Solution and Solid-State Emission Toggling of a Photochromic Hydrazone

The proliferation of light-activated switches in recent years has enabled their use in a broad range of applications encompassing an array of research fields and disciplines. All current systems, however, have limitations (e.g., from complicated synthesis to incompatibility in biologically relevant media and lack of switching in the solid-state) that can stifle their real-life application. Here we report on a system that packs most, if not all, the desired, targeted and sought-after traits from photochromic compounds (bistability, switching in various media ranging from serum to solid-state, while exhibiting ON/OFF fluorescence emission switching, and two-photon assisted near-infrared light toggling) in an easily accessible structure

Photochromic Hydrazone Switches with Extremely Long Thermal Half-Lives

A family of easily accessible light-activated hydrazone switches has been developed having thermal half-lives of up to 2700 years! Structure–property analysis shows that replacing the rotor pyridyl group of our typical hydrazone switch with a phenyl one leads to the long-lived negative photochromic compounds. The switching properties of the hydrazones in both toluene and DMSO were assessed offering insights into the kinetics and thermodynamics of the switching process

Standardized PDF for the Vicsek model: (a) Standardized PDF in Eq (11) of the modified Vicsek model. Note that the subscript is changed from <i>τ</i> to <i>η</i>.

We set δ = 1.0 and the number of steps 10000. (b) Standardized PDF in Eq (11) of the modified Vicsek model. Note that the subscript is changed from τ to δ. We set η = 10.0 and the number of steps 10000.</p

Pairwise KL divergence between standardized partial correlation PDFs for 6 years of analysis: Dark blocks along the major diagonal (circumscribed in blue) indicate that when the invariance is visually observed (1000 ≤ <i>τ</i> ≤ 30000), the pairwise KL divergence is low.

Pairwise KL divergence between standardized partial correlation PDFs for 6 years of analysis: Dark blocks along the major diagonal (circumscribed in blue) indicate that when the invariance is visually observed (1000 ≤ τ ≤ 30000), the pairwise KL divergence is low.</p

Dependence of the scaling factor <i>b</i>(<i>τ</i>) on <i>τ</i>: (a) from 2004 to 2011; and (b) from 2012 to 2020.

From τ = 1000 min to 30000 min (the regime highlighted by light cyan), observe the near-linear relationship between lnτ and lnb. A similar visualization with Tint = 3 months is presented in the Fig 6 in S1 File.</p

Leptokurtic-to-platykurtic kurtoses transition in the correlation PDFs as the scaling (shaded cyan) takes effect: The higher values of kurtosis for smaller <i>τ</i> indicate sharper peaks in the correlation PDFs (compared to a normal distribution) (leptokurtic regime).

As τ increases, the correlation distribution becomes more flat resulting in lower kurtosis (platykurtic regime).</p

Qualitatively demonstrating the stability of the functional form for increasing <i>τ</i>: Standardized PDF in Eq (11) visualized for 6 years—1 year per row: (a) Left: <i>τ</i> = 1 min to 1000 min and (b) Right: <i>τ</i> = 1000 min to 30000 min.

As τ exceeds 1000 min, the shape of takes a more stable form. A similar analysis with Tint = 3 months is presented in the Fig 5 in S1 File.</p

Minimum Spanning Trees (MSTs) obtained from the modified Vicsek generative model with varying <i>η</i> values: We generated MSTs using the modified Vicsek generative model with different values of <i>η</i>: (a) <i>η</i> = 0.010, (b) <i>η</i> = 1.0, and (c) <i>η</i> = 100.0.

The number of steps was set to 10000, and δ was fixed at 0.10. For η = 100.0, the vine structure is apparent and we used these vines to define the analogs of sectors in stocks. In particular, we performed a community finding on MST [33] corresponding to the vine structure, and identified 11 communities corresponding to the number of GICS sectors. These communities indeed constitute individual vines, as shown by colored nodes in the right-most figure. Next we tracked the associated stocks as η decreased based on the fixed δ condition. Notably, as η decreases, the sectors collapse due to the fixed neighborhood of δ, which encourages more particles (stocks) to interact with one another. This increased interaction arises as the particles experience less perturbation from Ξ, leading to homogeneous behavior and radial MSTs.</p

Capturing the onset of function invariance by fitting 2-mode GMM onto the standardized partial correlation PDFs: Across 6 years of analysis, we plot the weights of the 2 GMM components after fitting to for different <i>τ</i>.

Mode 1 corresponds to the mode with the lower standard deviation. As τ is increases, the second mode starts contributing significantly to the fit signaling the onset (shaded cyan).</p

Model architecture search—Training and validation MSE: The MSE (CI = <i>σ</i> between folds) is reported as a measure-of-fit of every model for each year for {<i>τ</i>, <i>b</i>(<i>τ</i>)} samples within the identified <i>τ</i> regime.

Observe that the Power Law and the Stretched Exponential fits consistently reports lower validation MSE. Error bars are computed across 4 folds of cross-validation. Polynomial models demonstrate clear signs of overfitting while the exponential model (β = 1) is only slightly worse than the best fits. A similar analysis with Tint = 3 months is presented in the Fig 7 in S1 File.</p