J . Phys. Chem. 1991, 95, 3866-3873
3866
1 3-.1 1
D, in excellent agreement with our fit. When performing the least-squares fit while constraining p2 = 1.58 D, we obtain pl = 3.00 0.06 D, PE = -5.74 f 0.19 kJ/mol. Kalasinsky et aLZ5 have measured with Raman spectra AE = -4.43 f 1.6 kJ/mol, in agreement with our value.
*
3.0
.
N
0
z
2.9
2.8 300
340
380
420
TIK
Figure 5. Square of the dipole moment of R143 as a function of tempeiature. The solid circles are the experimental determinations,and the curve represents the best-fit values using the functional form of eq 8 and assigning w 2.0. The best-fit parameter values are p , = 2.84 D, p2 = 1 .SO D, and AE = -3.90 kJ/mol. 1
1
-
are so close to those obtained with w = 2.0 that we conclude that our approximation of w cannot account for the discrepancy. We conclude that our results are inconsistent with those of refs 24, 25, and 26. In Figure 5 we plot p2(T) for R143 along with a best-fit curve of the data to eq 6. The best-fit parameters are pl = 2.84 f 0.08 D (C, conformer), p2 = 1.50 f 0.15 D (C, conformer), and PE = -3.90 f 2.2 kJ/mol. The fit to the data is very good. Mukhtar~v,~' through the Stark effect, measures p2 = 1.58 f 0.02 (27)
Mukhtarov, I. A. Dokl Akad. Nauk. SSSR 1963, 151,
1076.
V. Conclusion We have measured the dipole moments of R125, R152a, R134a, R143a, R134, R143, and R124. Our measured moments of R125, R 152a, R 134a, and R143 agree well with previous measurements made on these molecules, and all have uncertainties of less than 1%. We have presented the first measurement of the dipole moment of R124. In addition, we have made the first measurements of the temperature dependence of the dipole moments of R134 and R143 using dielectric-constant measurements. While our value of the moment of the C,conformer of R 143 agrees well with that obtained from spectroscopic measurements, our value of the moment of the gauche conformer of R134 does not. For both R134 and R143 our value for the energy difference between the two conformers is higher than that measured for the enthalpy difference from spectroscopic measurements.
Acknowledgment. We are grateful to Dr. Sandra Greer of the University of Maryland for the loan of her capacitance cell and to Dr. James Schmidt of NIST for loaning to us his index of refraction cell. We thank Mr. D. Defibaugh for the use of his density measurements before their publication. C.W.M. is grateful to the National Research Council and the National Institute of Standards and Technology for the granting of an NRC-NIST Postdoctoral Research Associateship.
Dynamic Instability and Light-Induced Spatial Bifurcation of Hg12 and External Electric Field Experiments in Two-Dimensional Gel Media Isbwar Dah* Anal Pushkarma, and Anunita Bhattacharjee Department of Chemistry. University of Gorakhpur, Gorakhpur- 273 009, India (Received: June 6, 1990; In Final Form: December 3, 1990) New results on two-dimensional propagation of a single red/yellow wave of mercuric iodide in gel media in batch,continuous-flow, and gel-ring reactors are reported. The influence of electrolyte concentrations, temperature, thickness of the gel, and type of the reactor on the kinetics of wave propagation has been studied. Light-induced spatial bifurcation of yellow wave into alternate yellow and red bands is observed at low pH of the gel containing mercuric chloride. Experiments to study the precipitation pattern and crystal growth on a thin film of agar-agar gel sandwiched between microslides were carried out. Rhythmicity was observed during red-wave propagation at low [KI].A new type. of continuowflow reactor has been designed to carry out experiments in the presence of an external electric field. Transitions from yellow to red and red to yellow forms have been observed in the presence of an external electric field. A critical field intensity at 0.283 V cm-* exists at which the yellow form changes into a red variety.
Introduction There is considerable scientific interest in the crystal growth, development of chemical waves, and rhythmic precipitation in gel media. The subject has been of practical importance for many years. In recent years, a reactivation of experimental and theoretical research in the field of periodic precipitation in gel media can be Light absorption also plays an important role Muller, S.C.; Kai. S.;Ross,J. J. Phys. Chem. 1982.86, 4078. ( 2 ) Kai, S.;Muller, S.C.; Ross, J. J. Phys. Chem. 1983,87,606. (3) Muller, S. C.; Kai, S.;Ross, J. Science 1982, 216, 635. (4) Das, I.; Pushkama, A.; Lall, R. S . J. Crysl. Gmwrh 1987,82, 361. (5) Das, 1.; Lall, R. S.;Pushkama, A. 1. Phys. Chem. 1987, 91, 747. (6) Das, 1.; Pushkama, A. J. Non-Equilib. Thermodyn. 1w18,13, 209. (7) Das, I.; Das, S.S.;Pushkarna. A.; Chand, S . J. Colloid Interfie Sci. (1)
1989,130(1), 176. (8) Das. I.; Chand, S.;Pushkama, A. J . Phys. Chem. 1989. 93, 7435.
0022-3654191 12095-3866$02.50/0
in the macroscopic structure development,c6*"' and the phenomenon can be influenced in the presence of an external electric field."-" It is possible to stop, reverse, or destroy chemical waves by imposed electric field.I3 In earlier we reported results on the onedimensional propagation of yellow/red mercuric iodide, influence Nitzan, A.; Ortoleva, P.; Ross, J. J. Chem. Phys. 1974, 60,3134. (10)Das, I.; Pushkama, A,; Agrawal, N. R. J. Phys. Chem. 1989, 93, (9) 7269. .
(1 1) Das, I.; Pushkama,A.; Bhattacharjec, A. J. Phys. Chem. 1990.94, 896. (12) Schmidt, S.;Ortoleva, P. 1.Chcm. Phys. 1977,67,3771. (1 3) Ortoleva, P.Theoretical Chemistry, Periodiciries in Chemistry and Biology; Eyring, H.,Ed.;Academic Prws: New YwL, 1978; Vol. IV,p 235. (14) Fecney, R.;Schmidt, S.L.;Strickholm, P.;Chadam, J.; Ortoleva, P. J. Chem. Phys. 1983,78, 1293.
0 1991 American Chemical Society
HgI2 in Two-Dimensional Gel Media
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3067
b 3 ipitation patterns of (a) yellow and (b) red mercuric iodide iuous-flow reactor at 20.0 i 0.1 O C . Conditions: (a) II M in 1% agar-agar gel (outer portion), [KI] = 0.2 M 1; (b) [KI] = 0.01 M in 1% agar-agar gel (outer portion) = 0.1 M (inner portion); flow rate Q = 2 mL/h. 5.0
6.0
Figure I. Precipitation pattern of yellow mercuric iodide in batch reactor. Conditions: [ HgCI,] = 0.01 M in 1 % agar-agar gel (outer portion) and [ K l ] = 0.2 M (inner portion); temperature = 20.0 f 1 OC. 3.0
3 0
20
LO
2 0:"
0,' '
00
0
2
0
4
0
6
0
8
0
1
0
0
~
mull ( 01
(b)
Figure 2. Experimental setup of (a) DPL continuous-flow reactor. The petri dish contains 1% agar-agar gel and a reactant of lower concentration. (b) Gel-ring reactor, 1% aqueous agaragar was used to form gel-ring, (01, 0,) outlet nozzles; (B,, B2)Corning burets, (R,,R2)reservoirs containing aqueous solutions of reactants.
of light, extemal electric field, gravity, pH of the medium, changes in potential/[H+], and kinetics of propagation at various experimental conditions in an agar-agar gel. In the present article we report new results on two-dimensional propagation of yellow/red mercuric iodide in batch and continuous-flow reactors (DPL and gel-ring). Light-induced spatial biflrrcation of yellow mercuric iodide at low pH and kinetics of wave propagation at various experimental conditions are reported. A new continuous-flow reactor has been designed to carry out experiments in the presence of an external electric field. The influence of gel thickness on propagation of mercuric iodide in an agar-agar gel sandwiched between two glass plates and the pattern formation in a thin film of agaragar have been studied. Experimental Section
Materials. Mercuric chloride, potassium iodide (AR., S. Merck), and agar-agar (Difco, USA)were used as such without further purification. Procedure. Propagation of a yellow wave in a batch reactor: A mercuric chloride solution of known concentration was prepared in doubly distilled water containing 1% agaragar and heated at 85-90 "C. The solution was homogenized with a magnetic stirrer with a hot plate. To obtain a two-dimensional precipitation pattern of mercuric iodide, the bottom of the square petri dish (10 cm
Figure 4. Plots of location of precipitate front from the initial junction as a function of time for precipitation of yellow mercuric iodide in (a) DPL reactor (QKi = 2 mL/h) and (b) gel-ring continuous flow reactor (QHIC12 = QKI = 2 mL/h). Conditions: [HgCI,] = 0.01 M in 1% agar-agar gel and [KI]= 0.2 M. 1% agar-agar aqueous solution was used to prepare gel-ring. Temperature = 20.0 f 0.1 OC. X 10 cm) with a flat surface was covered with mercuric chloride solution. A circular portion of the gel layer (diameter 2.18 cm) was removed from the center of the dish, and subsequently the empty section was filled with more concentrated aqueous potassium iodide solution. To prevent evaporation of the solution, the dish was covered with a glass plate. To check the reproducibility of the pattern, two dishes were prepared simultaneously for each set of experiments. Experiments were performed in an air thermostat fitted with a glass door to pass natural light through it. The temperature was maintained accurately to k0.1 OC. Results of an experiment performed in a batch reactor are shown in Figure 1. In this experiment the concentration of potassium iodide decreased continuously due to diffusion and chemical reaction processes, and ultimately the precipitation stopped. This difficulty was removed by performing the experiment in a continuous-flow reactor, also known as Das-Pushkarna-La11 reactoe (DPL reactor, Figure 2a) in which the concentration and level of the entering reagent in the empty space were always kept constant. The inner solution was fed continuously at a rate of 2 mL/h. Results of the experiments performed in the DPL reactor for the propagation of yellow and red waves of mercuric iodide are shown in Figure 3. A plot of the location of the yellow wave front from the junction as a function of time is shown in Figure 4 (curve a). Two-dimensional experiments in a DPL reactor that
Das et al.
3868 The Journal of Physical Chemistry, Vol. 95, No. 9. 1991 5.0
4.0
3.0
3 W
20
LO
00
I
I
0
2
I
0
4
1
0
1
I
6
0
~
1
"
TYM
Figure 5. Plots of location of yellow precipitate front from the junction as a function of time at various KI concentrationsin DPL continuous flow reactor. Conditions: [HgCI2]= 0.01 M; [KI]= 0.1 M ( I ) , 0.2 M (2). and 0.4 M (3); Q K I = 2 mL/h; temperature = 20.0 f 0.1 OC.
a
A
3.0
LO
I
1
0
2
0
4
0
1
1
1
6 0 " p T Y W
1
o
Figure 6. Plots of location of yellow precipitate front from the initial junction as a function of time at different temperatures in DPL continuous flow reactor. Conditions: [HgCIJ = 0.01 M in I% agar-agar gel and [KI]= 0.2 M, Q K I = 2 mL/h. Curve 1 20.0 f 0.1 OC, curve 2 30.0 f 0.1 OC, and curve 3 40.0 f 0.1 OC.
is open with respect to the flow of one reactant have also been carried out at different potassium iodide concentrationsand various temperatures during the precipitation of yellow mercuric iodide. Results are shown in Figures 5 and 6. An experiment was also performed in a continuous-flow gel-ring reactor (Figure 2b) that was open with respect to the flow of both reactants and fed at definite flow rates. Description of a Gel-RingReactor. The gel-ring reactor consists of a square flat-bottom petri dish (1 5 cm X 15 cm) having two holes, one at the center and the other at the corner, fitted with outlet nozzles (01, 02).The bottom of the petri dish was covered with a 7.5-mm-thick mercuric chloride solution of known concentration in 1% agar-agar gel. A gel-ring (G) having inner and outer diameters of 12 and 77 mm, respectively, was cut with an annular device. Aqueous solutions of KI (0.2 M)and H&I2 (0.01
b Figure 7. Light-induced periodic precipitation patterns of mercuric iodide
in agar-agar gel containing glacial acetic acid in (a) DPL continuous flow reactor containing 1% agar-agar, HgCI2(0.01 M) and acetic acid: (b) tubular reactor contains 1.5% agar-agar HgCI2(0.01 M) and acetic acid. pH of the gel in both the cases was 2.55, Q K I = 2 mL/h. Temperature = 30.0i 0.1 OC.
M)were continuously fad into the outer and inner sections of the reactor, respectively, from the reservoirs RI and R2. Flow rates were adjusted with the help of burets BI and B2 The reactor was covered with a glass plate to avoid evaporation of the solution. The entire assembly (Figure 2b) was put into a thermostat maintained at a fixed temperature. The location of the wave front from the initial junction is plotted as a function of time for yellow wave propagation and shown in Figure 4 (curve b). Dependence of p H on Precipitation Pattern. The dependence of [H+) on the precipitation pattern has also been studied in the DPL continuous-flow reactor. The pH of a HgC12solution in 1% agar-agar gel was lowered from 4.68 to 2.55 by using a small
Hgli in Two-Dimensional Gel Media
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3069
b
Q
Figure 8. Photographs showing propagation of (a) yellow and (b) red mercuric iodide in agar-agar gel containing an electrolyte sandwiched between two glass plates. Conditions: (a) [KI]= 0.2 M solution diffuses into mercuric chloride (0.01 M) containing 1% agar-agar gel and (b) [HgCI2]= 0.1 M solution diffuses into potassium iodide (0.01 M) containing 1% agar-agar gel at 21.0 f 0.1 "C.
amount of glacial acetic acid. The pH of the solution was measured by using a Toshniwal pH meter. Experiments were performed in an air thermostat at 30.0 f 0.1 OC. Two identical sets of experiments were performed at pH 4.68 and 2.55. One set was kept in complete darkness and the other was illuminated with natural light. The precipitation pattern thus obtained in the presence of natural light is shown in Figure 7a. Influence of Gel Thickness on '15uo-DimensionalPropagation of Mercuric fodide. The reaction between mercuric chloride and potassium iodide was performed in 1% agar-agar gel containing one of the reactants A or B of relatively low concentration (A = HgCI2 for yellow-wave and B = KI for red-wave propagation). The hot gel was poured on a flat glass petri dish and allowed to cool. A microslide was put above it. The remaining portion of the gel outside the microslide was removed. The petri dish was then filled with another electrolyte B or A of relatively high concentration for getting a yellow or red wave, respectively. Results are shown in Figure 8. The kinetics of propagation of the yellow/red wave have been studied at various thicknesses of gel (2.5-10.0 mm) by measuring the location of the wave front from the initial junction as a function of time. Results are shown in Figure 9. Crystal Growth and Pattern Formation in Thin Films of AgapAgar Gel. Pattern formation processes have been of considerable scientific interest and practical importance for many decades.') Interest in the growth of complex structures under nonequilibrium conditions has been stimulated by several recent developments. In the present investigation one of the electrolytes diffuses into a thin film of 1 % agar-agar gel containing another electrolyte, sandwiched between two microslides. Rhythmic or complex patterns of mercuric iodide are formed depending on the experimental conditions. The slides were put horizontally in a glass petri dish containing another electrolyte of relatively high concentration and allowed to diffuse from all sides. A number of experiments have been performed: (i) HgC12(0.05 M)diffuses into 1% agaragar gel, (ii) KI (0.05 M)diffuses into I% agaragar gel, (iii) KI (0.2 M)diffuses into 1% agar-agar gel containing HgC12 (0.01 M), (iv) K1 (0.04 M)diffuses into 1% agar-agar gel containing HgCI2 (0.01 M), (v) HgClz (0.1 M) diffuses into 1% agar-agar gel containing KI (0.01 M), (vi) HgCI2 (0.1 M) diffuses into 1% agar-agar gel containing KI (0.05 M). In experiments i-iv slides were taken out after completion of the reaction, whereas in experiments v and vi reaction was allowed to take place for 2 h. Experiment v was also carried out with relatively high gel thickness containing KI (0.01 M), and reaction was allowed to take place for 2 h. All slides were dried in an incubator at 50 OC and viewed through an Olympus microscope (magnification X50). Results are shown in Figure 10. Influence of External Electric Field on Wave Propagation. Interaction of chemical waves with an applied electric field is an important feature of electrochemical systems.I3 The influence (IS) Meakins, P.; Tolman, S.f m . R. Sm.London 1989,423, 1.
0.9 0.8
0.7 0.6
-b
b
0.5 0.4
0.3 0.2
01 00
0 3 0 6 0 9 0 1 2 0 1 5 0 TMEM
P3 0.7 0.6
0.5
-3 0.4 0.3 0.2 OJ
00
I
0 3 0 6 0 9 0 1 2 0 1 5 0 T M E m
Figure 9. Plots of location of (a, top) yellow and (b, bottom) red prtcipitate fronts from the junction as a function of time at different thickness of the gel. Conditions: (a) [KI]= 0.2 M, [HgCI2J= 0.01 M in 1% agar-agar gel. Temperature 2 1 .O f 0.1 OC. (b) [HgCI2]= 0.1 M, [KI)= 0.01 M in 1% agar-agar gel. Gel thickness 2.5 mm (curves YI,R,), 5.0 mm (curves Y2,R2),and 10.0 mm (curves Y3,R3);temperature 29.0 i 0.1 OC.
Das et al.
3870 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
H
I
H
II
0-5mm
0.5 mm
L v
0.5"
iii
H
0.5"
Figure 10. Microphotographs(i, ii), obtained at different [KI] after completion of the reaction. Conditions: [KI] 0.04 M (i) and 0.2 M (ii) diffuses into thin films of HgCI2 (0.01 M) containing 1% agar-agar gel sandwiched between two microslides. Microphotographs (iii-v) show the influence of [KI] and gel thickness on precipitation pattern in a thin film of 1% agar-agar. Conditions: [HgCI] = 0.1 M; [KI] = 0.01 M (plate iii), 0.05 M (plate iv) in agar-agar gel of 0.4-mm thickness when dried; [HgCI,] = 0.1 M, [KI] = 0.01 M (plate v) in agar-agar gel of 1.8-mm thickness when dried. Reaction was checked after 2 h at 30.0 f 0.1 OC (magnification XSO).
s
A-
B J - 7
D :
0"
Figm 11. Experimental setup of a continuous-flowreactor to carry out experiments in presence of extemal electric field: (PI,P2) platinum electrodes; (B) dc voltage output source; (M) digital multimeter; (0) outlet nozzle; (C) petri dish containing one of the electrolytes in 1% agar-agar gel; (R) reservoir containing another electrolyte.
of an extemal electric field on the precipitation of yellow and red mercuric iodide in gel media has been studied in a specially designed continuous-flow reactor as shown in Figure 11 and described below. Description of Continuous-FlowReactor for Electric Field Experiments. The experimental setup consists of a square petri dish (IO cm X 10 cm)with a flat surface having an outlet nozzle (0)at the center. The reactor was filled with 1% agar-agar containing one of the reactants (C) of relatively low amcentration. A circular ring of platinum wire was placed in the gel, and one end was taken out to act as an anode/cathode (PI). After the gel was solidified, a circular portion of the gel (diameter = 2. I8 cm) was removed from the center of the dish. Another circular platinum electrode cathode/anode (P2) was put in a solution (A) of relatively high concentration taken in the center of dish and was influxed from the reservoir (R)through polyethylene tubing
and buret (D)at a definite flow rate. The level of the solution in the empty space was kept constant by the continuous filling of the entering reagent. The excess solution automatically passes through the outlet nozzle. Electrodes were placed at the same distance (5.3 cm) in each experiment. A dc output source (B) was connected with bright platinum electrodes PI and P2. The field intensity was varied with the help of potential divider. A digital multimeter M (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 the thermostat. Experiments were performed at the field intensity 0.567 V cm'l, and the results were compared with those obtained in absence of an electric field for the precipitation of yellow and red Hg12. Results are shown in Figure 12. Experiments at varying field intensity in the range 0 . 0 . 5 6 7 V cm'l for the propagation of yellow Hg12 in gel media in presence of natural light have also been carried out. Results are shown in Figure 13.
Results a d Discussion In earlier communications,IO*Il we reported propagation of yellow and red waves of mercuric iodide and light-induced spatial bifurcation of red mercuric iodide in agamgar gel. A yellow wave propagates when an aqueous KI solution diffused into gel containing mercuric chloride of relatively low concentration, whereas a red-wave precipitate formed when the foregoing system was inverted (mercuric chloride solution diffuses into potassium iodide of relatively low concentration containing agar-agar gel). The following reactions take place:
-
2KI(Cl) + HgC12(C2) HgC12(Cl)
+ 2KI(C2)
2KCl + Hg12 (yellow) 2KCl
+ Hg12 (red)
where CI (aqueous) and C2 (in gel media) represent the concentration of the electrolytes and Cl > C2. Experiments were performed in complete darkness. Onedimensional studies on this system reported earlierloJ1described some interesting features
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3871
Hg12 in Two-Dimensional Gel Media
r
I
I!
i
I1
I I
tc
EiD
a
C
9
e Y
b
h
d ( ii )
(i>
Flgaw 12. Photographsshowing initial and final stages of precipitation patterns of mercuric iodide .1 agar-agar gel: (i) at zero field intensity (plates a-d) and (ii) in presence of extemal electric field (field intensity 0.567 V cm'l, plates t h ) . Conditions: (KI] = 0.2 M, [HgCIz] = 0.01 M in 1% agar-agar gel (plates a, c, e, g); and [HgCI2] = 0.1 M, [KI] = 0.01 M in 1% agar-agar gel (plates b, d, f, h). QKI = QHm2= 2 mL/h.
a
b
C
d
e
Figure 13. Precipitation patterns of mercuric iodide in agar-agar gel at field intensitiesin the range 0.0-0.567 V cm'l. Conditions: [HgCIJ = 0.01 M in 1% agar-agar gel (outer portion); [KI] = 0.2 M (inner portion), QKg = 2 mL/h. Field intensity (a) 0.00, (b) 0.189, (c) 0.283, (d) 0.378, (e) 0.567 V cm''.
of this system such as the bifurcation of a single red band into several thin revert spaced red bandslo and bifurcation of yellow bands" at low [H+] when illuminated with natural light. Besides these studies, influences of gravity and extemal electric field on the wave propagation at various field intensities, electrolyte concentration, and tube diameters have also been described. These results invoked us for two-dimensional studies in the presence and absence of an electric field. In the absence of an electric field two-dimensional experiments in (i) a batch reactor, (ii) a DPL continuous-flow reactor, and (iii) a gel-ring continuous-flow reactor have been performed. In a batch reactor, potassium iodide diffuses into agaragar gel containing HgCI2of relatively low concentration. As a result of diffusion and chemical reaction, precipitation occurs. Initially the color was red; later on, it precipitated out in the yellow form, and finally precipitation stopped (Figure 1). Experiments were then performed in DPL and gel-ring continuous flow reactors (Figure 2), which can serve as a tool for systematic studies of spatial pattern formation in the same way that the CSTR has served in studies of homogeneous reactions.16J7 The electrolytes are influxed through the reservoirs at definite flow rates. Constant electrolyte concentrations at the liquid/gel interface were maintained throughout the experiment in the reactor, and the system (16) Noszticzius, Z.; Honthemke, W.; McCmick, W. D.; Swinney, H.
L.; Tam, W. Y.Nufun 1987,329, 169.
(17) Tam, W. Y.; Horsthemke, W.; Noszticzius, Z.; Swinney, H. L. J . Chem. Phys. 19%%,38(5), 3395.
TABLE I: D e p d m w of Slope kaad Conclrtion Coefficient Ran tbe T Y Dof~Reactor for Yellow-Wnve Proprgation in Agar-Amf thickness of k/(cm2/ type of reactor the gel/" h) R continuous-flow reactor (DPL reactor) gel-ring reactor
7.5
0.219
0.99
7.5
0.076
0.99
'Conditions: [HgCI2] = 0.01 M in I% agar-agar gel, [KI] = 0.2 M, temperature = 20.0 i 0.1 "C.
was maintained far from equilibrium. Figure 3 shows the precipitation patterns of yellow and red mercuric iodide in agar-agar gel by using a DPL amtinuous-flowreactor. Identical precipitation patterns for yellow mercuric iodide were obtained in DPL and gel-ring continuous-flow reactors. The location of the precipitate front from the initial junction was measured as a function of time for both cases and is shown in Figure 4. In the DPL reactor, the velocity is fast as compared to the velocity in the gel-ring reactor. In the DPL reactor, KI diffuses into the gel, whereas KI and HgClz both diffuse into each other in the gel-ring reactor, and thus the velocity is reduced in the latter case. Plots of dz vs t (Figure 14) yield straight lines obeying the equation dz = kt + C. The values of slope k are recorded in Table I. The kinetics of yellow wave propagation at different [KI]were studied in the DPL reactor, and the location of the precipitate front from the junction was plotted as a function of time. Results recorded in Figure 5 show that the velocity of propagation increases
3872 The Journal of Physical Chemistry, Vol. 95, No. 9, 1991
Das et al.
TABLE II: Ekctrdyte Collecatntieo, Gel Tbickneas, Cdor of the Propagating Band, Temperature, Slope k , rad Comlrtloa Coefficient R for Stnight lines^ Plotted in Flgwe~1517 color of the [HgCI,I/M WI/M gel thickness/" propagating band temp/+O.l OC k/(cm2/min) R 0.014 0.1 7.5 yellow 20.0 0.087 0.99 0.219 0.99 yellow 20.0 0.2 7.5 0.014
0.4 0.1
0.10
0.014
0.01@
0.20
7.5 7.5 7.5 7.5 2.5 5.0 10.0 2.5 5.0
yellow
10.0
yellow
20.0 20.0 30.0 40.0 21.0 21.0 21.0 29.0 29.0 29.0
yellow
yellow yellow red red red yellow yellow
0.202 0.087 0.102
0.99 0.99 0.99 1.00 0.99 0.99 0.99 0.99 0.99 0.99
0.113 0.003 0.004 0.005
0.004 0.005
0.006
OSolution contains 1% agar-agar. 20.0 18.0
2 /
20.0
6'
d
18.0
I
/
I
16.0
/
16.0
14.0
14.0
-
t2.0 N
t2.0
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0
0.0
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8.0
8.0
6.0
6.0
4.0
2.0 0.0
0.0
0
20
40
60
l w Ll
80
I00
Figure 14. Plots of d2 versus time t for the values plotted in Figure 4.
+
are best fitted by the empirical equation 8 = kr Cas evidenced by the plots of d2 vs r, which yield straight lines (Figure 15). The slope k depends on [KI]. It has been observed that the velocity depends on temperature. Results of the location of the wave front as a function of time for yellow wave propagation obtained at different temperatures are shown in Figure 6. The velocity increases with temperature. Plots of d2 vs t yield straight lines (Figure 16). Data are best fitted by the empirical equation d2 = kt + C. Values of slope k increase with a rise in temperature. Values are recorded in Table 11. The kinetics of wave propagation at various gel thickness containing one of the electrolytes between two glass plates have also k n studied (Figure 9). It has been observed that the velocity of wave propagation depends on the thickness of the gel between two glass lates. It increases with an increase in the gel thickness. Plots of t yield straight lines (Figure 17). The data are best fitted by the empirical equation d2 = kr + C, where the values of k depend on gel thickness (Table 11). Figures 7a shows the light-induced spatial bifurcation of a yellow wave into alternate red and yellow bands at low pH in the DPL reactor. In this case the pH was lowered to 2.55 by adding a small amount of glacial acetic acid. The initial pH of the solution containing 1% agar-agar was 4.68. A similar observation was obtained in a one-dimensional experiment (Figure 7b). The intensity of the yellow band was less in the two-dimensional case as compared to that obtained in the one-dimensional case. The reason may be the change in experimental condition. In two-
Jvs
I 0
I
20
40
60
80
100
TME LI
Figure 15. Plots of d2 versus time t for the values plotted in Figure 5.
dimensional studies there is a continuous influx of an electrolyte KI, whereas in one-dimensional studies there is a continuous decrease in the KI concentration during precipitation. Different types of patterns are observed when KI diffuses into a thin film of 1% agar-agar gel containing HgCI2. Plant type structures shown in plates i and ii of Figure 10 are obtained when aqueous KI solutions of 0.04 and 0.2 M, respectively, diffuse into a thin film of 1% agar-agar gel containing 0.01 M HgClz sandwiched between two microslides. The structure may be due to K2HgI,, or KI present in excess. It has been established in separate experiments that HgClz or KI alone does not produce any such type of structure under these experimental conditions. Thus it may be inferred that the plant type structures is due to KZHg14. Figure 10, plate iii, shows the rhythmicity during crystalllzatlon of red mercuric iodide at low [KI] (0.01 M), whereas at relatively high [KI] (0.05 M) rhythmicity disappeared and a complex pattern comprising of yellow/red crystals was observed (Figure 10, plate iv). In this experiment the gel thickness was 0.4 mm when dried. The influence of film thickness on crystal growth and pattern formation of the reaction product has been studied. It has been observed that at the same concentration but at relatively high gel thickness (1.8 mm when dried) a transition from rhythmic to plant type structure is observed (Figure 10, plate v). The influence of an external electric field on the two-dimensional propagation of yellow/red mercuric iodide in agar-agar gel has
The Journal of Physical Chemistry, Vol. 95, No. 9, 1991 3813
Hg12 in Two-Dimensional Gel Media
Obr
0.0
0.4 N -0
0.2 e.0
ob
-44
.
60
60
- 120. TIMEMN)
lb
00
30
a
90 120 l50 TI ME(MYIO
60
b
Figure 17. Plots of d2 versus time t for the values plotted in Figure 9.
near the anode in the gel and Hg2+ ion concentration would comparatively be increased, resulting in the precipitation of red Hg12 A similar explanation may be given for a red-to-yellow transition. A schematic representation showing ion movements during precipitation of (a) yellow and (b) red mercuric iodide in the presence and absence of an electric field may be given as
4.0
2.0
-' - He
A$=O.OO V m - ' 00 0
20
40
60
80
00
TM hl
Figure 16. Plots of dr versus time f for the values plotted in Figure 6.
been studied at the field intensity 0.567V cm-I. The experimental setup employed for this purpose is shown in Figure 11. In the absence of an electric field, the color of the precipitate remains unchanged up to the end of the experiment. Precipitation patterns of yellow and red Hg12 at initial and final stages are shown in Figure 12, plates a, c and b, d, respectively. In the presence of an electric field transitions from yellow to red (Figure 12e,g) and red to yellow (Figure 12f,h) mercuric iodide are obtained at the field intensity 0.567 V cm-I. In the absence of an electric field I- diffuses into the gel due to concentration gradient and a yellow precipitate is formed. When an electric field was imposed, I- moved toward the anode, but at the same time Hg2' would also have the tendency to move toward the cathode. As a result of counterdiffusion, the movement of I- ions would be restricted,resulting in reduced I- ion concentration
*=O0.567V~-'
I-
11-1 Wg27
Hg2'
1-
W t + l > 11-1
In a separate experiment, the field intensity was also varied in the range 0.0-0.567 V cm-I during the precipitation of yellow mercuric iodide in agar-agar. KI (0.2 M) diffuses into 1% agar-agar containing HgCI2 (0.01 M) with the same experimental setup described earlier and shown in Figure 11. Precipitation patterns at various field intensities are shown in Figure 13. It has been observed that a critical field intensity u, exists at 0.283 V cm-', at which a transition from yellow to red wave takes place.
Acknowledgment. We thank Prof. R. P. Rastogi, ViceChancellor, BHU, and Prof. (Mrs.) Pratima Asthana, ViceChancellor, Gorakhpur University, for help and encouragement. We are also grateful to a reviewer for suggestions, Head, Department of Chemistry, for providing necessary laboratory facilities, and Dr. Kehar Singh for helpful discussion. Financial assistance received from CSIR, New Delhi, is thankfully acknowledged.
