Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

The cascade unzipping of ladderane reveals dynamic effects in mechanochemistry


Force can induce remarkable non-destructive transformations along a polymer, but we have a limited understanding of the energy transduction and product distribution in tandem mechanochemical reactions. Ladderanes consist of multiple fused cyclobutane rings and have recently been used as monomeric motifs to develop polymers that drastically change their properties in response to force. Here we show that [4]-ladderane always exhibits ‘all-or-none’ cascade mechanoactivations and the same stereochemical distribution of the generated dienes under various conditions and within different polymer backbones. Transition state theory fails to capture the reaction kinetics and explain the observed stereochemical distributions. Ab initio steered molecular dynamics reveals unique non-equilibrium dynamic effects: energy transduction from the first cycloreversion substantially accelerates the second cycloreversion, and bifurcation on the force-modified potential energy surface leads to the product distributions. Our findings illustrate the rich chemistry in closely coupled multi-mechanophores and an exciting potential for effective energy transduction in tandem mechanochemical reactions.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: The mechanochemistry of ladderane/ene consists of tandem cycloreversions.
Fig. 2: Mechanochemistry of chain-centred [4]-ladderene.
Fig. 3: Mechanochemistry of chain-centred [4]-ladderane.
Fig. 4: Mechanochemistry of a multi-mechanophore polymer containing multiple [4]-ladderane units.
Fig. 5: Computational analysis of the unzipping of [4]-ladderane using AISMD under different forces.
Fig. 6: Analysis of the origin of stereochemical product distribution in the mechanochemistry of [4]-ladderane.

Data availability

Optimized geometries for the structures discussed in the text are available in the supplementary files in the online version of the paper. The experimental and simulation data that support the findings of this study are available from the authors upon request.

Code availability

The program TeraChem (v1.92), used for steered ab initio molecular dynamics calculations and reaction path optimization, is available from PetaChem, LLC ( The scripts used to analyse the trajectories are available upon request from T.J.M.


  1. Li, J., Nagamani, C. & Moore, J. S. Polymer mechanochemistry: from destructive to productive. Acc. Chem. Res. 50, 2181–2090 (2015).

    Google Scholar 

  2. Hickenboth, C. R. et al. Biasing reaction pathways with mechanical force. Nature 446, 423–427 (2007).

    CAS  PubMed  Google Scholar 

  3. Lenhardt, J. M. et al. Trapping a diradical transition state by mechanochemical polymer extension. Science 329, 1057–1060 (2010).

    CAS  PubMed  Google Scholar 

  4. Piermattei, A., Karthikeyan, S. & Sijbesma, R. P. Activating catalysts with mechanical force. Nat. Chem. 1, 133–137 (2009).

    CAS  PubMed  Google Scholar 

  5. Davis, D. A. et al. Force-induced activation of covalent bonds in mechanoresponsive polymeric materials. Nature 459, 68–72 (2009).

    CAS  PubMed  Google Scholar 

  6. Robb, M. J. et al. Regioisomer-specific mechanochromism of naphthopyran in polymeric materials. J. Am. Chem. Soc. 138, 12328–12331 (2016).

    CAS  PubMed  Google Scholar 

  7. Chen, Y. et al. Mechanically induced chemiluminescence from polymers incorporating a 1,2-dioxetane unit in the main chain. Nat. Chem. 4, 559–562 (2012).

    CAS  PubMed  Google Scholar 

  8. Ducrot, E., Chen, Y., Bulters, M., Sijbesma, R. P. & Creton, C. Toughening elastomers with sacrificial bonds and watching them break. Science 344, 186–189 (2014).

    CAS  PubMed  Google Scholar 

  9. Larsen, M. B. & Boydston, A. J. ‘Flex-activated’ mechanophores: using polymer mechanochemistry to direct bond bending activation. J. Am. Chem. Soc. 135, 8189–8192 (2013).

    CAS  PubMed  Google Scholar 

  10. Gossweiler, G. R. et al. Mechanochemical activation of covalent bonds in polymers with full and repeatable macroscopic shape recovery. ACS Macro Lett. 3, 216–219 (2014).

    CAS  Google Scholar 

  11. Nagamani, C., Liu, H. & Moore, J. S. Mechanogeneration of acid from oxime sulfonates. J. Am. Chem. Soc. 138, 2540–2543 (2016).

    CAS  PubMed  Google Scholar 

  12. Verstraeten, F., Gostl, R. & Sijbesma, R. P. Stress-induced colouration and crosslinking of polymeric materials by mechanochemical formation of triphenylimidazolyl radicals. Chem. Commun. 52, 8608–8611 (2016).

    CAS  Google Scholar 

  13. Imato, K. et al. Repeatable mechanochemical activation of dynamic covalent bonds in thermoplastic elastomers. Chem. Commun. 52, 10482–10485 (2016).

    CAS  Google Scholar 

  14. Klukovich, H. M., Kouznetsova, T. B., Kean, Z. S., Lenhardt, J. M. & Craig, S. L. A backbone lever-arm effect enhances polymer mechanochemistry. Nat. Chem. 5, 110–114 (2013).

    CAS  PubMed  Google Scholar 

  15. Ong, M. T., Leiding, J., Tao, H., Virshup, A. M. & Martínez, T. J. First principles dynamics and minimum energy pathways for mechanochemical ring opening of cyclobutene. J. Am. Chem. Soc. 131, 6377–6379 (2009).

    CAS  Google Scholar 

  16. Chen, Z. et al. Mechanochemical unzipping of insulating polyladderene to semiconducting polyacetylene. Science 357, 475–479 (2017).

    CAS  PubMed  Google Scholar 

  17. Hermes, M. & Boulatov, R. The entropic and enthalpic contributions to force-dependent dissociation kinetics of the pyrophosphate bond. J. Am. Chem. Soc. 133, 20044–20047 (2011).

    CAS  PubMed  Google Scholar 

  18. Akbulatov, S. et al. Experimentally realized mechanochemistry distinct from force-accelerated scission of loaded bonds. Science 357, 299–303 (2017).

    CAS  PubMed  Google Scholar 

  19. Kryger, M. J. et al. Masked cyanoacrylates unveiled by mechanical force. J. Am. Chem. Soc. 132, 4558–4559 (2010).

    CAS  PubMed  Google Scholar 

  20. Kryger, M. J., Munaretto, A. M. & Moore, J. S. Structure–mechanochemical activity relationships for cyclobutane mechanophores. J. Am. Chem. Soc. 133, 18992–18998 (2011).

    CAS  PubMed  Google Scholar 

  21. Klukovich, H. M., Kean, Z. S., Iacono, S. T. & Craig, S. L. Mechanically induced scission and subsequent thermal remending of perfluorocyclobutane polymers. J. Am. Chem. Soc. 133, 17882–17888 (2011).

    CAS  PubMed  Google Scholar 

  22. Kean, Z. S., Black Ramirez, A. L., Yan, Y. & Craig, S. L. Bicyclo[3.2.0]heptane mechanophores for the non-scissile and photochemically reversible generation of reactive bis-enones. J. Am. Chem. Soc. 134, 12939–12942 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  23. Kean, Z. S., Niu, Z., Hewage, G. B., Rheingold, A. L. & Craig, S. L. Stress-responsive polymers containing cyclobutane core mechanophores: reactivity and mechanistic insights. J. Am. Chem. Soc. 135, 13598–13604 (2013).

    CAS  PubMed  Google Scholar 

  24. Robb, M. J. & Moore, J. S. A retro-Staudinger cycloaddition: mechanochemical cycloelimination of a beta-lactam mechanophore. J. Am. Chem. Soc. 137, 10946–10949 (2015).

    CAS  PubMed  Google Scholar 

  25. Wang, J., Kouznetsova, T. B., Boulatov, R. & Craig, S. L. Mechanical gating of a mechanochemical reaction cascade. Nat. Commun. 7, 13433 (2016).

    PubMed  PubMed Central  Google Scholar 

  26. Bowser, B. H. & Craig, S. L. Empowering mechanochemistry with multi-mechanophore polymer architectures. Polym. Chem. 9, 3583–3593 (2018).

    CAS  Google Scholar 

  27. Nayler, P. & Whiting, M. C. Researches on polyenes. Part III. The synthesis and light absorption of dimethylpolyenes. J. Chem. Soc. 3037–3047 (1955).

  28. Thompson, L. H. & Doraiswamy, L. K. Sonochemistry: science and engineering. Ind. Eng. Chem. Res. 38, 1215–1249 (1999).

    CAS  Google Scholar 

  29. El-Agamey, A. et al. Carotenoid radical chemistry and antioxidant/pro-oxidant properties. Arch. Biochem. Biophys. 430, 37–48 (2004).

    CAS  PubMed  Google Scholar 

  30. Schügerl, F. B. & Kuzmany, H. Optical modes of trans‐polyacetylene. J. Chem. Phys. 74, 953–958 (1981).

    Google Scholar 

  31. Knoll, K. & Schrock, R. R. Preparation of tert-butyl-capped polyenes containing up to 15 double bonds. J. Am. Chem. Soc. 111, 7989–8004 (1989).

    CAS  Google Scholar 

  32. Ribas-Arino, J., Shiga, M. & Marx, D. Mechanochemical transduction of externally applied forces to mechanophores. J. Am. Chem. Soc. 132, 10609–10614 (2010).

    CAS  PubMed  Google Scholar 

  33. Carpenter, B. K. Nonstatistical dynamics in thermal reactions of polyatomic molecules. Annu. Rev. Phys. Chem. 56, 57–89 (2005).

    CAS  PubMed  Google Scholar 

  34. Carpenter, B. K. Energy disposition in reactive intermediates. Chem. Rev. 113, 7265–7286 (2013).

    CAS  PubMed  Google Scholar 

  35. Oyola, Y. & Singleton, D. A. Dynamics and the failure of transition state theory in alkene hydroboration. J. Am. Chem. Soc. 131, 3130–3131 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  36. Bailey, J. O. & Singleton, D. A. Failure and redemption of statistical and nonstatistical rate theories in the hydroboration of alkenes. J. Am. Chem. Soc. 139, 15710–15723 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  37. Doering, W. E., Cheng, X., Lee, K. & Lin, Z. Fate of the intermediate diradicals in the caldera: stereochemistry of thermal stereomutations, (2 + 2) cycloreversions, and (2 + 4) ring-enlargements of cis- and trans-1-cyano-2-(E and Z)-propenyl-cis-3,4-dideuteriocyclobutanes. J. Am. Chem. Soc. 124, 11642–11652 (2002).

    PubMed  Google Scholar 

  38. Collins, P., Kramer, Z. C., Carpenter, B. K., Ezra, G. S. & Wiggins, S. Nonstatistical dynamics on the caldera. J. Chem. Phys. 141, 034111 (2014).

    PubMed  Google Scholar 

  39. Grimme, S. Supramolecular binding thermodynamics by dispersion-corrected density functional theory. Chem. Eur. J. 18, 9955–9964 (2012).

    CAS  PubMed  Google Scholar 

  40. Doubleday, C., Suhrada, C. P. & Houk, K. N. Dynamics of the degenerate rearrangement of bicyclo[3.1.0]hex-2-ene. J. Am. Chem. Soc. 128, 90–94 (2006).

    CAS  PubMed  Google Scholar 

  41. Ess, D. H. Bifurcations on potential energy surfaces of organic reactions. Angew. Chem. Int. Ed. 47, 7592–7601 (2008).

    CAS  Google Scholar 

  42. Hare, S. R. & Tantillo, D. J. Post-transition state bifurcations gain momentum—current state of the field. Pure Appl. Chem. 89, 679–698 (2017).

    CAS  Google Scholar 

  43. Wollenhaupt, M., Schran, C., Krupička, M. & Marx, D. Force-induced catastrophes on energy landscapes: mechanochemical manipulation of downhill and uphill bifurcations explains the ring-opening selectivity of cyclopropanes. ChemPhysChem 19, 837–847 (2018).

    CAS  PubMed  Google Scholar 

  44. Lee, B., Niu, Z., Wang, J., Slebodnick, C. & Craig, S. L. Relative mechanical strengths of weak bonds in sonochemical polymer mechanochemistry. J. Am. Chem. Soc. 137, 10826–10832 (2015).

    CAS  PubMed  Google Scholar 

  45. Ufimtsev, I. S. & Martinez, T. J. Quantum chemistry on graphical processing units. 3. Analytical energy gradients, geometry optimization and first principles molecular dynamics. J. Chem. Theory Comput. 5, 2619–2628 (2009).

    CAS  PubMed  Google Scholar 

Download references


This work was supported by the US Army Research Office under grant no. W911NF-15-1-0525. J.A.M.M. thanks the National Science Foundation for a graduate fellowship. T.J.M. acknowledges support from Office of Naval Research grant no. N00014-12-1-0828. This work used the XStream computational resource supported by the National Science Foundation Major Research Instrumentation programme (ACI-1429830). We thank B. M. Trost for the use of the ozone generator and S. R. Lynch for advice on NMR spectroscopy.

Author information

Authors and Affiliations



Z.C., X.Z., T.J.M. and Y.X. conceived this project. Z.C. and Y.X. designed the experiments and X.Z. and T.J.M. designed the computations. Z.C. and J.Y. prepared the polymers and performed the mechanoactivation, characterizations and data analysis, under the guidance of Y.X. X.Z. performed calculations and data analysis under the guidance of T.J.M. J.A.M.M. synthesized starting materials 1 and 8 under the guidance of N.Z.B. Z.C., X.Z. and Y.X. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Todd J. Martinez or Yan Xia.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary information

Supplementary information, including materials and methods, calculations and synthetic procedures.

Computational dataset

Calculated optimized molecular geometries, in XYZ format and in angstroms, of the minima and transition states of key structures during [4]-ladderane unzipping under different external forces are provided in separate files. The geometries are calculated at UB3LYP/6-31g* level using TeraChem, available from PetaChem, LLC.

Supplementary Video 1

One example of AISMD simulation showing tandem unzipping to 21 (EE, EE product) from 17.

Supplementary Video 2

One example of AISMD simulation showing tandem unzipping to 22 (EE, EZ product) from 17.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chen, Z., Zhu, X., Yang, J. et al. The cascade unzipping of ladderane reveals dynamic effects in mechanochemistry. Nat. Chem. 12, 302–309 (2020).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing