Anal. Chem. 2003, 75, 6958-6962
Characterization of Pigment Particle Absorption Efficiencies Using Frequency Domain Photon Migration Yingqing Huang and Eva M. Sevick-Muraca*
Photon Migration Laboratories, Texas A&M University, TAMU 3573, College Station, Texas 77843-3573
Time-dependent measurements of multiply scattered light were made using frequency domain photon migration (FDPM) techniques in polystyrene latex as a function of ppm pigment concentration (by weight) in order to determine the wavelength-dependent absorption efficiencies for three different pigment particles. The results demonstrate that the absorption spectra of pigment particles within their dispersing vehicles concur with the complementary color chart. FDPM offers a first-principles method for assessing optical characteristics of pigments within their dispersing vehicles and without the need to resort to conventional measurement of diffuse reflectance from coatings and data analysis using phenomenological theory. Gloss and color are important product attributes in the textile and automobile industries and are key performance properties for printing ink, cosmetics, hair dyes, and many other products. Pigments, which refer to insoluble colorants, determine the color of paints and numerous plastic products through their optical properties of scattering and absorption. Light scattered outwardly from the particle changes the direction of light propagation, whereas light scattered inward into the particle can result in light absorption. The color of coatings is mainly determined by the wavelength-dependent light absorption efficiency of pigments, while the gloss of coating is typically related to scattering properties. Color matching, which guarantees agreement of color feature with the designed pattern of products and ensures uniformity among products in massive production, requires accurate measurements of absorption and scattering properties of pigments. An understanding of light interaction with pigment particles is paramount in the coatings industry and is conventionally described through the phenomenological Kubelka-Munk (KM) theory.1 In K-M theory, the scattering coefficient, S(λ), and absorption coefficient, K(λ), which are used to describe optical properties of coating layers, reflect the percentage loss of the forwardly propagated radiation per unit distance due to media scattering and absorption, respectively. Since K-M theory treats dispersions as continuous uniform media, K(λ) and S(λ) cannot be related through first principles to the physical properties of pigment particles and their dispersing vehicles. The “dispersion * Corresponding author. Tel: (979) 485-3206. Fax: (979) 485-1011. E-mail:
[email protected]. (1) Kubelka, P.; Munk, F. Z. Tech. Phys. 1931, 12, 593-601.
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vehicle” is a widely accepted nomenclature in the pigments and paints industry. It refers to a dilution medium, usually a polymer dispersion, in which a suitable amount of pigment and other additives are added and homogenized in formulating paint and pigment products. The formulated dispersion containing pigments and other additives is then applied to substrate to form a coating layer for testing pigments. Since the dilution dispersion is the medium that delivers pigments to a coating application, it is called the “vehicle”. To determine the absorption and scattering properties from pigments using conventional K-M theory, one needs to first disperse pigments in suitable dispersing vehicles and then coat the dispersions on standard substrates. The value of K(λ) and S(λ) can then be evaluated from measured reflectance with suitable empirical correction,2,3 and measurements repeated as a function of pigment concentration enable distinction of the pigment scattering and absorption from that arising from the dispersing vehicle. While the measurements of diffuse reflectance can be easily reproduced within the same laboratory, one cannot guarantee reproducibility from one laboratory to another.4 Consequently, comparison of optical properties of pigments between laboratories usually requires a third commonly accepted pigment as reference. Previous work has been accomplished to obtain pigment physical properties though measured phenomenological scattering and absorption data in order to improve efficiencies in paints formulation. Billmeyer et al. reported an approach to estimate the complex refractive index of pigment.5 They measured angledependent (14°-166°) scattering intensity of dilute pigment dispersions in order to obtain scattering phase function P(θ), which when fitted against Mie theory prediction provided the complex refractive index of pigment particles. The time-consuming method requires extrapolation of scattering intensity in forward and backward directions in dilute pigment suspensions (10-4% by volume). Vargas and Niklasson6 reported a method based on fourflux theory in order to extract complex refractive index and mass density of pigments from reflectance and transmittance measurements of pigment coating layers. Unfortunately, since they (2) Saunderson, J. L. J. Opt. Soc. Am. 1942, 32, 727-736. (3) Marcus, R. T.; Pierce, P. E. Prog. Org. Coating 1994, 23, 239-264. (4) Vo ¨lz, H. G. Industrial Color Testing: Fundamentals and Techniques, 2nd ed.; Wiley-VCH: Weinheim, 2001. (5) Billmeyer, F. W.; Chassaigne, P. G.; Dubois, J. F. Color Res. Appl. 1980, 5 (2), 108-112. (6) Vargas, W. E.; Niklasson, G. A. J. Phys. Condes. Matter 1997, 9, 16611670. 10.1021/ac0346353 CCC: $25.00
© 2003 American Chemical Society Published on Web 11/06/2003
change of scattering power without influencing the absorption capacity of the suspension. As a result, the absorption efficiency of a dispersion, µa (cm-1), varies linearly with its particle volume concentration (PVC), φ:12
µa ) φµa,p + (1 - φ)R
Figure 1. Methodology of FDPM measurements.
neglected interference effects owing to correlated particle positions that impact scattering efficiency, their approach may result in a misprediction of particle absorption efficiency. Frequency domain photon migration (FDPM) techniques enable accurate determination of the optical properties of a multiple scattering medium.7-9 Briefly, FDPM involves launching intensity-modulated light through a fiber optic into a multiply scattering medium. The amplitude of the “photon density wave” will attenuate and will be phase-shifted as the wave travels within the medium away from its source (Figure 1). Another fiber optic is used to collect the photon density wave and direct it to a detector. In this study, the distance of the collecting fiber from the source fiber was adjusted using a computer controlled motion device (ESP 300 Motion Controller, NewPort, CA). Upon detecting the phase shift and amplitude attenuation as a function of distance away from the source and upon fitting the measured data to the diffusion equation describing the propagation of multiply scattered light, accurate measurement of the isotropic scattering coefficient, µs′ and absorption coefficient, µa, can be simultaneously obtained.8,9 The total absorption of a scattering medium is attributable to both the particles and the suspending fluid. The well-known interference approximation10,11 in physics states that, in dense suspensions, (i) the incident electric fields and (ii) the resultant scattered fields from closely positioned, individual particles are not impacted by their nearest neighbor. Instead, the interference of scattered light from closely positioned particles adds up destructively or constructively in the far field and results in a (7) Sevick, E. M.; Chance, B.; Leigh, J.; Nioka, S.; Maris, M. Anal. Biochem. 1991, 195 (2) , 330-351. (8) Fishkin, J. B.; So, P. T. C.; Cerussi, A. E.; Fantini, S.; Franceschini, M. A.; Gratton, E. Appl. Opt. 1995, 34 (7), 1143-1155. (9) Sun, Z.; Huang, Y.; Sevick-Muraca, E. M. Rev. Sci. Instrum. 2002, 73 (2), 383-393. (10) Vrij, A.; Nieuwenhuis, E. A.; Fijnaut, H. M.; Agterof, W. G. M. Faraday Discuss. 1978, 65, 101-113. (11) Dick, V. P.; Ivanov, A. P. J. Opt. Soc. Am. A 1999, 16 (5), 1034-1038.
(1)
where absorption coefficient of suspending fluid, R, can be related to the imaginary refractive index of the medium, n′′, and the wavelength, λ, by R ) 4πn′′/λ. The term µa,p is the volume-based averaged absorption efficiency over all particles in the suspension. The value of µa,p can be calculated from µa,p ) 1/φ ∑iNicabs,i, where Ni and cabs,i are respectively the number density and the absorption cross section of particle species i in the suspension. The absorption cross section, cabs,i, can be calculated from the particle size, shape, and refractive indices of particle and suspending fluid using Mie theory. Upon measuring µa at varying PVC, φ, one can obtain the absorption efficiencies of both particles and suspending fluid via least-squares linear regression analysis.12 In this work, we demonstrate measurement of particle absorption efficiencies of three different pigments dispersed in multiply scattered polystyrene latex using FDPM measurement of absorption. MATERIALS AND METHODS Samples. Three different water-dispersed pigments: Phthalo Green (CI 74260), AAA Diarylide Yellow (CI 21090), and Naphthol Red (CI 12315), were obtained from the Riotech Corp. (Reading, PA). The pigments concentrations were used as received [∼45% (in weight)] and diluted in water. Polystyrene latex of size 226 ( 43 nm (measured by Zetasizer 3000 HS, Malvern Instrument) was obtained from Dow Chemical (Midland, IL) and used as a dispersing vehicle for the pigments. To remove surfactant and salt, the polystyrene latex was dialyzed (Spectra/Pro: MWCO 6-8000, Spectrum Laboratories Inc., Rancho Dominguez, CA) using ultrafiltered-deionized water until the conductivity of equivalent dialyzing water was less than 6 ppm NaCl equivalent measured using a titration controller (Accumet model 150, Fisher). The dialyzed polystyrene latex was then conditioned to the NaCl concentration of 120 mM by adding 2 M NaCl solution (S1240, Spectrum Chemical Mfg. Corp., Gardena, CA). The conditioned polystyrene latex was then diluted using 120 mM NaCl solution to the desired particle volume fraction. The particle volume fraction was measured using the evaporation method, which simply involved weighting polystyrene sample using a 1/10 000g resolution balance (Denver Instrument M-220D, Fisher) before and after drying in an oven at 90 °C for 8 h. FDPM Measurements. Seven wavelengths were used for FDPM measurements of absorption and isotropic scattering coefficients of each dispersion. An argon-krypton gas discharge laser (643 R-AR-A01, Melles-Griot Laser Group, Carlsbad, CA) provided light at wavelengths of 488, 514, and 568 nm, and laser diodes (Thorlabs) provided light at the wavelengths of 650, 687, 785, and 828 nm. At each of the wavelengths at 650 nm or lower, a corresponding band-pass filter, which only allows the light within a narrow region ((3-10 nm) about the light source to pass through, was positioned at the photon detector to remove potential fluorescence from the polystyrene particles. Measurements were (12) Huang Y.; Sevick-Muraca E. M. Appl. Opt., in press.
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conducted according to the methods outlined elsewhere,9 with the exception that laser diode modulation was accomplished directly through the application of an rf signal through a bias tee on the laser diode driving current; and continuous wave light from the gas discharge laser was externally modulated using an acoustooptical modulator.13 For each dispersion, FDPM measurements were conducted three times at the modulation frequencies of 70, 80, and 90 MHz. The FDPM measurements of relative phase and amplitude at each of these three frequencies were then averaged and fitted to the diffusion equation to obtain the final isotropic scattering and absorption coefficients. Experimental Design. The isotropic scattering and absorption coefficients were measured as a function of pigment concentrations, while polystyrene PVC was maintained constant. Aliquot dispersions of pigments with concentrations of ∼1 wt % were first prepared by diluting commercial pigment dispersions in 120 mM NaCl solution. After each addition of pigment aliquot to the polystyrene vehicle, the dispersion was homogenized using a sonic stirrer (Dismembrator, model 60, Fisher) for ∼10 min at a power of 4 W. A 100-mL sample of the polystyrene dispersion of 5 vol % was used as the vehicle for assessment of pigment absorption by FDPM measurement. FDPM measurements were conducted 30 min after sonication to ensure equilibrium conditions. RESULTS AND DISCUSSION FDPM Measurements and Data Analysis. Figure 2 is an example of typical FDPM measurements of AC and PS represented as (a) the logarithmic ratio of amplitude, ln(AC(r)r/AC(ro)ro), and (b) the relative phase difference, PS(r) - PS(ro), as a function of the relative distance, (r - ro), between two measured positions of the collecting fiber at distances r and ro away from the fiber delivering the incident photon density wave. We refer to r - ro as the relative source-detector position. The sample consists of a polystyrene latex dispersion (with the mean particle size of 226 nm and standard size deviation of 43 nm) at a volume fraction of 5%. The minimum relative source-detector separation distance for the example of data illustrated in Figure 2 was 0.6 cm. Since the standard deviation of AC(r) measurement is typically 0.1% of the measured AC amplitudes and the standard deviation of PS(r) measurement is within 0.5% of the PS measurement, the propagated error presented in Figure 2 is smaller than the symbols representing the data. Figure 2 shows that the logarithmic ratio of the relative AC and the relative PS vary linearly with relative source-detector fiber separation distance, (r - ro), at each modulation frequency. These linear relationships agree with the prediction of photon diffusion theory,9 and the two slopes obtained from a linear regression at each frequency can be used to determine µs′ and µa analytically and simultaneously. The values of µs′ and µa determined at different modulation frequencies were averaged to obtain the final FDPM results. Due to the high precision in the intensity and phase shift measurements, FDPM can determine the isotropic scattering coefficient and absorption coefficient with both precision and accuracy.9 The detailed FDPM data analysis methods and the precision analysis have been detailed elsewhere and will not be presented here for brevity.8,9 Absorption Coefficient as a Function of Pigment Concentration. The symbols in Figure 3 indicate the measured absorption (13) Kuwana, E.; Sevick-Muraca, E. M. Biophys. J. 2002, 83, 1165-1176.
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Figure 2. FDPM measured (a) logarithmic amplitude AC ratio and (b) relative phase shift (degrees) as a function of relative sourcedetector separation distance r - ro (1/cm) for a polystyrene dispersion with a particle size of 226 ( 43 nm and a particle volume concentration of 5% at modulation frequencies of 50, 70, and 90 MHz.
Figure 3. Absorption coefficient (cm-1) versus phthalo green pigment concentration (ppm, w/w) in polystyrene latex with 5% PVC at wavelengths of 828, 785, 687, and 650 nm. (Symbols denote FDPM measurement; lines denote least-squares regression.)
coefficients plotted as a function of pigment concentration in the polystyrene latex as measured at four wavelengths, 650, 687, 785, and 828 nm. The unit for the pigments concentration is weightbased part per million (ppm). The measured absorption coefficient increases linearly with the concentration of pigments as indicated by the least-squares regression lines. Since the total amount of pigment (
