Assessment of Electrostatic Interactions in Dense Charged Colloidal

Chapter 9

Downloaded by CORNELL UNIV on May 29, 2017 | http://pubs.acs.org Publication Date: April 20, 2004 | doi: 10.1021/bk-2004-0878.ch009

Assessment of Electrostatic Interactions in Dense Charged Colloidal Suspensions Using Frequency Domain Photon Migration Yingqing Huang, Zhigang Sun, and Eva M. Sevick-Muraca* Department of Chemical Engineering, Texas A&M University, College Station, TX 77843-3122 *Corresponding author: phone: 979-458-3206; fax: 979-845-6446; email: [email protected]

The electrostatic repulsive force between particles impacts the colloidal structure, which mediates the bulk properties of the suspensions and dramatically hinders visible light scattering. In this investigation, we explored the impact of effective surface charge and ionic strength on the multiple scattering measured by frequency domain photon migration (FDPM). First, we employed F D P M to measure the isotropic scattering coefficients of dialyzed polystyrene (PS) latex suspensions at 687 and 828 nm as a function of ionic strengths at 65, 25 and 5 m M NaCl equivalents. Measured isotropic scattering coefficients decreased with decreasing ionic strength of the suspensions, suggesting that changes in electrostatic interactions could be evaluated from ensemble measurements of multiply scattered light. At each ionic strength, the isotropic scattering coefficients at varying colloidal volume fractions were regressed to scattering theory which incorporated the mean spherical approximation (MSA) with hard sphere Yukawa (HSY) interaction and Primary model (PM) interaction for monodisperse suspensions in order to

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Somasundaran and Markovic; Concentrated Dispersions ACS Symposium Series; American Chemical Society: Washington, DC, 2004.

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yield an effective surface charge given the particle size and ionic strength. The estimates of surface charges obtained from scattering data at 687 and 828 nm were consistently similar but varied with ionic strength. We further investigated the impact of effective surface charge on the multiple scattering through modifying the surface by Rhodamine 6G (R6G) adsorption. Measurements were conducted on dense suspensions (volume fraction = 0.186) at an ionic strength of 5 m M NaCl equivalents with varying amount of positively charged R 6 G adsorbed on the particle surface. F D P M detected the increase in isotropic scattering coefficient due to decreased electrostatic interaction as a result of R6G adsorption. The corresponding effective surface charge fitted using hard sphere Yukawa interaction model and mean spherical approximation decreased as R6G concentration increased. F D P M can be a potential tool for assessing electrostatic interaction in charged dense suspensions. This research is supported by National Science Foundation (CTS-9876583).

Introduction The interactions among colloidal particles determine the local structure, which mediates rheology, colloidal stability and impact light scattering efficiency. The structure of a suspension not only should be taken into account when sizing particles using ensemble light scattering techniques, but can also provide information about particle interactions within an ensemble (1,2). Typically, the static structure of complex fluids can be obtained from small angle light, neutron, and X-ray scattering measurements. However, concentrated colloidal suspensions multiply scatter light (3, 4), making small angle light scattering measurements impractical without tedious refractive index matching, which itself may affect the interaction, and therefore the structure. Neutron and X-ray scattering require a nuclear reactor or a synchrotron source, which limit their practical and ubiquitous application in complex fluids. In addition, these techniques are limited to nanometer-sized colloids (< 100 nm).


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In industrial processes involving dense dispersions such as emulsions, techniques capable of directly characterizing dense suspensions are required, since dilution alters original solvent conditions, and therefore alters interparticle interaction and structures. Although a few techniques have recently been developed to characterize electrostatic interactions in dense suspensions, the measurement of parameters that govern electrostatic interactions remains elusive. For example, electroacoustic techniques (5, 6) have been applied in measuring zeta potential as well as particle size distribution of concentrated suspensions. Values representing zeta potentials obtained from electroacoustic sonic amplitude (ESA) measurements or colloidal vibration potential (CVP) measurements differ from those obtained from standard electrophoresis (7, 8). Furthermore, these perturbative techniques require an oscillatory electric force or sonic field, which may disturb the original position correlations among particles and resultantly, the structure of the dispersions. In our laboratory, we have used frequency domain photon migration techniques for accurate and precise measurements of isotropic scattering coefficients which are sensitive to microstructure (9, 10). In brief, F D P M involves launching an intensity sinusoidally modulated light wave in a multiply scattering medium through an optical fiber. When the light wave propagates through the media, its intensity attenuated and it is phase shifted relative to the incident light. The "photon density wave" propagating through the medium is collected by another fiber optic located some distance away from the source. B y approximating the transportation of light wave as a photon diffusion process and applying diffusion theory, the relative values of average intensity (DC), amplitude (AC) and phase shift (PS) measured as a function of distance away from the source or modulation frequency can be used to independently extract the isotropic scattering coefficient and absorption coefficient. Using F D P M , Sun et. al. successfully obtained size information of dense monodisperse, polydisperse, and bidisperse suspensions in which volume exclusion effects dominated (11, 12, 13, 14). F D P M has been also been showed capable of probing the structure of dense suspensions of volume exclusion interaction and electrostatic interactions respectively (15, 16). Historically, the hard sphere model is widely used to model colloidal particle interactions. Actually, almost all colloidal suspensions are charged owing to charged surface groups and adsorption of ions from the solution. In this work, we seek to extend time-dependent multiple light scattering techniques to assess the impact of ionic strength and effective surface charge upon the electrostatic interaction.


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Background

Interaction models among charged particles


The hard - sphere Yukawa interaction (HSY) model and primary interaction (PM) model are two of the most popularly used models describing electrostatic among charged particles (17). H S Y describes the interaction among a monodisperse charged suspension as hard sphere interaction with a Yukawa tail: (1) where e is electron charge; ε is the electric permittivity of vacuum; and ε is dielectric constant of the suspending medium. The parameter σ is the particle diameter; z jj- is the effective particle surface charge; and κ is the inverse Debye screening length. In H S Y , a charged particle is surrounded by a cloud of counter ion layer, whose thickness is characterized by Debye screen length, κ\ which decreases with increasing ionic strength. The charged particles repulsively interact through volume exclusion and double layer overlapping. The H S Y model is also usually termed as one component model (OCM) (17). 0

e

The primary model describes the interactions among charged colloidal particles as direct Columbic interactions: (2) Where ^p. . z

=0»

a n c

s

* A * &e number density of the component / in the

1

colloidal mixture. In the primary model, counter ions are also considered as components in the dispersions, and presence of the counter ions will not impact the direct interaction among charged particles significantly.

Scattering properties of dense colloidal suspension For a well-characterized monodisperse colloidal suspension, the isotropic scattering coefficients of the suspension, μ , can be predicted by: χ


125 iS(aXe ç)F(aXe)sinQ(l-cosQ)de

/ / / ( λ ) = -4^7

kσ *

t

(3)

where F is form factor, which addresses the scattering amplitude of light with optical wave length λ at scattering angle 9by a particle of diameter σ. The form factor can be calculated from M i e theory. The structure factor S(q) accounts for the interference effects of scattered light from different particles, at wave vector g = ^EH (g/2)

and contains the information of particle position

sm


À

correlation, and therefore of structure information. Here, m is the refractive index of the medium. In diluted suspensions (volume fractions < 1%), particles are randomly oriented and scatter independently. In this case, the interference of scattered light is not significant, and S(q) is close to one. The structure factor S(q) can be predicted with Ornstein-Zernike (O-Z) integral equation employing a first principles model of interaction, such as H S Y or P M models, and a approximate closure model relating structure with the interaction, such as mean spherical approximation (MSA), and Perçus-Yevick (PY) models (17). The analytical forms of structure model of monodisperse suspensions are available through integral equation approach using M S A - H S Y (18, 19). The analytical solution by Herrera et al. (19) is used owing to its simplicity. Blum and Hoye (20, 21) solved the O-Z equation analytically using M S A associated with P M interaction model. Hiroike (22, 23) reorganized Blum's solution and derived an explicit expression of direct correlation function, whose Fourier transform can be used to directly calculate the partial structure factor In this study, two analytical solutions of the structure models from the solution of O-Z equation using M S A - H S Y (Herrera et. al.) and M S A - P M (23) closure and interaction potential models are used to fit the experimental data of isotropic scattering coefficient as a function of ionic strength and volume fraction.

Theory of frequency domain photon migration F D P M is based on photon diffusion theory which assumes that the transport of multiple scattering light in dense suspension can be approximated by "random walk" of photon, and one can use "frequency domain photon diffusion equation" to describe the optical fluence, Φ, modulated at frequency, m at position r in terms of absorption coefficient, μ , and isotropic scattering coefficient, μ '. ά

θν Φ (Γ ω)-[μ -l^} (r m) c 2

Α(:

9

α

AC

9

5

= S(r,a>)

(4)


126

l s

where D = ΐ/3(μ +μ )> β

the source term.

$

called the optical diffusion coefficient. S(r,œ) is

In infinite media, the decay of photon density wave can be

obtained from the solution of above frequency domain diffusion equation to obtain the photon density U(r,t) = Φ/c, at position r and time t as: U =^

S

^ ^

e x

e*V(-M+r) + AC S

D C

l

r

P ( " Meff -

x c o t

- Φο ))

(

ι/2

where μ# = (μ^) , and c is the the speed of light. S S , average intensity, amplitude and initial phase associated with source. By applying analytical solution of photon diffusion equation taking measurement at multiple detecting positions, we can information and subsequently source calibration.


AC%

I n ( ^ ^ r ) = -(r-r )[3 (M 0

PS(r)-PS(r ) 0

Ma

a

DC

α

of eq. 4, and avoid source

() 6

= (r-τ,)}~μ,{μ, + μ,')

Assessment of Electrostatic Interactions in Dense Charged Colloidal

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