Controlled Clustering in Binary Charged Colloids by Adsorption of

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Controlled Clustering in Binary Charged Colloids by Adsorption of Ionic Surfactants Yuki Nakamura, Manami Okachi, Akiko Toyotama, Tohru Okuzono, and Junpei Yamanaka Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b02778 • Publication Date (Web): 19 Nov 2015 Downloaded from http://pubs.acs.org on November 29, 2015

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Controlled Clustering in Binary Charged Colloids by Adsorption of Ionic Surfactants Yuki Nakamura, Manami Okachi, Akiko Toyotama, Tohru Okuzono, and Junpei Yamanaka* Graduate School of Pharmaceutical Sciences, Nagoya City University, 3-1 Tanabe, Mizuho, Nagoya, Aichi 467-8603, Japan.

Abstract We report on the controlled clustering of oppositely charged colloidal particles by the adsorption of ionic surfactants, which tunes charge numbers Z of partilces. In particular, we studied the heteroclustering of submicron-sized polystyrene (PS) and silica particles, both of which are negatively charged, in the presence of cetylpyridinium chloride (CPC), a cationic surfactant. The surfactant concentration Csurf was selected below the critical micelle concentration. As CPC molecules were adsorbed, Z values of the PS and silica particles decreased, inverting to positive when Csurf exceeded the isoelectric point Ciep. Hydrophobic PS particles exhibited much lower Ciep than hydrophilic silica particles. At Csurfs between their Cieps, the particles were oppositely charged, and clustering was enabled. To explain the clustering

behavior,

we

investigated

adsorption

isotherms

of

the

CPC

and

screened-Coulomb-type pair potential. Expected applications of the present findings are the control of colloidal associations and construction of various particle types into heterogeneous colloidal clusters.

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1. Introduction The aggregation of colloidal particles is a widely observed natural phenomenon, from random coagulations in unstable colloidal dispersions to highly organized associations of protein molecules in living cells. 1-10 The aggregation of colloids with the same composition, charge, or size is called homoaggregation, whereas the aggregation of multicomponent colloids with varying composition, charge, or size is usually denoted as heteroaggregation. 1-3 The aggregations composed of small number of particles are sometimes referred to as “cluster”. The colloidal clustering4-10 has been studied from various viewpoints: (i) the early coagulation stages and crystallization processes of colloids, (ii) models of atomic and molecular clusters, (iii) the geometry of sphere associations, and (iv) the fabrication of mesoscopically ordered structures, such as novel photonic materials, from colloidal cluster building blocks. Colloidal clusters spontaneously form when the attractive force among their particles overcomes the random thermal force at sufficiently small particle separations. Besides van der Waals (VDW) forces, which are usually attractive forces, clustering can occur by electrostatic interactions among oppositely charged particles7, 11-13, bridging of particles by linear polymers14,15, depletion forces6, DNA-mediated attraction7 , and hydrophobic interactions16. Colloidal clustering experiments are typically conducted on colloidal silica and polymer particles; more recently, the clustering of charged hydrogel particles has been reported17. We have been studying control of the electrostatic interactions among colloidal particles by tuning the particle charge numbers Z18-20. Recently, we reported that the Z values of negatively charged particles are altered by the adsorption of anionic surfactants (sodium alkylsulfates). Exploiting this phenomenon, we controlled the crystallization (the disorder-to-order phase transition)21 of charge-stabilized colloids of various particles, including polystyrene (PS), silica, titania, and gold22. The Z values were continuously increased by the addition of like-charged surfactants. The increased surfactant concentration Csurf enhances the electrostatic interparticle interactions, thereby leading to crystallization at sufficiently large Csurf.

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On the other hand, when the particles and ionic surfactants are oppositely charged, adsorption should decrease the particle charge, driving it to zero at the isoelectric point (iep). When Csurf approaches the concentration at the iep (Ciep) and the attractive component of the interaction (e.g., VDW force) is sufficiently strong, the colloidal particles may form heteroclusters or heteroaggregations. At very high surfactant concentrations (Csurf >> Ciep), the colloids may re-stabilize as the sign of the particle charge reverses. The re-stabilizations of charged colloids following the addition of oppositely charged polyelectrolytes have been reported14,15,23,24. Heteroaggregations in multicomponent metal oxides having different iep’s have also been extensively studied. The theory on the stability of metal oxide colloids has been developed by Hogg, Healy and Fuerstenau.25 The charge inversion at Csurf > Ciep can be exploited for controlling the associations among colloidal particles. The Ciep of the colloidal particles significantly depends on the affinity between the surfactants and particles. For example, in aqueous media, the Ciep of hydrophilic particles should far exceed the Ciep of hydrophobic particles with the same charge. Between their Cieps, the hydrophilic and hydrophobic particles should be oppositely charged and amenable to cluster formation. The present study investigates heteroclustering of binary charged colloids. First, we report the clustering of oppositely charged particles in the absence of the surfactant. As N+ ( CH2 )

CH3

-

15 colloidal particles, we used poly(styrene-styrenesulfonic negatively and positively charged

acid) and poly(styrene-(2-vinylpyridine)), respectively. We then investigate the clustering behavior in the presence of a cationic surfactant, cetylpyridinium chloride (CPC, Scheme 1).

[

]

N+

-

Scheme 1 Chemical structure of a CPC molecule. The selected Csurfs was below the critical micelle concentration (c.m.c.) of CPC (Approximately 1100 µM in water at 25 °C). We focus on the clustering of negatively charged PS and silica particles, whose Ciep values are significantly different. All of the investigated clusterings were irreversible. The observed clustering behavior was explainable

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in terms of the adsorption isotherms and electrostatic interaction pair potentials. The rest of this paper is organized as follows. The experimental details and results are provided in sections 2 and 3, respectively. Subsection 3-1 discusses the clustering of oppositely charged particles in the absence of a surfactant, and subsection 3-2 presents the adsorption isotherms of the surfactant CPC on the PS and silica particles. The effect of Csurf on the surface charge and clustering behavior and a mechanism for the clustering of the PS and silica particles are described in subsections 3-3 and 3-4, respectively. Study conclusions are presented in section 4.

2. Experimental Section 2-1. Materials Table 1 lists the characteristics of the colloidal particles used in this study. Negatively charged

poly(styrene-styrenesulfonate)

particles

PS(-)1

and

positively

charged

poly[styrene-(2-vinylprydine)] particles PS(+)1 and PS(+)2 were synthesized as described below. All reagents were purchased from Wako Chemicals Co., Ltd, Tokyo, Japan. Negatively charged PS particles, PS(-)2 and PS(-)3, were purchased from Thermo Scientific Co., Ltd., MA. Silica 1 and silica 2 particles were obtained from Japan Catalyst Co., Ltd., Osaka, Japan. PS(-)1 were synthesized by the emulsifier-free polymerization method26 as follows. Prior to use, styrene (St) and divinylbenzene (DVB) were washed with 1 M NaOH aqueous solution to remove any coexisting polymerization inhibitors. Next, 30 ml of St, 0.3 g sodium p-styrenesulfonate (NaSS), and 1.5 ml DVB were dissolved in a mixture of 150 ml water and 225 ml methanol in a four-necked separable flask placed in a thermostated water bath maintained at 80 °C. The reaction solution was then stirred by a propeller-type mixer for 90 min at 100 rpm, and the solution was purged with argon gas to remove the dissolved oxygen and carbon dioxide. After adding an anionic radical polymerization initiator, potassium persulfate (0.075 g), the solution was further stirred at 80 °C under an argon atmosphere, yielding a turbid colloidal dispersion of PS(-)1 after 6 h.

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The PS(+)1 and PS(+)2 particles were synthesized similarly to PS(-)1 by previously reported method27,28. Here we dissolved 20 ml St, 0.4 ml 2-vinylprydine (cationic co-monomer), and 1 ml DVB in a mixture of 210 ml water and 15 ml ethanol. As the cationic initiator, we added 0.1 g of 2,2’-azobis(2-aminopropane) dihydrochloride. Despite being synthesized from identical start solutions, the particle size and charge numbers of the PS(+)1 and PS(+)2 were significantly different (see Table 1). We attribute these differences to the different adsorptions of cationic monomer and initiator molecules onto the glassware, which might cause uncontrollable concentration variations in the reaction solutions.

Table 1 Characteristics of the colloidal particles investigated in this study. Sample

d Zeff σeff ζ (nm) (mV) (µC/cm2) (103) PS(+)1 420 +0.136 +4.7 ─ PS(+)2 250 +0.046 +0.6 ─ PS(-)1 380 −60 −0.076 −2.2 PS(-)2 600 −71 −0.070 −6.0 PS(-)3 1200 −75 −0.090 −25.6 silica1* 110 −47 −0.075 −0.2 silica2 1000 −42 −0.041 −7.7 *The silica1 data are taken from Ref. 35.

All of the colloid samples were purified by dialysis against Milli-Q water for at least three weeks using dialysis tubes (Nihon Medical Science, Inc., Osaka, Japan) and were further deionized by using a mixed bed of anion- and cation- exchange resin beads [AG501-X8(D), 20–50 mesh, Bio-Rad Labs Inc., CA]. Reagent grade CPC was purchased from Wako Co., Ltd. and used without further purifications29-31. In Table 1, d is the particle diameter determined by the dynamic light-scattering method, and ζ denotes the zeta potential of the particles. The ζ values were calculated by rearranging the Henry equation (1), where the average mobility u was obtained from at least 100 particles.

.

(1)

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Here εr and ε0 are the permittivity of the medium (water) and a vacuum, respectively, and η is the viscosity of the medium (water). κ is the Debye parameter, defined as 𝜅 ! = 𝑒! 𝜀! 𝜀! 𝐼, where e0 is the elementary charge and I = Σ zj2cj is the ionic strength of the medium (zj and cj are the valences and concentrations, respectively, of the j-th small ion). a is the particle radius, and f(κa) is a Henry function, which can be well approximated as 32

.

(2)

The positive ζ values of PS(+)1 and PS(+)2 particles were difficult to evaluate, because these particles strongly adsorbed to the negatively charged glass cell, preventing precise measurements. The microscopic electrophoresis was not applicable to silica1 particles, because of their small sizes. ζ of silica1 shown in Table 1 was a value determined in our previous study35 by means of electrophoretic dynamic light scattering. The σeff value determined by the electrical conductivity measurements was -0.086 µC/cm2, which showed a close agreement with calculated σeff value from the ζ value. The overall charge of the particles is reduced by counter-ions that partially condense inside of the Stern layer. The effective surface charge densities of the particles, σeff, were calculated from the ζ values using the Poisson–Boltzmann equation33.

(3) with

.

(4)

In (4), kBT is the Boltzmann temperature. The effective charge numbers Zeff of the particles other than PS(+)1 and PS(+)2 were calculated as Zeff = 4πa2 σeff/e0. The Zeff and σeff values of

6


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PS(+)1 and PS(+)2 were determined by electrical conductivity measurements, as reported in our previous papers18,34. To avoid elution of ionic impurities from the container walls, the samples for the cluster experiments were prepared using PS or Teflon apparatus rather than glassware. Water was purified through a Milli-Q Integral system (Millipore, MA) and collected in Teflon bottles, where its electrical conductivity was measured as 0.4–0.6 µS cm−1.

2-2. Methods Dynamic light scattering experiments Particle diameters were determined using a dynamic light scattering apparatus (FDLS-3000 system; Photal Co., Ltd., Osaka, Japan), equipped with a solid laser (100 mW, wavelength = 532 nm). The diffusion coefficients D of the particles were measured at particle concentration Cp ≤ 0.01% and at sodium chloride concentration [NaCl] = 10 µM. From D, the particle diameters were estimated by the Stokes–Einstein equation. Electrical conductivity measurements The conductivity measurements were performed using a type DS-52 conductivity meter (Horiba Co., Ltd., Kyoto, Japan) and a conductivity cell with a cell constant of 1.00 cm−1. The temperature of the sample was controlled at 25.0 ± 0.3 °C in a thermostat water bath. All values are the averages of at least three independent measurements. Ζeta potential measurements The electrophoretic mobility of the colloidal particles was measured by microscopic electrophoresis using a Zeecom system (Microtec Co., Ltd., Chiba, Japan). The particle number concentration np was 109–1011 L−1 and [NaCl] was 10 µM. The ζ of silica1 in Table 1 was taken from reference35. Optical microscopy

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Samples were observed under an inverted-type microscope (ECLIPSE Ti-S, Nikon Co., Ltd., Tokyo, Japan) with an oil immersion objective (×100). The micrographs were recorded by a high-speed camera (type FASTCAM Viewer, Photron Co., Ltd., Tokyo, Japan) at a sampling rate of 60 frames/s. Adsorption isotherms Aqueous solutions of CPC at specific concentrations were mixed with colloidal samples and subjected to ultracentrifugation in an Optima XE-90 centrifuge apparatus (Beckman Coulter, CA) at 40,000 rpm for 60 min. The temperature was controlled at 25 °C. The concentrations of non-adsorbed CPC molecules in the resulting supernatants were determined in a UV-VIS spectrophotometer (UV-2400PC; Shimadzu Co., Ltd., Kyoto, Japan) by measuring the optical absorption at 257 nm (the absorption wavelength of CPC). The amount of CPC (near its cmc) adsorbed to the PS particles was determined by conductivity titration of CPC against a PS dispersion. The conductivity vs. Csurf plot for aqueous CPC solution featured a clear bending point near Csurf = c.m.c. In the titration curve for the PS dispersion the bend appeared at higher Csurf, reflecting the adsorption of CPC molecules to the PS particles. From these data, we calculated the adsorbed amount of CPC. The titration curves are provided in Supporting Information.

3. Results and Discussion 3-1. Clustering of oppositely charged particles This subsection reports the clustering of oppositely charged particles in the absence of surfactants. In particular, we describe the experimental conditions under which isolated clusters form. The electrostatic interaction between two spherical particles 1 and 2 is often modeled by the Yukawa potential36.

,

(5)

where r is the center-to-center distance between the two particles and ai and Zi (i = 1 or 2) are

8


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the radius and charge number, respectively, of particle i. Thus, the major governing parameters of the clustering are Zi, ai, and I (∝ κ2). In the present study, we treat Zi as a tunable parameter and investigate its influence on the clustering behavior. We selected low I conditions to ensure strong electrostatic interactions. Specifically, I was maintained at 10 µM by NaCl addition, buffering it against changes caused by trace amounts of ionic contaminants. The present study is limited to a specific range of particle radii (ai = 125–600 nm). The lower limit is imposed by the spatial resolution of the optical microscope, whereas particles larger than 600 nm undergo remarkable sedimentation. Figure 1(a) shows micrographs of typical clusters, in which negatively charged PS particles [PS(-)1, PS(-)2, or PS(-)3] are associated with PS(+)1 particles.

Figure 1 (a) Micrographs and illustrations of the clusters composed of PS(+)1 and PS(-)1, PS(-)2, or PS(-)3.（b）States of binary colloids of PS(+)1 and PS(-)2, defined by the total particle concentration Ctotal and the mixing ratio R = CPS(+)1/CPS(-)2. Observed 24 h after preparation. The mixing ratio in terms of particle numbers (RN) is also shown.

The relationship between the number of associated particles n and the size ratio Rs = a1/a2 of the particles presents an intriguing problem. Schade et al.7 reported that tetrahedral clusters

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are formed in binary colloids of Rs = a1/a2 = 2.45. On the other hand, at the low I of the present study, the n for Rs ≤ 2.86 was limited to 4 by electrostatic repulsions between the attached positive particles. The influence of I on the geometry of the clusters requires further investigation. The particle concentration Cp is another important clustering parameter, because the average interparticle distances are proportional to Cp−1/3. The effects of Cp were examined in binary colloids of PS(+)1 and PS(-)2 particles (with concentrations denoted by CPS(+)1 and CPS(-)2, respectively). Aqueous dispersions of each particle were mixed and shaken for 24 h in an automatic shaker, and the association states were observed by optical microscopy. Figure 1(b) shows the states of the colloids in a plot of particle concentration Ctotal (= CPS(+)1 + CPS(-)2) [in vol%] versus mixing ratio R = CPS(+)1/CPS(-)2. The upper abscissa of Fig. 1(b) represents the concentration ratio in terms of the particle numbers (RN). At sufficiently high Ctotal and small R, the PS(+)1 and PS(-)2 particles formed large aggregations; conversely, isolated clusters formed at sufficiently low Ctotal and large R. In subsequent work, we fixed the RN at 100 and prepared dilute colloids (Ctotal < 0.006vol%). Under these conditions, the clusters were isolated. Namely, they were composed of a single particle of one component and associated particle(s) of another component. Hereafter, we refer to the single and associated particles as central and excess particles, respectively, and express the binary colloids in central/excess format, such as PS(-)2/PS(+)1.

3-2. Adsorption isotherms of CPC onto the PS and silica particles To determine the adsorption isotherms of CPC onto the PS and silica particles, we detected the concentration of the non-adsorbed CPC molecules, C. The adsorbed amounts of CPC, S, were then calculated as S = Csurf − C. The adsorbed amount per (geometrical) unit surface area is given by S/Atot, where Atot = 4πa2Np is the total surface area of the particles (here, Np is the number density of the particles). Figure 2 (a) plots the S/Atot vs. C trends for the PS(-)1 and silica1 particles.

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Figure 2 (a) Adsorbed amounts per unit surface area (S/Atot) vs. concentration of non-adsorbed CPC (C). Blue and green symbols represent PS(-)1 and silica1, respectively. Orange symbols are the data of PS(+)2. Solid and dashed curves are fitted to the Langmuir adsorption curve. (b) A magnified plot of silica1. (c) The plot in a wider C region; the data at C above c.m.c. are included. The data for positively charged PS(+)2 are also shown for comparison (orange symbols). The results for silica1 are clarified in Fig.2(b), which enlarges the lower part of the vertical axis of Fig.2(a). The Cp values for PS(-)1, PS(+)2, and silica1 were 0.7vol%, 1.3vol%, and 1.7vol%, respectively, giving Atot values of 103 cm2/mL for PS(-)1 and PS(+)2, and 104 cm2/mL for silica1. In Fig.2(c) is the plot in a wider C range. Apart from Csurf ~1120 µM for PS(-)1, which was determined from the conductivity titration, all of these results were determined from ultracentrifugation data. We did not use the data above c.m.c. ( = approximately 1100 µM) on analyzing the adsorption isotherm, because then we have to take both the adsorption and association (micelle formation) equilibrium into account. Cationic surfactant molecules are thought to adsorb onto negatively charged PS surfaces in water by two mechanisms37: first, their cationic head groups electrostatically adsorb to the negative charge groups on the PS surfaces; next, the alkyl groups of the surfactants adsorb by hydrophobic interaction to the PS surfaces and also to already adsorbed CPC molecules37. According to the electrical conductivity titrations, a single PS(-)1 particle

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had 20,500 negatively charged groups (sulfonic and sulfuric acid groups). From this result, the concentration of the charged groups on the PS(-)1 colloids was calculated as 40 µM. As seen in Fig. 2, the C of PS(-)1 was nearly zero below S/Atot = 0.04 µM/cm2, i.e., S = 40 µM, indicating strong electrostatic adsorption to the charged groups. Under this condition, the net charge of PS(-)1 should be zero. Therefore, for this sample, Ciep is 40 µM, and the PS(-)1 particles should become positively charged at Csurf > 40 µM. Within this positively charged region, the S–C curves are well-fitted to a Langmuir-type adsorption isotherm; that is, S = ΔS + k1CΓ1/(1+ k1C), with ΔS = 40 µM, k1 = 0.013 M−1, and Γ1 = 246 µM. We note that CPC molecules also significantly adsorbed onto the positively charged PS(+)2 particles (Fig. 2). Thus, we may reasonably surmise that adsorption onto PS(-)1 occurred after the charge inversion. The adsorption of alkylpyridinium cations to silica surfaces has been extensively studied38,39. The adsorption amount increases with increasing pH36,37,40 because the Zeff of silica enlarges at higher pH. Under neutral conditions, however, adsorption is not remarkable because of the low charge number and hydrophilic nature of the surfaces. The pH of the sample in the present study was around 6 because of dissociations of silanol groups (Si-OH) on the silica particles and dissolution of airborne carbon dioxide. Thus, the adsorption amount of CPC was much lower on silica particles than on PS particles (see Fig. 2). The entire adsorption isotherm (covering the entire Csurf region) was well-fitted by a Langmuir-type adsorption; that is, S = k2CΓ2/(1+ k2C), with k2 = 0.069 M−1 and Γ2 = 24 µM.

3-3. Association states of various colloids on additions of CPC Using optical microscopy, we then examined the clustering in the presence of CPC. For this investigation, we used charged PS(-)2 and silica2 and positively charged PS(+)1. The Ctotal of all samples was 0.01vol%. Table 2 illustrates the states of the various colloids after CPC addition. The dashes, circles, and triangles in Table 2 indicate stable conditions (under which no association was observed), conditions under which isolated clusters were formed, and conditions leading to large aggregations, respectively. We note that both the clustering and aggregations states were irreversible. That is, once formed at a certain Csurf, the clusters did not dissociate into individual particles in the presence of CPC, implying that Csurf is stable.

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None of the samples formed clusters solely of excess particles. The association behavior in Table 2 can be explained in terms of the changing interparticle interactions as Csurf is varied. Table 2 States of colloids in the presence of cethylpyridinium chloride (CPC) at various concentrations Csurf, determined by optical microscopy: dashes, no cluster formation; circles, isolated clusters; triangles, aggregation containing multiple central particles.

one component

sample

two components

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0

5

Csurf ( M) 50 100 500

PS(+)1

PS(-)2 cent.

PS(-)2

ex.

PS(+)1

cent.

silica2

ex.

PS(+)1

cent.

silica2

ex.

PS(-)2

(i) One-component colloids of the positively charged PS(+)1 failed to associate at any Csurfs, implying that Z should monotonously increase with increasing Csurf. At higher Csurf, the interparticle interaction was more significantly screened by non-adsorbed CPC ions; however, the screening was insufficient to initiate coagulations under these conditions. (ii) The binary mixtures of oppositely charged particles (PS(-)2/PS(+)1 and silica2/PS(+)1) clustered in the absence of CPC. No PS(-)2/PS(+)1 clusters were formed at Csurf > 50 µM, probably because of the charge reversal at high Csurf. The expected mechanism is illustrated in Fig. 3(a).

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Figure 3 Changes in particle charge number Z as Csurf is varied; (a) positively and negatively charged particles and (b) two negatively charged particles with different iep. Clusters form when the two particles are oppositely charged. The silica2/PS(+)1 clusters was formed at Csurf = 500 µM, which was two orders of magnitude larger than the Csurf (5 µM at the largest) for PS(-)2/PS(+)1 cluster. This is apparently because the Ciep is much larger (indicating lower CPC adsorption) for silica than for PS(-)2. (iii) Finally, the negatively charged PS(-)2 and silica2/PS(-)2 binary colloids formed clusters at moderate Csurf. We note that the Ciep of PS(-)2 at these concentration was approximately 10 µM, close to the coagulation concentration of PS(-)2. Here, the clustering should be mainly driven by VDW attraction and/or hydrophobic interactions between the particles. (Furthermore, because the adsorbed amounts of CPC molecules differ among the individual particles, the distribution of net charges must be polydispersed. Thus, clusters may form among oppositely charged particles coexisting around the iep.) Binary colloids of silica2 and PS(-)2, with very different Cieps, can cluster by electrostatic attraction between the oppositely charged particles, as illustrated in Fig. 3(b). Since the silica2/PS(-)2 colloids formed isolated clusters over a wide range of Csurf, we selected them for more detailed study in the following analyses.

3-4. Clustering of negatively charged PS and silica particles via CPC adsorption We determined distribution of associated particle number n of the cluster of silica2/PS(-)2 (CPS(-)2 = 5 ×10-3vol%, Csilica2=5 ×10-5vol%) from optical micrographs. First we

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examined a number of images i required to obtain statistically reliable results. We have counted n values of 1000 images of the central particle, and tested a convergence of the average value on increasing i. Figure 4 shows / vs. i plot determined from the micrographs taken at various Csurfs (t = 2h). /< n1000> approached 1 at i = approximately 600~1000. Thus, in the followings experiments, we analyzed at least 1000 images of the central particles.

Csurf = 5 M = 10 M

2.0

= 25 M = 75 M = 100 M = 200 M

1.5

/

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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> 1000

1.0

>/> 1 (PS) and Γ3 = 0 (silica). Γ2 and Γ4 were assigned as the Γ values determined for non-electrostatic adsorption for PS and silica, respectively (subsection 3-2).

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2

(b) 100

10 0 10-2 10

C

80

SPS

60

C( M)

C, SPS, SSi ( M)

(a)10

SSi

-4

10-6 1

10

0

100

Csurf( M)

0

50

100

50

100

Csurf( M)

(d) 60 50

SSi( M)X10-6

0.3 0.2 0.1 0.0

40 20

(c) 0.4

SPS( M)

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0

50

100

Csurf( M)

40 30 20 10 0 0

Csurf( M)

Figure 7 Non-adsorbed and adsorbed amounts of CPC in binary colloids of PS(-)2 (5 ×10−3vol%) and silica2 (5 ×10−5vol%), calculated by equation (8). (a) Concentration of non-adsorbed CPC (C), amounts adsorbed to PS (SPS) and amounts adsorbed to silica (SSi) particles, plotted against Csurf on a double logarithmic scale. The relationships are linear in Panels (b), (c), and (d). The dotted curves in (a)–(d) are the results of one-component colloids. Based on these data, we calculated C and the adsorbed amounts of PS and silica particles, SPS (= S1 + S2) and SSi (= S4), as functions of Csurf under the conditions of the clustering experiments (Fig. 5). The results are shown in Panels a–d of Fig.7. Because the particle concentrations and CPC adsorption is much lower for silica2 than for PS(-)2, we found that SSi approximately 150 µM, because both ZPS and ZSi were inverted to be positive. Nevertheless the clusters were formed under this high Csurf conditions. This appears be due to a large distribution in ZSi [cf. Figure 6(a)], that is, coexistence of negatively charged silica particles in the sample. It should be noted, however, that the interparticle force is difficult to evaluate at very small H. First, the validity of the Yukawa [Equation (5)] and VDW [(9)] potentials between two spheres is questionable. In addition, because counter-ions (mainly Cl- anions of the adsorbed CPC molecules) are condensed in the gap between the PS and silica particles, the effective κ at such small distances might be much larger than estimated. Furthermore, to more precisely estimate the interparticle force, we should account for the thicknesses of the hydration layer of water molecules and the adsorbed CPC molecules and the roughness of the particle surfaces. Interaction potentials for osmotic and elastic effects due to the adsorbed molecules have been proposed; an estimated attraction was ~100 kBT at H < a few nm for adsorbed surfactant.45-48 At this stage, we can conclude that the interparticle force is sufficiently larger than kBT at small separations, and that the clustering is optimized at small Csurf. We emphasize that the above discussion is based on pair potentials and cannot describe the attachments of second (and further) particles. A detailed numerical study on the attachments of multiple particles is ongoing in our laboratory.

4. Conclusions The present paper reports clustering of charged colloidal particles by tuning the charge number of the particles, mediated by the adsorption of cationic surfactant, CPC. In particular, we examined heteroclustering in binary colloids of negatively charged PS and silica particles. The clustering was dominated by electrostatic interaction, whose magnitude could be estimated from the adsorption isotherms. The present findings should assist the construction of heterogeneous colloidal clusters composed of various kinds of particles. Because the association number of the present clusters has large distribution, fractionation of the cluster will be necessary. Then, in addition to a density gradient centrifugation,6 the electrophoresis would be useful for the present clusters, because they have large distribution

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also in the net charge number.

Acknowledgements We sincerely thank Dr. C. Patrick Royall, Bristol University, for his kind help and valuable discussions. Supporting Information Conductivity titration data to estimate c.m.c. of CPC. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author E-mail: [email protected] Author Contributions The manuscript was written through contributions from all authors. All authors have given approval to the final version of the manuscript. Funding Sources This work was partly supported by KAKENHI, Japan Society for the Promotion of Science (24550160, to JY).

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Controlled Clustering in Binary Charged Colloids by Adsorption of

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