Simple and Accurate Calibration of the Flory–Huggins Interaction Parameter

Exploring the effects of excipients on complex coacervation

Complex coacervation is an associative liquid-liquid phase separation phenomenon that takes place due to the electrostatic complexation of oppositely-charged polyelectrolytes and the entropic gains associated with the release of bound counterions and rearrangement of solvent. The aqueous nature of coacervation has resulted in its broad use in systems requiring high biocompatibility. The significance of electrostatic interactions in coacervates has meant that studies investigating the phase behaviors of these systems have tended to focus on parameters such as the charge stoichiometry of the polyions, the solution pH, and the ionic strength. However, the equilibrium that exists between the polymer-rich coacervate phase and the polymer-poor supernatant phase represents a balance among attractive electrostatic interactions and excluded volume repulsions as well as osmotic pressure effects. As such, we hypothesize that it should be possible to tune coacervate phase behavior via the addition of non-electrostatic excipients which would partition between the two phases and potentially alter both the solvent quality and the osmotic pressure balance. In particular, our work focuses on small molecule excipients such as sugars, amino acids, and other additives that have a history of use in vaccine formulation. We quantified the ability of these excipients to partition into the coacervate phase, and their potential for destabilizing the phase separation. Furthermore, we demonstrate that these additives can be combined with complex coacervation in the context of a virus formulation.

Thermo-Responsive Polymer-Based Nanoparticles: From Chemical Design to Advanced Applications

Thermo-responsive polymers have emerged as a cutting-edge tool in nanomedicine, paving the way for innovative approaches to targeted drug delivery and advanced therapeutic strategies. These "smart" polymers respond to temperature changes, enabling controlled drug release in pathological environments characterized by high temperatures. By exploiting their unique phase transition, occurring at the lower or upper critical solution temperatures (LCST and UCST), these systems ensure localized therapeutic action, minimizing collateral damage to healthy tissues. The integration of these polymers into nanoparticles with hydrophilic shells and hydrophobic cores enhances their stability and biocompatibility. Furthermore, advanced polymer engineering allows precise modulation of LCST and UCST through adjustments in composition and hydrophilic-lipophilic balance, optimizing their responsiveness for specific applications. In addition to drug delivery, thermo-responsive nanoparticles are gaining attention in several fields such as gene therapy and imaging. Therefore, this review explores the chemical and structural diversity of thermo-responsive nanoparticles, emphasizing their ability to encapsulate and release drugs effectively. Second, this review highlights the potential of thermo-responsive nanoparticles to redefine treatment paradigms, providing a comprehensive understanding of their mechanisms, applications, and future perspectives in biomedical research.

Stabilizing complex-Langevin field-theoretic simulations for block copolymer melts

Complex-Langevin field-theoretic simulations (CL-FTSs) provide an approximation-free method of calculating fluctuation corrections to the self-consistent field theory (SCFT) of block copolymer melts. However, the complex fields are prone to the formation of hot spots, which causes the method to fail. This problem has been attributed to an invariance under complex translations, which allows the system to drift away from the real-valued saddle-point of SCFT. Here, we apply dynamical stabilization to CL-FTSs of diblock copolymer melts, whereby the drift is suppressed by a small imaginary force on the composition field. The force needs to be sufficient to hold the system near the real saddle-point but also small enough not to significantly bias the statistics. Although larger forces are required as the fluctuations become more intense, we are able to lower the invariant polymerization indices of the CL-FTSs by several orders of magnitude before this becomes a problem. The new CL-FTS results are then used to test conventional Langevin simulations (L-FTSs), in which the instability is removed by a partial saddle-point approximation to the pressure field. As found previously, the L-FTSs agree accurately with the CL-FTSs, provided that the comparison is performed using a Morse calibration.

Accelerated Prediction of Phase Behavior for Block Copolymer Libraries Using a Molecularly Informed Field Theory

Solution formulations involving polymers are the basis for a wide range of products spanning consumer care, therapeutics, lubricants, adhesives, and coatings. These multicomponent systems typically show rich self-assembly and phase behavior that are sensitive to even small changes in chemistry and composition. Longstanding computational efforts have sought techniques for predictive modeling of formulation structure and thermodynamics without experimental guidance, but the challenges of addressing the long time scales and large length scales of self-assembly while maintaining chemical specificity have thwarted the emergence of general approaches. As a consequence, current formulation design remains largely Edisonian. Here, we present a multiscale modeling approach that accurately predicts, without any experimental input, the complete temperature-concentration phase diagram of model diblock polymers in solution, as established postprediction through small-angle X-ray scattering. The methodology employs a strategy whereby atomistic molecular dynamics simulations is used to parametrize coarse-grained field-theoretic models; simulations of the latter then easily surmount long equilibration time scales and enable rigorous determination of solution structures and phase behavior. This systematic and predictive approach, accelerated by access to well-defined block copolymers, has the potential to expedite in silico screening of novel formulations to significantly reduce trial-and-error experimental design and to guide selection of components and compositions across a vast range of applications.

Bicontinuous microemulsion in binary blends of complementary diblock copolymers

The phase behavior of binary blends of AB diblock copolymers of compositions f and 1 - f is examined using field-theoretic simulations. Highly asymmetric compositions (i.e., f ≈ 0) behave like homopolymer blends macrophase separating into coexisting A- and B-rich phases as the segregation is increased, whereas more symmetric diblocks (i.e., f ≈ 0.5) microphase separate into an ordered lamellar phase. In self-consistent field theory, these behaviors are separated by a Lifshitz critical point at f = 0.2113. However, its lower critical dimension is believed to be four, which implies that the Lifshitz point should be destroyed by fluctuations. Consistent with this, it is found to transform into a tricritical point. Furthermore, the highly swollen lamellar phase near the mean-field Lifshitz point disorders into a bicontinuous microemulsion (BμE), consisting of large interpenetrating A- and B-rich microdomains. BμE has been previously reported in ternary blends of AB diblock copolymer with its parent A- and B-type homopolymers, but in that system the homopolymers have a tendency to macrophase separate. Our alternative system for creating BμE is free of this macrophase separation.

Bioinspired Formation of Anti-Ultraviolet Micro-Goose Bump PDMAEMA/PS Coatings

In this paper, inspired by the human-giving goosebumps process, we demonstrated a rapid, versatile, and simple method to prepare anti-UV microstructures polymer blend films with good morphology based on phase separation. Through the results of characterizations, it is proved that the microstructures are formed by polymer phase separation. Then the formation possibility of microstructures is proved by thermodynamic analysis. Moreover, the phase-field model is used to simulate the formation of microstructures by the finite element method, which can illustrate the evolution process of the microstructures. Besides, the microstructures were prepared on different substrates through the simple phase separation method, which can verify the versatility of this method. In addition, the anti-UV performance of the micro-structure films was evaluated. This work proposed a simple and versatile route to prepare microstructures coating in different substrates, which exhibit well anti-UV performance, and this work has the application potential for preventing material aging caused by UV radiation.

Fluctuation-Corrected Phase Diagrams for Diblock Copolymer Melts

New developments in field-theoretic simulations (FTSs) are used to evaluate fluctuation corrections to the self-consistent field theory of diblock copolymer melts. Conventional simulations have been limited to the order-disorder transition (ODT), whereas FTSs allow us to evaluate complete phase diagrams for a series of invariant polymerization indices. The fluctuations stabilize the disordered phase, which shifts the ODT to higher segregation. Furthermore, they stabilize the network phases at the expense of the lamellar phase, which accounts for the presence of the Fddd phase in experiments. We hypothesize that this is due to an undulation entropy that favors curved interfaces.

Miscibility and exchange chemical potential of ring polymers in symmetric ring-ring blends

Generally, differences of polymer topologies may affect polymer miscibility even with the same repeated units. In this study, the topological effect of ring polymers on miscibility was investigated by comparing symmetric ring-ring and linear-linear polymer blends. To elucidate the topological effect of ring polymers on mixing free energy, the exchange chemical potential of binary blends was numerically evaluated as a function of composition ϕ by performing semi-grand canonical Monte Carlo and molecular dynamics simulations of a bead-spring model. For ring-ring blends, an effective miscibility parameter was evaluated by comparing the exchange chemical potential with that of the Flory-Huggins model for linear-linear polymer blends. It was confirmed that in the mixed states satisfying χN > 0, ring-ring blends are more miscible and stable than the linear-linear blends with the same molecular weight. Furthermore, we investigated finite molecular weight dependence on the miscibility parameter, which reflected the statistical probability of interchain interactions in the blends. The simulation results revealed that the molecular weight dependence on the miscibility parameter was smaller in ring-ring blends. The effect of the ring polymers on miscibility was verified to be consistent with the change in the interchain radial distribution function. In ring-ring blends, it was indicated that the topology affected miscibility by reducing the effect of the direct interaction between the components of the blends.

Imaging Block-Selective Copolymer Solvation

Understanding individual-block solvation in self-assembled block copolymer systems is experimentally difficult, but this solvation underpins the assembly and disassembly observed at the bulk scale. Here, covalently attached viscosity-sensitive molecular rotors for fluorescence lifetime imaging microscopy uncover and quantitatively elucidate previously undisclosed differential block-selective responses toward solvation changes upon addition of DMSO and THF to self-assembled ROMP-based amphiphilic block copolymers. The sensitivity of this method provides unique information on block-selective solvent-triggered assembly and disassembly mechanisms, revealing behaviors invisible to or with superior sensitivity to traditional ¹H NMR spectroscopy. These experiments demonstrate an analytical method and provide a granular mechanistic understanding, both suitable for fine tuning block copolymer assembly and disassembly processes.

Accounting for the ultraviolet divergence in field-theoretic simulations of block copolymer melts

This study examines the ultraviolet (UV) divergence in field-theoretic simulations (FTSs) of block copolymer melts, which causes an unphysical dependence on the grid resolution, Δ, used to represent the fields. Our FTSs use the discrete Gaussian-chain model and a partial saddle-point approximation to enforce incompressibility. Previous work has demonstrated that the UV divergence can be accounted for by defining an effective interaction parameter, χ=z_∞χ_b+c₂χ_b ²+c₃χ_b ³+⋯, in terms of the bare interaction parameter, χ_b, used in the FTSs, where the coefficients of the expansion are determined by a Morse calibration. However, the need to use different grid resolutions for different ordered phases generally restricts the calibration to the linear approximation, χ ≈ z_∞χ_b, and prevents the calculation of order-order transitions. Here, we resolve these two issues by showing how the nonlinear calibration can be translated between different grids and how the UV divergence can be removed from free energy calculations. By doing so, we confirm previous observations from particle-based simulations. In particular, we show that the free energy closely matches self-consistent field theory (SCFT) predictions, even in the region where fluctuations disorder the periodic morphologies, and similarly, the periods of the ordered phases match SCFT predictions, provided the SCFT is evaluated with the nonlinear χ.

Well-tempered metadynamics applied to field-theoretic simulations of diblock copolymer melts

Well-tempered metadynamics (WTMD) is applied to field-theoretic simulations (FTS) to locate the order-disorder transition (ODT) in incompressible melts of diblock copolymer with an invariant polymerization index of N̄=10⁴. The polymers are modeled as discrete Gaussian chains with N = 90 monomers, and the incompressibility is treated by a partial saddle-point approximation. Our implementation of WTMD proves effective at locating the ODT of the lamellar and cylindrical regions, but it has difficulty with that of the spherical and gyroid regions. In the latter two cases, our choice of order parameter cannot sufficiently distinguish the ordered and disordered states because of the similarity in microstructures. The gyroid phase has the added complication that it competes with a number of other morphologies, and thus, it might be beneficial to extend the WTMD to multiple order parameters. Nevertheless, when the method works, the ODT can be located with impressive accuracy (e.g., ΔχN ∼ 0.01).

Modeling the Phase Equilibria of Associating Polymers in Porous Media with Respect to Chromatographic Applications

Associating copolymers self-assemble during their passage through a liquid chromatography (LC) column, and the elution differs from that of common non-associating polymers. This computational study aims at elucidating the mechanism of their unique and intricate chromatographic behavior. We focused on amphiphilic diblock copolymers in selective solvents, performed the Monte Carlo (MC) simulations of their partitioning between a bulk solvent (mobile phase) and a cylindrical pore (stationary phase), and investigated the concentration dependences of the partition coefficient and of other functions describing the phase behavior. The observed abruptly changing concentration dependences of the effective partition coefficient demonstrate the significant impact of the association of copolymers with their partitioning between the two phases. The performed simulations reveal the intricate interplay of the entropy-driven and the enthalpy-driven processes, elucidate at the molecular level how the self-assembly affects the chromatographic behavior, and provide useful hints for the analysis of experimental elution curves of associating polymers.

Field-Theoretic Simulations for Block Copolymer Melts Using the Partial Saddle-Point Approximation

Field-theoretic simulations (FTS) provide an efficient technique for investigating fluctuation effects in block copolymer melts with numerous advantages over traditional particle-based simulations. For systems involving two components (i.e., A and B), the field-based Hamiltonian, Hf[W-,W+], depends on a composition field, W-(r), that controls the segregation of the unlike components and a pressure field, W+(r), that enforces incompressibility. This review introduces researchers to a promising variant of FTS, in which W-(r) fluctuates while W+(r) tracks its mean-field value. The method is described in detail for melts of AB diblock copolymer, covering its theoretical foundation through to its numerical implementation. We then illustrate its application for neat AB diblock copolymer melts, as well as ternary blends of AB diblock copolymer with its A- and B-type parent homopolymers. The review concludes by discussing the future outlook. To help researchers adopt the method, open-source code is provided that can be run on either central processing units (CPUs) or graphics processing units (GPUs).

Field-theoretic simulations beyond δ-interactions: Overcoming the inverse potential problem in auxiliary field models

Modern field-theoretic simulations of complex fluids and polymers are constructed around a particle-to-field transformation that brings an inverse potential u^-1 in the model equations. This has restricted the application of the framework to systems characterized by relatively simple pairwise interatomic interactions; for example, excluded volume effects are treated through the use of δ-function interactions. In this study, we first review available nonbonded pair interactions in field-theoretic models and propose a classification. Then, we outline the inverse potential problem and present an alternative approach on the basis of a saddle-point approximation, enabling the use of a richer set of pair interaction functions. We test our approach by using as an example the Morse potential, which finds extensive applications in particle-based simulations, and we calibrate u^-1 with results from a molecular dynamics simulation. The u^-1 thus obtained is consistent with the field-theoretic model equations, and when used in stand-alone self-consistent field simulations, it produces the correct fluid structure starting from a random initial state of the density field.

Fluctuation correction for the order-disorder transition of diblock copolymer melts

The order-disorder transition (ODT) of diblock copolymer melts is evaluated for an invariant polymerization index of N¯=10⁴, using field-theoretic simulations (FTS) supplemented by a partial saddle-point approximation for incompressibility. For computational efficiency, the FTS are performed using the discrete Gaussian-chain model, and results are then mapped onto the continuous model using a linear approximation for the Flory-Huggins χ parameter. Particular attention is paid to the complex phase window. Results are found to be consistent with the well-established understanding that the gyroid phase extends down to the ODT. Furthermore, our simulations are the first to predict that the Fddd phase survives fluctuation effects, consistent with experiments.