Zeta Potential of Mica Covered by Colloid Particles: A Streaming

pubs.acs.org/Langmuir © 2010 American Chemical Society

Zeta Potential of Mica Covered by Colloid Particles: A Streaming Potential Study Zbigniew Adamczyk,* Maria Zaucha, and Maria Zembala Institute of Catalysis and Surface Chemistry, Polish Academy of Science, Niezapominajek 8, 30-239 Cracow, Poland Received January 25, 2010. Revised Manuscript Received March 12, 2010 The streaming potential of mica covered by monodisperse latex particles was measured using the parallel-plate channel, four-electrode cell. The zeta potential of latex bearing amidine charged groups was regulated by the addition of NaCl (10-4-10-2 M) and MgCl2 (10-4-10-2 M) at a constant pH 5.5 and by the change in pH (4-12) at 10-2 M NaCl. The size of the latex particles, determined by dynamic light scattering, varied between 502 and 540 nm for the above electrolyte concentration range. Mica sheets have been covered with latex particles under diffusion transport conditions. The latex coverage was regulated by the bulk suspension concentration in the channel and the deposition time. The coverage was determined, with a relative precision of 2%, by the direct enumeration of particles by optical microscopy and AFM. The streaming potential of mica was then determined for a broad range of particle coverage 0 < θ < 0.5, the particle-to-substrate zeta potential ratio ζp/ζi, and 8.8 < κa < 143 (thin double-layer limit). These experimental data confirmed that the streaming potential of covered surfaces is well reflected by the theoretical approach formulated in ref 32. It was also shown experimentally that variations in the substrate streaming potential with particle coverage for θ < 0.3 and ζp/ζi < 0 are characterized by a large slope, which enables the precise detection of particles attached to interfaces. However, measurements at high coverage and various pH values revealed that the apparent zeta potential of covered surfaces is 1/21/2 smaller than the bulk zeta potential of particles (in absolute terms). This is valid for arbitrary zeta potentials of substrates and particles, including the case of negative particles on negatively charged substrates that mimics rough surfaces. Therefore, it was concluded that the streaming potential method can serve as an efficient tool for determining bulk zeta potentials of colloids and bioparticles.

1. Introduction Understanding deposition (irreversible adsorption) mechanisms of colloids and bioparticles at solid/liquid interfaces is of major significance in a variety of fields ranging from geophysics, material and food sciences, pharmaceuticals, cosmetics, medical sciences, electrophoresis, chromatography, catalysis, and so forth. Protein adsorption processes are involved in artificial organ failure, plaque formation, fouling of contact lenses and heat exchangers, ultrafiltration, and membrane filtration units. Controlled protein deposition (irreversible adsorption) on various surfaces is a prerequisite for their efficient separation and purification by chromatography and filtration and for biosensing, bioreactors, immunological assays, and so forth. Because of its major significance, much experimental work has been devoted to the subject of protein deposition using various techniques, for example, the solution depletion methods,1 the gravimetric methods, especially the quartz microbalance (QCM),1-3 optical methods such as ellipsometry and reflectometry,4-6 fluorescence methods, e.g., total internal fluorescence (TIRF),7,8 and isotope *Corresponding author. E-mail: [email protected]. (1) Ramsden, J. J. Q. Rev. Bipohys. 1993, 27, 41–105. (2) Reisch, A.; Voegel, J. C.; Gonthier, E.; Decher, G.; Senger, B.; Schaaf, P.; M
esini, P. J. Langmuir 2009, 25, 3610–3617. (3) Choi, K. H.; Friedt, J. M.; Frederix, F.; Campitelli, A.; Borghs, G. Appl. Phys. Lett. 2002, 81, 1335–1337. (4) Melmsten, M. J. J. Colloid Interface Sci. 1994, 166, 333–342. (5) Buijs, J.; van den Berg, P. A. W.; Lichtenbelt, J. W. Th.; Norde, W.; Lyklema, J. J. Colloid Interface Sci. 1996, 178, 594–605. (6) Buijs, J.; White, D. D.; Norde, W. Colloids Surf., B 1997, 8, 239–249. (7) Lin, Y. Sh.; Hlady, V. Colloids Surf., B 1994, 2, 481–491. (8) Yoon, J. Y.; Park, H. Y.; Kim, J. H.; Kim, W. S. J. Colloid Interface Sci. 1996, 177, 613–620. (9) Hlady, V.; Reinecke, D. R.; Andrade, J. D. J. Colloid Interface Sci. 1986, 111, 555–569. (10) Zembala, M.; Voegel, J. C.; Schaaf, P. Langmuir 1998, 14, 2167–2173. (11) Zembala, M.; Dejardin, P. Colloids Surf., B 1994, 3, 119–129.

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labeling.9-11 For the low-coverage range, the AFM methods can be quite efficient in the direct determination of protein coverage.12-14 However, despite significant progress in the field of protein and biomolecule deposition, there are still discrepancies, even conflicting reports in the literature, concerning the kinetics and reversibility. This is caused by the limited availability of direct experimental techniques working under dynamic conditions (e.g., in flowing cells used to enhance mass-transfer rates). One of a few such in situ methods for determining the particle and protein deposition kinetics and properties of their monolayers is based on streaming current or streaming potential measurements. Such electrokinetic experiments have been carried out using parallel plate channel cells devised originally by van Wagenen and Andrade15 and then using widely determined electrokinetic characteristics of bare surfaces (mica and silica slides)16-18 and colloid particle19-26 or protein-covered surfaces.11,27-30 (12) Ortega-Vinuesa, J. L.; Tengwall, P.; Lundstrom, I. Thin Solid Films 1988, 324, 257–237. (13) Marchin, K. L.; Berrie, C. L. Langmuir 2003, 19, 9883–9888. (14) Toscano, A.; Santore, M. Langmuir 2006, 22, 2588–2597. (15) van Wagenen, R. A.; Andrade, J. D. J. Colloid Interface Sci. 1980, 76, 305–314. (16) Scales, P. J.; Grieser, F.; Healy, T. W. Langmuir 1990, 6, 582–589. (17) Scales, P. J.; Grieser, F.; Healy, T. W. Langmuir 1992, 8, 965–974. (18) Debacher, N.; Ottewill, R. H. Colloids Surf., A 1992, 65, 51–59. (19) Adamczyk, Z.; Warszy
nski, P.; Zembala, M. Bull. Pol. Acad. Sci., Chem. 1999, 47, 239–258. (20) Zembala, M.; Adamczyk, Z. Langmuir 2000, 16, 1593–1601. (21) Zembala, M.; Adamczyk, Z.; Warszy
nski, P. Colloids Surf., A 2001, 195, 3–15. (22) Hayes, R. A. Colloids Surf., A 1999, 146, 89–94. (23) Hayes, R. A.; Biehmer, M. R.; Fokkink, L. G. J. Langmuir 1999, 15, 2865–2870. (24) Michelmore, A. P.; Hayes, R. A. PhysChemComm 2000, 3, 24-28. (25) Zembala, M.; Adamczyk, Z.; Warszy
nski, P. Colloids Surf., A 2003, 222, 329–339. (26) Zembala, M. Adv. Colloid Interface Sci. 2004, 112, 59–92. (27) Norde, W.; Rouwendal, E. J. Colloid Interface Sci. 1990, 139, 169–176. (28) Norde, W.; Takaaki, A.; Hiroyuki, S. Biofouling 1991, 4, 37–51.

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The major advantages of such streaming potential cells are a large working area that increases measurement precision, the possibility of direct microscope observation of surfaces under wet conditions, and a simpler theoretical interpretation of results. However, a disadvantage of the setup is the very tedious, timeconsuming assembly prior to experiment, sealing problems, and the necessity of determining the correction due to surface conductance of the cell. To reduce sealing problems, in measurements of protein deposition kinetics, circular channel cells were also used11 whose construction is simpler than that of the plate channel cells. However, the range of capillary materials available for such studies is rather limited, and there are also significant problems with cleaning and examining surfaces by microscopy or by other surface-oriented techniques. Recently, an efficient approach aimed at the complex characterization of protein monolayer formation at polymeric substrates has been developed.31 The method is based on a combination of electrokinetic (streaming potential and streaming current) measurements carried out in the microslit setup with in situ reflectometric interface spectroscopy and QCM. Although streaming potential/current methods have been successful in determining protein adsorption kinetics,11,27-31 their widespread use is hindered by the lack of appropriate calibrating experiments performed for well-defined colloid suspensions. A few exceptions represent previous work performed for latex particle/mica systems.19-25 However, these results have been obtained for a limited particle coverage range not exceeding 0.3. Moreover, because of the lack of an appropriate theoretical background, these results were interpreted in terms of a semiempirical model, which prohibited one from deriving conclusions of more universal validity. Recently, exact theoretical results became available, describing the dependence of the streaming potential on particle coverage, which are valid for a broad range of particle coverage up to 0.5.32 These results, derived from numerical solutions of the Navier-Stokes hydrodynamic equation for particle-covered surfaces, enable a proper interpretation of the experimental data for the entire range of particle coverage used. Until now, however, the validity of these theoretical predictions has not been confirmed, which prohibits the use of the theory for interpreting experimental results obtained for more complicated systems such as proteins. Therefore, the goal of this article is to verify experimentally, using well-defined colloidal particle suspensions, the range of validity of the new theoretical results, with emphasis on the highcoverage asymptotic behavior. These experiments will allow one to determine a unique relationship between the zeta potential measured in the bulk by electrophoresis and the apparent zeta potential of particles attached to surfaces. This issue is essential for the entire field of electrokinetics. It may also have far reaching practical consequences because measurements of low zeta potentials are impractical in view of the inherent instability of particle suspensions. In contrast, such low zeta potentials can easily be determined by the streaming potential/current measurements, which allow one to determine protein isoelectric points. This, however, requires a proper calibration, involving well-defined colloid particle systems. (29) Elgersma, A. V.; Zsom, R. L. J.; Lyklema, J.; Norde, W. Colloids Surf., A 1992, 65, 17–28. (30) Vasina, E. N.; Dejardin, P. Langmuir 2004, 20, 8699–8706. (31) Osaki, T.; Renner, L.; Herklotz, M.; Werner, C. J. Phys. Chem. B 2006, 110, 12119–12124. (32) Sadlej, K.; Wainryb, E.; Bzawzdziewicz, J.; Ekiel-Je_zewska, M; Adamczyk, Z. J. Chem. Phys. 2009, 130, 144706–144711.

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2. Theoretical Model The streaming current Is is the result of the convective flux of ions from the thin double-layer region adjacent to solid/electrolyte interfaces. It is induced by a macroscopic flow of the liquid, usually driven by the hydrostatic pressure gradient (e.g., for channel and capillary flows). The constitutive equation for the streaming current is33 ZZ Is ¼ Fe V 3 dS ð1Þ S

where S is the surface area, Fe is the electric charge density, V is the macroscopic fluid velocity field, and dS is the surface element. Assuming that the electric charge density is governed by the Poisson-Boltzmann equation, unperturbed by the flow Fe ¼ -ε r2 ψ

ð2Þ

where ε is the dielectric permittivity of the medium (dimensional) and ψ is the electric potential. One can formulate the expression for the streaming current, eq 1, in the form ZZ ð3Þ -Is ¼ -ε r2 ψV 3 dS S

For many types of flow (e.g., channel flow), the fluid velocity distribution in the region adjacent to solid interfaces can be well approximated by a simple shear flow, described by the equation V ¼ Go zix

ð4Þ

where V is the liquid velocity vector, Go = (rV)0 is the shear rate at the interface, z is the coordinate locally perpendicular to the interface, and ix is the unite vector in the direction parallel to the interface. For such types of flow, one can integrate eq 3 by parts, which results in the following expression for the streaming current Is for homogeneous surfaces (in the absence of particles)33 - Is ¼ εGo lζ ¼ Cl ζ

ð5Þ

where l is the width of the interface, Cl = εGol, and ζ is the electric potential in the slip plane, referred to as the zeta potential.34-36 Equation 5 is valid for an arbitrary charge of the interface, electrolyte concentration, and composition, including mixtures of electrolytes of arbitrary valency. It can be evaluated explicitly for some geometries of major practical significance, where the shear rate at the interface is known from analytical solutions of the Navier-Stokes equation. For example, in the case of a cylindrical plate channel (capillary) with radius Rc, where the perimeter of the capillary is l = 2πR and Go = ΔPRc/2ηL,37 eq 5 becomes - Is ¼ ε

πΔPRc 2 ζi ¼ - Is0 ηL

ð6Þ

where ΔP/L is the hydrostatic pressure gradient along the capillary of length L and η is the dynamic viscosity of the liquid. For a parallel-plate channel with a cross section of 2bc  2cc (where 2bc is the channel height and 2cc = l is the channel width) characterized by bc/cc , 1 (which is usually the case in experimental (33) Adamczyk, Z.; Nattich, M.; Zaucha, M. Curr. Opin. Colloid Interface Sci., in press. (34) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press: London, 1981; pp 1-386. (35) Werner, C.; Koerber, H.; Zimmermann, R.; Dukhin, S.; Jacobasch, H. J. J. Colloid Interface Sci. 1998, 208, 329–347. (36) Delgado, A. V.; Gonzales-Caballero, F.; Hunter, R. J.; Koopal, L. K.; Lyklema, J. J. Colloid Interface Sci. 2007, 309, 194–224. (37) Adamczyk, Z. Particles at Interfaces: Interactions, Deposition, Structure; Elsevier/Academic Press: Amsterdam, 2006; pp 214-219.

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studies), the expression for IS becomes33 "

 # bc ζ2 ζi - Is ¼ 2εGo cc 1 - 0:54 1cc ζi

ð7Þ

where ζ2 is the zeta potential of the side walls of the channel. Equation 7 can be used to estimate the correction associated with the fact that the side walls of a parallel-plate channel are usually made of a different material than the base walls (usually made of the substrate to be studied). For bc/cc = 1/20 (which is a typical value for the channel used in our work) assuming ζ2/ζi = 0.5, the correction is 0.014. In the extreme case of ζ2/ζi = 0 (if the side walls are not charged), the correction equals 0.027. This error is significantly smaller than others, connected mostly to the electrode asymmetry potential and surface conductivity, and therefore can be neglected. It is to be mentioned, however, that the above expressions for Is are valid only if the double-layer thickness remains considerably smaller than the channel width 2bc, which is fulfilled for most experiments. Flow-induced electric charge transport away from the doublelayer region adjacent to the interface results in the appearance of an electric potential difference, referred to as the streaming potential Es. This generates a backward electric current Ib = -Is due to the electric conductance of the cell. As discussed in refs 34-36, the streaming potential is connected to the streaming current by the Ohmic dependence Es ¼ - Is Re ¼ Ib Re

ð8Þ

where Re is the overall electric resistance of the cell governed mainly by the specific conductivity of the electrolyte in the cell. However, for dilute electrolytes and thin channels, the contribution stemming from surface conductance starts to play a significant role34-36 and thus special procedures are to be undertaken to correct for this effect. Thus, in the general case Re can be expressed as Re ¼

L L ¼ ΔSc Ke ΔSc ðKe0 þ Ks Þ

ð9Þ

where ΔSc is the channel cross-sectional area, K0e is the specific conductivity due to electrolyte, and Ks is the surface conductivity, depending in the general case on the channel shape.35,36 By considering eq 9, one can specify the following formula for the streaming potential in the case of the rectangular channel " Es ¼ Es0

 # bc ζ2 1 - 0:54 1cc ζi

ð10Þ

where Es0 ¼ 4ε

ΔPbc cc Re ΔP ζi ¼ ε ζ ηKe i ηL

ð11Þ

is the streaming potential for the parallel-plate channel. For the cylindrical channel with radius Rc, one obtains an identical expression33 ΔPπRc 2 Re ΔP ζi ¼ ε Es0 ¼ ε ζ ð12Þ ηKe i ηL As can be noticed, when introducing the specific conductivity, the expressions for the streaming potential are the same for 9370 DOI: 10.1021/la1003534

arbitrary channel cross sections if the walls are made of the same material. This is so, however, only if the surface conductivity contribution can be neglected. Equation 12 was first derived by Smoluchowski.38 By knowing the effective conductivity and the slope of the Es versus ΔP dependence ΔEs/Δ(ΔP), one can calculate the apparent zeta potential of the channel from the formula20,26 ζ ¼

ηKe ΔEs ε ΔðΔPÞ

ð13Þ

We mention, however, that all of the above formulas are valid for a homogeneous charge distribution over interfaces and for uniform (position independent) flow. When particles are present at interfaces, both of these conditions are violated because they disturb the electric charge distribution near interfaces and the macroscopic flow V in their vicinity. As discussed in ref 33, the general expression for the streaming current of a homogeneous interface covered uniformly by particles is given by " Is ðθÞ ¼ Is0

#    a a ζp θ þ Ap 1 - Ai θ Le Le ζi 

ð14Þ

where Ai(θ) and Ap(θ) are the dimensionless functions of particle coverage and a/Le (where Le = κ-1) is the thickness of the double layer. In the limit of low coverage, functions Ai(θ) and Ap(θ) approach the constant values of C0i = 10.2 and C0p = 6.51, respectively,19,32 and remain practically independent of a/Le for the range of a/Le> 2 as shown in ref 21. However, the following semiempirical fitting functions for Ai(θ) and Ap(θ) have been proposed in refs 20 and 21 and are applicable to the arbitrary range of particle coverage reaching 0.5 1 - e - Ci θ θ 1 - e - Cp θ Ap ðθÞ ¼ θ Ai ðθÞ ¼

ð15Þ

Recently, exact theoretical results have been derived in the limit of thin double layers,32 and these can be used to determine the range of validity of these semiempirical correction functions. These results were obtained by evaluating numerically the flow in the vicinity of adsorbed particles using the multipole expansion method for a coverage range of up to 0.5. The numerical results allowed us to formulate the analytical interpolation functions, which approximated the exact numerical results to a precision of better than 1%. 10:2 - 5:75θ Ai ðθÞ ¼ 1 þ 5:46θ ð16Þ 6:51 - 2:38θ Ap ðθÞ ¼ 1 þ 5:46θ As shown in ref 32, the interpolating expression for the Ai function given by eq 16 coincides over the entire range of coverage with the semiempirical function given by eq 15. However, the exact expression for Ap shows a larger deviation from the semiempirical counterpart, eq 15, in the limit of higher coverage. (38) von Smoluchowski, M. Bull. Int. Acad. Sci. Cracovie 1903, 182–199.

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For the interpretation of the experimental results, it is advantageous to express eq 14 in reduced form. For interfaces covered uniformly with particles (e.g., the capillary tube or a homogeneous parallel-plate channel), one has the expression Is ¼ Es ¼ 1 - Ai ðθÞθ þ

ζp Ap ðθÞθ ζi

ð17Þ

where Is ¼

I E , Es ¼ Is0 Es0

However, in the case of a heterogeneous parallel-plate channel composed of two plates of different zeta potentials: ζ1, ζ3 and different coverage on the two basal plates θ1 and θ2, eq 17 can be generalized to the form Es ¼

Es Es 0

¼ 1 - Ai ðθ1 Þθ1 þ Ai ðθ2 Þθ2 þ

ζp ζi

½Ap ðθ1 Þθ1 þ Ap ðθ2 Þθ2  ð18Þ

where Es ¼

εΔP ζ and ζi ¼ ðζ1 þ ζ3 Þ=2 ηKe i

It is interesting to mention that eq 17 can also be used to determine in a convenient way the zeta potential of particles in the bulk if the apparent zeta potential of the interface covered with particles is known from the streaming potential measurements. To do so, eq 17 is rearranged to the form ζp ¼

ζ - ζi ½1 - Ai ðθÞθ Ap ðθÞθ

ð19Þ

In the high-coverage limit where 1-Ai(θ)θ f 0 and Ap(θ)θ f 1/21/2, eq 19 reduces to the simple form ζp ¼

pffiffiffi 2ζ

I [M], pH

κa

10-4 (NaCl), 5.5 10-3 (NaCl), 5.5 10-2 (NaCl), 5.5 9  10-4(MgCl2), 5.5 9  10-3(MgCl2), 5.5 3  10-2(MgCl2), 5.5 10-2 (TRIS), 9.95 10-2 (NaCl), 10.2 10-2 (NaCl), 11 10-2 (NaCl), 11.8

8.82 27.8 82.5 26.4 80.5 143 82.5 82.5 82.5 82.8

ζi [mV] ζp [mV] -112 -85 -70 -38 -14 -8 -80 -80 -80 -80

49 53 72 75 85 96 10 -20 -44 -70

ζp/ζi

particle size 2a [nm]

-0.44 -0.62 -1.0 -2.0 -6.1 -12 -0.125 0.25 0.55 0.87

538 536 503 540 517 502 503 503 503 503

The real latex particle size as a function of ionic strength and pH was determined by a laser diffractometer (Beckman Coulter LS 13 320 particle size analyzer) with an accuracy of few percent and independently by dynamic light scattering (DLS) using the Malvern Zetasizer Nano. The agreement between both methods was (2%. Values of particle diameter measured under various conditions using the DLS method are collected in Table 1. The zeta potential of the latex was determined for ionic strengths of I = 10-4 and 3  10-2 M (regulated by NaCl and MgCl2 addition) over a pH range of 3.0-12.0 (regulated by HCl or NaOH addition) using a ZetaPals from Brookhaven and a Zetasizer Nano ZS from Malvern. 3.2. Methods. The streaming potential was determined using a homemade apparatus described in detail previously.30,31 The solution flows, because of hydrostatic pressure ΔP exerted between inlet and outlet compartments, through a parallel-plate channel with dimensions of 2bc  2cc  L = 0.027  0.29  4 cm3 formed by mica sheets separated by a perfluoroethylene spacer. The streaming potential was measured for each applied pressure to obtain the slope of the Es versus ΔP dependence. The cell electrical resistance Re was determined to incorporate the surface conductivity effect influencing the streaming potential measured in solutions of lower ionic strength. A correction for surface conductivity was introduced according to eq 9. It is worthwhile to mention that this correction was negligible when the ionic strength of the electrolyte was larger than 10-3 M. The experimental procedure of determining the zeta potential of polyelectrolyte-covered mica consisted of three stages: (i)

ð20Þ

This formula indicates that the bulk zeta potential of a particle is larger by a factor of 21/2 than the limiting value of the apparent zeta potential of an arbitrary substrate surface determined at a high coverage of particles. The main goal of our experimental measurements was to determine the applicability of eqs 17 and 19, especially the possibility of determining bulk zeta potentials from measurements of the streaming potential of a mica surface covered with particles.

3. Experimental Section 3.1. Materials. Ruby mica sheets supplied by Continental Trade Ltd. (Poland) were used as substrates for polystyrene latex particle deposition. Thin mica sheets were freshly cleaved and used in experiments without any pretreatment. Sodium chloride, sodium hydroxide, magnesium chloride, hydrochloric acid, and tris(hydroxymethyl)aminomethan (Tris) were commercial products of Fluka. Ultrapure water (Elix & Simplicity 185 system, Millipore SA Molsheim, France) was used for the preparation of all solutions. Positively charged amidine polystyrene latex particles (a commercial product of Invitrogen) having a nominal size of 520 nm was used as a model colloid suspension. Langmuir 2010, 26(12), 9368–9377

Table 1. Experimental Parameters Characterizing the Mica/A500 Latex Particle System Studied in This Work

measuring the reference zeta potential of bare mica in pure electrolyte, (ii) the formation of the particle monolayer with controlled coverage under diffusion-controlled deposition conditions by filling the cell with the latex suspension for an appropriate time period, (iii) washing the cell with pure electrolyte and measuring streaming potentials for the polyelectrolyte-covered surface, and (iv) determining the surface coverage from pictures taken either with an optical microscope or AFM. As far as step (ii) is concerned, particle deposition experiments were performed by filling the channel with a latex suspension typically having a number concentration of (1 to 2)  1010 cm-3 and an appropriate ionic strength and pH. The volumetric flow rate was 0.2 cm-3, which corresponds to an average suspension velocity of 25.5 cm s-1 and a wall shear rate of Go = 5.55  103 s-1. The relaxation time for establishing steady-state flow conditions was about 0.15 s. Then particle deposition proceeded over the desired time, which was preselected on the basis of theoretical solutions of the governing mass -transfer equation as described previously.37 The true coverage of particles was determined by direct optical microscope counting under wet conditions, as described in our previous work.19-21 Typically, particles were counted over 10-20 equally sized areas chosen randomly over the mica sheet. The net DOI: 10.1021/la1003534

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Figure 1. Dependence of the zeta potential of polystyrene latex particles (A500) ζp on the ionic strength at pH 5.5 and T = 293 K. The points denote experimental values determined for (1) (O) MgCl2 solutions and (2) (b) NaCl solutions. The solid lines represent nonlinear fits to the experimental results. number of deposited particles considered was ca. 1500- 3000, which ensures a relative precision of these measurements of 10.3 was probably due to the specific adsorption of the OH- ions. The zeta potential of the mica substrate was determined via the streaming potential measurements according to the procedure described above. The results obtained in the case of the NaCl electrolyte are shown in Figure 3, in part a (dependence on the ionic strength at constant pH 5.5) and in part b (dependence on pH at a constant ionic strength of 10-2 M). As can be seen in part a, at a low NaCl concentration of 10-4 M the zeta potential of bare mica was -112 mV and increased with NaCl concentration up to -70 mV for a 10-2 M salt concentration. It is interesting to mention that our results agree well with previous data obtained by Scales et al16 at pH 5.8 using the same type of streaming potential cell. At a constant ionic strength of 10-2 M, the zeta potential of mica decreased moderately with increasing pH, varying between -50 mV at pH 4 and -77 mV at pH 10.5 (Figure 3b). As suggested by Scales et al.,16 this behavior can be interpreted by assuming the competitive adsorption of the Hþ and Naþ cations on the surface-binding sites of mica. In this work, a somewhat simplified version of this model was used by assuming that adsorption of both cations occurred in the same plane, characterized by the electric potential equal to ζi. Accordingly, the Langmuir adsorption isotherms for both species can be formulated as θ1 ¼ KaHþ 10 - pH e - ζi e=kT 1 - θ1 - θ2 θ2 ¼ KaMþ aMþ e - ζi e=kT 1 - θ1 - θ2

ð21Þ

where θ1 and θ2 are the hydrogen and sodium cation coverages, respectively, KaHþ and KaMþ are the equilibrium adsorption constants of these cations, a is the activity of the cation in the bulk solution, e is the elementary charge, k is the Boltzmann constant, and T is the absolute temperature. (41) B€ohme, F.; Klinder, C.; Bellmann, C. Colloids Surf., A 2000, 189, 21–27.

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Figure 4. Dependence of the zeta potential of mica ζi on the ionic strength regulated by MgCl2 addition at pH 5.5 and T = 293 K. The points denote experimental results obtained using the parallelplate streaming potential cell, and the solid line represents a linear fit to the experimental results.

Figure 3. Dependencies of the zeta potential of mica ζi on the solution composition. (a) Dependence of the zeta potential of mica ζi on the ionic strength regulated by NaCl addition at pH 5.5 and T = 293 K. (b) Dependence of the zeta potential of mica ζi on pH for the ionic strength regulated with 10-2 NaCl at T = 293 K. The points denote experimental results obtained using the parallel-plate streaming potential cell; the solid lines represent theoretical results calculated from the site-binding model for σ = -0.18 e nm-2, KaMþ = 5  10-5 mol-1, and KaHþ = 0.5 mol-1; and the dashed lines denote results calculated from the Gouy-Chapmann model by neglecting specific adsorption.

Therefore, the net electrokinetic charge σ for a given ionic strength and pH can be expressed in terms of the hydrogen and cation surface coverages as follows σ ¼ -eNo ð1 - θ1 - θ2 Þ

ð22Þ

where No is the surface concentration of binding sites. By knowing the electrokinetic charge, one can calculate the zeta potential of the interface from the constitutive dependence37 pffiffiffiffiffiffiffiffiffiffiffiffi 2kT j σh j þ σh þ 4 ζi ¼ ln e 2

ð23Þ

where σh = σ/2εkTnb is the dimensionless electrokinetic charge and nb = 6.023  1020I (where I is expressed in M) is the number concentration of cations in the bulk. Obviously, in the case of no adsorption, one obtains from eq 23 the standard Gouy-Chapman relationship ζi ¼ -

pffiffiffiffiffiffiffiffiffiffiffiffiffi 2kT j σh 0j þ σh 0 þ 4 ln 2 e

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ð24Þ

where σh0 = σ0/2εkTnb and σ0 = -eN0 is the effective charge of the bare mica surface. As can be noticed, eqs 21-23 represent a set of coupled nonlinear equations. They can be easily transformed to a fourth-order equation, which can be solved in the standard way. As can be noticed in Figure 3, the theoretical results derived from the above model, represented by solid lines, reflect the main features of the dependence of the zeta potential of mica on the ionic strength and pH for the following set of parameters: σ0 = -0.18e nm-2, KaHþ = 5  10-5 mol-1, and KaMþ = 0.5 mol-1. It is interesting to observe that the results derived from the standard GouyChapman model (shown by the dashed lines in Figure 3) deviate significantly from the experimental data, indicating that the effects of the specific adsorption of both cations are significant. As can be observed in Figure 3, the range of zeta potential variation of mica, which can be induced by monovalent cation adsorption, was rather limited and the maximum zeta potential attainable in this way was -55 mV (experimental value) at high ionic strength and pH 4. To increase the available range of mica zeta potential variations, which is important for the precise verification of theoretical predictions, we exploited the phenomenon of pronounced adsorption of divalent cations on mica, as reported previously.17,25 As can be seen in Figure 4, the use of MgCl2 solutions instead of NaCl enabled one to increase the zeta potential of mica significantly, which varied from -70 mV for the 10-5 M salt solution (I = 3  10-5 M) to -8 mV for the 10-2 M salt solution (I = 3  10-2 M). In the latter case, the mica zeta potential was practically negligible in comparison with the particle zeta potential (equal to 96 mV under the same conditions), which allowed us to mimic the conditions of neutral surfaces well. These results suggest that the zeta potential of mica can be adjusted within broad limits by variations of the pH and composition of the supporting electrolyte. This property was exploited in our studies aimed at the verification of the theoretical approach in describing the zeta potential of particle-covered surfaces, which is discussed next. 4.2. Streaming Potential Measurements of Particle-Covered Mica. In the first series of experiments, it was proven that particle deposition was irreversible over the time of the streaming potential measurements under the prevailing flow conditions. No detectable detachment of particles from the mica surface was DOI: 10.1021/la1003534

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Figure 5. (a) AFM (scan size 20  20 μm2) and (b) optical microscopy images (image size 26  36 μm2) of latex particle monolayers on mica (formed at pH 5.5, I = 10-3 M NaCl, θ = 0.1).

observed, not even in the case where the latex potential was converted to negative values, where the repulsive electrostatic interactions were likely to appear. In Figure 5, typical AFM images (surface area of 20  20 μm2) of latex particle monolayers on mica (formed at pH 5.5, I = 10-3 M NaCl) are shown for particle coverage θ = 0.1. After particle monolayers of uniform (in a statistical sense), defined coverage were produced, the streaming potential measurements were carried out according to the procedure described above. In this way, the dependences of the streaming potential Es(θ) and the apparent zeta potential of the channel ζ(θ) have been determined as a function of particle coverage for various physicochemical parameters. In the first series of experiments performed at a fixed pH of 5.5 (water buffered by CO2), the role of the ζp/ζi parameter was determined which was changed by increasing the ionic strength of the suspension. Accordingly, for I = 10-4 M NaCl, ζp/ζi= -0.44; for I = 10-3 M NaCl, ζp/ζi = -0.62; and for I = 10-2 M NaCl, ζp/ζi = -1.0 (Table 1). In Figure 6, the experimental results obtained in this series of experiments are compared with theoretical predictions calculated from eq 19 using the semiempirical and exact correction functions Ai(θ) and Ap(θ), respectively. As can be 9374 DOI: 10.1021/la1003534

Figure 6. Dependencies of the reduced streaming potential of mica Es on the coverage of particles θ. The points denote experimental results obtained for the A500 latex at pH 5.5 and T = 293 K and various ionic strengths: (a) I = 10-4 M NaCl, ζp/ζ i = -0.44; (b) I = 10-3 M NaCl, ζp/ζ i = -0.62; and (c) I = 10-2 M NaCl, ζp/ ζi = -1.0. The solid lines represent exact theoretical results derived from eq 16, and the dashed line shows the results calculated from the exponential fitting function (eq 15).

seen, the theoretical results derived using the exact functions (solid lines in Figure 6) properly reflect the experimental data for the entire range of ζp/ζi and particle coverage studied (up to 0.5). Langmuir 2010, 26(12), 9368–9377

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Figure 7. Dependence of the reduced streaming potential of mica

Es on the coverage of particles θ. The points denote experimental results obtained for the A500 latex at pH 10.5, I = 10-2 M NaCl, and T = 293 K. (1) ()) ζp/ζi = 0.87 (pH 11.8), (2) (þ) ζp/ζ i = 0.55 (pH 11), (3) (O) ζp/ζi = 0.25 (pH 10.2), and (4) (b) ζp/ζi = -0.125 (pH 9.95). The solid line represents the exact theoretical results derived from eq 16, and the dashed line shows the results calculated from the exponential fitting function, eq 15.

However, the results derived from the semiempirical model tend to underestimate the experimental data for θ > 0.2. It is interesting to mention that for such a system of oppositely charged particles and interfaces the sensitivity of the streaming potential measurements is high because the initial slope of Es versus θ was much larger than unity. Therefore, the results shown in Figure 6 suggest that the coverage of particles oppositely charged with respect to the interface can be precisely determined by the streaming potential method, especially for the lowercoverage range below 0.3. In the second series of experiments, the more complicated case of the positive ζp/ζi ratio has been investigated, where both the particles and the interface zeta potentials were negative. This unusual situation has been realized by depositing particles at the desired coverage at pH 5.5. Then, the streaming potential of mica covered with particles was measured by flushing the electrolyte (NaCl þ NaOH, TRIS þ NaOH) having an appropriate value of pH >10. As can be deduced from the previous results shown in Figure 2, this converted the zeta potential of latex particles to negative values, which can be adjusted by a change in pH. As a result, the ζp/ζi parameter assumed positive values in this case, equal to 0.87 at pH 11.8, 0.55 at pH 11, and -0.125 at pH 9.95 (Table 1). Experimental results obtained for this set of ζp/ζi parameters are compared with theoretical predictions calculated from eq 19 using the semiempirical and exact correction functions Ai(θ) and Ap(θ). The most interesting results are those depicted by curve 1 in Figure 7 for ζp = -67 mV and ζi = -80 mV because they approximate the situation of rough interfaces. The degree of surface roughness can be identified with the coverage of spheres θ. As can be seen in Figure 7, the reduced streaming potential for rough surfaces Es decreases with the interface roughness and then approaches a limiting value close to 0.6. These results enable one to draw the conclusion that the zeta potential of rough surfaces is considerable reduced in comparison with the zeta potential of smooth surfaces for a degree of roughness exceeding 0.1. Another interesting case studied in this series of experiments was ζp/ζi = -0.125 (curve 4 in Figure 7), where the zeta potential of the latex was reduced to a negligible value (ζp = 10 mV) by the Langmuir 2010, 26(12), 9368–9377

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increase in pH up to 10.2. Under these conditions (I = 10-2 M), the zeta potential of mica remained highly negative, equal to -80 mV. Thus, in this case of almost neutral particles, the overall effect of the reduction of Es is governed by the Ai(θ) function. As can be seen in Figure 7, the experimental data obtained in this case are reflected properly by the theoretical results derived using the semiempirical and exact correction functions Ai(θ). This confirms that the semiempirical correction function Ai(θ), which has a simple form that is useful for practical applications, can be used as a good approximation for the entire range of particle coverage. It is also interesting that these results have major significance, proving that hydrodynamic effects alone due to flow damping in the vicinity of deposited particles induce considerable changes in the zeta potential. In other words, the zeta potential of particlecovered (heterogeneous) surfaces is determined not only by the value of the particle zeta potential but also by the flow-damping effects controlled by the coverage of particles. This is a direct manifestation of the irreversibility of electrokinetic phenomena, which depend on hydrodynamic rather than thermodynamic conditions. It is also interesting that the slope of the dependence of the reduced streaming potential on the neutral particle coverage is rather large, which suggests that the presence of adsorbed particles (even those not exhibiting any charge) can be precisely detected by the streaming potential measurements, especially for θ < 0.1, where other experimental methods are less accurate. Upon checking the validity of the semiempirical and exact correction functions Ai(θ), an additional series of experiments have been performed with the goal of determining the asymptotic behavior of the Ap(θ) function for the higher-coverage range. As suggested by eq 20, this function can be exploited to determine the zeta potential of particles in the bulk. In this series of experiments, the zeta potential of mica was regulated by MgCl2 addition. Because this electrolyte simultaneously increased the zeta potentials of both mica and latex particles (Table 1), the ratio ζp/ζi was large in these experiments (in absolute terms), varying between -2.0 for I = 9  10-4 M and -12 for I = 3  10-2 M MgCl2. Consequently, the role of charge transport from the double-layer region of adsorbed particles described by the correction function Ap(θ) dominated, which allowed us to determine its applicability experimentally. The results obtained in this series of experiments are plotted in Figure 8 in the form of the ζ/ζp versus particle coverage relationship, which is more suitable for the interpretation of streaming potential measurements for the high-particle-coverage range, as shown in parts a-c of Figure 8. As can be observed, the theoretical results derived using exact functions Ap(θ) (solid lines in Figure 8) reflect well the experimental data for the entire range of ζ/ζp and particle coverage. It is interesting that the asymptotic value of the ratio ζ/ζp determined experimentally seems to approach the theoretical value of 1/21/2 for particle coverage >0.4. Because this finding has major practical consequences, it has been tested in more detail by expressing the experimental results of this work as well as previous results for polyelectrolytes42,43 in the form of the dependence of ζ/ζp on the particle coverage θ. As can be observed in Figure 9, the experimental results obtained for various substrate zeta potentials and particle zeta potentials are well reflected for θ > 0.3 by the theoretical dependence obtained by transforming eq 19 to the form ζ/ζp = ζi/ζp[1 - Ai(θ)θ] þ Ap(θ)θ. Also, the asymptotic theoretical result (i.e., ζi/ζp = 1/21/2) is approached by the experimental data in the limit of high coverage. (42) Adamczyk, Z.; Michna, A.; Szaraniec., M.; Bratek., A.; Barbasz, J. J. Colloid Interface Sci. 2007, 313, 86–96. (43) Adamczyk, Z.; Zembala, M.; Michna, A. J. Colloid Interface Sci. 2006, 303, 353–364.

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Figure 9. Universal graph showing the dependence of the reduced streaming potential of mica ζ/ζp on the coverage of particles θ. The points denote experimental results obtained for the A500 latex at pH 5.5, T = 293 K and various ionic strengths. The triangles show the previous experimental results obtained for PEI42, and the squares show those obtained for PAH43. The solid line represents the exact theoretical results derived from eq 19 converted to the form ζ/ζp = ζi/ζp[1 - Ai(θ)θ] þ Ap(θ)θ (for ζi/ζp = -1), and the dashed line shows the asymptotic result (i.e., ζi/ζp = 1/21/2). Table 2. Values of the Correction Functions f1 and f2 in the Zeta Potential Equation ζp = (2)1/2ζl þ ζl f1 - ζl f2 θ

f1

f2

0.3 0.35 0.4 0.45 0.5

0.105 0.051 0.019 0 0

0.071 0.041 0.025 0.015 0.0086

these conditions, the mica substrate zeta potential was ζi = -76 mV and ζp = 65 mV. Analogously, the results obtained for polyallylamine (PAH) having an average molecular weight of 70 kD43 at pH 6, I = 10 -2 M NaCl, ζi = -76 mV (mica substrate), and ζp = 50 mV agree quite well with the theoretical results. The good correlation of these experimental results with theoretical predictions can be exploited for an efficient determination of the particle zeta potential from the streaming potential measurements, which can be more reliable than the bulk electrophoretic measurements, especially for low zeta potentials. This can be achieved by converting eq 19 to a form suitable to practical applications pffiffiffi ζ - ζi e - 10:2θl ¼ 2ζl þ ζl f1 - ζi f2 ð25Þ ζp ¼ l Ap ðθl Þθl

ζ/ζp on the coverage of particles θ. The points denote experimental results obtained for the A500 latex at pH 5.5, T = 293 K, and various ionic strengths regulated by MgCl2 addition: (a) I = 9  10-4 M MgCl2, (b) I = 9  10-3 M MgCl2, and (c) I = 3  10-2 M MgCl2. The solid line represents exact theoretical results derived from eq 16, and the dashed line shows the results calculated from the exponential fitting function, eq 15.

where θl is the experimentally accessible high coverage of particles, ζl is the apparent zeta potential of the channel determined for this coverage, and f1 and f2 are the correction functions given by pffiffiffi 1 f1 ¼ - 2 Ap ðθl Þθl ð26Þ e - 10:2θl f2 ¼ Ap ðθl Þθl

Also, the results obtained previously for poly(ethylene imine) (PEI) with an average molecular weight of 75 kD42 approach the master curve for θ > 0.3. The pH of these experiments was 6.1-6.4, and the ionic strength was I = 10-2 M NaCl. Under

for θl = 0.3, f1 = 0.105, and f2 = 0.071 (Table 2); for θl = 0.4, f1 = 0.019, and f2 = 0.025; and for θl = 0.5, f1 = 0, and f2 = 0.0086. As can be noticed from eq 26, for θl > 0.4 the bulk zeta potential of particles can be calculated with a few percent

Figure 8. Dependence of the reduced streaming potential of mica

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direct methods (e.g., the AFM method) for substrates with controlled, well-defined surface properties.

5. Conclusions The experimental data collected over broad ranges of coverage and the particle-to-substrate zeta potential ratio ζp/ζi confirmed the validity of the theoretical model formulated in refs 19 and 32. In particular, the normalized streaming potential Es or the apparent zeta potential of mica ζ is well reflected by the general equation ζp Es ¼ ζ ¼ 1 - Ai ðθÞθ þ Ap ðθÞθ ζi

Figure 10. Dependence of the zeta potential of polystyrene latex particles (A500) ζp on pH at T = 293 K and I = 10-2 M NaCl. The points denote experimental values determined for (b) particles in the bulk and (O) particles deposited at mica (from the streaming potential measurements). The solid line represents a nonlinear fit to the experimental results.

accuracy from the simple relationship ζp ¼

pffiffiffi 2ζl

ð27Þ

It is interesting that eq 27 is valid for an arbitrary zeta potential of the substrate surfaces and for a/Le > 1, although a precise estimation of this range requires additional experiments. Because the relationship expressed by eq 27 is valid for an arbitrary zeta potential, it can also be exploited to determine the isoelectric point of particles by measuring the dependence of ζp on pH at a fixed particle coverage, exceeding the limiting value of 0.3. Experimental results confirming this hypothesis are shown in Figure 10. In these experiments, the saturated latex particle monolayer at mica was formed at pH 5.5. Then, changes in the streaming potential were monitored at various pH values, adjusted within the range of 4-12 by the addition of an appropriate amount of HCl or NaOH by keeping the ionic strength constant, equal to I = 10-2 M NaCl. In this way, the dependence of the apparent zeta potential of mica covered with latex on pH has been obtained, which was compared with the analogous dependence of ζp determined in the bulk by electrophoresis. As can be observed, the ζ and ζp potentials were strictly correlated with the ratio ζ/ζp, being fairly constant over the entire pH range. Also, the isoelectric point of 10.2 found in the streaming potential experiments agrees well with its bulk counterpart (i.e., 10.3). The results shown in Figures 9 and 10 suggest that the streaming potential method can serve as a convenient, precise tool for determining bulk zeta potentials of colloid particles, polyelectrolytes, and probably globular proteins, in particular, their isoelectric points. However, an unequivocal estimation of the range of applicability of our results to other systems requires further experiments in which protein coverage is determined via

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with the correction functions Ai(θ) and Ap(θ) given by eqs 15 and 16. Using this equation, the apparent zeta potential of particlecovered substrates ζ can be described by the following equation that is valid for arbitrary ζp/ζι ratios ζ ¼ ζi e - 10:2θ þ ζp Ap ðθÞθ This equation can be rearranged to a form suitable for the convenient determination of the particle zeta potential ζp pffiffiffi ζp ¼ 2ζl þ ζl f1 ðθl Þ - ζi f2 ðθl Þ where ζl is the apparent zeta potential of the covered substrate and f1 and f2 are the correction functions given explicitly by eq 26. It has been shown that for θ > 0.4 these corrections are on the order of only a few percents (Table 2) and can be neglected, especially for ζp/ζi > 1. Accordingly, in this case, the bulk zeta potential of particles can be calculated from the simple relationship ζp ¼

pffiffiffi 2ζl

This equation also indicates that the apparent zeta potential of covered surfaces is 1/21/2 smaller than the bulk zeta potential of particles (in absolute terms). This statement is valid for arbitrary zeta potentials of substrates and particles, including the case of negative particles on negatively charged substrate. This means that the apparent zeta potential of rough surfaces is reduced by a factor of 1/21/2 compared to that for smooth surfaces. Our experimental results, obtained over a broad range of particle and substrate zeta potentials in the thin double-layer limit, suggest that the streaming potential method can serve as a useful tool for determining the bulk zeta potentials of particles. Therefore, it can be exploited to determine the isoelectric points of particles, polyelectrolytes, and globular proteins. Also, because of analogous physical mechanism of streaming potential generation, the results obtained in this work for planar substrates can be used for the interpretation of zeta potential variations of larger particles covered with nanoparticles or bioparticles. Acknowledgment. This work was supported by the COSTD43 Action Special Grant and the Ministry of Science and Higher Education (MNiSzW) (grant no. N N204 137537).

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