Prediction Model for the Odor Intensity of Fragrance Mixtures: A

Article pubs.acs.org/IECR

Prediction Model for the Odor Intensity of Fragrance Mixtures: A Valuable Tool for Perfumed Product Design Miguel A. Teixeira, Oscar Rodríguez, and Alírio E. Rodrigues* LSRE−Laboratory of Separation and Reaction Engineering, Associate Laboratory LSRE/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

Rebecca L. Selway, Michelle Riveroll, and André Chieffi Procter & Gamble Tecnical Centre Limited, Whitley Road, Longbenton, Newcastle upon Tyne, NE12 9TS, United Kingdom ABSTRACT: In this work a previous model developed to account for the odor intensity of liquid perfumes was validated using sensory evaluations performed by two different panels, one of professional perfumers and another of nontrained individuals (consumers). For that purpose, several fragrance mixtures containing three perfumery raw materials (having different physicochemical properties) and a solvent were formulated attending to the expertise of experienced perfumers. These mixtures were then placed on textiles, allowed to evaporate, and then were subjected to experimental olfactory evaluations, being their perceived intensity rated by perfumers and nontrained panelists. The perceived odor intensity of these samples was also predicted using our model that considers fragrance release and intensity perception. The results obtained show a good correlation with the ratings from both perfumers and nontrained panelists. In this way, it was shown that odor intensity can be predicted using a structured model which accounts for the evaporation and olfactory perception of fragrances.

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base notes.9 A note, for itself, defines the olfactory impression of a single smell, or more specifically the perceived scent of a single or mixture of fragrance ingredients and/or essential oils.7,10,11 Psychophysically it is the perceived odor sensation induced by a stimulus magnitude.12 In this way, top and base notes are the most and least volatile ones, respectively, while middle notes are in between. According to Carles, we would perceive top notes more strongly in the first moments after application of the perfume and as these start to fade, the odor would evolve into the middle notes and, finally, would reach that of the base notes (some of which are often used as fixatives because they can change the tendency of evaporation of the remaining fragrances, thus allowing the perfume to last longer). However, in terms of olfactory perception this is an oversimplification because all fragrant species evaporate continuously, though at different rates (which depend on volatility, composition, molecular structure, and molecular interactions). These and other effects make it extremely complex to formulate a perfume which will later have the desired smell whereby predicting that behavior becomes even harder. Due to these issues, perfumers play an important role in the formulation of such products. They have a deeper and more detailed perspective of the structure of a perfume, dividing it into three important aspects: (i) the perfumery accord (aesthetical pleasantness of a mixture of fragrances); (ii) the relationship between top, middle, and base notes (composition); (iii) the balance between simplicity and complexity

INTRODUCTION Product development has been evolving rapidly since the 1990s where globalization pressures have triggered the need for better product designs, faster time to market, and lower cost of production.1,2 The flavor and fragrance business is no exception on this matter, with new trends and consumer products being launched every year. However, the creation of perfumed products, especially fine fragrances, is still an artistic, highly individualistic, and creative job developed by well-trained perfumers. Consequently, the application of Product Engineering to fragrance design emerges as a valuable tool for introducing scientific knowledge into a so far empiric and experimental area. Product design for fragrances will differ from other formulated products as well as within its final application (eau de toilette, shampoos, or soaps). However, recent works suggest that it is possible to reduce the number and quantity of chemicals used in perfume formulation through the use of scientific principles, without any measurable reduction in perceptual complexity.3−6 Fragrances are intrinsic to many consumer products globally and are known to be a predominant reason for consumer delight, thus motivating purchase and repurchase. The main function of a fragrance is, probably, to instill a pleasant and harmonious odor to the product in which it has been incorporated and, thus, translate pleasant sensations when one perceives it.7 In short, fragrances have the role of enhancing products′ performance and attractiveness to consumers.8 However, perfumes are complex mixtures comprising different fragrance ingredients mixed in a solvent matrix along with other stabilizing compounds. In simple terms, the famous perfumer J. Carles compared the structure of a perfume to a pyramid composed by three types of fragrant notes: top, middle, and © 2012 American Chemical Society

Received: Revised: Accepted: Published: 963

September 18, 2012 December 11, 2012 December 18, 2012 December 18, 2012 dx.doi.org/10.1021/ie302538c | Ind. Eng. Chem. Res. 2013, 52, 963−971

Industrial & Engineering Chemistry Research

Article

Figure 1. Molecular structures of the perfumery raw materials (PRMs) used in the formulation of the studied mixtures.

Table 1. Properties of the Chemical Components Used in This Work compound name

CAS

mineral oil (considered as hexadecane for calculations)

8042-47-5 544-76-3 106-24-1 111879-80-2 54464-57-2

geraniol habanolide iso-e-super a

mol. form.

mol. weight (g/mol)

ODT P&Gc (mg/m3)

226.4 154.2 238.4 234.4

odorless odorless 0.077c 13.717c 0.107c

C16H34 C10H18O C15H26O2 C16H26O

vapor pressure (Pa)a 6.66 2.67 7.05 7.17

× × × ×

10−1 10−0 10−3 10−2

log Pa 8.86 4.95 4.95 5.29

n

odor family

0.36b,c 0.80c 0.35c

odorless odorless floral amber-musk fresh-woody

From the Chemspider−RSC Database.35 bFrom the work of Devos et al.23 cCalculated from P&G data.

Table 2. PRM Mixtures with Corresponding Concentrations and Compositions in the Liquid Phase, Predicted Odor Intensities (ψi), Together with Their Olfactory Evaluations Performed by Perfumers and Panelists concentration (mg/fabric) N

geraniol

habanolide

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.8 0.8 0.8 0.8

1.0 1.0

mineral oil

4.0

0.929 0.973 0.939 0.985 0.941 0.988 0.953 1 0.995 0.996 0.949 0.997 0.985 0.997 0.982 0.984 0.985

4.0 1.0 1.0

4.0 4.0

0.1 0.1 0.1 0.1 0.1 0.0 0.8 0.7 0.3

0.2 0.2 0.2 0.0 1.0 0.2 0.2 0.2 0.4

0.1 4.0 0.1 0.1 0.1 0.1 0.1 0.3

ψi

mole fraction

iso-esuper

geraniol

habanolide

0.014 0.015 0.014 0.015

0.011 0.012

iso-esuper 0.046 0.047

0.012 0.012

geraniol

habanolide

6.21 6.52 6.27 6.61

3.70 × 10−3 4.00 × 10−3

0.047 0.002 0.002 0.002 0.002 0.002 0.015 0.013 0.006

0.002 0.002 0.002 0.012 0.002 0.002 0.002 0.005

0.001 0.047 0.001 0.001 0.001 0.001 0.001 0.004

(number of ingredients) which also influences the price.7 Altogether, these facts are reasons enough to consider human sensory perception when designing new chemical products, despite the difficulties that may arise.4,13 For that purpose, the process of evaporation of a fragrance from a specific substrate presents itself as an important step for the design and evaluation of novel fragrance materials or products containing fragrance ingredients. Other authors have reported that fragrance evaporation from different substrates like the skin, clothes, or a paper blotter (often used in perfume try-outs) may be completely different, thus changing the perceived odor (intensity, character, or both).14,15 This is so because the process depends not only on the fragrances’ properties (physicochemical properties, molecular interactions within fragrance molecules, temperature, or pH, just to mention a few) but also on fragrance interactions with the substrate in which they are applied.15 When measuring odors there are some parameters to be considered: (i) detectability (detection or recognition thresholds); (ii) intensity scale (the perceived

perfumer average

panelist average

1.74

108.8 105.0 107.5 107.5 65.0 32.5 81.3 26.3 63.8 47.5 71.3 43.8 82.5 45.0 126.3 97.5 86.3

6.2 6.1 6.0 4.8 5.0 1.9 1.9 0.5 3.6 2.4 5.4 4.3 2.6 1.5 5.0 6.6 5.3

1.75 3.80 × 10−3 4.10 × 10−3

0.047

intensity grade iso-esuper

1.76 1.78

3.23 3.23 3.05 3.23 3.20 6.59 6.30 4.71

1.10 × 10−3 1.10 × 10−3 1.10 × 10−3 4.10 1.10 1.10 1.10 2.00

× × × × ×

10−3 10−3 10−3 10−3 10−3

0.50 1.77 0.50 0.50 0.50 0.49 0.50 0.74

sensation with concentration increase); (iii) perceived character or quality (classification into olfactive families like floral or citrus); (iv) hedonic tone (the degree of pleasantness or annoyance of an odor).16−18 For all these reasons, the evaluation of the desired perceived odor is extremely difficult to predict and so it is often experimentally determined by olfactory evaluations performed by trained or nontrained panelists.19 The use of nontrained panelists relies on the fact that although perfumers play a key role in the formulation and evaluation of fragrances, the final product will ultimately be evaluated by consumers who buy them. Thus, the design of perfumed products must take into account both quantitative and qualitative parameters for odor perception. Although the latter is without a doubt very important from the consumer point of view, the former is easier to be evaluated. In this work, the odor intensity of several fragrance mixtures (binary, ternary, and quaternary, including the solvent) placed on textiles (substrate) were evaluated with two different panels and also predicted with a theoretical model. This model 964

dx.doi.org/10.1021/ie302538c | Ind. Eng. Chem. Res. 2013, 52, 963−971


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ether, and an alcohol of low olfactive intensity) for the dissolution of the PRMs, but these performed poorer than the mineral oil because they either left residues or significantly hampered the perceived odor. Olfactory Evaluations. The headspace of the fragrance mixtures applied on the textiles was evaluated for all samples, after equilibration and near the point of application. It should be highlighted that the solvent matrix (mineral oil) is odorless and so is not perceived. For the case of the binary mixtures, they consist of a single PRM dissolved in the odorless mineral oil (matrix), hence what is expected to be perceived is the PRM alone. Samples were evaluated through olfactory analysis made by perfumers from P&G and nontrained panelists. This panel was composed by 30 nontrained people, 13 men and 17 women aged between 17 and 57 years. The panelists presented averages of 31.6 and 35.9 years for male and female panelists, respectively. For the olfactory evaluations, panelists were able to smell the pure fragrance components prior to the analysis of the samples. These were presented to panelists and perfumers enclosed in tin foil and were analyzed independently in blind tests (without knowing the concentrations). These evaluations were performed at controlled room temperature, were not intensive, and were carried out at the same time of the day per mixture stimulus and subject. Throughout the testing protocol each nontrained panelist evaluated five samples randomly (which could be repeated, although every sample was new and not reused). This corresponds to an incomplete block design, as panelists only judge a subset of the samples (more details on this type of design of experiments are given by Lawless and Heymann,20 and examples of this design applied for fragrance mixtures and olfactory evaluations are presented in the extensive compilation of design of experiments from Cochran and Cox21). Panelists rated the perceived intensity on a 10 cm line scale as described in the literature.22 This linear or line scale method uses marks or anchors at both ends of the scale, starting from “none” or zero perceived stimulus (at the left end of the scale) to “strong” or high intensity stimulus (at the right end of the scale). Panelists rated the perceived odor intensity of each sample by placing a mark on the horizontal line scale. Such marks were then converted to numbers by measuring the position of each mark on the scale using a ruler.22 Moreover, fresh coffee beans were used to clear the nose receptors in between every evaluation. Four perfumers also rated samples randomly in nonintensive tests using an olfactive scale as presented in Figure 2. This intensity scale ranges from 0 to 200 units where values close to zero mean no detection, values near 20−30 represent recognition thresholds, values above 120 may provoke nuisance and at the top end of the scale (200 units) they are considered as painful. Odor Detection Thresholds and Intensity−Concentration Plots. Odor detection thresholds (ODT) and powerlaw exponents (n) were calculated by P&G. The ODT data were calculated by P&G using a QSAR (quantitative structure− activity relationship) model that is proprietary from P&G. The power-law exponents were calculated from line scale experiments carried out by P&G perfumers, as presented for geraniol, habanolide, and iso-e-super in Figure 3. Throughout these experiments, samples with increasing concentrations were rated by perfumers using a line scale. The same intensity scale previously used for the samples was applied here (see Figure 2), while concentrations are indicated as headspace chromatographic areas (arbitrary units). This allows avoiding a complex

accounts for fragrance evaporation and human perception, predicting the odor intensity from the liquid composition of perfumery raw materials (PRMs) using physicochemical and psychophysical properties that can be estimated from correlations or obtained from the literature. The different intensity ratings were correlated in order to demonstrate that human evaluations and predicted odor intensities are comparable and simply recall different scales of the same property. Three PRMs selected by perfumers from Procter & Gamble were used. The PRMs partly follow the definitions of Carles:9 geraniol is a middle note, habanolide is a typical base note and also a fixative, and iso-e-super represents a low middle to base note.

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MATERIALS AND METHODS The experimental work was carried out at Procter & Gamble (P&G) while all the modeling was performed at LSRE. Materials. Two of the fragrance ingredients used in this work were supplied by IFF as geraniol (3,7-dimethyl-2,6octadien-1-ol, CAS no. 106-24-1) and iso-e-super (1(1,2,3,4,5,6,7,8-octahydro-2,3,8,8-tetramethyl-2-naphthalenyl)ethan-1-one, CAS no. 54464-57-2) while habanolide (12Eoxacyclohexadec-12-en-2-one, CAS no. 423773-57-3) was obtained from Firmenich. The mineral oil was supplied by Sigma-Aldrich (CAS no. 8042-47-5). Textiles used in this work were woven cotton towels with 100 cm2 (10 cm × 10 cm, dry textile). The molecular structures of fragrant molecules studied in this work are presented in Figure 1, and their corresponding psycho-physicochemical properties are shown in Table 1. Perfume Mixture Formulation and Application on Textile. Fragrance mixtures were formulated by P&G perfumers, who defined the required concentrations of each PRM for each sample in order to obtain a pleasant odor as presented in Table 2. This is based on the olfactory expertise of P&G perfumers (both in terms of quality and intensity) for the formulation of different fragranced consumer products with specific concentrations that correspond to pleasant odors in the olfactive intensity scale shown in Figure 2. Consequently, these

Figure 2. Olfactive intensity scale used from perfumers at Procter & Gamble.

mixtures have a combination of a blooming floral note (geraniol) with a heavier fresh-woody scent (iso-e-super) together with a fixative compound (habanolide) to increase its long lastingness. For that purpose, different fragrance mixtures were formulated comprising seven quaternary, six ternary, and three binary mixtures plus a blank and two validation samples. In all mixture formulations, the PRMs (Table 2) were made into respective one, two, or three stock solutions (the PRMs added gravimetrically into 10 mL of mineral oil) of varying ratios with aliquots of 100 μL taken and added to the fabric as per the design of experiments (DoEs). Each 100 μL fragrance solution was dispensed onto a 10 cm × 10 cm square of cotton textile (dry textile), which was immediately enclosed by hand in a flat tin foil and left to equilibrate (at controlled room temperature) for 2 h prior to the olfactory analysis of their headspace (by panelists who opened the foil and smelled the fabric immediately after). It is to be noted that other matrices were tested (e.g., pentane, ethyl 965



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contained only three odorant species the PTD methodology is perfectly suitable to predict and graphically represent the perceived odor intensity and character of any ternary fragrant mixture.10,26 For that purpose, the odor intensity above a liquid mixture of any volatile PRM (ψi) can be calculated using Stevens’ Power Law for olfaction as presented in eq 1.12,27 ⎛ C g ⎞ni ψi = ⎜ i ⎟ ⎝ ODTi ⎠

(1)

where Cgi is the concentration of an odorant i in the gas phase (g/m3), ODTi is its corresponding odor detection threshold (g/m3), and ni is the power law exponent for intensity perception. As previously mentioned, the ODT and n parameters were calculated by P&G, and a summary of these results is presented in Table 1. Moreover, once we did not know the concentrations in the gas phase for each fragrance compound, we have used the PTD predictive methodology to calculate it, which is based on the (liquid) mass composition of each PRM (plus the solvent) applied in the fabric as experimentally performed by P&G. From that, mole fractions for those mixtures can be calculated and then the perceived odor intensity (ψi) of each PRM can be predicted using the PTD methodology.10,26 For that objective, in a mixture of N fragrant components it is necessary to account for the molecular interactions in the liquid phase and so the composition of the different fragrant components in the gas phase above the liquid can be calculated from the modified Raoult’s law for vapor−liquid equilibria (VLE) as previously reported elsewhere.10,26,28 That includes the determination of activity coefficients in the liquid phase (γi) due to nonidealities, reflecting the affinity and interactions of each molecule with the other compounds. While for an ideal solution γi is unity, for a nonideal solution γi ≠ 1, evidencing deviations from Raoult’s Law.28 Therefore, in a perfume mixture, the activity coefficient can be seen as a measure of the tendency of a fragrance molecule to stay in the liquid phase or to be “pushed out” into the headspace. In this way, if γi > 1, the concentration of the fragrant component i in the headspace will be higher than in an ideal solution, which means that molecules will be more pushed out from the solution into the gas phase. When γi < 1, the opposite effect happens and so lower concentrations of the odorant species i will be found in the headspace due to a higher affinity to the surrounding medium.10,26 Like this, eq 1 can be rewritten as:

Figure 3. Curves of odor intensity versus headspace peak areas for geraniol, habanolide, and iso-e-super.

experimental setup for the measurement of fragrance concentrations in air. It is important to note that the powerlaw exponent calculated for geraniol is the same as that recommended by Devos et al.23 Iso-e-super is a mixture of isomers so its intensity scale depends on their relative composition, which is critical once they have very different ODTs.24 The power-law exponent for habanolide is not available in the literature. Moreover, the character classification of each PRM was defined by the perfumers through olfactory evaluations (see Table 1). Modeling of Perceived Odor. In order to establish a simple model that could replicate the physical experiments performed in this work, it is necessary to account for fragrance evaporation and odor perception. A previously developed methodology at LSRE, called Perfumery Ternary Diagram (PTD) seems to be suitable for modeling these phenomena as will be presented ahead.10,25 For that purpose, it was assumed a dry fabric substrate where the fragrance ingredients placed on it were evaporating into the air. Since the perfumery mixtures

⎡ ⎛ P satM ⎞⎛ 1 ⎞⎤ni ⎟⎥ ψi = ⎢γixi⎜ i i ⎟⎜ ⎢⎣ ⎝ ODTi ⎠⎝ RT ⎠⎥⎦

(2)

As a result, the odor intensity of each perfumery raw material (ψi) can be predicted from pure component data as the composition in the liquid phase (xi), molecular weight (Mi), saturated vapor pressure (Psat i ), and odor detection threshold (ODTi), plus the psychophysical power law exponent (ni). R and T are the universal gas constant and absolute temperature, respectively. The molecular weight appears in the numerator due to unity consistency with the ODT. Additionally, in eq 2 appears the activity coefficient (γi), which is a function of the composition and can be calculated from experimental vapor− liquid equilibrium (VLE) data or predicted using suitable methods. In this work the UNIFAC28,29 group contribution method was used for the prediction of the VLE and the activity coefficients of the chemical components. The solvent used in 966



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Table 3. UNIFAC Groups Used for the Perfumery Raw Materials (PRMs) with the Corresponding Volume and Surface Parameters molecule (i) geraniol

habanolide

iso-e-super

hexadecane

subgroup (j)

group number

subgroup number

νj(i)

Rj(i)

Qj(i)

CH3 CH2 CHC OH CH2 CHCH CH2COO CH3 CH2 CH C CC CH3CO CH3 CH2

1 1 2 5 1 2 9 1 1 1 1 2 9 1 1

1 2 8 15 2 6 19 1 2 3 4 70 18 1 2

3 3 2 1 11 1 1 4 5 2 1 1 1 2 14

0.9011 0.6744 0.8886 1.0000 0.6744 1.1167 1.6764 0.9011 0.6744 0.4469 0.2195 0.6605 1.6724 0.9011 0.6744

0.848 0.540 0.676 1.200 0.540 0.867 1.420 0.848 0.540 0.228 0.000 0.485 1.488 0.848 0.540

Carles. It allows mapping the perceived dominant odor for any possible ternary/quaternary mixture of fragrance ingredients. In the case of a ternary mixture, the three components A, B, and C, represent three types of fragrant notes used in the formulation where each one will be placed in the vertex of the triangle. Within this diagram it is then possible to express any composition of three components by a set of ternary fractions (e.g., molar, volume, weight). It is possible, though, to incorporate another component in the system (for example a solvent, S) in order to differentiate it from the concentrated perfume mixtures and also to get closer to a real perfume formulation, as was done in this work. In a four component mixture, it is necessary to define pseudoternary compositions using a solvent-free basis composition, which is performed by recalculating the ternary molar fractions of the three other components as follows: xB xA xA′ = , x B′ = , xA + x B + xC xA + x B + xC xC xC′ = xA + x B + xC (5)

the experiments (mineral oil) is a mixture of hydrocarbons. Thus, in order to estimate the solvent activity coefficients, it was considered as hexadecane, since their physical and chemical properties are similar (see Table 1). For the intensity of a mixture of PRMs with N fragrant components, there will be N different odor intensities, one for each component, to be calculated in the headspace. In order to account for the odor intensity of such mixtures, the stronger component (SC) model was used. It states that within a mixture of perceived scents in the air the odorant with the highest odor intensity will be more strongly perceived and recognized by the human nose.30,31 This model is expressed by eq 3: ψmix = max{ψi },

i = 1, ..., N

(3)

Like this, if we consider a quaternary fragrance mixture, eq 3 reduces to ψmix = max{ψA , ψB , ψC , ψS}

(4)

where the subscripts are defined in this case as follows: A geraniol, B habanolide, C iso-e-super, and S mineral oil. This SC model is an approximation to the odor intensity of mixtures of odorants and presents several advantages when compared with others like the vectorial model, U model, UPL2 model, additivity model, the equiratio mixture model, or the euclidean additivity model.27,30,31 Most of them use binary parameters that need to be obtained from experimental data (e.g., for a quaternary mixture, there are six different binary pairs for which these parameters have to be determined). The SC and euclidean models are simpler since they do not need such parameters, but even so, they perform as well as the others.25,26 Note that the SC model (as well as others) does not reflect quite common observations in olfaction (like weaker odors being able to increase or decrease the intensity of a strong odorodor enhancementor effects of hypoadditivity or hyperadditivity). It is a simple method for the prediction of odor intensities of mixtures and gives some assurance that the intensity of a mixture will not be grossly larger than the odor intensity of its strongest odorant. PTD Methodology. The concept of PTD10,32 is a combination between engineering ternary diagrams (commonly used in thermodynamics or phase separation processes) and the tripartite, pyramidal structure of a perfume suggested by J.

where xi′ is a pseudoternary composition for the corresponding fragrant component (A, B, C) in the quaternary system (A, B, C, S). So, for any composition of a mixture of PRMs, it is possible to predict the perceived odor intensity and, thus, map in the PTD the different odor zones where one PRM presents the highest odor intensity, dominating the scent over the others. Finally, it is noteworthy that in this odor perception model no interactions between the textiles and the PRMs were considered (e.g., adsorption of PRMs to the fibers and their partitioning between air and fibers). To support this premise, it was assumed that a thin film of a liquid mixture of PRMs highly dissolved in the mineral oil was placed over a textile (dry fabric) and from that point the evaporation of PRMs occurred at different rates. All calculations were computed in MATLAB software. Molecule group assignments for the UNIFAC method are shown in Table 3. For each fragrant molecule it is presented the division into groups and subgroups, the number of groups of type j in molecule I (v(i) j ); the parameters of molecular van der (i) Waals volumes (R(i) j ), and surface area (Qj ). As the solvent (mineral oil) is a mixture of paraffins, hexadecane was 967



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in the reported evaluations than with perfumery experts. Nevertheless, a good correlation was obtained between the predicted odor intensities and the evaluations from nontrained panelists (r2 = 0.70, F = 35.6, p-value < 0.0001). Again, the correlation is statistically significant, and the existence of a linear relationship (r2 = 0.70) indicates that both odor intensity scales are equivalent. Thus, it seems reasonable to assume that to the light of the model applied here for odor intensity, the evaluations performed by panelists are not so different from those of the perfumers. This shows that, in terms of quantifying odors, the olfactory mechanism presents little discrepancies (especially for higher concentrations) between perfumers and nontrained panelists, although it is known that, in terms of qualitative classification, the latter have much more difficulty to assign fragrances to words.33,34 Finally, in order to avoid getting results affected by the properties of the original sample we have performed a validation test using the jackknife procedure for the experiments with perfumers and nontrained panelists. The jackknife estimate of standard error for the reference set is determined by successively leaving one sample out. This means that applied to a sample with size N, it performs the computation of each sample statistics on N separate samples of size N − 1 (where each sample contains the original data with a single observation omitted). From the jackknife statistical analysis applied to our samples for the correlation coefficient, it was seen that the bias for this statistic is equal to −0.0044 and −0.0081 for perfumers and panelists, respectively. This means that the sample correlation is probably underestimating the true correlation by these amounts. Moreover, it was obtained a low value for the estimate of the standard error which was equal to 5.1% and 8.1% for perfumers and panelists, respectively. Consequently, it is concluded that the jackknife estimates are very consistent, indicating that our results are not biased by the influence of any sample. Therefore from the jackknife analysis alone, it is possible to say that our results are consistent and valid. Finally, from the obtained correlations with perfumers and nontrained panelists, we have also calculated the estimated error for the two validation samples (N = 16 and 17). It was observed an average error in the prediction of 14.5% (average of 19.8% and 9.3%) and 4.9% (average of 2.7% and 7.2%) for perfumers and panelists, respectively. Application of the PTD Methodology. The previous section shows the proof of concept for our model and its predictive ability for the perceived odor intensity of simple fragrance mixtures. It is possible at this point to extend its applicability to all the composition range of three PRM mixtures or even to other ternary/quaternary mixtures using the PTD methodology. Such a model would be extremely helpful for designing new fragranced products. This perfumery tool combined with the psychological power law and the stronger component model was used to predict the perceived odor of any possible mixture with the selected three PRMs and a constant amount of solvent. The obtained PTDs are presented in Figure 6 showing the map of the perceived dominant odors for any mixture of three fragrant components (the perfume concentrate, left) and for the quaternary mixtures (right) with an average molar composition of mineral oil (xS = 0.975). This composition (xS) is an average value obtained from all mixtures used in the experiments (see Table 2) which have a very narrow range (from 0.928 to 1.000). It is seen that the middle note (geraniol) and the middle-to-base note (iso-esuper) divide the left diagram into two parts, while the fixative

considered for calculation purposes and it is included in Tables 1 and 3 with its properties and UNIFAC groups. Further details on the UNIFAC method can be obtained from the literature.28

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RESULTS AND DISCUSSION Comparison between Olfactive Evaluations and the Model. One of the targets of this work was to evaluate the relationship between olfactive evaluations carried out by perfumers and the predicted odor intensity for each mixture (ψi) using the proposed model. For that purpose, the evaluations from perfumers were arithmetically averaged (four perfumers) as presented in Table 2. It should be noted that 13 out of the 17 experiments are mixtures, while the remaining refer to pure raw materials (PRMs) dissolved in mineral oil and a blank. A correlation between the perfumers’ average evaluations and the predicted maximum odor intensity values was obtained. This correlation is presented in Figure 4 together

Figure 4. Correlation between the predicted mixture odor intensity (ψ) and the arithmetic average grade from perfumers.

with the statistics obtained (r2 = 0.81, F = 62.4, p-value < 0.0001). It is seen that the correlation is statistically significant and that the coefficient of correlation between the two variables is very good, showing a strong linear relationship between perfumers’ evaluations and the maximum odor intensity (ψmix) predicted from the odor perception model. The existence of a linear relationship (r2 = 0.81) indicates that predicted odor intensities and perfumers’ olfactive evaluations are equivalent odor intensity scales. It is also seen that the two validation samples (N = 16 and 17) are well-predicted by the correlation represented in Figure 4 (squares). Furthermore, an olfactory intensity analysis was also performed by nontrained panelists at P&G. In this way, it was intended to correlate the maximum predicted odor intensity (ψi) with the olfactory evaluations performed by panelists. Each sample was rated by nontrained panelists at least 8 times (see Table 4). From these evaluations the arithmetic averages were calculated and then correlated with the predicted intensities from the odor perception model. The obtained correlation using the evaluations from nontrained panelists is shown in Figure 5. It is seen that the correlation performed with nontrained panelists is not as good as that obtained with perfumers. However, it should be emphasized that the use of a nontrained panel together with the incomplete block design used for their evaluations is likely to introduce more variability 968



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Table 4. Evaluations of the PRM Mixtures Carried out by the Panel of ConsumersReference Number (ref) and Intensity Grade (IG) sample

panelist

1

ref IG ref IG ref IG ref IG ref IG ref IG ref IG ref IG ref IG ref IG ref IG ref IG ref IG ref IG ref IG ref IG ref IG ref IG

2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17

4 7.5 2 8.7 1 2.1 8 8.9 3 4.3 1 0.6 2 4.9 2 0.3 1 0.5 1 0.9 2 1.2 4 5.3 6 3.3 4 6.7 1 0.3 3 8.1 10 6.9 3 7.3

12 4.9 9 9.6 9 4.3 16 3.3 3 5.8 3 0.4 5 0.2 5 0.1 2 2.5 4 2 12 2.5 6 6.4 7 4.4 5 1.5 7 1.1 5 3.6 22 9.4 14 4.9

20 5.6 13 7 9 9 20 2.2 7 6.9 6 3.7 6 5.4 14 0.7 4 0.4 5 1.4 13 0 6 5.1 10 5.3 7 4.5 8 2.6 18 5.5 24 2.4 15 6.1

24 4.2 13 3.9 10 6.4 20 3.1 11 3.3 9 1.9 9 0.4 19 0 7 1.6 8 5.9 14 5.8 8 6.1 15 4.1 13 2.7 11 3.2 19 2.6 27 8.2 17 5.2

25 7.6 16 4 11 8.9 21 4.9 17 1.6 11 5.1 13 0 23 2.1 10 4.8 10 1.8 14 5 8 8.2 15 5.1 16 1.2 11 1.8 20 3.6 28 5.9 26 7.1

25 3.9 23 6.2 12 6.2 22 8.5 18 5 16 0.3 15 0.8 26 0.2 14 8.2 15 10 18 1.7 12 6.8 17 3.8 16 1.5 12 0.3 22 9.8 28 7.9 29 3.3

26 7.5 26 5.4 21 5.4 25 3 23 6.5 18 2.8 18 5.5 27 0.8 17 3.6 17 2.9 19 1 24 1.4 20 1.1 19 2.1 19 0.3 25 2.5 30 5.7 29 3.6

26 9.1 28 3.8 23 5.6 27 4.6 27 6.2 21 0.4 22 4.4 29 0.1 23 8.4 28 4.3 21 1.3 24 3.8 22 6.7 21 0.3 25 4 29 4.4 30 6.3 30 4.6

30 5.1

29 0.3

average

standard deviation

6.2

1.8

6.1

2.2

6.0

2.3

4.8

2.6

5.0

1.8

1.9

1.8

2.4

2.5

0.5

0.7

3.6

2.9

2.4

1.9

5.4

2.1

4.3

1.6

2.6

2.1

1.5

1.4

5.0

2.7

6.6

2.1

5.3

1.5

28 1.8

24 3.1

27 4.9

30 0.3

since habanolide is a fixative. The odor zone for geraniol is also larger than for iso-e-super as expected for a middle and a middle-to-base note, respectively. On the other hand, a significant difference in the odor zones of the PTDs is observed when the mineral oil is introduced. It appears that when the PRMs are dissolved in mineral oil, iso-e-super tends to be more retained in the solution, and so, it is only strongly perceived at low geraniol concentrations. This prediction was in fact reported by P&G perfumers throughout their olfactory evaluations. Consequently, the PTD can be used as a tool to map the odor character as shown in Figure 6, and it can also represent the odor intensity of each PRM as a function of its concentration in the mixture. Thus, the predicted odor intensities for each PRM are shown separately in Figure 7 for the perfume concentrate as a function of the composition. It is seen that the odor intensity scales plotted on the right of the PTDs have different ranges (so that the gradient colors for odor intensity can be discriminated), especially for habanolide whose odor intensity range is very low as expected for a fixative note. It is known from perfumery that this component is not strongly perceived but has an important role when in a mixture by

Figure 5. Correlation between the predicted mixture odor intensity (ψ) and the arithmetic average grade from panelists.

(habanolide) is only strongly perceived when pure. This phenomenon was expected from the perfumery point of view 969



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Figure 6. PTDs for the ternary mixture (left) of geraniol (A, green squares) + habanolide (B, pink triangle) + iso-e-super (C, yellow circles) and quaternary mixture (right) including a fixed composition of mineral oil (xS).

Figure 7. Predicted odor intensities for each fragrance ingredient as a function of its composition in the ternary mixture: (A) geraniol, (B) habanolide, (C) iso-e-super.

retaining longer in the solution the other PRMs. Finally, it is also observed that geraniol has higher odor intensities than isoe-super for low concentrations of it (lower part of the diagram) because it is typically more volatile than the latter.

ACKNOWLEDGMENTS

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REFERENCES

This work is partially supported by project PEst-C/EQB/ LA0020/2011, financed by FEDER through COMPETE− Programa Operacional Factores de Competitividade and by FCT−Fundaçaõ para a Ciência e a Tecnologia. O.R. acknowledges financial support of Programme Ciência 2007 (FCT). M.A.T. acknowledges his Postdoc. grant from FCT (SFRH/ BPD/76645/2011).

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CONCLUSIONS Two correlations were obtained between both the perfumer average and panelist average olfactory evaluations with a predictive model for the odor intensity of fragrance mixtures. Although these use different metric scales and comparisons are not straightforward, the obtained results have shown a good agreement between our predictive model and the experimental evaluations, which are very difficult to model at this level so far. It should be noted, however, that although the applied model neglects specific fragrance−textile interactions, it is able to describe a large part of the variance from olfactory evaluations using humans. And very important from a product engineering perspective, it is a purely predictive model. In this way, it is possible to use the proposed odor perception model, which has its own metric scale for odor intensity, for comparison with the intensity rating scales obtained from perfumers or panelists. The achievements found in this work are of great relevance once the developed odor perception model can be applied for the prediction of the odor intensity of fragrance mixtures and, thus, be useful in the preformulation stages of fragrance design.

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Corresponding Author

*Phone: +351 22 508 1671. Fax: +351 22 508 1674. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 970



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Prediction Model for the Odor Intensity of Fragrance Mixtures: A

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