Concentrated $\to$ transient polymer networks (useful as e.g. model biosystems[2])
Strong but exchangeable bonds $\to$ covalent adaptable networks (e.g. vitrimers[3])
[1] A. P. P. Kröger and J. M. J. Paulusse, J. Control. Release (2018) [2] J.-M. Choi, A. S. Hoblehouse, and R. V. Pappu Annu. Rev. Biophys. (2020) [3] W. Denissen, J. M. Winne, and Filip E. Du Prez, Chem. Sci. (2016)
What contributes to the thermodynamics of associative polymers?
I will focus on models that can form both intra- and inter-molecular bonds
At low concentrations polymers don't meet: intra-molecular bonds are more likely
Forming an intra-molecular bond costs entropy
All things being equal, inter-molecular bonds are combinatorially favoured
Overall, the number of inter-molecular bonds increases with density
The thermodynamics of associative polymers - results from literature
According to theory, "simple" associative polymers do not phase separate[1]
The conversion of intra- to inter-molecular bonds is continuous
SCNPs start to bind to each other and form transient polymer networks
Experiments[2] and simulations[3] confirm this picture
[1] A. N. Semenov and . Rubinstein, Macromolecules (1998) [2] D. E. Whitaker, C. S. Mahon, and D. A. Fulton Angew. Chem. (2013) [3] M. Formanek et al., Macromolecules (2021)
Associative polymers models
The goal: control the thermodynamics by manipulating the sequence
Equispaced reactive monomers along the chain
Three models: one, two or three types of (alternating) reactive monomers
Only like-type reactive monomers can bind to each other
The low-density fully-bonded limit
In all three cases the energy is the same
To satisfy all bonds, polymers have to "fold"
Closing a loop costs entropy: the longer the loop, the higher the cost
The largest the distance between "compatible" monomers, the longer the loop
The cost per reactive site is $\approx -4\, k_B$ for $(AAAA)_6$ and $\approx -5\, k_B$ for $(ABCD)_6$
Effective potentials from two-chain simulations
Only intra-molecular bonds $\to$ strong repulsion
Intra- and inter-molecular bonds $\to$ from weakly repulsive to strongly attractive
In the $(AAAA)_6$ system, $\beta V \approx 0$ $\to$ attraction $\approx$ repulsion
All bonds are formed $\to$ the only contribution is entropic
Equations of state in the fully-bonded limit
The $(AAAA)_6$ behaves like an ideal gas in a large density range
Both "designed" systems display a non-monotonic equation of state
Signature of phase separation?
Signature of phase separation!
In the $(AAAA)_6$ system, the interfaces melt
In the designed systems, the density remains heterogeneous
Phase diagram of the (ABAB)$_6$ model
Direct-coexistence simulations
$T$ is fixed, $\epsilon$ is the depth of the attraction between reactive monomers
Robustness checks
Phase separation is retained under extensive variations of the polymer architecture
Conclusions & perspectives
We find a way to controllably tune the behaviour of associative polymers
The resulting phase behaviour is fully determined by entropy
Future work: experimental realisation (with DNA?) and dynamics
Thank you!
Questions?
Reference: L. Rovigatti and F. Sciortino, Phys. Rev. Lett. (2022)
Model & methods - details
Implicit-solvent, coarse-grained description: polymer connectivity (Kremer-Grest) + attraction between the reactive monomers
Molecular dynamics simulations to compute two-body (effective interactions) and many-body (e.g. pressure) quantities
A three-body potential to enforce a single-bond-per-site constraint and enable a bond-swapping mechanism to speed-up the dynamics
The three-body potential
Configuration
V2
$-\epsilon$
$-2\epsilon$
$-\epsilon$
V3
$0$
$\lambda\epsilon$
$0$
V2 + V3
$-\epsilon$
$-2 \epsilon + \lambda\epsilon$
$\epsilon$
The value of $\lambda$ controls the behaviour
$\lambda \geq 1$ $\to$ single-bond-per-patch
$\lambda = 1$ $\to$ free swapping!
F. Sciortino, Eur. Phys. J. E (2017), L. Rovigatti et al., Macromolecules (2018)
Weak dependence of the # of bonds and $\beta V$ on the spacing
Here $M$ is the number of inert monomer separating two nearby attractive monomers
The bond-bond autocorrelation function decays to $\approx 0$
Probability that a bond existing at $t = 0$ is still there at $t = 0$ (two-chain simulations)