J. Phys. Chem. 1987,91, 747-150
747
SCHEME I
conductor
insulator pH 9
(e;&-) 3 -{Q#Q"N)
+Q~&--) .( a N Q N - 1 ,
~QNQN-)
(11)
(1.21
Reduced
-
x-2
X-1
i n su la tor
(1,l)
(1 3)
insulator
Oxidized
2
-'+
(1,2)
insulator
2
++
l (1 , 3 )
insulator
spin density (Figure 2 of ref 21) increases sharply for -0.1- to +0.1-V region. It then levels off to a plateau in the 0.1- to 0.3-V region. Therefore, for pH close to 1, the insulator-to-conductor transition occurs at the same switching potential as the diamagnetic-to-paramagnetic transition. We now examine prediction B. Travers et aI.l3 reported that acid treatment of polyaniline induces an insulator-to-conductor transition and an accompanying increase in spin density. This shows that the protonic acid doped polyaniline is paramagnetic. The above-mentioned two ESR measurements are consistent with our assignment of the radical cation structure to the conductive form.
Figure 6. Interconversion among different protonation and oxidation
states of polyaniline. protonation and oxidation state. It corresponds to the northeast corner of the map in Figure 5. The structure (1,l) at the lower-left corner in the reaction matrix corresponds to the southwest corner of the map. The structures ( l , l ) , (3,1), (2,3), and (3,3) corresponding approximately to the lA, lS, 2A, and 2 s forms discussed by Ma~Diarmid.','~ The basic assumptions of the scheme are the following: (1) The closed-shell reduced and oxidized forms are electrical insulators. (2) The radical cations (3,2), (2,2), and (3,3), possibly supporting polarons or bipolarons as charge carriers, are electrical conductors. Our previous spectroscopic study of model oligomer compounds supports this assumption. The encircled positive charges, e, in the scheme signify the mobile charge that delocalizes over x units of the monomers. The reaction scheme in Figure 6 implies two interesting predictions concerning in-situ ESR spin density measurement: (A) As (2,l) and (3,l) are oxidized to (3,2) and (2,2), the ESR spin density will increase. (B) As (1,2) and (2,3) are protonated to form (2,2) and (3,3), the ESR spin density is also expected to increase. Experimental results in the literature agree with these predictions. We first examine prediction A. Our conductivity data for pH 1 (the squares connected by the dash-dot line in Figure 4) indicate that a t 0.1 V the p-doping induced insulator-to-metal transition is completed. The spin density measured by Kaya et aLzl in pH -0.7 solution (0.1 M H2S04)has a similar pattern: The ESR
Conclusion This paper describes the strong influences of both the oxidation and the protonation states on the conductivity of polyaniline. The three-dimensional plot in Figure 5 shows the interplay of two unusual properties of polyaniline: (1) Electrochemical doping induces a three-state switching of electrical conductivity. (2) Protonic acid doping of (2,3) results in an insulator-to-conductor transition. With the recognition that the radical cation is a conductor but the neutral aromatic amine and the neutral quinonediimine are insulators, the structure-property correlations are summarized in Scheme I, where the matrix notations corresponds to the structures in Figure 6. This scheme satisfactorily explains the topography of the experimental results in Figure 5 . Acknowledgment. This work was supported in part by the National Science Foundation through Grant No. CHE-8216482. Registry No. Polyaniline, 25233-30-1.
Mechanism of Periodic Precipitation in an Illuminated Lead Chromate System lshwar Das,* R. S. LaU? and Anal Pushkarna Department of Chemistry, Gorakhpur University, Gorakhpur 273 009, U.P., India (Received: September 19, 1985; In Final Form: March 26, 1986) It was observed that the presence of light is essential for pattern formation and chemical instability to occur in a lead chromate system. No bands are formed in the dark. Using filters of different wavelength ranges, it was observed that light of wavelength 400~550nm is most effective and hence chromate ions having absorption maximum in this region are the active species which absorb light. In the formulation of the mechanism, it has been established that enhancement of the degree of ionization of lead chromate is an important step for autocatalytic colloidal growth in the illuminated system. It was further supported by experiments designed to study the effect of light radiation on ionic conductivity of lead chromate which is almost insoluble otherwise. On the basis of the Glansdorff-Prigogine criterion it has also been established theoretically that its homogeneous steady state is unstable under illumination. Introduction Interdiffusion of one electrolyte into another reacting electrolyte m a y lead to a rhythmic deposition of a precipitate,' which is known t Department of Chemistry, St. Andrew's College, Gorakhpur, India.
0022-365418712091-0747$01 SO10
commonly as the Liesegang phenomenon.2 When a solution of larger concentration of potassium chromate is allowed to diffuse (1) Hedges, E. S. Liesegang Rings and other Periodic Structures; C h a p man and Hall: London, 1932.
0 1987 American Chemical Society
748 The Journal of Physical Chemistry, Vol. 91, No. 3. 1987
into a less concentrated solution of lead nitrate contained in a lyophilic gel (agarcagar) medium, periodic deposition of precipitate appears after several hours of time. Similar type of periodic precipitation has been investigated and studied by a number of author^.^.^ The pattern formation or chemical instability or inhomogeneity in nucleation of colloidal particles may arise due to several factors. Interdiffusion due to concentration gradient may be one of them. But this factor becomes less important in the case of lead iodide sy~tem."~It has been observed that band formation may take place even in the absence of imposed gradient of concentration, i.e., from an initially homogeneous solution of lead iodide.5 But lead chromate is insoluble in hot water and a homogeneous solution in gel cannot be prepared. Moreover the study of illuminated lead chromate system becomes important as it was interesting to note that in this case band formation takes place only in the presence of light? Several other types of illuminated systems of periodic deposition of precipitate have been analyzed by some workers.' The mechanism of irregular deposition of precipitate (ring or band formation) has been discussed from time to time. The theories proposed earlier were based on the hypothesis of supersaturation,* coagulation of colloid? and generally postulating that the nucleation of particles is discontinuous.l0*I' Recent theories postulate that colloid formation and crystal growth of the reacting system when coupled with diffusion leads to periodic precipitation.I2 The situations in illuminated system are slightly different. The interaction of light radiation with one of the species becomes an important and necessary step. Nitzan, Ortoleva, and Ross, in their communication' have analyzed the general illuminated reacting-diffusing system. They classified the symmetry-breaking instability leading to periodic growth of precipitates into two main types; extrinsic length scaling in which characteristic length of developing spatial patterns is determined by the dimensions of the system; and intrinsic length scaling in which that characteristic length is determined by the reaction rates and transport relations of the system, Le., the dynamics of the system, and not by its dimensions. In the lead chromate system, the band formation does not depend upon the dimensions of the system. Therefore it is postulated, in formulating the mechanism, that this system is intrinsic length scaling and involves more than two reacting species. The light absorption by one of the species, nucleation of colloidal particles, and colloidal growth which is found to be an autocatalytic step are important steps in the mechanism. The main feature of this communication is the enhancement of ionic conductivity of lead chromate in the presence of light. Lead chromate is almost insoluble in water;I4 therefore the degree of ionization is very very small. It is proposed therefore that the degree of ionization increases in the illuminated system.
Experimental Section Materials. Potassium chromate (A.R., S.Merck), lead nitrate (A.R., BDH), agar-agar gel (Difco, USA) were used as such. Preparation of Bands at Varying Wavelengths. Banded precipitation pattern was obtained with lead nitrate and potassium chromate as the diffusing electrolytes by the method employed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2) Stern, K. H. A Bibliography of Liesegung Rings, 2nd ed.;U.S. Government Printing Office: Washington, DC, 1967. (3) Chatterji, A. C.; Dhar, N. R. Kolloid-2. 1926. 40, 97. Isemura, T. Bull. Chem. Soc. Jpn. 1939.14, 179. Ramaiah, K. S. Prm. lndiun Acud. Sei. Sect. A 1939, 9, 467. (4) Muller, S. C.; Kai, S.; Ross. J. Science 1982, 216. (5) Feinn, D.; Ortoleva, P.; Scalf, W.; Schmidt, S.; Wolff, M. J . Chem. Phys. 1978, 69, 27. (6) Ishwar Das, and Pushkama, A. J . Non-Eq. Thermodn., in press. (7) Nitzan, A.; Ortoleva, P.; Ross, J. J . Chem. Phys. 1974, 60, 3134. (8) Ostwald, W. Lehrbuch der AIIgemeinen Chemie; Engleman: Leipzig, 1897. (9) Dhar, N. R.;Chatterji, A. C. Kolloid-2. 1925, 37, 2. (IO) Prager, S. J . Chem. Phys. 1956,25, 279. ( 1 1) Keller, J. B.; Rubinow, S . I. J . Chem. Phys. 1981, 74, 5000. (12) Flicker, M.; Ross, J. J . Chem. Phys. 1974.60. 3458. (13) Nitnn. A.; Ross, J. J . Chem. Phys. 1973. 59, 291. (14) Solubility of PbCrO, is 0.000005 8 g/IOO mL at 25 OC,insoluble in hot water. CRC Hundhook of Physics and Chemistry; CRC Press: Roca Raton, FL, 198 1 ;Table B- I 1 1.
Das et al.
Figure 1. Prccipitation pattern of lead chromate in 1.5% agar-agar gel illuniinated with light of different wavelengths. Tubes were illuminated with ( I ) white, (2) blue, (3) green, (4) yellow, (5) red light. respectively (from left to right). Tube 6 was kept in the dark. The tubes (inner diameter 11.7 mm) were kept in the vertical position. [K,CrO,] = 0.015 M (upper portion) and [Pb(NO,),] = 0.001 M (lower portion); temperature = 25.0 f 0.1 OC.
t
O6 0.5
f
't
0.4 -
Q
3 0.3 -
v
z 4
8 0.2 0 z -
a
k 04 d
I
$ 5 I
2 3 4 5 6 7 8 9 1011 12
R Figure 2. Plot of separation of bands ( A x ) vs. the number ( n ) of separations between two successive bands vertically down wards for tubes 1 and 2 in Figure 1. 0,tube 1; A, tube 2.
in previous work.6 Lead nitrate solution of known concentration (0.001 M) was prepared in double distilled water containing 1.5% agar-agar at 85-90 "C and thoroughly mixed by using a magnetic stirrer for 15 min until a homogeneous solution was formed. The hot solution was poured in a clean and presteamed cylindrical Corning tube of inner diameter 1 1.7 mm. It was allowed to cool at room temperature until it solidified. The upper portion of the tube was filled with the same volume of aqueous solution of potassium chromate (0.015 M). The upper end of the tube was then sealed. Twelve identical tubes were taken for two sets of experiments. In one set of experiments, four tubes were wrapped with transparent paper of different colors (blue, green, yellow, and red); one tube was unwrapped to pass light of all wavelengths (white) and the last tube was wrapped with a black paper which did not allow any light to pass through it. Experiments were performed in an air thermostat fitted with a glass door which allowed sunlight to enter in it. Besides this, thc thermostat was continuously illuminated with a 25-W tungsten bulb. The thermostat can be maintained very accurately to fO.1 "C. Figure 1 shows the precipitation patterns of PbCr04 on illumination with light of various wave lengths. Tube 1 was unwrapped to pass light of all wavelengths (white); tubes 2, 3, 4, and 5 were wrapped with transparent papers of blue, green, yellow, and red colors, respectively, and the last tube was kept in the dark. From the figure it was clear that sharp bands are formed in tube 2 with blue filter (A range 435-480 nm). The separation between the bands is shown in Figure 2 for tubes 1 and 2. The results show that the separation between the bands decreases more rapidly in
Precipitation in Illuminated Lead Chromate System
The Journal of Physical Chemistry, Vol. 91, No. 3, 1987 149
TABLE I: Enhancement in Ionic Conductivity of the Illuminated Lead Chromate System Relative to Dark System at Different Time Intervals % ' enhancement
7%enhancement
time, h
in ionic conductivity
time, h
in ionic conductivity
5 17 21 27
0.9 24.8 23.1 21.7
69 76 93 117
35.0 43.8 43.6 42.0
case of tube 2 vertically downward and beyond n = 4 it does not change very significantly as the uncertainty in band width measurement is f0.02 cm. Effect of Light Radiation on the Ionic Conductivity of Lead Chromate Solution. The lead chromate is practically insoluble in water (solubility is 0.0000058 g/100 mL at 25 "C). To observe the effect of light on ionic conductivity, equal amounts of lead chromate (30 mg) were mixed with distilled water (50 mL) taken in two 100-mL Corning beakers. One of these was kept in the dark and the other was kept in light. The conductivities of the solutions were measured with a conductivity cell at different time intervals. It has been observed that conductance of lead chromate suspension in water increases with time. The percentage enhancement of conductivity relative to dark system is reported in Table I. Formulation of Mechanism A number of theories were proposed to explain the mechanism of periodic precipitation. These theories include Ostwald's supersaturation theory* and colloid formation and coagulation theory.9 It was also emphasized that prior to any visual appearance of periodic precipitation, an inhomogeneous macroscopic structure builds up.'5 Colloidal formation prior to the appearance of bands was supposed to be an essential condition. The development of spatially inhomogeneous structure from initially homogeneous reacting-diffusing system was theoretically discussed by Turing16 and analyzed by Prigogine and Nicolis17 (also see ref 18). A general mechanism was presented schematically by Flicker et a1.I2 It has been emphasized that nucleation of colloidal particles and colloidal growth are the important steps for band formation in reacting-diffusing systems. For an illuminated system, it was postulated that chemical instability may occur due to light absorption by one of the species.13 In lead chromate systems it has been observed that a uniform precipitation occurs in the dark and periodic precipitation takes place in light.6 It was also ,observed in our experiments that the band formation further ceased after a few hours when light radiations were cut off or system was put in dark, after band formation to some extent.6 From these observations it is concluded that light absorption by one of the species is an important and essential step in lead chromate systems. Now we have mentioned that the lead chromate system is an intrinsic length scaling type7 and therefore it involves more than two reacting species. We postulate that these species are lead ions, chromate ions, and lead chromate itself. Using different filters it is observed that light of wavelength 400-550 nm is most effective and the bands appeared in this range. Chromate ions have absorption maximum in this region. Therefore chromate ions is the active species which absorbs light.20 This may be the first step in the mechanism
c1-0~~+ hv
-
(Cr042-)*
energized particle has been made to explain the nature of lead chromate equilibrium.
(2) The solubility product in water is water2' X M2. The eq 2 will almost be one directional. Crystal formation or nucleation of particles will be uniform and dissolution or reionization of particles of PbCrO, will not be possible as it is practically insoluble. In illuminated systems, therefore, the situation will be different and assumption of energized PbCrO,, which has a higher degree of ionization, is essential. In the dark process the formation of PbCr0, is instantaneous and is less ionized. The enhancement of conductivity is experimentally examined in our experiments. The growth of illuminated PbCr0, particles is different from that of the dark system. The mechanism of PbCrO, periodic precipitation is therefore different from that proposed by Flicker and Ross for the lead iodide system.I2 For a complete reacting-diffusing system of illuminated lead chromate, the following sequence of events is therefore required to formulate a satisfactory theory: (a) absorption of light by one of the species; (b) nucleation of energized particles and colloidal growth; (c) distribution of colloids and band formation. The mechanism may be formulated by following this sequence of events, and the reaction steps when coupled with diffusion will give periodic nature of precipitation. The formation of colloids and its existence has been discussed by some a ~ t h o r s . ~In~ the ,~~ lead iodide system it was demonstrated that spatially inhomogeneous structures or band formation may occur from initially uniform dispersion in agar-agar.5 Lead chromate is insoluble in hot water and therefore a homogeneous solution of it cannot be prepared. It may be concluded that diffusion is also an important event in this system but it is not a sufficient condition as no band formation takes place in dark even in the presence of diffusion. The concentration gradients were found to be a necessary condition for diffusion processes. The nucleation of particles and crystal growth in concentration gradients have been studied in detail by Muller, Kai, and Ross.24 In the lead chromate system we now have the following sequence of reaction steps (a) absorption of light by Cr042- ions Cr042-
-
(Cr042-)*
(3)
Pb2+
+ (Cr042-)*
(PbCr04)*
(4)
(c) particle growth which is an autocatalytic step Pb2+
+ Cr042-+ (PbCr04)*,
(PbCr04),+1
(5)
The termination of this sequence in a dark reaction step of precipitation
-
Pb2+ + Cr042-
PbCr0,
(6)
Taking into consideration the chances of deactivation, the whole process may be symbolized as
KI
+ hv A* activation 4 A* + A 2A deactivation K3 C, energized particle A* + B A+B dissociation and recrystallization A
-
C1
A (15) Fricke, R.; Suwelack, 0. 2.Phys. Chem. 1926, 124, 359. (16) Turing, A. M. Philos. Trans. R . SOC.London 1952, 8237, 31. (17) Prigogine, I.; Nicolis, G. J . Chem. Phys. 1967, 46, 3542. (1 8) Glansdorff, P.; Prigogine, I. Thermodynamics of Structure, Stability and Fluctuations; Interscience: New York, 1971. (19) Kai, S.; Muller, S. C.; Ross, J. J . Chem. Phys. 1982, 76, 1392. (20) A,, for aqueous K2Cr04solution is 405 nm. (21) C.R.C. Handbook of Physics and Chemistry: CRC Press: Boca Ratdn, FL, 1981; Table B-242.
+ hv
(PbCr04)
(b) formation of energized (PbCr04) * particles
(1)
The activated chromate ions thus formed react with lead ions to form an energized particle of PbCrO,. The assumption of
+ (Cr042-)
(Pb")
+ B + C * & 2C, A
+B
K6
K-5
C
particle growth
precipitation in dark
(74 (7b) (7c)
(7d) (7e) (70
(22) Ghosh, D. N. J . Indian Chem. SOC.1930, 1 , 509. (23) Matalon, R.;Packter, A. J. Colloid Sci. 1955, 10, 46. (24) Miiller, S. C.; Kai, S.; Ross, J. J . Phys. Chem. 1982,86, 4078. Kai, S.; Muller, S. C.; Ross, J. J . Phys. Chem. 1983, 87, 806.
750
Das et al.
The Journal of Physical Chemistry, Vol. 91, No. 3, 1987
TABLE II: Excess Entropy Production for All Reaction Steps in the Proposed Mechanism variation in reaction sign of excess reaction step rate 6 q affinity 634; entropy” 1 Bw, a I6[A] 634, 0: 6 In K,[A] 2 6w2 a IB[A] 6 3 4 2 a I 6 In l / [ A ] 3 6w, = 0 6A3 a I 6 In l / [ A ] zero 6A4 a I 6 In l / [ A ] 4 Sw4 a 6[A] 5 6w5 a -6[A] 6A5 a 6 In [A] -
+
if the equilibrium state is stable. The chemical flux is given by Ji = ai,the rate of chemical reaction, and the force Xi is given by = Air‘
xi
where Ai is the affinity of ith chemical reaction step. For calculating excess entropy production for the chemical reaction step in the proposed mechanism (7a-f) we consider first the steady-state treatment for the species A* and C,, respectively, which are given by d[A*I d[C*1 = 0 and -= 0 dt dt
“Sign of excess entropy production, 6ai = 6w, M i .
~
There are three species which may diffuse through gel A, B, and C, as C is completely insoluble (unenergized PbCr04). The diffusion flux Ji of ith species is given by
Ji = DiV2xi
(8)
where xi is concentration of ith species, Di its diffusion coefficient, and V2 its Laplacian operator. Including the fluxes of chemical reactions the rate of change of xi is given by 6Xi _ - ~ i ( ~ +i )DiV2xi
6t
d2xi dt2
uchem
+
udiff
(1 1)
cchem is entropy production due to chemical reaction and crdiff is due to diffusion. The excess entroy production in the neighborhood of equilibrium state should be positive for the stability of the system.Is According to this criterion, a steady state will be stable provided that CiSJiSX,> 0. The excess entropy production due to diffusion flux is always positive. The excess entropy production due to the fluxes of chemical reactions is given by the Glansdorff-Prigogine equationIs 6uchem
= CSJI
6x1 > O
+
Similarly for the equilibrium concentration of C,
+ K-4[A![BI + Ks[Al[Bl - K-s[C*l
= 0 (16)
taking appropriate approximation in the equilibrium state (7d) and (7e), the equilibrium concentration of C, is obtained as [C*leq = W [ B I + K”[Al[BIl assuming [A]
where a depends upon the diffusion coefficient and b and F depend upon the rate constants of different reaction steps. F is also a function of concentration. The solution of the differential eq 9 or 10 may be obtained by the method of normal-mode analysis as described by other worker^.^^.^^ The solutions show oscillation in x,. On the basis of the linear thermodynamics of irreversible proces~,~’ it may be shown that the entropy production due to chemical fluxes and that due to diffusion fluxes may be separated. The total entropy production u is given by =
KAAI [A*1q = K2[A] K3[B] 4 [ A * l [ B l - K4[Cil
+ b-dxi +F =0 dt
(12)
I
(25) Shyldkrot, H.; Ross, J. J . Chem. Phys. 1985, 82, 113. (26) Kastogi, R. P.; Gupta, M. C. Indian J . Chem. 1978, lbA, 272. (27) Peacocke, A. R. The Physical Chemistry of Biological Organization; Clarendon: Oxford, UK, 1983; Chapter 2.
(14)
where Z is the intensity of light; hence,
(9)
The concentration xi is a function of both space and time.25 The eq 9 becomes a second-order differential equation, which includes the velocity of propagating profile U-
The former gives KIZ[A] - K2[A] [A*] - K,[A*] [B] = 0
(17)
>> [B] and
The excess entropy production of the equilibrium state in the proposed mechanism are calculated by using relationship 6q
a
6wi6Ai
(19)
For all reaction steps, the values of 6wi and 6Ai are reported in Table 11. This shows that equilibrium state is very unstable under illumination ( I > 0). Therefore the dynamic equation shows the chemical instability of the system under illumination. In dark the excess entropy production is always positive (70. In presence of light the theory agrees with the experiment as the system readjusts itself to some other equilibrium state and there are chances of periodic precipitation. The dark reaction step proceeds with positive entropy production and is more stable. The instability of the illuminated system is therefore based on the assumption of formation of energized PbCr04 particles (step 4). This step for the illuminated system is unstable while that of dark system is stable.
Acknowledgment. This work was supported by the Department of Science and Technology, New Delhi. We are very grateful to the referee for valuable suggestions. Registry No. PbCrO,, 7758-97-6; K2Cr0,, 7789-00-6; Pb(NO,),,
10099-74-8.
