Langmuir 1999, 15, 5649-5653
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Attachment of Oil Droplets and Cells on Dropping Mercury Electrode Roumen Tsekov* Department of Physical Chemistry, University of Sofia, 1126 Sofia, Bulgaria
Solveg Kovacˇ and Vera Zˇ utic´ Center for Marine and Environmental Research, Ru]er Bosˇ kovic´ Institute, POB 1016, 10001 Zagreb, Croatia Received July 29, 1998. In Final Form: April 1, 1999 The process of attachment of organic droplets and cells at a liquid-liquid interface is studied in the system of a dropping mercury electrode in an aqueous cell suspension. Attachment frequency of droplets and cells is experimentally monitored, and a model for the dynamics of arrival and attachment of particles at the expanding mercury interface is proposed. The model accounts for the van der Waals and hydrophobic forces between the mercury and oil droplets and cells while the electrostatic force is negligible due to the high salt concentration. The important role of the Marangoni convection is emphasized as an active flow pushing the particles to attach on the mercury surface.
Introduction Studies of adhesion of particles, droplets, and cells on surfaces are important not only for better understanding of the complex processes involved but also for engineering aims. For instance, vesicles are used as original carriers of drugs in medicine and pharmacology, and their efficiency depends strongly on the vesicle ability to attach and disrupt on contact with interfaces. The problem of attachment is also relevant to coagulation of disperse systems, the elementary act of which can be considered as adhesion of the system units on each other.1 The process of attachment of deformable droplets or cells on surfaces involves many subprocesses.2-4 The most important steps are diffusion to the surface, deformation under the action of interfacial and hydrodynamic forces, formation of liquid thin films dividing the particle and the interface, thinning and rupture of the films that cause a three-phase contact, and expansion of the latter toward the equilibrium state. As seen, it is a complex phenomenon, and for this reason, it is important to find model systems which are relatively well-studied and easily manipulated. Previous studies5-8 showed that a dropping mercury electrode is a proper tool for investigation of the adhesion of oil droplets and cells from aqueous suspensions. The advantage is that the mercury surface is atomically smooth, renewable, and electrically chargeable.9,10 By variation of the externally applied potential, one is able to change the interfacial tension and surface (1) Dimitrova, M. N.; Matsumura, H.; Neitchev, V. Langmuir 1997, 13, 6516. (2) Danov, K.; Denkov, N.; Petsev, D.; Ivanov, I. B.; Borwankar, R. Langmuir 1993, 9, 1731. (3) Alexandrova, L.; Tsekov, R. Colloid Surf. A 1998, 131, 295. (4) Tsekov, R.; Radoev, B. Intl. J. Miner. Process 1998, in press. (5) Tomaic´, J.; Legovic´, T.; Zˇ utic´, V. J. Electroanal. Chem. 1989, 259, 49. (6) Zˇ utic´, V.; Svetlicˇic´, V.; Tomaic´, J. Pure Appl.Chem. 1990, 62, 2269. (7) Zˇ utic´, V.; Kovacˇ, S.; Tomaic´, J.; Svetlicˇic´, V. J. Electroanal. Chem. 1993, 349, 173. (8) Ivosˇevic´, N.; Tomaic´, J.; Zˇ utic´, V. Langmiur 1994, 10, 2415. (9) Adamson, A. W. Physical Chemistry of Surfaces; Wiley-Interscience: New York, 1982. (10) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: London, 1991.
Figure 1. Electrochemical measuring system.
charge at the mercury/water interface. In this way, it is possible to study the specific interactions between mercury and particles that are strongly related to the interfacial properties of the system, such as hydrophobic forces. In a series of papers,5-8,11-13 we have reported experimental measurements for attachment of oil droplets and cells to a dropping mercury electrode. The registration of attachment events is possible by measuring the chronoamperometric response of the system (Figure 1), which is due to the double-layer charge displacement during particle adhesion and spreading over the surface of the mercury drop. Using this method, we were able to record individual attachments in time, and the attachment frequency was calculated.5 To study the effect of the interfacial interactions, we have investigated the dependence of the attachment frequency on the applied potential.7 The potential change affects the system both explicitly and via other parameters, such as the interfacial tension. The goal of this paper is to explore some theoretical models to describe the experimental observations. Particularly, we are interested in the process of particle supply to the mercury surface and in the elementary step of attachment of a single particle. The juxtaposition of theory and experiment shows that the usual Brownian motion is not sufficient and that the main flux of particles toward (11) Tomaic´, J.; Legovic´, T.; Zˇ utic´, V. J. Electroanal. Chem. 1992, 322, 79. (12) Ivosˇevic´, N.; Zˇ utic´, V. Croat. Chem. Acta 1997, 70, 167. (13) Kovac´, S.; Svetlicˇic´, V.; Zˇ utic´, V. Colloid Surf. A 1998, in press.
10.1021/la980944q CCC: $18.00 © 1999 American Chemical Society Published on Web 07/20/1999
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Figure 2. Attractive interaction between dispersed organic particles and a positively charged mercury electrode in an aqueous electrolyte solution.
the mercury surface is due to the Marangoni effect at the liquid interface.14-17 Such a conclusion is in accordance with our static experiments showing that mercury-drop expansion is an essential factor for particle attachment. Moreover, there is a strong influence of the addition of surfactants on the dynamics of adhesion; the observed decrease of the attachment frequency with increasing surfactant concentration12,13 could be attributed to the relatively fast molecular adsorption leading to suppression of the Marangoni effect caused by the mercury-drop expansion. Particle Supply to the Mercury-Drop Interface. The attachment of droplets and cells on a dropping mercury electrode involves several hydrodynamic and thermodynamic effects. To answer the question of how the particles attach on a mercury surface, one should model the mass transfer from the bulk to the surface, the elementary process of adhesion involving particle deformations, and the following spreading of the three-phase contact (Figure 2). Let us start chronologically by the process of the supply of particles to the mercury/water interface. Obviously, the mercury-drop expansion causes a liquid flow in the adjacent solution layer.14 Supposing radial symmetry of this flow, the continuity equation acquires the form
(∂r∂ + 2r)ν ) 0
(1)
where ν is the radial component of the hydrodynamic velocity. Integrating this equation under the kinematic condition on the mercury surface ν(R) ) R˙ yields the solution ν ) (R/r)2R˙ , where R is the radius of the mercury drop changing in time with rate R˙ . The distribution of particles trough the suspension is governed by the corresponding mass balance. In the frame of a stationary approach, the diffusion equation of the particles reads
(
)
2 ∂ ∂2 ∂ c ν c)D 2+ ∂r r ∂r ∂r
(2)
where c is the particle local concentration and D is the diffusion coefficient. The term on the left-hand side accounts for the convection generated by the mercurydrop expansion. Substituting in eq 2 the expression ν ) (R/r)2R˙ and integrating the result, one obtains the local concentration of particles in the form (14) Levich, V. G. Physicochemical Hydrodynamics; Prentice-Hall: Englewood Cliffs, 1962. (15) Sterling, C. V.; Scriven, L. E. AIChE J. 1959, 5, 514. (16) Sorensen, T. S. Dynamics and Instability of Fluid Interfaces, Lecture Notes on Physics 276, Springer Verlag: Berlin, 1978. (17) Aogaki, R.; Kitazawa, K.; Fueki, K.; Mukaibo, T. Electochim. Acta 1978, 23, 867; 875.
exp c ) c∞
R ˙ 1 - )] - 1 [RR D ( r RR˙ exp( ) - 1 D
(3)
where c∞ is the particle concentration far away from the mercury surface. The second boundary condition employed in the derivation of eq 3 is zero concentration on the mercury surface, which presumes instantaneous adsorption of the particles. It is easy now to calculate the number of particles attached per unit time on the mercury surface via the relation
∂ ω0 ) 4πR D c ∂r 2
( )
4πR2R˙ c∞ ) R RR˙ exp -1 D
( )
(4)
A simple estimate of the diffusion coefficient of micrometer particles via the Stokes formula reveals a value of the order of square micrometers per second. This means that eq 4 predicts practically zero attachment frequency, which is in contrast to our experimental observations. This discrepancy cannot be explained as the nonrigidity of the droplets or the active motion of the living cells, which could result only in a slight increase of the diffusion coefficient. Another flux pushing the particles toward the mercury surface should be involved. The origin of this flow can be interpreted in terms of the Marangoni effect.14-17 Stationary and nonstationary convective streaming is generated at a liquid metal-liquid electrolyte interface (mercury electrode/aqueous electrolyte solution) by gradients of the surface tension γ and the microscopic perturbations at the interface are amplified to macroscopic instabilities. The Marangoni instability is demonstrated by a manifold increase in current above the diffusioncontrolled value as a result of coupling of the perturbation in a cyclic chain: surface tension f surface motion f bulk motion f diffusion mass transport f surface electrochemical potential f surface tension. During the mercury-drop expansion, a new area of fresh, bare surface appears. The surface tension on the fresh surface is larger than that on the surface already covered by adsorbed species or a monolayer formed by adhesion of droplets or cells. For this reason, a gradient of surface tension appears which causes a hydrodynamic flux in the adjacent solution layer. The streamlines of this flow are schematically shown in Figure 3. As shown here, the corresponding hydrodynamic velocity is directed away from the mercury surface on the bare patches and toward the covered ones. Hence, the additional flow pushes particles to attach at the covered mercury surface neighbor to the bare spots. Because the process of creation of bare islands is stochastic, the corresponding Marangoni flow could be considered as random. The result is local turbulence where the turbulent
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Figure 3. Marangoni flow driven by the surface tension gradient.
diffusion constant is much higher than the molecular one. Therefore, the net Marangoni effect will result in an increase of the effective diffusion coefficient of the particles close to the mercury surface (the depth of the affected shelf is on the order of the mercury-drop radius). The Marangoni induced microturbulence around dropping mercury has been studied in pure electrolytes,17 too. In this case, the Marangoni flow originates from nonuniformity of the surface potential, and for this reason, it decreases with increasing electrolyte concentration. To estimate the effective diffusion coefficient near the mercury surface, one can employ the detailed stress balance of the Marangoni effect. The velocity of the generated turbulent flow is proportional to the difference of surface tensions, S ) γWM - γOM - γOW (which is known as the spreading coefficient and plays an important role in the three-phase contact motion) divided by the liquid viscosity η, i.e., u ) S/2η. Here, γWM, γOM, and γOW are surface tensions on the water/mercury, oil/mercury, and oil/water interfaces, respectively. By use of the fact that the only length scale of the flow is the radius of the mercury drop, the diffusion coefficient can be estimated as D ) uR/2 ) RS/4η. The magnitude of D now is on the order of square centimeters per second, which confirms our expectations that the usual Brownian motion of the particles is very slow and thus unimportant for the system and that the transport induced by interfacial turbulence plays a crucial role in the observed phenomenon. The latter eliminates the unfavorable effect caused by the mercurydrop expansion. Because the effective diffusion coefficient is much larger than the product RR˙ , eq 4 simplifies to
ω0 ) 4πDRc∞ ) πR2c∞S/η
(5)
In the derivation of eq 5, adhesion of particles is allowed all over the mercury surface. Therefore, it is valid for conditions when the surface is still not covered by the organic monolayer, generally the initial phase of mercurydrop growth. At later stages, the attachment occurs only on the area surrounding fresh surface created by the mercury-drop expansion. In this case, the frequency of attachment is given by the following formula
ω0 ) x8πRR˙ D(∂c/∂r)R ) x2πRR˙ c∞S/η
(6)
which is the geometric average of the frequencies of fresh area creation and particle supply. Here, eq 6 predicts a different dependence of the attachment frequency on the particle concentration as compared to that of eq 5. Hence, there will be a transition point in the ω0 versus c∞ curve at ω0 ) 2R˙ /R and c∞ ) 2ηR˙ /πR3S that corresponds to a complete coverage of the mercury surface by a monolayer.
Figure 4. (a) Dependence of attachment frequency on the cell density in the suspensions of D. tertiolecta cells in 0.1 M NaCl and pH ) 8.2, 20 °C. Measurements were performed at -400 mV, where surface charge density is +3.8 µC/cm2. (b) Dependence of surface coverage of DME (at the end of drop life) on the cell density.
Indeed, we have observed experimentally such behavior in cell suspensions of increasing concentrations Figure 4. Moreover, the frequency of attachments after the monolayer formation depends substantially on the rate of growth of the mercury drop, and it correlates with the experimental observations that the attachments of particles on a static mercury drop are extremely rare events.18 Attachment. Equation 5 predicts a linear dependence between the attachment frequency and mercury-drop area during its growth. Our analysis of the time dependence of attachment frequency confirms this conclusion,5 but the magnitude of ω0 predicted by eq 5 is much larger than the experimental value. This fact indicates that the attachment process is not instantaneous and that the particle should escape over a potential barrier to stick on the mercury surface.19 Hence, the proper expression for the attachment frequency should read
ω ) ω0exp(-a/kT)
(7)
where ω0 is given by eqs 5 or 6 and a is the activation energy of attachment. The problem of attachment of a deformable particle on the mercury/water interface is equivalent to the problem of rupture of the thin aqueous film formed between the (18) Tomaic´, J.; Chevalet, J.; Svetlicˇic´, V., unpublished result. (19) Islam, A. M.; Chowdhry, B. Z.; Snowen, M. J. Adv. Colloid Interface Sci. 1995, 62, 109.
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particle and the mercury drop.20 It is well-known that film stability is strongly related to the specific interactions in the film.21 Classical Darjaguin-Landau-VerweyOverbeek theory considers only the van der Waals and electrostatic forces.22 It has been recognized at present that there are many other macroscopic interactions in the films, such as hydration and hydrophobic forces. The simplest expression for the van der Waals interaction energy is
WVW ) - A/12πh2
(8)
The Hamaker constant A, which is not reported in the literature, is taken here to be equal to A ) -7.5 × 10-19 J because the interaction in the mercury/water/oil system is stronger than that in the mercury/water/air system where A is 10 times larger.23 The sign of the Hamaker constant for hydrocarbons is not well-known, however, it seems reasonable for the Hamaker constant to possess the same sign as that for the mercury/water/air film. An a posteriori argument for the van der Waals repulsion is the lower value of the attachment frequency ω as compared to ω0, which requires an energy barrier of attachment. The classical expression for the electrostatic energy at constant surface potentials is given by22
Figure 5. Dependence of attachment frequency on the initial surface charge density of mercury electrode in the suspensions of D. tertiolecta cells (7.2 × 104 cells/cm3) in 0.1 M NaCl.
WEL ) 64nkTd tanh(eψWM/4kT) tanh(eψOW/4kT) exp(-h/d) (9) where d is the Debye length, n is the electrolyte concentration, and ψWM and ψOW are the surface potentials at the water/mercury and oil/mercury interfaces, respectively. As shown here, depending on the surface potentials, the electrostatic disjoining pressure could be either positive or negative. Finally, the present system is strongly affected by a hydrophobic force. The latter accounts for the density and structural changes of the water induced by the film interfaces. The corresponding component of the potential energy is equal to24
WHP ) ∆E exp(-h/a)
(10)
where ∆E is the difference of the Gibbs elasticity on the mercury/water and mercury/oil surface and a is the characteristic decay length. The values of ∆E and a are difficult to calculate, but for the sake of our analysis, we will consider ∆E equal to -S.24 The full energy of interaction is a sum of the above contributions. However, because of the large electrolyte concentration (0.1 M), the Debye length is short and the contribution of the electrostatic component is negligible. This fact is confirmed by the attachment experiments performed in a broad range of electrode potential. Comparable attachment frequencies were recorded at positive and negative electrode surface charges of the same absolute value.7 A particular dependence of attachment frequency on surface charge of the mercury electrode in the suspension of D. tertiolecta cells, 7 × 104 cells/cm3, is shown in Figure 5. Lower attachment frequencies at the negatively charged surface can be interpreted by a secondary effect of the electrostatic repulsion, as the cell (20) Tsekov, R.; Ruckenstein, E. Langmuir 1993, 9, 3264. (21) van Oss, C. Interfacial Forces in Aqueous Media; Dekker: New York, 1994. (22) Verwey, E.; Overbeek, J. Theory of the Stability of Lyophobic Colloids; Elsevier: Amsterdam, 1948. (23) Usui, S.; Sasaki, S.; Hasegawa, F. Colloids Surf. 1986, 18, 53. (24) Tsekov, R.; Schulze, H. J. Langmuir 1997, 13, 5674.
Figure 6. Dependence of the excess energy per unit film area on the film thickness.
surface bears a negative charge. Hence, the overall interaction energy is given by
W)-
A h - S exp 2 a 12πh
( )
(11)
A plot of this function is given in Figure 6. If the product 8πSa2 is larger than -A, there are a minimum and a maximum in the dependence on the film thickness. At large particle separation (larger than 100 nm), the van der Waals and hydrophobic force have no effect on the particles. When particles (cells or oil droplets) approach to the surface, there is an increase of WVW and decrease of WHP. As the WHP term decreases slower then WVW at large distances, there is a slight domination of the repulsive force. As the distances decrease even further, WHP has a stronger effect on the particles, and at separation distance of approximately 20 nm, this results in an energy well corresponding to attachment. A particle approaching the mercury surface will feel a repulsive force before the thickness of the formed film reaches h* corresponding to the energy maximum. If the particle possesses kinetic energy enough to escape over the barrier, it will drop in the potential well corresponding to attachment. Hence, the attachment is possible if the spreading coefficient S is larger than a critical value of -A/8πa2, and this is our experimental observation. The value of the barrier thickness h* can be calculated via the relation
(h*/a)3 exp(-h*/a) ) -A/6πSa2
(12)
A useful method to get h* is shown in Figure 7. In the interesting region 4a e h* e 7a, the barrier thickness could be well-approximated by h* ≈ 8a + 2A/3πSa, and
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W* increases, but because of the steeper dependence of the correlation area on S, the final result is a decrease. The spreading coefficient can be changed by variations of the water/mercury surface potential ψWM which affect the surface tension γWM via the electrocapillary effect. The decrease of γWM causes a decrease of S and hence in reduction of the potential barrier. It is essential also to note that the preexponential factor ω0 in eq 5 also decreases with decreasing S.
Figure 7. Thickness of the equilibrium film after the attachment and the transition state. The solid and dashed lines present the left-hand side and right-hand side of eq 12, respectively. Thus, it is satisfied at the cross-sections of the two lines.
Figure 8. Activation energy of attachment as a function of the characteristic dimensionless parameter of the balance between the van der Waals and hydrophobic forces.
the thickness corresponding to the energy minimum can be estimated as a/2 - A/5πSa. According to the picture above, the activation energy of attachment is proportional to W*. The coefficient of proportionality is the so-called correlation area o, a ) oW*. Because the film rupture is a random process, o is the area of the first spot formed in the film. For droplets, the correlation area of the capillary waves can be estimated as o ) -γOW/W′′(h*),25 where W′′ means the second derivative of W in respect to the film thickness. Hence, the activation energy amounts to
W(h*) ah* h* - 2a ) γOW ≈ 2 h* - 3a W′′(h*) A A A γOWa2 4 + 3+ / 2.5 + (13) 3πSa2 3πSa2 3πSa2
a ) -γOW
(
)(
)(
)
The last formula is valid for -Ae6πSa2, and the plot of dependence of the activation energy of attachment versus the characteristic dimensionless parameter of the balance between the van der Waals and hydrophobic forces is given in Figure 8. Surprisingly, with decrease of S, the activation energy decreases, too. In fact, the barrier height (25) Tsekov, R.; Radoev, B. Adv. Colloid Interface Sci. 1992, 38, 353.
Experimental Section The electrochemical technique employed is a modification of a widely used polarographic technique for measuring surface active constituents in environmental samples.6 The method is based on chronoamperometric measurement of supression of the interfacial turbulence during oxygen reduction at a fast dropping mercury electrode in aqueous electrolyte solutions.14,16,17,26 The adsorption of dissolved surfactants is manifested as a gradual decrease of the oxygen reduction current, and the adhesion of fluid organic particles causes a transient increase in interfacial turbulence resulting in the spike-shaped adhesion signals of individual particles.7,8,12,13 We used Dunaliella tertiolecta (6-10 µm), a marine nanoflagellate without a cell wall, as a model cell. The organism is simple to grow and forms stable suspensions. Because of the flexibility of the cell membrane, we can measure characteristic electrical signals for the attachment of single cells. Attachment signals in the presence of oxygen reduction possess durations of 60-200 ms and amplitudes of 0.6-2.2 µA.13 Cells were harvested after 8 days of growth with mild centrifugation. The maximum cell density in stock suspensions was 1010 cells/L. Aliquots of stock cell suspensions were added to organic-free electrolyte (0.1 M NaCl) prior to the measurements. The latter were performed in a standard Methrom vessel with 20 mL of cell suspension, at 20 °C. The measured samples were saturated by air, and the vessel was open to air throughout the experiments. A dropping mercury electrode (drop life 2.0 s, flow rate 6.03 mg/s, maximum surface area 4.57 mm2) was used in electrochemical measurement with a 0.1 M Ag/AgCl electrode as a reference in a threeelectrode configuration (Figure 1). Chronoamperometric measurements were performed using a PAR 174A polarographic analyzer. Current-time (I-t) curves at a constant potential were recorded and stored using a Nicolet 3091 digital oscilloscope connected to a PC. Because of stochastic nature of the processes in cell suspensions, at least 30 current-time curves were recorded in each sample. Results of electrochemical measurement of the attachment frequency are presented as mean values obtained by analyzing 15 or 30 I-t curves.13 Acknowledgment. This study was sponsored in part by the Ministry of Science and Technology of the Republic of Croatia (Project P-1508). R.T. is grateful to the Alexander von Humboldt Foundation for the granted fellowship. LA980944Q (26) Barradas, R. G.; Kimmerle, F. J. Electroanal. Chem. 1966, 11, 163.
