Interactions between nodes in a physical gel network of telechelic polymers; self-consistent field calculations beyond the cell model

Computer modeling of polymer stars in variable solvent conditions: a comparison of MD simulations, self-consistent field (SCF) modeling and novel hybrid Monte Carlo SCF approach

Computer-aided modeling is a systematic approach to grasp the physics of macromolecules, but it remains essential to know when to trust the results and when not. For a polymer star, we consider three approaches: (i) Molecular Dynamics (MD) simulations and implementing a coarse-grained model, (ii) the self-consistent field approach based on a mean-field approximation and implementing the lattice model due to Scheutjens and Fleer (SF-SCF) and (iii) novel hybrid Monte Carlo self-consistent field (MC-SCF) method, which combines a coarse-grained model driven by a Monte Carlo method and a mean-field representation driven by SF-SCF. We compare the performance of these approaches under a wide range of solvent qualities. The MD approach is formally the most exact but suffers from reasonable convergence. The mean-field approach works similarly in all solvent qualities but is quantitatively least accurate. The MC-SCF hybrid allows us to combine the benefits of the simulation route and the effective performance of SCF. We consider the center-to-end distance R_ce, the radius of gyration R_g² of the star and the polymer density profiles φ(r) of polymer-segments in it. All three methods show a good qualitative agreement one to another. The MC-SCF method is in good agreement with the scaling predictions in the whole range of solvent quality values showing that it grasps the essential physics while remaining computationally in bounds.

Toward a neurospheroid niche model: optimizing embedded 3D bioprinting for fabrication of neurospheroid brain-like co-culture constructs

A crucial step in creating reliablein vitroplatforms for neural development and disorder studies is the reproduction of the multicellular three-dimensional (3D) brain microenvironment and the capturing of cell-cell interactions within the model. The power of self-organization of diverse cell types into brain spheroids could be harnessed to study mechanisms underlying brain development trajectory and diseases. A challenge of current 3D organoid and spheroid models grown in petri-dishes is the lack of control over cellular localization and diversity. To overcome this limitation, neural spheroids can be patterned into customizable 3D structures using microfabrication. We developed a 3D brain-like co-culture construct using embedded 3D bioprinting as a flexible solution for composing heterogenous neural populations with neurospheroids and glia. Specifically, neurospheroid-laden free-standing 3D structures were fabricated in an engineered astrocyte-laden support bath resembling a neural stem cell niche environment. A photo-crosslinkable bioink and a thermal-healing supporting bath were engineered to mimic the mechanical modulus of soft tissue while supporting the formation of self-organizing neurospheroids within elaborate 3D networks. Moreover, bioprinted neurospheroid-laden structures exhibited the capability to differentiate into neuronal cells. These brain-like co-cultures could provide a reproducible platform for modeling neurological diseases, neural regeneration, and drug development and repurposing.

(Homo)polymer-mediated colloidal stability of micellar solutions

Despite their wide range of applications, there is a remarkable lack of fundamental understanding about how micelles respond to other components in solution. The colloidal stability of micellar solutions in presence of (homo)polymers is investigated here following a theoretical bottom-up approach. A polymer-mediated micelle-micelle interaction is extracted from changes in the micelle-unimer equilibrium as a function of the inter-micelle distance. The homopolymer-mediated diblock copolymer micelle-micelle interaction is studied both for depletion and adsorption of the homopolymer. The fluffy nature of the solvophilic domain (corona) of the micelle weakens the depletion-induced destabilization. Accumulation of polymers into the corona induces bridging attraction between micelles. In fact, both depletion and adsorption phenomena are regulated by the coronal thickness relative to the size of the added polymer. Penetration of guest compounds into the coronal domain of crew-cut micelles, with a narrower yet denser corona, is less pronounced as for starlike micelles (with a more diffuse corona). Therefore, crew-cut micelles are less sensitive to the effect of added compounds, and hence more suitable for applications in multicomponent systems, such as industrial formulations or biological fluids. The trends observed for the colloidal stability of crew-cut micelles qualitatively match with our experimental observations on aqueous dispersions of polycaprolactone-polyethylene glycol (PCL-PEO) micellar suspensions with added PEO chains.

Simulations of ionization equilibria in weak polyelectrolyte solutions and gels

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

On the Colloidal Stability of Spherical Copolymeric Micelles

Using self-consistent field (SCF) calculations, we systematically quantify the pair interactions between spherical diblock copolymer micelles following a bottom-up approach. From the equilibrium properties of self-assembling micelles at different separation distances, a simple yet insightful pair interaction can be extracted. The SCF results match with an analytical model based upon closed expressions for the free energy change per diblock copolymer in the micelle. To gain insights into the colloidal stability of dilute micelle suspensions, the second virial coefficient normalized by the undistorted micelle volume (B ₂ ^*) is evaluated. For stable micelles (B ₂ ^* ≳ -6), we find a weak dependence of B ₂ ^* on solvophilic block length for varying core-forming block properties (core solvation and block length). The micelle suspension gets unstable (B ₂ ^* ≲ -6) when the corona-forming block crosses Θ-solvent conditions toward poor solvency. In contrast with what is expected from models where the soft nature of the micelle is not taken into account, increasing the effective grafting density of solvophilic tails from the core then leads to colloidal destabilization of the micelle suspension.

A Hybrid Monte Carlo Self-Consistent Field Model of Physical Gels of Telechelic Polymers

We developed a hybrid Monte Carlo self-consistent field technique to model physical gels composed of ABA triblock copolymers and gain insight into the structure and interactions in such gels. The associative A blocks of the polymers are confined to small volumes called nodes, while the B block can move freely as long as it is connected to the A blocks. A Monte Carlo algorithm is used to sample the node configurations on a lattice, and Scheutjens-Fleer self-consistent field (SF-SCF) equations are used to determine the change in free energy. The advantage of this approach over more coarse grained methods is that we do not need to predefine an interaction potential between the nodes. Using this MC-SCF hybrid simulation, we determined the radial distribution functions of the nodes and structure factors and osmotic compressibilities of the gels. For a high number of polymers per node and a solvent-B Flory-Huggins interaction parameter of 0.5, phase separation is predicted. Because of limitations in the simulation volume, we did however not establish the full phase diagram. For comparison, we performed some coarse-grained MC simulations in which the nodes are modeled as single particles with pair potentials extracted from SF-SCF calculations. At intermediate concentrations, these simulations gave qualitatively similar results as the MC-SCF hybrid. However, at relatively low and high polymer volume fractions, the structure of the coarse-grained gels is significantly different because higher-order interactions between the nodes are not accounted for. Finally, we compare the predictions of the MC-SCF simulations with experimental and modeling data on telechelic polymer networks from literature.

Self-Consistent Field Lattice Model for Polymer Networks

A lattice model based on polymer self-consistent field theory is developed to predict the equilibrium statistics of arbitrary polymer networks. For a given network topology, our approach uses moment propagators on a lattice to self-consistently construct the ensemble of polymer conformations and cross-link spatial probability distributions. Remarkably, the calculation can be performed “in the dark”, without any prior knowledge on preferred chain conformations or cross-link positions. Numerical results from the model for a test network exhibit close agreement with molecular dynamics simulations, including when the network is strongly sheared. Our model captures nonaffine deformation, mean-field monomer interactions, cross-link fluctuations, and finite extensibility of chains, yielding predictions that differ markedly from classical rubber elasticity theory for polymer networks. By examining polymer networks with different degrees of interconnectivity, we gain insight into cross-link entropy, an important quantity in the macroscopic behavior of gels and self-healing materials as they are deformed.