Anal. Chem. 2000, 72, 4428-4434
Nanoparticle Characterization in Nanoliter Volumes by Grating Light Reflection Spectroscopy Sean A. Smith, Anatol M. Brodsky, Paul G. Vahey, and Lloyd W. Burgess*
Center for Process Analytical Chemistry, University of Washington, 160 Chemistry Library Building, Seattle, Washington 98195
We present both theoretical and experimental results demonstrating that grating light reflection spectroscopy (GLRS) can provide information about the concentration and average size of particles of nanometer dimensions distributed in liquid-phase media. To demonstrate this, we have performed experiments on various concentrations of dendrimeric oligomers in water. Our results show that, with GLRS, we can determine the mean radius of particles with sizes on the order of molecular dimensions. The measurements were carried out in a continuous-flow format using a microchannel flow system and in a detection volume of less than 200 nL. We have developed an optical diagnostic method that we term grating light reflection spectroscopy (GLRS) that is based on measurements of light scattered from a transmission diffraction grating in contact with a sample matrix.1-4 We observe the spectra of reflected light when the incident optical beam matches a certain set of parameters that constitutes a threshold condition, under which a transmitted diffraction beam with an order mcr is transformed from a traveling wave in the bulk sample medium to an evanescent wave. Near such thresholds or critical points, the reflected light characteristics in all diffraction orders display singular behavior that is relatively simple to observe and interpret. An especially important consequence of this is that GLRS allows us to determine with high precision both the real and effective imaginary portion (Imeff) of the optical dielectric permittivity of the sample. The sensitivity to refractive index allows for the determination of volume fraction of solute species, while the effective imaginary contribution to the response arises from light scattering by nonuniformities in the sample medium. The latter results in a loss of coherence with respect to the incident evanescent beam and prevents this light from contributing to the interference pattern generated at the grating. For the case where this occurs in a sample of particles much smaller than the wavelength of the scattered beam, the loss of coherence can be simply related to the mean size of the particles. * To whom correspondence should be addressed: (phone) (206) 543-0579; (fax) (206) 543-6506; (e-mail)
[email protected]. (1) Brodsky, A. M.; Burgess, L. W.; Smith, S. A. Appl. Spectrosc. 1998, 52, 332-343. (2) Anderson, B. B.; Brodsky, A. M.; Burgess, L. W. Anal. Chem. 1996, 68, 1081-1088. (3) Anderson, B. B.; Brodsky, A. M.; Burgess, L W. Phys. Rev. E 1996, 54, 912-921. (4) Anderson, B. B.; Brodsky, A. M.; Burgess, L. W. Langmuir 1997, 13, 42734279.
4428 Analytical Chemistry, Vol. 72, No. 18, September 15, 2000
The most effective way to conduct these measurements is to place the grating sampling interface into an automated flow channel with a very small volume, such that dynamic measurements may be reproduced with the greatest possible speed and precision. To meet this demand, we utilize UV soft lithography methods for forming a square channel of micrometer dimensions in poly(dimethylsiloxane) (PDMS) that, in turn, we interface with a microliter flow rate liquid chromatography pump. To model the GLRS response for very small particles, we chose to look at various volume fractions of dendrimer molecules suspended in water. Dendrimers were chosen because they have an approximately spherical symmetry, are self-similar, and are available in nanometer-scale diameters. Dendrimers are polymers that grow radially outward from a common “seed” or core element. They are produced with various functional groups, but we used the Starburst brand of polyamidoamine (PAMAM) dendrimers produced by Dendritech, Inc. The PAMAM dendrimers are constructed by repeatedly attaching amine/amide structural units to the original ethylenediamine (EDA) core.5 THEORY The general scheme of GLRS is presented in Figure 1. The critical points or thresholds described in the Introduction are defined by
[
(
δ ≡ Re 2(ω) - sin θ +
)]
mcrλ Λ
2
) 0, mcr ) ... -1,0,+1, ... (1)
where Λ is the grating interval, 2(ω) is the dielectric permittivity of the studied sample, θ is the incident angle, mcr is the transmitted diffraction order containing the critical wavelength, and λ is the critical wavelength. Equation 1 supposes that the incident plane is oriented perpendicular to the grating lines. The condition set by this equation corresponds to the combination of parameters that define when the wave vector component normal to the grating/sample interface in the mcr diffraction order is equal to zero (see Figure 1). At δ ∼0, the characteristics of light reflection and transmission become very sensitive to the values of Imeff (which includes the effects of coherence loss due to scattering by nonuniformities) even when Imeff , Reeff. (5) For general information regarding the structure, production, and potential uses of dendrimers visit: http:/www.mmi.org/mmi/dendritech. 10.1021/ac000533q CCC: $19.00
© 2000 American Chemical Society Published on Web 08/17/2000
constituents of the sample media possess broad absorption bands within the above frequency interval. To relate changes in Re2(ω) and Im2(ω) with the properties of particles distributed in the sample medium we can use the following expression
2 = m + 4π(c/ω)2
∑N A (0)
(6)
R R
R
Figure 1. Schematic of the GLRS sensor interface. The 0th order reflection is used to monitor changes in the transmitted critical order (mcr) due to changing dielectric properties of the sample matrix, represented here be (2) or eff.
where m is the permittivity of the suspending medium, NR is the mean concentration of particles of type R, and AR(0) is the complex forward scattering amplitude of those particles. This approximation holds in the case of not-very-high volume concentrations of particles and not very large optical contrasts between the particles and the suspending medium. For particles with dimensions less than the critical wavelength, we can express AR(0) using the Rayleigh-Gans approximation that states
( ()∑ c
Re 4π In a description of GLRS experiments with a wide frequency interval, it is convenient to introduce the following decomposition
δ(ω) = a(ω - ω0), a )
∂δ(ω) ∂ω
|
ω)ω0
for
ω - ω0
