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J. Phys. Chem. B 2009, 113, 3894–3900
Phase Diagram Approach to Evaporation from Emulsions with n Oil Compounds† Stig E. Friberg* Chemistry Department, Southeast Missouri State UniVersity, Cape Girardeau, Missouri 63701 ReceiVed: June 26, 2008; ReVised Manuscript ReceiVed: December 3, 2008
The initial evaporation path was calculated for an emulsion of water and a multicomponent oil phase under the following conditions. The computations were based on the phase diagram of the emulsion system combined with an algebraic system to extract information from phase diagrams to facilitate the mathematical treatment. An inherent consequence of the use of the phase diagram as a basis to calculate an evaporation path is the condition of equilibrium between the phases in the emulsion as well as between the vapor and the condensed phases. In addition to this fundamental limitation, the features of the phase diagram of the actual emulsion were restricted as follows. There is no solubility of significance in the water of either the oil or of the surfactant. The nonaqueous compounds display extensive mutual solubility with the solutions being close to ideal. This solution of the nonaqueous compounds does not dissolve nor solubilize water to a degree to affect the calculations in the stage of evaporation treated; an emulsion in the two-phase region of lowest surfactant content. Introduction The evaporation of emulsions is an essential feature with a huge number of industrial applications,1,2 and among the myriad of these may be mentioned the use of emulsions as vehicles to prepare solid particles.3 This area has become one of the most active with a rich literature on the preparation of particles of different kinds; especially nanoparticles.4-8 Recent emphasis on a combination of emulsion and solvent evaporation9,10 has opened new avenues to create materials with complex structures. Among the specific commercial applications of emulsion evaporation, the area of general cosmetics may be mentioned11 and especially fragrance emulsions.12,13All these applications have given the impetus to extensive fundamental research on the evaporation process of emulsions, especially in two-phase emulsions. Over the past decade the University of Hull in the United Kingdom have been the leading institution in the area, investigating basic aspects of evaporation from a variety of emulsions14-17 and microemulsions.18 One key insight obtained into emulsion evaporation was that the evaporation from the dispersed drops proceeds by dissolution of the dispersed compound into the continuous phase followed by diffusion into the thin water film present at the emulsion surface and release into the vapor. The oil drops do not break through into the emulsion surface prior to evaporation.14,15 The composition of these emulsions was chosen with surfactant concentration at a sufficiently low level to ensure the two-phase state to be retained during the evaporation. Most evaporation of commercially essential emulsions is from a thin layer on a solid surface and the surface properties could potentially have a substantial effect on the emulsion behavior during the process. The investigation by Kapilashrami et al.19 brought to light the distinct difference between evaporating on hydrophilic versus hydrophobic surfaces. The latter surface caused destabilization of the emulsion in contrast to the effect of the former.This research was restricted to the behavior of two-phase emulsions. However,early investigations indicated †
Part of the “PGG (Pierre-Gilles de Gennes) Memorial Issue”.
evaporation from emulsions to involve additional factors to the fundamental diffusion/evaporation combination. Seattone et al.20 measured electrical impedance of thin layers (0.1 mm) of O/W emulsions during evaporation at constant air temperature (25 °C) and relative humidity (55%). The measured impedance of the emulsion layers increased by 3 orders of magnitude during the evaporation cycles. The logarithm of the electric impedance versus water content gave several linear portions in the graph indicating evaporation to proceed via distinct stages; potentially including phase changes. This deduction led Friberg et al. to determine the phases appearing during the evaporation under ambient conditions of a simple 2-phase emulsion21 finding radical phase changes to occur. This result was considered significant, considering the fact that the evaporation from phases with different structures has been shown to be substantially dissimilar22 and resulted in later research into the colloid structures in the evaporation process from emulsions. The research in the latter area used the results from determinations of vapor pressure at selected sites in the phase diagram23 to predict the vapor pressure of phenethyl alcohol versus emulsion weight during evaporation. The investigation evaded the problem of the equilibrium condition by the use of a system in which the vapor pressure of the volatile was vanishingly small in comparison with that of water, resulting in an unambiguous evaporation path. Hence, the predicted values agreed excellently with measured ones.24 It is vital to emphasize that the information in this special case is accurate as far as the evaporation path is concerned, but leaves no information about the evaporation rate.14-19,25 Even with this restriction duly considered, these investigations found the combination of phase diagrams and the algebraic system to extract information from them26,27 to be useful to delineate the evaporation path in emulsion systems. The approach is attractive, because it offers information about potential phase changes during the process, essential information regarding the different evaporation rates from different phases.22 However, a serious drawback of the approach is the fact that the phase diagram per se leaves information solely on equilib-
10.1021/jp8056338 CCC: $40.75 2009 American Chemical Society Published on Web 02/09/2009
Evaporation from Emulsions with n Oil Compounds rium conditions, while evaporation is kinetically monitored, as has been amply demonstrated.14-19,25 On the other hand, even tentative knowledge about potential phase changes is essential,22 and the phase diagram method has subsequently been applied to emulsions with a volatile compound as the oil phase. With the qualification of the equilibrium condition, the results revealed a potentially decisive effect on the evaporation direction of initial water content28 as well as a consequence of the relative humidity. Recently ternary diagrams of a different nature have been developed for liquid solutions of three fragrance compounds and a solvent base.29-31 The diagrams are established using a diffusion model to simulate the evaporation of a small amount of perfume as function of time and space giving the composition of both the liquid phase as well the headspace including the effect of nonideality. The approach provides an estimation of all the performance parameters and will have a decisive impact on the formulation of solutions of fragrances in the future. However attractive the approach is to extract and extend information from graphic representation of phase diagrams of different kinds, its limitation is palpable. A graphic representation of a complete phase diagram cannot be extended to more than a total of four components using the three available dimensions. This fact severely restricts the application of the method and excludes a number of commercially essential emulsion systems. The algebraic approach,26,27 to its advantage, does not have this limitation. With this in mind, the goal of the present contribution is to change the assessment of the algebraic approach from being perceived as an aide in the interpretation of graphic phase diagrams but instead extending the phase diagram approach to the realm outside of graphic representations. In the following narrative, the fundamentals are delineated for treating the evaporation from a system of an arbitrary number of volatile compounds in the oil phase. The evaluation is based on restrictions on the mutual solubilities involved as well as the overriding constraint of a system in equilibrium. Fundamentals As emphasized, the phase diagram of an emulsion system with a number of oil components greater than two cannot be visualized graphically, but the example given in the Appendix may be useful to illustrate some of the phenomena in such a system. The present system contains, in addition to water (W) and a single surfactant (S), a number n of volatile oil compounds, H1-Hn, all virtually insoluble in water but with complete mutual and ideal solubility. The surfactant is not soluble in water but, when combined with it, forms a lamellar liquid crystal for concentrations in excess of the lowest association concentration in water, lac, which has an extremely small value; several magnitudes less than the traditional cmc values. The lac is, hence, sufficiently minute for the chemical potential of water in the aqueous phase not significantly to deviate from the value of pure water. Furthermore, the solubility of water in the oil phase is sufficiently small to be neglected, while there are no restrictions on the solubility of the surfactant in that phase. The composition of the total emulsion in weight fractions of the compounds is (WE, SE, H1E,..., HnE), that of the aqueous phase, Aq, (1, 0, 0,..., 0), of the oil phase, Oi, (SOi, H1Oi,..., HnOi), and of the liquid crystal phase, LC, (WLC, SLC, H1LC,..., HnLC). The corresponding weights are given as lower case letters, and also for these, the subscripts indicate the location in the
J. Phys. Chem. B, Vol. 113, No. 12, 2009 3895 phase diagram; as an example, SOi means the weight of surfactant in the oil phase. (The WAq would, of course, be equal to 1 for the emulsion in question, but WAq varies with the evaporation.) The composition of the oil phase, (SOi, H1Oi,..., HnOi), is directly obtained by extrapolation of a line from (1, 0, 0, 0,..., 0) through (WE, SE, H1E,..., HnE) to W ) 0.
XOi)XE(W - 1)/(WE - 1)
(1)
in which X is S or Hν. Hence,
SOi)SE /(1 - WE)
(2)
HνOi ) HνE /(1 - WE)
(3)
The oil phase liquid is presupposed as an ideal solution based on earlier determinations of vapor pressures;12,13 hence, the vapor pressures of the individual oil compounds are n
∑ (HνOi/MHν)]
PHν ) P0HνHνOi /MHν[(SE /MS) +
(4)
ν)1
in which the Mν values are the molecular weights. The summation over ν goes from 1 to n and superscript 0 indicates the property of the pure compound. The water vapor pressure is constant and equal to the pressure for pure water PW ) P0W. The weight fractions of the volatile compounds in the vapor are n
Wv ) P0WMw /(P0WMw +
∑ PHνMHν)
(5)
ν)1 n
Hνv ) PHνMHν /(P0WMw +
∑ PHνMHν)
(6)
ν)1
These are the weight fractions of volatile components in the vapor, nota bene, in the entire gas phase into which the evaporation occurs and which, furthermore, is in equilibrium with the condensed phases. The composition of the vapor leaving the emulsion is different, since the process takes place against an atmosphere with a relative humidity, RH%. The apparent vapor pressure of the evaporating water is P0W (1 0.01RH), and in the numerical calculations, eqs 5 and 6 are modified to reflect the water vapor pressure in the vapor departing the emulsion. The actual computations are made stepwise by reducing the water weight in the emulsion by a constant amount, KW in each calculation step. This specific process has the advantage of enabling the report of the evaporation path to be perceived also to describe the time dependence, since the water vapor pressure is constant during the analyzed part of the evaporation process. With KW being the amount of water evaporated within a certain time lapse the corresponding weight of the oil compounds is directly obtained
KHν ) KWHνv/Wv
(7)
In this equation, Hνv is the value of eq 6 corrected for the influence of the relative humidity; i.e. the fraction fragrance compound in the exiting vapor. With the new weights of water and oil compounds calculated the total weight of the emulsion is computed and with it the values for W, S, and H. A new evaporation step is initiated, and the entire evaporation path is gradually established.
3896 J. Phys. Chem. B, Vol. 113, No. 12, 2009
Friberg
The composition after each step is tested against the location of the limit for the original 2-phase volume, Figure A1, because exceeding this limit means entering a 3-phase space, Figure A3. This phase change composition is defined by the value of the M , at which the equilibrium changes from surfactant fraction, SOi the aqueous/oil phase two-phase state to the three-phase aqueous/oil/liquid crystal phase condition with increasing surM is calculated from the linear relationship factant fraction. SOi n
M SOi )
∑
ν)1
n
ν SOi HνOi
/∑
HνOi
(8)
ν)1
n ν j νOi * 1 and SOi in which ∑ν)1 H is the value of S at point at which a system of only one oil component ν the equilibrium changes from two to three phases. This value is compared to the value of SOi acquired from eq M , the composition has entered the 3-phase realm. 2. If SOi > SOi Equation 8 is an approximation assuming linear variation of M j νOi. This relation was adopted from empirical results with H SOi of phase diagrams with limited number of oil compounds. In the following section, the approach is applied to numerical calculations of the evaporation path in a system of water, surfactant, and three oil compounds: linalool, geraniol, and geranyl acetate. Professor Abeer Al-Bawab, Chemistry Department, University of Jordan, kindly provided the necessary numbers of the composition of the phases included in the computation.
M Figure 1. Space in the system for W ) 0: (A) (0, SOi (L), LM, 0, 0); M M (G), 0, GM, 0); (C) (0, SOi (GA), 0, 0, GAM); (A1) essential (B) (0, SOi features in the phase diagram of water (W), surfactant (S), and two mutually soluble oil compounds, H1 and H2 with restrictions according to the investigated emulsion.
Numerical Example The algebraic system permits the details of the evaporation path to be offered in a large number of different manners.27 In the following the results are presented versus time or emulsion weight, since these are experimentally the most easily available. The preference for one of the two was decided considering to what extent the mode of presentation could also reflect more fundamental features of the process. The section presents the changes in the amount of the two phases involved, it gives the variation of the composition of the oil phase, it relates those changes to the vapor pressure values, and it demonstrates the significant influence by the relative humidity on the direction of the evaporation path. The system32 consists of water, a commercial surfactant, Laureth 4 (mostly C12EO4), geraniol, linalool, and geranyl acetate. In the features of interest, it should be noted that the space of the oil liquid does not exactly coincide with the W ) 0 section of the diagram (Table 1). Nonetheless, the difference between the approximate and exact values was truly insignificant for the numerical computations, and the approximate algebraic expressions were applied. The vapor pressures in millimeters of Hg were calculated from the values for the pure substances geraniol (G) ) 0.04888; geranyl acetate (GA) ) 0.03810; and linalool (L) ) 0.3874 from the Handbook of Chemistry and Physics. Although the complete diagram for the system cannot be graphically displayed, it is feasible and useful to present a diagram illustrating the limit for the system to remain in the initial two-phase space. Since the approximation W ) 0 for the oil phase was well justified, Table 1, a three- dimensional diagram of the oil phase per se is possible and is displayed in Figure 1. The two-phase state of the emulsion is distinguished by the composition of the oil phase falling within the space A, B, C, L, GA, and G in Figure 1. Hence, the value of SOi, as defined by eq 2, should be located between the plane A, B, C (A ) (0,
Figure 2. Weights (open symbols) and weight fractions (filled symbols) of the aqueous (squares) and the oil phase (triangles) during evaporation in the primary two-phase space. Relative humidity: 60%.
TABLE 1: Equilibrium Compositions in Weight Fractions for the Three-Phase Part of the System of Lowest Surfactant Content oil phase
liquid crystal phase
compound
W
S
X
W
S
X
linalool geraniol geranyl acetate
0 0.03 0
0.37 0.34 0.181
0.63 0.63 0.819
0.51 0.40 0.713
0.45 0.49 0.269
0.04 0.11 0.018
M M M M SM Oi(L), L , 0, 0), B ) (0. SOi(G), 0, G , 0), and C ) (0, SOi(GA), 0, 0, GAM)) and plane L ) (0, 0, 1, 0, 0), GA ) (0, 0, 0, 0, 1), and G ) (0, 0, 0, 1, 0) in Figure 1. The significance of the superscript M has been given in the Fundamentals section. The coordinates for the plane dividing the two-phase space from the three-phase section are found in Table 1, and the equation for the plane becomes.
SOi ) 0.34G¯Oi + 0.181GAOi + 0.37L¯Oi
(10)
in which SOi means the surfactant fraction in the plane, while the fractions with a single overline mean the coordinates according to eq 3 but with the added condition
XOi ) XOi /
∑ XOi
(11)
in which the sum is over the volatile oil components only. Consequently, the condition for a 2-phase emulsion with pure water as the aqueous phase is now established
Evaporation from Emulsions with n Oil Compounds
J. Phys. Chem. B, Vol. 113, No. 12, 2009 3897
Figure 3. Weights (left) and weight fractions (right) of the individual fragrance compounds in the oil phase versus the weight of evaporated water. The abscissa may also be read as time: (filled circles) linalool; (filled squares) geraniol; (open triangles) geranyl acetate.
SOi[eq(2)] > SOi[eq(10)]
(12)
The initial composition in weight fractions of the emulsions was identical (0.60, 0.05, 0.10, 0.10, 0.10), and in this introductory contribution, the evaporation was restricted to the initial 2-phase emulsions and discontinued, when the composition reached the limit for this space. The effect of relative humidity was exemplified by evaporating the emulsion against an atmosphere of 60 and 85% relative humidity. The approach of combining information from the phase diagrams with the algebraic system permits the depiction of details of the emulsion, such as its phases and the composition of the total emulsion as well as that of the individual compounds within each phase as function of any of them as variable. A suitable illustration of that versatility is the corollary of the fact that the emulsion for the calculations was specifically chosen to retain a constant water vapor pressure during the involved period of evaporation. As a result, the weight loss of the water is also a measure of time and this fact has been used in Figure 2 to illustrate the weights and weight fractions of the two phases versus time. The weight of the aqueous phase varies linearly with time, of course, because of the constant vapor pressure of the medium, but the weight fraction versus time is far from linear, Figure 2, with a rapid decline of the fraction aqueous phase during the last time period of the evaporation. The weight of the oil phase also deviate from linearity, because the vapor pressure changes during the evaporation and the surfactant weight in the oil phase remains invariant. The distinction between the curves for weights and weight fractions may be seen as a trivial algebraic detail, but the general distinction is in fact of critical importance for the commercial application of formulations. As an example may be sited, the variation of the composition of the oil phase. The variation in weights versus the weight of evaporated water of the oil compounds is displayed in Figure 3 left, and the numbers for weight fractions are displayed in the right in the diagram. The change from the plot versus weight, Figure 3 left, to the one versus weight fraction, right, introduces a most essential feature. The weights of all the compounds all decrease, since all compounds do evaporate, but counted as weight fractions, instead an increase is found for the geraniol and the geranyl acetate. The consequence of this feature is obvious; the vapor pressure of the two latter compounds should increase instead of being reduced with time, while a reduction of the linalool pressure is expected. This conclusion is corroborated by the actual values shown in Figure 4.
Figure 4. Vapor pressures (mmHg) of the individual fragrance compounds in the oil phase versus the weight of evaporated water. The abscissa may also be read as time (The geraniol and geranyl acetate pressures are multiplied by a factor of 10 to make the diagram more illustrative.): (filled circles) linalool; (filled squares) geraniol; (open triangles) geranyl acetate.
The contrast between the vapor pressure change of linalool and two remaining compounds is notable; the linalool pressure is reduced by approximately 50%, while that of the geraniol and geranyl acetate is increased by half-that amount. These differences are of real significance for the application of formulations of this kind. The final factor to be treated is the effect of the relative humidity on the evaporation path per se. This feature is exposed by a comparison of the evaporation path versus the emulsion weight. The relative humidity was increased from 60% to 85%, and the variation in the emulsion total composition is compared in Figure 5. The difference in the water fraction is the expected one; the evaporation of water is faster at 60% RH, and the water fraction versus emulsion weight is more rapidly reduced for this relative humidity. However, the relative humidity also has an influence on the variation with emulsion weight of the weight fractions of the fragrance compounds. The smaller emulsion content of water at 60% relative humidity causes the weight fraction of each of the fragrance compounds to be at a higher level than the corresponding numbers for 85%. However, it is vital to realize that the weight fractions of the compounds as counted on the total emulsion are of essence only for specific applications, such as stationary entities, for which potential phase changes may influence the behavior.22 For other applications such as personal care the change with time of the
3898 J. Phys. Chem. B, Vol. 113, No. 12, 2009
Figure 5. Weight fractions of individual compounds counted on the entire emulsion (On the scale used, the difference between the values for geraniol and geranyl acetate was not visible and only the numbers for geraniol are displayed.): (diamonds) water; (squares) geraniol; (circles) linalool; (filled symbols) 85% RH; (open symbols) 60% RH.
Figure 6. Vapor pressures in millimeters of Hg of linalool (circles), geraniol (squares), and geranyl acetate (triangles) versus time for the two relative humidities in the investigation: (filled symbols) 85% RH; (open symbols) 60% RH.
vapor pressure is the more vital feature. With this in mind the versatility of the algebraic approach was used to attain information about the vapor pressures versus time. In Figure 6, the slower evaporation rate at 85% relative humidity is compensated leaving the time scale comparable. The results disclose the true effect of the relative humidity from an application point of view. The faster evaporation of water at 60% relative humidity does not modify the vapor pressure variation with time; the effect is to shorten the active time of evaporation from the two-phase branch of the emulsion. In the present contribution, only this time is explored; the effect on the continued evaporation in the three-phase region and more concentrated sections of the emulsion is at present investigated. Discussion Prior to discussing the results per se and their implication, it is vital to summarize the limitations and advantages of the phase diagram approach to describe the evaporation process from an emulsion. The most obvious restriction is the fact that the estimations are based on equilibrium between the condensed phases as well as between them and the vapor. As shown by Fletcher and Binks,14-19 the ratio of evaporation rates of the compoundsfrom the continuous and dispersed phases may be far from those expected from the vapor pressures under equilibrium conditions. Finally, being aninterpretation based on
Friberg static equilibrium conditions, information about time factors is not a priori available. This last restriction is generally valid, but an estimation is possible about the time dependence of the evaporation for specific systems. An example is the present emulsion, in which the vapor pressure of the water is constant. In general, the approach is applicable without limitations to the large number of emulsions, in which the water is the only volatile compound. For these, the phase diagram provides complete knowledge about phases disappearing and new phases formed during evaporation and will in addition offer some indication as to potential inversions and similar modifications of the emulsion configuration. In the same manner, the approach is valid without restrictions to the case in which the evaporation path has been experimentally determined. Now the phase diagram approach gives information about the continuous variation in the composition of the vapor during evaporation under the specific experimental conditions. If the vapor pressures are sufficiently small to make the ideal gas law valid, information about the thermodynamics of the exiting vapor is available and also about the atmosphere into which the evaporation occurs, if the relative humidity is known. However, these values leave no information about the thermodynamics of the condensed phases. For the cases in which both the water and the oils are volatile, the fact that the phase diagram approach inherently assumes equilibrium must be respected. As a consequence the system offers information about the evaporation path only as a result of an extrapolation into equilibrium of the system and the deductions about phase changes must be considered in this light. However, even information about potential appearance and disappearance of phases is of value and merits some consideration. Without the phase diagram, results from the kinetics of evaporation20 would not be amenable to interpretation. It is worth mentioning that phase changes during evaporation are not only of importance for the evaporation rate;20 they may in fact have a decisive effect on the application performance per se of an emulsion in several applications. As a case in point may be cited emulsions within personal care, in which the action of an active substance may critically depend on the phase into which it is dissolved or solubilized. A phase change may alter the chemical potential in a most pronounced manner and affecting the tendency to penetrate the stratum corneum, as illustrated by the difference in the behavior of two hydroxy acids, salicylic, and tartaric acids during evaporation of two identical emulsions.33 In the emulsion with salicylic acid, the composition of the involved emulsion phases is unchanged for 99% evaporation of the water, while in the tartaric acid system evaporation of even 50% of the water leads to a concentration increase of tartaric acid in the aqueous solution from 5% to 50%. The effect on the skin of the latter change warrants consideration. Another consequence of the approach on the phase conditions is the fact that it offers a convenient means to select the truly essential features of the system for immediate evaluation. The present contribution offers an illustrative example in the difference between the variation in the total composition of the emulsion, which is experimentally easy to attain, and the composition of the individual phases, (which experimentally requires extensive separation efforts in addition to the analysis). A comparison of the information in Figures 5 and 6 brings attention to this fact. Conclusions The algebraic system for extraction of information from phase diagrams was applied to evaporation from emulsions with a large
Evaporation from Emulsions with n Oil Compounds
Figure A1. Essential features in the phase diagram of water (W), surfactant (S), and two mutually soluble oil compounds, H1 and H2, with restrictions according to the investigated emulsion.
J. Phys. Chem. B, Vol. 113, No. 12, 2009 3899 the liquid solution of the oils and surfactant. Figure A2 displays the area of this solution for the system with two oils and gives an example of a tie line connecting it with the aqueous phase. In it the limit A to B is approximated with a straight line, which in the algebraic treatment of the case with n oil components is expressed as a linear equation of first order. Exceeding the surfactant fraction limit of the two-phase region, a three-phase space is found. It is depicted in Figure A3. Since the diagram describes a system of four compounds, the three-phase space has one degree of freedom. However, the interdependence of the equilibrium composition of the oil and liquid crystal phases should be noticed, being a consequence of the fact that none of the compounds has a solubility in water of any significance. References and Notes
Figure A2. Equilibrium between the aqueous phase and points in the oil solution area (striped).
Figure A3. Three-phase equilibrium between the aqueous phase (W), the oil phase (A-B), and the liquid crystal phase (C-D).
number of oil compounds but with limitations on the solubility of the surfactant and the oil compounds in the water. With the vapor pressure of the water invariant with the emulsion composition in the investigated part of the system, an evaluation of the relative time dependence of the evaporation path could be made for the case of equilibrium between the phases and between them and the vapor. Appendix As mentioned in the narrative, a complete graphic representation of a phase diagram is not possible for more than four components, and the analysis in the text has with necessity been limited to the algebraic version. However, the graphics for a system of water, surfactant, and two oil compounds may be useful to visualize the algebra in the text. Figure A1 gives an overview of the part of such a diagram that is essential for the present publication. In the figure, the areas for the liquid crystal phase are given as two separate regions for oil H1 and H2. In reality the space for the liquid crystal is continuous throughout the diagram, but the present arrangement made for improved overview of the conditions. The phenomena in the present contribution are concerned with the two-phase region, in which the water is in equilibrium with
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