Influence of adsorbed particles on streaming potential of mica

Colloids and Surfaces A: Physicochemical and Engineering Aspects 195 (2001) 3 – 15 www.elsevier.com/locate/colsurfa

Influence of adsorbed particles on streaming potential of mica Maria Zembala *, Zbigniew Adamczyk, P. Warszyski Institute of Catalysis and Surface Chemistry Polish Academy of Science, Niezapominajek 8, 30 -239 Cracow, Poland

Abstract Zeta potential of natural mica covered by polystyrene and melamine latex particles, was determined by the streaming potential method. Measurements were carried out using the parallel-plate channel formed by two mica sheets separated by a teflon spacer. The dependence of streaming potential on surface coverage (reaching 0.45) was determined at pH 5.3, when the particles were positively charged and at pH 7.8, when the melamine particles became neutral. The coverage was determined directly by optical microscope counting procedure. It was found that the negative streaming potential for bare mica Es was significantly increased by the presence of adsorbed particles. The experimental data were interpreted in terms of a theoretical model postulating that the streaming potential change was due to flow damping over the interface and by charge transport from the double-layer surrounding adsorbed particles. In contrast to earlier approaches, no assumption of the slip (shear) plane shift upon particle adsorption was made. The experimental data allowed one to determine empirically the universal correction function, which can be exploited for quantitative measurements of bioparticle adsorption kinetics via the streaming potential method. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Colloid particles; Zeta potential of mica; Streaming potential

1. Introduction Adsorption or deposition (irreversible adsorption) of colloids and bioparticles at solid/liquid interfaces is of large significance in many practical processes, e.g. various filtration procedures, papermaking, electrophoresis, chromatography, etc. Learning about mechanisms and kinetics of particle adsorption phenomena is also relevant for polymer and colloid science, biophysics and medicine enabling one to control protein and cell separation, enzyme immobilization, thrombosis, * Corresponding author.

biofouling of membranes and artificial organs, etc. A difficulty often encountered by studying adsorption of colloids and bioparticles at solid surfaces is the lack of direct experimental methods of surface coverage determination. Usually indirect methods are applied like ellipsometry [1,2], reflectometry [3–5], total internal reflection fluorescence [6,7], concentration depletion method [8,9] or the radiotracer techniques using labelled particles [10 –12]. Adsorbed particle coverage can be measured directly by AFM as recently done in [13,14]. However, this method gives the most satisfactory

0927-7757/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 0 1 ) 0 0 8 2 5 - 1

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M. Zembala et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 195 (2001) 3–15

results when working ex situ only, after drying the sample. This may produce a considerable distortion of particle mono-layer. Other class of indirect methods, more sensitive for low coverage range is based on measurements of streaming potential changes induced by particle adsorption. Many experiments of this type involving protein solution were performed in the circular [15] or parallel-plate channel arrangement [4,16,17]. Although the streaming-potential method performs well for low coverage where other methods fail, it can only be used as a relative method due to the lack of well-established theory connecting streaming potential changes with particle coverage. As a consequence, adsorption kinetics can only be studied quantitatively if independent measurements of surface coverage are carried out. This may decrease accuracy of the data obtained because the surface coverage and streaming potential measurements are done under different conditions. Recently, Hayes [18] used this procedure (based on scanning electron microscope measurements of particle coverage) for determining zeta potential of aminopropylsilane modified glass surface covered with 90 nm of diameter silica particles. The results were interpreted in terms of empirical models postulating a shift of the slip (shear) plane at the interface proportional to particle coverage. Moreover, an exponential decay of the interface potential with the distance was assumed. This allowed to formulate an empirical relationship describing the apparent zeta potential of the interface covered by particles. Experimental results for mica covered in situ by precisely controlled amount of colloid particles (polystyrene latex) were reported in [19,20]. In this case, the absolute surface concentration of adsorbed particles was known a priori from direct optical microscope counting. The experimental data were interpreted in terms of a theoretical model postulating that the change in streaming current (potential) induced by particle adsorption was due to (i) damping of fluid velocity in their vicinity resulting in decreased charge transport from the double-layer at the interface; and (ii) transport of charge from the double-layer surrounding adsorbed particles. Hence, the theoreti-

cal model predicts, in contrast to what is usually accepted, that streaming potential should also be significantly modified by adsorption of uncharged (neutral) particles. This prediction has a considerable practical significance for protein adsorption whose overall charge is usually rather small. Therefore, the goal of this work was to verify experimentally the validity of this theoretical postulate by performing model experiments for natural mica covered by controlled amount of melamine latex particles whose charge becomes neutral at pH close to 7. 2. The theoretical model The fully-developed laminar flow in a channel of rectangular cross-section 2b× 2c (see Fig. 1) was analysed in [17,19]. It was demonstrated that the fluid velocity vector V is directed parallel to the channel walls (along the x-axis), i.e. V= u(y, z)ix

(1)

where u(y, z) is the tangential component of fluid velocity and ix is the unit vector of the x-axis. An analytical expression for the u(y, z) function was given in the form of infinite series [19]. It was also shown in [19] that close to the channel walls, the local fluid flow reduces to simple shear, described by the equation: V=G 0hix 0

(2)

where G is the local shear rate depending on the position on the wall (but independent of the x co-ordinate) and h is the distance from the wall. By deriving Eq. (2), the secondary liquid flow due to streaming potential difference leading to the electroviscous effect has been neglected. This is justified as discussed in [19] for channels of macroscopic dimensions, which has been confirmed by numerical calculations of Yang and Li [21]. They have demonstrated that the electroviscous effect plays a role for channels whose dimensions are comparable with the double-layer thickness (micro-channels). Knowing the fluid velocity field, one can calculate the amount of charge leaving the channel due to convection per unit time (streaming current) from the constitutive expression [19]

I=

&& S

&&

M. Zembala et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 195 (2001) 3–15

zeVdS =

z(y, z)u(y, z)dydz

(3)

S

where S is the channel cross-section perpendicular to the x-axis, dS is the surface element vector, b ze =e N i = 1 zi n i is the electric charge density, e is the elementary charge, zi is the valency of i-th ion, and n bi is the bulk concentration of this ion. Substituting the expression for ze from the Poisson –Boltzmann equation and assuming a linear velocity increase within the double-layer (described by Eq. (2)) one can evaluate the above double integral explicitly which results in the expression [20]

5

mb mc I= ŽG 0yn1 + ŽG 0z n2 y y =

  

n1 n 1− 1− 2 R0 n1 ×

1 16h (2n + 1)y % tanh y 3 n = 0 (2n + 1)3 2h

n

(4)

where m is the dielectric constant of water, n1, n2 are the zeta potentials of the channel walls, ŽG 0y,ŽG 0z  are the local shear rate averaged over the x,z plane and the x,y plane, respectively, h= b/c, R0 = yb/2muchc= yp/(m(DP/L)bc) is the dynamic resistance of the channel, DP/L is the hydrostatic pressure gradient along the channel and p is the fluid dynamic viscosity. Eq. (4) represents the general solution valid for arbitrary channel shape (including the case of a square cross-section channel). In practice, instead of I, one is measuring the potential difference Es (called the streaming potential) between the inlet and the outlet from the channel and the channel ohmic resistance Rc. Then, equating I with Es/Rc (ohmic current) one can express Eq. (4) as:

  

nc = n1 1− 1− ×

n2 n1

16h 1 (2n + 1)y % tanh 3 3 y n = 0 (2n + 1) 2h

 

= n1 f h,

n

n2 ER = s o n1 Rc

(5)

where nc can be treated as the effective zeta potential of the channel and f(h, n2/n1) is the universal correction function. For thin channels, when hB 0.1, Eq. (5) reduces to:



nc = n1 1−

n

yp 16h 16h n2 Es + 3 = y3 y n1 Rc mbc(DP/L)

(6)

By introducing the specific conductivity of the solution u=L/4Rcbc one can convert Eqs. (5) and (6) to the Smoluchowski expression [22], i.e. nc =

Fig. 1. A schematic view of the laminar flow in the parallelplate channel.

4ypu Es m DP

(7)

When adsorbed particles are present at the interface the streaming current can also be determined from Eq. (3) written as [19]

6

DIp = Ip −I=

&&

M. Zembala et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 195 (2001) 3–15

(z*V* − zV) ’ dS

(8)

S

where Ip is the streaming current for particle covered surface, I is the current for bare surface given by Eq. (3), z*, V* are the perturbed (due to adsorbed particles) electric charge density and fluid velocity in the S plane, respectively. These quantities obviously depend on particle coverage and distribution over the surface. Therefore, it is impossible to evaluate the surface integral in the general case because this would require a solution of the Poisson– Boltzmann and Navier–Stokes equations for multibody problems. Due to lack of appropriate coordinate systems and nonlinearity of the Poisson– Boltzmann equation no results of general validity were found yet. However, one can derive exact solutions for the case of a single spherical particle attached to the surface. The electrostatic field „* around the sphere and consequently the local charge density z*e can be calculated numerically in the bipolar coordinate system by using the finite-difference method described in [23]. Obviously, for a sphere bearing an opposite charge as the interface, the local charge density will be decreased. One can, therefore, predict from Eq. (8) that the presence of an adsorbed particle should decreased the streaming current (its absolute value) even if the velocity field remained unchanged. An opposite effect is expected for a sphere bearing the same charge sign as the interface if the flow remained unperturbed. However, one can deduce that the particle attached to the interface should also perturb the local fluid velocity field. This hydrodynamic problem, i.e., flow distribution around sphere immersed in a simple shear described by Eq. (2), can be solved analytically in terms of Bessel functions [24] or Legendre polynomials in bispherical coordinates [25]. In this way the velocity field V* can be evaluated explicitly which allows one to calculate also the perturbed velocity gradients at the interface. The calculations demonstrated that the presence of particles decreases fluid velocity at distances exceeding considerably its radius a. This will result in the decrease in the shear rate at the wall as shown in Fig. 2 where the contours of the function G*/G 0 are plotted (G* is the perturbed

wall shear rate). The data shown in Fig. 2 were derived by applying the Legendre polynomial expansion method. It is interesting to note that this perturbation is symmetric relative to the flow direction. Due to decreased flow rate the amount of charge transported from the region attached to the interface, according to Eq. (3) will be considerably decreased independently of the charge of the particle. Knowing the electrostatic and hydrodynamic fields, one can calculate in an exact way via Eq. (8) the incremental change in the streaming current due to one adsorbed particle. Then, knowing the solution for one particle one can construct solutions for dilute multiparticle systems assuming that the perturbations to the electrostatic and hydrodynamic fields do not interfere and particle distribution remains uniform. In this case the streaming current change for particle covered surface can be formulated as [19] lDIp = −

mG 0ni C(sa, n1, np)[ 4y

(9)

where lIp is the streaming potential change per unit length, C(sa, n1, np) =

1 yniG 0a

&

(u*92„* −G 0z%92„)dx%dy%dz%

(10)

w%

is the universal function of sa (where s − 1 is the double-layer thickness), ni and np are the zeta potentials of the interface and the particle respectively, u* is the component of fluid velocity parallel to the channel wall, (x%, y%, z%) are the local Cartesian coordinates with the origin in the particle centre, [= ya 2N is the dimensionless surface concentration (coverage) and N is the number of particles adsorbed per unit area. The volume integral in Eq. (10) should be carried out over the region 6% where the electric charge density and fluid velocity deviates from the corresponding unperturbed values, u, ze. Calculation of the function C in the general case is rather cumbersome and can only be done numerically. Typical results showing the dependence of C on the sa parameter at fixed zeta potential of the interface ni and np = 0 are shown in Fig. 3. One can notice that the absolute value

M. Zembala et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 195 (2001) 3–15

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Fig. 2. The contours showing the relative shear rate at the interface G*/G 0 in the vicinity of an adsorbed particle.

of the function increases with sa attaining − 10.21 for sa  1. This limiting value (hereafter referred to as C 0i ) was independent on n potential of the wall and of the particle as demonstrated in separate calculations. This behaviour is confirmed by analytical results which can be derived in the limit of thin double-layers when the volume integral in Eq. (10) is reduced to surface integrals extending over the particle and the interface separately. In this case, by assuming the linear velocity distribution within the double layers, the C function assumes the simple form [20] C=C 0i + C 0p 0 p

n np = − 10.21 +6.51 p ni ni

where C = 6.51.

In this limiting case the dimensionless constant C 0i describes the purely hydrodynamic effect of flow shear rate decrease over the interface as a result of the presence of adsorbed particles, whereas the constant C 0p is a measure of the flow shear rate averaged over adsorbed particles. Eq. (11) remains exact as long as the flow perturbations stemming from individual particles remain additive which is fulfilled for low coverages only. For higher coverages one can introduce, however, correction functions in analogy to the flow model parameter Af used for describing 3D flows in packed bed columns or filtration mats [26,27]. Then, the C function can be formally expressed [20] as

(11) C= Ci + Cp

np n = C 0i Ai ([)+ p C 0pAp([) ni ni

(12)

M. Zembala et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 195 (2001) 3–15

8

where the correction functions (flow model parameters) Ai, Ap are dependent on the surface coverage [ only. By definition, Ai =Ap “1 when [ “0. Using Eqs. (11) and (12) one can calculate the overall streaming current change by integrating the expression for dIp (Eq. (9)) over the channel perimeter (− cB zB c and −b B y Bb) assuming the coverage [ to be uniform. In this way one obtains the expression [20] m DIp = [cŽG 0yn1 +bŽG 0z n2]C 0i Ai ([)[ y + =

m np[cŽG 0y +bŽG 0z ]C 0pAp([)[ y

nc 0 np C i Ai ([)[ + C 0pAp([)[ R0 R0

(13)

Eq. (13) can also be expressed in the equivalent form as: na = C 0pAp([)[np +[1 − C 0i Ai ([)[]nc

(13a)

where na = IpR0 = 4Es pypu/mDP is the ‘apparent’ zeta potential of the channel in the presence of deposited particles. It should be mentioned that no shift in the shear plane was postulated by deriving Eq. (13a). Eq. (13) can also be expressed in the form more suitable for interpretation of experimental results. Ip = 1− C 0i Ai ([)[ I cŽG 0y+ bŽG 0z  + np C 0 A ([)[ (14) cŽG 0yn1 + bŽG 0z n2 p p In the case when h= b/c 1 (thin channel), Eq. (14) simplifies to Ip n = 1− C 0i Ai ([)[+ p C 0pAp([)[ (14a) I ni Assuming that the ohmic resistance of the channel is not affected by adsorbed particles one can identify the Ip/I ratio with the streaming potential ratio Esp/Es where Esp is the streaming potential in the presence of particles. This assumption can be validated by the fact that the relative ohmic resis-

Fig. 3. The dependence of the C function on the sa parameter calculated numerically for ni = −100 mV (empty points) and ni = −50 mV (full points). The lines denote the interpolation functions.

M. Zembala et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 195 (2001) 3–15

tance increase due to adsorbed particles is very small [20]. It can easily be deduced from Eq. (14) that for neutral (uncharged) particles one has always: Ip Es = p = 1 − C 0i Ai ([)[ I Es

(15)

Note that in this case the Ip/I or Esp/Es ratio does not depend on any parameters characterising the channel shape, its surface properties or flow rate (governed by pressure difference). This conclusion has a considerable practical impact indicating that one can determine the Ai ([) function empirically for arbitrary surface coverage just by measuring the ratio of the streaming currents or streaming potentials. Once this universal function is known, one can determine particle surface coverage in other experimental systems, when direct observation of particles is not feasible. The only limitation is the requirement that the double layer thickness should be much smaller than particle radius, which is fulfilled for higher electrolyte concentrations. The primary goal of our experimental work discussed below was to determine the correction function empirically.

3. Material and methods Natural ruby mica sheets supplied by Dean Transted Ltd. England were used without any pre-treatment. Thin sheets were freshly cleaved for each experiment. Three samples of positively charged polystyrene lattices (L+ 39, L+57 and L+53) were synthesised according to the method described in [28,29] without using a surfactant. In the case of L+ 39 latex, the 1,2-azo-bis-(2-methyl propamidinum) dichloride (ABA) initiator was used [28] whereas the L +53 and L+ 59 latexes were produced using the N,N%-dimethyl-4,4%-azo-bis-4-cyano-1methylpiperidine (DACMP) initiator [29]. The latex suspensions were charge stabilised by positive amino groups stemming from the initiators. The melamine latex sample (M 25) was produced in a polycondensation reaction of melamine and formaldehyde carried out at 80 °C in the presence of formic acid. After synthesis, the lattices were

9

Table 1 Physicochemical characteristics of the latexes Latex

d (mm)

n (mV)

1/sa

L+53 L+57 L+39 M-25

0.15 0.55 1.13 1.52

+25a +24a +20a +47b

0.4a 0.11a 0.05a 0.02b

a b

10−4 M KCl. 3.3×10−4 M PB, (pH 5.3).

purified by steam distillation under decreased pressure and by prolonged membrane filtration until the conductivity of filtrate reached the value of water used for washing. In the case of the melamine latex, a repeated decantation and sedimentation procedure was found more efficient for cleaning the sample. The filtrates were also checked for the presence of traces of initiator and non-reacted styrene using UV spectroscopy. The size of larger particles determined by ZM Coulter Counter was 1.13 mm for L+ 39, 0.55 mm for L+57 and 1.52 mm for the M 25 sample. The size of smallest latex L+53 equal 0.15 mm was determined by Coulter N4 Plus Sizer. The zeta potential of latex particles was obtained by microelectrophoresis using the Brookhaven Zeta-Potential Analyzer (Zeta Plus). For suspensions in 10 − 4 M KCl solutions at pH 5.8, the np potential was: +20 mV for L+39, + 24 mV for L + 57, + 25 mV for L + 53. Zeta potential of M 25 particles was determined in phosphate buffer (PB) of ionic strength equal to 3.3× 10 − 4 M and it reached + 47 mV for pH 5.3. For sake of convenience, the relevant physicochemical characteristics of these latexes are collected in Table 1. In contrast to the polystyrene lattices, zeta potential of melamine latex was sensitive to the pH of particle suspension which was adjusted by addition of the phosphate (PB) buffer. At pH 7.0, the apparent isoelectric point was attained as discussed later on. Streaming potential of mica, bare and covered by latex particles was determined as described earlier [19,20] using the apparatus shown schematically in Fig. 4. The cell, being in principle the improved version of earlier ones used in [4,16,17],

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M. Zembala et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 195 (2001) 3–15

consisted of two polished teflon blocks one of them containing two rectangular, inlet and outlet compartments. Two thin mica sheets were placed on the teflon blocks separated by a teflon gasket of the thickness of 0.025 cm serving as a spacer. The parallel plate channel of the dimensions: 2b × 2c ×L= 0.025 ×0.33 ×6.0 cm was formed by clamping together the teflon blocks with two mica sheets and the spacer between them, using a press under constant torque conditions. The whole set-up was placed inside the earthened Faraday cage to avoid any disturbances stemming from external electric fields. The streaming potential Es occurring when an electrolyte was flowing through the cell under regulated and constant hydrostatic pressure difference, was measured using the two Ag/AgCl electrodes. These electrodes were located in two glass tubes having a direct contact with inlet and outlet compartments of the cell. A series of streaming potential measurements was done for at least five various pressures forcing the flow through the cell. Keithley 6512 Electrometer having the input resistance of more than 200 TV was used for potential measurements. The high resistance allowed potential measurements to be carried out at practically zero current conditions.

Another pair of electrodes situated outside the teflon cell (along the flow path) was used for determination of the cell resistance Rcell. This parameter was determined after the streaming potential measurements for each experiment. The surfaces covered with particles were produced in situ by filling the channel with an appropriate polystyrene latex suspension of appropriate particle concentration (typically in the range of 108 − 1010 cm − 3). The KCl concentration in polystyrene particle deposition process was equal to 10 − 4 M and pH 5.8. The fluid flow rate during the deposition step of the experiment was kept as low as possible (volume flow rate being of an order of 0.02 cm3 s − 1 corresponding to the Reynolds number equal to six and wall shear rate about 100 s − 1) to create the diffusion-controlled transport conditions. Under these conditions, the particle coverage along the channel remained constant within the experimental error being of an order of 10%. The particle deposition time was typically 30 min. Then, the cell was washed with pure electrolyte solution without allowing air bubbles to enter the channel. When the outlet solution was free of latex particles, the streaming potential measurements were performed using the

Fig. 4. A schematic view of the set up used for the streaming potential measurement: (1) the cell; (2) electrodes for streaming potential measurements; (3) electrometer; (4) electrodes for cell resistance measurements; (5) conductivity cell; (6) conductometer.

M. Zembala et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 195 (2001) 3–15

KCl or buffer solutions of appropriate concentration or pH value. In the case of the melamine-formaldehyde latex suspensions, the experimental procedure was slightly modified. After finishing particle deposition carried out at pH 5.3 (when particles and mica surfaces were oppositely charged) the pH was changed to 7.8 by filling the channel with PB buffer of appropriate composition. Then, the sample was allowed to equilibrate for 5 min and the streaming potential was measured. After finishing the experiment, the cell was washed with water, opened and mica sheets covered by polystyrene particles were dried in the air. In separate deposition experiments, it was proven that no polystyrene particle desorption was observed neither by KCl nor pure water stream even at high flow rates. The dry mica sheets with deposited larger latex particles were examined under optical microscope whereas for the smallest latex (L+ 53), the particle counting was done using a scanning microscope. Special care was taken in case of larger melamine-formaldehyde particles. The sheets with deposited layer after streaming potential measurements were placed onto special glass support filled with buffer solution of pH 5.3. The coverage was determined by counting particles on microscopic pictures of the layer being in contact with buffer solution. No drying or washing procedure was applied in this case. Particle surface concentration was obtained by determining the number of particles Np found over equal sized surface areas (of geometrical area DS equal typically few thousands of mm2) chosen at random over the interface. The total number of particles used in surface concentration determination was typically 1000– 3000. The averaged surface concentration N was calculated in the usual way as the mean value of ŽNp/DS. The averaged surface coverage was calculated as [ =ya 2N. Special precautions were undertaken to assure the high purity of the studied latex suspensions. The purity level was checked by controlling conductivity and UV spectrum of the filtrate obtained from the membrane filtration. Additionally, it was also proven that none of the filtrates, at concentrations exceeding those used in deposition experiments, was influencing zeta potential of bare mica.

11

4. Results and discussion In the first series of experiments, zeta potential of bare mica (uncovered by particles) was measured as a function of pH regulated by addition of the PB buffer. For each experiment, the dependence of Es on the hydrostatic pressure gradient DP was measured in order to increase the experimental precision of the streaming potential determination. Then, the cell resistance Rcell was measured and the correction function f(1/Rcell u)) describing a deviation of the cell conductivity from that resulting from bulk conductivity u was determined. This function incorporates inter alia the surface conductivity effects expecting to play a role for lower ionic strength. Knowing Es/DP and the conductivity u, zeta potential of mica n1 was calculated from Eq. (6) (with the appropriate correction for temperature dependence of viscosity and of dielectric constant) by assuming that the zeta potential of teflon n2 = n1. It should be mentioned that the uncertainty in n2 exerted very little effect on calculated values of mica zeta potential because the term 16h/y 3 was equal 0.04 for our channel geometry (h=0.076). This was additionally checked by performing separate series of experiments with two times thicker spacer. The results were found to be the same within the experimental error bounds. In this way we found n1 = − 103 mV for pH 5.3, − 104 mV for pH 6, −126 mV for pH 7 and − 119 mV for pH 7.8. For sake of convenience, the dependence of n1 on pH for bare mica is plotted in Fig. 5. The dependence of zeta potential np of melamine latex on pH determined by microelectrophoresis is also plotted in Fig. 5. As one can notice, at pH around 7.0, np is practically reduced to zero. The data shown in Fig. 5 enabled one to chose the pH range when the particle zeta potential vanished which was exploited in a series of experiments aimed at determining the correction function Ai ([) for particle covered surfaces. The measurements for particle covered mica were done according to the procedure described above. In the first step particles were adsorbed to a desired surface concentration within the coverage range 0– 0.28 in the case of polystyrene lattices particles. For the melamine–formaldehyde latex,

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M. Zembala et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 195 (2001) 3–15

Fig. 5. Zeta potential of bare mica ( ) and melamine – formaldehyde particles (") at various pH values regulated by the PB buffer.

the accessible coverage range was broader, i.e. 0–0.45 due to larger particle size which facilitated the microscope counting procedure. It is interesting to note that the maximum coverage predicted theoretically for the M25 sample (1/sa = 0.02, see Table 1) is 0.5. This was calculated from the formula discussed in [30], which considers the lateral electrostatic interactions in the particle monolayer. After completing the particle deposition procedure, the streaming potential measurement was carried out in situ. As mentioned earlier, for each experiment the dependence of Esp on the hydro-

static pressure gradient DP was determined in order to increase the experimental precision. A quantitative comparison with experiments can be carried out when plotting the universal dependence Esp/Es versus [, where Es is known from earlier measurements for bare mica. The data obtained for the three positively charged polystyrene latex samples at ionic strengths 10 − 5, 10 − 4, and 10 − 3 M and for melamine–formaldehyde particles at pH values 5.3 and 7.8 are collected in Fig. 6. As can be seen, the data seem to exhibit an universal character being independent (within experimental error) of particle size and

M. Zembala et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 195 (2001) 3–15

ionic strength in accordance with the theoretical predictions. It should also be noted that for low coverage range the experimental data are well reflected by the linear model (broken line in figure 7) derived from Eq. (14) by assuming n1 =n2 and the flow parameters Ai =Ap =1.





Esp np =1− 10.21 +6.51 [ Es n1

(16)

where np is the average value of the particle zeta potential determined by electrophoresis (see Table 1). It can be seen in Fig. 6 that the linear model performs well for coverages smaller than 0.05. It should be noted, however that even for this small

13

coverages the relative change in the streaming potential can reach 50%. For higher coverages, however, the experimental results shown in Fig. 6 deviate from theoretical predictions stemming from the linear model. This can be interpreted, in accordance with earlier discussion, as due to the fact that the flow fields stemming from individual particles are no longer additive so the functions Ai and Ap become smaller than unity. As mentioned, the Ai function can be determined empirically by performing experiments for neutral particles. The results of such experiments obtained for the melamine latex at pH 7.8 are also shown in Fig. 6. It was found that the experimental dependence Esp/Es on [ can well be reflected by the interpolation function

Fig. 6. The dependence of Esp/Es on surface coverage of particles [. The empty diamond points denote experimental results obtained for melamine latex at pH 7.8 (neutral particles) and the full diamond points the results for pH 5.3 (positively charged particles). All other full points represent the data obtained for positively charged polystyrene particles at KCl concentrations equal to 10 − 5, 10 − 4, 10 − 3 M. The broken lines denote the initial slope calculated from the linear model, Eq. (16) and the solid line presents the data calculated from Eq. (17).

M. Zembala et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 195 (2001) 3–15

14 0 Esp Ip = =e Ci [ Es I

(17)

The function used earlier for positively charged particles [20] reduces exactly to the linear model in the limit of low coverage. A physical justification of its validity stems from the fact that the probability of finding an empty surface area DS over the interface uncovered by particles can be 2 approximated by e − (DS/ya )[ [31]. As a consequence, the streaming potential ratio Esp/Es should be proportional to this quantity. Eq. (17) implies that the correction function Ai ([) describing the flow damping by the adsorbed particle layer assumes the form 0

1− e Ci [ Ai ([)= C 0i [

(18)

One can easily calculate from Eq. (18) that for the maximum coverage of 0.5 the value of A becomes close to 0.2. Eq. (17) seems to have a practical impact because once knowing Ai ([) one can determine quantitatively surface coverage of colloid particles or proteins by measuring the streaming current (or potential) ratio, i.e., Ip/I or Esp/Es for such a ionic strength that 1/sa parameter becomes smaller than unity. Then, for uncharged or slightly charged particles one has [=

) )

) )

1 I 1 E ln p = 0 ln sp 0 Ci Ci I Es

For thin double-layers (1/sa B0.5) and low coverage this effect becomes linear, given by the equation





Esp Ip na n = = = 1− 10.21+ 6.51 p [ Es I ni ni In contrast to earlier approaches, no assumption of the slip plane shift was necessary to formulate this equation. It was also found that for neutral or slightly charged interfaces, the Esp/Es or Ip/I dependence can be described for arbitrary coverage range by the semiempirical function independent of particle size, ionic strength, shape of the channel etc. 0 Esp Ip = = e Ci [ Es I

This relationship can be used for determining surface coverage of arbitrary sized particles (colloids, proteins) by measuring experimentally the streaming potential ratio.

Acknowledgements This work was partially supported by the EC Grant ERBIC15CT980121 and KBN Grant 3T09A10518.

(19)

In order to generalise this expression to larger zeta potentials of particles, one needs, however, the Ap([) function which can be determined from streaming potential measurements carried out for uncharged interfaces. The experiments of this kind are planned in the future.

5. Conclusions It was confirmed experimentally that the presence of adsorbed particles influences the streaming potential and the apparent zeta potential of interfaces as a result of damping of fluid motion in the vicinity of particles and additional charge transport from the ionic atmosphere surrounding particles.

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