[1] The present invention relates to characterization of internal stresses inside materials, in particular residual stresses inside solid polymeric objects produced from liquid polymers.

[2] Producing a solid polymeric material (e.g. in the form of a crystalline polymer or an amorphous solid polymer such as a polymer glass) from liquid polymers (e.g. solution or melt) generally causes accumulation of internal stresses in the final product. These stresses are a type of mechanical stress emerging when solids form from liquids and are intrinsic to the material and its forming process. In this context, such internal stress is also termed residual stress. Internal or residual stresses affect the strength of solid polymeric materials and thus affect deformation and breaking characteristics of objects made from solid polymeric materials. For critical parts in particular, knowledge of internal stresses can be used to evaluate or predict performance of a component made of a solid polymeric material,

[3] Conventional techniques to assess internal stresses are limited to experimentally fracturing or breaking of polymeric objects or theoretically simulating internal forces. A method to determine, and preferably even visualize, internal stresses inside a polymeric material, in particular solid polymers such as polymer glasses, is yet lacking.

[4] It is an objective of the present invention to provide a method of determining internal stress inside a polymeric material, preferably in situ, i.e. while leaving said material intact.

[5] This objective is achieved by a method of measuring internal stress of a material, said material comprising a matrix material and a mechanophore, said mechanophore equilibrating between a compacted state and an extended state dependent on local internal stress environment. The method comprises perturbing mechanophore equilibrium in favor of one of the compacted state or the extended state and measuring recovery rate of the mechanophore equilibrium towards the other of the extended state or the compacted state at one or more than one location within the material and outputting the recovery rate, thereby providing a measure of the internal stress at the one or more than one location.

[6j The method provides localized information on internal stress in the polymeric material by providing a measure of the internal stress via the recovery rate of the mechanophore equilibrium at a particular location in the material . The recovery rate reflects a level of internal stress. This enables measuring an internal stress distribution over the polymeric material under study and adapt material, process and/or product design of an object made from the material to locally and/or globally reduce internal stresses. The invention thus also offers advantages in product prototyping, for example bv shortening design cycles. Determining internal stresses in a prototype may be sufficient to test the prototype and, when needed, adapt its form and/or composition to obtain an improved prototype. Conventional testing of such prototypes in prolonged application tests can be avoided, at least in the first iterations of the design process.

[7] In principle, this method is applicable to various materials, in particular to solid polymeric materials such as polymer glasses, though the invention is not limited to that application. Rather than being limited to polymeric materials or even to polymer glasses, the method is also applicable to other types of amorphous solid polymers. Even internal stresses in polymers in a liquid state can be investigated, for example w'ben solidification has only partly occurred in the process of forming a solid polymeric object. Other suitable polymeric materials include polyurethanes, hydrogels and biopolymers. Even non-polymeric materials may be considered. When the material is a polymeric material, tire matrix material may be formed by a polymer. Though application of the method to other materials is thus conceived and possible, the invention is explained below using the example of a polymeric material, in particular a polymer glass, comprising a polymer as the matrix material,

[8] The term solid polymeric material covers polymers and polymeric compositions, including mixtures, in a solid phase, that is below' their solidification temperature. The term polymer glass covers polymers and compositions of polymers in the glass phase, i.e. below their glass transition temperature. This presumes that the material in question has a solid phase and/or a glass phase, respectively.

[9] A mechanophore is a compound with a response to mechanical force. Mechanophores are molecular probes sensitive to forces in their local environment. In the present invention, mechanophores are used as molecular sensors of local stress inside a material in which the mechanophore is embedded.

[ 10] The present invention is based in part on the insight that mechanophores can be used to sense available space for the mechanophore in a polymeric material, thereby indicating internal forces that work to confine available free space within the polymer network. Such forces and/or space correlate to internal stress of the polymer glass. Less space implies more internal stress. The mechanophore thus acts as a molecular probe or sensor of local internal stress inside the polymer glass. [ 1 1] The mechanophores can be blended into the matrix material such as polymers of the polymeric material when the product is formed. Though covalent linking is possible, it is preferred to simply combine the mechanophores with the polymers by mixing/blending without performing a particular reaction to that end. This increases versatility of the method. Further, physical mixing prevents interfering with the chemical nature of the polymers, so that the polymer glass or the polymer glass object under study exhibits properties mainly due to the unaltered polymers.

[12] Measuring recover}' rate can be performed by conventional techniques, including spectroscopic techniques such as NMR, IR, UV-vis, Raman and fluorescence. The measurement technique determines the type of data that is measured.

[13] Outputting may refer to providing data to a user via a user interface such as a display or to a computer for further processing of the data. The outputting of the recovery' rate means that it is made available in tangible or intangible form and in particular as a measure of the internal stress at the one or more than one location where the recovery' rate is or was measured.

[14] Measuring recovery rate can comprise spectroscopic measurement of the recovery rate. In other words, the measuring of the recovery rate may be performed by spectroscopy. This may involve using a fixed bandwidth or scanning over multiple bandwidth s. Useful technologies include NMR spectroscopy and optical spectroscopies in infrared, visible and/or ultraviolet range, such as absorbance, emission, fluorescence and Raman spectroscopy. Photoluminescent spectroscopy in particular is favored for minimizing mechanical interference with the material under study. [15] Measuring recovery rate comprises perturbing mechanophore equilibrium in favor of one of the compacted state or the extended state and measuring recovery of the mechanophore equilibrium towards the other of the extended state or the compacted state. The measured recovery' of the mechanophore equil ibrium may then provide data associated with the recovery rate of the perturbed mechanophore equilibrium. This recovery' may relate to decrease of the state favored by the perturbation (the one of the compacted state or the extended state) and/or increase of the state not favored, or even unfavored, by the perturbation (the other of the compacted state or the extended state).

[16] Preferably, mechanophore equilibrium is perturbed towards to extended state, which is then again forced back into the compacted state dependent on the local stress environment experienced by the mechanophore. Alternatively, the compacted state can be favored by the perturbation while recovery of the extended state is observed. Both can provide a sensitive measure of local internal stress. In solid or solidified polymers, such as amorphous solid polymers and polymer glasses, perturbing towards the extended state of the mechanophore causes relatively fast recovery towards the compacted state due to compressive forces such material, while extension under compressive stress is generally a slower process. Therefor, perturbing towards the extended state is considered advantageous for faster measurement.

[17] The mechanophore equilibrium may relate to thermodynamic equilibrium between the compacted and the extended state at each location. The polymer glass is preferably studied as it is, without external, macroscopic deformation being applied to it.

[18] Measuring recovery' of the mechanophore equilibrium is preferably performed after ceasing perturbing the mechanophore equilibrium. In other words, perturbation is ended and is leaving the mechanophore equilibrium free to recover. In this way, elastic or plastic deformation of the polymer glass is excluded, for example caused bv external mechanical force that can result in permanent damage. External stress can interfere with measurement of internal stresses and is therefore preferably avoided.

[19] Alternatively or additionally, perturbing the mechanophore equilibrium can comprise excitation of the mechanophore, preferably photoexcitation, more preferably photoexcitation by ultraviolet irradiation. For example, the polymer glass sample can be illuminated to isomerize the mechanophore into its compacted and extended states. This may include probing a fluorescent mechanophore and observing decay over time. One of the states may be selecti vely excited to cause the perturbation of the mechanophore equilibrium, in particular the one of the extended state or the compacted state.

[20] Measuring the recovery' of the mechanophore equilibrium may comprise measuring recovery rate. The measured data may thereby comprise recovery' rate of the mechanophore equilibrium from the perturbed situation to, or at least towards, thermal equilibrium. The recovery rate can reflect decrease of the one of the compacted state or the extended state, favored by the perturbation, and/or reflect increase of the other of the compacted state or the extended state. Any of the spectroscopic techniques mentioned can be employed to measure recovery rate. For example, recovery' rate of the other of the compacted state or the extended state can be measured by absorbance or emission spectroscopy on said state. [21] It is particularly advantageous to employ recover}' rate as a measure of local internal stress. When the state recovers faster, it is less constricted to do so, which indicates less internal stress at the location of the mechanophore molecule. Advantages of measuring rate as opposed to e.g. intensity, is that the absolute amount of mechanophore present at each location is factored out of the measured data. The metric of the internal stress obtained based on recovery rates is therefore less prone to error, in contrast to measuring population data, such as abundance, of mechanophore states at various locations within the sample. In particular since the distribution of mechanopbores throughout the polymer glass is likely to be affected by internal stresses built up during solidification, in particular vitrification, of the polymer glass.

[22] Measuring the recovery rate of the mechanophore equilibrium can additionally or alternatively comprise recording a spectroscopic signal of at least one of the compacted state or the extended state over time, preferably one of absorbance or emission, more preferably luminescence. A preferred example of luminescence is fluorescence, A spectroscopic signal of only the compacted state or the extended state may be recorded, or of both. In particular, the more absorbing, emissive or luminescent of the two states providing the strongest signal is recorded.

[23] Preferably, the method comprises associating a rate constant with the measured recovery rate for each location and outputting the rate constant as the recovery' rate, or at least as part of the recovery rate. The rate constant may thus be comprised by the recovery rate. Said associating may involve fitting of the rate constant to measured recovery, in particular fitting with an exponential function. The rate constant is inversely related to a lifetime reflecting the same recovery process.

[24] The recovery^ rate may comprise the rate constant or lifetime for each location at which it is measured. In other words, the rate constants may form (at least a part of) the recovery rate. Rate of recovery' can be measured by taking multiple measurements over time. A rate constant can be fitted to the measured recovery at each location, e.g. increase of absorbance over time, which time constant can be output as the metric of the internal stress. [25] In general, the method may comprise measuring internal stress inside a material by measuring kinetics conversion between the compacted state and the extended state of the mechanophore, wherein one or more rate constant derived from the measured kinetics of conversion provide a measure of the internal stress. [26] Measuring the recovery rate can be performed under temperature control at one or more than one temperature. A higher temperature can shorten the measurement, e.g. to obtain a recovery rate in a shorter time frame. [27] Additionally or alternatively, the method can comprise quantifying internal stress at die one or more than one location using die recovery' rate measured under temperature control at multiple temperatures. The local stress, experienced as a mechanical force by the mechanophore, can be quantified using temperature-dependent recovery rate, in particular' in the form of an associated rate constant measured at multiple temperatures.

[28] Curves reflecting the measurement of the recovery towards the mechanophore equilibrium after perturbation, can be fitted with the exponential function of Eq. 1 (here assuming a decaying curve), where I and Io are current and initial population of a state, respectively, which may be measured via a spectral intensity, k is the rate constant and t is the elapsed time. A is a fitting parameter.

(Eq. 1) I = / ₀ + A - e~ ^fe - ^£

[29] It is preferred that each curve is measured at a constant temperature. Obtaining rate constant k as a function of temperature T can provide additional insights. The extracted rate constants k can be used in the Arrhenius equation (Eq. 2) to obtain an activation energy’ E _a for the conversion between the compacted and the extended state of the mechanophore. This can be facilitated in the linearized coordinates in a plot of ln(fr) versus 1000ZRT(also termed an Arrhenius plot), where R is the gas constant. The slope change then gives an activation barrier change A£ _a for the mechanophore in the altered environment, for example due to solidification of surrounding polymers, in which case it indicates internal stress due to solidification of the polymer. Such measurements preferably involve measurements above as well as below the solidification temperature or the glass transition temperature T _g of the polymeric material under study.

-Eq (Eq. 2) k = k _o e RT

[30] The values for zVty can be converted to force values using the relation in Eq. 3. The activation barrier is thought to depend on free space available to the mechanophore for converting between the compacted and extended states, which free space is in turn determined by internal stresses in the polymeric material. A change of internal stress inside the polymer, e.g. due to vitrification of the polymer, is thus understood to cause a change of activation energy of the 1 mechanophore. Population kinetics of mechanophore equilibrium is thus used to assess mechanical forces inside a material in which the mechanophore is embedded.

(Eq. 3) F = &EJV

[31] The force F is a quantification of the internal stress experienced by the mechanophore. It can be expressed as a force per mole or per molecule. It is computed with activation length I*, or cubic root of activation volume, which can be estimated experimentally or via molecular modelling. For example, in merocyanine (the extended state of spiropyran) the activation length is 4.6 A, while it is 3.5 A for spiropyran. This shows an example of estimating the internal, local forces experienced by a mechanophore from measuring recovery data on the two states of the mechanophore, in particular via associated rate constants.

[32] The method may comprise imaging the recovery' rate in at least part of the polymer glass or the material more generally. For example, when the recovery' rate is measured at multiple locations, a distribution of internal stress over the polymer glass can be provided. Imaging can be implemented with known techniques, for example by microscopy.

[33] The outputing of the recovery rate may comprise visualizing the recovery rate measured at the one or more than one location. As a result of such visualization, an image may be output. The image may include false-color intensity maps of the local internal stress as determined by measuring the recovery' rate at each location. This image can present any of the measures explained herein, in particular recovery rate, rate constant or lifetime of the at least one of the compacted state and the extended state of the mechanophore. The recovery' rate in the form of measured kinetics at various locations in (a part of) the material can be imaged as representative of a distribution of internal stress therein.

[34] Outputting the recovery rate can in particular comprise mapping the recovery rate in an image at image positions corresponding to the one or more than one location, thereby visualizing a distribution of the internal or residual stress in the polymer glass.

[35] Though it is not required to perform the method, it may be advantageous to provide the polymer material under study. In particular, the method can comprise providing the polymer glass, preferably in the form a polymer glass object, more preferably a prototype. [36] Providing the polymer glass can comprises producing the polymer glass from at least the polymer and the mechanophore. Producing the polymer glass may comprise solidifying the polymer from melt having the mechanophore dispersed therethrough, preferably by vitrification. Vitrification is bringing a polymer melt to below its glass transition temperature. The internal stress may then mainly result from residual stress due to solidification, in particular vitrification.

Other forms of solidification include cross-linking and polymerization reactions. Hie mechanophore can be dispersed through the liquid polymer, preferably as a physical mixture, though it may also be covalently coupled to the polymer. Producing the polymer glass may further include forming it into the polymer glass object, e.g. by forming the yet liquid polymer, such as by injection molding, or by shaping the polymer glass after or during it has solidified.

[37] When the method is directed to measuring internal stress in other materials or object, examples of which are given herein, the method can of course involve providing or producing this other material instead of the polymer glass just mentioned, e.g. by combining at least a matrix material with the mechanophore dispersed therethrough.

[38] The method is applicable to various polymers. The polymer may be a thermoplastic polymer. The polymer may alternatively or additionally comprise a synthetic polymer. [39] The polymer can comprise at least one compound from the polymer groups of: acrylate polymers, methacrylate polymers, polycarbonates, polyolefins, polystyrenes, vinyl polymers or derivatives thereof, preferably poly(methyl methacrylate), poly(tert-butyl methacrylate) and/or polystyrene. [40] Examples of polymers deemed suitable for the method include: poly (methyl acry late), poly(methyl methacrylate), polycarbonate, po1y(tert-butyl methacrylate), polystyrene, poly(vinyl alcohol), poly(vinyl chloride), poly(ethylene terephthalate), polyethylene or polyolefins in general, polypropylene, poly(acrylic acid), poly(lactic acid) and polyoxymethylene. Also, derivatives of the above polymers can be employed, in particular but not necessarily, when these exhibit a polymer glass phase.

[41] The method is also applicable with a wide range of mechanophores. In particular, the mechanophore may transform between the compacted state and the extended state by means of an intramolecular reaction. However, mechanophores exhibiting intermolecular reactions in their response to mechanical forces are also possible. [42] Preferably, the mechanophore is reversibly transformable between the compacted state and the extended state. Reversible may mean that an activation energy for converting between the compacted state and the extended state can be overcome by thermal energies available in the material under study at room temperature.

[43] The compacted state and the extended state may be isomers of the mechanophore. This isomerism may include bond breaking and/or conformational changes to transform from one isomer to another.

[44] The compacted state and the extended state can comprise different reactants defining the mechanophore. The mechanophore may react when transitioning between the compacted state and the extended state by failing apart into two or more molecules, which can preferably again recombine into one or more molecules when reversing the reaction. Examples of such mechanophores include diarylbibenzofuranone, diarylbibenzothiophenonyl, tetraarylsuccinonitrile, and difhiorenylsuccinonitrile, which are radical-based mechanochromophores exhibiting a color change upon reversible reaction involving homolytic bond cleavage and radical formation. Another example is 1,2-dioxane, a mechanophore generating chemiluminescence upon breaking into tw o ketones in an irreversible way. Final examples of mechanophores involving reactants are maleimide-anthracene cycloadducts releasing fluorescent anthracene, and anthracene-dimer mechanophores which can reversibly dimerize triggered by UV irradiation to generate two emissive anthracenes. Some of these and others are based on Diels-Alders reaction mechanisms and exhibit bimolecular reactions that proceed faster trader local compressive stress. Reaction products may be observed by fluorescence or IR spectroscopy.

[45] It is preferred that the mechanophore is dispersed in the polymer as a physical mixture. That is, the mechanophore is not covalently coupled to the polymer. This is preferred for ease of processing and avoiding modification of the polymer, while also providing good measurements of the internal stresses as shown in the examples below.

[46] However, as an alternative, the mechanophore may be covalently coupled with the polymer, preferably at a side of the polymer chain, an end of the polymer chain and/or within the polymer chain. When the mechanophore is defined by different reactants, at least one of these reactants can be covalently coupled with the polymer. Examples of suitable mechanophores include tetraaryl succinonitriles, spiropyran and the other mechanophores mentioned herein, which can be covalently coupled to the polym er, if necessary' via linking moieties. [47] The mechanophore may be a mechanochromophore. A mechanochromophore is a mechanophore in which the transition between the compacted state and the extended state is accompanied by an optically observable change, for example in absorption, emission, and/or luminescent activity, such as fluorescence and phosphorescence. The optically observable change need not be limited to the visible range but can also manifest itself in the infrared or ultraviolet spectrum. In particular, mechanochromic moieties change their absorption spectrum upon mechanical activation. In many cases, the change in absorption is caused by expansion of conjugation in the molecular structure, which leads to a red shift of the absorption maximum.

[48] The compacted state and the extended state of the mechanophore may each have a different spectral response, preferably involving a spectral shift. The mechanophore may be selected on that basis. For example, one of the two states is emissive and/or absorptive in a bandwidth in which the other state is not, or one state is fluorescent while the other is not, etc.

[49] The at least one of the compacted state and the extended state of the mechanophore, i.e. the state(s) of which the recovery rate is measured, may be absorptive, emissi ve or photoluminescent. Or at least a difference in luminescence between the compacted state and the extended state is present so that these states can be distinguished from each other in the measurement, e.g. by color filtering illuminating light and/or emitted light.

[50] The mechanophore may comprises at least one of: spiropyran, naphthopyran, rhodamine, spirothiopyran or derivatives thereof, preferably spiropvran or derivatives thereof. These moieties are preferred as these have proven to be combinable with a wide range of polymers as a physical mixture. Spiropyran (SP) and derivatives therefore represent a compacted state of a mechanophore which is convertible to merocyanine (MC) and associated deri vales representing an extended state of the same mechanophore, the MC state being luminescent in contrast to the SP state. Other examples are naphthopyran, rhodamine and spirothiopyran.

[51] Using a combination of various mechanophores mentioned herein is also considered. This can be advantageous to measure distinct ranges of internal stress, with one mechanophore compound used to provide a measure of the internal stress in each of these ranges. Such mechanophores may be selected based on their respective activation barriers, for example with the aid of Eq. 2 and Eq. 3.

[52] The present invention also provides a computer-implementation of the method . In particular, a computer-readable storage medium carrying instructions that, when executed bv a computer of a prototyping system, cause the prototyping system to perform the method of any of the previous claims. The prototyping system may include an analytical platform to perform the measuring and outputting of the recovery rate in addition to a production platform to provide and/or produce the polymer glass, e.g. by 3D printing, injection molding, mold casting, drop casting, spin coating, extrusion and roiling. The analytical platform may comprise a conventional microscope, preferably equipped with a digital camera to process images. Further, appropriate light sources for excitation of the mechanochromophore, inciting photoluminescence and other interaction with the mechanophore can be provided.

[53] Finally, the invention provides use of a recovery rate of a perturbed mechanophore equilibrium in an object in a computer-implemented method to measure or determine internal stress at one or more than one location within the object, in particular residual stress due to vitrification of the object. The object may be of any of the materials disclosed herein, such as a polymeric material or polymer glass in which the matrix material is a polymer. This use may relate to a computer-implemented method in which internal stress at one or more than one location within the object is determined based on previously recorded data on recovery of mechanophore equilibrium at the one or more than one location. Though manual methods are also conceivable, said method is preferably computer-implemented.

[54] Aspects of the invention are further explained in the following examples dial are further elucidated in the appended figures, in which:

- FIG. 1 A shows an example of a mechanophore with a compacted state and an extended state, here spiropyran (SP) and merocyanine (MC), respectively, which are isomers.

- FIG. IB shows photoinduced and thermal isomerization of SP/MC and associated changes in activation lengths and energetic barriers under mechanical stress.

- FIG. IC shows a typical phase diagram of a polymer capable of forming a polymer glass from a polymer melt as it passing through the glass transition at the glass transition temperature T _g .

- FIG. 2 shows synthesis of poly(methyl methacrylate) (PMMA) samples with different placement of the mechanophore SP in relation to the PMMA chain, w'here p-MIX is a physical mixture of mechanophore and polymer, p-CC is mechanophore covalently coupled in the center of the polymer chain, p-SC is the mechanophore covalently coupled to the side of the polymer chain, and p-CE is the mechanophore covalently coupled to tire end of the polymer chain. Further, FIG. 2 show's photographs of the resulting samples under white light, 405 nm light and after exposure to UV light, respectively.

- FIGS. 3 A - 3D show experimental data for MC-SP equilibria establishment kinetics, each figure presenting data from one of the four different PMMA samples of FIG. 2. In each of these four figures: graph A presents a typical profile for time evolution of a transmittance spectrum recorded at 105°C; graph B presents kinetic traces over a broad temperature -time range (note the log scale used for time axis to reflect a timescale span of several orders of magnitude): and graph C presents an Arrhenius plot with activation barrier change and local force analysis. - FIGS. 4A - 41 address aspects of thermal probe recovery' lifetime (TPRL) imaging as an example of a method to measure recovery rate of mechanophore states and present it as measure of internal stress inside a sample. Two of the samples of FIG. 2, p-CC and p-CE, are analyzed as examples. In particular: FIG. 4A shows setup schematics and processing routine; FIG. 4B shows time -evolution of intensity maps of recorded images; FIG. 4C shows time-evolution of two selected pixels R and B indicated in FIG. 4B; FIG. 4D presents a graph with a lifetime t fitted to the intensity decay profile of each pixel R and B; FIGS. 4E and 4F show recovery lifetime images of p-CC samples compared with recorded intensity' images; FIGS. 4G and 4H show recovery lifetime images of p-CE samples compared with recorded intensity images; FIG. 41 shows the same lifetime images now normalized to average integral lifetime, thus representing the same p-CC and p-CE samples in recovery' lifetime change images.

- FIG. 5 shows an Arrhenius plot for two further polymer materials: polystyrene and poly(tert-butyl acrylate), while the method of analysis corresponds to that of the previous figures.

[55] Nearly all performance polymers experience mechanical stresses within their lifetime. Decades of research in polymer mechanochemistry targeted the molecular level manifestations of mechanical stress and revealed a plethora of stress-induced phenomena at molecular level. A large fraction of this progress can be attributed to the use of mechanophores -- small force sensitive molecules which are the major molecular tools used for investigating stress-induced polymer transformations. A mechanophore can thus be seen as a molecular probe. An example of a mechanophore is the spiropyran (SP) moiety that can undergo reversible ring opening and produce the intense!}' colored luminescent merocyanine (MC) isomer (FIG. 1A). SP-MC isomerization has been proven to allow' tracking of the extent of bond scission upon application of external forces or identical phenomena induced by physical swelling of polymer networks. While swelling or external stress are fairly common types of ex trinsic stress know n to bias mechanophore behavior, the present approach targets internal stresses that are intrinsic and common to the majority of polymers, in particular in their solid state, in the form of internal or residual stresses.

[56] Internal or residual stresses most commonly build up in the polymers as they solidify from their melts or, in some specific cases, crystallize from it. Since formation of polymer solids is ubiquitous, so is the phenomenon of internal stress, that contributes to behavior of polymer parts produced by extrusion, 3D printing and injection molding, among many other production technologies. Distribution of internal stresses and their magnitude can be investigated both theoretically and experimentally, with the latter typically involving extensive testing of prototype components are by assessing macroscopic properties that rarely encompasses molecular level complexity of the real polymers, e.g. by birefringence.

[57] In the present disclosure, it is shown that internal stresses in polymer glass have profound and informative molecular level manifestations. These forces strongly affect photo- and mechanochemistry of mechanophores like spiropyran or derivatives thereof, which can be used to estimate internal stress magnitude and distribution. Specifically, high compressive stresses developed in the course of vitrification inflict large changes to mechanophore isomerization kinetics, which when quantified, allows for unprecedented direct analytical measurement of internal stresses from a molecular level perspective. It is also demonstrated that spiropyran activation in PMMA is topologically sensitive to the extent that mechanophore placement relative to the polymer chain can affect isomerization barriers or completely invert photochemical equilibrium in the SP-MC isomers (FIG. 213). Finally, tire new approach is extended to wide field imaging that enables micro- and macroscopic analysis of stress heterogeneity inside sample such as a polymer object. Spectroscopy and imaging are shown to be simple and practical in their implementation especially when combined with known photothermal equilibria of mechanophores such as spiropyrans.

[58] This disclosure was prompted by investigation of whether kinetics of small molecule transformations can be affected by vitrification and associated internal stress buildup. Spiropyrans proved an excellent probe for this task due to the high robustness and the ease of the spectroscopic analysis of their isomerization. Since the SP-MC transformation is associated with expansion and contraction, mechanical force will affect population of each of these two states of the mechanophore, including SP-MC transformation kinetics. The inventor expected to observe alterations to the activation barrier between the extended and the compacted state of the mechanophore as a consequence of compressive or tensile forces that create additional kinetic bias for either isomerization direction. Further, the inventor resolved to study the temperature dependence of i somerization kinetics to provide a direct measurement of activation barrier for the transformation between the mechanophore isomers

[59] Four sets of samples were prepared for this work (FIG. 2), all featuring the derivatives of a common nitro spiropyran SP-I as a probe or sensory molecule. Sample containing SP unit in the chain center (p-CC) was prepared via RAFT -polymerization using difunctional SP-2 as a chain transfer agent. Further, PMMA samples with SP units located at the chain end (p-CE) or introduced randomly into the sidechain (p-SC) were prepared. These samples contain monofunctional SP derived from SP-4 that ensures a single point of connection to the polymer chain. Finally, a physical mixture (p-MIX) of PMMA polymer and SP-3 was prepared featuring no covalent connection between polymer and SP unit. After preparation, all samples were drop cast from chloroform solution, dried under vacuum at 65 °C overnight and annealed at 125 °C for 10 minutes before analysis.

[60] Examining behavior of tire PMMA samples under white and UV light (405 nm), the qualitative differences in their ability to sustain SP photoisomerization was noted. While the physically mixed SP sample p-MIX readdv converted to MC form under brief exposure to UV light, the p-SC and p-CC samples exhibited suppressed SP activation (see again FIG. 2). Notably, the p-CE sample, where the SP unit is located at the chain end, showed significant degree of MC formation, despite the fact that SP unit was attached to the polymer chain covalently. Having observed these differences, the SP isomerization kinetics were investigated (results presented in FIGS. 3A - 3D). The latter is challenging to investigate in a purely thermal setting as the time necessary to heat the sample might obscure the accuracy of the measurements. Instead, tracking of thermal recovery of the mechanophore after photoinduced isomerization was utilized. In particular, once SP containing samples are equilibrated thermally, the thermal equilibrium can be perturbed by irradiation with UV light (375 nm), shifting it to favor the MC form. Once the UV irradiation is suspended one can track the SP recovery kinetics using absorption spectroscopy (see also FIG. IB).

[61] FIGS. 3 A - 3D present the results of studying the isomerization kinetics under internal stress. It was found that SP isomerization kinetics change dramatically in response to vitrification of all test samples. For example, in the p-MIX sample (FIG. 3A) above the glass transition temperature, a drop of the rate constant down to 85°C in PMMA/SP mixtures was consistent with an activation energy of 151 kJ mol' ¹ for ring closure (MC to SP transformation). Upon vitrification, however, this value drops to 82 kJ -mol" ¹ indicating that mechanical stresses reduce the activation barrier of this reaction by' 69 kJ -mol' ¹ . Given that the ring closure reaction monitored in this experiment is associated with molecular contraction, it is concluded that the change in E _a is associated with compressive stresses developed during vitrification of the polymer. Using the Bell- Evans model, it is estimated that a 69 kJ mol' ¹ change in activation energy corresponds to local compressive forces of ca. 327 pN imposed on mechanophore in the MC state in the PMMA polymer glass. This value is in line with a force of ca. 260 pN reported for the ring opening reaction found by single molecule force spectroscopy. [62] Covalent attachment of the SP unit to the PMMA chain affects the vitrification response of the mechanophore. p-CE samples, with the mechanophoric probe at the chain end, feature a lower of ca. 143 kJ -mor ¹ in the melt state, indicating that even in monofunctional SPs, the isomerization is affected by the presence of the polymer chain in the melt. This sample shows a somewhat lower magnitude of response to vitrification with AE _O = 51 kJ mol’ ¹ (FIG. 3B). These findings are consistent with recent insights reported by the inventor that polymer end groups confine to free volume voids in the vicinity of the polymer chain ends, partially separating the confined molecule from host-induced behavior. Several earlier reports place die estimate of the average free volume element size in PMMA at ca. 5 A in radius, which is close to the MC activation volume of ca. 4.5 A. This indicates the possibility of MC confinement in chain-end labelled samples.

[63] A more profound example of topologically influencing mechanophore behavior is observed when positioning the mechanophore in the polymer backbone, as in the p-CC samples (FIG. 3C). The activation barrier of 110 kJ mol’ ¹ found for ring closure in die melt state is significantly lower than that of mono- and non-functionalized SPs suggesting the additive effect of covalent incorporation of SPs in linear polymers. However, vitrification produces a further decrease of E _a to 47 kJ mol’ ¹ suggesting that a chain center position of the mechanophore in the polymer is subject to much larger forces in absolute terms in both melt and glassy states.

[64] The presence of side groups on the polymer chain is known to affect their rheological behavior, which is understood to imply that the local stresses along the polymer chain might be distributed unevenly with chain center subjected to the highest loads while periphery and side groups of linear polymers experiencing significantly lower local loads. In the p-SC samples (FIG. 3D), the SP is contained at the side of the polymer chain, in particular as a side chain, a location with a high steric congestion. In this arrangement, the composition showed strikingly different behavior compared to the other PMMA samples. Introduction of SP to the polymer side chain led to the complete reversal of the photochemical equilibrium. Namely, photoexcitation of p-SC samples at 405 nm promoted ring closure reaction instead of ring opening reaction, i.e. formation of SP form, rather than colored MC. Thus, an increase of transmittance over time was observed rather than a decrease of transmittance (compared graphs A in FIGS. 3A - 3D).

[65] This behavior allows monitoring the reverse ring opening reaction (SP to MC, i.e. ring closing reaction) associated with mechanophore expansion that, in the presence of compressive stresses, results in an increase of the apparent E _a . The activation barrier of 162 kJ-mol’ ¹ observed in the melt state increased bv 38 kJ-mol’ ¹ as the sample vitrified to ca. 200 kJ mol’ ¹ . This suggests that vitrification inhibits reactions associated with extension and promotes ones associated with contraction. Side chain placement of stress responsive probes provides the lowest magnitude of internal stress at this location. Taken together, the four samples provide insight into internal stress on a molecular level at different topological sites. The method presented here is thus topologysensitive.

[66] FIGS. 4A - 41 present approach and results of measuring recovery rate by thermal probe recovery lifetime (TPRL) imaging. Since tracking mechanophore recovery as utilized above relies on simple spectroscopic measurements, it can easily be replicated in a wide-field imaging setting. For example, recovery of photoactivated MC can be tracked using time-dependence of MC fluorescence intensity. However, it is preferred to combine conventional imaging with local kinetic measurements to produce lifetime images. The latter, unlike intensity data, has the benefit of being independent of probe concentration, while cartying local stress information. To demonstrate the feasibility of this imaging technique, it was performed in an epifluorescence microscope with green light excitation at 65°C, a temperature at which MC recovery is sufficiently rapid so that the whole measurement sequence and associated intensity decay can be performed in under 5 minutes. An image processing setup is depicted in FIG. 4A. Measuring recovery rate involves analysis of intensity evolution in at least on part of pixel of the image (FIG. 4B), fitting of resulting intensity decay profiles (FIGS, 4C and 4D) and reconstruction of resulting images, also here termed “lifetime maps”, where MC ring closure lifetime, reciprocal of rate constant, is used as a pseudocontrast (FIGS. 4E - 41). In this setting, low lifetime represents fast MC decay, i.e. high compressive stress, while high lifetime translates to low' compressive stress experienced by the mechanophores at the location concerned.

[67] Similar to conventional lifetime imaging techniques, such as fluorescence-lifetime imaging microscopy, the data of FIG. 4 reflects fluorophore consumption lifetime rather than fluorophore concentration, making this imaging approach insensitive to irregularities in sample thickness or other imperfections. Further, the method is insensitive to any inhomogeneities in mechanophore concentration that may be caused by solidification/vitrification of the polymeric material in w hich the mechanophore is embedded. This advantages can be seen by comparing the original intensitybased images (left-hand graphs) with the lifetime maps (right-hand graphs) given in FIG. 4E - 4H. Several drop-cast samples of round, cross and filament shapes were examined and it w as found that wide-field imaging reveals stress heterogeneity in all of them. Specifically, local compressive stress accumulations are clearly resolvable immediately beneath edges of all samples, which is expected for melt-quenched samples regardless of their shape. Large deviations from the average MC decay lifetune is also observed within all samples (FIG. 41), which indicates that both positive and negative stresses can accumulate within glassy PMMA. For example, the edges of ail samples show significantly higher lifetime values indicating the low degree of compression, which is consistent with the high surface tension expected to develop at the sample edges as they vitrify. [68] FIG. 5 presents data on polystyrene and poly(tert-butyl acrylate) samples. The data was gathered and analyzed as outline with FIGS. 1 - 4 using the same mechanophore which was here combined with the polymer as a physical mixture. For polystyrene, a difference in activation energy A£' _a = 167 kJ-moT ¹ while for poly(tert-butyl acrylate) it is 154 kJ-moi" ¹ . Using Eq. 3 and an activation volume of 3.5 A, this corresponds with internal stresses experienced by the mechanophore of 790 pN and 730 pN per molecule in the two materials upon vitrification of the polymer from the melt, respectively.

[69] These examples demonstrate that conventional mechanophores have the capacity to capture and characterize the development of internal stresses intrinsic to the majority of solid polymers. The approach is based on characterization of mechanophore thermal isomerization kinetics by spectroscopy to measure internal stresses in PMMA, polystyrene and poly(te:rt-butyl acrylate). It has been determined that these polymers create molecular level forces of 100-300 pN upon vitrification. Importantly, these forces are shown to be topology dependent, with chain center location affected the most in both melt and glassy state. The effects of local environment were found to be strong enough to affect the thermodynamics behind mechanophore speciation, in particular photoinduced spiropyran ring opening was nearly suppressed in favor of ring closure when the mechanophore is placed in an environment with high steric congestion (here at the side of the polymer chain). Finally, the method provides a highly informative and operationally simple way of measuring internal stress. U sing spectroscopy and imaging techniques it is possible to survey polymeric solids for internal stresses, map their heterogeneity and analyze the magnitude of local forces,

[70] In summary, mechanophores are powerful tools of polymer mechanochemistry for characterizing bond rupture and tracking mechanical damage in polymers. Majority of mechanophores are known to respond to external stresses and here, mechanochemical response to internal, residual stresses accumulated during polymer vitrification is presented. While internal stress is intrinsic to polymers that can form solids, it is demonstrated that these stresses dramatically affect mechanochemistry of spiropyran probes and alter their intramolecular isomerization barriers by up to 70 kJ mol’ ¹ . This effect can be observed spectroscopically and can be employed to evaluate local stress values at different polymer locations. The disclosed methodology is thus topologically sensitive. Moreover, the molecular nature of this technique allows for wide field imaging of stress heterogeneities in polymer samples of irregular shapes and dimensions, making it feasible to directly observe stresses inside polymeric materials, in particular stresses that accompany polymer solidification, such as vitrification of a polymer melt into a polymer glass.

[71] Though the invention is described in the context of its application to polymer glasses, the technology of measuring internal stresses using mechanophore states is not in fact limited to that class of materials and can also be applied to polymers in a liquid state such as a solution or a mel t, or in a partly solidified sate, and even to non-polymeric materials. Further examples of the applicability of the technology of mechanophore s tates as described herein include silicones such as poly dimethylsiloxane (PDMS), or biopolymers such as polypeptides, nucleic acids, sugars, cellulose or lignin. In general, the invention can be performed on a material comprising a matrix material and a mechanophore.