944
Ind. Eng. Chem. Res. 1998, 37, 944-951
Initial Mechanisms of the Electrocoating Process Nikos Vatistas† Chemical Engineering Department, University of Pisa, Via Diotisalvi 2, 56126 Pisa, Italy
A significant increase in the quality of cataphoretic paint has been observed experimentally when suitable initial operating conditions for the deposition process are used. These results show the effect of the initial mechanisms on the quality of the paint. In this work we point out that during the initial step of the process, both the local increase in the pH and other mechanisms not yet studied occur in the cathode; for examples, partial packing of the charged micelles and the overlay of their double layers. The effect of the initial conditions on the increase in pH, on the partial packing, on the overlay of the double layers, and on the heating stress of the film just deposited have been studied. Introduction
Mechanisms of the Cataphoretic Process
The cataphoretic deposition of water-dispersed organic coating has gained world-wide acceptance, especially by the automotive industry, because of its numerous benefits; for examples, ability to coat recessed areas, uniform coating thickness, almost complete paint utilization, and reduction of environmental pollution. The ability of the cataphoretic process to deposit paint films in highly recessed areas increases with the deposition voltage. The upper limit of the applicable deposition voltage is usually set by the film rupture on the phosphated steel (Brewer and Hines, 1971) and by the defect of cratering on the phospated zinc-plated steel (Froman and Franks, 1981; Hart and Townsend, 1984; Hart 1986; Schoff, 1990). The more important mechanisms that occur during the cataphoretic paint process are known (Beck, 1976; Pierce, 1981); they are (i) hydroxide production at the cathode that increases locally the local value of pH; (ii) migration of the charged micelles to the cathode; (iii) discharge and coagulation of the micelles due to pH local increase, and (iv) elimination of water from the deposited paint by electroosmosis. The migration of the micelles to the cathode starts immediately and the cathodic region reaches is critical pH value after a short time, consequently, the discharge and coagulation of the micelles begin at an early stage. These initial mechanisms occur at very short time intervals, and some of them act together, so the interactions occurring between them complicate the study of the initial mechanisms of the electrocoating process. A resistance between the electric source and the cathode has been proposed to reduce the initial operating conditions and make the experimental study of the initial mechanisms easier. In this work, the mechanism of the local increase of pH due to the cathodic production and diffusion of OH (Pierce, 1981) is discussed and other, as yet unstudied induction step mechanisms are pointed out, these mechanisms are (i) the partial packing due to the migration of the charged micelles toward the cathode, (ii) the overlay of the double layer of the charged particles due to the electric field between the anode and cathode, and (iii) the heating stress on the film just deposited that has a considerable effect on the quality of the paint.
The cataphoretic deposition of water-dispersed organic coating includes the following principal mechanisms: The hydrogen and hydroxide production by H2O discharge on the cathode according the following electrochemical reaction:
†
E-mail:
[email protected].
H2O + 2e- ) H2 + 2OH-
(1)
The cataphoretic migration of the charged micelles toward the cathode due to the applied electric field E, the migration velocity u, can be obtained with the Helmholtz-Smoluchowski equation:
u)
ζ dU ζ E) µ µ dx
(2)
where is the permittivity of the solution; ζ is the zeta potential of the charged micelles, µ is the viscosity of the solution, U is the electric potential in the solution, and x is the distance. The coagulation of the charged micelles occurs at the cathode surface after the neutralization of the positively charged groups in the resin with the generated OHions:
-R-NH3+ + OH- ) -R-NH2 + H2O
(3)
Probably only a small number of initial micelles are discharged on the metal substrate, whereas the massive coagulation of the micelles is due to the discharge according to the reaction in eq 3. The electroosmosis of water in the pores of the deposited films is caused by the potential difference across the film and the surface charges on the pores of the film; the value of the electroosmotic velocity is given by the same equation of Helmholtz-Smoluchowski proposed for the migration velocity. The Induction Step. The cataphoretic process begins with the immersion of the metallic piece in the cataphoretic bath and the application of a potential between this piece and the anode. The positively charged micelles of paint are moved toward the piece (cathode), but these micelles are charged, so in the cathodic region a partial packing occurs due to the overlay of their double layers. More packing occurs
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Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 945
when the increase of the local pH due to the water decomposition in the cathode is enough to discharge the micelles of the paint (coagulation of the paint). The coagulation of the paint on the cathode does not occur immediately but after some time, which is known as induction time. The previous studies on the cataphoretic painting focused attention on the local increase of the pH (Beck, 1976) that allows the calculation of the induction time (Pierce, 1981), but the partial packing of the charged micelles in the same region has been omitted, as well as the effect of the partial packing on the successive mechanisms of the cataphoretic deposition. The Use of a Resistance To Control the Induction Step. The voltage normally used during the cataphoretic paint (Coon and Vincent, 1986) is an initial medium value voltage (250-275 V) following by a higher one (325-375 V). This operating condition is combined with the low initial resistance of the system to create a high initial current density and a very short induction time. Immediately after the induction time, the high resistance of the deposited film causes a sharp decrease in the current density. The voltage initially applied performs a sharp and rather uncontrollable initial induction, conditions that can be reduced by changing the cell and the bath parameters, but a relationship between them is not always simple to obtain. The introduction of a resistance between the electric source and the cathode allows us to obtain both the easy reduction of the sharp initial conditions and a simple relationship regarding this reduction. The introduced resistance has been defined as control resistance. The value of the control resistance is higher than the resistance of the cataphoretic bath and much smaller than the resistance of the deposited film of the paint. The suitable value of the control resistance has as a direct effect the fact that the effective applied voltage between the anode and cathode at the initial moment of the cataphoretic process is lower than the supplied voltage; so, as the film increases, its resistance becomes higher than the control resistance and the effective applied voltage reaches the value of the supplied voltage. The effect of this resistance on the mechanisms of the induction step, as well as some results concerning the effect of the initial condition on the quality of paint, have been reported here. More details concerning the experimental setup and the effect of the control resistance on the quality of paint have been reported elsewhere (Vatistas, 1998). The Cathodic Variation of the pH during the Induction Step. The time between the applied voltage and the beginning of the massive coagulation is defined as induction time. This time is needed to produce a sufficient quantity of hydroxide ions for the coagulation of the micelles. The critical concentration of HO- close to the surface of substrate is given by Fick’s second law:
∂c ∂2c )D 2 ∂t ∂x
(4)
that has the following initial and boundary conditions:
∂c(0,t) J ) c(x,0) ) c0, c(∞,t) ) c0, ∂x zFD
Figure 1. Induction time versus bath resistance for some values of the applied voltage, (DOH- ) 5.23 × 10-5 cm2/s; cc ) 10-5 mol/ cm3; A ) 70 cm2).
and will be solved by Laplace transform to obtain the following solution:
c(t,x) ) c0 +
2J zF
(
x
( )]
(6)
The induction time of the coagulation to be obtained is given by following equation (Pierce, 1981):
( )
zFcc 2 1 2 J2
ti ) πD
(7)
by assuming that cc . c0. In eqs 4-7, c is the concentration of OH-, cc is the critical coagulation concentration of OH-, x is the distance from the substrate, t is the time, ti is the induction time, D is the diffusion coefficient of OH-, F is Faraday’s constant, J the current density, and z is the valence of ion. Equation 7 relates the induction time to the current density, and a constant mean current density on the whole cathode is assumed. When the control resistance is not applied, the value of the mean current density J0 during the induction step is
J0 )
U ARb
(8)
where U is the applied potential and A is the surface of the cathode. When the control resistance is applied, the current density during the induction step becomes
J)
U A(Rb + Rc)
(9)
When the control resistance is not applied, the induction time ti,0 is derived from eq 7 and is related to the applied potential and the bath resistance by the following equation:
( )
ti,0 ) πD (5)
) [
t x2 exp πD 4Dt Jx x 1 - erf zFD 2xDt
zFccA 2U
2
R2b
(10)
Figure 1 shows the variation of the induction time
946 Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998
Figure 2. Dimensionless induction time versus dimensionless control resistance.
Figure 3. Thickness of compact region versus dimensionless control resistance for some values of the applied voltage.
versus bath resistance for some values of the applied voltage using the data of a typical experimental setup (A ) 7 × 10-3 m2; cc ) 10 mol/m3; D ) 5.23 × 10-9 m2/ s). The induction time ti increases when the control resistance is used:
velocity:
( )
zFccA 2 (Rb + Rc)2 2U
ti ) πD
(11)
The dimensionless induction time ϑ is defined as the ratio of the induction time ti with the control resistance Rc to the induction time ti,0 without the control resistance; this dimensional number is
ϑ)
(
)
ti Rb + Rc ) ti,0 Rb
2
) (1 + R)2
(12)
where R ) Rc/Rb is the dimensionless control resistance. Figure 2 shows the dimensionless induction time versus dimensionless control resistance. It is evident that a limited value of the dimensionless control resistance is enough to obtain a high value of the dimensionless induction time. The Partially Compact Region of the Charged Micelles during the Induction Step. The migration velocity u of the micelles toward the cathode during the induction time is given by the eq 2. When the control resistance is not applied, the value of u can be calculated using the characteristics of the cataphoretic system; that is, the anode to cathode distance lb and resistance of the bath Rb:
u0 )
ζ Rb I µ lb 0
(13)
When the control resistance is applied, the value of the velocity is
u)
ζ Rb I µ lb
(14)
where I and I0 are the currents with and without the control resistance, respectively. By combining eqs 8, 9, and 14 we obtain the effect of the dimensionless control resistance on the migration
u)
1 u 1+R 0
(15)
The effect of the control resistance on the whole movement of the micelles during the induction time is derived by combining eqs 12 and 15:
s ) (1 + R)s0
(16)
where s and s0, are the whole movement of the micelles within and outside the control resistance, respectively. The last value has been calculated using our experimental setup:
(
)
ζ zFccARb 2 1 µ 2 l x b Ub
s0 ) u0ti,0 ) πD
(17)
The movement of the micelles during the induction time creates a compact zone of micelles close to the cathode. The fraction of the volume occupied by the micelles in the compact is φf, and the initial value of the fraction volume of the micelles in the bath is φb. The thickness of the compact zone increases during the induction and at the end of the induction step its value, sf, is related to the whole movement of the charged micelles, s, and to the fraction volumes φb and φf as follows:
sf ) [1 - (ff - φb)]s ) [1 - (φf - φb)](1 - R)s0 ) (1 + R)sf,0 (18) where sf,0 is the thickness of the compact region when the control resistance is not used. The thickness of the compact region increases linearly with the dimensionless control resistance, and Figure 3 shows the thickness of the compact region using the data of a typical experimental setup (Rb ) 100 ohm; lb ) 0.12 m; ) 6.906 C/V m; ζ ) 0.11 V; φb ) 0.2; φf ) 0.7; µ ) 0.78 × 10-3 Pa s). The partially compact zone of the micelles close to the cathode probably has different transport properties than the initial solution; for examples, a lower value of the diffusion coefficient and higher value of the viscosity. More details about this partially compact region will be given.
Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 947
The Drag Forces and the Dissipated Energy during the Induction Step. At the induction step of the cataphoretic process at the cathode, the hydrogen and hydroxide production by the H2O discharge and the migration of the whole charged micelles toward the cathode principally occur. At the induction time, a portion of the supplied energy is used to move the micelles to the cathode. To estimate the energy dissipation of the migration during the induction step we assumed that the charged micelles were spherical and then we applied the Stokes drag equation to a micelle:
Fa ) 6πµau
(19)
where Fa is the drag force, a is the radius of the micelles, and µ is the viscosity. The energy that is dissipated for the migration of the micelle, Lm, during the induction step is
( )(
Lm ) Fas ) 6π2µD
ζ µ
2
)
zFccARb 2 a 2lb
(20)
It is important to point out that the control resistance does not affect the energy dissipation, but with the use of the resistance this process is completed in a longer time. It is interesting to calculate the energy dissipation concerning the micelles of unit volume; the volume of these micelles is φb, and the number of the micelles, Nb, in the unit volume is
Nb )
3 φb 4 πa3
(21)
Combining eqs 20 and 21 results in the following equation for the energy dissipation that concerns the micelles of unity volume of the cataphoretic bath:
L)
( )(
ζ 9 πφ µD 2 b µ
2
)
zFccARb 2 l 2lb a2
(22)
Equation 22 shows the considerable effect of the dimension of the micelle on the energy dissipation of the drag forces during the induction step; in other words, the migration of the bigger micelles is easier than the smaller ones. The Overlap of the Double Layers of the Charged Micelles in the Partially Compact Region. During the induction step the micelles reach the cathode and as their distance decreases, the overlap of the double layers occurs and the ion concentration in this region increases. As a result, an excess of pressure (osmotic pressure) exists between the micelles. The overlap of the double layers is due to the action of the electric field in this region, and the equilibrium conditions of the overlap are reached when the action of the electric field on the charges is balanced by the action of the osmotic pressure (Probstein, 1989). In the partially compact region we have two phases, the micelles and the solution around the micelles, and the distance between the micelles in this region changes with time. To perform a theoretical analysis of such a complex problem it is necessary to establish the essential features of the actual system without going into the exact microscopic detail of the system.
Figure 4. Potential in the compact region versus distance: (i) the micelles and (ii) the whole potential.
If we assume an ordinary distribution of the micelles in the compact region, as shown in Figure 4, the detailed distribution of potential is due to two effects: (i) the applied potential between anode and cathode and (ii) the local effect of the charged micelles on the potential. In Figure 4, the whole potential variation has been indicated. It is known that the osmotic pressure at any point of the fluid phase increases with the gradient of the potential, so we expect that the potential and the pressure will have an opposite trend. It is sound to neglect the microvariation of the potential and of the pressure and consider the mean macroscopic variation of this partially compact region. At the equilibrium and in the absence of migration, we applied a forces balance on a portion of the compact region (film) with a thickness (dx), that is longer than the distance between the micelles but smaller than the compact region. The forces acting on the solution of this portion are the pressure gradient and the force due to the electric field, which balance each other to give (Probstein, 1989)
dp ) FfEf dx
(23)
where Ef is the electric field of the solution in the compact zone of micelles close to the cathode, p is the pressure, and Ff is the electric charge density in the same solution. It is interesting to point out that the overlap of the double layers in the compact zone region during the induction step has as a principal effect the accumulation of a potential energy that will be dissipated after the induction step when the discharge of the micelles begins. If the Poisson equation is applied to eq 23 we obtain
dp d2U dU ) dx dx2 dx
(24)
with the following conditions outside of the compact region:
p ) pb and
dU =0 dx
This equation permits the following solution:
(25)
948 Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998
pf - pb )
dU 2 2 dx
( )
(26)
This relationship shows the considerable effect of the potential gradient on the pressure in the compact region. The use of the control resistance has a double effect: (i) it reduces the potential drop in the compact zone and (ii) it increases the thickness of the compact zone. Therefore, according to eq 26, the use of the control resistance reduces the overlap of the double layers and prevents the high local pressure in the compact region. The Characteristic Time of the Overlap Process of the Double Layers. The characteristic time of the induction time is known (eqs 11 and 12) but not the characteristic time of the overlap. The last mechanism occurs because a charged micelle with a velocity u reaches the charged micelles that have just arrived at the cathodic region. As the relative distance decreases, the overlap of the double layers generates a new effect that is the osmotic pressure; because the last effect, the micelle needs some characteristic time to reach its equilibrium position close to the other micelles. It is well known that the double layer has the properties of a capacitor (Newman, 1973), whereas the motion of a charge in a solution has the properties of a resistance. Therefore, it is correct to assume the process of the overlap as the electrical equivalent of the charge of a capacitor, C, in series with a resistance, R, when a constant voltage, U, is applied at the time t ) 0:
R
dQ Q + )U dt C
(27)
where Q is the charge of the capacitor. Equation 27 allows the potential drop in the capacitor, UC, to be obtained with eq 28:
[
( )]
UC(t) ) U 1 - exp -
t tC
(28)
The current decreasing during time t is given by eq 29:
I(t) )
( )
t U exp R tC
(29)
where tC is the characteristic time of the electrical circuit, which is given by eq 30:
tC ) RC
(30)
The characteristic time of the electrical circuit, tC, is different from the characteristic time of the overlap, to. The first time, tC regards the distribution of the electronic charge on the faces of one or more capacitors, whereas the time of the overlap process, to, in the partially compact region regards the redistribution of the ionic charge in the solution of the same region. If the induction time, ti, is small with respect to the overlap time, to, the micelles are close to the end of the induction time and the overlap mechanism occurs immediately after the induction step. In this case, the aforementioned relationships take into account the overlaps of all the charged micelles that are in the partially compact region. The Accumulated Energy during the Overlap of the Double Layers The electric circuit that has been proposed to simulate the overlap of the double layers allows the accumulate
energy, W, to be calculated as follows:
1 W ) CU2 2
(31)
This relationship does not need the overlap mechanism to occur simultaneously and is also valid when the characteristic time of the overlap, to, is smaller than the induction time, ti. The accumulated energy will be transformed into heat that increases the temperature of the film, so it is very important to know the variation of the accumulated energy when the control resistance is used. The effective potential applied between anode and cathode, U, during the induction time decreases with the use of the control resistance:
U)
1 U 1+R 0
(32)
where U0 is the effective applied potential when it is not used the control resistance. The capacitor indicates that in the aforementioned relationships there is overlay of the whole charged micelles of the partially compact region, so it is really a high number n of capacitors in series, CS:
1 n ) C CS
(33)
where CS is the value of the capacitor concerning the overlap of one double layer. The number of the double layer is proportional to the thickness of the partial compact region, and by considering the eq 18, the number of the single overlaps, nf, increases with the use of the control resistance:
nf ) (1 + R)nf,0
(34)
where nf,0, is the number of the single overlaps when the control resistance is not used. The last relationship combined with eq 33 allows the relationship between C and C0 to be found:
C)
1 C 1+R 0
(35)
where C is the value of the capacitor when the control resistance is used and C0 is the value of the resistance without the use of the control resistance. Finally, by combining the eqs 31, 32, and 35, the effect of the control resistance on the accumulated energy of the overlay, W, is given by eq 36:
W)
1 W0 (1 + R)3
(36)
where W0 is the accumulated energy without the use of the control resistance. The last relationship points out that with the introduction of the control resistance we reduce the accumulated energy that will be dissipated in heat immediately after the induction time. The Heating Stress of the Deposited Film. The heating stress of the film during the cataphoretic process has many effects on the process and on the quality of the obtained film of paint. As the temperature of the film increases, the hydrogen that is accumulated in the film has a higher probability of
Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 949
creating bubbles that make the film unstable, and evaporation of the solvents can occur if the temperature increases further. The increase of temperature can also create conditions of a partial premature baking of the paint during the cataphoretic process that reduces the fluidity of the film during the next baking process; the last condition is a fundamental factor in determining the final quality (Drazic et al., 1989). The study of the mechanisms in this work during the induction step point out the quantity of the dissipated energy concerning the migration of the charged micelles during the induction time that is relative to the drag forces (eq 23); this energy accounts for all the charged micelles and therefore the whole cataphoretic bath. The effect of this step is a rather small increase in the mean temperature of the cataphoretic bath. The overlay of the double layer of the charged micelles has as energetic effect on the accumulation of a quantity of energy; this form of potential energy is dissipated after the induction step in heat during the discharge of the micelles. It is correct to assume that the dissipation occurs in two consecutive processes: in the first process, the discharge of the micelles in the partially compact region occurs, then the double layers collapse and the local pressure is not balanced any more. The effect of the unbalanced pressure creates a high local microagitation in the film that is finally dissipated in heat. The introduction of the control resistance has a considerable effect on the accumulated energy (eq 36). If it is assumed that the dissipation of this accumulated energy is used to increase the temperature of the partially compact film, it is possible to correlate the increase in the temperature of the film with, ∆T, and without the use of the control resistance, ∆T0, by considering the eqs 18 and 36:
∆T )
1 ∆T0 (1 + R)4
(37)
Equation 37 shows that the initial increase in temperature of the film just coagulated is highly affected by the control resistance. The discharge of the particles and the dissipation of the accumulated energy leaves the film more compact because of coagulation of the discharged particles. This condition of the film allow us to assume that now it has a rather resistive behavior. This resistance is proportional to the compact film and, by considering eq 18, the following correlation regarding the resistance is obtained:
Rf ) (1 + R)Rf,0
(38)
where Rf is the resistance of the film when the control resistance is used and Rf,0 is the resistance of film without the use of the control resistance. The resistance of the film is now higher than the bath and control resistances and most of the applied voltage and, therefore, the dissipated energy concentrates in the thin paint film. The electric power (Pf,0) that is dissipated in the film resistance when the control resistance is not used is given by
Pf,0 ) I20Rf,0 )
( )
U 2 Rf,0 Rf,0
(39)
When the control resistance is used, the dissipated electric power (Pf,0) is
Pf ) I2Rf )
()
U 2 1 P Rf ) Rf 1 + R f,0
(40)
Finally, by considering that the increase in the temperature of the film depends on the dissipated power (eq 40) and on eq 18, we find that its variation is given by
dT0 1 dT ) 2 dt dt (1 + R)
(41)
where T is the temperature of the film when the control resistance is used and T0 is the temperature of the film without the use of the control resistance. Equations 37 and 41 are valid immediately after the discharge of the partially compact region and they point out that the introduction of the control resistance drastically reduces the heat stress of the initially deposited film of paint. Experimental Section The more experimental work will be reported elsewhere (Vatistas, 1998), but here the experimental setup is described briefly. Results on the quality of paint that is obtained when the control resistance is used are reported as well as data concerning the induction step and the mechanisms of this step. The deposition of the cationic primer was performed using a Catolac ED 5000 produced by PPG Italia S.p.A. The bath proprieties were pH ) 6.1, and conductivity at 25 °C, 1950 µs cm-1. The pH was measured using a Hanna pH meter (model 8417), and a conductivity meter (Amel, model 123) was used to measure the conductivity of the bath. Deposition was performed at constant voltage using ∼0.75 dm3 bath volume. Different phosphated substrates were used; these included steel, zincelectroplated steel, and hot-dipped galvanized steel. To avoid any ripple a series of 12 V batteries was used as electrical source. The control resistance was introduced between the batteries and the cathode (sample to paint), and various values of the resistance were used initially (from 305 to 1820 ohm). The cathodic panels were cut out of steel sheets and had an area of 70 cm2. The area of the anode was 80 cm2. The anode was made of titanium with a special treatment to avoid any corrosion. The cathode-to-anode distance was 7.5 cm, and all the experiments were performed at 30 °C. A magnetic stirrer provided moderate stirring. A different system was used to measure the current and the other parameters of the bath like temperature, pH, and conductivity. The final quality thickness of the deposited paint after baking was determined by stereo microscopy and scanning electronic microscopy, whereas the thickness and its standard deviation were measured. Results and Discussion The first experimental results concern the final quality of the paint. Figure 5 shows two samples of paints that have been obtained using identical operating conditions except the use of the control resistance. It is observed that the film that is obtained without the control resistance has some craters that are the usual defects that occurs when the zinc-electroplated and phosphated steel are used as substrate. The paint on the same substrate with the use of the control resistance is free of any kind of defect and has a smooth surface.
950 Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998
Figure 5. Micrographs of paints with and without the use of control resistance. Figure 7. Current versus deposition time for some values of the applied potential and with the use of control resistance.
Figure 6. Current versus deposition time for some values of the applied potential and without the use of control resistance.
We note that the use of the control resistance has the effect of reducing only the effective applied potential during the induction step. So, these results confirm the importance of the various mechanisms that occur during this initial step of the cataphoretic process. The current versus time data during the initial time of the cataphoretic process are reported in Figure 6, using different values of applied voltage and without the use of the control resistance. An almost constant high current for a very short time is observed. The experimental results do not allow an easy determination of the experimental induction time, ti,e. In contrast, the theoretical induction times at the same conditions (ti,t ) 0.023 s at U ) 307 V; ti,t ) 0.021 s at U ) 319 V; ti,t ) 0.019 s at U ) 331 V, and ti,t ) 0.018 s at U ) 338 V) have been obtained using eq 10. After this time, an exponential decrease of the current occurs. These results indicate that the overlap of the double occurs and that the behavior of this process is similar to the charging of the capacitors. Therefore, we use eq 29 to estimate the overlap time (to ) 0.15 s). Comparison of the results of Figure 6 at different applied voltage indicates that the characteristic time of the overlap process is quite independent of the applied voltage. The same results show that the overlap process is not completed, particularly if the applied voltage increases. The interruption of the process is due to the discharge of the micelles. The comparison of the current before
this time shows that almost the same quantity of OHhas been produced (a maximum difference of 5% is observed in the reported experimental results), so the premature discharge of the micelles at higher voltage seems a paradox. To explain this result we need to consider that all micelles are charged positively and the double layer of the micelles has an excess of anions (principally OH-). Therefore, as the overlap of the double layer increases, the local concentration of the anions in this region increases; this letter condition allows the discharge of the micelles. We note here that the electric field has a destabilizing effect on the charged particles; in other words, the increase of the applied voltage increases the overlap and consequently the OHconcentration that causes the premature discharge of the micelles. The value of the current reaches a minimum and then increases again and reaches a maximum value (Ie ) 1.16 Å at U ) 307 V; Ie ) 1.39 Å at U ) 319 V; Ie ) 1.70 Å at U ) 331 V, and Ie ) 1.80 Å at U ) 331 V). We consider that this increase is due to the local microagitation that occurs with the discharging of the micelles and the collapse of double layers. Comparison of the current at different applied voltages shows that its maximum increases with the applied potential. The previously studied mechanism explain this behavior; that is, as the applied potential increases, the osmotic pressure is higher and its collapse creates a higher microagitation close to the cathode and, consequently, a higher current. Another observation regards the microagitation time. Comparison of the aforementioned data at different applied voltage shows that as the applied potential decreases, the microagitation step needs more time (∆t = 1.00 s at U ) 307 V; ∆t = 0.80 s at U ) 319 V, and ∆t = 0.65 s at U ) 331 V). Two combined effects explain this behavior; the first is due to the higher value of the thickness (see the eq 17) and the second is due to the lower intensity of microagitation that makes the discharge process longer. The current versus time data are reported in Figure 7, whereas more results of the same operating conditions and at lower values of the control resistance have been reported elsewhere (Vatistas, 1998). These results show that when the control resistance was used, the induction time increases. The experimental induction time, ti,e, and the theoretical one, ti,t, according to eq 12
Ind. Eng. Chem. Res., Vol. 37, No. 3, 1998 951
have been reported (ti,t ) 2.64 s, ti,e = 2 s and ti,t ) 11.31 s, ti,e = 6 s). The obtained lower experimental value is probably due to the partially compact region that reduces the diffusion coefficient in this region. In the reported data after the initial decrease of the current, a new increase due to the microagitation of the discharge is not observed. The observed high reduction of the energy dissipation during the discharge process has also been obtained theoretically by eq 36. Conclusions In this work we have studied in detail all the cathodic mechanisms that occur during the induction step of the cataphoretic process; that is, local increase of pH, partial packing of the micelles in the region of the cathode, and overlap of the double layers of the partially packed micelles. We also studied the discharge mechanisms of the compact region that creates local microagitation and the heat stress of the initial film just coagulated. A very simple and efficient technique, the control resistance, was used to change only the operating conditions of the induction step by the introduction of a resistance between the cathode and the electric source. All the studied mechanisms have been correlated with the initial operating condition and in particular with the control resistance. We have analytically correlated the initial conditions of the process with (i) the migration of the micelles, (ii) the thickness of the of compact region, (iii) the overlap of the double layers, (iv) the accumulated energy of the overlap, and (v) the heating stress of the deposited film. Experimental data are reported that show (i) the variation of current due to effect of the overlap and discharge mechanisms, (ii) the effect of the high electric field in the compact region to accelerate the discharge of the micelles, and (iii) that the technique of the control resistance avoids the defects of the paint and improves its quality. Nomenclature Fa ) drag force, N a ) radius of the micelles, m A ) surface of the cathode, m2 C ) capacitor, F E ) electric field, V/m I ) current, Å J ) current density, Å/m2 l ) anode to cathode distance, m L ) energy dissipation, J N ) number of micelles in the unit volume n ) number of single overlaps of double layer p ) pressure, Pa P ) dissipated electric power, W Q ) charge of the capacitor, C
R ) resistance of the discharged film, ohm s ) thickness of the compact region, m T ) temperature, °C u ) migration velocity, m/s U ) applied potential, V z ) valence of the ion W ) accumulate energy, J Greek Letters R ) dimensionless control resistance ) permittivity of the solution, F/m ζ ) zeta potential of the charged micelles, V ϑ ) dimensionless induction time µ ) viscosity of the solution, Pa s F ) electric charge density, C/m3 φ ) fraction of the volume occupied by the micelles Subscripts 0 ) without the use of the control resistance b ) cataphoretic bath c ) control resistance C ) capacitor e ) experimental i ) induction f ) film of the paint particles m ) micelle t ) theoretical S ) single overlap of double layer
Literature Cited Acamovic, N. M.; Drazic, D. M.; Mikovic-Stankovic, V. B. Prog. Org. Coating 25, 1995, 293. Beck, F. Prog. Org. Coating 1976, 4, 1. Brewer, G. E. F.; Hines, R. F. J. Paint Technol. 1971, 43, 71. Brown, W. B. J. Paint Technol. 1975, 47, 43. Coon, C. L.; Vincent, J. SAE, Technical Paper 850466; Society of Automotive Engineers: Warrendale, PA, 1986. Drazic, D. M.; Acamovic, N. M.; Stojanovic, O. D. J. Coating Technol. 1989, 61, 27. Froman, G. W.; Franks, L. L. Am. Soc. Metals, Metals Park, OH, 1981, 27. Hart, R. G. SAE, Technical Paper 850237, Society of Automotive Engineers: Warrendale, PA, 1986. Hart, R. G.; Townsend, H. E. SAE, Technical Paper 831818; Society of Automotive Engineers: Warrendale, PA, 1984. Newman, J. Electrochemical Systems; Prentice-Hall: Englewood Cliffs, NJ, 1973. Pierce, P. E. J. Coating Technol. 1981, 53, 52. Probstein, R. F. Physicochemical Hydrodynamics; Butterworths: Boston, 1989. Vatistas, N. Prog. Org. Coating, in press.
Received for review July 21, 1997 Revised manuscript received December 2, 1997 Accepted December 8, 1997 IE970517S
