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Mechanism of Revert Spacing in a PbCrO4 Liesegang System Tony Karam, Houssam El-Rassy, and Rabih Sultan* Department of Chemistry, American University of Beirut, P.O. Box 11-0236, Riad El Solh 1107 2020, Beirut, Lebanon ABSTRACT: Periodic precipitation of sparingly soluble salts yields parallel Liesegang bands in 1D whose spacings obey either one of two known trends. The overwhelming trend is an increase in spacing as we move away from the junction, while some systems display a decrease in spacing as the bands get further away from the interface. The latter trend is much less common and is known as the revert spacing law. Whereas the direct (normal) spacing law is generally well-undertsood, the revert spacing trend has not been explicitly and distinctly elucidated. In this paper, we propose a mechanism of revert spacing governed by the adsorption of the diffusing CrO42 ions on the formed PbCrO4 Liesegang bands and carry out a set of experiments that support the suggested scenario. It is shown that this adsorption increases as the band number (n) increases in revert spacing systems, while it decreases as n increases in direct spacing systems. It is concluded that this correlation in opposite directions decisively reveals the role of adsorption in the mechanism. The attraction between the CrO42 and Pb2þ in the gel causes the bands to form gradually closer and closer. Secondary structure (thinner bands formed within the main ones) obtained under some conditions is discussed in view of the light sensitivity of the chromate ion and the stability of the lead chromate sol.
1. INTRODUCTION Periodic precipitation displays a wide scenery of beautiful band and ring patterns, similar to naturally occurring strata, most notably the process of geochemical self-organization. In this socalled Liesegang phenomenon, named after the famous experiment of Raphael E. Liesegang,1 an outer electrolyte diffuses through a gel medium containing an inner electrolyte, forming distinctly spaced precipitate bands. Although the majority of the Liesegang-type experiments involve the interdiffusion of coprecipitate ions in a gel matrix, some bands can be formed in nongelatinous aqueous media.2,3 Two opposing spacing laws have generally been reported: the overwhelming case or the direct law in which the spacing between consecutive bands increases with distance from the interface,4 and the much less frequent case known as revert spacing wherein the spacing between consecutive bands decreases with distance from the interface.5 Several systems with the latter spacing law were reported such as HgS,6 CuS,7 Ag2CrO4,8 AgI,9 and PbCrO4 (in 1D10 and 2D11). A few theories treating the revert spacing law exist in the literature, mostly based on ionic adsorption phenomena. In 1957, Mathur et al.8 attributed the formation of the revert pattern to the high peptizability of the precipitating salt in the gel medium. Das et al.10,11 proved that the formation of lead chromate (PbCrO4) bands showing revert spacing is highly induced by light. They argued11 that when the system is exposed to light, the photochemical processes change the composition of the system by driving the latter from an equilibrium, zero radiation state, to an out-of-equilibrium state. In a later study,12 Das et al. proposed a light-induced mechanism involving the activation of chromate ions, yielding energized PbCrO4, which has a higher degree of ionization, and hence an enhancement in r 2011 American Chemical Society
the ionic conductivity of the solution. The selective light absorption by one of the species is followed by the nucleation of colloidal particles and an autocatalytic colloidal growth step. Dynamic entropy production calculations reveal the instability of a homogeneous steady state under illumination. It is to be noted that this study, though very enlightening about the mechanism of periodic precipitation of PbCrO4, does not address the revert spacing situation. The work of Isemura13,14 displays a pattern of PbCrO4 in silica gel, showing clear revert spacing followed by a switch to a direct spacing pattern. The study however does not discuss revert spacing. In the presence of light, it was established that pH effects influence the width of the diffused PbCrO4 portion.11,15 Antal et al.16 noted that the behavior of the guiding field velocity decides on the type of pattern obtained. They demonstrated that the distance between successive bands can be controlled by changing the dynamics spinodal of a nonautonomous Cahn Hilliard equation.17 Kanniah et al.18 proposed a new spacing law for the revert and direct rings, based on the theory of preferential adsorption of the diffusing electrolyte on the formed band, inducing the decrease in spacing between two consecutive bands. The adsorption is maximum (in the case of revert spacing) at the first band and decreases as we go downward. A transition from revert to direct spacing is observed, corresponding to the switch in the charge on the band surface,18 across a zero-adsorption isoelectric point. The aforementioned theories suffer from the absence of experimental evidence and thus do not decisively Received: January 20, 2011 Revised: March 2, 2011 Published: March 23, 2011 2994
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Table 1. Conditions for the Experimental Sets I, II, and III: Varying Gel Concentration, Concentration of Inner Electrolyte [Pb2þ]0 and Concentration of Outer Electrolyte [CrO24 ]0, Respectively set I: varying gel 2þ
run [agar] %w/w [Pb
]0 (M)
set II: varying inner electrolyte [CrO24 ]0
2þ
(M) run [agar] %w/w [Pb
]0 (M)
[CrO24 ]0
set III: varying outer electrolyte (M)
run
[agar] %w/w [Pb2þ ]0 (M) [CrO24 ]0 (M)
IA
0.50
0.0010
0.020
IIA
1.0
0.0010
0.020
IIIA
1.0
0.0010
0.015
IB
0.75
0.0010
0.020
IIB
1.0
0.0015
0.020
IIIB
1.0
0.0010
0.020
IC
1.0
0.0010
0.020
IIC
1.0
0.0020
0.020
IIIC
1.0
0.0010
0.030
Figure 1. (a) Three tubes of PbCrO4 Liesegang patterns with three 2þ different agar gel concentrations. [CrO2 4 ]0 = 0.020 M; [Pb ]0 = 0.0010 M. Left to right: [agar] = 1.0% w/w, 0.75% w/w, and 0.50% w/w, respectively. (b) Average band location (L) versus band number n for each of the three tubes, with [agar] indicated in the legend.
Figure 2. (a) Three tubes of PbCrO4 Liesegang patterns with three different Pb2þ concentrations. [CrO2 4 ]0 = 0.020 M; [agar] = 1.0% w/w. Left to right: [Pb2þ]0 = 0.0020 M, 0.0015 M, and 0.0010 M, respectively. (b) Average band location (L) versus band number n for each of the three tubes, with [Pb2þ]0 indicated in the legend.
unravel the mechanism of revert spacing. In this paper, we carry out a full experimental investigation of the revert spacing scenario, in a PbCrO4 Liesegang system. To our knowledge, no such systematic study has ever been reported. We study here the adsorption of the diffusing CrO2 4 ions on PbCrO4 precipitate bands, and its role in promoting revert spacing. It is demonstrated that ion adsorption could be a precursor to the revert spacing mechanism. Finally, we report a new type of secondary banding that was very scarcely described in the literature.19
characterization of band spacing in Liesegang systems.2022 The experimental conditions are summarized in Table 1. In each experiment, the interband spacing and bandwidth were measured using a vernier caliper (Scienceware) with a precision of (0.05 mm. Note that in the direct (normal) spacing case, the general known trend is the increase in spacing with increase in the gel concentration and that of the inner electrolyte concentration, and a decrease in spacing upon increase of the outer electrolyte concentration.20 2.2.1. Varying the Agar Concentration. Figure 1a displays tubes IAC (wherein the agar concentration is varied as we go from one tube to the next). Figure 1b shows a corresponding plot of band spacing plus half the width (L = (Δxn þ wn)/2) versus band number n for the three tubes. All three curves show a decreasing trend that is typical for a system showing revert spacing. The higher gel concentration curves lie above the lower concentration ones. These results are in complete agreement with the findings already mentioned.20 The increase in the concentration of the gel causes the band to precipitate further away from the preceding one because of the lower diffusion rate but preserving an overall revert spacing situation within the same tube. 2.2.2. Varying the Inner Electrolyte Concentration (Pb2þ). Set II, consisting of three tubes IIAC, focused on varying the concentration of the inner electrolyte, while keeping the concentration of the gel and the outer electrolyte constant. Figure 2 shows the three tubes of set II (frame a), along with a plot of the band spacing plus half the width (L) defined above, versus band number n (frame b). The higher inner concentration curves lie above the lower concentration ones. As reported previously in the literature,4,20,21 an increase in the inner electrolyte concentration obstructs the ion product from exceeding supersaturation,
2. REVERT SPACING IN PbCrO4 SYSTEMS 2.1. Experimental Section. A sample of lead nitrate, Pb(NO3)2 (weighed to the nearest 0.1 mg), was dissolved in 50.00 mL of double distilled water with the desired amount of agar powder. The mixture was heated to 90 °C under constant stirring until a homogeneous solution was obtained. The resulting solution was then poured into a set of 1D Pyrex tubes of 5 mm diamater, filling each to two-thirds. The solution was left to gel for 4 h at room temperature. Then a solution of the outer electrolyte (K2CrO4) was gently poured on top of the lead chromatedoped gel. The tubes were then covered with parafilm and left in an air thermostat at 20.0 ( 0.1 °C. 2.2. Controlling the Interband Spacing. We first carry out a phenomenological study and a characterization of the revert spacing trends. Three sets of experiments were performed, each time varying one typical experimental parameter: the gel concentration, the inner electrolyte concentration, and the outer electrolyte concentration. In each tube, we measured the band spacing Δxn and width wn of each band, n being the band number. The varied parameters and their effect are typical indicators in the
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Figure 3. (a) Three tubes of PbCrO4 Liesegang patterns with three 2þ different CrO2 4 concentrations. [Pb ]0 = 0.0010 M; [agar] = 1.0% 2 w/w. Left to right: [CrO4 ]0 = 0.015 M, 0.020 M, and 0.030 M, respectively. (b) Average band location (L) versus band number n for each of the three tubes, with [CrO2 4 ]0 indicated in the legend.
which will result in the formation of the precipitate band at relatively longer distance than at a lower inner concentration. However, within the same tube, i.e., at fixed chosen concentrations, the overall trend remains a decrease in spacing, the unusual revert spacing law in this PbCrO4 system. 2.2.3. Varying the Outer Electrolyte Concentration (CrO2 4 ). A set of three tubes IIIAC was prepared, as shown in Table 1, keeping the concentration of the gel and the inner electrolyte constant while varying the concentration of the outer electrolyte. Figure 3 depicts the three tubes of the set (Figure 3a), together with a plot of the quantity L versus band number n (Figure 3b). Here again the revert spacing trend is decisive. Note that here, however, the higher outer concentration curves lie underneath the lower ones. Thus, an increase in the outer electrolyte concentration induces the next band to form closer than at the lower concentration, obviously due to a higher rate of diffusion.20 Nevertheless, the overall trend remains a revert spacing situation, implying the interplay of another factor, characteristic of the PbCrO4 system.
3. MECHANISM Many interpretations of revert spacing in the literature involve a mechanism based on the preferential ionic adsorption theory, wherein the diffusing analyte (CrO2 4 ) gets adsorbed on the surface of the formed band (PbCrO4) in the gel medium (agar) containing the inner electrolyte (Pb(NO3)2). In the present PbCrO4 system, we expect that the negatively charged chromate ions adsorbed on the surface of the lead chromate band will attract the positively charged lead ions in the gel. This Coulombic attraction will allow the ion product to exceed supersaturation at a distance closer to the band than usual, which will decrease the spacing between the two precipitate bands. Thus, if the amount of adsorbed chromate ions on successive bands increases with distance from the junction, we anticipate that the bands form closer and closer to their preceding ones. Under such conditions, the band spacing decreases with distance (revert spacing law) instead of increasing (direct spacing law). In this section, we perform experiments in support of the adsorption mechanism, responsible for revert spacing. Measurements of CrO2 4 adsorption on consecutive PbCrO4 bands were performed on a typical revert pattern. Then the same type of measurements were done on a CuCrO4 Liesegang pattern,
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Figure 4. (a) PbCrO4 tube used in the adsorption analysis. [Pb2þ]0 = 0.0010 M; [CrO2 4 ]0 = 0.015 M; [agar] = 1.0%. (b) Plot of the relative fraction of adsorbed CrO2 4 on PbCrO4 bands per unit volume (f) versus band number n. The adsorption increases as n increases.
displaying the normal direct spacing. The main difference thus lies in the nature of the cations (Pb2þ and Cu2þ) and thus the respective idendities of the precipitates. It is important to note that the ion whose adsorption is tested is the same (CrO2 4 ). 3.1. Experimental Section. A PbCrO4 tube was prepared, as described in section 2.1, with the following concentrations: 1.0% agar, [Pb(NO3)2]0 = 0.0010 M, [K2CrO4]0 = 0.015 M. The tube was cut at the bottom, and the gel and its contents were allowed to slide out and placed on a clean glass plate. Each band (numbered n) was cut into two halves: the upper part labeled nu and the lower part nd (u for up and d for down) as well as the gel spacing between bands n and n þ 1, called gn. Each fragment was immersed in 5.00 mL of double distilled water and left for 12 h at 20.0 °C, making sure that all the chromate ions adsorbed on the surface have desorbed and diffused into the aqueous solution. The amount of chromate ions desorbed was measured by means of a UVvis spectrophotometer at λ = 375 nm. The relative fraction f of chromate ions adsorbed (i.e., per unit volume) is calculated by the formula: f ¼
And þ Aðn þ 1Þu ½And þ Aðn þ 1Þu þ Gn Vn
ð1Þ
where Vn is the volume of gel portion between bands n and n þ 1 in mm3, And is the absorbance of the chromate ions desorbed in the bathing solution from the lower part of the nth band (nd), and A(nþ1)u is the absorbance of the chromate ions desorbed in the solution from the upper part of the (n þ 1)st band ((n þ 1)u). Gn is the absorbance of the gel portion (gn) between the two. Exactly the same procedure was followed for the tube prepared with the CuCrO4 precipitate, showing direct spacing. 3.2. Results. Figure 4b highlights a plot of the fraction of (f) versus band number n, for the typical adsorbed CrO2 4 PbCrO4 pattern shown in Figure 4a. We clearly see that f increases with increasing band number n, which means that as we go down the tube within the revert PbCrO4 pattern, the relative amount of diffusing CrO2 4 ions adsorbed on band n is increasing. Because the cations in the gel medium (Pb2þ) are effectively attracted by the adsorbed counteranions, the new band forms closer to the previous one than normal. For the next gel portion, the diffusion of CrO2 4 is diminished, but the relative amount of adsorbed CrO2 4 is more, probably because of a larger number of free adsorption sites (away from saturation) for much lesser adsorbate. In order to compare this behavior with a situation where direct spacing is encountered, we study the absorption trend in a system involving the same diffusing anions 2996
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Figure 5. (a) CuCrO4 tube used in the adsorption analysis. [Cu2þ]0 = 0.010 M; [CrO2 4 ]0 = 0.20 M; [agar] = 1.0%. (b) Plot of the relative fraction of adsorbed CrO2 4 on CuCrO4 bands per unit volume (h) versus band number n. The adsorption decreases as n increases. The high band numbers were selected for analysis because of the better resolution of the bands compared with the upper ones. 2þ (CrO2 4 ), but different inner cations (Cu ), yielding a Liesegang pattern of CuCrO4 bands with a normal spacing law. A CuCrO4 tube (Figure 5a) was prepared as described in section 2.1 with the following initial concentrations: 1.0% Agar, [CuSO4]0 = 0.010 M, [K2CrO4]0 = 0.20 M. Note that the concentrations here are 1 order of magnitude higher than those used for the PbCrO4 case, a requirement for the formation of more distinct bands. Every band n along with the interband spacing beneath it, gn, were cut and analyzed. Each fragment was immersed in 10.00 mL of double distilled water and left for 12 h at 20.0 °C. The following day, the absorbance of chromate ions desorbed in the solution was measured spectrophotometrically at λ = 375 nm. The fraction (h) of chromate ions adsorbed per unit volume was calculated using the formula:
Figure 6. Secondary structure in PbCrO4 Liesegang patterns, manifested as thin bands within the thick (primary) ones. [agar] = 1.0% w/w; 2 [Pb2þ]0 = 0.0010 M. (a) [CrO2 4 ]0 = 0.050 M; (b) [CrO4 ]0 = 0.070 M. (c) Plot of ln (width) versus ln (n) showing linearity in conformity with the power law for width. The measured widths correspond to the black bars shown in frame a.
ð2Þ
We note that the current mechanism differs from that proposed by Kanniah et al.,18 wherein the effects of adsorption and revert spacing are anticorrelated. They advanced a theory postulating that the amount of adsorbed ions decreases with band number because of the gradual decrease of [CrO2 4 ] by virtue of diffusion, and the point of transition from revert to direct spacing in their AgI system9 is marked by a point of zero adsorption. However, no adsorption measurement was performed in their study. Furthermore, the present study demonstrates that it is the relative adsorption that governs the dynamics of revert spacing.
where Bn is the absorbance of the desorbed chromate ions from the nth band, Gn is the absorbance of chromate in the gel portion gn (between bands n and n þ 1), and Vn is the volume of gel portion between bands n and n þ 1 in mm3. Note that eq 2 differs from eq 1 in that no upper/lower parts are included, because of the difficulty in slicing the very thin CuCrO4 bands (compare Figure 5a with Figure 4a). Furthermore, it is interesting to realize that the quantity Bn/(Bn þ Gn) does not exhibit any discernible trend with band number n, and hence the quantity h in eq 2 becomes strictly linear, only after dividing by the volume Vn. Thus h clearly indicates the relative amount of adsorbed CrO2 4 . The results are plotted in Figure 5b. Remarkably, the adsorption trend in the direct spacing case (CuCrO4) exactly opposes the one obtained for revert spacing (PbCrO4). This is a clear indication of the role of adsorption of CrO2 4 on the PbCrO4 precipitiate in steering the system dynamics toward a revert spacing pattern. To further confirm our demonstrated mechanism, we perform a special set of experiments, in which the roles of the electrolytes are reversed, i.e., Pb2þ up, and CrO2 4 down, in the gel. As expected, the experiments yielded Liesegang patterns with direct (normal) spacing and not revert spacing. The obtained patterns essentially displayed smaller spacings but which distinctly increase as we go down the tube. This last observation gives decisive evidence in favor of our mechanism, wherein the adsorbed CrO2 4 ions from the diffusing solution attract the Pb2þ ions in the gel.
4. SECONDARY STRUCTURE Many authors have reported the formation of microrings or fine secondary structure within main precipitate bands of silver chromate in gelatin.23,24 In what seems to be opposite to the normal trend observation25 (i.e., secondary banding via Ostwald ripening26), Holba27 showed that these rings precede the formation of the primary pattern in the Ag2CrO4 system, and the latter emerges from the intensification and strengthening of the secondary rings. This observation was also reported by Ramaiah,28 for the same precipitate system. Each aggregate in the primary pattern, can be considered as a self-similar pattern of parallel, equidistant rings. The final primary pattern is the result of coarsening and strengthening of the secondary rings following the Ostwald ripening theory.26,29 Parallel sheets of CuO colloidal precipitate forming a secondary structure were observed by Hantz.30 In our experiments, we observe secondary structure, when the concentration of CrO2 4 is increased above 0.050 M. Figure 6 shows PbCrO4 patterns with [Pb2þ]0 = 0.0010 M, and with [CrO2 4 ]0 = 0.050 and 0.070 M (frames a and b, respectively). The displayed pattern (Figure 6a and 6b) formed over a continuous period of four days, thus spanning a sequence of day/night cycles. We see that a primary pattern displaying revert spacing (note width of the broad bands represented by black bars) also exhibits
h¼
Bn ½Bn þ Gn Vn
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Figure 7. Secondary structure in the patterns of Figure 6 viewed under a 2 fluorescence microscope. (a) [CrO2 4 ]0 = 0.050 M; (b) [CrO4 ]0 = 0.070 M. A 1.00 cm scale is displayed. The thin secondary bands are essentially equidistant.
secondary structure, embedded in the thin parallel bands constituting a broad precipitate zone. The bandwidth and the band spacing exhibit revert spacing laws. Because here the width is distinctly visible in size (more than the spacing), we plot ln w (where w denotes the width) versus the band number n. The resulting plot is shown in Figure 6c. The linearity of the plot is evident, thus satisfying the “inverse” power law, in conformity with revert spacing. The length scale for the formation of the thin bands (secondary structure), viewed under a fluorescence microscope, is highlighted in Figure 7. It is interesting to see that the thin bands (black) are almost equidistant. Their thickness is of the order of 1 mm and the spacing around 0.3 mm for the 0.050 M case (frame a). Kant19 observed that the broad bands form in the presence of light, whereas the finer bands are obtained in the dark. He attributed that difference to the fact that lead chromate forms a more stable sol in light, as compared to that in the dark. We attempt to explain our observations through a combination of both Kant’s observations19 and Das’s theory.12 CrO2 4 being the light sensitive species appears to become significantly photochemically active above a critical concentration (here 0.050 M, over a spanned range of 0.010 to 0.090 M). The energized PbCrO*4 increases the solubility of the precipitate and hence promotes the formation of primary bands according to the mechanism proposed by Das et al.12 In the dark, the precipitate sol is destabilized, and breaks causing the formation of the thinner bands. It seems that the latter phenomenon is strictly a sol destabilization phenomenon, not coupled to diffusion, as clearly revealed by the nearly equal spacing between the secondary bands (Figures 6 and 7).
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(3) Ghosh, D. N. J. Indian Chem. Soc. 1930, 7, 509. (4) Jablczynski, C. K. Bull. Soc. Chim. Fr. 1923, 33, 1592. (5) Stern, K. Chem. Rev. 1954, 54, 81. (6) Mehta, B.; Kant, K. Kolloid Z. Z. Polym. 1965, Band 209, Heft 1, 58. (7) Mehta B; Kant, K. Kolloid Z. Z. Polym. 1964, Band 209, Heft 1, 54. (8) Mathur, P. B.; Ghosh, S. Kolloid Z. Z. Polym. 1957, Band 159, Heft 2, 143. (9) Kanniah, N. F. D.; Gnanam, F. D.; Ramasamy, P.; Laddha, G. S. J. Colloid Interface Sci. 1981, 80, 369. (10) Das., I.; Pushkarna, A. J. Non-Equil. Thermodyn. 1988, 13, 209. (11) Das, I.; Pushkarna, A.; Lall, R. S. J. Cryst. Growth 1987, 82, 361. (12) Das, I.; Lall, R. S.; Pushkarna, A. J. Phys. Chem. 1987, 91 (3), 747. (13) Isemura, T. Bull. Chem. Soc. Jpn. 1933, 8, 11. (14) Isemura, T. Bull. Chem. Soc. Jpn. 1933, 8, 108. (15) Das, I.; Pushkarna, A.; Lall, R. S. J. Cryst. Growth 1987, 84, 231. (16) Antal, T.; Bena, I.; Droz, M.; Martenz, K.; Racz, Z. Phys. Rev. E 2007, 76, 046203. (17) Cahn, J.; Hilliard, E. J. Chem. Phys. 1958, 28, 258. (18) Kanniah, N.; Gnanam, F. D.; Ramasamy, P. Proc. Indian Acad. Sci. (Chem. Sci.) 1984, 93, 801. (19) Kant, K. Kolloid Z. Z. Polym. 1963, Band 191, Heft 2, 145. (20) Shreif, Z.; Mandalian, L.; Abi-Haydar, A.; Sultan, R. Phys. Chem. Chem. Phys. 2004, 6, 3461. (21) Sultan, R.; Sadek, S. J. Phys. Chem. 1996, 100, 16912. (22) M€uller, S.; Kai, S.; Ross, J. J. Phys. Chem. 1982, 86, 4078. (23) Hedges, E. S.; Henley, R. V. J. Chem. Soc. 1928, 129, 2714. (24) Dounin, M. S.; Shemyakin, F. M. Kolloid-Z. 1928, 48, 167. (25) Feeney, R.; Ortoleva, P.; Strickholm, P.; Schmidt, S.; Chadam, J. J. Chem. Phys. 1983, 78, 1293. (26) Ostwald, Wi. Z. Phys. Chem. 1900, 34, 495. (27) Holba, V. Colloid Polym. Sci. 1989, 267, 456–459. (28) Ramaiah, K. S. Proc. Indian Acad. Sci. A 1939, 9, 467. (29) Ratke, L.; Vorhees, P. W. Growth and Coarsening, Ostwald Ripening in Material Processing; Springer: Berlin, 2002. (30) Hantz, P. Phys. Chem. Chem. Phys. 2002, 4, 1–6.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported by a grant from the Lebanese National Council for Scientific Research (LNCSR). The authors thank Dr. Mazen Al-Ghoul for useful discussions. All the UVvis spectrophotometry measurements and the fluorescence microscopy pictures were taken in the Central Reseacrh Science Lab (CRSL), American University of Beirut. ’ REFERENCES (1) Liesegang, R. E. Naturwiss. Wochenschr. 1896, 11, 353–362. (2) Flicker, M.; Ross, J. J. Chem. Phys. 1974, 60, 3458. 2998
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