6. Both systems can be viewed as more representative of the initial perfume formulation, having its three different notes and a solvent. Visual inspection of Figures 36 shows small differences among all predictive methods and the experimental data: vapor compositions are grouped around the experimental value in most cases, with some exceptions in Figures 3 and 5. Toward a quantitative comparison, the average relative deviations (ARD, %) between experimental and predicted values were calculated as ARDð%Þ ¼
exp
100 NP jyi ycalc i j exp NP 1 yi
∑
ð6Þ
where NP stands for the number of experimental data points, yi for the vapor molar fraction of component i, and superscripts exp and calcd for experimental or calculated compositions, respectively. The absolute relative deviations for each single composiexp ycalc tion (δy = 100|yexp i i |/ yi ) between the experimental data and those predicted with the four methods are presented in Supporting Information Table S1. Results can be as good as 0.001% or as bad as 530% (observed for only one system, the quaternary mixture FS16, with the A-UNIFAC) depending on the method, fragrance components, and compositions considered. Table 4 summarizes the results for each system and component. At the bottom of Table 4 are shown the global average deviations for the vapor composition for each component. Here, it is clear that results are really good for the most volatile components (ethanol and R-pinene with ARD’s of 3% and 2%, respectively) and not so much for the less volatile fragrances. However, it should be underlined that the use of relative errors leads to situations like this, although absolute deviations may not be as significant given the magnitude of the compositions studied. Careful inspection of values in either Table S1 (see Supporting Information) or Table 4 raises the cause for such difference: the large difference in volatility of the different components studied. The perfume formulation combining top, middle, and base notes produces mixtures with volatilities covering a range of several orders of magnitude. For 9394
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9395
7.84 10
7.95 10
1
1
6.72 10
2
1
8.47 10
1
1
2.13 10 7.51 102
4.93 102
1.26 101
2
2
1
8.73 10
9.95 10
1.87 10 1.56 101
5.84 101
2.31 101
34
35
36 37
38
39
5.28 10
5.13 101
7.53 102
1.03 10 5.30 102
1
1.14 10
8.27 10
33
1
1
1
3.75 10
32
3.86 10
1
1
1.65 10
31
1.30 101
2.92 101
1
4.97 10 7.16 101
3.06 10
1
6.54 10
2
5.88 10
2
2.39 10
1
6.88 10
1
1.46 10
8.22 101
1
30
1
1.87 10 5.77 101
8.13 10 4.23 101
28 29
1.78 101
1
1.97 10
1
8.03 10
6.35 10
1
3.65 10
26
1
2.21 10
1
7.53 10
2
7.51 10
2
2.06 101
6.70 10 6.49 101
2
8.22 10
1
7.79 10
27
2
2
2
2.37 10
1
1
8.45 10
25
24
1.41 10
1
4.37 101
23
3.57 101
1.66 10
22
5.47 10 1.85 101
1
8.78 10
20 21
7.83 10
1
1.35 10
1
19
2.96 10
1
4.67 10
1
1.68 10
6.88 10
8.06 10
1.94 10 1
1
5.78 10
1 1
1
4.22 10
1.92 101
1
xGer
8.08 101
8.09 10 8.32 102
1
1.44 10
1
6.25 10 6.38 102
1
1
1
1
1
1
18
17
16
15
14
1.28 10 8.53 101
12 13
2
3.48 10
2.14 10
1
4.38 10
11
1.82 10
1
6.34 10
1
1.83 10
10
2.36 10
1
7.64 10
9
1
4.67 10
5.33 10
8
1
7.88 10
1
2.12 10
7.55 101
2.45 101
6
7
1.98 10 5.79 101
8.02 10 4.21 101
4 5
2.36 10
1
1
7.64 10
1
3
1
1
1
4.16 101
7.96 10
xPin
5.84 101
1
2.04 10
xLOH
2
xLim
1
N
xEtOH
xLin. ac.
xVan
1
1.39 101
7.04 101
3.36 10 4.40 101
1 1
2.50 10
4.73 10
1
9.66 10
1
8.85 10
1
8.96 10
1
9.43 101
9.72 10 9.70 101
1
8.33 10
1
6.30 10
2
3.55 10
1
2.11 10
1
5.59 10 7.50 101
2
2.95 10
1
2.20 10
1
5.26 10
1
2.93 10
1
9.66 10
2
7.46 101
9.43 10 8.49 101
yLim 2
1.41 102
7.86 103
2
4.23 10 1.56 102
1.33 10
1
1
5.13 10
3.00 10
2
1.06 10
1
5.78 10
2
5.73 10
1
7.61 10
1
9.40 10
1
1.64 10
1
1.32 10
2
3.53 102
1.69 10
2
1.14 10 2.08 102
2
2
3.21 10
8.40 10
2
2.54 101
5.67 10 1.51 101
2
1.03 10
1
5.29 102
2.01 10
yLOH 1
8.44 101
2.79 101
1
6.09 10 5.21 101
6.01 10
1
1
8.30 10
9.85 10
1
9.60 101
1
1
1.62 10 9.68 101
9.35 10
6.40 10
1
1
1
7.79 10
9.89 10
9.95 10
1
9.98 101
9.33 101 2.29 101
6.73 101
6.96 101
4.74 101
7.07 101
9.03 101
8.97 101
9.47 101
9.80 10
yPin
3.04 103
8.89 103
1.29 102 2.39 102
1.50 102
1.35 102
3.80 103
9.73 103
4.61 102
5.70 102
2.79 102 3.05 102
4.27 101
2.39 101
5.99 102
5.90 103
2.18 103
4.59 103
5.90 103 1.47 102
2.18 103
4.59 103
1.47 102
1.14 102
5.31 103
2.44 103
yGer
yEtOH
yLin. ac.
Table 3. Experimental Compositions of the Liquid (xi) and Vapor (yi) Phases for the Different Binary, Ternary, and Quaternary Systems Studied in This Work yVan
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2
1
2.24 10
3.58 10
8.39 10
9.16 10
1
1.04 101 1.08 101
1
1
1
4.67 10
1.19 10
8.64 10
1.41 10
1.38 101 1.82 101
49
50
51
52 53
54
9396
1
1
1
1
2
2.06 10
5.99 10
1.91 10
55
56
57 1
1
2.47 10 4.93 101
2
2.03 10
2.67 10 1.33 102
59
60 61
62 1
1
1
1
1
1
2.06 10
5.27 10
1.66 10
63
64
65
6.53 10
1.90 10
1.84 10
1.56 101
3.27 101
2.27 10
1.42 10
1.27 10
2
3.61 10
1
2.62 10
58
1
1.35 10
1
2.42 10
1
1.19 10
1
3.61 101
4.20 101 4.70 101
1
2
1
1
1.28 10
2.36 10
1.00 101
1.53 101
1.89 10
48
47 1
3.58 10
1.60 10
2.48 10
5.37 10 1
1
1
4.56 101
1
1
1
1
6.39 10 4.35 101
6.63 10
3.70 10
4.12 10
5.70 10
1
4.39 10
1
3.86 101
3.37 101 2.40 101
4.44 10
2
4.22 10
2
1.75 10
1
6.04 10
1
2.07 10
7.25 101
2.75 101
46
1
1.71 10 5.25 101
8.29 10 4.75 101
44 45
1
1
1
2.77 10
1
7.22 10
2.78 10
43
1
1
xLin. ac.
4.98 10
41
1
xEtOH
1
5.13 10
xGer
5.02 10
1
42
1.43 10
xPin
1
5.05 10
xLOH
1
1
1.46 101
2.94 10
xLim
8.54 101
40
N
Table 3. Continued
2
2.17 10
2
3.38 10
2
7.31 10
2
6.21 102
8.71 10 5.92 102
2
9.03 10
xVan
8.20 10
8.83 10
6.52 10
2
2
2
7.84 102
2
2
1.49 10 6.63 103
1.21 10
9.11 10
2
6.71 10
2
2.68 10
2
6.44 10
2
4.98 102
5.07 102 7.65 102
4.77 10
2
7.54 10
1
5.28 10
2
3.10 10
1
1.95 10
1
6.96 101
9.53 10 8.30 101
1
1
3.92 10
yLim
3.38 10
3
3.24 10
3
3
2.67 10
6.05 10
3
1.89 103
2.01 103 2.68 103
4.45 10
3
3
6.13 10
yLOH 1
2.39 10
9.45 10
6.73 10
7.16 10
8.95 10
9.49 10
1
1
1
1
1
1
9.90 101
5.93 10
yPin 3
1.81 10
2
1.93 10
3
1.61 10
3
1.38 103
3.84 10 7.43 104
4
3.90 10
4
5.09 10
4
3
1.07 10
8.81 10
4
3.82 10
4
1.31 103
1.73 103 2.59 103
1.09 10
3
9.13 10
yGer
1
9.00 10
9.10 10
9.33 10
1
1
1
9.20 101
9.85 10 9.93 101
1
9.88 101
9.05 101
9.29 101
9.70 101
9.29 101
9.47 101
9.46 101 9.18 101
9.47 10
yEtOH
6.25 103
2.70 103
1.68 102
8.88 102
3.04 101
4.65 102 1.70 101
1.05 101
5.11 102
1.03 102
yLin. ac.
3.94 106
1.28 106
9.17 107
7.28 107
2.67 107 4.90 107
6.53 107
yVan
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Figure 5. Representation of the liquid composition and comparison between the experimental and predicted vapor compositions for ternary system limonene + linalyl acetate + R-pinene. Figure 3. Representation of the liquid composition and comparison between the experimental and predicted vapor compositions for the binary and ternary subsystems in the quaternary system limonene + Rpinene + linalool + geraniol.
Figure 4. Representation of the liquid composition and comparison between the experimental and predicted vapor compositions for the quaternary system limonene + R-pinene + linalool + geraniol.
the case studied here, this range is of 5 orders of magnitude (see Table 1). Thus, it leads to compositions in the vapor phase (e.g., mole fractions) also differing in several orders of magnitude, from 0.90 or higher for ethanol and 0.50.9 for R-pinene down to 102103 for linalool and geraniol or even 106107 for vanillin (see Table 3). As mole fractions should sum for unity, errors in the most volatile component below 5%, which are good for a prediction, drive to large relative errors in other components with much lower volatility and vapor compositions. This fact is clearer when errors in limonene compositions are inspected in Table 4: independently of the predictive method chosen, errors for limonene are acceptable (114%) except for systems with ethanol (quaternary systems FS15 and FS16), this is, when a component significantly more volatile is introduced in the mixture. For this reason, ARD values were also calculated for all
components excluding these quaternary systems FS15 and FS16 and are presented at the bottom line of Table 4. These values are acceptable for all components except perhaps geraniol and linalyl acetate where higher deviations were found. Even so, it should be noted that in most cases the order of magnitude of the composition is well predicted for all components: even for vanillin in system FS16 (which involves ethanol and a difference in their vapor composition of 7 orders of magnitude), errors using UNIFAC, ASOG, or UNIFAC-D methods are around 40%. Evaluation of Predicted Activity Coefficients. Another point for discussion concerns the role of activity coefficients predicted by the different group-contribution methods, which are presented in Table S2 (see Supporting Information). It is important to highlight that the predicted activity coefficients do not deviate much from ideality for binary mixtures, while greater deviations are observed for some ternary and quaternary mixtures. In this regard, mixtures with structurally similar components present activity coefficients close to unity (e.g., binary geraniollinalool). However, it is also seen that in some cases where activity coefficients significantly deviate from ideality, the liquid composition (xi) for the corresponding component is also low, and consequently, it will not produce significant differences in the perceived odor as will be discussed later. Moreover, as aforementioned, ethanol is a commonly used solvent in perfumery, and so its role on the evaporation should be evaluated. For that, comparison of systems FS10 and FS15 (samples N = 31 and 32 with 52 and 55, see Tables 3 and S2, Supporting Information) is pertinent. Considering the liquid compositions in an ethanol-free basis they are very similar mixtures. However, if we analyze the vapor compositions once more in a solvent-free basis, it is possible to see that the presence of ethanol has a retention effect on the release of geraniol and linalool while the relatively nonpolar component, limonene, is pushed out of solution. This behavior is reflected in changes for the components’ activity coefficients: it increases for limonene and has a slight decrease for linalool and geraniol. This happens in a similar extent for all group-contribution methods, less pronounced with ASOG. Issues and Selection of VLE Predictive Method. In order to select a predictive method, the ARD for each system and for all systems are presented in Table 5. The UNIFAC method resulted 9397
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Figure 6. Representation of the liquid composition and comparison between the experimental and predicted vapor compositions for the quaternary systems of (a) limonene + geraniol + linalool + ethanol and (b) limonene + geraniol + vanillin + ethanol.
in the lowest errors, whether the quaternary systems with ethanol are considered or not. Nevertheless, differences among all the used methods are not large. In general, A-UNIFAC performed worse than other methods, despite this is the most complete equation and includes associative interactions. Some considerations should be taken into account: the group assignment used in A-UNIFAC is the same as in the UNIFAC method. Linalool, geraniol, and ethanol have the hydroxyl associative group, and vanillin has the hydroxyl and aromatic ring groups. The two-site hydroxyl group is able to self- and cross-associate, and the onesite aromatic ring can only cross-associate in the presence of an electropositive site. Linalyl acetate has the ester group, but it can only cross-associate in the presence of an electropositive site, such as a hydroxyl or carboxyl group, which do not appear in that system. Most of the molecules under study have the double-bond group which is not included in the A-UNIFAC interaction group parameters’ table. However, this is a nonassociative group, and so UNIFAC parameters were used. The same was done for vanillin, except for the group ACOH, whose parameters were obtained recently.48 The use of UNIFAC parameters (which do not separate associative interactions) in the A-UNIFAC method (which separate these interactions) may be behind the worse results obtained with this method, especially for the system containing vanillin. The issue of available parameters is related to the size of the experimental database used in the parametrization itself (which in our opinion may be the limitation of A-UNIFAC). This database (see refs 40, 47, and 48) cannot be compared in number of experimental points and/or types of components with the Dortmund Data Bank used in the UNIFAC and UNIFAC-D revisions (a larger database with more experimental data to obtain the interaction parameters somehow corrects the lack of the associative term). These assumptions may be behind the slightly worse results obtained with A-UNIFAC, although its theoretical foundations are more suitable for this kind of molecules. Even so, considering systems without ethanol, the A-UNIFAC predicted comparable results with other models, as shown in Table 5. It is also important to note that for several systems involving predominantly alcohols (like geraniol and linalool) ASOG performed slightly better. This finding was already shown by Gupte and Daubert,50 who compared a large experimental VLE database with predictions from ASOG and UNIFAC. They have
shown that for ternary systems (at low pressures) containing alcohols and water, the ASOG method gave marginally better predictions. From their work it was possible to see that systems with chemically similar components tended to be better predicted by the ASOG method. Moreover, other studies found in the literature have pointed out slightly better predictions obtained from the ASOG method when compared with the UNIFAC method (for example, for ketones).51 However, the ASOG method gives much higher deviations for system FS14 (R-pinene + limonene + linalyl acetate) probably due to the presence of esters in solution.52 Besides, the ASOG method has not been updated for many years. On the contrary, UNIFAC has been continuously (and recently) updated and extended,37 covering a larger number of functional groups and their interactions and making this method strongly recommended. An example of this limitation of the ASOG method is seen for the vanillin used in this work. Vanillin (4-hydroxy-3-methoxybenzaldehyde) is constituted by a benzene ring with aldehyde, methoxy, and hydroxyl groups linked in the aromatic carbons 1, 3, and 4, respectively. As the hydroxyl group is linked to an aromatic carbon, it should be considered “aromatic” (group 7 in the ASOG parameters’ matrix, instead of group 6).41 The problem here is that there are not available interaction parameters for this group 7 with groups 4, 10, and 11.41 This is a major problem for group-contribution methods. For the particular systems studied in this work, the limitation was overcome simply by considering the normal hydroxyl group (group 6). Nevertheless, such solution would not be possible for other molecules and/or functional groups. Considering the number of different functional groups present in fragrance molecules and the large number of components used in perfume formulation, the problem is likely to happen with ASOG rather than with the more developed methods (e.g., UNIFAC and UNIFACDortmund), similarly to what happens for A-UNIFAC with other functional groups. Prediction of Perceived Odor. The relevance of the data presented so far concerning the compositions in the liquid and gas phases is increased when applied to the prediction of the dominant fragrance odors as they are perceived by humans. Following Stevens’ power law for olfaction, as presented in eq 1, the odor intensity of each fragrance ingredient in each mixture 9398
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9399
a
2
4
FS3
FS4
10
8
FS11
UNIFAC Dortmund
4 60
53
21
6
FS14 FS15
FS16
ARD (%)
ARD (%)
13
30
84
2
2
2
3
4
26
41
65
73
14
28
38
6
21 35
44
4
4
3
41
41
29
56
41
40
40
5
22
52
7 68
14
7
3
1
4
5
3
3
24
32
60
19
22
6
41
40
23
12
3
3
3
3
5
4 3
0.3
4
2
0.3
43
21
38
62
73
19
18
38
11
19 10
5
4
3
44
44
23
56
1 62
13
59
7
all systems without ethanol
59
all systems
74
54
44
10
10
1
5
7
2
6
16
28
71
13
20
1
11
16
29
21
2
2
2
3
5
3 1
0.3
2
1
2
42
25
40
64
71
17
29
39
6
13 35
Average deviations are presented at the bottom for each ingredient in different systems containing or not containing ethanol.
12
FS13
12
20
1
FS10
7
FS8
1
3 0.3
FS9
0.3
FS6 FS7
2
2
2
FS5
3
27
11
19
6
FS2
FS12
ASOG
A-UNIFAC
4
4
3
49
49
31
56
66
38
38
10
23
46
10 57
12
18
11
1
9
10
2
6
16
29
71
12
22
1
16
15
30
21
4
4
3
2
10
5 1
0.3
5
2
1
25
40
61
71
16
30
41
6
10 34
43
4
3
3
47
47
42
56
44
327
327
δyLim δyLOH δyPin δyGer δyEtOH δyLin. ac. δyVan δyLim δyLOH δyPin δyGer δyEtOH δyLin. ac. δyVan δyLim δyLOH δyPin δyGer δyEtOH δyLin. ac. δyVan δyLim δyLOH δyPin δyGer δyEtOH δyLin. ac. δyVan
FS1
system
UNIFAC
Table 4. Average Relative Deviations (ARD) between Experimental and Predicted Vapor Compositions for All Fragrance Ingredients in Each Fragrance Systema
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Table 5. ARD Obtained for Each System and for All Systems with Different Models UNIFAC
ASOG
UNIFAC Dortmund
A-UNIFAC
FS1
10
6
11
11
FS2 FS3
16 2
13 3
18 2
18 2
FS4
6
16
8
10
FS5
22
22
21
22
FS6
9
9
7
8
FS7
14
18
16
17
FS8
4
8
4
4
FS9
20
20
20
21
FS10 FS11
19 9
14 12
20 11
21 14
FS12
22
24
35
23
FS13
34
34
34
34
FS14
12
28
12
18
FS15
56
51
52
51
FS16
40
40
41
109
ARD (%)
24
25
29
35
ARD (%)
13
all systems
all systems without ethanol 16
14
15
was calculated from the vapor-phase concentration measured by HS-GC. These odor intensities can then be compared with those predicted using eq 4, which used the thermodynamic models presented before for estimation of activity coefficients. The results were also compared with an olfactory analysis performed by two panelists (for details, see Experimental Section, olfactory analysis). A compilation of these results is presented in Table S3, Supporting Information. The results have shown a very good agreement for the perceived dominant odorant between the experimental and the predicted odor intensities. Considering all the fragrance mixtures studied in this work (binary, ternary, and quaternary for a total of N = 65 samples) similar deviations for the different predictive models were observed between the predicted dominant odor and experimental values. Using the UNIFAC and UNIFAC-D methods for prediction of the activity coefficients, the dominant odor is correctly predicted in 95.4% of the cases, while the ASOG and the A-UNIFAC performed marginally poorer with 93.8% and 90.8%, respectively. However, it should be highlighted that deviations were only observed for quaternary mixtures having ethanol in its composition, except for the ASOG that failed to predict the dominant odor of one ternary mixture (see Table S3, Supporting Information, N = 33, where a slight difference is observed). Binary and ternary systems have shown a full agreement between dominant odors obtained by predicted and experimental gas compositions. Additionally, it should be noted that when deviations were found for the quaternary mixtures, it was observed that the predicted strongest odorant corresponded to the second more intense obtained from the experimental measurement. This fact shows once more the good predictability of the model for odor perception, regardless of the thermodynamic model used for the vaporliquid equilibrium. Despite these great results, the use of a group-contribution model could be questioned to consider an ideal mixture in the liquid phase (γ = 1). This effect was previously studied by our
group, showing significant differences in the perceived odor.15,53 Moreover, considering an ideal solution for the liquid phase for all the fragrance systems, it is observed that the dominant odor is only correctly predicted 73.4% of the times, compared with experimental headspace measurements. Olfactory Evaluations. The olfactory evaluation of some fragrance mixtures was also performed in order to evaluate and validate the odor intensity model and involved two panelists. For the olfactory evaluations, four replicates were used and classified in terms of the strongest fragrance odor by the panelists. In some of the selected mixtures a similarity for the odor character classification was observed between two fragrance ingredients, so that two olfactory descriptors were assigned, as presented in Table S3 (see Supporting Information). The olfactory evaluations when compared with the dominant note experimentally obtained (using chromatographic analysis) have shown an agreement of 65% and 68% for panelist 1 and panelist 2, respectively. The vast majority of the differences were seen for ternary and quaternary mixtures, which are more difficult to assess by the nose at the sensorial point of view. In fact, if the average sniffing duration is about 1.6 s54 and that is enough to correctly identify distinct pure odorants with only one sniff,55 it is also true that identification of odors within mixtures is far more difficult. According to the literature, humans have difficulty in identification of single odorants in mixtures containing three or more compounds,5658 although this process may be significantly improved after presenting the other pure components of the mixture to the panelists (as done in this work).57 Finally, it was seen an average agreement of 54% (panelist 1) and 59% (panelist 2) between the olfactory evaluation and the dominant odor obtained with the predictive method using the different thermodynamic models. The majority of the mismatches were observed for the quaternary mixtures with ethanol in the composition. It was seen that for those, prediction of the dominant odor intensity often indicated a stronger ethanol perception, although from the perfumery point of view, ethanol will be a solvent that evaporates quickly and thus is not expected to be perceived. This fact has mainly to do with the psychophysical model used for the intensity scale and the high exponent value n for ethanol (see Table 1). It also worth noting that these predictions are performed at time zero for equilibrium conditions (without considering diffusion or convection effects). It was previously observed by the authors that predicted odor intensities using this model for systems containing ethanol resulted in stronger perceptions of this component than in other perception models like the OV model.21 In summary, the odor character evaluation performed by sensorial analysis has shown a good correlation with the odor character obtained from the headspace concentrations measured by gas chromatography and also with those from the predictive methods.
’ CONCLUSIONS The vaporliquid compositions of several fragrance systems were evaluated by HS-GC and compared with those predicted by four group-contribution methods. The results have shown that the UNIFAC method is a suitable model for predicting the headspace composition, performing marginally better than the remaining methods. Moreover, a methodology to describe the odor character of multicomponent mixtures was applied using the predicted vapor compositions from perfumery mixtures, showing very good agreement with the experimental 9400
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Industrial & Engineering Chemistry Research measurements. Besides, their comparison with an olfactory evaluation has shown relatively good agreement. From this point, it can be said that this methodology is suitable for prediction of the odor character of fragrance mixtures. In this way, the repetitive and costly trial-and-error experimental assays may be reduced in perfume formulation. This type of prediction will speed up the preformulation process and reduce final product costs, enhancing the development of perfumed products.
’ ASSOCIATED CONTENT
bS
Supporting Information. Tables on the average relative deviations (ARD) between experimental and predicted vapor compositions, predicted activity coefficients and odor intensities, and character of perfumery mixtures are provided. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Tel.: +351 22 508 1671. Fax: +351 22 508 1674. E-mail: arodrig@ fe.up.pt.
’ ACKNOWLEDGMENT Financial support for this work was in part provided by Fundac) ~ao para a Ci^encia e a Tecnologia (FCT) and LSRE financing by FEDER/POCI/2010, for which the authors are thankful. O.R. acknowledges financial support of Programme Ci^encia 2007 (FCT). M.A.T. and F.L.M. acknowledge their Ph. D. grants of FCT (SFRH/BD/37781/2007 and SFRH/BD/ 32372/2006). ’ REFERENCES (1) Butler, H. Poucher’s Perfumes, Cosmetics and Soaps, 10th ed.; Kluwer Academic Publishers: Boston/London, 2000. (2) Calkin, R.; Jellinek, S. Perfumery: Practice and Principles; John Wiley: New York, 1994. (3) Teixeira, M. A.; Rodríguez, O.; Rodrigues, A. E. Perfumery Radar: A Predictive Tool for Perfume Family Classification. Ind. Eng. Chem. Res. 2010, 49, 11764–11777. (4) Cussler, E. L.; Wagner, A.; Marchal-Heussler, L. Designing Chemical Products Requires More Knowledge of Perception. AIChE J. 2010, 56 (2), 283–288. (5) Behan, J. M.; Perring, K. D. Perfume interactions with sodium dodecyl-sulfate solutions. Int. J.Cosmet. Sci. 1987, 9 (6), 261–268. (6) Wei, J. Product engineering. Molecular structure and properties; Oxford University Press: New York, 2007. (7) Costa, R.; Moggridge, G. D.; Saraiva, P. M. Chemical product engineering: an emerging paradigm within chemical engineering. AIChE J. 2006, 52 (6), 1976–1986. (8) Ulrich, K. T.; Eppinger, S. D. Product Design and Development, 2nd ed.; McGraw-Hill: New York, 2000. (9) Hill, M. Chemical Product Engineering-The third paradigm. Comput. Chem. Eng. 2009, 33 (5), 947–953. (10) Friberg, S. E. Constant vapor pressure evaporation from emulsions. Colloid Polym. Sci. 2008, 286, 47–50. (11) Friberg, S. E. Phase Diagram Approach to Evaporation from Emulsions with n Oil Compounds. J. Phys. Chem. B 2009, 113 (12), 3894–3900. (12) Friberg, S. E.; Al-Bawab, A.; Odehb, F.; Bozeya, A.; Aikens, P. A. Emulsion evaporation path. A first comparison of experimental and calculated values. Colloids Surf. A: -\Physicochem. Eng. Aspects 2009, 338 (13), 102–106.
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