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Experimental quantitation of molecular conditions responsible for flow-induced polymer mechanochemistry


Fragmentation of macromolecular solutes in rapid flows is of considerable fundamental and practical importance. The sequence of molecular events preceding chain fracture is poorly understood, because such events cannot be visualized directly but must be inferred from changes in the bulk composition of the flowing solution. Here we describe how analysis of same-chain competition between fracture of a polystyrene chain and isomerization of a chromophore embedded in its backbone yields detailed characterization of the distribution of molecular geometries of mechanochemically reacting chains in sonicated solutions. In our experiments the overstretched (mechanically loaded) chain segment grew and drifted along the backbone on the same timescale as, and in competition with, the mechanochemical reactions. Consequently, only <30% of the backbone of a fragmenting chain is overstretched, with both the maximum force and the maximum reaction probabilities located away from the chain centre. We argue that quantifying intrachain competition is likely to be mechanistically informative for any flow fast enough to fracture polymer chains.

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Fig. 1: Molecular models of flow-induced mechanochemistry and the experimental approach to testing them.
Fig. 2: The studied polymers.
Fig. 3: Summary of sonication experiments.
Fig. 4: Summary of the DFT calculations.
Fig. 5: Illustrative comparisons of experiments with predictions of the molecular models.
Fig. 6: Summary of molecular conditions yielding the observed mechanochemistry.

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Data availability

The data discussed in the main text and Supplementary Information are tabulated in the Supplementary Data file suppdata.mat.

Code availability

This work used a simplified version of the previously reported MATLAB code for simulating the composition of a sonicated solution, provided in Supplementary Information along with the instructions for use. The full code with examples of input/output datasets is available at


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The work was funded by the Engineering and Physical Sciences Research Council under grant EP/L000075/1; R.T.O. received support from the University of Liverpool. We thank S. Akbulatov and L. Anderson for preliminary studies that enabled the design of this project and Waters Corporation for the gift of Acquity ultraperformance liquid chromatography system and the technical help in converting it to SEC.

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Authors and Affiliations



R.T.O. performed all experiments and contributed to data analysis and writing. R.B. designed the study, developed the model and wrote the paper.

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Correspondence to Roman Boulatov.

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Extended data

Extended Data Fig. 1 Summary of the UVvis absorption properties.

(a) Wavelength-dependent extinction coefficients of polystyrene and the two isomers of stiff stilbene, SS, in THF at 30 °C and ~1500 psi (the pressure of the PDA detector). (b) An example of deconvolution of the absorption spectrum of 1c to PS, Z-SS and E-SS contributions using the reference spectra in (a). The plotted data is tabulated in the supplementary data file, suppdata.mat.

Extended Data Fig. 2 The calculated contributions of different backbone bonds to chain fracture.

(a) Calculated force-dependent activation free energies, ΔG for homolysis of the color-matching bonds in the inset structure. ΔG for the C-C bonds of the PS backbone is black. (b) The calculated fraction of mechanochemical fractures of the polymer shown in the inset (n = 125, m = 124) by homolysis of the C-C bond of the PS backbone as a function of fmax of a parabolic force distribution in a macromolecular ensemble with the SS(OCH2CO2(CH2)3O2C)2 moiety distributed as in 1c. The calculations are at uBMK/6-31 + G(d) level in the gas phase. Homolysis of the endocyclic bond of cyclopentane of SS (dark purple line in a) doesn’t fracture the chain but probably destroys SS. Undetectable bleaching of SS in sonicated solutions suggests that this reaction is negligible in our polymers. The plotted data is tabulated in the supplementary data file, suppdata.mat.

Extended Data Fig. 3 An illustrative summary of the capacity of different models to reproduce observed mechanochemistry of 4o.

(a, b) measured MMDs and \({\chi }_{{Z}}\); (c, d) dynamic model; (e, f) overstretched-chain model; (g, h) overstretched segment model. The legend in (a) applies to all panels. The plotted data is tabulated in the supplementary data file, suppdata.mat.

Extended Data Fig. 4 The chain-size-dependent distributions of molecular parameters responsible for observed mechanochemistry from the dynamic model.

(a) the time a chain remains loaded to fmax ≥ 2.5 nN, Δtstretch; (b) fmax at chain fracture; (c, d) the overstretched backbone fraction, λos, at fmax = 2.5 (c) and at chain fracture; (e, f) the backbone fraction between the middle of the overstretched segment and the closest chain terminus, δ, at fmax = 2.5 nN (e) and at chain fracture (f). In all distributions the listed x value correspond to the center of each bin of width 0.3 μs (a), 50 pN (b) and 0.05 (cf). The legend in (a) applies to all panels. The plotted data is tabulated in the supplementary data file, suppdata.mat.

Extended Data Fig. 5 Calculated discrete distributions of the fitted parameters of the dynamic model.

(a) ks; (b) kd; (cf) 0th and 1st order Taylor expansion coefficients (α and β) of the coupling between fmax and the squared fractional length of the overstretched segment, λos2. These distributions apply only to chains with fmax ≥ 2.5 nN: the available data do not allow parameterization of the model at lower forces, because the underlying mechanochemical reactions are too slow to affect the bulk compositions. The distributions of ks, kd and α/β pairs are cross-correlated so that the probability of a mechanochemically-reactive chain to experience a specific combination of the 4 model parameters does not equal the product of the fractions of chains experiencing the same parameter values individually. The bin size of each distribution was selected to eliminate artifactually non-monotonic variations in each parameter due to this cross-correlation. The plotted data is tabulated in the supplementary data file, suppdata.mat.

Extended Data Fig. 6 The calculated localization of mechanochemical reactivity at chain center.

(a) fraction of PS chains fragmenting by dissociation of a backbone C-C bond within the central portion of the backbone of increasing fractional width; (b) fraction of Z-SS moieties that are calculated to isomerize before fracture of a hypothetical poly(Z-SS) chain of the same number of monomers as in (a). The plotted data is tabulated in the supplementary data file, suppdata.mat.

Supplementary information

Supplementary Information

Supplementary Figs. 1–29, discussion, Tables 1–3 and equations (S1)–(S12).

Supplementary Data

All data underlying the results in the paper.

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O’Neill, R.T., Boulatov, R. Experimental quantitation of molecular conditions responsible for flow-induced polymer mechanochemistry. Nat. Chem. 15, 1214–1223 (2023).

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