J. Phys. Chem. 1982, 86, 4078-4087
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Perlodic Preclpltatlon Patterns In the Presence of Concentration Gradients. 1. Dependence on Ion Product and Concentratlon Difference Stefan C. Muller, Sholchl Kal,t and John Ross' Depertment of Chembby, Stanford Unlverstiy, Stanford. California 94305 (Recelved: January 5, 1982; I n Final Form: June 7, 1982)
A study of Liesegang band formation is presented with emphasis on the dependence of the precipitation patterns on the initial concentrations of reactants. We have chosen Pb(N03)2and KI as the interdiffusing electrolytes for periodic precipitation of Pb12 in an agar-agar gel. Four series of experiments are reported in which we investigate the influence of the electrolytes on the number N , the location x,, and the width Awn of bands. The experiments were planned for comparison with structure formation in the absence of gradients and for guidance in a theoretical analysis. (I) Experiments in test tubes placed in the vertical direction in which we varied the concentration of one electrolyte demonstrated that the initial concentrationdifference, A = 1/2[1-] - [Pb2+],and the initial ion product, u = [Pb2+][I-I2, are useful parameters to characterize the variability of the patterns with concentrations,especially when either A or u is small (corresponding to small N). A simple spacing law is obeyed only when u and A are large ( N large). In vertical tubes, however, gravity influences pattern formation. We excluded this influence from the remaining experiments by simply letting the patterns develop in tubes held in a horizontal position. (11)When u is varied while A remains fixed, the bands broaden as u decreases. Below a minimum value, u*, no band formation takes place. (111) When A is varied at constant u, the location of bands varies with A in a complex manner. When A is low, only one band forms; its distance from the origin increases as A approaches zero. For low values of A and u, zones of colloid of finite width evolve before one or two sharp bands of precipitate appear within such zones in agreement with our prior work. (IV) When we vary the diameter of the tube, 4, beyond 1 cm, we observe that the bands become broader and more diffuse and the spacing coefficients p , = x,+l/x, decrease.
I. Introduction and Summary When concentrated potassium iodide (about 0.5 M) is placed in contact with lead nitrate at substantially lower concentration (of the order of 0.05 M), the iodide ions being present in excess diffuse into the lead solution where they react to form the weakly soluble salt, lead iodide. Subsequently, Pb12 precipitates discontinuously in space, in that well-separated narrow bands of precipitate appear sequentially in a period of hours to several days, parallel to the front surface of the diffusing reagent. Such a periodic precipitation, first observed in 1896l and since then investigated by many authors,24 is commonly called the Liesegang phenomenon. The patterns consist of a set of concentric rings when diffusion occurs from the center of a flat, circular container such as a Petri dish. When the two reactants are placed in a test tube, the direction of diffusion is confined to essentially one spatial coordinate; and a "one-dimensional" set of numerous parallel bands of precipitate results (see Figure 1, A and BLS Many electrolyte combinations lead, on interdiffusion, to similar rhythmic deposition of a precipitate.2i6 Normally the spacing between adjacent rings increases with increasing distance from the origin of the imposed gradient, but there is experimental evidence for the opposite (revert spacing).'^^ In most experiments, a gel-forming material (such as agar-agar or gelatin) is added to the solutions which effectively prevents convection and sedimentation of the solid phase. The gel may influence some structural details of the patterns but is not essential for structure formation.83 More complex structural features have been noted; these include secondary structures (the separation of one band into several closely adjacent thinner bands),1° segmentation of concentric rings into radially aligned convex sections," spirals instead of concentric rings,12and Preaent address: Department of Electronics, Kyuahu University, Fukuoka, Japan. 0022-3654/02/2O86-4O78$0 1.2510
helicoidal precipitation bands instead of sets of parallel bands.'+" Macroscopic structure also arises from electrolytic solutions in the absence of concentration gradients. For instance,if an initially homogeneous solution of lead iodide is supercooled sufficiently to induce uniform nucleation of colloidal lead iodide, precipitation occurs in irregular patterns reminiscent of Liesegang structures, but more randomly a r r a ~ ~ g e d . ~ ? ' ~ Most theories of Liesegang bands3 have been based on Ostwald's supersaturation hypothesis which postulates that nucleation is discontinuous and that the spatial pattern of nucleation determines the ring l~cations.'~J~ In a recent investigation of temporal and spatial sequences of events in Liesegang systems, we presented experimental evidence that structure formation is a postnucleation phenomenon and that repetitive ring formation comes about by spatially continuous nucleation and colloid formation followed by a focusing mechanism which partially depletes the regions (1) R. E. Lieaegang, Naturwiss. Wochenschr., 11, 353 (1896). (2) E. S. Hedges, 'Liesegang Rings and Other Periodic Structures", Chapman and Hall, London, 1932, and references therein. (3) K. H. Starn, Chem. Rev., 54, 79 (1964). (4) K. H. Stern, "A Bibliography of Lieaegang Rings", 2nd ed., U.S. Government Printing Office, Washington, DC, 1967. (5) In the following the bands of precipitate are oftan called rings. (6) A. C. Chatterji and N. R. Dhar, Kolloid-Z., 40, 97 (1926); F. E. Lloyd and V. Moravek, J. Phys. Chem., 35,1512 (1931); T. Iaemura, Bull. Chem. SOC.Jpn., 14, 179 (1939). (7) E. S. Hedges and R. V. Henley, J. Chem. Soc., 2714 (1928). (8) . . M. Flicker and J. Row.J. Chem. Phvs.. 60. 3458 (1974). . . (9) H. W. Morae, J. Phys. Chem., 34, 16j4'(1930). (10) K. S. Ramaiah, Roc.-Zndian Acad. Sci., Sect. A, 9,467 (1939). (11) S. C. Miller, S. Kai, and J. Ross, Science, 216, 635 (1982). (12) R. E. Lieaegang, 2.Phys. Chem., 88, 1 (1914). (13) D. Feinn, P. Ortoleva, W. Scalf, S. Schmidt, and M. Wolff, J. Chem. Phys., 69, 27 (1978). (14) W. Ostwald, "Lehrbuchder Aligemeinen Chemie",2nd ed., Engelman, Leipzig, 1891. (15) S. Prager, J. Chem. Phys., 25, 279 (1956); J. B. Keller and S. I. Rubinow, ibid., 74, 5000 (1981).
0 1982 American Chemical Society
Periodic Precipitation Patterns
neighboring a ring of colloidal material and gives rise to a sharply defined ring of visible precipitate.16 These experiments contradict Ostwald's hypothesis. The mechanism responsible for focusing has been suggested to be closely related to a chemical instability due to the competitive growth of the colloidal particles coupled with diffusion.13J7 That work was primarily concerned with structure formation in gradient-free systems, and the detailed connection with Liesegang-type precipitation patterns remains to be worked out. In this article, we describe some investigations of variations of Liesegang pattern formation with changes in the concentrations of the reactants. The literature on this subject is considerable; 2,3+5 however, in most previous studies, qualitative descriptions prevail. Few attempts have been made to analyze the patterns quantitatively. We especially wanted to explore in detail the behavior of patterns near critical initial concentrations below which no patterns appear in order to find suitable parameters to characterize the onset of pattern formation. We find that the initial difference between the concentration of the two soluble electrolytes, A, and the initial concentration product, u, are useful variables. Variations of A and Q to low values, where only few or no rings form, are important in order to determine the difference in pattern development between strong and low gradients; this may lead to a better understanding of the connection with gradient-free structures. Our experiments were performed with lead iodide in agar-agar gel because it usually forms sharply defined and clearly separated r i n g ~ , and ~ J ~some measurements of the spacing between rings, the number of rings, and the influence of the gel on the precipitation process have been reported for the case of relatively high concentrations and concentration difference^.'^^^^ Our preparation of Liesegang systems is described in section 1I.A. In section ILB, we specify the initial conditions of four groups of experiments with similar concentrations: (I) variation of one electrolyte concentration from fairly high (0.15 M) to very low values (0.003 M) while the other remains constant at values ranging from 0.03 to 0.12 M and vice versa; (11) variation of the initial concentration product u = [Pb2+][I-I2 at fixed initial concentration differences A = l/z[I-] - [Pb2+];(111)variation of A at fixed a;and (IV) variation of the container size at fixed concentrations. The tubes were kept in the vertical direction in group I and in the horizontal direction in the other groups. After a discussion of the pattern reproducibility in section II.C, we describe our visual observations and measurements of the dependence on the initial conditions of the total number of rings N in each tube, the ring locations x , (or their spacing Ax,, = x , - x ~ - ~ and ) , the ring widths Awn ( n = 1,
..., N).
A summary of the main correlationsamong the variables A, a, and the quantities N , Ax,,, Awn is given in section 1II.A. Preparations with large values of A or u yield patterns with many sharp, closely adjacent rings, while, for small A or u, we find small N and large Ax,, Awn. Examples of systems with large and small N and the temporal evolution of some of these systems are shown in section 1II.B. In a detailed description of these patterns we point to several structural details which are related to (16)s. Kai, s. C. Miiller, and J. Ross, J.Chem. Phys., 76,1392(1982). (17)R. Lovett, P. Ortoleva, and J. Ross, J. Chem. Phys., 69, 947 (1978);G.Venzl and J. Ross, ibid., submitted for publication. (18)E.Hatschek, Kolloid-Z., 10, 124 (1912). (19)S. C.Bradford, Biochem. J.,10, 169 (1916);K. Kant, Kolloid-Z., 189, 153 (1963);191, 143 (1963). (20)T. R. Bolam, Trans. Faraday SOC.,24,463(1928);26,133 (1930).
The Journal of Physical Chemistry, Vol. 86, No. 20, 1982 4079
the formation of broad but spatially well-defined zones of low-density colloid of lead iodide prior to the evolution of one or two much thinner bands of dense precipitate within these zones. The temporal sequence of formation of poorly structured colloid and, subsequently, highly structured precipitate is in good agreement with recent results on Liesegang patterns of magnesium hydroxide which establish that the essential step of pattern formation occurs in the postnucleation phase by a mechanism which focuses colloidal material into a narrow spatial region.I6 These findings are therefore also contrary to the Ostwald-Prager theory and tend to support an instability mechanism. Measurements of N and x, in group I of the experiments are described in section 1II.C and are summarized as follows: (1) N and xn depend significantly on both electrolyte concentrations, and this dependence is particularly pronounced when either A or u is small; (2) a simple ring spacing law is approximately obeyed only when N is large; and (3) the details of the patterns depend on whether the rings form in the lead or in the iodide solution and whether the direction of ring formation is parallel or antiparallel to the direction of the gravitational field. We conclude from these findings that for the discussion of the Liesegang phenomenon, in particular at low concentrations and concentration gradients, A and u are more useful variables than the individual electrolyte concentrations. The results of independent variations of u and A, as obtained in groups I1 and 111, are described in section 1II.D. By decreasing u at constant A, we observe a decrease in N and a pronounced increase in Awn until a lower limit u* is reached below which no spatial focusing of the colloidal material takes place. A decrease of A also results in a decrease in N , and only one broad ring appears when A is close to zero. These results need to be correlated with a theoretical analysis of an instability mechanism in the presence of concentration gradients. The value of A also influences the location of the first ring xl. We find the following: (1) as A approaches zero, xl increases substantially, but a distinct stochastic element is superposed on this increase; (2) as A is increased from small to slightly larger values, x1 varies in a complex manner. This subject and the randomness in the Liesegang patterns for low concentration gradients are treated in more detail in a following paper.21 Finally, in section III.E, evidence is presented that the details of the patterns and their temporal evolution have some dependence on the diameter of the tubes. In particular, the extent of focusing in the ring formation decreases as the tube diameter increases. 11. Experiments
A . Preparations. Banded precipitation of lead iodide in undialyzed agar-agar gel was obtained with lead nitrate and potassium iodide as the diffusing reagents. Gel solutions were prepared by adding l % agar-agar (Difco) to distilled water at 90 OC and thoroughly mixing each solution for 15 min until each was homogeneous. At the same temperature, varying amounts of Pb(NO& and KI were dissolved in the gel solutions in two separate beakEach electrolyte concentration ranged between 0.003 and 0.15 M. A predetermined volume (typically 1 mL) of one of the hot solutions was poured into cylindrical con(21) S. Kai, S. C. Miiller, and J. Ross, J. Phys. Chem., submitted for publication. (22)The agar-agar gels show a weak colorless turbidity which is slightly enhanced when Pb(NOJ2 is added (possibly due to lead sulfate as suggested in ref 20). This turbidity does not interfere with the visual observationsand measurementsof the PbIz precipitation patterns which, owing to the distinct yellow color of Pb12,can be easily distinguished from the turbid background.
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tainers of (inner) diameter 4 = 5.3 mm, usually glass pipets, and then allowed to cool at room temperature (22 "C) until a gel had formed. The Liesegang experiment was then started by filling the space above the solidified gel with 1 mL of the second electrolyte solution while its temperature (40 f 3 "C) was still slightly higher than the gelation temperature of the agar. About 3 min later, a gel had formed in the second solution; and after 15 min, the system had come to a common temperature of 22 "C, which subsequently was controlled within i0.5 "C. A t least three tubes were prepared simultaneously for each combination of KI and Pb(N03), concentrations in order to determine the reproducibility of the pattern formation (see section ILC). In several cases, to be specified below, containers of different (inner) diameter 4 were used. The tubes were sealed and left undisturbed until the formation of the precipitation pattern was completed, typically after several days for high differences and up to 1month for low differences in the concentrations of the two electrolytes. During this time some of the tubes were kept in vertical, others in horizontal, orientation. The same preparation procedure was applied for all Liesegang experiments without modifications, particularly in regard to temperature specifications and cooling rates, in order to exclude effects that may be caused by differences in the gelation history of the samples.23 B. Specification of Initial Conditions and Measurements. We conducted several series of Liesegang experiments with PbIz in which the initial concentrations of the electrolytes, [Pb(N03),] and [KI], were systematically varied. The following quantities are used to describe the initial conditions of the experiments: the initial difference between the ion concentrations in the two solutions, A = 1/2[1-]- [Pb2+];the initial concentration product of the ions (ion product) u = [Pb2+][I-]2;and the quotient S = u / u o , where uo denotes the solubility product of PbI,.in water (ao = 1.39 X lo-* M3 at 25 0C).24 We characterize Liesegang patterns in terms of the total number of bands (or rings) N , the location of the individual rings x,, the spacing between rings Ax, = x, - x,,-~, the spacing coefficients p , = X , + ~ / X , , and the width of the rings Awn, where n ranges from 1 to N in each tube. The extent of the zones of dense precipitate along the tube direction for each individual ring determines Awn, and x, is taken as the distance between the center of the space interval Awn and the initial electrolyte junction at x = xo = 0 (compare Figure 1in section 1II.B). Usually we restrict our investigations to the final ring patterns; however, observations of the early stages of the patterns and of the approximate times of ring appearance t, are included in several cases. The series of Liesegang experiments are subdivided into four groups, labeled I-IV. In group I, we investigate the dependence of the number of rings N , the ring locations x,, and the spacing coefficients p , on variations in concentration of one electrolyte, while the concentration of the second electrolyte is kept constant. This procedure is comparable to previous experimental studies; ,319 however, we have extended the investigations to low concentrations and concentration differences where the number of rings N approaches zero. To our knowledge such studies have not been reported before. We prepared four series of Liesegang experiments, labeled a-d, in 5.3-mm diameter tubes which were kept in the vertical direction during the (23) Changes in the cleaning procedure of the glass containers influenced the times of ring appearance within about 20%, but not the ring spacings and the ring widths. The same cleaning procedure was used for all experiments reported here. (24) The solubility product of Pb12 in 1% agar is assumed to be the same a~ in pure water.
Muller et al.
TABLE I: Concentration Ranges of Pb(NO,), and KI for Group I of the Experimentsa series upper portion of tube lower portion of tube ~~
~~~
a-1 a-2 b-1 b-2 c-1 c-2 d-1 d-2 a
0.12 M KI 0.003-0.06 M Pb(NO,), 0.06 M Pb(NO,), 0.006-0.12 M KI 0.06 M KI 0.003-0.06 M Pb(NO,), 0.03 M Pb(NO,), 0.006-0.12 M KI
0.003-0.06 M Pb(NO,), 0.12 M KI 0.006-0.12 M KI 0.06 M Pb(NO,), 0.003-0.06 M Pb(NO,), 0.06 M KI 0.006-0.12 M KI 0.03 M Pb(NO,),
All solutions contained 1%agar-agar gel.
pattem formation process. In each series the concentration of one electrolyte was varied in seven to nine steps. The concentration ranges and values of the fixed electrolyte concentration are listed in Table I. These concentrations correspond to a range of the concentration difference A from -0.06 to +0.06 M; for A = 0, Pb2+and I- ions are present in stoichiometric amounts to form PbI,. The ion product c ranges between 80u0 and (6 X 104)up Both A and u vary simultaneously. Each series was further subdivided into two parts. Identical solutions were used in both parts; but the solution that occupied the upper portion of the tubes in part 1 was placed in the lower portion of the tubes in part 2 and vice versa. Consequently, the direction of ring development in parts 1 and 2 were reversed with respect to the direction of the gravitational field. The number of rings N and the individual ring locations x, (n = 1, ...,N) in the final patterns were taken to be positive or negative depending on whether the rings appeared in the upper section (+) or in the lower section (-) of the tubes. From the results of the group I experiments,we conclude that A and u are important parameters for the characterization of Liesegang patterns and that the gravitational field influenced the patterns (section II1.C). We used these results to design several experiments in which we investigated changes in the precipitation patterns with respect to either u (group 11) or A (group 111) with particular emphasis on the behavior of the systems for decreasing values of both u and A. Group I1 consists of two series, labeled A-1 and A-2;group 111includes four series, labeled S-1, S-2, S-3, and S-4. Table I1 lists the values for A, u, and S ( = u / u o ) and the ranges for the electrolyte concentrations required to obtain these values. From 8 to 15 concentration combinations were investigated for each series; the tubes were always kept in the horizontal direction. The tube diameter was 5.3 mm for series S-1to S-4 and series A-1; for series A-2 tubes of diameter 5.3 and 12.4 mm were used. For the experiments of groups I1 and III the quantity A was always positive (2LI-I 2 [Pb2+J),and rings appeared only in the lead solution (compare section 1II.C). The number of rings N a n d the ring locations x,, which were always taken to be positive, as well as the ring widths Awn were measured as a function of A and u. In group IV, we examined the influence of the size of the container on the precipitation patterns. We performed Liesegang experiments with identical initial electrolyte solutions in cylindrical tubes with inner diameters 4 ranging from 4.0 to 22.4 mm and measured the ring locations x, and ring widths Awn as a function of 4. The electrolyte concentrations used in this study are specified in the figure captions in section 1II.E. C. Reproducibility of Precipitation Patterns. For each combination of initial concentrations, in each group, we prepared at least three identical tubes. The number of rings N is reproducible within fl for systems with N > 4;no variations in N occur for systems with N < 4. The
The Journal of Physical Chemistry, Vol. 86, No. 20, 1982 4081
Periodic Precipitation Patterns
TABLE 11: Dependence of the Number of Rings N, the Ring Spacing Ax,, and the Ring Width A w n on lAla and S b s = UIO, IAI = 0 lAl is low (m0.002 M) + IAI is high (>0.03 M ) low (=300), none of the N very small for all N very small (1-3), Ax, ion concentrations values of S (0-2) very large (order of 10 mm), 5 mM and after 15 days for the tube with A = 0. The solid horizontal line indicates the initial electrolyte junction.
10
s (~10~) Flgure 7. (A) Location of the first ring, x l , as a function of S = a/ao for A = 15 mM (series A-2) after 10 days in tubes of diameter 5.3 (curve I) and 12.4 (curve 11) mm. The measured points are connected by straight lines which intersect the horizontal axis at S = S *. (B) Spacing coefficient for the first two rings, p = x,/x as a function of S for A = 30 mM (0)and A = 15 mM (O), after 20 days. The tube diameter is 5.3 mm.
several millimeters from the initial junction into the lead solution. For t . ~< 0.28 X 10+ M3 (S < 200), essentially no precipitation or colloid could be detected visually. The second and third rings in this series were always broad and transparent (type 3 of section 1II.B) and sometimes not clearly separated from each other. A second ring is observed only for S 1 500 (see, for instance, Figure 2H, zone 7); its width exceeds 8 mm at S = 500 and decreases slightly with increasing S. In Figure 7A, we plot the location of the first ring, xl,vs. S for systems in tubes of diameter @ = 5.3 and 12.4 mm. The values of x1 decrease linearly with decreasing S, and extrapolation of both straight lines to low S values yields x1 = 0 for S = S* = 200. We take this value as a critical lower limit of the ion product t.~* = S*ao below which no spatial focusing of colloidal material takes place to form a ring. This is consistent with the result of section III.C, where no ring formation was observed for S I 150, at least for the constant value A = 15 mM chosen. The effects of the tube diameter are further discussed in section 1II.E. A plot of the first spacing coefficient p1vs. S for both series of group I11 is shown in Figure 7B. The values of p1for series A-1and A-2 can be represented approximately by the same curve. For large S, p1does not change significantly; however, we observe a steep increase p1for S < 103 which results in a divergence to infinitely high values at S = 500. (No second ring is observed for smaller S.) These observations indicate that, within a set of tubes with S decreasing down to S*, the first ring can be seen to approach the initial junction of the electrolytes, while the distance of the second ring gradually increases. This behavior of Liesegang patterns in a region of very low S was determined so far only for A = 15 mM.
A (mM) Flgure 9. Locations of the first ring x 1 as a function of the concentration differences A for group I11 of the experiments (see Table 11), 30 days after the start of the experiment. The ion products for series S I to S-4 are respectively 0.7 X 10" (O), 1.4 X IO" (O), 1.5 X (A)M3. (0),and 1.8 X
2. Variation of the Concentration Difference at Fixed Ion Product. The Liesegang patterns in group 111,where A was varied down to A = 0 at fixed u (or S),consisted of no more than three or four rings at the upper limit of A (=30mM), and usually only one ring appeared when A was close to zero. Compared to experiments with much larger numbers of rings, these experiments correspond to relatively low concentration gradients. The variation of ring locations and widths with A revealed many interesting and complex structural features. Of special interest are "spatial bifurcation", that is formation of two rings instead of one in a given region as A increased, and a pronounced stochastic element in the ring locations, as A approached zero. The details of these findings are the main issue of a separate publication.21 Here, we only describe the dependence of the location of the first ring, xl, on A. Except for A < 5 mM, this quantity can be reproduced deterministically (compare section 1I.C). In Figure 8 we show a set of tubes with 0 IA I10.5 mM from series S-3, and in Figure 9 we plot x1 vs. A for all series of group III. There is no smooth variation of x1 with 4 each curve has several minima and maxima. Common features of the four curves are as follows: (1) As A 0,
-
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The Journal of Physical Chemistry, Vol. 86, No. 20, 1982
A
A -
B 5r
II
I
4 -
B 0
E E
40
3-
W
3
Q
2 -
n
E E
W
1 -
C
20
0 0
10
20
30
@ (mm) 0
0
2
4
6
n Figure 10. Influence of the tube diameter 4 on the spacing and the width of Liesegang rings. (A) Tube I:6 = 5.3 mm; tube 11: 4 = 22.4 mm. The initiil electrolyte concentrations in both tubes were [KI] = 0.066 M and [Pb(NO,),] = 0.003M (A = 0.03 M, u = 1.31 X M3, S = 950). The photograph was taken 4 days after the start of the experiment. The s o l i horizontal line indicatesthe initial electrolyte junction. (B)Plots of the location of rings x, in tubes Iand I 1 vs. n, after 10 days.
x1 always increases (seealso Figure 8);the increase is more
substantial for high than for low initial values of Q. This tendency still holds when uncertainties in xl, due to higher randomness at low A, are accounted for by appropriate averaging. (2) With increasing A, all curves pass through a first minimum; it is located at approximately AZIn = 1.8, 3.0,4.4, and 6.5 mM for series S-1 to S-4, respectively. (3) A second minimum occurs around AEL = 8.5, 14.5, 15.0, and 19.0 mM for the same sequence of series. This minimum is closely related to the phenomenon of a spatial bifurcation.21 E. Changes in Liesegang Patterns with Variation of Container Size. In group IV,we determined the effect of the diameter 4 of the tubes on the Liesegang patterns. In large-diameter tubes, the final patterns tend to blur. Therefore, x, values were measured during early stages of the ring formation. Examples for the changes in the patterns with varying 4 are shown in Figures 10, 11, and 7A. The ring locations in the two tubes shown in Figure 10A are plotted as a function of n in part B of the figure. The different slopes of these plots indicate that the tube diameter influences the spacing between rings. The ring
Figure 11. (A) Early stage of pattern formation of PbI, (19h) in four tubes with 4 = 4.0,8.1,12.6,and 22.2 mm containing the same initial electrolyte solutions (top: [KI] = 0.059 M; bottom: [Pb(N03),] = 0.0043 M; A = 0.025M, Q = 1.48 X lo5 S = 1070). The arrows mark the extent of diffuse colloid formation; the solid horizontal line indicates the initial electrolyte junction. (B)Ring width Aw for rings at a distance x = 10 f 2 mm from the electrolyte junction as a function of the tube diameter 4 . The electrolyte concentrations were K I = 0.066 M, [Pb(NO,),] = 0.003M, A = 0.03 M, u = 1.3 X 10- M , S = 950. The bars indicate the uncertainties in the measurementsdue to the diffusiveness of the ring edges
w,
6 1
width is generally larger, and the edges of the rings are more diffuse in the wide tube (11)than in the narrow tube (I). However, over the commonly used diameter range, 5-10 mm, the variation of ring locations is small (less than 10%). In Figure 11A, we show four tubes with 4 ranging from 4 to 23 mm, with identical initial salt solutions, at an early stage of the experiment. No sharp rings can be detected, but we observe diffuse zones of colloid, the extent of which from the initial electrolyte junction is marked by arrows. The zone is widest in the largest tube. In the two narrowest tubes, two ring structures are barely visible on the photographs. Analogous rings developed at later times in the diffuse colloid regions of the two widest tubes. This shows that the temporal development of the patterns is influenced by the tube geometry. We also observed that the final widths for those rings that were located at a distance of about 10 mm from the initial electrolyte junction, which indicate the extent to which the precipitate is focused, also decrease significantly with increasing tube diameter. Within the interval 4 5 4 I23 mm, the spacing coefficientp n also decreases with increasing 4 such that, in most cases, an empirical relation
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pn-’ = (Axn+l)/(zn)Qc 6 7 with y ranging from 0.4 to 0.6 is approximately fulfilled. Acknowledgment. This work was supported in part by
the National Science Foundation and the Air Force Office of Scientific Research. A fellowship from the Deutsch Forschungsgemeinschaft for S.C.M. is gratefully acknowledged.
COMMENTS Contrlbutlon of Gemlnate Pairs to the CIDEP Durlng Photoreduction of Acetone wlth 2-Propanol
Sir: If transient 2-propyl-2-01 radicals in liquid solution are generated by photoreduction of acetone with 2propanol (reaction 1) and subsequently destroyed in bi-
4
(CH3)2C0+ (CH3)2CHOH-!!L 2(CH3)2COH (1)
-
2(CH3)2COH
k2
products
(1)F. J. Adrian, Rev. Chem. Intermed., 3,3 (1979). (2)P. J. Hore, C. G. Josh, and K. A. McLauchlan,Spec. Period. Rep.: Electron Spin Resonance, 6, 2 (1979). (3)J. H.Freed and J. B. Pedersen, Adu. Magn. Reson., 8,1 (1976). (4)H. Paul, Chem. Phys., 40,266 (1979);43,294 (1979). (5)G.P. Zientara and J. H. Freed, J. Phys. Chem., 83,3333 (1979). (6)S.K.Wong, T.-M. Chiu, and J. R. Bolton, J.Phvs. Chem., 85.12 (1981). 0022-3654/82/2086-4087$01.25/0
XJ LJ
E
(2)
molecular radical termination reactions (reaction 2) the populations of their electron spin Zeeman levels deviate from thermal equilibrium. This polarization of the spin system is caused by a radical pair mechanism (RPM).1-3 Reaction 1forms geminate pairs (G pairs) and the product formation (2) mainly proceeds via encounters of independently generated free-radical pairs (F pairs). Some time ago I analyzed the polarizations with a modulation EPR technique4 and found that the G pairs formed in a ITo)electronic spin state contribute the same amount of RPM polarization as do the F pairs forming a ITo)spin state at their first encounter. This result seems to agree with theory1” as long as anisotropies in the relevant interactions can be neglecteda6 Recently, Wong, Chiu, and Bolton6 reexamined the above system using timeresolved EPR spectrmcopy. They found the spin system to be strongly polarized for a few microseconds following a flash lamp pulse, and demonstrated this polarization to stem predominantly from the G pairs. The authors considered this finding to disagree with my previous data4 and stated without any reasoning: “The recent work by Paul on the same ketyl radical system... using modulated EPR spectroscopy also identified the role of G pairs but failed to observe its dominance. The approach of the modulated EPR is less direct and therefore less convincing than the time-resolved flash photolysis EPR”. In my opinion, this statement is wrong and probably due to some confusion with respect to the word “polarization”. Reference 4 gives polarizations p1and pF which are built up at the initiation stage (mainly due to G-pair RPM) and subsequently during F-pair encounters. p’ and p F are defined4as z magnetizations created per unit rate of radical initiation and radical decay, respectively, and are measured in units of the Boltzmann magnetization. They are
it
E
i
. Flgue 1. AmpHtudes of the M, = f 1 EPR ~esonancesof 2propyI-24 as functlon of time for initial radical concenlratbn 3.6 (a), 1.4 (b), and 0.3I.~M(c). E denotes emission and A absorption. Different scaling are used and indicated on the right.
time-independent quantities and characterize the ability of G and F pairs to develope CIDEP. The modulation experiment yields4 pF/pl = 3, i.e., in terms of these polarizations a dominance of the F-pair polarization. Wong et aL6 seem to use polarization for the EPR signal enhancement, i.e., the magnetization present at a certain time divided by the Boltzmann magnetization. This is a different, time-dependent quantity, which is determined not only by p1and pF but also by other parameters depending on the kind of e~periment.~*~J In a time-resolved EPR experiment the G- and F-pair polarizations contribute on different time scales to the signal enhan~ement.~*~,’ Without doubt, the enhancement observed by Wong within the first few microseconds after a flash lamp pulse is dominated by the G-pair polarization p’. However, this is so because F pairs have not yet formed within this short (7)J. B.Pedersen in ‘Chemically Induced Magnetic Polarization”,L. T. Muus, P. W. Atkins, K. A. McLauchlan, and J. B. Pedersen, Ed., D. Reidel, Dordrecht, 1977,pp 169 ff.
0 1982 American Chemical Society
