Do self-growing hydrogels grow and strengthen infinitely? Recently, there was a publication [1] (/., YouTube) on self-growing materials using mechanoradically-generated double-network (DN) hydrogels, closely resembling self-strengthening of muscles.


  We used a series of DN gels consisting of poly(2-acrylamido-2-methylpropanesulfonic acid) sodium salt (PNaAMPS) as the brittle network
  and poly(acrylamide) (PAAm) as the stretchable network. Each network is covalently cross-linked.
  
  
  
  Fig. 1. Conceptual scheme of the self-growth of materials induced by mechanical training. (A) A skeletal muscle becomes bigger and stronger
  under the application of repetitive mechanical stress and a continuous nutrient supply through metabolic cycles. (B) As a result, such a tissue is
  initially weakened (purple arrows) but then recovers or even shows enhanced performance (red arrows) due to mechanical stimuli. The green outline indicates one mechanochemical cycle. (C) Our strategy to develop self-growing materials based on mechanical training of DN gels. Mechanical stress leads to breakage of the brittle network (blue), whereas the highly stretchable
  network (pink) maintains the integrity of the gel. The mechanoradicals generated at the broken ends of the brittle network strands trigger polymerization of monomers supplied from the external environment to form a new network
  (orange). The chemistry of the newly formed network can be the same or differ from that of the original brittle network, as required.


The process is reported to be repeatable and reproducible:


  With proper conditions, our DN gel exhibits persistent growth in strength and size under repetitive mechanical training. Two requirements must be satisfied: Enough monomers should be continuously externally supplied, and the newly formed
  network should serve the role of a brittle network that then breaks during the next deformation to trigger subsequent network formation.


However, with muscle growth there are limiting factors such as hormones and bones structure, and even supplying enough protein one cannot grow the mass infinitely*. Considering constant feeding with monomer, is there a theoretical/practical limit for strength and growth for these DN-hydrogels?

*not even Tetsuo Shima — sorry, couldn't resist considering the origin of this work and the anime.

References


Matsuda, T.; Kawakami, R.; Namba, R.; Nakajima, T.; Gong, J. P. Mechanoresponsive Self-Growing Hydrogels Inspired by Muscle Training. Science 2019, 363 (6426), 504–508. https://doi.org/10.1126/science.aau9533.
"Strength" is a dubious quantity. The E-modulus will rise, and as the material swells with more and more monomer diffusing in, it will at some point rupture when the brittle network cracks. Like a fruit gum that was put in water overnight.

I have no idea if the two networks actually stay separated, or if they interconnect more and more. I suspect the latter, with radicals at work. That would make the brittle part softer -> no further hardening, and the soft network more brittle -> it snaps under increasing load.

But the point is moot imho: "Self-healing" makes sense if you had a smaller damage due to light overload. Then this material here can become twice as hard, and you're fine. I don't think it makes sense to "train" sth to become fifty times as strong.