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the desired lineage, as well as enable transport or confinement of cells to/within
defect sites. Yet, in spite of the significant progress in polymer-based tissue
engineering during the past decade, important challenges remain to be addressed
in order to restore tissues that serve a predominantly biomechanical function
[
132
-
134
]. Recent experiments demonstrate the existence of high strength double
network polymer-based combinations [
135
] that may serve as potential candidates
for cartilage tissue scaffold development, yet little is known about the atomic
composition and the nanometric structures that lead to the enhanced response.
We have developed a multiscale approach to characterize the nature of this phe-
nomena [
130
], and to provide an in silico framework for developing improved
materials for cell-therapies with high mechanical loading requirements.
Our approach to characterizing the mechanisms and for tuning the mechanical
response of polymer-based hydrogels involves a first principles QM-derived Dreid-
ing force field to investigate the thermodynamic and composition conditions for the
gel point near the Flory-Stockmayer transition in selected double network hydrogel
combinations (poly(acrylamide)-PAAm and poly(2-acrylamido-2-methylpropane-
sulfonic acid)-PAMPS), with
N
,
N
0
-methylene bisacrylamide (NNMBA), and a first-
principles coarse-grain model for describing the long-term dynamics of percolation
based on composition and density ratios between the polymeric and crosslinking
agents. We found that percolation events at particular threshold ratios (between
polymer components and crosslinker concentrations) are a key atomistic mecha-
nism to promote enhanced mechanical strength in crosslinked hydrogel networks.
We used atomic charges and torsional potential energy curves from QM to calculate
single chain statistics (including radius of gyration as a function of degree of poly-
merization). Substituting the radius of gyration in an adjusted continuum model for
percolation from [
136
] led to an estimate of the number of polymer molecules
required to achieve percolation using the critical number density found from our
atomistic simulations (see Fig.
18
). Using our constrained MD with a coarse-grain
potential based on a QM parameterized finite extensible nonlinear elastic (FENE)
[
137
], we have been able to determine percolation thresholds as a function of
composition (i.e., solvent, crosslinking agent concentration, molar ratio between
polymer component, among others) on single and double solvated networks.
Figure
19
shows two snapshots of our coarse-grain representation, on the left
a set of linear poly(acrylamide) chains mixed at a particular proportion with solvent
(water), starter, and crosslinking molecules, and on the right the appearance after
running MD-NVE (from a starting temperature of 300K) of a percolated structure
of poly(acrylamide). Our results are consistent with experimentally measured gel
points and help explain the precipitous loss of the high fracture energy in double
network hydrogels at particular crosslink densities [
138
]. We have also confirmed
the mechanical strengthening process via calculation of elastic constants and visco-
elastic response of the final networked structures, relative to the single network
components. These results will be reported in a separate publication. We were
able to determine the critical cross-link concentrations as a function of starting
monomer concentrations and degree of polymerization required for improved
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