IEEE Robotics & Automation Magazine - December 2020 - 48

In what follows, it will be experimentally demonstrated that the DPBM-FT5000 network with an off-stoichiometric maleimide-to-furan ratio of r = 3/6 = r0.5 has
enough network mobility and reactive components to
heal macroscopic damage at room temperature with high
efficiency. A high network mobility is translated into a
very flexible character, as indicated by the mechanical
properties in Table 1 and 2. Because of the low crosslink
density, the available reactive components on the fracture
surfaces are limited, resulting in slow healing that takes
several days to fully recover initial properties. When an
increase in network mobility is required to perform healing, it is recommended to decrease the crosslink density
by lessening the maleimide-to-furan (r) ratio (as done
with the r0.5 material), rather than reducing both the
maleimide and the furan concentration in a stoichiometric network by using larger FTxs. The excess furan present in the off-stoichiometric network provides more
reactive furan components on the fracture surface, which
enhances healing.

16 s

20 s

Conversion

(a)

1
0.5
0

20
Time (h)
xM

xDA

(b)
Figure 2. (a) The DPBM-FT5000-r0.5 sample with a width of 5.5
mm and a thickness of 2.5 mm is completely cut in two using
a knife. Immediately after cutting, the two halves are manually
put back together at room temperature. After pressing the two
parts together for 3 s, the fracture surfaces merge, and the
sample can already be strained by a few percentage points
without fracturing (a video is available at https://youtu.
be/2A7eKtRixOU). (b) A simulation of the relative maleimide
content (xM), the relative furan content (xF), and the DA
conversion (xDA) as a function of time at 25 °C.

IEEE ROBOTICS & AUTOMATION MAGAZINE

Instantaneous Room Temperature Healing
To check the healing properties at room temperature,
DPBM-FT5000-r0.5 samples with a width of 5.5 mm and a
thickness of 2-2.5 mm were synthesized. A first test was performed by cutting a sample in two with a knife and immediately putting the fracture surfaces back together manually
[Figure 2(a)]. After firmly pressing the two halves together
for 3 s, the pieces were already merged, and the sample could
be strained by a few percentage points without fracturing.
This first nonquantitative experiment illustrates that a small
amount of the healing is instantaneous. When fractures
occur, DA bonds are broken at the surface, and reactive
maleimide and furan components are generated. Upon
bringing the fracture surfaces back into contact only a few
seconds later, the available reactive components start to interact with one another. The first interfacial covalent bonds as
well as physical interaction, such as van der Waals forces, and
the interdiffusion of pendant chains lead to the instantaneous healing of the parts. Since only a few covalent bonds
are immediately formed due to slow reaction kinetics, the
interface still has very limited strength. It mainly relies on
adhesion rather than covalent bonding, and the sample can
resist only very limited stresses.
For all autonomous SH networks (Table 1), this instantaneous healing works only if the fracture surfaces are brought
back into contact soon after damage takes place. Otherwise, the available reactive groups (in this case, maleimide
and furan) will react with one another in the separate
parts. As a result, the healing efficiency decreases significantly if the waiting time between the damage and the
contact of the fracture surfaces is too long [24]. Under the
hypothesis that all bonds are broken at the fracture surfaces, the availability of the reactive maleimide and furan
as a function of time can be modeled using the kinetics/
thermodynamics simulation [Figure 2(b)]. Details on the
simulation can be found in [26]. In Figure 2(b), the conversions are calculated using following equation:

DECEMBER 2020

xM =

6M@
6F@
6DA@
/ xF =
/ x DA =
.(2)
6M 0@
6F0@
6M 0@

Looking at the maleimide content (x M), after 1 h, only 84%
of the reactive maleimide groups that were immediately available after damage occurred are expected to remain present on
the fracture surfaces. After 12 and 24 h, this amount is
reduced to only 23 and 10%, respectively. This emphasizes the
importance of bringing the fracture surfaces back into contact
as soon as possible. Although the duration between the fracture happening and the mending might not influence the
eventual healing efficiency, it most certainly strongly influences the speed of the healing.
Healing Efficiency as a Function
of the Healing Time
Because of the limited number of available reactive components at the fracture surface in low-crosslink-density
DA networks and given the slow reaction kinetics at 25 °C,

https://youtu.be/2A7eKtRixOU https://youtu.be/2A7eKtRixOU

IEEE Robotics & Automation Magazine - December 2020

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - December 2020