Azo Dyes

To measure the collagenase inhibitory activity, a weight of 1 mg of azo dye-impregnated collagen was mixed with 800 μL of 0.1 M Tris-HCl (pH 7.0), 100 μL of 200 units/mL collagenase (stock solution), and 100 μL sample and incubated at 43 °C for 1 h under shaking condition. Subsequently, the reaction mixture was centrifuged at 3000 rpm for 10 min and the absorbance of the supernatant was detected at 550 nm in a microplate reader (BioTek Synergy HT, Woburn, MA, USA).

The polymer chains (single or matrix) are in thermal equilibrium at temperature T in the absence of light illumination. The typical configurations can be sampled using Metropolis Monte Carlo (MC) algorithm [64 ]. To this end, an instantaneous configuration with energy $E_{old}$ undergoes a trial change (trial movement) which yields a trial configuration with energy $E_{new}$ . The Metropolis rule accepts the trial configuration as a member of a set of typical equilibrium configurations at temperature T with probability equal to the smaller value of two expressions: 1 and $e^{-(E_{new}-E_{old})/\left(k_{B}T\right)}$ . One MC step (MCS) corresponds to a sweep of trial movements over all the monomers and sets a unit of MC “time” t measured in the number of MCS.
In a single MCS each of the monomers performed two kinds of trial movements: driven by thermal fluctuations and non-thermal one, resulting from the interaction with light. The former, performed along one of randomly chosen three directions $x,y,z$ , has unit length. It is accepted if the following three conditions are fulfilled [65 ]: (i) a length of a trial bond does not violate imposed restrictions; (ii) steric constraints are obeyed; and (iii) the Metropolis acceptance rule does not reject the movement.
Non-thermal trial movements of the monomers reflect the effects of light–matter (polymer chains) interaction. They mimic, in MC simulations, the action of Newtonian forces and torques on the monomers, resulting from $trans\leftrightarrow cis$ photoisomerization cycles of azo-dye molecules. The corresponding generic model, introduced in our paper [38 (link)], was used without any modifications in this study, because the objective was to get a deeper insight into the mechanisms that promote light-driven transport of functionalized polymers, reported in the framework of this particular model. It mimics the mechanical impact of $trans\to cis$ transition by granting an additional, non-thermal trial movement (of unit length along one of the three directions $x,y,z$ ) to the monomer closest to the dye, with probability per unit MCS equal to reduced local light intensity $I\left(x\right)$ . The trial movement of the monomer is accepted if Conditions (i) and (ii) formulated above are satisfied. The Metropolis acceptance rule (Condition (iii)) is not taken into account because the trial movement is not driven by thermal fluctuations—the typical thermal energy at room temperature $k_{B}T\approx 3\times {10}^{-2}$ eV is much smaller than typical energy (a few eV) of light quanta that trigger the photoisomerization transition.
The original model [38 (link)], which plays a role of a “minimal” model of light-induced transport of azo-polymers, uses some simplifications in modeling of the photoisomerization cycles. Firstly, it does not account directly for the kinetics of $cis\to trans$ transitions: after the photoisomerization transitions the molecules return to $trans$ states. This choice was motivated by the fact that taking into account $cis\to trans$ transitions introduces an additional parameter to the model [66 (link)], which gives rise to another temporal scale but, on the other hand, does not modify the effect of mass transport in a qualitative way. Secondly, the angular dependence of the transition rate—term ${cos}^2\left(\theta \right)$ —was replaced by a step function with value 0 for a small interval of angles around $\theta =\pi /2$ : $\pi /2-\delta <\theta <\pi /2+\delta (\delta <<1)$ (see Figure 1 (right)); for the remaining angles, the step function has value 1. This choice was motivated by the fact that ${cos}^2\theta$ is close to 1 in some interval of angles around $\theta =0$ and is small in some interval around $\theta =\pi /2$ . In the lattice model, the angles $\theta$ form a discrete set. The choice of $\delta$ from Ref. [38 (link)] corresponds, in a continuous model, to a deactivation of photoisomerization transitions for the chromophores with $\delta <{18}^{\circ }$ . To summarize, the transition rate $p(x,\theta )$ is either $I\left(x\right)<1$ or 0; the latter applies only when the dye in trans state is strictly perpendicular to the light polarization direction.
The selection of the correct length of MC simulation run is crucial since, in general, the type of dynamics of a polymer chain depends on the time interval [43 ]. The current project was oriented towards the dynamics of polymer chains during the process of inscription of SRG which, according to our previous study [38 (link)], requires about $5\times {10}^4$ MCS. Thus, the same MC interval was used in this study.

The CD-EPI polymers were synthesized following the method described by Pellicer et al. (2018) [36 (link)], which is a modification of the protocol of Renard et al. (1997) [37 (link)]. In brief, NaBH₄ and each CD were mixed in water, and then, a NaOH solution and EPI were sequentially added and mixed until the polymer becomes formed. This was washed with acetone and dried overnight.
Solutions of the azo dye Direct Red (CAS 90880-77-6, C₃₃H₂₀N₆Na₄O₁₇S₄, molecular weight (MW): 992.77) were prepared in the range of 25–300 mg/L, in order to evaluate the adsorption capacity of the polymers [36 (link)].