A mechanochromic donor-acceptor torsional spring

Mechanochromic polymers are intriguing materials that allow to sense force of specimens under load. Most mechanochromic systems rely on covalent bond scission and hence are two-state systems with optically distinct “on” and “off” states where correlating force with wavelength is usually not possible. Translating force of different magnitude with gradually different wavelength of absorption or emission would open up new possibilities to map and understand force distributions in polymeric materials. Here, we present a mechanochromic donor-acceptor (DA) torsional spring that undergoes force-induced planarization during uniaxial elongation leading to red-shifted absorption and emission spectra. The DA spring is based on ortho-substituted diketopyrrolopyrrole (o-DPP). Covalent incorporation of o-DPP into a rigid yet ductile polyphenylene matrix allows to transduce sufficiently large stress to the DA spring. The mechanically induced deflection from equilibrium geometry of the DA spring is theoretically predicted, in agreement with experiments, and is fully reversible upon stress release.

3 Differential Scanning Calorimetry. DSC measurements were carried out on a DSC 2500 (TA Instruments) in aluminum standard pans under nitrogen atmosphere. Sample masses were between 2.5 and 4.5 mg and the heating-/cooling rate was 10 K min -1 .
Thermogravimetric Analysis. TGA measurements were performed on a Mettler-Toledo TGA/DSC 3+ with HT/1600/557-DTA sensor in nitrogen atmosphere. The heating rate was 10 K min -1 .
Tensile Testing. Stress-strain experiments were carried out on a Linkam TST-350 using a displacement ramp of 5 mm min -1 . A standard specimen shape according to DIN 53504 type 3 was used. The shown values of stress were calculated by considering the constant cross-section area of the specimen's mid-point at 0% strain.

Theoretical Investigation
We modeled the structures within Density functional theory (DFT) as implemented in the GPAW package. 1,2 The smooth Kohn-Sham wave functions were represented on real space grids, with grids spacing of 0.15 Å and the electronic density on grids of 0.075 Å spacing. The grid was ensured to cover at least 4 Å around each atom. The relaxation of the structures is considered converged if no force exceed 0.01 eV/Å. The exchange correlation potential is modeled in the generalized gradient correction modeled as devised by Perdew, Burke and Ernzerhof (PBE). 3 Optical properties are calculated by time dependent DFT (TDDFT) in Casidas linear response formalism. 4,5 The number of unoccupied orbitals considered are chosen to be the same as the number of occupied orbitals. All transitions between Kohn-Sham orbitals within an energy range of 8 eV are considered in the linear response calculations, which is checked for convergence for excitations in the optical range (< 3 eV) of interest here. we already discussed in the main text (Fig. 2), and ii) rotation of only one BrPh ring (α). Both kinds of rotation started from equilibrium geometry with 30° and 67° for p-BrPhDPP and o-BrPhDPP, respectively. In Supplementary Fig. 2a we see that for both cases the rotational barrier of o-BrPhDPP is larger than in p-BrPhDPP due to the strong sterical hindrance between Br and Me. As expected, rotation of one-ring (α) shows about half of the energy barrier compared to the rotation of two rings (α, β). Similarly, a change of both dihedral angles (α, β) is shown to have a higher impact on the CT peak than the rotation of a single ring (α) ( Supplementary Fig. 2b). The modeling of the influence of the external force on the structures was conducted using the constrained geometries to simulated external force (COGEF) strategy. [6][7][8] There the energy path depends on the outer distance between the two atoms in the structure where the external force is thought to act on (see Supplementary Fig. 3). The potential ( ) is obtained via the relaxation of all other degrees of freedom. The parameter d is then increased stepwise. The force can be determined either from the derivative δU ⁄ δd or equivalently from the forces acting on the constrained atoms. The resulting COGEF energies are depicted in Supplementary Fig. 4 and show very spring-like behavior, which allowed assigning an effective spring constant to each structure.
The dihedral angle N-C-C-C between DPP core and Ph ring ( Supplementary Fig. 3) has a severe effect on its CT peak due to effectiveness of the π-orbital overlap (see main text Fig. 2). Figure   3b shows the change in dihedral angles of o-/m-MeOBuDPP with increasing external forces.
The dihedral angles α and β are practically symmetric independent of the external force. The angles of m-MeOBuDPP and o-MeOBuDPP change from 30° to 12° and 58° to 21°, respectively, with an external force. The ortho-derivative shows a larger shift of dihedral angle compared to meta-configuration resulting in a higher mechanochromic response. MeOBuDPP. The star symbols represent the constrained rotation and square and circle represent stress to the orthoand meta-DPP, respectively.
The CT peak shift is not only due to changes in the dihedral angle, but also to other deformations of the DPP molecules. The effect of the deformation itself can be seen from the CT peak difference between pulling (COGEF) and constrained rotation ( The effect of force on the optical spectra for different rotamers is summarized in Supplementary   Fig. 12. The absorption wavelength of the cis rotamers is rather constant in the force range below 1 nN. Interestingly, the cis forms flip to the trans forms due to force, leading to a nonlinear relation between force and CT transition wavelength in this force region. However, the resulting trans structures in c) and d) follow the trend seen in a) and b). Assuming all rotamers to be present with equal probability, the averaged optical response Δλmax,abs/F is 5 ± 1 nm nN -1 and 17 ± 2 nm nN -1 for m-MeOBuDPP and o-MeOBuDPP, repectively.  due to force and only after this, a meaningful force-wavelength relation can be extracted. We therefore use the trans-structure for the fitting process. Assuming all rotamers to be present with equal probability, this leads to an averaged Δλmax,abs/F of 12 ± 1 nm nN -1 and 45 ± 3 nm nN -1 for meta and ortho, respectively.
General synthesis of functionalized poly(meta,meta,para-phenylene) (PmmpP) 6a,b 11  0.76 mol%) and one drop of Aliquat336 were added to a 15 mL screw capped vial, and the mixture was purged with argon for 30 min. After addition of degassed toluene (1.5 mL) and degassed H2O (1.8 mL), the reaction mixture was stirred 24 h at 70 °C. Following cooling to room temperature, the aqueous phase was removed via pipette. The organic phase was diluted with toluene (5 mL) and precipitated in methanol (80 mL). The polymer was purified by Soxhlet extraction with ethyl acetate and chloroform. After concentrating the chloroform fraction under reduced pressure, the polymer was precipitated in methanol (80 mL Fig. 25a) and therefore does not interfere significantly with the DA spring.
One major drawback of the standard dumbbell shape used here is the onset of necking, which does not necessarily occur at the specimen's mid-point where the absorption/emission measurement takes place. For this reason, detection of the mechanochromic response is inevitably delayed until necking reaches this region, and thus artificially suggests a lower sensitivity of strain. For this reason, we carried out additional experiments using the specimens 6a-K and 6b-K shown in Supplementary Fig. 24. The shape of the latter ensures that the area of maximum tensile stress is always in the middle of the specimen and thus enables observation of mechanochromic response for low strains.
Supplementary Figs. 24a and 24b report a series of normalized and non-normalized UV-vis absorption spectra of 6a-K, respectively, during uniaxial tensile testing. With increasing elongation, the absorption band broadens and slightly shifts towards longer wavelengths. In order to enable a clearer observation of changes in absorption, the absorption maxima λmax,abs