Article
https://doi.org/10.1038/s41467-024-50860-6
Molecular control via dynamic bonding
enables material responsiveness in additively
manufactured metallo-polyelectrolytes
Seola Lee
1,4
, Pierre J. Walker
2,4
, Seneca J. Velling
1
,AmylynnChen
1
,
Zane W. Taylor
1
,CyrusJ.B.MFiori
2
, Vatsa Gandhi
1,3
, Zhen-Gang Wang
2
&
Julia R. Greer
1,3
Metallo-polyelectrolytes are versa
tile materials for applications like
fi
ltration,
biomedical devices, and s
ensors, due to their metal-organic synergy. Their
dynamic and reversible electrostatic interactions offer high ionic conductivity,
self-healing, and tunable mechanical properties. However, the knowledge gap
between molecular-level dynamic bonds and continuum-level material prop-
erties persists, largely due to limited
fabrication methods and a lack of theo-
retical design frameworks. To addre
ss this critical gap, we present a
framework, combining theor
etical and experimental insights, highlighting the
interplay of molecular parameters in go
verning material properties. Using
stereolithography-based additive m
anufacturing, we produce durable
metallo-polyelectrolytes gels with tu
nable mechanical properties based on
metal ion valency and polymer charge sparsity. Our approach unveils
mechanistic insights into how these i
nteractions propagate to macroscale
properties, where higher valency ions yield stiffer, tougher materials, and
lower charge sparsity alters material phase behavior. This work enhances
understanding of metallo-polyelectrol
ytes behavior, providing a foundation
for designing advanced functional materials.
Metallo-polyelectrolyte Complexes (MPEC) are a class of soft mate-
rials that exhibit unique mechanical and physical properties through
reversible electrostatic interactions between dynamic crosslinkers
(multivalent metal ions) and charged polymer chains. MPECs consist
of polyanions that are electrostatically crosslinked by labile metal
cations with secondary metal
–
ligand coordination
1
–
3
. In concert with
the polymer chain conformations that arise from electrostatic
interactions, these molecular-level processes govern global phe-
nomena in the gels. For example, the local coordination environment
yields distinct stiffness response
4
,
5
, while the oxidation state of the
metal ion has a signi
fi
cant impact on the ionic conductivity
6
. This
molecular-level control offers a wide range of opportunities to
explore for a range of applications
—
from
fi
ltration to biomedical
devices and sensors
7
–
10
.
The multiscale physical behavior of MPEC gels, ranging from
local coordination environment at the atomic level to mesoscale
polymer conformation to macroscopic material properties, is
strongly affected by the chemical nature of metal complexation
1
,
11
,
12
,
solution pH
13
and solvent quality
14
. The knowledge gap between the
molecular-level chemistry of the dynamic bonds and the
continuum-level material properties, combined with the lack of
mechanistic insight from theory and simulations, have limited the
development and utilization of this class of materials in real-world
applications
2
. Existing state-of-the-art fabrication methods are
Received: 28 November 2023
Accepted: 23 July 2024
Check for updates
1
Division of Engineering and Applied Science, California Institute of Technology, 1200 California Boulevard, Pasadena 91125 CA, USA.
2
Division of Chemistry
and Chemical Engineering, California Institute of Technology, 1200 California Boulevard, Pasadena 91125 CA, USA.
3
Kavli Nanoscience Institute, California
Institute of Technology, 1200 California Boulevard, Pasadena 91125 CA, USA.
4
These authors contributed equally: Seola Lee, Pierre J. Walker.
e-mail:
seolalee@caltech.edu
Nature Communications
| (2024) 15:6850
1
1234567890():,;
1234567890():,;
typically complicated and require multiple steps of solution-based
metallo-polyelectrolyte synthesis
2
,
15
to produce samples, most of
which have been reported to lack long-term stability, suffering
from inhomogeneity, and in some cases requiring the addition of
non-dynamic covalent crosslinkers for synthesis
11
,
16
. The use of
theoretical methods to gain intuition of and alleviate these experi-
mental complications is also hampered by computational chal-
lenges, arising from the large range of length and time scales
involved
2
,
12
,
17
,
18
.
To close this substantial knowledge gap between the molecular-
level chemistry of dynamic bonds and the continuum-level material
properties, we fabricated homogeneous, stable, and long-lived poly(-
acrylic acid) (PAA) MPEC gels using a single-step stereolithography and
conducted a theory-guided, physically-informed multi-scale study of
MPEC gels. Through holistic material characterization, we probe the
relevant length scales to corroborate theoretical and computational
predictions. Based on these
fi
ndings, we present a roadmap that out-
lines the effect of chemical composition on the MPEC gel properties
that can be used to tailor their functionality and responsiveness at the
material level. The overall framework and chemical species explored in
this work are common in soft materials formed with dynamic bonds,
which renders our
fi
ndings readily applicable to different material
systems.
Results
Chemically-tunable synthesis of MPECs
We synthesized acrylate-based MPECs using a facile, single-step fab-
rication method via Liquid Crystal Display (LCD)-stereolithography.
We
fi
rst prepared a homogeneous photoresin solution that consisted
of acrylic acid (AA) monomers and sodium acrylate (SA) co-monomer
buffer that serve as chain builders, combined with metal ion
species as dynamic crosslinkers. As illustrated in Fig.
1
a, PAA was
formed by photopolymerization, initiated by addition of ethyl (2,4,6-
trimethylbenzoyl) phenylphosphinate (TPO-L) photoinitiator and tar-
trazine UV blocker (yellow-dye). To produce environmentally-stable,
high-longevity materials, glycerol and water were used as co-solvents
to suppress gel dehydration. For fair comparison, most of synthesis
parameters, except the metal valency and system pH, were kept con-
sistent between the gels. The total monomer concentration was kept
constant at 8.8 M to ensure consistent polymerization. Concurrently,
the maximum number of potential carboxylate
–
metal cation bonds
was conserved at 2 mol% of monomer concentration, irrespective of
the number of available binding sites on the polymer chains (see
details in Methods and Supplementary Tables 1 and 2). The 3D-printed
gels, after post processing, maintained their mass at 85%
–
90% of the
as-printed state for more than 90 days (Supplementary Fig. 2). The-
mogravimentric analysis (TGA) con
fi
rms that all equilibrated gels,
Dynamic crosslinker
(Metal salt)
Acrylic acid (AA)
Photo-blocker
(Dye)
Sodium
acrylate (SA)
Solvent = Water/NaOH + Glycerol + DMF
Resin formulation
Photo-Initiator
a
b
Al
3+
Fe
3+
Cr
3+
Ga
3+
Ni
2+
Ca
2+
Zn
2+
Co
2+
Na
+
Li
+
c
UV Source
LCD Screen
Transparent film
Movable
Build plate
Vat
LCD-Stereolithography
Photo-resin
d
e
0
-3
-2
-1
1
Multivalent metal cation
Polyanion Charge sparsity
pH scale
0
14
4
2
6
8
10
12
Δ
pH = pH - pKa
Al
3+
Fe
3+
Cr
3+
Ni
2+
Na
+
Ca
2+
(1)
M
3+
M
2+
M
2+
M
3+
M
+
(2)
ℓ = [COOH]/[COO
–
]
10
-1
10
0
10
1
10
2
10
3
M
n+
Carboxylate
group
Multivalent
metal cation
Water/Glycerol
PAA
(protonated)
C
O
O
O
H
H
(3)
M
n+
M
n+
M
n+
M
n+
Fig. 1 | Fabrication of Metallo-polyelectrolytes with different metal ions.
a
Single-pot synthesis of MPEC using stereolithography.
b
Optical images of syn-
thesized photo resins (without tartrazine to show coordination color) and 3D-
printed lattices (with tartrazine) with different metal ions. Scale bar 15 mm.
c
Magni
fi
ed images of 3D-printed octet lattices, showing multiple unit cells. Scale
bar 2 mm.
d
Binding energy vs. metal-carboxylate separation of multivalent metal
ions printable with the developed fabrication method. Dashed curves represent
theoretical metal cation-PAA dipole interactions. The inset highlights how the dif-
ferent charges of metal cations lead to distinct coordination numbers around the
metal center.
e
pH versus charge sparsity of polyanion chains, with varying cation
valency of
fi
xed concentration (2 mol%). Strong association of multivalent metal
cations pushes the equilibrium forwards below the Henderson
–
Hasselbach theory
in the range of pH of interest.
Article
https://doi.org/10.1038/s41467-024-50860-6
Nature Communications
| (2024) 15:6850
2
irrespective of the metal ions and the system pH chosen, contain
~14% ± 2.14% water by weight. This uniformity underscores the con-
sistency in solvent content across all samples (Supplementary Dis-
cussions 6). X-ray
fl
uorescence mapping con
fi
rmed that metal
crosslinkers were homogeneously distributed throughout the sample.
This methodology is generic and can be used to produce a broad range
of material with different compositions through selection of an aqu-
eous anionic monomer and various metal salts in the initial resin.
Figure
1
b demonstrates several multivalent metal species used to
synthesize MPECs into 3D structures with
μ
m to mm resolution and
complex geometries.
To screen for candidate metal nitrate salts we used quantum
Density Functional Theory (DFT) to calculate the binding energy
between various metal cations and carboxylate (acetate) (see Methods
and Fig.
1
d). The binding energy scales linearly with the cation valency,
highlighting control over both the coordination number of complexed
polyanion sites
19
–
21
and the binding energy. We observe that metal ions
with available d-orbitals, such as Ni
2+
and Cr
3+
, typically deviate from
the expected scaling behavior due to the formation of overlapping
π
-
orbitals (see Supplementary Discussions 1). We focus on three repre-
sentative hard-ions for each valency, Na
+
,Ca
2+
,andAl
3+
, to isolate the
effects of valency without the concomitant effects of d-orbital inter-
actions. Discussions relating to the metal identity can be found in
Supplementary Discussion 2. Owing to the low binding energy of Na
+
relative to protonation, pure PAA gels and Na
+
-MPEC gels are used as a
system control, depending on the pH range explored. The weak elec-
trostatic interactions of Na
+
ions allow the monovalent gel to serve as a
reference system where entanglement is the major contributor to the
material response. For comparison, non-dynamic PAA-gels covalently
crosslinked with N,N
’
-Methylenebisacrylamide (MBAA) were also fab-
ricated to demonstrate the contribution of the dynamic bonds. For the
remainder of this article, each crosslinker is represented by a con-
sistent color except where otherwise speci
fi
ed: blue for Na
+
, green for
Ca
2+
, yellow for Al
3+
,andgrayfortheMBAA.
Another key parameter is the pH of the resin, which was con-
trolled using nitric acid and sodium hydroxide, complementary to the
sodium acrylate buffer and nitrate salts. During printing, each ~5 um-
thick layer is saturated in the resin with exposure time of 30 s, allowing
for equilibration with the solution. To minimize pH-dependent chain
conformation effects induced from anion repulsion and the changes in
hydrogen bonding
22
, we maintained the pH in our experiments below
the pKa of polyacrylic acid (~4.5). Fourier Transform Infra-red Spec-
troscopy (FTIR) con
fi
rmed that the change of hydrogen bonding was
minimal within the range of pH explored (Supplementary Discus-
sions 4). The high ionic strength of the gel
23
,
24
, at pH far from the pKa of
the system, allows us to correlate the pH with charge sparsity of
polymerized polyanion following the Henderson
–
Hasselbach (HH)
equation,
〈
ℓ
〉
= [COOH]:[COO
−
]. The strong association of multivalent
metal salts with the charged sites on the polymers shifts the depro-
tonation equilibrium forwards
25
,
26
, reducing the charge sparsity of the
polyanion relative to the HH expectation. We account for this effect
usingamodi
fi
ed HH equation, as shown in Fig.
1
e(seeSupplementary
Discussions 3 for derivation). Under
the experimental conditions, the
modi
fi
ed HH equation demonstrates the availability of suf
fi
cient
number of binding sites on the polymer backbone to complex with the
available metal ions ([COO
−
]
≫
n
[M
n
+
]). Figure
1
econveysthethreepH
regimes experimentally explored in this work: (1) low (1.5 < pH < 2.5),
(2) intermediate (2.5 < pH < 3.0), and (3) high (3.0 < pH < 3.5). Using pH
measurements of the photoresin as a proxy, these values correspond
to the range of polyanion charge sparsity
〈
ℓ
〉
, of ~100:1
–
10:1. (see
Supplementary Table 3).
The presented fabrication platform lends itself to modulating the
two key levers, metal valency and pH, to understand the extent of
molecular control on the material properties. Another lever, albeit less
impactful and more challenging to control, is the solvent content,
which, for the sake of conciseness, is examined in greater detail in
Supplementary Discussions 7.
Structural bonding of metal
–
carboxylates
In Fig.
2
a, representative FTIR spectra are shown for MPEC samples
with Na
+
,Ca
2+
,andAl
3+
. These spectra indicate that metal ions associate
with the polymer, forming stoichiometrically charge balanced com-
plexes. The polyacid nature of MPEC gels gives spectral character for
carboxyl (R-COOH) and carboxylate (R-COO
−
) functional groups, with
the local modes of R-COOH/COO
−
groups identi
fi
ed in Fig.
2
a, at
characteristic carboxyl absorption at ~1760 cm
−
1
(monomer) /
~1700 cm
−
1
(dimer) and alcohol C-OH stretch at ~1240 cm
−
1
.Thecar-
boxylate anion exhibits clear bond-and-a-half character with asym-
metric and symmetric stretches at ~1545 cm
−
1
and ~1410 cm
−
1
,
respectively. Pure PAA gels exhibited the expected carboxyl stretches
only, which indicates that the polymer is completely protonated (see
Supplementary Discussions 4). The presence of symmetric and asym-
metric modes of the carboxylate anion at pH
≲
2.5 indicates com-
plexation of metal cations in MPECs. The structural mode of
complexation of each metal species was revealed by the separation of
the R-COO
−
stretches, using sodium polyacrylate salt at pH = 13 as a
spectral reference
27
,
28
. Taken together with the hard ionic nature of the
selected metal cations, these results support a bidentate chelation of
each metal cation, with direct coordination of the metal species by the
polymer. Maintaining charge neutrality requires correspondence
between the number of coordinating carboxylates and the metal
cation valency, respectively. Our interpretation of the local coordina-
tion environment is further supported by DFT simulations of pure
acetate anions (CH3COO
−
) bonding to each dynamic crosslinker and
their associated IR signature, irrespective of the presence of solvent
(see Supplementary Discussions 4).
Thermal characterization
Differential thermal analysis was conducted at a low-ramp rate of
∼
5
°
C
min
from
−
30 °C to 200 °C to identify phases and phase transitions
of the gels at ambient conditions. The Differential Scanning Calori-
metry (DSC) thermogram (Fig.
2
b, bottom) reveals the existence of a
water solvation shell that participates in two processes: solvating the
polymer and contributing to the metallo
–
polyelectrolyte complexa-
tion. The MPEC gels show a distinct and repeatable non-crystallization
exotherm at 140 °C <
T
< 170 °C prior to an evaporative endotherm,
caused by desolvation and evaporation of water in a manner consistent
with the literature for the dehydration of related oxalate compounds
within a similar temperature range. This evaporative thermal sig-
nature, with associated nucleation of vapor pockets, persists even
when other co-solvents are removed. It is observable in dimethylfor-
mamide free MPECs synthesized by use of a water soluble photo-
initiator, lithium phenyl (2,4,6-trimethylbenzoyl) phosphinate (Sup-
plementary Discussions 7.1.2). Optical micrographs in the insets show
the presence of water vapor pockets within the gels, with no other
observable phase transitions present. Thermogravimetric analysis of
MPECs con
fi
rms that the extent of loosely bound (
≈
15%) and solvated
(
≈
5%) water remains in all equilibrated gels, which allows for segmental
polymer motion and ion exchange (Supplementary Discussions 6).
Dynamic Mechanical Analysis (DMA) demonstrates visually no
dependence of the thermal-phase transitions on metal valency: glassy
regime below 0 °C followed by 10
2
–
10
3
fold decrease in the storage
modulus (
E
0
)around5
–
50 °C, indicative of the glassy-to-rubbery
transition (Fig.
2
b, top). The rubbery phase initiates above 50
–
70 °C,
characterized by enhanced polymer chain mobility at higher tem-
peratures. The thermal signatures from DSC and DMA indicate the
absence of gel melting until the onset of water evaporation at 170 °C.
Water evaporation embrittles the material, increasing
E
0
by a factor of
20
–
30 and leading to unstable measurements of the loss factor
(tan(
δ
)) at temperatures higher than 170 °C (Fig.
2
b, c). This signi
fi
es
Article
https://doi.org/10.1038/s41467-024-50860-6
Nature Communications
| (2024) 15:6850
3
the importance of the solvent phase in mediating the polymer motions
in MPEC gels. Figure
2
c shows that the peak of tan(
δ
) occurs at 15
–
25 °C
for all samples, with a broad transition range in 0
–
50 °C, characteristic
of glass transition
T
g
in radical acrylate chemistries. In contrast to the
similar phase transitions among different metal species, increasing pH
from 1.5 to 3.5 induces a noticeable shift in
T
g
and the emergence of a
secondary transition at 70
–
100 °C, (as seen in Fig.
2
c). This
T
g
shift with
a wider distribution implies a signi
fi
cant effect of pH on polymer
morphology and uniformity.
Mechanical characterization
We conducted uniaxial tensile experiments on dog bone-shaped spe-
cimens at a constant strain rate,
_
ε
≈
0.03 s
−
1
at 25 °C. In Fig.
2
d, we show
the stress
–
strain data for MPEC gels infused with different metal ions
within the low pH regime. This
fi
gure demonstrates a valency-
dependent effect: gels with higher valency metal ions have greater
stiffness and strength, and a lower stretchability. The Young
’
smod-
ulus, estimated as the slope of the initial linear regime up to 10% strain,
increases from 0.92 MPa for Na
+
-MPEC gel to 1.30 MPa for Ca
+
-MPEC
Na
+
Ca
2+
Al
3+
Covalent
1.5 2.5
pH
Critical Strain
(%)
Fracture Energy
(kJ/m
2
)
0
50
100
150
0
2
4
6
8
10
Storage modulus
(MPa)
Thermo-Physical behavior
Secondary T
g
T
g
shift
Stiffness and Stretchability
Fracture resistance
Ca
2+
Al
3+
Covalent
(Non-Dynamic)
~1000%
~1500%
0%
Na
+
1.5
2.5
pH
3.5
1.5
2.5 3.0
pH
Na
+
pH increase
Ca
2+
Al
3+
pH increase
pH increase
d
f
g
Strain (%)
Strain (%)
Stress (MPa)
Stress (MPa)
Stress (MPa)
h
e
Stress (MPa)
Exo Endo
transition
Initial (Strain = 0%)
Crack initiation (Strain ~ 85%)
Crack propagation (Strain ~ 225%)
Ca
2+
Al
3+
Heat flow
(Cal/g·s)
Glass
Transition
Leathery-Rubbery
Embrittlement
Al
3+
Covalent (Non-Dynamic)
Ca
2+
Al
3+
Na
+
Ca
2+
Al
3+
Na
+
3.5
1.5
2.5 3.0
pH
Strain (%)
Strain (%)
(i)
(ii)
(iii)
(iv)
(i)
(ii)
(iii)
(iv)
Ca
2+
Al
3+
0
0
200
400 600
200
400 600 800
0.00
0.02
0.04
0.06
(i)
(iv)
(ii)
(iii)
(i)
(ii)
(iii)
Strain (%)
0
200
400
600
800
(iv)
Ca
2+
Na
+
PAA
Wavenumber (cm
-1
)
1800
1600
1400
1200
Transmittance (%)
20
30
40
50
60
70
80
90
a
b
c
800
0
400
800
1200
1600
0
2
4
0
2
4
0
2
4
0
1
4
3
2
0
300
600
1200
1800
900
1500
Temperature (°C)
0
50
100
150
200
Temperature (°C)
0
50
100
150
200
10
0
10
2
10
4
0
-0.1
-0.2
tan ( ) (-)
Na
+
Ca
2+
Al
3+
Covalent
Critical Strain
(%)
Fracture Energy
(kJ/m
2
)
3.0 3.5
pH
0
50
100
150
0
2
4
6
8
10
Stress (-)
Fig. 2 | Material-level properties of the additively manufactured MPECs cross-
linked with Na
+
,Ca
2+
,andAl
3+
in all plots. a
FTIR spectra exhibit signatures of both
carboxyl and carboxylate functional groups, with the later being associated with
bidentate chelation of Na
+
,Ca
2+
,andAl
3+
.
b
Storage modulus with overall DSC
thermogram and
c
Loss factor of MPECs at different pH (curves are vertically
shifted for visual aid). Inset: Optical images of water pocket formed within gel. Scale
bar 2 mm. Different linestyles on the pH scale in inset represents pH regime of the
characterized gels.
d
Experimental stress
–
strain data of gels crosslinked with each
metal crosslinks versus with MBAA under uniaxial tensile loading. Inset: Optical
images of Ca
2+
stretchability. Scale bar 10 mm.
e
MD simulation snapshots (top) and
stress
–
strain data (bottom) for different valency (left: divalent, right: trivalent) and
charges parsity (solid: high sparsity, dashed: low sparsity) under uniaxial tensile
loading.
f
Experimental stress
—
strain data as a function of pH, which shows
degradation in mechanical performance in increasingly alkaline environments.
g
Optical snapshots obtained at strains of 0%, 85%, and 225% during quasi-static
fracture experiments on MPEC samples subjected to pure shear loading. Scale bar
20 mm.
h
Box plots depicting fracture energy and critical strain for crack initiation
calculated based on stress
–
strain data (inset) during fracture experiments for
charge-sparse MPEC (left panel) and charge-dense MPEC (right panel).
Article
https://doi.org/10.1038/s41467-024-50860-6
Nature Communications
| (2024) 15:6850
4
gel to 2.82 MPa for Al
+
-MPEC gel. The stresses and strains at rupture are
2.68 MPa and 1750% for the Na
+
-MPEC gel, 3.12 MPa and 1600% for the
Ca
2+
-MPECgel,and3.56MPaand870%fortheAl
3+
-MPEC gel. These
results reveal that despite the maximum number of potential
carboxylate
–
metal bonds being kept constant for all gels, local func-
tionality induces a noticeable difference in mechanical response. The
covalently-crosslinked gel, shown in Fig.
2
d, has a similar elastic
modulus to the mono- and divalent gels, most probably due to similar
molecular network connectivity, which governs the material proper-
ties at low strains
29
. The permanent nature of covalent bonds leads to
stiffening of the gel at larger strains and results in limited stretchability
of 550%. This implies that the dynamic ion crosslinkers can dissociate
at the time scale of the applied deformation, allowing stretched chain
relaxation and a local slip-and-stick motion of bonds under stress
(Supplementary Fig. 4).
In Fig.
2
e (solid lines), the mechanical response of the
experimentally-equivalent polyelectrolyte gel networks in the low pH
regime obtained from coarse-grained Molecular-Dynamics (MD)
simulations is shown. These simulations qualitatively reproduce the
trends of metal ion valency on gel
stiffness. The evolution of the
polymer network at different strains (Fig.
2
e, top) reveals that polymer
chains in the divalent gels are able to re-orient along the loading
direction during uniaxial deformation; in the trivalent gels, the poly-
mer chains are more-closely packed and tend to form large percolating
structures through the dynamic crosslinks (clusters) that inhibit re-
orientation. This behavior is supported by the observation that triva-
lent gels maintain a higher fraction of inter-crosslinked metal ions,
f
inter
than that of divalent gels under high strains (Supplementary Fig. 5).
The MD simulations predict that reducing the charge sparsity on
the polyanion (increasing pH) leads to a reduction in
f
inter
relative to
the high sparsity system, with a corresponding reduction in gel stiff-
ness (dashed lines in Fig.
2
e, bottom). This is consistent with experi-
mental results, shown in Fig.
2
f. Gels with charge-dense polyanions
exhibit a 2 × reduction in modulus and tensile strength and a con-
comitant decrease of tensile strain from >1600% to 1000% for Na
+
-and
Ca
2+
-MPEC samples. The stiffness and stretchability of Al
3+
-MPEC gels
are reduced by a lesser amount.
To probe the effects of the molecular-level controls on the poly-
mer network topology, we conducted pure shear fracture experiments
of MPECs. Using a notched thin gel sheets in MTS load frame (MTS
Systems Co., Eden Prairie, MN), we followed the methodology
fi
rst
developed by Thomas, Rivlin, and Lake
30
,
31
and more recently adapted
to probe fracture of tough hydrogels
32
(Details in Methods and Sup-
plementary Fig. 6). During the experiment, a thin MPEC sample with
dimensions (
W
×
H
0
×
th
)of40×10×1.5mm
3
and an initial notch (
a
0
)
of 16 mm (
a
0
/
W
= 0.4) was stretched uniaxially at a strain rate of
_
ε
≈
0.02 s
−
1
, to induce crack propagation from the notch until complete
sample rupture (Fig.
2
g). We used Digital Image Correlation (DIC) to
capture the exact event of crack initiation, de
fi
ned as critical strain (
ε
c
),
which allowed for calculating the fracture energy,
Γ
=
H
0
R
ε
c
0
σ
d
λ
.
In Fig.
2
h, we show the
Γ
and
ε
c
for MPEC samples cross-
linked with each metal ion and d
emonstrate that the fracture
energy increases with stiffness. In a range of pH of 1.5
–
2.5
(left panel), the Al
3+
-MPEC gels achieve fracture energies of
7.32 ± 1.04 kJ/m
2
,
≈
50% greater than that of the Ca
2+
MPEC, whose
fracture energy is 4.66 ± 0.98 kJ/m
2
and
≈
120% higher than that of
the Na
+
-MPECgel,3.27±0.94kJ/m
2
.Weobservedasimilartrend
for higher pH (right panel). Stiffer gels that correspond to MPECs
with highest valency (Al
3+
-MPEC gels) are also the toughest.
Additionally, the critical strain for crack propagation correlates
with fracture energy. As the functionality of the dynamic cross-
linker increases, gels become stiffer and tougher, exhibiting
greater resistance to crack initiation. We
fi
nd all MPEC gels are
2
–
10 times tougher than thei
r covalently crosslinked
counterparts.
Discussions
The experiments in this work reveal different material behavior of
metal ion-coordinated polyelectrolyte gels with distinct molecular
characteristics: metal ion valency and polymer charge sparsity. To gain
insights into how molecular-level interactions govern properties at the
material level, we investigated molecular interactions using a multi-
scale approach
—
from the local coordination environment to gel-
network topology as a function of synthesis parameters.
MD simulations provide a useful platform for probing the impact
of dynamic bonds on the local coordination environment and gel
network topology. Figure
3
a shows the relaxation times of the different
modes within the system and is consistent with the tendency of higher-
valency ions to form stronger bonds, which results in longer ion-pair
relaxation times,
ρ
ion
(0,
t
) by almost an order of magnitude. Polymer
relaxation times, de
fi
ned here using the end-to-end vector auto-
correlation function,
ρ
poly.
(0,
t
), has a similar trend with valency. The
longer bond lifetime of the higher-valency ions and polymer chains
imposes a larger energy barrier for polymer motion and impedes chain
relaxation. The most conspicuous manifestation of the inhibited
polymer motion is the plateau modulus of the polymer in the rubbery
state (Fig.
2
b). Compared to the theoretical limit of the plateau mod-
ulus for purely entangled polymer chains (
G
e
≃
0.12 MPa), pure PAA
and Na
+
-MPEC gels at all pH have almost identical values owing to the
lack of crosslinking (see Supplementary Fig. 8). Multivalent gels devi-
ate from this limit where the plateau modulus scales with valency
(Fig.
3
b). As expected, covalent gels observe the most-limited polymer
motion available with the largest plateau modulus.
Figure
3
a, top also reveals that the ion-pair relaxation,
ρ
ion
(0,
t
), is
affected by changes in polyanion charge sparsity. This arises from the
increased competition between available sites and the metal ions.
However, this decreased ion-pair relaxation time is not signi
fi
cantly
large, in contrast to the polymer end-to-end vector relaxation
time,
ρ
poly
(0,
t
), as shown in Fig.
3
a, bottom. This trend is consistent
with the fact that plateau modulus was not signi
fi
cantly affected by the
pH of the gels (Fig.
3
b and Supplementary Fig. 8). Reducing the charge
sparsity dramatically impacts the polymer relaxation times (Fig.
3
a,
bottom). The relaxation times of the multivalents gels signi
fi
cantly
decrease, approaching the relaxation times of the monovalent gels.
This trend is consistent with the results shown in Fig.
2
f where all
stress-strain curves collapse to that of a Na
+
-MPEC gel. This non-
intuitive shift with decreasing sparsity appears to be correlated with
the evolution of network topology, comprised of intrachain-molecular
and interchain-molecular junctions and loops.
Following the approach of Semenov and Rubinstein
33
(see Meth-
ods and Supplementary Discussions 5 for details), we estimate theo-
retically the impact of charge sparsity on the fraction of interchain-
crosslinks and compared these predictions (lines) to the simulated
results (symbols), shown in Fig.
3
c. The higher functionality of a single
trivalent ion leads to higher fraction
f
inter
compared to a divalent ion.
We observe optimal charge sparsity to occur at a maximum fraction of
interchain-crosslinking metal ions where a balance between entropic
and enthalpic effects is struck. The experimental system described in
this work contains an excess of charged sites relative to metal ion
concentration, a regime where entropic effects dominate (left region
of Fig.
3
c).
The interchain-crosslinks play a key role in the formation of gel
network. In Fig.
3
d, we show the largest cluster size normalized by the
total number of particles as a function of charge sparsity as obtained
from MD. The simulations indicate that the di- and trivalent gels form
clusters which span nearly all polymer chains within the system, with
trivalent gels having the narrowest cluster distribution resulting from
stronger binding and slower relaxation. No pathway to directly
crosslink two chains exists in the monovalent gels, with interchain
entanglements being the only mechanism to form clusters, leading to
smaller clusters. The trend of the cluster size with respect to the charge
Article
https://doi.org/10.1038/s41467-024-50860-6
Nature Communications
| (2024) 15:6850
5
sparsity has a similar trend to the fraction
f
inter
in Fig.
3
c, suggesting
that the distribution of interchain-crosslinks in the gel network
represents the driving force for polymer topology evolution. The dis-
tribution of these clusters also widens with decreasing sparsity, which
may contribute to the faster polymer relaxation times.
Confocal microscopy images of the additively manufactured
MPEC samples with Ca
2+
and Al
3+
(Fig.
3
e, up-down) captures the effect
of valency and pH on the gel microstructure. In higher valency sys-
tems, the gel retains the voxelized printing pattern (50 × 50
μ
m
2
),
indicating the slower ion and polymer relaxation freezes the micro-
structure in-place as it polymerizes. The larger fraction
f
inter
and
stronger binding of higher valency systems result in enhanced
stiffness
34
and toughness
35
due to ef
fi
cient distribution of load across
the chains during mechanical deformation. However, the suppressed
chain and network mobility induces reduced material-level extensi-
bilty and favors chain scission as a failure mechanism under fracture
loading, instead of chain extension or crack deviation within the
network
36
. The effect is apparent from the different crack morphology
during fracture experiments: Ca
2+
samples exhibit signi
fi
cant crack
blunting even at 225% strain; crack tips in Al
3+
-MPEC gels become
sharper immediately after crack opening Fig.
2
g. With increasing pH,
the polymers are able to relax faster and diffuse away from the original
printing pattern, as observed visually in the right panels of Fig.
3
e. This
faster relaxation, coupled with a reduced fraction
f
inter
leading to
more-mobile clusters, is responsible for the gels weakening under
global mechanical perturbation and trading elasticity for a more
viscoelastic/plastic response as veri
fi
ed from the stress relaxation and
recovery experiments (see Supplementary Fig. 12).
With the mechanistic insights drawn from the presented
experiments, simulations, and theory providing a comprehensive
understanding of how molecular-level bonding mechanisms propa-
gate to the material-level properties of MPEC gels, we have identi
fi
ed
and demonstrated the role of metal ion valency and charge sparsity
on their deformation and fracture response. To layout the full para-
meter space of MPECs, we have constructed phase diagrams for the
gels with each metal ion valency and polyanion sparsity using an
associative mean-
fi
eld theory (Fig.
4
a) (see Supplementary Discus-
sions 5 for details). These phase diagrams help identify conditions
where the gel exists as a single phase and where the system will split
into two-phases, with the boundaries denoted by the colored con-
tours. The insets in Fig.
4
a (and in Supplementary Fig. 11), obtained
from gel dissolution in water, demonstrate the typical supernatant-
coacervate phase split observed in polyelectrolytes (seen in both
divalent and trivalent gels). The
‘
notch
’
at low metal ion concentra-
tions in the phase diagram of the trivalent system arises from a gel-
gel phase split, where one phase is more concentrated in trivalent
metal ions. This behavior is unusual and serves as a way to discover
and elucidate material properties (see more experimental results in
Supplementary Fig. 14 - 16).
From the developed theory, the impact of pH can be inferred
from the polymer charge sparsity. A reduction in the charge sparsity
of the polymer dramatically increases the area of the two-phase
Fig. 3 | Ionic and charge sparsity effects on gel microstructure.
a
Autocorrelation functions of the ion-pair (top) and polymer (bottom) end-to-end
vector for MPECs with different ion valencies and charge sparsity obtained from
MD simulations: solid lines correspond to the low pH and dashed ones correspond
to high pH. Higher valency induces slower relaxation for both ion-pairing and
polymer relaxations.
b
Effects of pH and metal ion valency on plateau modulus of
MPEC in the rubbery state. Plateau modulus of MPECs were measured from Fig.
2
b
and the entanglement modulus was analytically estimated (see Supplementary
Fig. 8).
c
Theoretically- (lines) and computationally- (markers with 95% con
fi
dence
interval) predicted fraction of inter-crosslinked ions for divalent (green) and tri-
valent (yellow) systems at different charge sparsity. Dotted line corresponds to the
sparsity where the metal ions perfectly neutralize the polyanion.
d
Violin plot of
simulated cluster distribution in MPECs. Wider distributions represents larger
fl
uctuations of the cluster size. MD snapshots illustrate representative clusters for
each valency.
e
Confocal microscopy conducted at the depth of 50 ± 25 um on as-
printed thin
fi
lms of MPECs showing Poly(acrylic acid) auto
fl
uorescence (purple) at
640 nm where negative void space corresponds to
fl
uid
fi
lled regions. Due to
instantaneous process of vat
–
polymerization, the voxelized printing pattern
(50
μ
m×50
μ
m) is locked in the topology for both Ca
2+
and Al
3+
—
MPEC. Higher pH
of the gels demonstrating severe phase separation of
fl
uid
fi
lled regions from
polymeric region. Scale bar for all images 150 um. The lower-panel schematic
represents the effects of metal ion valency and charge sparsity on the distribu-
tion of inter vs. intrachain-crosslinks and gel microstructure.
Article
https://doi.org/10.1038/s41467-024-50860-6
Nature Communications
| (2024) 15:6850
6