Optical effects of charges in colloidal solutions

doi:10.1016/j.optmat.2017.01.040

Optical Materials

Volume 66, April 2017, Pages 43-47

https://doi.org/10.1016/j.optmat.2017.01.040 Get rights and content

Highlights

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Charge-induced optical effects in colloids.
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Significance for polymeric colloids.
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Optical signature for charge effects.
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Signatures for coalescence of colloidal particles.

Abstract

The optical response of charged polymeric and metallic colloids is investigated using effective medium theories for composite systems of nanoparticles. Based on the Bohren-Hunt theory for generalized Mie scattering from charged particles, an effective quasi-static dielectric function previously obtained is applied to the present study to characterize the response from the various colloidal particles. It is found that such effects are more prominent for polymeric and nonmetallic colloidal solutions in general. In addition, the effects of clustering among the colloidal particles are also studied via a fractal model available from the literature. Detailed numerical studies of the dependence of these effects on the amount of extraneous charge, as well as on the geometry and volume fraction of the colloidal particles are presented.

Introduction

Among the various colloidal systems, polymer [1] and metal [2] colloids are the two most intensively studied due to their distinct properties leading to various important applications. These include, for example, various biomedical and pharmaceutical applications of the former and spectroscopic enhancement applications of the latter [3]. Of the many physical and chemical properties, the optical properties are significant since light scattering has remained one of the powerful probes for the understanding of the structure and behavior of these colloidal solutions. While there have been many studies in the literature on these properties [4], [5], most of them have been limited to neutral colloidal particles leaving the effects due to possible presence of extraneous charges [1], [2] unaccounted for in such studies. Though the first study on light scattering from colloidal electrolytes including charge effects dates back to the 1950's, it was limited to a semi-empirical statistical approach accounting for the decrease in optical effectiveness of fluctuations due to the presence of charge in the electrolyte [6]. To our knowledge, the only study based on fundamental optical theories was limited to a single metallic colloidal particle and the charge-induced optical effects were found to be rather insignificant [7]. The more recent study has indeed considered low (RF) frequency scattering from charged colloids as a composite of metal particles, but its focus has been on the effects due to the counterions and the motions of the particles and was limited only to metallic colloids [8].

It is the purpose of our present work to study exclusively these charge-induced optical effects in both nonmetallic (polymeric) and metallic colloids via the application of electromagnetic scattering and effective medium theories. We focus on higher frequency scattering and the metallic surface plasmons can be excited while the particle motion can be ignored in this case. Our interest is mainly in the optical response of the excess (free) charges on the colloidal particles in both the polymeric and metallic cases. While in the literature, there have been many well-established effective medium theories (e.g., the Maxwell-Garnett; the Bruggeman theory and their extensions) for the optical properties of composites [9], most of them have considered only neutral particles, and composites of charged particles have not been systematically studied previously. Moreover, synthesis of various colloids often lead to charged ingredient particles [1], [2]. Hence it will be of interest to study these “charge-induced” optical effects in a composite of nanoparticles and the results will provide an extra dimension for the control of the optical response of these materials besides manipulations over the shape, size, material, concentration, … of the nanoparticles.

It is of interest to note that the charge state of single emitting quantum dots has been recognized to be of high significance in some recent studies on the fluorescence intermittency [10], [11] of these emitters; as well as in higher order fluorescence from single atomic emitters doped within a crystalline host [12], [13], [14], [15]. However, our present focus here is mainly on the optical response from the plasmonic motion of these extraneous surface charges on various polymeric and metallic colloidal particles, rather on the atomic emitters. Nevertheless, these plamonic effects could indeed modify the fluorescence properties of nearby atomic emitters as demonstrated in one of our previous works [16].

In the literature, Bohren and Hunt (BH) [17] were among the first to have studied the optical response of charged particles with their generalization of the Lorenz-Mie scattering theory to apply to a charged sphere. By characterizing the extraneous surface charges with an effective surface conductivity, BH were able to derive modified Mie coefficients via an implementation of a modified boundary condition for the discontinuity of the tangential components of the magnetic field across the surface of the particle. The problem of light scattering from charged spherical particles has since been studied by many people, including some very recent works in the literature (see, e.g., [18], [19], [20], [21], [22]). In particular, effective modified dielectric functions have been derived from the BH theory in the long wavelength limit [19], [20] which highly simplified the incorporation of such charge effects into the optical response from small particles. The BH theory in the lowest (dipole) order has been previously applied to a single metallic colloidal particle [7]. Our previous formulation [19] allows one to extend to include higher order multipoles in conjunction with the extended effective medium theories available in the literature [23]. In the following, we shall apply these effective dielectric functions [19] to study such “charge-induced” optical response from different colloidal systems, and we shall start with a brief review of the previous theories.

Section snippets

Theoretical models

To account for the surface charge effects, we recall the generalized Mie coefficients obtained in the BH theory [17] for the electromagnetic scattering from a charged sphere (in vacuum): $a_{ℓ} = - \frac{ψ_{ℓ}^{'} (x) ψ_{ℓ} (n x) - ψ_{ℓ} (x) [n ψ_{ℓ}^{'} (n x) - i τ ψ_{ℓ} (n x)]}{ξ_{ℓ}^{'} (x) ψ_{ℓ} (n x) - ξ_{ℓ} (x) [n ψ_{ℓ}^{'} (n x) - i τ ψ_{ℓ} (n x)]},$ $b_{ℓ} = - \frac{ψ_{ℓ} (x) ψ_{ℓ}^{'} (n x) - ψ_{ℓ}^{'} (x) [n ψ_{ℓ} (n x) + i τ ψ_{ℓ}^{'} (n x)]}{ξ_{ℓ} (x) ψ_{ℓ}^{'} (n x) - ξ_{ℓ}^{'} (x) [n ψ_{ℓ} (n x) + i τ ψ_{ℓ}^{'} (n x)]},$ where $ψ_{ℓ}, ξ_{ℓ}$ are the Riccati-Bessel functions, $x = k a$ is the size parameter of the sphere, $n = \sqrt{ε}$ is the refraction index of the (nonmagnetic) sphere (assumed

Numerical results

We first make a comparison between the charge-induced optical effects from a metallic and a polymeric colloid, respectively, by considering silver and polystyrene colloidal particles in a solution which we just take to be water. We shall assume a constant refractive index of 2.4 for polystyrene while a Drude model applies to silver [19]. Both colloids have been reported to be likely highly charged during their fabrication processes [29], [30]. We shall illustrate the charge effect on the

Conclusion

We have thus carried out a comprehensive study on the optical effects due to the surface charges on the colloidal particles in both polymeric and metallic colloids using various effective medium theories, and have come to the conclusion that such effects are only significant for nonmetallic (polymeric) colloids. For such colloids, these charges will lead to new plasmon and absorption peaks which are enhanced and blue-shifted with the increase in the amount of charges. However, when coalescence

Acknowledgments

The authors are grateful to the Ministry of Science and Technology of Taiwan, republic of China for supporting this research with contract number MOST 103-2112-M-019-003-MY3.

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Electromagnetic (EM) scattering by electrically charged particles has received significant attention in the last decade due to the revelation of new physical phenomena and their potential for new technologies [22]. For instance, Chang et al. [5] have found that silver and polystyrene colloidal particles in solution can resonate with the incident EM wave, showing a blue wavelength shift of absorption peaks for elevated surface charges. However, the excess-charge impacts on metallic particles were much weaker than those on dielectric particles.
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In this paper we introduce a method to calculate the optical response of charged particles at wavelengths where charge-induced resonances typically occur. The method takes advantage of the interfaces to DDSCAT, while the conductive shell is simulated by a multi-level material distribution. The discretization involves both the 3D model of the particle and the charge distribution. The latter is determined numerically by solving the Laplace equation. The surface- and volume-averaging parameter is used to avoid large refractive indices, but the results are still accurate within a few percent. The method is validated for sensitivity and specificity in modeling optical resonances that are analytically retrievable for ideal spheres. The applicability to an irregularly shaped particle is demonstrated consequently. Implementation algorithms and numerical solvers are made publicly available, which allows light-scattering modelers to study particles in different media under different conditions.
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Zhou et al. investigated the attenuation of EMWs caused by charged sand particles based on the Rayleigh approximation [22], and their model could give theoretical prediction of EMW attenuation in sand/dust storms that could agree with the experimental results given by Haddad [23] for the first time; and they proposed that the net charges on the sand particles’ surfaces made a significant attenuation of the EMWs [22]. In addition, many studies on the scattering of EMWs by charged particles have been conducted in different research fields [24–28], and the results indicated that the charges carried by the particle made the scattering/extinction enhanced, especially for the particle size parameter less than 0.01 [20]. In order to explain the strong enhancement of extinction by a charged particle, Wang et al., based on effective-medium theory, pointed out that the enhancement resulted from the change of dielectric constant when the particle surface carried net charges [29].
In this paper, a method is proposed to solve the scattering of electromagnetic waves (EMWs) by a uniformly charged non-spherical scatterer. Based on Waterman's extended boundary method, a transition matrix between coefficient of the scattering field and incident field of a charged non-spherical scatterer is derived, called T_c-matrix. By using T_c-matrix, the scattering fields of charged non-spherical scatterers can be numerically solved. In the case of a charged rotationally symmetric non-spherical scatterer, the analytic mathematical expression of T_c-matrix is obtained, thus the analytical expression of scattering field is obtained. And the extinction characteristics of charged non-spherical scatterers, making use of charged spheroids as examples, are investigated. It is found that absorption is still the dominant mechanism of attenuation when electromagnetic waves travels through small charged spheroidal particles suspended in atmosphere, though the net surface charges can enhance the extinction/scattering/absorption of particle. The enhancement factors of extinction/absorption increases with increasing surface charge density and are much higher than the enhancement factor of scattering. It is shown that the equivalent sphere assumption, which was used in theoretical models of optical or scattering properties of charged or uncharged atmospheric or interstellar particles, could result in large errors, e.g., even over 100% for charged prolate spheroids, in theoretical prediction of absorption/extinction. Moreover, this inaccuracy due to the sphere assumption worsens for spheroids with either low or high aspect ratios h (i.e., prolate spheroid with h << 1, or oblate spheroids with h >> 1).
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View full text

Optical effects of charges in colloidal solutions

Highlights

Abstract

Introduction

Section snippets

Theoretical models

Numerical results

Conclusion

Acknowledgments

J. Colloid Sci.

J. Quant. Spectrosc. Radiat. Transf.

J. Colloid Inteface Sci.

Polymer Colloids, a Comprehensive Introduction

Metallic colloids

Optical properties of the self-assembling polymeric colloidal systems

Int. J. Polym. Sci.

Optical properties of gold colloids formed in inverse micelles

J. Chem. Phys.

Effect of a surface charge on the halfwidth and peak position of cluster plasmons in colloidal metal particles

Colloid Polym. Sci.

Radio frequency absorption in gold nanoparticle suspensions: a phenomenological study

J. Phys. D.

Effective Medium Theory, Principles and Applications

Enhanced fluorescence intermittency in Mn-doped single ZnSe quantum dots

J. Phys. Chem. C

Controlling fluorescence intermittency of a single colloidal CdSe/ZnS quantum dot in a half cavity

Phys. Rev. B

All-optically controlled fourth-and sixth-order fluorescence processes of Pr3+:YSO

Appl. Phys. Lett.

Observation of Autler-Townes splitting of second-order fluorescence in Pr3+:YSO

J. Phys. Chem. C

All-optically controlled fourth-and sixth-order fluorescence processes of Pr³⁺:YSO

Observation of Autler-Townes splitting of second-order fluorescence in Pr³⁺:YSO