Webbing structures are extensively employed in engineering systems as load-bearing components. In a field setting, webbings are frequently subject to extended ultraviolet (UV) light irradiation, which can affect their integrity and reduce their mechanical strength. Despite technological advancements in structural health monitoring, long-term UV sensing techniques for webbings remain under-developed. To fill this gap, we propose a photochromic nylon webbing that demonstrates color variation in response to extended UV exposure. The webbing offers a rich, yet controlled, color variation over multiple time scales that is conducive to UV sensing. A mathematical model grounded in photochemistry is developed to interpret experimental observations, unveiling the photochromic phenomenon as a multi-step, multi-timescale photochemical process involving several chemical species. The model captures the evolution of the coexisting species through a system of nonlinear, coupled ordinary differential equations, offering the basis for the inference of the webbing’s color. The proposed photochromic webbing and the photochemistry-based mathematical model could inform future designs of UV-sensitive structures that maintain sensitivity under weeks of continuous sunlight UV exposure.

Webbing structures are ubiquitous in engineering systems. From chin-straps of military helmets1 to reinforcement structures of parachutes2 and inflatable space habitats,3 webbings are routinely employed as critical load-bearing components. In a field setting, all these engineering systems are exposed to the ultraviolet (UV) component of sunlight, which could lead to degradation of the webbings’ polymer chains and loss of mechanical strength over an extended time period.4 Monitoring the long-term UV irradiation is pivotal to ensure the integrity and safety of webbings.

Existing health monitoring technologies do not yet afford long-term UV irradiation sensing. A potential candidate to fill this gap is represented by photochromic materials—functional materials that exhibit color variation in response to UV irradiation. In particular, spiropyran (SP) functionalized polymers have demonstrated outstanding sensitivity to UV.5–7 A typical SP molecule consists of an indole and a benzopyran moiety, bonded through a spiro-carbon atom, as shown in Fig. 1. The physical principles underlying the photochromic response of SP have been well understood owing to continued experimental efforts dating back to the 1950s.8,9

FIG. 1.

Schematic of the photochemical reactions of SP, consisting of Reactions 1, 2, and 3, marked through green circles. Molecular structures of the major reactants and products of each reaction are illustrated.

FIG. 1.

Schematic of the photochemical reactions of SP, consisting of Reactions 1, 2, and 3, marked through green circles. Molecular structures of the major reactants and products of each reaction are illustrated.

Close modal

Briefly, UV energy elicits an isomerization reaction, in which the closed-ring SP molecules experience a cleavage of the spiro-carbon—oxygen bond, resulting in the open-ring form of the molecule, merocyanine (MC) (see Fig. 1). While the closed-ring SP absorbs minimal visible light energy, the open-ring MC has strong absorbance of visible light, with a typical absorbance peak between 500 and 600nm.10,11 Owing to this change in optical absorbance, the originally colorless SP-functionalized polymers will assume a deep blue color. This isomerization process could be accompanied by a reverse-isomerization process, where the open-ring MC transforms back into the closed-ring SP in the presence of visible light or heat12,13 (see Fig. 1).

For most derivatives of SP, their color change associated with the SPMC isomerization is highly sensitive to UV, whereby a low level of UV fluence could result in a pronounced color variation. In addition, the reverse-isomerization process makes repeated UV sensing feasible,14,15 further enhancing its superior performance as a short-term UV sensor. In this context of short-term sensing, we recently proposed16 a photochromic webbing functionalized by a polydimethylsiloxane (PDMS) polymer matrix embedded with SP (SP-PDMS). Through experiments, we demonstrated the capability of a functionalized webbing to sense low levels of UV irradiation, equivalent to less than 15min exposure of the UV component of sunlight. The extent of color variations presented a monotonic dependence on the UV fluence irradiated to the webbings, thereby facilitating application for UV sensing.

To date, the feasibility of long-term UV sensing through SP-functionalized materials has never been explored. Upon extended UV irradiation, SP-embedded materials have been observed to display an irreversible brown or dark red color.17,18 This phenomenon was corroborated by some pilot trials presented in our recent study,16 where SP-PDMS functionalized webbings exhibited a deep brown color upon extended UV irradiation. Through analysis of the chemical products, previous studies17,18 have attributed the emergence of the brown color to an irreversible photo-induced oxidation process, whereby the MC molecules were decomposed into smaller molecules by UV exposure. Remarkably different from the blue color elicited by the SPMC isomerization, the photodegradation products of extended UV irradiation absorb strongly in the blue spectrum,17 giving rise to the dark red or brown color. Photodegradation has been thus far regarded as a chief limitation of SP-based UV sensors, hampering their performance in long-term UV sensing.14,19,20

The first major objective of the present work is to systematically assess the feasibility of sensing extended UV irradiation using the photochromic webbings proposed in Zhang et al.16 In contrast to conventional notions about photodegradation, here, we capitalize on the color variation arising from photodegradation for long-term UV sensing. Different from Zhang et al.,16 we now examine the response of photochromic webbings to a substantially longer UV irradiation, equivalent to 56 days of continuous sunlight exposure (5000 times longer exposure than Zhang et al.16). Photochromic responses of the webbings are recorded at finely resolved temporal resolution through a vision-based data acquisition system to shed light on both the transient and later stage of the degradation.

From a theoretical perspective, the existing understanding of the photochromic mechanisms of SP-functionalized materials has often benefited from physics-based mathematical models.5,9 Most models developed so far have focused on deciphering the underpinnings of the SPMC processes.5 The variation in the concentration of SP during SPMC isomerization could be accurately described as an exponential decay.9 Similarly, the simultaneous thermal process, MCSP, could be regarded as a decay process with a relatively lower decay rate. This could be attributed to the molecular structures of MC. At sufficiently high concentrations, MC molecules tend to form aggregations through dipole-dipole interactions and π-stacking, generating “H-aggregates,” in which the molecules align head to tail, or “J-aggregates,” where they form side-by-side patterns.21,22 Due to the increased stability at the aggregated state, the MCSP process typically occurs at a slower rate.21–23 

Analogous mathematical models that could offer quantitative insights into the response of SP to extended UV exposure have yet to be developed, thereby limiting our understanding to largely qualitative descriptions. To bridge this gap, the second main objective of the present work is to put forward a model to explain the photochromic response of the functional webbing. The proposed model captures underlying chemical reactions, where the reactants and products are identified from previous experimental efforts.9,17,18 Rooted in fundamental principles of photochemistry, the model anticipates the rate of change in a chemical species based on their quantum yield and their ability to absorb light energy.9 The dynamic evolution of the chemical species is described by a system of differential equations, offering a basis for the inference of the webbings’ color. Accuracy of the proposed model is tested against experimental observations.

The rest of the paper is organized as follows. The fabrication method for the photochromic webbings and analysis of their responses to extended UV irradiation is detailed in Sec. II. The derivation of the mathematical model and validation against experimental observations is presented in Sec. III. Major conclusions of the current work are summarized in Sec. IV.

The spiropyran dye (SP), 1,3-dihydro-8-methoxy-1,3,3-trimethyl-6-nitrospiro[2H-1-benzopyran-2,2-(2H)-indole], conventionally known as 6-nitro-8-methoxyBIPS,9 was purchased from Sigma-Aldrich (CAS No. 1498-89-1). The two-part Sylgard 184 silicone elastomer kit (Dow Corning, Midland, MI), consisting of a base and a curing agent, was used to fabricate the PDMS matrix. All materials were used as received.

The photochromic nylon webbing was fabricated through a cast coating process, similar to the procedure detailed in Zhang et al.16 Briefly, a pre-determined amount of the Sylgard 184 base was deposited in a beaker. The spiropyran dye was then mixed into the base through vigorous stirring for 5min. The Sylgard 184 curing agent was subsequently added to the mixture according to a 10:1 base to curing agent ratio, followed by vigorously stirring for another 5min. In this study, samples with four concentrations of the SP dye were prepared, corresponding to 0.25, 0.50, 0.75, and 1.00wt.% of the total weight of the polymer matrix.

To prepare for coating, a section of a 2-wide nylon webbing was fitted into a 3D-printed plastic mold of 6.0×5.0cm2 in size. In each mold, 7.0ml of the silicone/SP mixture was cast uniformly on top of the webbing. The mold was then left on a horizontal surface at room temperature. Webbings with a thin layer of SP-PDMS coating were obtained following 48h of polymerization. To facilitate testing, each coated webbing section was cut into smaller samples of 2.0×3.0cm2 in size.

To investigate the response of the photochromic webbing to extended UV irradiation, we conducted testing in a QUV accelerated weathering tester (Q-Lab Corporation, model QUV, Westlake, OH). The QUV tester was quipped with eight UVA-340 lamps (Q-Lab Corporation, Westlake, OH), emitting light energy in the long-wave UV spectrum (315400nm) with a peak intensity at 340nm. The coated webbing samples were fixed on the testing panel of the tester using double-sided tapes. The samples were exposed to UV continuously for 56 days, with the temperature inside the tester maintained at 35°C. In this study, three samples were tested at each dye concentration, corresponding to a total of 12 samples.

During testing, the samples were taken out of the tester to quantify their photochromic responses at predetermined times. Specifically, the color of the samples was recorded at 1, 6, and 24h during the first day following the start of the QUV test. Data were subsequently acquired each day until day seven, at three-day intervals until day 28, and at seven-day intervals until day 56. We purposefully collected data more frequently in the initial phase to more accurately capture the transient responses of the webbing.

Data acquisition was conducted in a custom-designed true-color data acquisition chamber. The chamber consisted of six walls made of 61×61×0.6cm3 fiberboards to block ambient light. The inside of the chamber was illuminated by five 28×2cm2 D65 LED lights (Waveform Lighting, Absolute Series 99 CRI, Vancouver, WA) fitted to the bottom surface of the top wall, providing 6500K natural daylight. During data acquisition, the samples were placed at the bottom of the chamber, and a Nikon D7000 camera was used to capture photos of the webbings at a resolution of 4928×3264 pixels with a shutter speed of 1/1600s. The camera was fitted through a 10.0×20.0cm2 window carved through the top wall of the chamber.

The color of the samples was extracted from the recorded photos through a custom-built image analysis program written in the commercial software MATLAB. From each photo, the red/green/blue (RGB) values, ranging between 0 and 1, were extracted from pixels within a 100×100 pixel window near the center of the sample. The RGB values were averaged among all pixels to represent the color of the sample at the corresponding time instant. Similar to our previous work,16 we estimated the yellowness of the sample, I, as a potential proxy for UV sensing. The value of I was estimated as the average of the R and G values. We further introduced ΔI, defined as ΔI=1I, to score the darkness of the sample. To adjust for the limited exposure of the camera, we re-scaled the value of ΔI such that among all images of webbings recorded, the darkest and the lightest intensities corresponded to ΔI=1 and ΔI=0, respectively.

The color of the photochromic webbings during QUV irradiation exhibited a transition over a range of color regimes, as evidenced by snapshots of the samples taken at a few select time instants illustrated in Fig. 2(a). For all dye concentrations, the webbings were observed to attain a deep blue color following a few hours of UV irradiation, which was representative of the SP to MC isomerization arising from short UV irradiation. A different color was observed as the webbings were exposed to UV irradiation for a longer time, where the deep blue color transitioned into a dark maroon color after 6h and subsequently into a dark brown color after one to three days. This was consistent with the brown color obtained in our pilot trials.16 

FIG. 2.

(a) Snapshots of SP-functionalized webbings over eight weeks of UV exposure. (b) Temporal evolution of the webbings’ color represented in the CIE 1976 color space. The inset is a zoomed-in view, and the black dashed arrows indicate the direction of color evolution.

FIG. 2.

(a) Snapshots of SP-functionalized webbings over eight weeks of UV exposure. (b) Temporal evolution of the webbings’ color represented in the CIE 1976 color space. The inset is a zoomed-in view, and the black dashed arrows indicate the direction of color evolution.

Close modal

In the present effort, data acquired at a finer temporal resolution unveiled a rich color shift from deep blue to dark brown over a period of a few days. As the webbings experienced longer irradiation, the brown color gradually and monotonically faded as they recovered toward their original color before irradiation. The rate of this decoloration depended on the initial dye concentration in the coating, whereby at the lowest concentration, the webbings were completely bleached following approximately 30 days of irradiation, while samples with the highest dye concentration still displayed a light brown color by the end of 56 days.

The intricate variation in the webbings’ color was also reflected in the CIE plot based on their RGB values. As displayed in Fig. 2(b), the color spanned the blue–red–brown–white spectrum during the entire test. Although the color spanned a broad spectrum of the color space, beyond one day of irradiation, the color transitioned monotonically from deep to light brown, covering a nearly one-dimensional manifold near the red/yellow spectrum. Such a dependence hints at the feasibility of UV sensing through the yellow intensity of the samples.

To assess the feasibility of using the yellowness of the sample as a potential proxy for UV sensing, we inspected the webbings’ darkness in the yellow spectrum, ΔI, as shown in Fig. 3. For all dye concentrations, the values of ΔI exhibited an initial fast increase, reaching a peak value close to 1 at approximately t=1day. The values of ΔI were weakly dependent on the initial dye concentrations for t1day. This could be attributed to the large dye concentrations employed in our study and the strong absorbance of visible light by MC such that webbings at even the lowest dye concentration produced a significant darkening equivalent to ΔI=0.87. A further increase in the dye concentration only led to a marginal increment in ΔI.

FIG. 3.

(a) Variation in the darkness of the webbings, ΔI, over 56 days of UV irradiation. Dots and errorbars represent the mean values and standard deviations of experimental measurements of three samples, respectively. Dashed curves represent mathematical predictions. The inset is a zoomed-in view of data for the first five days. The legend indicates the initial wt. % of SP. Data in (a) are displayed in logarithm scale in (b).

FIG. 3.

(a) Variation in the darkness of the webbings, ΔI, over 56 days of UV irradiation. Dots and errorbars represent the mean values and standard deviations of experimental measurements of three samples, respectively. Dashed curves represent mathematical predictions. The inset is a zoomed-in view of data for the first five days. The legend indicates the initial wt. % of SP. Data in (a) are displayed in logarithm scale in (b).

Close modal

Corresponding to the decoloration of the webbings, ΔI monotonically decreased after t=1day. Compared with the initial rapid increase, the decay of ΔI was significantly slower for t>1day such that no webbing was completely bleached for the first 30days. The decay rate of ΔI for t>1day was dependent on the initial dye concentration, whereby faster decay rates were registered at lower dye concentrations. Interestingly, following 56 days of irradiation, bleached webbings at 0.25 and 0.50wt.% concentrations attained brighter colors than their initial ones prior to UV irradiation due to the slight color absorption by SP in the pristine samples.

The monotonic decrease in ΔI as a function of time for t>1day was a favorable feature that could support sensing of extended UV irradiation. The dependence of the decay rate of ΔI on the initial dye concentration was another desirable characteristic, allowing for choosing the dye content to balance between sensitivity and sensing lifetime according to practical applications. Such a design-based approach would benefit from physics-based mathematical models that can elucidate the physical underpinning of the photochromic phenomenon, which is still lacking to the best of our knowledge. The remainder of this work is focused on the development of a mathematical model that could explain our experimental observations.

Here, we establish a theoretical framework grounded in photochemistry to explain the experimental observations. We first reconstruct a multi-step reaction process associated with the isomerization and photodegradation processes taking place during extended UV irradiation based on the degradation products reported in the literature. We then posit a system of nonlinear differential equations to describe the temporal evolution of the chemicals involved in the reaction process. The proposed mathematical model was calibrated against the experimental data using unknown material properties as fitting parameters. The calibrated model offers insights into the physical underpinnings of photochromism by unveiling the temporal evolution of the reactants.

The photochemical reactions taking place during extended UV irradiation could be considered a multi-step process involving the formation and decomposition of a series of chemical species across a range of time scales.9 Through the schematic illustrated in Fig. 1, we articulate the process into three major reactions. Reaction 1 is the SPMC isomerization/reverse-isomerization occurring at short-term UV irradiation. UV irradiation causes the cleavage of the oxygen–spiro-carbon bond in the SP molecule, resulting in open-ring MC molecules that produces the deep blue color emerged in the webbings following the first few hours of irradiation. The simultaneous reserve-isomerization process, MCSP, could be considered a thermal process with a thermal rate constant k.

Extended UV exposure of SP for days could be associated with further decomposition of MC,17,18 triggering Reaction 2. For webbings exposed to air, this decomposition process is dominated by the oxidation of MC molecules. Through proton nuclear magnetic resonance (1H-NMR) and Fourier transform infrared spectroscopy analyses of SP-doped films, Yoshida and Morinaka17 registered the cleavage of the C=C bond and the NCH3 bond of the opened ring MC molecules, giving rise to degradation products consisting of smaller molecules that could render the films reddish. This is corroborated by the work of Brown9 and Malatesta,18 in which UV irradiation of 6-nitro-8-methoxyBIPS for approximately 42h produced 5-nitro-3-methoxysalicylaldehyde (SA), 1,3,3-trimethyloxindole (OI1), and 3,3-dimethyloxindole (OI2), which are likely the degradation products of MC molecules following the cleavage of the C=C and NCH3 bonds (see Fig. 1). Gases CO and CO2 were also detected among the photodegradation products.9,18 The emergence of the brown color in the webbing likely resulted from the generation of SA, which has a strong absorbance in the blue spectrum and exhibits a yellowish color. In contrast, oxindoles (OI1 and OI2) are not expected to influence either the photochemical reactions or color of the webbings, as they demonstrate negligible absorbance of both long-wave UV and visible light.24–26 

The gradual decay of the webbings’ brown color upon further UV irradiation can be associated with additional decomposition of the photodegradation products, summarized here as Reaction 3. The possibility of the oxidation of SA into smaller molecules was reported in Brown,9 where the generation and oxidation of SA was detected to take place simultaneously during photodegradation. Although this additional photodegradation step has never been quantified in previous studies, it is reasonable to hypothesize that smaller molecules, including phenol (PH), formaldehyde (FA), and CO and CO2 gases, could result from this reaction. These molecules are colorless and are not expected to influence the photochromic responses of the webbing.

We emphasize that the reactions detailed in Fig. 1 are valid only in the presence of oxygen, which is representative of the in-air experimental condition employed in this study. For instance, during Reaction 2, the benzopyran oxygen in MC is transferred to SA, while the oxygen in the C=O group of oxindoles is likely assimilated from oxygen in the air.18 The oxygen atoms in CO and CO2 could also be traced back to oxygen in the air.9 

With reference to the chemical reactions detailed in Fig. 1, here, we establish a mathematical model to describe the dynamic evolution of the major chemical species. In a photodegradation process of a single chemical species, the time derivative of its molar concentration, C, can be determined through9 

dC(t)dt=ΦIabs(t),
(1)

where Φ is the quantum yield of the molecule, a nondimensional quantity that measures the number of molecules decomposed for every photon absorbed; Iabs is the light intensity absorbed by the species (einsteincm3s1).

Equation (1) can be extended to a mixture of several coexisting species.9 To study the photochemical reactions and color of the webbing, we focus on three major species: SP, MC, and SA. The influence of other degradation products and the PDMS matrix is neglected as they show minimal absorbance of long-wave UV and visible light. As evident from Eq. (1), to estimate the rate of change in the concentration of each species in the mixture, we must determine the light intensity absorbed by the corresponding species.

Considering the presence of all species, the UV light intensity absorbed by each species can be estimated as a fraction of the total intensity absorbed by the material, IaUV, which reads9 

ISPUV(t)=ϵSPUVCSP(t)F(t)IaUV(t),
(2a)
IMCUV(t)=ϵMCUVCMC(t)F(t)IaUV(t),
(2b)
ISAUV(t)=ϵSAUVCSA(t)F(t)IaUV(t),
(2c)

where I()UV is the long-wave UV light intensity absorbed by a chemical species, ϵ()UV is the light extinction coefficient of a chemical species for long-wave UV (M1cm1), and F is defined as

F(t)=ϵSPUVCSP(t)+ϵMCUVCMC(t)+ϵSAUVCSA(t).
(3)

In Eq. (2), the total UV light intensity absorbed by the material is determined through

IaUV(t)=[110AUV(t)]I0UV,
(4)

where I0UV is the total long-wave UV light intensity incident on the material (considered to be constant over time) and AUV is the total absorbance of UV light by the mixture of all species, which can be quantified by the Beer–Lambert law27 as

AUV(t)=hF(t),
(5)

where h=1.0mm is the pathlength of the UV light, equivalent to twice the thickness of the coating. The Beer–Lambert law in Eq. (5) predicts a linear relationship between absorbance and molar concentrations, which has been demonstrated to be accurate at sufficiently low molar concentrations.27 

Within the mixture of chemical species, the time rate of change in the molar concentration of SP can be estimated as

dCSP(t)dt=ΦSPISPUV(t)+kCMC(t)=ΦSPϵSPUVCSP(t)F(t)IaUV(t)+kCMC(t),
(6)

where we consider the influence of the MCSP reverse-isomerization process on the concentration of SP as a thermal process with rate constant k.

The time rate of the change in the concentration of MC can be estimated by taking into consideration its generation through Reaction 1 and decomposition through Reaction 2, which reads

dCMC(t)dt=ΦMCIMCUV(t)+ΦSPISPUV(t)kCMC(t)=ΦMCϵMCUVCMC(t)+ΦSPϵSPUVCSP(t)F(t)IaUV(t)kCMC(t).
(7)

Similarly, the concentration of SA is determined simultaneously by Reactions 2 and 3 as

dCSA(t)dt=ΦSAISAUV(t)+ΦMCIMCUV(t)=ΦSAϵSAUVCSA(t)+ΦMCϵMCUVCMC(t)F(t)IaUV(t).
(8)

Equations (6)–(8) constitute a system of nonlinear, coupled differential equations governing the evolution of the concentration of the chemical species, which are subject to the following initial conditions:

CSP(0)=c0,CMC(0)=0,CSA(0)=0.
(9)

The color of the webbings can be readily inferred from the concentrations of all species. Specifically, at a constant incident visible light intensity I0vis, the intensity transmitted through the material can be quantified through

Ivis(t)=I0vis10Avis(t),
(10)

where Avis is the absorbance of visible light, determined again through the Beer–Lambert law,

Avis(t)=h[ϵSPvisCSP(t)+ϵMCvisCMC(t)+ϵSAvisCSA(t)],
(11)

where ϵ()vis is the light extinction coefficient of visible light. Consistent with Fig. 3, we focus on the absorbance of visible light in the yellow spectrum (520580nm) and normalize Ivis in Eq. (10) by I0vis to eliminate dependence of model prediction on the intensity of the light source. We emphasize that in Eqs. (10) and (11), we have neglected the absorbance of visible light by the substrate material. Such a treatment is valid for the webbings considered in this study, which exhibit a white color; substrate materials with different optical properties could lead to different absorbance of visible light.

The solution of the governing equations relies on the knowledge of a series of material constants, most of which can be inferred from past experimental data.9,23,28–30 Details on the relevant data identified from the literature, together with additional tests conducted in this study for the quantification of some material properties, are reported in  Appendix A; these physical parameters are summarized in Table I.

TABLE I.

Parameter values employed in the proposed analytical model.

Parameter (unit)Value
ΦSP (1) 0.5 
k (s−11 × 10−4 
ϵSPUV (M−1 cm−18.42 × 103 
ϵMCUV (M−1 cm−11.03 × 104 
ϵSAUV (M−1 cm−14.74 × 103 
ϵSPvis (M−1 cm−11.12 × 102 
ϵSAvis (M−1 cm−11.46 × 102 
h (mm) 1.0 
I0UV (einstein cm−3 s−15.63 × 10−8 
c0 (M) [7.24 × 10−3, 2.89 × 10−2
Parameter (unit)Value
ΦSP (1) 0.5 
k (s−11 × 10−4 
ϵSPUV (M−1 cm−18.42 × 103 
ϵMCUV (M−1 cm−11.03 × 104 
ϵSAUV (M−1 cm−14.74 × 103 
ϵSPvis (M−1 cm−11.12 × 102 
ϵSAvis (M−1 cm−11.46 × 102 
h (mm) 1.0 
I0UV (einstein cm−3 s−15.63 × 10−8 
c0 (M) [7.24 × 10−3, 2.89 × 10−2

Despite continued efforts devoted to the characterization of the majority of the chemical species involved in our mathematical model,23,29,30 a few material properties are still unknown. Among them, the photodegradation quantum yield of MC has never been quantified, likely due to the difficulties in generating pure open-ring form MC molecules that is essential to the assessment of their rate of degradation. Similarly, the quantum yield of SA has never been reported in the literature. Consequently, the values of ΦMC and ΦSA were treated as free parameters to calibrate the model against experimental observations. In this study, we discovered that the value of ϵMCvis identified from the literature29 was over-estimated, causing a significantly larger absorbance than experimental observations. This over-estimation was likely due to a nonlinearity in the light extinction coefficient emerging at large MC concentrations.31 To mitigate this issue, we treated ϵMCvis as another fitting parameter. Overall, we identified three parameters of the model, consisting of three coupled nonlinear differential equations with other seven parameters taken from the literature.

To quantify the error between the model predicted and the experimentally observed photochromic response, ΔI, we introduced an error function, defined as

E=1T0T|ΔImod(t)ΔIexp(t)|2dt.
(12)

Through an exhaustive search of the parameter space, an optimal fitting that minimized E was obtained. Along with their optimal values, confidence intervals were determined for the fitting parameters ΦMC, ΦSA, and ϵMCvis, corresponding to values that lead to errors that are at most 5% larger than the minimum error.

The proposed analytical model was calibrated by tuning the fitting parameters at each initial dye concentration. As shown in Fig. 3, model predictions were in excellence agreement with experimental data, capturing the main features of the color variation of the webbing, from the initial, rapid darkening to the gradual decoloration at the later stage. The model was also successful in anticipating some salient features noticed from experiments, including an apparent drop in the decay rate at approximately t=510days at 0.75 and 1.00wt.% initial dye concentrations and the complete bleaching of webbings at 0.25 and 0.50wt.% initial dye concentrations that resulted in a brighter color than their initial state.

To elucidate the mechanisms underlying the multi-timescale photochromic responses, we examined the time-histories of the concentrations of all chemical species in Fig. 4. The three species exhibited a distinct dynamics associated with different time scales, which appeared largely independent of the initial SP concentrations. Consistent with previous studies,16,29,32 the SPMC isomerization was elicited immediately upon UV irradiation, leading to a rapid decrease in CSP and an increase in CMC within a few hours. This could explain the fast peaking of the webbings’ darkness shown in Fig. 3.

FIG. 4.

Time-histories of the concentrations of (a) SP, (b) MC, and (c) SA during photo-degradation. The legend indicates the initial wt. % of SP.

FIG. 4.

Time-histories of the concentrations of (a) SP, (b) MC, and (c) SA during photo-degradation. The legend indicates the initial wt. % of SP.

Close modal

In contrast to SP, the evolution of MC occurred over a relatively longer time scale, with the decay in its concentration spanning several days. The slower decay could be attributed to a higher energy level required for the cleavage of the C=C and NCH3 bonds. Another contributing factor could be the molecular structure of MC. At sufficiently high concentrations, the MC molecules could aggregate through dipole–dipole interactions and π-stacking, forming “H-aggregates” or “J-aggregates.”5 The aggregated MC molecules are more stable and would likely require a higher energy level for decomposition.

The decay rate of SA was observed to be slower than both SP and MC. At the lowest initial dye concentration, the evolution of SA from its peak concentration to complete decomposition spanned a total of 20 days. At the highest concentration, SA was not fully decomposed by the end of 56days of irradiation, with 16% of SA still remaining. The slower decay rate was likely a result of a higher energy required for the further decomposition of SA into smaller molecules. The varying decomposition rates of the three species was mirrored by the values of their quantum yield determined through model calibration, satisfying ΦSP>ΦMC>ΦSA (see Table II).

TABLE II.

Optimal values and 95% confidence intervals (CIs) of the fitting parameters for the analytical model.

wt. %ΦMC (1)ΦSA (1)ϵMCvis (M−1 cm−1)
0.25% Optimal value 1.00 × 10−4 4.00 × 10−5 9.80 × 102 
 CI [0.94, 1.06] × 10−4 [3.52, 4.48] × 10−5 [9.21, 10.39] × 102 
0.50% Optimal value 1.95 × 10−4 6.00 × 10−5 5.70 × 102 
 CI [1.76, 2.34] × 10−4 [5.28, 6.36] × 10−5 [5.24, 6.61] × 102 
0.75% Optimal value 3.00 × 10−4 4.70 × 10−5 3.92 × 102 
 CI [2.46, 3.72] × 10−4 [4.32, 5.08] × 10−5 [3.36, 4.76] × 102 
1.00% Optimal value 9.87 × 10−4 4.80 × 10−5 3.78 × 102 
 CI [7.50, 12.83] × 10−4 [4.61, 4.99] × 10−5 [3.31, 5.67] × 102 
wt. %ΦMC (1)ΦSA (1)ϵMCvis (M−1 cm−1)
0.25% Optimal value 1.00 × 10−4 4.00 × 10−5 9.80 × 102 
 CI [0.94, 1.06] × 10−4 [3.52, 4.48] × 10−5 [9.21, 10.39] × 102 
0.50% Optimal value 1.95 × 10−4 6.00 × 10−5 5.70 × 102 
 CI [1.76, 2.34] × 10−4 [5.28, 6.36] × 10−5 [5.24, 6.61] × 102 
0.75% Optimal value 3.00 × 10−4 4.70 × 10−5 3.92 × 102 
 CI [2.46, 3.72] × 10−4 [4.32, 5.08] × 10−5 [3.36, 4.76] × 102 
1.00% Optimal value 9.87 × 10−4 4.80 × 10−5 3.78 × 102 
 CI [7.50, 12.83] × 10−4 [4.61, 4.99] × 10−5 [3.31, 5.67] × 102 

In principle, the material properties determined from model calibration, ΦMC, ΦSA, and ϵMCvis, should be independent of the initial concentrations of SP. While this was the case for ΦSA, which distributed within a narrow range between 4.00×105 and 6.00×105, we discovered that the optimal values of ΦMC and ϵMCvis exhibited a marked dependence on c0, as shown in Table II. Notably, the ϵMCvis values demonstrated a counterintuitive monotonic decrease as a function of c0. This could be attributed to nonlinearities in the Beer–Lambert relationship that could arise at high molecular concentrations.31 Different from the linear dependence of A on C in Eq. (5) that is strictly valid only at small C, the absorbance was found to have a slower rate of increase as a function of molar concentration above a certain threshold. Similar to Tolbin et al.,31 a modified Beer–Lambert relationship that incorporates a nonlinear dependence of A on C is expected to improve the accuracy of the proposed model.

Although the optimal values of ΦMC exhibited an order of magnitude variation, we emphasize that such a wide distribution does not influence the overall performance of the model. To demonstrate model robustness, in  Appendix B, we calibrated the model using the mean values of the fitting parameters averaged among the four dye concentrations. Model predictions were still successful in capturing the main characteristics of the experimental measurements with a moderate increase in the error. We deem the proposed model a reliable means to elucidate the underlying photochemical reactions and predict the photochromic responses of the webbings.

From chin-straps of military helmets to reinforcement structures of parachutes, webbings are employed in a wide range of engineering systems. Due to their pivotal role as load-bearing components, health monitoring techniques that can sense degradation of the webbings’ integrity and mechanical strength are critical to structural safety. In this work, we demonstrated, for the first time, a photochromic webbing that is capable of sensing extended UV irradiation. The webbing exhibited a rich optical response as a function of irradiation time, transitioning from a deep blue color upon a few hours of exposure to a deep brown color after one day of irradiation. Further exposure to UV for several weeks led to a monotonic brightening of the webbing, which was conducive to long-term UV sensing.

The decay rate of the webbings’ color demonstrated a dependence on the initial concentration of the SP dye. Webbings with the lowest dye concentration maintained sensitivity for four weeks, whereas at the highest dye concentration, they exhibited sensing capability after eight weeks. This is a favorable feature that could facilitate design, whereby dye concentration could be customized to meet the lifetime of the targeted applications. In a field setting, the intermittent exposure to the UV component of sunlight as a result of the day/night cycle is another factor that could extend the sensitivity lifetime of the functional coating. With a moderate increase in the initial dye concentration, we anticipate that the photochromic webbing could maintain sensitivity in the field for up to a year.

To elucidate the physical underpinnings of photochromism, we examined the photochemical processes that the SP molecules underwent over their entire sensitivity lifetime. While the short-term color variation could be attributed to the reversible isomerization of SP, the long-term optical response was most likely a result of the photo-oxidation of MC and its degradation products. This photochemical process was described by a chain of photo-induced chemical reactions involving degradation products identified in previous experimental characterizations.9 

A mathematical model was developed to quantitatively elucidate the proposed photochemical process. The model anticipated the rate of degradation of the chemical species based on their quantum yield and their ability to absorb light energy. The temporal evolution of the reactants was captured by a system of coupled, nonlinear ordinary differential equations, offering a basis for the inference of the webbings’ color. Using unknown material properties as calibration parameters, the model was successful in predicting the experimental observations, unveiling the photochemical reactions as a multi-timescale process driven by continued UV irradiation.

The mathematical model was calibrated against experimental data by tuning a set of fitting parameters. In principle, the model should be calibrated through a universal set of fitting parameters for all dye concentrations. Here, we opted for an alternative approach, whereby the model was calibrated for each dye concentration toward improved accuracy in the interpretation of the experimental data. This approach could mitigate potential nonlinearities in the light extinction coefficient at sufficiently high concentrations. The validity of this calibration strategy was evidenced by the consistent values adopted by the fitting parameters, distributing within one order of magnitude across all dye concentrations. Indeed, upon calibration by a universal set of fitting parameters, the model was still capable of capturing the main features of the experimental data at the cost of a moderate increase in the error (see  Appendix B).

A number of future works could be designed to improve our understanding of the photochromic responses of the webbings. The accuracy of the proposed mathematical model relies on the validity of the reconstructed photochemical reactions detailed in Sec. III A. Although the proposed reactions could be indirectly inferred from previous studies, systematic experimental characterizations to pinpoint the reactants and products of each reaction have never been pursued. Future efforts to identify the photodegradation products could rely on 1H-NMR, a standard technique for the diagnosis of the structure of molecules by evaluating their chemical shift, signal intensity, and spin–spin couplings of hydrogen atoms based on magnetic resonance data. Additionally, isotopic labeling techniques combined with NMR (such as 13C-NMR) can be leveraged to infer the photochemical reaction processes. By tracing the stable isotope 13C labeled at specific locations of SP molecules throughout the reaction, the cleavage positions and the formation of new bonds associated with each photodegradation step could be identified.

The accuracy of the proposed model could also benefit from an improved understanding of the nonlinearity in the light extinction coefficients of the molecular species involved in the photochemical reactions. Conventional characterization methods have demonstrated a linear relationship between light absorbance and molecular concentration, which is encapsulated by the Beer–Lambert law.27 However, nonlinearities may arise at high molecular concentrations, whereby the light absorbance by a molecular species could exhibit a slower increase as a function of concentration, leading to a lower equivalent light extinction coefficient. This could partially explain the moderately larger value of the fitted light extinction coefficient of MC at a higher concentration. Future experiments should be designed to characterize the light extinction coefficients of the molecular species at a wide range of concentrations, which could inform the formulation of higher-order absorbance–concentration relationships31 that may improve the model accuracy.

Despite these limitations, the current work contributes the first photochromic webbing that is successful in UV sensing over an extended time period, a favorable feature that may facilitate health monitoring of engineering systems that withstand excessive UV irradiation. The photochemistry-based mathematical model provides an accurate and effective means to predict the photochromic responses, which could inform design toward targeted applications. The fabrication strategy and the physics-based mathematical model could potentially be adapted to realize UV sensing for structures beyond webbings.

This work was supported by the U.S. Navy through Contract Nos. N68936-20-C-0001 and N68936-21-C-0021. The authors thank Ms. Dahlia Milevsky for her assistance in assembling the data acquisition chamber, Mr. Simon Carrillo Segura for his help in preparing the samples and conducting some experimental trials, and Dr. Alain Boldini for useful discussions.

The authors have no conflicts to disclose.

Peng Zhang: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Project administration (lead); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review and editing (supporting). Osgar John Ohanian: Conceptualization (supporting); Formal analysis (supporting); Funding acquisition (equal); Investigation (supporting); Methodology (supporting); Resources (supporting); Supervision (supporting); Validation (supporting); Writing – review and editing (supporting). Maurizio Porfiri: Conceptualization (supporting); Formal analysis (supporting); Funding acquisition (equal); Investigation (supporting); Methodology (supporting); Resources (lead); Supervision (lead); Validation (supporting); Writing – review and editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1. Photochemical properties of SP and MC

Here, we estimate the photochemical properties of SP and MC listed in Table I. The quantum yield of SP was quantified by Brown9 to be ΨSP=0.5. For the SP derivative used in our experiments (6-nitro-8-methoxyBIPS), the thermal constant of its MCSP reverse-isomerization process, k, was not available in the literature. Instead, we estimated this value based on the thermal constant of an alternative derivative, 6-nitroBIPS29,30 to be k=1.0×104s1. Note that 6-nitroBIPS has a similar molecular structure to 6-nitro-8-methoxyBIPS and is expected to be characterized by comparable thermal properties.

The light extinction coefficients of SP at the long-wave UV spectrum, ϵSPUV, and the yellow spectrum, ϵSPvis, were determined from data provided in Darwish et al.29 Based on the absorbance spectrum in Darwish et al.29 (see Fig. SI2 therein), the light extinction coefficient of SP, ϵSP, as a function of the wavelength, λ, is displayed in Fig. 5. The values of ϵSPUV and ϵSPvis were determined as the mean values of ϵSP in the long-wave UV spectrum (λ[315,400]nm) and the yellow spectrum (λ[520,580]nm), respectively. Similarly, the light absorption properties of MC at the long-wave UV spectrum could be estimated from its light extinction coefficient, ϵMC, as shown in Fig. 5. The value of ϵSPUV was determined as the mean value of ϵMC in the long-wave UV spectrum.

FIG. 5.

Light extinction coefficients of SP and MC.

FIG. 5.

Light extinction coefficients of SP and MC.

Close modal

2. Photochemical properties of SA

The optical properties of SA were inferred from the data-base SciFinder.33 Therein, absorbance of SA was quantified between 200 and 500nm. The value of ϵSAUV was determined as the mean value of the estimated light extinction coefficient [see Fig. 6(a)] in the long-wave UV spectrum. To the best of our knowledge, the light extinction coefficient of SA at the yellow spectrum (520580nm) has never been quantified in previous studies. To fill this gap, we conducted additional experiments to measure the light extinction coefficient of SA for visible light.

FIG. 6.

(a) Light extinction coefficients of SA estimated based on data in SciFinder.33 (b) Absorbance of SA of the visible light wavelength quantified through experiments for a range of SA concentrations. (c) Light extinction coefficients of SA over the yellow spectrum, ϵSAvis, for a range of SA concentrations.

FIG. 6.

(a) Light extinction coefficients of SA estimated based on data in SciFinder.33 (b) Absorbance of SA of the visible light wavelength quantified through experiments for a range of SA concentrations. (c) Light extinction coefficients of SA over the yellow spectrum, ϵSAvis, for a range of SA concentrations.

Close modal

SA-doped PDMS films were used to characterize the optical properties of SA. SA-doped PDMS films were fabricated by mixing 5-nitro-3-methoxysalicylaldehyde (CAS No. 17028-61-4, Sigma-Aldrich) with the Sylgard 184 silicone base and curing agent through vigorous stirring. The mixture was cast in a mold and was left to cure at room temperature, producing SA-doped PDMS films of approximately 0.7mm in thickness after 48h. In our tests, films were fabricated with six SA concentrations in the range c[1.4×103,2.9×102]M.

The light extinction coefficient of SA was quantified by measuring the transmitted visible light intensity of the SA-doped PDMS film. Briefly, a SA-doped PDMS film was placed in front of a visible light source, and the light intensity transmitted through the sample was quantified by a spectrometer (OceanOptics, model USB2000+). An LED white light was used as the light source to illuminate the films, producing adequate intensity between 400 and 700nm. The absorbance of SA was estimated based on the intensity of the light source and the transmitted light through Eq. (10), as displayed in Fig. 6(b) for all SA concentrations tested. The light extinction coefficient of SA was evaluated from its absorbance through the relationship A=ϵSAvishc. The mean value of the light extinction coefficient in the yellow spectrum (λ[520,580]nm) was regarded as the value of ϵSAvis for the corresponding SA concentration, as shown in Fig. 6(c). The value of ϵSAvis adopted in our model was the mean value of those displayed in Fig. 6(c).

3. Estimation of I0UV

The value of I0UV was estimated from the intensity of the UVA-340 light source installed in the QUV environmental tester.34 Based on the irradiance of the light source (see Fig. 7), EUV, the UV energy density was estimated through the integration of EUV over the long-wave UV spectrum, which yielded I0UV through a conversion of unit. The UVA-340 light source could provide consistent light intensity over extended illumination periods. As a result, it is reasonable to assume I0UV to be invariant over time.

FIG. 7.

Irradiance of the UV light source in the QUV environmental tester. Data were extracted from the QUV environmental tester operating manual.34 

FIG. 7.

Irradiance of the UV light source in the QUV environmental tester. Data were extracted from the QUV environmental tester operating manual.34 

Close modal

Here, we demonstrate the performance of the proposed analytical model upon calibration with a fixed set of fitting parameters. The calibrated values of ΦMC, ΦSA, and ϵMCvis shown in Table II were averaged across all four initial dye concentrations as Φ¯MC=3.96×104, Φ¯SA=4.88×105, and ϵ¯MCvis=5.80×102M1mol1. These values were implemented in the proposed model Eqs. (6)–(8) to predict the color variation of the webbings.

The comparison between the experimentally measured and the model predicted webbing darkness is displayed in Fig. 8. We noticed that the model captured the trend in the evolution of the webbings’ color for all initial dye concentrations, c0. Compared with Fig. 3, the model predictions agreed well with experimental data for the intermediate initial SP concentrations, 0.50 and 0.75wt.%, while a modest discrepancy could be noticed between the model prediction and experimental results for the lowest and the highest concentrations, 0.25 and 1.00wt.%. At the lowest initial dye concentration, the model predicted earlier complete color bleaching compared with experimental data as a result of an over-estimated decay rate. On the other hand, the model under-estimated the decay rate for webbings with the highest initial dye concentration in the first 10days. Despite these discrepancies, results in Fig. 8 demonstrated that the proposed model was successful in explaining the underlying photochemical mechanisms and anticipating the photochromic responses of the webbing to extended UV irradiation.

FIG. 8.

Experimentally observed darkness of the webbings (dots and errorbars, representing mean values and standard deviations, respectively) overlaid with analytical predictions (dashed curves) calibrated with a universal set of parameters. The legend indicates the initial wt. % of the initial SP concentration.

FIG. 8.

Experimentally observed darkness of the webbings (dots and errorbars, representing mean values and standard deviations, respectively) overlaid with analytical predictions (dashed curves) calibrated with a universal set of parameters. The legend indicates the initial wt. % of the initial SP concentration.

Close modal
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