8968
J . Phys. Chem. 1990, 94, 8968-8973
In summary, the agreement between the theoretical and experimental results indicates that the measurement of the amolitudes of Brownian motion of electrostaticallv trapped lipid
the measurement system as well as monolayer preparation so as to test more critically the basic theory and to increase the utility of these experiments.
their Langmuir trough equipment in some of this work. ( 18) Gennis, R. B. Biomembranes; Springer-Verlag, Heidelberg, 1989; pp 251-253.
Registry No. DPPC, 2644-64-6; N B D - P C , 8 1005-34-7; cholesterol, 57-88-5.
New Results on LlgM-Induced Spatial BDfurcation and Electrical Field Effect on Chemical Waves In the HgCi,-KI System in Gel Media Ishwar Das,* Anal Pushkarna, and Anunita Bhattacharjee Department of Chemistry, University of Gorakhpur, Gorakhpur 273 009, India (Received: March 12, 1990)
Novel experiments on one-dimensional propagation of a single red/yellow band of mercuric iodide in gel media have been carried out. At low pH values of mercuric chloride solution containing agar-agar, a single yellow band propagates downward in complete darkness. However, it bifurcates into a number of colorful alternate red and yellow bands in the presence of natural light. The influence of gravity and electrical field effect on the wave propagation at various field intensities, electrolyte concentrations, and tube diameters have been studied. The dependence of band location (d)on time ( t ) at various experimental conditions obeys the relation d2 = k t + C,where k and C are the slope and intercept, respectively. At low [KI] the red band bifurcates into several revert spaced bands at low field intensity in the presence of natural light. A critical field intensity exists at 0.016 V cm-’ beyond which a single red wave propagates.
Introduction
Periodic precipitation in gel media is observed when two components in solution diffuse into each other and react to form an insoluble precipitate.’ Nitzan et aL2 theoretically investigated that light absorption may play an important role in the macroscopic structure development that was later on supported by the work of Das et al.34 Schmidt and Ortoleva’ have observed that electric fields may significantly affect the course of chemical wave propagation in reacting systems where ionic species play an important role. Ortolevas also reviewed the effect of an electric field on band spacing in the K2Cr207-AgN03system. Feeney et aL9 have also examined the influence of electric field and predicted that if a wave exists its velocity would be proportional to the applied field. A possible mechanism for the effect of an electric field on the rate of diffusion-controlled reactions was proposed by Tachiya.’O In our earlier paper,” we reported the development of chemical waves of Hglz (red/yellow) moving as a result of diffusion of HgCI, into KI in agar-agar gel and, vice versa, bifurcation of red wave into revert spaced bands in the presence of natural light. The influence of electrolyte concentration and temperature on the kinetics of ( I ) Hedges, E. S. Liesegang Rings and Other Periodic Structures; Chapman and Hall: London, 1932. (2) Nitzan, A.; Ortoleva, P.; Ross, J . J . Chem. Phys. 1974, 60, 3134. ( 3 ) Das, I.; Pushkama, A.; Lall, R. S. J . Crysf. Growrh 1987, 82, 361. (4) Das. 1.; Lall, R . S.; Pushkarna, A . J . Crysf. Growth 1987, 84, 231. ( 5 ) Das. 1.; Lall, R. S.;Pushkarna, A . J . Phys. Chem. 1987, 91, 747. (6) Das, 1.; Pushkarna, A. J . Non-Equilib. Thermodyn. 1988, 13, 209. (7) Schmidt, S.; Ortoleva, P. J . Chem. Phys. 1977, 67, 3771. (8) Ortoleva. P. Theoretical Chemisrry, Periodicifies in Chemisrry & Biology; Eyring, H.,Ed.; Academic Press: 1978; Vol. IV, p 235. (9) Feeney, R.; Schmidt, S. L.; Strickholm, P.; Chadam, J.; Ortoleva, P. J . Chem. Phys. 1983, 78, 1293. (IO) Tachiya, M . J . Chem. Phys. 1987, 87, 4622. ( 1 1) Das, 1.; Pushkarna. A,; Agrawal, N . R. J . Phys. Chem. 1989, 93. 7269.
0022-3654/90/2094-8968$02.50/0
red/yellow wave propagation in the absence of electric field has also been described. In the present paper we report the bifurcation of a yellow wave into alternate red and yellow bands at low [H’] when illuminated with natural light. New results on the kinetics of propagation of a single yellow or red band at various electrolyte concentrations and in tubes of different diameters in the presence of external electric field are also reported. Conditions for transition from the banded structure to the continuous propagation of red wave have been investigated. Experimental Section Materials. Mercuric chloride, potassium iodide (AR; S . Merck), agar-agar (Difco), and glacial acetic acid (LR; Ranbaxy) were used without further purification. Procedures. Propagation of the Yellow Wave and Its Spatial Bifurcation. Mercuric chloride solution of known concentration was prepared in doubly distilled water containing 1.5% agar-agar and heated at 85-90 OC. The solution was homogenized with a magnetic stirrer with hot plate. The hot solution (10 mL) was then poured into a clean and pre-steamed corning tube (1 1.7-mm i.d.) and cooled at room temperature to solidify. The pH of the gel was measured with a Toshniwal pH meter. An equal volume of the aqueous solution of potassium iodide of relatively higher concentration filled the upper portion of the tube containing solidified gel and the tube was sealed. Two tubes were simultaneously prepared. One tube was placed in complete darkness, and the other tube was exposed to natural light. Both tubes were placed in an air thermostat maintained accurately to f0.1 ‘C. As a result of diffusion and chemical reaction, the yellow precipitate propagates downward in both tubes, leaving behind the initial junction. The influence of an additive such as acetic acid on the precipitation pattern has also been studied. For this purpose four tubes were taken for one set of experiment. Mercuric chloride solution (0.01 M) containing 1.5% agar-agar was put in the lower portion of the first tube. The pH of the contents in the lower
0 I990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 8969
Chemical Waves in the HgCI2-KI System
2.0
1.5
I i-
E
V
I
//
a c I
g 1.0
,
L
n U
'
m
0.5
a
b
-
C
Figure 1. Precipitation patterns of yellow mercuric iodide in agar-agar gel: (a) light has no effect on the pattern for pH 4.68; (b) in complete darkness (pH 2.72); (c) in the presence of natural light (pH 2.72). pH values indicate the pH of 1.5% agar-agar gel containing mercuric chloride (0.01 M); [KI] = 0.2 M; temperature = 40.0 f 0.1 "C. Photographs are taken at 72 h after the start of the experiment.
i
1
0
20
L---l... .L
60
40
.
L
100
80 TIME Ih
-.-
120
160
140
I
Figure 3. Plots of bandwidth (Aw) as a function of time ( 1 ) obtained for tubes oriented in different directions. Other experimental conditions are the same as mentioned in the caption of Figure 2.
B
8.0 c
6.0 t-
E u -
-
4.0 .-
2.0
+
L
portion of the first tube, which did not contain acetic acid, was found to be 4.68. In the second and subsequent tubes glacial acetic acid was added to the gel containing mercuric chloride to lower their pH from 4.68 to 2.72, 2.55, and 2.42, respectively. Potassium iodide (0.2 M) solution was added in the upper portion of the tubes, sealed, and kept in complete darkness. Another identical set of four tubes was prepared and exposed to natural light. Experiments were performed in an air thermostat maintained at 40.0 f 0.1 "C. Precipitation patterns obtained at various conditions are shown in Figure 1. Influence of Orientation of Tubes on the Kinetics of Yellow Waoe Propagation. The influence of gravitational field on the characteristics of the yellow wave has been studied in the absence
Figure 4. Experimental setup of a batch reactor: (PI, P2)platinum electrodes; ( R I , R,) reservoirs containing aqueous electrolytes; (B) dc voltage source; (M) digital multimeter; (G) tubular reactor; (SI,S2) magnetic stirrers.
of electric field. To observe such an effect, three tubes containing identical reagents as per details mentioned in the caption of Figure 2 were oriented in th_e directions parallel (si),antiparallel ( g ? ) , and perpendicular ( H ) to the gravitational field. A simple glass apparatus described earlierI2 was used for performing experiment in the direction antiparallel to the gravitational field ( g f ) . The location of the lower front of the wave from the initial junction (d) and the band width (Aw) were measured as a function of time by using a cathetometer. The maximum uncertainty in the measurement was found to be h0.002 cm. Results are plotted in Figures 2 and 3. Propagation of the YellowlRed Wave in the Presence of an External Electric Field. The influence of an external electric field on the propagation of yellow and red waves in agar-agar gel medium has been studied in a specially designed batch reactor. ( i ) Description of the Batch Reactor. An experimental setup (Figure 4) consisted of two cylindrical glass chambers C, and C2 ~~
~ ~ _ _ _ _ _
(1 2) Das, I.; Das, S. S.; Pushkarna, A.; Chand, S.J . Colloid Interface Sci. 1989, 130, 176.
8970
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The Journal of Physical Chemistry, Vol. 94, No. 26, 1990
I
1.2
..
1.0
II
-
0.8
E
u
I
io
Gel+ B Aqueous solution of A
0.6
0.4
! Aqueous
i
j solution
;
y
i
1,
:
of
i
B
0.2
I
:
Gel+A
I
I
I
C
9
I
Figure 5. Precipitation patterns of (i) yellow and (ii) red mercuric iodide in agar-agar gel at 40.0 f 0.1 "C in the presence of an external electric field. Conditions: ( i ) [HgCI2] = 0.01 M (chamber Cl); [KI] = 0.2 M (chamber C,); tubular reactor contains 1.5% aqueous agar-agar and HgCI, (0.01 M). (ii) [HgCI,] = 0.2 M (chamber Cl); [KI] = 0.01 M (chamber C2); tubular reactor contains 1.5% aqueous agar-agar and KI (0.01 M). Y and R indicate yellow and red precipitate, respectively. Photographs are taken at 4 h after the start of the experiment.
60
120
L---
1
180 240 TIME ( MIN I
300
Figure 7. Plots of location of the yellow precipitate front from the junction as a function of time at various [KI]. Conditions: tubular reactor contains aqueous 1.5% agar-agar and HgCI, (0.01 M); chambers C I and C2 contain aqueous solutions of HgCl, (0.01 M) and KI at 0.2 (A 1 ), 0.15 (A2), 0.1 (A3), and 0.05 M (A4), respectively. Field intensity = 0.213 V cm-I; temperature = 40.0 f 0.1 " C .
1.6
c
/ A'
1.4 A2
1.2
E
u
1.0
r J
0.8
"0
60
120
180 2LO 300
TIME (min 1 Figure 6. Plots of location of the yellow precipitate front from the junction as a function of time at various field intensities: 0.0 V cm-I ( A l ) ; 0.213 V cm-' (A2); 0.383 V cm-I (A3). Conditions: tubular reactor contains aqueous 1.5% agar-agar and HgCI, (0.01 M); chambers CI and C2contain aqueous solutions of HgCI, (0.01 M) and KI (0.2 M), respectively; temperature = 40.0 f 0.1 "C.
which contained aqueous electrolyte solutions. These were separated by a tubular glass reactor G filled with 1.5% aqueous agar-agar gel and a reactant of relatively lower concentration. The distance between the electrodes were kept the same in each experiment. The dc output source was connected with two bright platinum electrodes (PI, P2). The field intensity was varied with the help of a potential divider. Digital multimeter (HIL, India) was used as a potential-measuring device. Experiments were carried out in an air thermostat having a glass door to allow sufficient natural light to enter into it. ( i i ) Kinetics of Propagation of the Yellow Waoe in the Presence of an Electric Field. The yellow wave is formed by putting aqueous solutions of mercuric chloride (0.01 M) and potassium iodide (0.2 M) in chambers Cl and C2, respectively. The tubular reactor contained 1.5% aqueous agar-agar gel and 0.01 M mercuric chloride as shown in Figure Sa(ii). The kinetics of propagation of the yellow wave has been studied by measuring the location of the wave front from the initial junction as a function of time. Electrical field experiments were carried out (a) at various field intensities, (b) with KI solutions of different concentrations, and (c) in tubular reactors of different diameters. ( a ) Variation of Field Intensities. The yellow band is formed near the cathode and moves toward the anode (Figure 5b). Ex-
0.6
0.4
0.2
0
60
120
I80 240 TIME (MINI
300
Figure 8. Plots of location o'f the yellow precipitate front from the junction as a function of time obtained in tubes of various diameters: 11.7 ( A l ) , 6.8 (A2), and 4.4 mm (A3). Conditions: tubular reactor contains aqueous 1.5% agar-agar and HgCl, (0.01 M); chambers C, and C2 contain aqueous solutions of HgCI, (0.01 M) and KI (0.2 M), respectively. Field intensity = 0.213 V cm-'; temperature = 40.0 f 0.1 OC.
periments were carried out at various field intensities (0, 0.21 3, and 0.383 V cm-I) while other experimental conditions, viz., electrolyte concentration, temperature, and diameter, of the tube, were kept unchanged. Plots of the location of the lower front of the precipitate ( d ) from the initial junction versus time ( t ) at various field intensities are shown in Figure 6. (b) Variation of Potassium Iodide Concentration. The concentration of potassium iodide solution was systematically varied between 0.05 and 0.2 M while other experimental conditions were the same. Plots of band location (6)from the initial junction versus time ( t ) at various concentrations of KI solution are shown in Figure 7 . (c) Variation of Tube Diameter. The kinetics of yellow wave propagation in the presence of an electric field has also been studied in tubes of various diameters (viz. 4.4,6.8, and 1 1.7 mm).
The Journal of Physical Chemistry, Vol. 94, No. 26, 1990 8971
Chemical Waves in the HgCi2-KI System
0.8 AI 1.6
0.7
-
0.6
-E
I
-5
0
0.5
fn
v
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z
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y
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OL 0
1
1
60
120
I
180 TIME I MIN 1
0
2
4
6 I ni+,- n, 1
8
IO
_ I -
240
Figure 9. Plots of location of the red precipitate front from the junction as a function of time at various concentrations of HgCl,. Conditions: tubular reactor contains aqueous 1.5% agar-agar and KI (0.01 M); chambers C I and C2contain aqueous HgCI, at 0.2 ( A l ) , 0.1 (A2), and 0.05 M (A3) and KI (0.01 M), respectively. Field intensity = 0.213 V cm-I; temperature = 40.0 f 0.1 OC.
Figure 11. Plot of AS versus (ni+l - ni) at 30.0 f 0.1 "C. Conditions: tubular reactor contains aqueous 1.5% agar-agar and KI (0.002 M); chambers C I and C2 contain aqueous solutions of HgC12 (0.1 M) and KI (0.002 M), respectively.
a
b 4
Figure 10. Precipitation patterns of red mercuric iodide in agar-agar gel at various field intensities at 30.0 f 0.1 "C. Conditions: tubular reactor contains aqueous 1.5% agar-agar and KI (0.002 M); chambers CI and C2 contain aqueous HgCI, (0.1 M) and KI (0.002 M), respectively. Field intensity = 0.0 (a) and 0.106 V cm-I (b). Direction of movement of the precipitate is indicated by an arrow.
The field intensity was 0.21 3 V cm-'. Plots of band location (6) versus time ( t ) are shown in Figure 8 . (iii) Kinetics of Propagation of the Red Wave in the Presence of an Electric Field. The red wave is formed in the tubular reactor containing potassium iodide (0.01 M) and 1.5% agar-agar. Aqueous solutions of mercuric chloride (0.2 M) and potassium iodide (0.01 M) were taken in chambers C1and C2, respectively. The red band is formed near the anode as shown in Figure 5b and moves toward the cathode. The kinetics of its propagation was studied in a manner similar to that described for yellow wave propagation. In this case two types of experiments were performed. ( a ) Variation of Mercuric Chloride Concentration. The concentration of mercuric chloride solution in the chamber C, was varied between 0.05 and 0.20 M, while other experimental conditions were the same. Plots of d versus t are shown in Figure 9. ( b ) Influence of the Electric Field on the Precipitation Pattern of Red Mercuric Iodide. Experiments were performed in the absence of an electric field as well as in the presence of an external
TIME ( h )
Figure 12. Plots of location of the red precipitate front from the junction as a function of time at 30.0 f 0.1 "C. Conditions: tubular reactor contains aqueous 1.5% agar-agar and KI (0.002 M); chambers C I and C2 contain aqueous HgC12 (0.1 M) and KI (0.002 M), respectively. Field intensity = 0.106 V cm-I.
electric field (intensity 0-0.128 V cm-I). In these cases, the concentration of potassium iodide in the tubular reactor and in the chamber Cz was considerably low (0.002 M). Precipitation patterns are shown in Figure 10, and results are plotted in Figures 1 1 and 12.
Results and Discussion In our earlier paper" we reported observations on the onedimensional propagation of red and yellow waves of mercuric iodide in agaragar gel in complete darkness. Yellow or red species are produced depending on the stoichiometry of the reactants in which they react. Yellow wave is produced when aqueous [KI] > [Hg2'] in gel, and red wave is produced when aqueous [Hg2'] > [KI] in gel. A single red band bifurcates into several revert spaced bands in the presence of natural light of wave length X < 600 nm. However, the yellow band did not bifurcate under these conditions. Yellow and red species were characterized as
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The Journal of Physical Chemistry, Vol. 94, No. 26, 1990
0
120
60
180 240 TIME I MIN I
300
Figure 14. Plots of cf versus f for the values plotted in Figure 7 .
0
L.-----L.--L--L0
60
120
I80
240 TIME I MIN
300
360
2.0
I
1
I
Figure 13. Plots of cf versus r for the values plotted in Figure 6 .
Hg12 by chemical methods. The kinetics of their propagation has been studied, obeying the equation d2 = kt, where d denotes the extent of propagation from the initial junction and k and t are rate constant and time, respectively. The main features of this paper are (i) light-induced spatial bifurcation of the yellow wave into a number of alternate red and yellow bands at low pH of the agar-agar gel containing Hg2+(pH 2.72), (ii) dependence of precipitation pattern on the orientation of tubes, and (iii) influence of an external electric field on the kinetics of yellow and red wave propagation including the dependence of K1 and HgCI2 concentrations and diameter of the tube. At low [KI], revert spaced red bands were formed in the presence of an electric field (field intensity < 0.106 V cm-I). However, propagation of a single front of continuous precipitation was observed at field intensity greater than 0.106 V cm-I. Figure 1 shows the precipitation pattern of mercuric iodide when aqueous K1 solution of relatively higher concentration diffused into the agar-agar gel containing another electrolyte, mercuric chloride. It was observed that the yellow wave propagated downward in the presence or absence of natural light when the pH of the lower content was 4.68 (Figure la). However, a remarkable change in its characteristics could be noticed when its pH was reduced by adding a small amount of acetic acid. At pH 1 2 . 7 2 the yellow wave bifurcates into a number of alternate red and yellow bands at the lower end of the tube in the presence of natural light (Figure IC). However, the bifurcation was not possible in complete darkness (Figure Ib) and only orange continuous precipitate propagated downward. An experimentation on the yellow wave propagation at different tube orientations revealed the dependence of the band location on the direction of tubes relative to the grjvitational field. The locations of bands in the horizontal tube. ( H ) were approximately halfway between those in the (gt)and (gl) directions (Figure 2). A similar effect on band location has also been observed by Kai et aI.l3 and Das et al.I2 The influence of gravity on the width of the band is clearly indicated in Figure 3. The influence of external electric field on the propagation of yellow wave has been studied in agar-agar gel. Field intensity was varied in the range 0-0.383 V cm-'. Nonlinear plots of location of bands as a function of time at various field intensities are shown in Figure 6. Plots of d2 versus t yield straight lines (Flgure 13), indicating that the relation 62 = kt + C is obeyed. (13) Kai, S.;Muller, S. C.;Ross, J. J . Chem. Phys. 1982, 76, 1392.
0
1.8
1
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08
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t
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9 0
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'
!
o
60
120
180 TIME IMINI
L .
240
300
Figure 15. Plots of d2 versus f for the values plotted in Figure 9.
Values of the slope ( k ) are recorded in Table 1. It is observed that in the absence of an electric field, the velocity of propagation is relatively faster in comparison to that observed in the presence of an external electric field (Figure 6 ) and further it decreases with increase in the field intensity. In the absence of an electric field, iodide ions diffuse into the gel from chamber C2on account of a concentration gradient. When an electric field was applied, Hgz+ ions which were very adjacent to the cathode would try to move with greater velocity and create difficulty in diffusing I- ions from chamber C1. As a result, the velocity of propagation decreased on applying voltage and the velocity was further decreased with increase in the field intensity. At a fixed field intensity, velocity would increase with an increase in [I-] in chamber C2 as shown in Figure 7. Plots of 62 versus t yield straight lines (Figure 13) obeying the relation = kt + C. A similar trend for the dependence of [Hg2'] on the velocity of red wave propagation has been observed in the presence
The Journal of Physical Chemistry, Vol. 94, No. 26. 1990 8973
Chemical Waves in the HgCI2-KI System
TABLE I: Electrolyte Concentration, Color of the Propagating Band, Tube Diameter, Field Intensity, Slope (k),and Correlation Coefficient ( R ) color of [HgC121/M 0.0 I*
[ W M 0.20
0.01"
0.15 0.10 0.05 0.01"
0.20 0.10 0.05 0.01'
propagating band yellow
tube diam/mm 6.8
yellow yellow yellow red red red yellow
6.8 6.8 6.8 6.8 6.8 6.8 11.7 6.8 4.4
0.20
field int/V cm-' 0.000 0.213 0.383 0.213 0.213 0.213 0.213 0.213 0.213 0.213 0.2 13 0.213
k/(cm2/min) 0.0064 0.0053 0.004 1 0.0044 0.0033 0.0017 0.0099 0.0063 0.0040 0.0082 0.0053 0.0048
R 1.000 0.998 0.998 0.998 0.998 0.994 0.999 0.998 0.994 0.996 0.998 0.996
"Tubular reactor contains aqueous solution of an electrolyte and 1.5% agar-agar. 22
20
I8
~
.
14
-
12
i.
IO
-
16
N
08
~
06 .
0
60
120
180 240 TIME I MN1
300
Figure 16. Plots of 62 versus t for the values plotted in Figure 8
of an electric field (Figures 9 and 15). Increase in the tube diameter also influences the velocity of propagation of yellow wave. Nonlinear plots of location of bands (d)versus time ( t ) at various tube diameters are shown in Figure 8. Plot of d2 versus t yields straight lines (Figure 16). Values of the slope are recorded in Table I. Another interesting feature of this system is the propagation of continuous precipitate of red Hg12 at low [KI] in the presence of an electric field intensity greater than 0.084 V cm-' and the development of revert spaced red bands at field intensity in the
range 04.084 V cm-l (Figure IO). Both experiments were carried out in the presence of natural light. A plot of the spacing between two consecutive bands (AS) as a function of (ni+l - ni) is shown in Figure 11. (ni+' - ni) indicates that the separation between the (i + I)th and ith bands has been considered. It obeys the = -m(ni+, - ni) C, as evident by the linear plot equation of (AS)4 versus (ni+l - ni) (Figure 17), where m and C are slope and intercept, respectively. It can be inferred from the electric field experiments that a critical field intensity exists (0.106 V cm-l) at which continuous precipitation occurs propagating in the tube (Figure lob) similar to that observed by OrtolevaBfor the K2Cr207-AgN03system.
+
Acknowledgment. We thank Prof. R. P. Rastogi, ViceChancellor, BHU, and Prof. (Mrs.) Pratima Asthana, ViceChancellor, Gorakhpur University, for help and encouragement and Prof. S . Giri, Head, Chemistry Department, University of Gorakhpur, for providing laboratory facilities. Financial assistance received from CSIR, New Delhi, is thankfully acknowledged. Registry No. Hg12, 7774-29-0; agar, 9002-18-0.
