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2006, 110, 23000-23003 Published on Web 10/28/2006
Probing Molecules Adsorbed at the Surface of Nanometer Colloidal Particles by Optical Second-Harmonic Generation Shih-Hui Jen and Hai-Lung Dai* Department of Chemistry, UniVersity of PennsylVania, Philadelphia, PennsylVania 19104-6323 ReceiVed: July 14, 2006; In Final Form: August 25, 2006
It is observed that optical second-harmonic generation from molecules adsorbed at the surface of nanometer size colloidal particles occurs at angles as large as 90° away from the fundamental beam direction. This phenomenon can be rigorously described by the nonlinear Rayleigh-Gans-Debye theory and used for probing molecules adsorbed on nanometer size colloidal particles.
Colloidal systems, heterogeneous media consisting of microto nanometer size objects, have become more of an important subject for study because of their relevance to a wide range of current science and technology developments such as new coating materials, soft materials, colloidal nanoparticles, colloidal crystalline photonic materials, colloid based solar cells, and pharmacology. A primary concern for any colloidal system is its dispersion stability versus the tendency for the colloidal particles to coagulate or crystallize. To affect the stability of a colloid or even the functions of colloidal particles, often molecules are added to colloids so that their adsorption onto the particle surface may change the particle-particle and particlesolvent interactions.1,2 To understand these interactions requires an experimental capability for characterizing the structure and kinetic/dynamic processes at colloidal particle surfaces. The nonlinear optical phenomenon, second-harmonic generation (SHG), induced at the colloidal particle surface when the adsorbed molecules have detectable second-order susceptibility, can be used for characterizing the particle surface. SHG is surface sensitive primarily because the molecules dissolved in the bulk solution with a random orientation would not facilitate SHG and do not present a background signal. On the basis of this sensitivity toward molecules adsorbed at the particle surface, SHG has been developed as an effective tool for in situ probing of the adsorption density, free energy,3-5 surface potential,6 and structure7 for a variety of molecules such as dye, surfactant, and biopolymers on a wide range of colloidal particles such as polystyrene beads, inorganic particles,8-10 and liposome vesicles.11-13 For SHG to be an effective probe of molecular adsorption, it has been generally expected that the particle should be about micrometer size, as this length is comparable to the coherent length of the incident light so that nonlinear polarization of molecules adsorbed on the opposite sides of the particle will not cancel each other.14 On the other hand, it would be highly desirable to be able to use SHG for studying nanometer size colloidal particles. In the presently commonly used experimental scheme for detecting SHG, however, the SH signal decreases dramatically with particle size and becomes undetectable for particles smaller than a few hundred nanometers. * Corresponding author. E-mail:
[email protected]. Phone: (215)8985077. Fax: (215) 898-2037.
10.1021/jp0644762 CCC: $33.50
Forward scattering was chosen in anticipation of phase matching along the fundamental beam direction. On the other hand, in an earlier study,15 measurements made on polystyrene particles with sizes ranging from 1 µm to 500 nm showed that the maximum of the SH signal shifts from near-forward direction to some small angle away from the fundamental beam. A recent study which appeared during the preparation of this report showed that SH light scattering from 100 to 200 nm diameter polystyrene beads adsorbed with malachite green (MG) molecules tilts toward even much larger angles.16 This phenomenon can be understood from the phase matching condition17-21 for molecules on a spherically shaped object and suggests the possibility that the SH signal detected at large scattering angles can be used for probing surfaces of nanometer size particles. To test this hypothesis, we first measure the angular distribution of the SH signal generated from molecules adsorbed from smaller, submicrometer- and nanometer-diameter size colloidal particles. The angle-resolved SH signal is detected for an aqueous colloidal system with malachite green (MG) dye molecules adsorbed on spherical polystyrene beads with a uniform diameter ranging between 250 and 50 nm. In the experiments, a Ti:sapphire laser pumped by an Ar ion laser provides the 840 nm fundamental light pulses, nominally 50 fs width at 76 MHz repetition rate. The linear polarization of the laser beam is set by a half-wave plate as s- or p-polarized, defined as perpendicular or parallel to the optical table. The laser beam, with a 0.4 W output, is focused by a 2 in. lens into a 54 µm beam waist inside the colloidal sample. The SH scattered light from the laser beam-sample intersection region is collected by a 3 in. lens, passed through a Glan Taylor prism polarizer for polarization selection and a band-pass filter for filtering out the fundamental, and collimated into an optical fiber. The SH light exiting the fiber is then focused by a 4 in. lens and passes through the filters for detection by a photomultiplier. The signal is then amplified and processed through a photon counter. The detection angle resolution is set by an iris with a 5° solid angle placed in front of the 3 in. lens. All optical elements are mounted on an arm of a rotating stage placed on the optical table. The center of the rotation circle is set at the focal point of the fundamental beam inside the sample cell, which is mounted on a two-dimensional translational stage for position adjustment. © 2006 American Chemical Society
Letters
Figure 1. The upper panels (a and b) display the SH intensity, measured in the s-in/p-out configuration, as a function of the scattering angle with respect to the fundamental beam direction (0°). Panel a is for the 56 nm diameter PPS particles, and panel b is for the 209 nm diameter PSC particles. Panel c shows the angle of the maximum intensity, measured with both the s-in/p-out and p-in/p-out configurations.
The aqueous colloid consists of polystyrene microspheres with either a plain (PPS) or carboxylate terminated (PSC) surface. All particles are uniformly spherical and supplied (Polysciences) monodispersed in DI water. In each experiment, a small amount of the stock solution is diluted up to a total volume of 250 mL with its pH adjusted to 4.1, at which both PPS and PSC particle surfaces are neutral without charge. (The pKa of carboxyl groups attached to long organic chains ranges in general between ∼5 and ∼6.) MG adsorption on micrometer size polystyrene particles has been characterized previously.7 For the angleresolved SHG experiments, the sample colloid is prepared at a MG concentration so that the particle surface is saturated with MG molecules. The contribution from two-photon fluorescence from the MG dye in the solution can be measured from a solution with the same MG concentration but without the PS particles and is subtracted from the total signal to reveal the true SH light profile. The magnitude of the two-photon fluorescence from the dye in the bulk solution increases linearly with the dye concentration. At 5 µM where adsorption on the colloidal particles has saturated, the two-photon fluorescence intensity is ∼5000 counts/s with a noise less than 5%. Angle-resolved SHG performed on six different particles with both s-in/p-out and p-in/p-out configurations at scattering angle θS measured clockwise, from -90 to 120°, shows patterns symmetrical with respect to θS ) 0° defined by the center of the fundamental beam direction. The SHG scattering patterns of PPS 56 nm in diameter and PSC 209 nm particles detected in the s-in/p-out polarization configuration, along with the angles of maximum SH intensity determined for the six different particle sizes, are shown in Figure 1. The maximum intensity shifts toward larger angles with decreasing particle size. As the particle size reaches below 100 nm, the maximum SH signal is at a scattering angle of around 90°. To understand the SHG angular dependence, we use the nonlinear Rayleigh-Gans-Debye (NLRGD) model in which the SHG source is the surface of a spherical particle with a similar refractive index to that of the solvent. Previously, the NLRGD model was developed for the specific condition that the absorbed dye molecules are oriented with its only nonzero hyperpolarizability along the direction normal to the local surface.15,17 We have generalized the NLRGD model so that it can be used to account for the SH signal generated from
J. Phys. Chem. B, Vol. 110, No. 46, 2006 23001
Figure 2. The left diagram shows the coordinate systems and their relationship in the NLRGD model. The XYZ axes represent the laboratory frame. kω and Eω represent, respectively, the wave vector and electric field of the fundamental beam. The scattering angle θS is defined by kω and the SH wave vector k2ω. The polarization angle φ is between the incident polarization and the scattering plane. The right diagram shows the transformation through Euler angles θ, φ, and Ψ between the local surface coordinates and the molecular frame.
molecules adsorbed in any orientation configuration. The model is described in detail elsewhere22 but is summarized here. For the MG molecule with C2V symmetry and the 420 nm SH light, the dominating second-order molecular polarizability in the molecular frame x′y′z′ (z′ is the C2 axis) is βz′x′x′.23 After relating, through Euler transformation, the molecular coordinates to the local coordinates rˆ′, θˆ ′, and φˆ ′, represented by unit vectors eˆ r′, eˆ θ′, and eˆ φ′, in which the orientation of the dye molecule on the surface is defined, the nonlinear susceptibilities can be expressed by the molecular hyperpolarizability.24-26 The SH electric field can then be computed using Green’s function method integrating over the spherical coordinates.27 In this computation, the local coordinates are related to the laboratory coordinates which, shown in Figure 2, are defined by the fundamental beam direction (Z-axis) and the s-polarized electric field (Y-axis). For the isotropic polystyrene surface, there are (2) (2) three nonzero second-order susceptibilities: χ⊥⊥⊥ , χ|⊥| , and (2) χ⊥||. | and ⊥ represent the direction parallel and perpendicular to the local surface, respectively.17,28,29 The SH field at any point in the laboratory coordinates is then ESH(2ω) ∝
[{ } [{
i qR
sin 2φ cos
θS (2) - F1 (F (θ )χ(2) - F2(θS)χ|⊥| 2 1 S ⊥⊥⊥
θS (2) (cos 2φF1(θS)χ⊥⊥⊥ - (F1(θS) 2 (2) (2) + (2F2(θS) - (1 + 2 cos2 φ)F1(θS))χ⊥|| )+ 2 cos2 φF2(θS))χ|⊥| θ S (2) cos2 φ cos3 ((2F2(θS) - F1(θS))χ⊥⊥⊥ + (-3F1(θS) + 2 (2) (θS)χ⊥|| ) yˆ +
cos
}] ]
(2) (2) + (F1(θS) - 2F2(θS))χ⊥|| ) 2F2(θS))χ|⊥|
F1(θS) ) F2(θS) )
[(
)
3 q 2R 2 1 sin(qR) - qR cos(qR) 3 q 3R 3
[(
)
(
)
]
oˆ
]
3 q2R2 q 3R 3 1 sin(qR) qR cos(qR) 2 6 q3R 3 (1)
The nonlinear wave scattering vector b q is defined as 2kω0 k2ω. The three wave vectors, kω0, k2ω, and b q, define the scattering
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Figure 3. Adsorption isotherms of MG on PPS (a) and PSC (b) particles measured as the SH intensity as a function of the MG concentration. The solid lines are fittings by the Langmuir adsorption model.
plane. θS is the scattering angle between kω0 and k2ω, and φ is the angle between the incident polarization direction and the scattering plane. R is the radius of the particle (|r′| ) R). The vectors yˆ and oˆ are the SH polarization vectors perpendicular and parallel to the scattering plane, respectively. The SHG efficiency can be computed by integrating |ESH(2ω)|2 for a specific set of SH collection angles, θS and φ, molecular orientation angles, SH wavelength, and particle size. The relative SH intensity as a function of the scattering angle calculated by the NLRGD model is shown as solid lines in Figure 1. The theoretical curves generated with all parameters fixed agree well with the experimental results. In the calculation, the refractive indices of water and polystyrene are set at 1.35 and 1.60, respectively. The ratio of the three nonzero susceptibilities on the PPS surface is evaluated from angle-resolved SHG measurements of micrometer size PPS particles.22 For PSC, this ratio is assumed to be the same as PPS, since both surfaces are charge neutral. It is apparent that the model can reproduce the scattering angle pattern and the observation that for PS particles with diameters smaller than 100 nm the maximum SHG occurs at angles nearly perpendicular to the fundamental beam propagation direction. Both the experimentally detected and theoretical SHG scattering angle patterns indicate that the adsorption isotherm of molecules on 100 nm or smaller size particles should be measured at scattering angles as large as 90°. The observations also explain clearly why the SHG measurement on 100-200 nm size vesicles had to be performed at large scattering angles.12,13 In experiments where the adsorption isotherm is measured, a flow system is used to produce a liquid jet for intersecting the laser beam. The colloidal solution is stored in a reservoir that is constantly stirred with a magnetic stirrer and circulated through a liquid pump to form a cylindrical liquid jet through a nozzle (inner diameter 1/16 in.). The flow system allows continuous monitoring of the SH signal during titration of the dye into the colloid solution. The MG dye, in a known high concentration in the same solvent as the colloid, is added into the reservoir through a digital titration buret. The SH collection and collimating lenses, filters, and PMT are mounted along an axis set at a specific angle away from the fundamental beam direction. Figure 3 shows the adsorption isotherms, which are measured in the form of the SH response with the dye concentration change, for the PPS and PSC particles each with three different
Letters
Figure 4. Points are experimentally measured SH intensity normalized by the number of surface-adsorbed molecules for the six different particles. The error bars are determined from at least four measurements per particle size. The solid curves, calculations by the NLRGD model, are placed on the graph by a fitting to minimize the deviations from the experimental points.
TABLE 1: Maximum Adsorption Density and Adsorption Free Energy (∆G) of MG on Polystyrene Colloidal Particles Obtained from Nonlinear Least-Squares Fitting of the Adsorption Isotherms in Figure 3 type of polystyrene beads PPS PSC
particle diameter (nm)
density of MG (number/µm2)
∆G (kcal/mol)
202 88 56 209 109 47
1.61 ((0.18) × 106 2.03 ((0.40) × 105 4.15 ((0.13) × 105 1.62 ((0.54) × 105 3.92 ((0.79) × 104 3.30 ((0.64) × 105
-14.69 ( 0.14 -13.24 ( 0.45 -13.45 ( 0.47 -12.44 ( 0.02 -12.17 ( 0.03 -11.65 ( 0.25
sizes. These isotherms, measured at their respective maximum SH intensity scattering θS angles, ranging from 60 to 120°, and φ ranging from 90 ( 19°, can be analyzed according to the Langmuir adsorption model for the determination of the adsorption free energy and maximum adsorption density which are listed in Table 1. The maximum density appears to vary greatly with the particle size. This observation in itself is interesting but can be understood as each particle size is a result of different synthesis processes. These changes are also confirmed in the comparison below between the experimentally determined, based on the measured density, and theoretically calculated SH efficiencies for different particle sizes. The adsorption free energies measured show that, even though both particle surfaces are neutral, the surface (PPS) with only aromatic functional groups has a different adsorption energy from the one (PSC) with carboxyl groups. It is speculated that the adsorption of the MG hydrophobic ion on the surface will displace water from the surface and causes a smaller adsorption free energy change on the more hydrophilic carboxyl surface. The determination of the density of the adsorbed molecules also affords us another way to examine the particle size effect through the second-harmonic efficiency, defined as the amount of the SH signal generated per surface-adsorbed dye molecule. Assuming that the dye orientation angles on one type of particle remain the same for all sizes, we obtain the experimental SH efficiency as14,26
SH efficiency )
I2ω anNs2〈β(2)〉2Iω2
(2)
Figure 4 shows the SH efficiency of MG adsorbed on PPS and PSC particles, each with three different particle sizes. The points are experimentally obtained with the measured SH intensity divided by the density squared. The solid lines are calculated from the NLRGD model with all parameters fixed.
Letters The calculation generates the SH efficiency in relative magnitude. The theoretical curve is placed on the figure after fitting to the three points to minimize the deviation. Once again, it is apparent that the NLRGD model describes the general trend of SH efficiency as a function of particle size. On the basis of the comparison of the model with the experimental points, the SH efficiency decreases to zero for PPS at about 54 nm and PSC at about 45 nm. From the signal/noise ratio displayed in Figure 3, it appears that SHG is good for polystyrene particles as small as, but not much smaller than, 50 nm. For future considerations, one should note that several factors may be used to further push the SH efficiency detectable for even smaller particles. Using shorter wavelength fundamental light will result in a shorter coherent length. The use of much larger refractive index materials for the particles, like the metallic particles which may be better treated by the nonlinear Mie scattering model,21 will likely allow phase matching at smaller scattering angles. Both conditions will facilitate phase matching to be satisfied for smaller particles. Acknowledgment. This work is supported in part by the National Science Foundation MRSEC Program, Grant No. DMR05-20020. Equipment support from an Air Force Office of Scientific Research DURIP grant is acknowledged. References and Notes (1) Evans, D. F.; Wennerstron, H. The colloidal domain: where physics, chemistry, biology, and technology meet, 2nd ed.; Wiley-VCH: New York, 1999. (2) Antonietti, M. Colloid chemistry; Springer: New York, 2003. (3) Wang, H.; Borguet, E.; Yan, E. C. Y.; Zhang, D.; Gutow, J.; Eisenthal, K. B. Langmuir 1998, 14, 1472. (4) Wang, H. F.; Troxler, T.; Yeh, A. G.; Dai, H. L. Langmuir 2000, 16, 2475.
J. Phys. Chem. B, Vol. 110, No. 46, 2006 23003 (5) Eckenrode, H. M.; Dai, H. L. Langmuir 2004, 20, 9202. (6) Yan, E. C. Y.; Liu, Y.; Eisenthal, K. B. J. Phys. Chem. B 1998, 102, 6331. (7) Eckenrode, H. M.; Jen, S. H.; Han, J.; Yeh, A. G.; Dai, H. L. J. Phys. Chem. B 2005, 109, 4646. (8) Liu, Y.; Dadap, J. I.; Zimdars, D.; Eisenthal, K. B. J. Phys. Chem. B 1999, 103, 2480. (9) Yan, E. C. Y.; Eisenthal, K. B. J. Phys. Chem. B 2000, 104, 6686. (10) Yan, E. C. Y.; Liu, Y.; Eisenthal, K. B. J. Phys. Chem. B 2001, 105, 8531. (11) Srivastava, A.; Eisenthal, K. B. Chem. Phys. Lett. 1998, 292, 345. (12) Liu, Y.; Yan, E. C. Y.; Eisenthal, K. B. Biophys. J. 2001, 80, 1004. (13) Shang, X. M.; Liu, Y.; Yan, E.; Eisenthal, K. B. J. Phys. Chem. B 2001, 105, 12816. (14) Wang, H.; Yan, E. C. Y.; Borguet, E.; Eisenthal, K. B. Chem. Phys. Lett. 1996, 259, 15. (15) Yang, N.; Angerer, W. E.; Yodh, A. G. Phys. ReV. Lett. 2001, 8710. (16) Martorell, J.; Vilaseca, R.; Corbalan, R. Phys. ReV. A 1997, 55, 4520. (17) Dadap, J. I.; Shan, J.; Eisenthal, K. B.; Heinz, T. F. Phys. ReV. Lett. 1999, 83, 4045. (18) Shan, J.; Dadap, J. I.; Stiopkin, I.; Reider, G. A.; Heinz, T. F. Phys. ReV. A 2006, 73. (19) Roke, S.; Schins, J.; Muller, M.; Bonn, M. Phys. ReV. Lett. 2003, 90. (20) Roke, S.; Bonn, M.; Petukhov, A. V. Phys. ReV. B 2004, 70. (21) Pavlyukh, Y.; Hubner, W. Phys. ReV. B 2004, 70. (22) Jen, S.-H.; Dai, H.-L. Manuscript in preparation. (23) Kikteva, T.; Star, D.; Leach, G. W. J. Phys. Chem. B 2000, 104, 2860. (24) Goldstein, H. Classical Mechanics; Addison-Wesley: New York, 1980. (25) Heinz, T. F.; Chen, C. K.; Ricard, D.; Shen, Y. R. Phys. ReV. Lett. 1982, 48, 478. (26) Heinz, T. F. In Nonlinear Surface Electromagnetic Phenomena; North-Holland: Amsterdam, The Netherlands, 1991. (27) Kerker, M. The Scattering of light and other Electromagnetic Radiation; Academic: New York, 1969. (28) Shen, Y. R. The Principles of Nonlinear Optics; Wiley: New York, 1984. (29) Giordmai, Ja. Phys. ReV. 1965, 138, 1599.
