Ind. Eng. Chem. Res. 2004, 43, 2067-2072
2067
Stability of Emulsions from Multiwavelength Transmission Measurements Maria-Teresa Celis*,† and Luis H. Garcia-Rubio*,‡ Laboratorio FIRP (Ingenierı´a Quı´mica), Facultad de Ingenierı´a, Universidad de los Andes, Me´ rida 5101, Venezuela, and College of Marine Science, University of South Florida, St. Petersburg, Florida 33701
Droplet populations are generated from the dynamic equilibrium between the breakup and coalescence phenomena occurring during the emulsification process. Adequate estimation of the droplet size and droplet size distribution is important, not only because they are related to the manufacturing process but also because the droplet size distribution provides information of the properties of the dispersed phase and the stability of the emulsions. This paper reports on a novel spectroscopy method that provides quantitative information for the assessment of the stability of liquid-liquid emulsions. The quantitative criterion is based on measurements of droplet populations as a function of the dispersed phase concentration. This technique is applied to fresh and aged emulsions of saturated hydrocarbons and monomers. The method reported for evaluation of the stability of emulsions is easy, inexpensive, and highly reproducible. Introduction Emulsions are dispersions of droplets of one liquid in another immiscible liquid that exhibit varying levels of stability. The dispersions are achieved by mechanical and/or chemical means and typically involve the use of surfactants. The extent of the stability is tailored to the application. In most cases, the emulsions are manufactured with a specification in mind (for example, the generation of a given surface area to enhance mass transport) or a particular rheological behavior. The droplet size distribution has an important effect on the stability and other important properties of liquid-liquid emulsions; therefore, measurement of the droplet size distribution has received considerable attention.1-5 Droplet sizes can be estimated from light transmission, reflectance, and light scattering data. In the diluted regime, Mie theory can be used for the interpretation of transmission and angular scattering data. Mie theory describes the absorption and scattering behavior of spherical particles of any size and refractive index, and it has shown to be very successful in a large variety of applications.6-8 Techniques for the estimation of particle size distribution from multiwavelength spectral data have been reported in the literature.8-10 However, most of these techniques require that the shape of the particle size distribution (PSD) be known or rely on the advantages inherent in the mathematical properties of particle size distributions such as log-normal, Gaussian, etc. In addition, most measurement techniques rely on a limited number of wavelengths and do not address issues related to differences in chemical composition.10,11 The spectroscopy technique proposed herein utilizes a broad wavelength range (190-820 nm), and it is based on the regularized solution to the inverse scattering problem posed by the multiwavelength turbidity equa* To whom correspondence should be addressed. Tel.: +58274-240 2954. Fax: +58-274-240 2957. E-mail: arceliso@ intercable.net.ve (M.-T.C.);
[email protected] (L.H.G.-R.). † Universidad de los Andes. ‡ University of South Florida.
tion. As such, it does not require prior assumptions regarding the shape of the PSD.12-15 In addition, the proposed method can take into consideration changes in the chemical composition of the components involved in the emulsion (dispersed phase and emulsifier). This technique has been successfully applied to the continuous estimation of the droplet size distribution (DSD) in liquid-liquid emulsions.16-18 The aim of this paper is to assess emulsion stability on the development and implementation of the multiwavelength spectroscopy technique. The quantitative analysis is based on the determination of droplet size and DSD to emulsions of saturated hydrocarbons and monomers as a function of the dispersed phase concentration. The stability criterion is developed from the observation that, if an emulsion is diluted, the dilution ratio necessary to reduce the emulsion droplet size is directly related to the emulsion stability. In the context of this paper. the terms PSD and DSD will be used interchangeably. Proposed Method Liquid-liquid emulsions have limited stability and are known to undergo dramatic changes in the DSD as their stability decreases.19,20 When an emulsion is diluted the chemical potential changes, leading to a change in surface area which implies a change in the DSD. Therefore, if the DSD can be monitored as a function of the dilution ratio, changes in the DSD can be used as leading indicators of the stability of the emulsion. Changes in the DSD can be quantified continuously using multiwavelength transmission spectroscopy. The UV-vis spectra of particle suspensions are known to contain information on the absorption and scattering properties of the particles.9 The interpretation of the spectra can be done in terms of the PSD, the particle shape, and the chemical composition of the oil phase and emulsifier. For spherical particles, Mie theory relates the transmission, τ(λ0), measured at a given wavelength, λ0, and the normalized particle size distribution, f (D), through the following equation:7,9,21
10.1021/ie030644q CCC: $27.50 © 2004 American Chemical Society Published on Web 04/02/2004
2068 Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004
(π4)∫ Q ∞
τ(λ0) ) Np
0
2
ext(m(λ0),D)D
f (D) dD
(1)
where D is the particle diameter, Qext(m(λ0),D) corresponds to the Mie extinction coefficient, and Np is the number of particles per unit volume. Equation 1 can be written in matrix form by discretizing the integral with an appropriate quadrature approximation:22,23
τ ) Af +
(2)
where A represents the discretized kernel; f is the discrete representation of the particle size distribution; and represents experimental errors, the errors associated with the adequacy of the model, and the errors resulting from the discretization procedure.22 The regularized solution to eq 2 is given by14,15,22
ˆf (γ) ) (ATA + γH)-1ATτ
(3)
where H is a covariance matrix that essentially filters the experimental errors and the errors arising from the model adequacy and the approximations required for its numerical implementation (); γ is the regularization parameter estimated using the Generalized CrossValidation technique.15 The Generalized Cross Validation technique requires the minimization of the following objective function with respect to γ:15,22,23
|[I - A(ATA + γH)-1AT]τ|2 V(γ) ) m1 [trace[I - A(ATA + γH)-1AT]]2
(4)
where m1 represents the number of discrete turbidity measurements. Simultaneous application of eqs 3 and 4 to the turbidity spectra yields the discretized DSD. The range of integration and the width of the discretization elements are algorithmically selected to achive an optimal solution for a desired number of discretization elements. Equation 1 can be explicitly expressed in terms of the absorption and scattering components:24
τ(λ0) ) Np
(π4)∫ Q ∞
0
2 sca(m(λ0),D)D f
Np
(π4)∫ Q ∞
0
(D) dD + 2
abs(m(λ0),D)D
f (D) dD (5)
where Qsca and Qabs represent the absorption and scattering efficiencies, respectively. Equation 5 can be used to evaluate the contribution of chromophoric groups present in the emulsion, typically the emulsifier. Equations 1-5 can be used to obtain the DSD from continuous spectroscopy measurements of the emulsions as functions of time and of dilution ratio. Upon convergence, eq 5 can be used to assess the relative contributions of the absorption and scattering components and to obtain estimates of the chromophore concentrations. Experimental Section Materials. The ionic emulsifier sodium dodecyl benzene sulfonate (SDBS) was obtained from Polysciences Inc. The absence of the characteristic dip prior to the critical micellar concentration (cmc) in the surface tension versus emulsifier concentration curve indicated the purity of this material. The cmc was 1.4 ( 0.1 g/L. Surfactants BRJ78 and BRJ72 were obtained from
Imperial Chemical Industries (ICI). Styrene (CH2dCHs C6H4) was obtained from Aldrich Chemical Co. with a 99% purity. For styrene, the inhibitor was removed by using a sodium hydroxide solution (styrene/NaOH molar ratio of 3:2). Doubly distilled water, with surface tension of 72.1 mN/m and conductivity of 0.97 µΩ was used for the preparation of the emulsions. Heptadecane was obtained from Aldrich Chemical Co. with a 99% purity and was used without purification. Mineral oil was obtained from ICI with a specific gravity of 0.838. The purity of both oils was verified spectroscopically. The equipment utilized for the preparation of the emulsions consists of a 100-mL glass reactor, an electric stirrer, and a temperature controller. Preparation of the Emulsions. Emulsions of styrene/SDBS/H2O and heptadecane/SDBS/H2O were prepared using the recipe based on a 39 wt % of dispersed phase and 1.2 wt % of emulsifier. The recipe for Mineral oil/BRJ78+BRJ72/H2O emulsion preparation was based on 30 wt % of oil phase and 4 wt % of emulsifier (BRJ78: 3.2 wt % and BRJ72: 0.8 wt %) The procedure used for preparation of emulsions is summarized as follows. The necessary amount of deionized water was added to the bottom of the small reactor together with the amount required of SDBS or mixture of BRJ78 and BRJ72. The aqueous solution of emulsifier was heated to 70 °C with stirring at 300 rpm. Dispersed phase is added to this mixture under agitation. After emulsification takes place, the temperature control is turned off, and the emulsion is cooled by convection maintaining the agitation until the desired temperature has been reached. After reaching 25 °C, the stirring is stopped and the sampling is carried out. Spectroscopy Measurements. The UV-vis transmission spectra from the liquid-liquid emulsions were recorded using a diode array spectrometer (HP 8452 Hewlett-Packard, Palo Alto, CA) having an acceptance angle smaller than 20 and a thermoelectric cell holder with a temperature controller with temperature programming capabilities. All measurements were conducted at room temperature using a 1 cm path length quartz cuvette. Prior to recording the spectrum of each sample, the spectrometer was zeroed to account for any stray light. To avoid the effect of inhomogeneities in the suspending medium, the background spectrum was taken using the respective suspending media from the batch utilized in the preparation of the original sample (sterilized deionized water). Extensive replication studies,18 for a variety of stable emulsions have demonstrated that the expected standard deviation for replicate measurements is better than 0.05 Au. This value has been used to assess the spectral differences observed as functions of time diluent concentration. Scattering Calculations. The Mie scattering coefficients in eq 1 were calculated with a computer program, which includes multiwavelength spectral calculations and has been adapted to calculate distributions of particle sizes.18 This program has been extensively tested against available computer codes and published tables.24,25 The refractive index of water no(λo) in eq 2 as a function of wavelength was calculated from the correlation reported in refs 22 and 23. Estimation of Optical Properties. Equation 1 requires as input the optical properties of the constituents of the emulsion The optical properties are represented through the complex relative refractive index (m(λ0)):
Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004 2069
m(λ0) )
n(λ0) + iκ(λ0) n0(λ0)
(6)
where n(λ0) corresponds to the real component of the refractive index of the droplets, and n0(λ0) corresponds to the refractive index the suspending medium. The imaginary part of the complex refractive index of the suspended droplets is represented by κ(λ0). Saturated hydrocarbons are known to have negligible absorption in the UV-vis portion of the spectrum. The real part of the complex refractive index as a function of wavelength for hydrocarbons was calculated, using a modification of the Sellmeier-Drude correlation.18 The values of κ(λ0) for styrene were estimated from solution spectra, and the real part of the complex refractive index for the monomer n(λ0) was estimated using Kramers-Kronig transforms (see ref 18 for details). Sample Preparation. For the dilution experiments, samples were taken from the top of the reactor by means of a disposable graduated pipet, and there was a time lapse of 30 s from the time the sample was taken until the first dilution was obtained. The dispersed phase concentration after of dilution was in the range 1 × 10-5 to 10-3 g/mL. The dilutions were done directly in the quartz cuvette. Successive dilutions were accomplished using deonized water. The same dilution procedure was used for both fresh and aged emulsions. The emulsions of styrene monomer were aged for 30 h, the emulsions of heptadecane were aged for 5 days, and the emulsions of mineral oil were aged for 5 min.
Figure 1. Variation of the optical density with the wavelength for different monomer phase concentrations: (A) Fresh styrene/ SDBS/H2O emulsion. (B) Aged styrene/SDBS/H2O emulsion.
Results Figures 1-3 show the spectra of fresh and aged emulsions of styrene/SDBS/H2O, heptadecane/SDBS/ H2O, and mineral oil/BRJ72+BRJ78/H2O, respectively. Figure 1 shows the spectra obtained as function of the monomer phase concentration for the styrene/SDBS/ H2O. In the case of styrene emulsions, the region between 190 and 240 nm is saturated, and it should be ignored along with the small peaks present at 490 and 670 nm that are due to the lamp. The region between 240 and 300 nm reflects absorption due to the phenyl group in the styrene moiety, and the region between 300 and 820 nm contains primarily information on the scattering behavior of the emulsions and, therefore, on the DSD. This feature facilities direct comparison of the measured spectra to assess if there are changes in the size distribution as a function of the process conditions. Figures 2 and 3 show the variation of the optical density with the oil phase concentration for heptadecane and mineral oil emulsions. The absorption bands present between 190 and 300 nm in Figure 2 are due to the phenyl moiety present in the emulsifier (SDBS). Notice the similarity of behavior of the three emulsions in the scattering sensitive portion of the spectrum (300-820 nm). According to eq 1, the optical density is directly proportional to the number of particles or droplets and their size distribution. To eliminate the effect of the number of particles, the spectra were normalized as a function of the dispersed phase concentration. This normalization was done by dividing the measured optical density by the area under the curve corresponding to the wavelength of 300-820 nm, which is directly proportional to the total number of particles. Figure 4 shows the normalized spectra for different dispersed phase concentrations of fresh emulsions of styrene and
Figure 2. Variation of the optical density with the wavelength for different oil phase concentrations: (A) Fresh heptadecane/ SDBS/H2O emulsion. (B) Aged heptadecane/SDBS/H2O emulsion.
Figure 3. Variation of the optical density with the wavelength as function of the oil phase concentration: fresh mineral oil/ BRJ72+BRJ78/H2O emulsion.
mineral oil. As it can be appreciated from Figure 4A, the normalized spectra of styrene emulsions do not change appreciably in the region between 300 and 820 nm. This is indicative of the DSD remaining relatively constant and reflects the stability of the emulsions. The changes observed in the region between 240 and 300 nm are indicative of changes in the population of small droplets, and these should be reflected in the variance of the estimated DSD. Figure 4B shows the spectral
2070 Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004
Figure 6. Variation of the number average diameter with the dispersed phase concentration for fresh and aged emulsions using single-scattering interpretation models: (A) Heptadecane/SDBS/ H2O emulsions. (B) Styrene/SDBS/H2O emulsions. Figure 4. Normalized spectra as function of the dispersed phase concentration: (A) Styrene/SDBS/H2O emulsion. (B) Mineral oil/ BRJ72+BRJ78/H2O emulsion.
Figure 5. Measured and calculated spectra for an aged heptadecane emulsion at a given oil phase concentration (C0 ) 6E-4 g/mL) using single-scattering interpretation models.
differences typically observed as function of the oil phase concentration for mineral oil emulsions. The spectral changes can be better appreciated in the inset and are related to changes in the droplet size due to the dilution (eq 2). The presence of large droplets could be visually identified in these emulsions over time. It is evident that the spectral changes observed can be used as indicators of emulsion stability. Quantitative analysis of the spectral region between 300 and 820 nm shows the adequacy of the model (eq 1). The excellent agreement between measured and calculated spectra for fresh and aged emulsions in the spectral region where scattering dominates suggests that quantitative features of the DSD (i.e., the mean and the variance) can be used to correlate the stability of the emulsion with the size distribution. As a sample, Figure 5 shows the comparison between both spectra for the aged heptadecane emulsion at a C0 ) 6E-4 g/mL. Figures 6 and 7 show the behavior of the DSD inferred from the multiwavelength spectroscopy measurements for stable emulsions. The behavior expected for unstable emulsions is shown in Figures 8 and 9. Figure 8 shows the changes observed in the DSD as a function of the oil phase concentration (dilution ratio), and Figure 9 shows the same information summarized in terms of the mean and the standard deviation of the DSD for the mineral oil emulsions (Figure 9a) and for the heptadecane emulsions (Figure 9b).
Figure 7. (A) Variation of the number-based particle size distribution of fresh and aged emulsions of styrene using singlescattering interpretation models at monomer concentration (Cm ) 4E-4 g/mL). (B) Droplet size distribution as function of the oil phase concentration: aged emulsion of heptadecane/SDBS/H2O.
Figure 8. Droplet size distribution and droplet size as function of the oil phase concentration: mineral oil/BRJ72+BRJ78/H2O emulsion.
Discussion The characterization of the emulsion was done from spectral data using the single-scattering interpretation model and the optical properties of the dispersed phase.18 Figure 6 shows the variation of number average diameter with the dispersed phase concentration for fresh and aged emulsions of heptadecane and styrene. As is suggested by Figure 4A, the droplet size is maintained as the dispersed phase concentration de-
Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004 2071
Acknowledgment The authors thank the Imperial Chemical Industries (ICI), the University of the Andes, and the (CDCHTULA) for supporting this research. Nomenclature
Figure 9. Variation of the standard deviation of the droplet size distribution as function of the oil phase concentration using singlescattering interpretation models: (A) Mineral oil/BRJ72+BRJ78/ H2O emulsion. (B) Aged heptadecane/SDBS/H2O emulsion.
crease. This is confirmed from a plot of variation of DSD for fresh and aged emulsions of styrene at a given monomer phase concentration (Figure 7A) and from a plot of variation of the distribution as function of the oil phase concentration for aged heptadecane emulsions (Figure 7B). Notice that there is no change of the DSD with the age of the emulsion as a function of the dilution process related to changing the dispersed phase concentration for both emulsions. From the behavior observed in the droplet size and distribution for styrene and heptadecane emulsions as function of the dilution for a given age of the emulsion, it is evident that the coalescence phenomenon does not take place. Figure 8 shows the variation of the DSD with the oil phase concentration for the emulsion of mineral oil. As if can be appreciated, the breadth of the distribution increases with the dilution process, which indicates that the coalescence phenomenon takes place. It is corroborated with the variation of the number average diameter with the oil phase concentration shown in the inset. As expected, the variance of the distribution increases as droplets coalescence takes place. It is seen from a plot of standard deviation of the DSD as function of the oil phase concentration (Figure 9). As noted, the statistical parameter increases as a function of the dilution process in the mineral oil emulsion (Figure 9A) and is not affected by the dispersed phase concentration in the aged emulsion of heptadecane (Figure 9B). Therefore, the dilution ratio or the dispersed phase concentration, at which an increase in number average diameter, or an increase in standard deviation of the droplet size distribution can be used as a criterion and as a quantitative measurement of the stability of the emulsions. Conclusion A rapid technique to assess emulsion stability has been developed and verified with analyses of fresh and aged emulsions. A quantitative criterion based on measurements of the size distribution throughout a dilution process has been established. The DSDs have been obtained from multiwavelength UV-vis transmission spectroscopy, which lends itself to continuous, online monitoring strategies. The technique is reliable, simple, fast, highly reproducible, and applicable to industrial processes.
UV-vis ) ultraviolet-visible cmc ) critical micellar concentration C0 ) oil concentration calculated from dilution process Au ) absorbance units Dn ) number average diameter Cm ) monomer concentration calculated from dilution process DSD ) droplet size distribution SD ) standard deviation
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2072 Ind. Eng. Chem. Res., Vol. 43, No. 9, 2004 (18) Celis, M.-T. Studies of the Initial Conditions in Emulsion Polymerization Reactors. Ph.D. Dissertation, University of South Florida, Tampa, 2000. (19) Ande´rez, J.; Bricen˜o M.; Pe´rez, M.; Ramirez, M.; Salager, J. L. Emulsification Yield Related to Formulation and Composition Variables as Well as Stirring Energy. Rev. Te´ c. Ing. 2002, 25 (3), 129-139. (20) Ma´rquez, L.; Mirra, I.; Pen˜a, A.; Tyrode, E.; Salager, J. L. Principles of Emulsion Formulation Engineering. In Adsorption and Aggregation of Surfactants in Solution; Mittal, K. L., Shah, D. O., Eds.; Marcel Dekker: New York, 2003. (21) Glatter, O.; Hofer, M. Interpretation of Elastic Light Scattering Data. J. Colloid Interface Sci. 1988, 122 (2), 496-506. (22) Elicabe, G.; Garcia-Rubio, L. H. Latex Particle Size Distribution from Turbidimetry Using Inversion Techniques. J. Colloid Interface Sci. 1988, 129 (1), 192-200.
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Received for review August 4, 2003 Revised manuscript received January 27, 2004 Accepted January 27, 2004 IE030644Q
