Chemical Tracking of Temperature by Concurrent Periodic Precipitation Pattern Formation in Polyacrylamide Gels

In nature, nonequilibrium systems reflect environmental changes, and these changes are often “recorded” in their solid body as they develop. Periodic precipitation patterns, aka Liesegang patterns (LPs), are visual sums of complex events in nonequilibrium reaction–diffusion processes. Here we aim to achieve an artificial system that “records” the temperature changes in the environment with the concurrent LP formation. We first illustrate the differences in 1-D LPs developing at different temperatures in terms of band spacings, which can demonstrate the time, ramp steepness, and extent of a temperature change. These results are discussed and augmented by a mathematical model. Using scanning electron microscopy, we show that the average size of the CuCrO4 precipitate also reflects the temperature changes. Finally, we show that these changes can also be “recorded” in the 2-D and 3-D LPs, which can have applications in long-term temperature tracking and complex soft material design.

S-2 Figure S1. The left side shows the dimensions of the spacer used for 1 D gels. The spacer was sandwiched between two Plexiglas pieces with the same dimensions, using screws. On the right, the gel samples in 1D gel samples without the addition of the outer electrolyte are shown.

Further discussions on the relationship between reaction coefficient (k p ), diffusion coefficient (k d ), and precipitation threshold (k sp ) and pushed and pulled fronts
The evolution of the patterns when subjected to a change in temperature can be understood using the triangular relationship between reaction coefficient (k p ), diffusion coefficient (k d ), and precipitation threshold (k sp ) and pushed and pulled fronts. Firstly, let's dissect a theoretical approach proposed by Antal et al. for such forced manipulation of an LP system. In their work, they suggested a diffusive guiding field, originating from one end could result in inverse and equidistant banding. Guiding field could be a temperature gradient such that the reaction front gets cooled down as it propagates through the system. As a result, the front propagates slowly as it moves along the temperature field and after certain point patterns form with decreasing distances between them (inverse banding). This is an example of coherent patterns forming behind a pulled reaction front. In our experimental conditions, a pulled reaction front occurs when temperature is lowered at a specific time ( Figure S9) and additionally, we also pull the reaction front at a specific rate as well ( Figures S10, S21, S22). Even though our system lacks a temperature gradient across the length of the gel, our results indicate manipulation of patterns and localized inverse banding. This is observed in terms of the decrease in the spacing coefficient ( Figure 2). Thus, pulling a front means lowering the diffusion coefficient of copper ions and thus, slowing down the flux of copper ions. At the same instant, the solubility product of copper(II) chromate decreases and the precipitation threshold is lowered, along with, the rate constant. With all three integral components of the equation lowered, LPs transition to a lower temperature regime. A halt in the supply of the copper ions from the source results in a wider depletion zone beyond the last pre-transition band formed. As the front moves slowly and lowered reaction rate, results in lower production of colloids, their dissolution, re-precipitation and aggregation. With the lowered precipitation threshold, it is expected to see a continuous precipitation beyond pre-transition patterns and before post-transition patterns; however, such a visual change is not observed. In this scenario, k p , and k d dominate k sp . Instead, a wide band appears as the first post-transition band. The width of this band indicates aggregation of a higher number of colloids to form a band. Additionally, this wider band requires higher time interval to form, and thus, lowers the slope of space-time plot ( Figure S10). This increased time interval refers to the relaxation time due to a pulled front. Figure S16. Histograms presenting particle size distributions (right) retracted from SEM micrographs (left) of band a) 1, and b) 5 formed at given temperature. The particle sizes increase with increasing temperature and also this increasing trend is observed moving from band 1 to 5.
The scale bar is 5 µm.

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Figure S17. Histograms presenting particle size distributions (right) retracted from SEM micrographs (left) of band a) 7, and b) 9 formed at given temperature. The particle sizes increase with increasing temperature and also this increasing trend is observed moving from band 7 to 9.
The scale bar is 5 µm. Figure S19. Histograms presenting particle size distributions retracted from SEM micrographs of bands 1 to 9 formed at 20 °C (bands: 1 -7) and 60 °C (bands: 8, 9). When the temperature was increased from 20 °C to 60 °C the particle sizes increased significantly. The scale bar is 5 µm.  Figure S20. Histograms presenting particle size distributions retracted from SEM micrographs of bands 1 to 9 formed at 60 °C (bands: 1 -6) and 20 °C (bands: 7 -9). When the temperature was decreased from 60 °C to 20 °C the particle sizes decreased significantly. The scale bar is 5 µm.

Temperature Ramping Rate Experiments
In case of ramping temperature down, the relaxation time is higher for a sudden temperature change (10 °C/min) compared to a gradual change in the system's temperature (0.1 °C/min). Thus, the slopes of cooling down LP system ( Figure S21) demonstrate such trend. Later on, the spacing between post-transition bands starts to increase, however, the increase is not comparable to pretransition patterns formed at higher temperatures. Thus, the system relaxes after the perturbation in the form of a pulled front and returns to its normal characteristics. Perturbing the system by heating up results in an increase in k p , k d and k sp and a pushed front ( Figure S22). In case of the pushed front, the flux of the copper ions from the source increases. The reaction rate constant indicates that all parts of the complex chain of events leading to periodic precipitation patterns i.e.
formations of colloids, their dissolution, re-precipitation as bigger colloids and aggregation into a periodic band structure occur at a higher rate ( Figure S22). Thus, bands start to occur immediately upon the rise in temperature. At this point the k p and k d dominate k sp , because if k sp had dominated an immediate zone would not be observed and wider depletion zone would have been observed.
The raised solubility product adds to the fact that wider depletion zones are observed posttransition patterns. With a pushed front, the system does not undergo a relaxation period and that is why the slopes of the space-time plots for post-transition patterns increase. Similarly, the rate at which temperature changes effects the extent of a pushed front and thus faster moving fronts (10 °C/min) will provide with steeper slopes ( Figure S22).