Fabrication of the PDA particle and evaluation of its FL response to stressesThe monodispersed stimulus-responsive fluorogenic PDA particle employed in this effort was fabricated using the co-flow microfluidic method. In the process, chloroform droplets containing 10 wt.% 10,12-pentacosadiynoic acid (PCDA) monomers were periodically generated along the flow of an aqueous outer phase (Fig. 1a and Supplementary Fig. 1)38,39. Typically, by using flow rates of the aqueous and chloroform phases of 400 µL·min–1 and 60 µL·min–1, respectively, micro-emulsion droplets having a mean diameter of ~400 ± 8.07 μm (Fig. 2a) were generated. The PCDA-chloroform droplets were collected in a 2 wt.% polyvinyl alcohol (PVA) water-filled petri dish that was subjected to chloroform removal by standing under ambient conditions for 12 h. The dried PCDA particles in water were then photopolymerized using a hand-held laboratory UV lamp emitting 254 nm at an intensity of 0.4 mW·cm–2. During this 10 min process, the container was gently shaken to ensure uniform UV exposure and effective photopolymerization. As a result, dark blue PDA particles with a uniform size distribution were produced, having a mean diameter of 2 R ≈ 200 ± 2.08 μm, as shown in Fig. 2b. Upon inspection of scanning electron microscope (SEM) images, it is apparent that the surface of the PDA particles features fuzzy domains, as depicted in Fig. 2c. This characteristic morphology has a resemblance to the structure of giant lipid/PDA vesicles, prepared using a simple solvent evaporation method40.Fig. 2: Structural and optical properties of PDA particles.a, b Optical microscopic images of PCDA-chloroform emulsions in water (a) and solid PDA particles in water (b). c Scanning electron microscope (SEM) image of PDA particles. d Confocal microscope image of a red phase PDA particle heated at 80 °C for 10 min, revealing a polymerized shell of a thickness hshell. Two additional images from different particles are shown below. e, f SEM images of a bisected PDA particle before (e) and after (f) chloroform treatment. g Thermo-FL response of PDA particles subjected to gradual heating from 40 °C to 100 °C. h Raman spectra of PCDA monomers (i), a blue PDA particle (ii), a red PDA particle produced by heating at 80 °C for 10 min (iii), and a mechanically crushed PDA particle (iv).Importantly, due to the finite penetration depth of the UV irradiation, the PDA particles underwent partial polymerization41. As evident from the confocal images of the red phase PDA particles in Fig. 2d, the polymerized shell is clearly visible with an approximate thickness of hshell ≈ 10.0 ± 0.03 μm, as averaged over nine different particles. This corresponds to a maximum volume degree of polymerization of ~27%. Furthermore, SEM analyzes of bisected PDA particles reaffirmed the partial polymerization of the PDA particles. The interior of the bisected particle appeared to be filled with a solid substance before the chloroform treatment (Fig. 2e) but appeared hollow after the treatment (Fig. 2f). Given that PCDA monomers are soluble in chloroform, these results demonstrate that the center region of the particle remained unpolymerized and contained residual PCDA monomers.The characteristic FL responses of the generated PDA particles to external stresses were evaluated prior to creating the mechano-FL sensor system. The thermo-FL behavior of the PDA particles was monitored using a FL microscope equipped with a thermal stage. As shown in Fig. 2g, the normalized FL intensity averaged over several PDA particles nonlinearly increases as the incubation temperature increases from 40 to 100 °C at a rate of 10 °C·min–1. A minor intensity increase occurs in the ~40 to ~70 °C range and then a steep increase occurs when the temperature increases from ~70 to ~90 °C at which the intensity plateaus and the PDA blue-to-red color transition is complete. Note that the FL intensity barely exhibit significant changes after the normalized FL intensity reaches ~1. This is because the PDA response occurs irreversibly, meaning that beyond this point, additional stresses unlikely result in a substantial change in the FL response. The observed thermally induced-FL response matches that observed in a previous study where a PDA powder underwent a significant colorimetric transition over the temperature range of ~65‒100 °C42,43. The nonlinear FL intensity response to temperature suggests that a critical energy point exists for creating the level of distortion of the PDA backbone structure required for substantial FL emission.The blue-to-red color transition of the PDA particles is a consequence of conformational changes within the highly conjugated polymer backbone44,45,46,47. In general, the blue phase represents a PDA state with a planar backbone structure, whereas the red phase exhibits a twisted, nonplanar geometry (Fig. 1c). Interestingly, some research has challenged the initial belief that disorder is a necessary condition for the red phase formation in PDA48,49. Raman spectroscopy was used to confirm that the generated PDA has a π-conjugated PDA backbone and evaluate changes taking place upon formation and stressing the PDA particles32. As can be seen in the spectrum displayed in Fig. 2h and Supplementary Fig. 2, the acetylenic (C ≡ C) stretching band of PCDA monomer is located at 2250 cm−1, and the bands associated with C ≡ C and C = C stretching in the alternating ene-yne backbone at 2099 cm−1 and 1450 cm−1, respectively, arise following polymerization. Thermal perturbation and crushing of the PDA lead to shifts of the alkyne and alkene bands to higher frequencies (2120 cm−1 and 1514 cm−1, respectively), a pattern that has been observed in a variety of PDAs subjected to stresses22,43. Note that the PCDA monomer peak observed in the crushed sample consistently demonstrates the presence of unpolymerized PCDA within the PDA particle. The typical mechanochromism of the PDA particles, manufactured through the microfluidic method, was further confirmed by subjecting them to common mechanical stresses, such as shearing, poking, and pressing. Each of these stresses induced FL emission, as shown in Supplementary Fig. 3.Optimization of the mechano-FL sensor systemIn the next phase of this investigation, we developed a single PDA particle mechano-FL sensor system having an optimized channel geometry, fluid flow rate, and exposure time to flows. When pure water at a flow rate of 25 mL·min–1 (maximum tolerated by experimental setup) was introduced into a blue PDA particle-containing device without or with an injection tube (Supplementary Fig. 4a, b), an observable FL response did not take place. In a study aimed at uncovering a mimic of blood components (e.g., RBCs) in a model of the vascular stenosis environment, a FL response arose when water containing 16.96 wt.% silica nanoparticles (SNPs, which are smaller than RBCs) was introduced to a device incorporating a narrow outer tube at a rate of 25 mL·min–1 for an exposure time (flow injection time) of 4.5 min (270 s) and a suction rate of 5 mL·min–1 to retain the PDA particle (Supplementary Fig. 4c and Supplementary Fig. 5). In addition, we observed that simple incubation of the PDA particles in stationary aqueous mixtures containing commercially available LUDOX TM-40, LUDOX HS-30, LUDOX AM-30, and LUDOX LS-30 resulted in detectable FL intensities (Supplementary Fig. 6a, b and Supplementary Table 1). This effect is likely caused by the presence of anionic components in the mixtures, which promote a pH triggering PDA response50,51,52,53. The use of a 20 mM phosphate buffer significantly reduced the FL intensity of the PDA particles, with values in the range of 0.0098 – 0.0132 arb. units for all types of SNPs, which were sufficiently minor (Supplementary Fig. 6c and Supplementary Table 1). Consequently, we chose to use LUDOX TM-40 (diameter ~19.6 ± 5.6 nm, Supplementary Fig. 7), which displayed the relatively lowest FL intensity in the buffer environment. However, the use of other types of SNPs would not have resulted in any significant differences in the mechano-FL sensor experiment. Additionally, before proceeding with the mechano-FL sensor experiments, we confirmed that all the solutions used in the experiments did not induce significant changes in the FL emission of the PDA particles under static conditions.Evaluation of the vascular mimicking mechano-FL sensor systemIn the designed vascular mimicking device, a single PDA particle is immobilized in the tip of the holding tube by using a suction syringe pump to create a negative pressure to counteract the fluid flow. Thinking that a strong negative pressure created by the suction system might cause mechanical stress, especially by pushing the round-shaped tip of the holding tube into the PDA (Supplementary Fig. 4c) and a consequent enhancement of FL intensity. However, we found that injection of pure water at a rate of 25 mL·min–1 for a flow injection time of 4.5 min, using suction rates of 2, 4, 5, 6, and 8 mL·min–1, has a negligible effect ( < 0.1 arb. units) on the FL intensity (Fig. 3a). Therefore, we selected 5 mL·min–1 as the optimized suction rate in the system that was subjected to further investigation.Fig. 3: Evaluation of the mechano-FL sensor system.a–d Normalized mean FL intensities of the PDA particles as a function of suction rate (a), injection rate (b), glycerin concentration (c), and SNP concentration (d). In each case, parameters were 4.5 min injection time, 25 mL·min–1 injection rate, and 5 mL·min–1 suction rate, except when used as variables. e SEM image of a PDA particle after SNPs bombardment for 4.5 min and the inset is the corresponding confocal fluorescence microscopic image. f, g Magnified SEM images of the regions indicated by the yellow (f) and green (g) dashed boxes of the image in panel (e). h FL emissions of PDA particles under the given experimental conditions depending on flow injection time. The injection and suction rates were 25 mL·min–1 and 5 mL·min–1, respectively. The injection time refers to the period of a PDA particle exposed to fluid flows for a given time. The data points and error bars in panels (a–d) and h indicate the mean FL intensity values and standard deviations from at least three independent experiments, respectively.The injection flow rate was another parameter that we anticipated could influence FL emission intensity response of the immobilized PDA particle. To probe this feature, pure water was introduced into the mechano-FL sensor system at rates of 5, 10, 20, and 25 mL·min–1 (constant 5 mL·min–1 suction rate), a flow rate range that is similar to the blood flow rate of 3‒26 mL·min–1 in 0.8‒1.8 mm arteries in the human finger54. After the 4.5 min injection time, the mean FL emission intensity gradually increases from 0.045 to 0.101 arb. units as the injection rate is increased (Fig. 3b). These observations suggest that flow-induced mechanical stress on the PDA is directly proportional to the flow rate. However, similar to the suction rates, the injection rates in the range explored only negligibly affect FL emission and, thus, 25 mL·min–1 was used as the optimized injection rate in subsequent studies.The effect of solution viscosity on the PDA FL response was assessed next. For this purpose, aqueous solutions containing 10, 20, and 30 wt.% glycerin were injected at an injection rate of 25 mL·min–1 for an injection time of 4.5 min using a suction rate of 5 mL·min–1. As demonstrated by the plot in Fig. 3c, injection of 20 and 30 wt.% results in relatively strong FL emissions of about 0.1262 ± 0.0025 arb. units and 0.1245 ± 0.0213 arb. units, respectively. Given that the viscosities of these solutions are proportional to the glycerin concentration, the similarities of these FL intensity responses might possibly result from the fact that both fluids do not cause sufficient mechanical energy in the PDA backbone to reach the critical value needed to promote a substantial FL change.Lastly, we explored the effects of SNP and biomolecule (i.e., RBCs and yeast cells) concentrations on the FL response of the PDA particle, expecting that higher mechanical stress would be imparted when higher concentrations are used. First, we assessed the FL intensity changes brought about by using aqueous SNP suspensions with concentrations of 0, 5.65, 11.3, and 16.95 wt.%, while keeping the other parameters constant (i.e., injection rate of 25 mL·min–1, suction rate of 5 mL·min–1, and flow injection time of 4.5 min). It should be noted that we used the 5.65 and 11.3 wt.% SNP suspensions because their viscosities are the same as those of respective 10 and 20 wt.% aqueous glycerin solutions, thereby enabling us to separate the effects of particle concentration and viscosity. As shown in Fig. 3d, the FL intensity drastically increases with increasing SNP concentrations, and it reaches 0.3096 ± 0.01802 arb. units at 16.95 wt.%. The results show that the FL response is more greatly governed by SNP concentration (Fig. 3c, d). The PDA particle was isolated after bombardment by 16.95 wt.% SNPs for 4.5 min. As can be seen in the image in Fig. 3e–g, local indentations are present mainly at the center region of the PDA particle, where it should be most heavily bombarded by the SNPs. Also, the images show that several cracks radiate outward from this central area. Interestingly, numerous fuzzy domains present on the intact PDA particle, as shown in Fig. 2c, appear to have been mechanically etched as a consequence of mechanical stress applied to the PDA surface during the SNPs injection. Finally, the confocal image shown in the inset of Fig. 3e reveals that the entire surface region of the PDA particle fluoresces after injection of the SNPs for 4.5 min. This illustrates how the localized mechanical stress, when continuously applied and accumulated, can affect the entire region of the PDA particle.The time-dependent response of the mechano-FL sensor system was examined by continuously monitoring FL intensities at various time points following injection (Figs. 3h and 4). We found that as the flow injection time increases the consequent FL intensity increases. For example, in contrast to the negligible effect caused by pure water (Fig. 4a) and relatively small FL intensity changes for the case of 20 wt.% glycerin (Fig. 4b), injection of 16.95 wt.% SNP promotes the most prominent time dependent FL intensity increases. Interestingly, as the SNP injection time is increased, the area of FL emission also gradually increases (Fig. 4c). Given that the impact location of SNPs remains constant throughout the injection, the continuous SNPs collision likely results in accumulated mechanical stress, causing the entire particle to fluorescence. Notably, using the 16.95 wt.% SNP solution, the FL intensity increases nonlinearly (Fig. 3h).Fig. 4: FL images of the PDA particle in the mechano-FL sensor system.a–d Representative FL images illustrating the variation in PDA particle FL emission upon injecting different types of solutions: pure water (a), 20 wt.% glycerin (b), 16.95 wt.% SNPs (c), 1.54 × 105 μL‒1 red blood cells (RBCs) (d), 4.80 × 104 μL‒1 yeast (e), and 2.40 × 104 μL‒1 yeast (f), corresponding to the results depicted in Fig. 3h. The images were captured at an injection rate of 25 mL·min–1 and a suction rate of 5 mL·min–1, with the flow injection time varied.We conducted further experiments to elucidate the effect of physical impact of SNPs on PDA particles on FL emission. The time-dependent FL response at different SNPs concentrations (5.65, 11.3, and 16.95 wt.%) was compared, as shown in Supplementary Fig. 8a. It was observed that the FL intensity value rapidly increased with time at higher concentrations, while the change was relatively minor at lower concentrations. The FL intensity change was then re-plotted against the number of injected SNPs, resulting in the data for the three different concentrations converging to a single master curve (Supplementary Fig. 8b). Additionally, we extended the injection time of 16.95 wt.% SNPs to 8.5 min (510 s) and found that the normalized FL intensity approached 1, indicating near saturation (Supplementary Fig. 9). Moreover, a 16.95 wt.% SNPs solution was injected and halted at 4.5 min (270 s), and the FL intensity was continuously monitored even after stopping the injection. It was found that the FL change after stopping was negligible (Supplementary Fig. 10). Based on these additional analyzes, we confirmed that the FL intensity values are primarily influenced by the number of SNPs colliding with the PDA particles. Furthermore, the gradual changes in PDA mechanochromism, along with the halt of FL intensity changes upon the removal of mechanical stress, underscore the important role that continuous application and accumulation of mechanical stress play in mechanochromism. This might be closely related to the nonlinear behavior of PDA mechanochromism55,56. For more information on the injected fluids used in this study, one can refer to Supplementary Table 2.Effect of biomolecule collisions on PDA FL responseInterestingly, injection of biomolecules (Supplementary Fig. 11a, b) also promotes similar FL responses. For these experiments, we used ovine RBCs because they are commercially available, and they have a biconcave morphology and size (~4 µm in ovine and ~7 µm in humans) that are similar to human RBCs, and a low aggregability57. After injecting ovine RBCs with a number density of ~1.54 × 105 μL‒1 (Supplementary Table 3) for 4.5 min under the standard conditions, we observed a FL intensity change of ~0.2751 ± 0.0171 arb. units (Fig. 3h). This change is significantly stronger than that promoted by 30 wt.% glycerin (Fig. 3c). Specifically, given that the viscosity of the RBC solution (~2.5 cP, Supplementary Fig. 11c) is comparable to that of the 30 wt.% glycerin solution, the ~3 times greater intensity change promoted by the RBCs (Figs. 3h and 4d) is directly related the collisions of solid objects, even when soft, with the PDA particle. Note that these observations were made using conditions that were comparable to present in human blood where the RBC number density is ~5 × 106 μL‒1 and the viscosity is ~3.5‒5.5 cP58. Additional experiments using yeast cells yielded similar results. Injection of solutions of yeast cell with concentrations of ~4.8 × 104 and ~2.4 × 104 μL‒1 (Supplementary Table 3) into the mechano-FL sensor system caused FL intensity responses of ~0.2265 ± 0.01147 and ~0.171 ± 0.012 arb. units, respectively (Figs. 3h and 4e, f), which are also greater than those promoted by glycerin solutions. Here again, because the viscosities of the two yeast solutions are ~1.3 and ~1.2 cP (Supplementary Fig. 11c), the collision effect clearly governs the response of this mechano-FL sensor system. Similar nonlinear responses were also found using the biomolecules (Fig. 3h), consistently demonstrating that a critical energy level exists for sufficient distortion of the PDA backbone to create a significant FL response55,56.CFD Simulations of the mechano-FL sensor systemWe utilized CFD simulations to formulate a rational interpretation of the experimental observations described above (Supplementary Fig. 12). For this purpose, calculations were conducted to quantitatively determine the total energy \({E}_{{{{{\rm{tot}}}}}}\) through hydraulic pressure and SNP collision absorbed by a PDA particle. The k-omega shear stress transport (k–ω SST) turbulence model was utilized because of its excellent capability of handling flow transition from laminar to turbulent regimes, and to accurately account for strong pressure gradients near walls (see the method section for more detailed explanation)59,60. The dimensions of the mechano-FL sensor system used in experiments were employed in the CFD simulation (Supplementary Fig. 13), and detailed descriptions of equations and modeling parameters are provided in Supplementary Tables 4 and 5.The results of these calculations clarify the dynamic behavior of the mechano-FL sensor system, as illustrated in Fig. 5a–c. Specifically, Fig. 5a provides a detailed visual representation of the flow velocity patterns observed when injecting a 16.95 wt.% SNP solution with a flow velocity of 3.317 m·s–1 (Supplementary Table 2). The maximum flow velocities are found to be approximately 3 m·s–1 in the microchannel following impact with the PDA particle surface. Figure 5b visualizes the corresponding shear and normal stress distributions. Notably, the normal stress peaks at a polar angle of \({\theta }_{{{{\rm{P}}}}}\) = 0°, which is the point where the SNPs collide perpendicularly with the PDA particle, as depicted in Fig. 5c. In contrast, the shear stress reaches a minimum value at the same polar angle (\({\theta }_{{{{\rm{P}}}}}\) = 0°) and increases as the angle \({\theta }_{{{{\rm{P}}}}}\) widens. Note that the stress scale obtained in these calculations is comparable to the scales obtained through the surface forces apparatus for PDA Langmuir films upon the blue-to-red transition (i.e., ~100 kPa for normal stress and ~3 kPa for shear stress)61.Fig. 5: Computational fluid dynamics (CFD) analysis of the mechano-FL sensor system.a, b Examples showing distributions of flow velocity (a) and stress (b) for the 16.95 wt.% SNP suspension. c Variation of shear and normal stresses on the PDA surface as a function of the polar angle \({\theta }_{{{{\rm{P}}}}}\). Error bars represent the standard deviation over the stress values across the azimuthal angle \(\alpha\). d, e Plots of \({E}_{{{{\rm{H}}}}}\) and \({E}_{{{{\rm{tot}}}}}\) as functions of glycerin (d) and SNPs (e) concentrations, respectively, at an injection rate of 25 mL·min–1 over 4.5 min. Corresponding experimentally measured FL intensity profiles are overlaid for comparison. f Time-dependent profiles of \({E}_{{{{\rm{tot}}}}}\) and FL intensity for the 16.95 wt.% SNP suspension injected at 25 mL·min–1 over an extended duration of 8.5 min. Inset indicates the comparison of the nonlinear property of normalized FL intensity profiles from the mechano-FL sensor experiment and the thermal stress analysis (from Fig. 2g) against the normalized torsion energy \({E}_{{{{\rm{tor}}}}}\) from a previous study56. The x-axis is normalized from 0 to 1, aligning maximum values of FL intensity and \({E}_{{{{\rm{tor}}}}}\) to 1. For panels d–f each experimental data point and corresponding error bar represent the mean intensity value of a minimum of three independent trials and its standard deviation, respectively.The hydraulic energy \({E}_{{{{\rm{H}}}}}\) absorbed by the PDA particle is proportional to the viscosity of the fluid. As depicted in Fig. 5d, the upward trend in calculated \({E}_{{{{\rm{H}}}}}\) values as the glycerin concentration increases from 0 to 30 wt.% is consistent with a typical characteristic of Newtonian fluid flows. The summary of fluid properties with varied viscosities is presented in Supplementary Table 6. Note that the shape of glycerin concentration dependent \({E}_{{{{\rm{H}}}}}\) profile does not completely match the corresponding experimentally determined FL intensity profile. This deviation likely arises because the conjugated structures of the PDA particle are not accounted for the CFD simulation. Additionally, the maximum calculated \({E}_{{{{\rm{H}}}}}\) values for 20 to 30 wt.% glycerin are ~50 and ~62 μJ, respectively, whereas the experimental FL intensity only shows a negligible change upon injection of these solutions. This result suggests that the conjugated PDA backbone may resist structural distortion caused by the flow-induced mechanical stress.The calculations show that bombardment by SNPs leads to an increase in \({E}_{{{{\rm{tot}}}}}\) absorbed by the PDA particle, considered to be the sum of the computed \({E}_{{{{\rm{H}}}}}\) and SNP collision energy \({E}_{{{{\rm{col}}}}}\) calculated using the Hertz contact equation (Supplementary Table 7)62. \({E}_{{{{\rm{tot}}}}}\) demonstrates an increasing trend as the SNP concentration increases, spanning 0, 5.65, 11.3, and 16.95 wt.% when injected for 4.5 min (Fig. 5e) and with an extended injection duration of 8.5 min at 16.95 wt.% concentration (Fig. 5f). Similarly, because the conjugated structure of the PDA was not considered in this simulation, the \({E}_{{{{{\rm{tot}}}}}}\) values do not accurately reflect the observed nonlinear behavior of FL intensities dependent on the SNP concentration. Nevertheless, this computational data suggests that the \({E}_{{{{\rm{tot}}}}}\) required to achieve a complete blue-to-red transition for a single PDA particle is approximately 307 μJ. The activation energy \({E}_{{{{\rm{act}}}}}\) for irreversible blue-to-red transitions in a variety of PDAs has been estimated to be ~17.6–22.5 kcal·mol–146,47. For instance, for a three-layer PDA film fabricated from the PCDA monomers, the predicted \({E}_{{{{\rm{act}}}}}\) was approximately 17.6 kcal·mol–1. Though our 200 μm PDA particles might differ from the previously reported PDA conditions, we presumed \({E}_{{{{\rm{act}}}}}\,\approx\) 17.6–22.5 kcal·mol–1 to roughly estimate \({E}_{{{{\rm{act}}}}}\) for our PDA particles. Considering ~27% polymerization (Fig. 2d) yields \(0.27\times \frac{{\rho }_{{{{{\rm{PDA}}}}}}\times {V}_{{{{{\rm{PDA}}}}}}}{{{MW}}_{{{{{\rm{PCDA}}}}}}}{E}_{{{{\rm{act}}}}}=289\!-\!369\) μJ, where the PDA density is \({\rho }_{{{{{\rm{PDA}}}}}} \, \approx \, 1.3\times {10}^{3}\) kg·m–3, the PDA volume is \({V}_{{{{{\rm{PDA}}}}}}=\frac{4{{{{\rm{\pi }}}}}{R}^{3}}{3}\), and the molecular weight of PCDA is \({{MW}}_{{{{{\rm{PCDA}}}}}}{{{\rm{=}}}}0.375\) kg·mol–1. This result aligns well with the energy requirement of ~307 μJ for the complete blue-to-red transition, as derived from our calculations. Additionally, we performed CFD calculations and experiments for different sizes of PDA particles. Given the polymerization degree of ~74% for 50 μm and ~37% for 140 μm PDA particles (Supplementary Fig. 14a), the energy required for the complete blue-to-red transition was ~12.4 μJ and ~141 μJ, respectively. These values are in good agreement with the predictions based on \({E}_{{{{\rm{act}}}}}\) values (Supplementary Fig. 14b). Furthermore, it was observed that the blue-to-red transition occurred more rapidly as the size of the PDA particles decreased (Supplementary Fig. 14c–f), demonstrating sensitivity tunability for PDA particles.The nonlinear FL intensity profile possesses a resemblance to the previously reported torsional energy \({E}_{{{{{\rm{tor}}}}}}\) calculations, which also exhibit nonlinear increases for various types of PDA materials55,56. Therefore, we compared the normalized \({E}_{{{{\rm{tor}}}}}\) profile with the normalized FL intensity profiles derived from both the mechano-FL sensor experiment (Fig. 5f) and the thermal stress analysis (Fig. 2g). As displayed in the inset of Fig. 5f, the experimental FL intensity’s nonlinear trajectory seems fairly consistent with the shape of \({E}_{{{{\rm{tor}}}}}\). This similarity allows us to reasonably postulate a close correlation between these two factors. Notably, recent experimental results have demonstrated that lateral stress applied parallel to the PDA backbone significantly influences the mechanochromism of thin PDA films63. Therefore, further experimental and/or theoretical studies are needed to clarify how torsional and lateral stresses contribute relative to each other depending on the PDA structures under various conditions.
