Predicting the Flory-Huggins χ Parameter for Polymers with Stiffness Mismatch from Molecular Dynamics Simulations

Coil-Helix Block Copolymers Can Exhibit Divergent Thermodynamics in the Disordered Phase

Chiral building blocks have the ability to self-assemble and transfer chirality to larger hierarchical length scales, which can be leveraged for the development of novel nanomaterials. Chiral block copolymers, where one block is made completely chiral, are prime candidates for studying this phenomenon, but fundamental questions regarding the self-assembly are still unanswered. For one, experimental studies using different chemistries have shown unexplained diverging shifts in the order-disorder transition temperature. In this study, particle-based molecular simulations of chiral block copolymers in the disordered melt were performed to uncover the thermodynamic behavior of these systems. A wide range of helical models were selected, and several free energy calculations were performed. Specifically, we aimed to understand (1) the thermodynamic impact of changing the conformation of one block in chemically identical block copolymers and (2) the effect of the conformation on the Flory-Huggins interaction parameter, χ, when chemical disparity was introduced. We found that the effective block repulsion exhibits diverging behavior, depending on the specific conformational details of the helical block. Commonly used conformational metrics for flexible or stiff block copolymers do not capture the effective block repulsion because helical blocks are semiflexible and aspherical. Instead, pitch can quantitatively capture the effective block repulsion. Quite remarkably, the shift in χ for chemically dissimilar block copolymers can switch sign with small changes in the pitch of the helix.

Renormalized one-loop theory of correlations in disperse polymer blends

Polymer blends are critical in many commercial products and industrial processes and their phase behavior is therefore of paramount importance. In most circumstances, such blends are formulated with samples of high dispersity, which have generally only been studied at the mean-field level. Here, we extend the renormalized one-loop theory of concentration fluctuations to account for blends of disperse polymers. Analyzing the short and long length-scale fluctuations in a consistent manner, various measures of polymer molecular weight and dispersity arise naturally in the free energy. Thermodynamic analysis in terms of moments of the molecular weight distribution(s) provides exact results for the inverse susceptibility and demonstrates that the theory is not formally renormalizable. However, physically motivated approximations allow for an "effective" renormalization, yielding (1) an effective interaction parameter, χe, which depends directly on the sample dispersities (i.e., Mw/Mn) and leaves the form of the mean-field spinodal unchanged, and (2) an apparent interaction parameter χa that depends on higher-order dispersity indices, for instance Mz/Mw, and characterizes the true limits of blend stability accounting for long-range off-critical fluctuations. We demonstrate the importance of dispersity on several example systems, including both "toy" models that may be realized in computer simulation and more realistic industrially relevant blends. We find that the effects of long-range fluctuations are particularly prominent in blends where the component dispersities are mismatched, especially when there is a small quantity of the high-dispersity species. This can be understood as a consequence of the shift in the critical concentration(s) from the monodisperse value(s).

Pulling simulation predicts mixing free energy for binary mixtures

Predicting the mixing free energy of mixing for binary mixtures using simulations is challenging. We present a novel molecular dynamics (MD) simulation method to extract the chemical potential μ(X) for mixtures of species A and B. Each molecule of species A and B is placed in equal and opposite harmonic potentials ±(1/2)U_ex(x) centered at the middle of the simulation box, resulting in a nonuniform mole fraction profile X(z) in which A is concentrated at the center, and B at the periphery. Combining these, we obtain U_ex(X), the exchange chemical potential required to induce a given deviation of the mole fraction from its average. Simulation results for U_ex(X) can be fitted to simple free energy models to extract the interaction parameter χ for binary mixtures. To illustrate our method, we investigate benzene-pyridine mixtures, which provide a good example of regular solution behavior, using both TraPPE united-atom and OPLS all-atom potentials, both of which have been validated for pure fluid properties. χ values obtained with the new method are consistent with values from other recent simulation methods. However, the TraPPE-UA results differ substantially from the χ obtained from VLE experimental data, while the OPLS-AA results are in reasonable agreement with experiment, highlighting the importance of accurate potentials in correctly representing mixture behavior.

Surface enrichment and interdiffusion in blends of semiflexible polymers of different stiffness

A model for a mixture of two kinds of semiflexible polymers (A and B) with the same chain length (N_A = N_B = 32), but different persistence lengths, confined between parallel planar repulsive walls in a common good solvent is studied by molecular dynamics simulations. In the isotropic phase at low polymer concentrations, both polymers are repelled by the walls, and the system is anisotropic near the walls over a range controlled by the polymer linear dimensions. Close to the concentrations where in the bulk nematic order sets in, precursors of thick nematic layers at the walls are observed, strongly enriched by a stiffer component, which hence is depleted in the center of the slit pore. At larger concentrations, where in the bulk a uniformly mixed nematic phase occurs, the enrichment of B-chains at the walls is rather minor, extending over the scale of the transverse correlation length of concentration fluctuations, which is of the order of a few monomeric diameters only for the present model. In this ordered phase, both self-diffusion and interdiffusion of chains (in the direction perpendicular to the director) are found to be significantly slowed down in comparison to dilute solutions. Since equilibration times scale with the square of the slit thickness, incomplete equilibration is predicted when polymeric coatings on substrate containing polymers differing in stiffness are produced.

Bespoke 3D-Printed Polydrug Implants Created via Microstructural Control of Oligomers

Controlling the microstructure of materials by means of phase separation is a versatile tool for optimizing material properties. Phase separation has been exploited to fabricate intricate microstructures in many fields including cell biology, tissue engineering, optics, and electronics. The aim of this study was to use phase separation to tailor the spatial location of drugs and thereby generate release profiles of drug payload over periods ranging from 1 week to months by exploiting different mechanisms: polymer degradation, polymer diluent dissolution, and control of microstructure. To achieve this, we used drop-on-demand inkjet three-dimensional (3D) printing. We predicted the microstructure resulting from phase separation using high-throughput screening combined with a model based on the Flory-Huggins interaction parameter and were able to show that drug release from 3D-printed objects can be predicted from observations based on single drops of mixtures. We demonstrated for the first time that inkjet 3D printing yields controllable phase separation using picoliter droplets of blended photoreactive oligomers/monomers. This new understanding gives us hierarchical compositional control, from droplet to device, allowing release to be "dialled up" without manipulation of device geometry. We exemplify this approach by fabricating a biodegradable, long-term, multiactive drug delivery subdermal implant ("polyimplant") for combination therapy and personalized treatment of coronary heart disease. This is an important advance for implants that need to be delivered by cannula, where the shape is highly constrained and thus the usual geometrical freedoms associated with 3D printing cannot be easily exploited, which brings a hitherto unseen level of understanding to emergent material properties of 3D printing.

Blends of Semiflexible Polymers: Interplay of Nematic Order and Phase Separation

Mixtures of semiflexible polymers with a mismatch in either their persistence lengths or their contour lengths are studied by Density Functional Theory and Molecular Dynamics simulation. Considering lyotropic solutions under good solvent conditions, the mole fraction and pressure is systematically varied for several cases of bending stiffness κ (the normalized persistence length) and chain length N. For binary mixtures with different chain length (i.e., NA=16, NB=32 or 64) but the same stiffness, isotropic-nematic phase coexistence is studied. For mixtures with the same chain length (N=32) and large stiffness disparity (κB/κA=4.9 to 8), both isotropic-nematic and nematic-nematic unmixing occur. It is found that the phase diagrams may exhibit a triple point or a nematic-nematic critical point, and that coexisting phases differ appreciably in their monomer densities. The properties of the two types of chains (nematic order parameters, chain radii, etc.) in the various phases are studied in detail, and predictions on the (anisotropic) critical behavior near the critical point of nematic-nematic unmixing are made.

Insights from modeling into structure, entanglements, and dynamics in attractive polymer nanocomposites

Conformations, entanglements and dynamics in attractive polymer nanocomposites are investigated in this work by means of coarse-grained molecular dynamics simulation, for both weak and strong confinements, in the presence of nanoparticles (NPs) at NP volume fractions φ up to 60%. We show that the behavior of the apparent tube diameter dapp in such nanocomposites can be greatly different from nanocomposites with nonattractive interactions. We find that this effect originates, based on a mean field argument, from the geometric confinement length dgeo at strong confinement (large φ) and not from the bound polymer layer on NPs (interparticle distance ID <2Rg) as proposed recently based on experimental measurements. Close to the NP surface, the entangled polymer mobility is reduced in attractive nanocomposites but still faster than the NP mobility for volume fractions beyond 20%. Furthermore, entangled polymer dynamics is hindered dramatically by the strong confinement created by NPs. For the first time using simulations, we show that the entangled polymer conformation, characterized by the polymer radius of gyration Rg and form factor, remains basically unperturbed by the presence of NPs up to the highest volume fractions studied, in agreement with various experiments on attractive nanocomposites. As a side-result we demonstrate that the loose concept of ID can be made a microscopically well defined quantity using the mean pore size of the NP arrangement.

Continuum-scale modelling of polymer blends using the Cahn-Hilliard equation: transport and thermodynamics

The Cahn-Hilliard equation is commonly used to study multi-component soft systems such as polymer blends at continuum scales. We first systematically explore various features of the equation system, which give rise to a deep connection between transport and thermodynamics-specifically that the Gibbs free energy of mixing function is central to formulating a well-posed model. Accordingly, we explore how thermodynamic models from three broad classes of approach (lattice-based, activity-based and perturbation methods) can be incorporated within the Cahn-Hilliard equation and examine how they impact the numerical solution for two model polymer blends, noting that although the analysis presented here is focused on binary mixtures, it is readily extensible to multi-component mixtures. It is observed that, although the predicted liquid-liquid interfacial tension is quite strongly affected, the choice of thermodynamic model has little influence on the development of the morphology.

The Sequence of a Step-Growth Copolymer Can Be Influenced by Its Own Persistence Length

Synthetic copolymer sequences remain challenging to control, and there are features of even simple one-pot, solution-based copolymerizations that are not yet fully understood. In previous simulations on step-growth copolymerizations in solution, we demonstrated that modest variations in the attractions between type A and B monomers could significantly influence copolymer sequence through an emergent aggregation and phase separation initiated by the lengthening of nascent oligomers. Here we investigate how one aspect of a copolymer's geometry-its flexibility-can modulate those effects. Our simulations show the onset of strand alignment within the polymerization-induced aggregates as chain stiffness increases and demonstrate that this alignment can influence the resulting copolymer sequences. For less flexible copolymers, with persistence lengths ≥10 monomers, modest nonbonded attractions of ∼k_BT between monomers of the same type yield A and B blocks of a characteristic length and result in a polydispersity index that grows rapidly, peaks, and then diminishes as the reaction proceeds. These results demonstrate that for copolymer systems with modest variations in intermonomer attractions and physically realistic flexibilities a nascent copolymer's persistence length can influence its own sequence.

Predicting the Mixing Behavior of Aqueous Solutions Using a Machine Learning Framework

The most direct approach to determining if two aqueous solutions will phase-separate upon mixing is to exhaustively screen them in a pair-wise fashion. This is a time-consuming process that involves preparation of numerous stock solutions, precise transfer of highly concentrated and often viscous solutions, exhaustive agitation to ensure thorough mixing, and time-sensitive monitoring to observe the presence of emulsion characteristics indicative of phase separation. Here, we examined the pair-wise mixing behavior of 68 water-soluble compounds by observing the formation of microscopic phase boundaries and droplets of 2278 unique 2-component solutions. A series of machine learning classifiers (artificial neural network, random forest, k-nearest neighbors, and support vector classifier) were then trained on physicochemical property data associated with the 68 compounds and used to predict their miscibility upon mixing. Miscibility predictions were then compared to the experimental observations. The random forest classifier was the most successful classifier of those tested, displaying an average receiver operator characteristic area under the curve of 0.74. The random forest classifier was validated by removing either one or two compounds from the input data, training the classifier on the remaining data and then predicting the miscibility of solutions involving the removed compound(s) using the classifier. The accuracy, specificity, and sensitivity of the random forest classifier were 0.74, 0.80, and 0.51, respectively, when one of the two compounds to be examined was not represented in the training data. When asked to predict the miscibility of two compounds, neither of which were represented in the training data, the accuracy, specificity, and sensitivity values for the random forest classifier were 0.70, 0.82 and 0.29, respectively. Thus, there is potential for this machine learning approach to improve the design of screening experiments to accelerate the discovery of aqueous two-phase systems for numerous scientific and industrial applications.

Phase Separation and Nematic Order in Lyotropic Solutions: Two Types of Polymers with Different Stiffnesses in a Common Solvent

The interplay of the isotropic-nematic transition and phase separation in lyotropic solutions of two types of semiflexible macromolecules with pronounced difference in chain stiffness is studied by Density Functional Theory and Molecular Dynamics simulations. While the width of the isotropic-nematic two-phase coexistence region is narrow for solutions with a single type of semiflexible chain, the two-phase coexistence region widens for solutions containing two types of chains with rather disparate stiffness. In the nematic phase, both types of chains contribute to the nematic order, with intermediate values of the order parameter compared to the corresponding single component solutions. As the difference in bending stiffness is increased, the two chain types separate into two coexisting nematic phases. The phase behavior is rationalized by considering the chemical potentials of the two components and the Gibbs excess free energy. The geometric properties of the chain conformations under the various conditions are also discussed.

Entropic Unmixing in Nematic Blends of Semiflexible Polymers

Binary mixtures of semiflexible polymers with the same chain length, but different persistence lengths, separate into two coexisting different nematic phases when the osmotic pressure of the lyotropic solution is varied. Molecular Dynamics simulations and Density Functional Theory predict phase diagrams either with a triple point, where the isotropic phase coexists with two nematic phases or a critical point of unmixing within the nematic mixture. The difference in locally preferred bond angles between the constituents drives this unmixing without any attractive interactions between monomers.

Molecular recognition mechanisms directing the self-assembly of biological structures

Self-assembling may be defined as the spontaneous association of material units into structures that are often capable of cyclic reorganization and functional behavior. Various molecular recognition processes stabilize assemblies of polymers and biological structures. The present article analyzes cases in which chemical, shape and other recognition mechanisms are individually or cooperatively operative. Simpler self-assembling theories reported in the literature are highlighted. Detailed processes for which chemical recognition is the prevailing, enthalpy-driven, process include the non-ideal component of miscibility, supramolecular polymerization, host-guest complexes and template polymerization. Also discussed are systems such as liquid crystalline closed polymers, ternary mesogenic systems and rigid crystalline polymers for which shape recognition is the prevailing entropy-driven process. Other recognition mechanisms include ion condensation effects, hydrophobic bonding and growth-coupled-to-orientation. Combinations of various recognition mechanisms are particularly evident in biological structures. Self-assembling mechanisms involved in the genesis of some biological systems can be scientifically identified, but much more needs to be known to describe the "engineered" assembling modes that support complex functional organs.

The effect of bioadhesive on the interfacial compatibility and pervaporation performance of composite membranes by MD and GCMC simulation

Combing molecular dynamics (MD) and Grand Canonical Monte Carlo (GCMC) simulation, the effect of bioadhesive transition layer on the interfacial compatibility of the pervaporation composite membranes, and the pervaporation performance toward penetrant molecules were investigated. In our previous experimental study, the structural stability and permeability selectivity of the composite membranes were considerably enhanced by the introduction of bioadhesive carbopol (CP). In the present study, the interfacial compatibility and the interfacial energies between the chitosan (CS) separation layer, CP transition layer and the support layer were investigated, respectively. The mobility of polymer chains, free volume in bulk and interface regions were evaluated by the mean-square displacement (MSD) and free volume voids (FFV) analysis. The diffusion and sorption behavior of water/ethanol molecules in bulk and interface regions were characterized. The simulation results of membrane structure have good consistency, indicating that the introduction of CP transition layer improved the interfacial compatibility and interaction between the separation layer and the support layer. Comparing the bulk region of the separation layer, the mobility and free volume of the polymer chain in the interface region decreased and thus reduced the swelling of CS active layer, revealing the increased diffusion selectivity toward the permeated water and ethanol molecules. The strong hydrogen bonds interaction between the COOH of the CP transition layer and water molecules increased the adsorption of water molecules in the interface region. The simulation results were quite consistent with the experimental results.

Predicting Flory-Huggins χ from Simulations

We introduce a method, based on a novel thermodynamic integration scheme, to extract the Flory-Huggins χ parameter as small as 10^{-3}kT for polymer blends from molecular dynamics (MD) simulations. We obtain χ for the archetypical coarse-grained model of nonpolar polymer blends: flexible bead-spring chains with different Lennard-Jones interactions between A and B monomers. Using these χ values and a lattice version of self-consistent field theory (SCFT), we predict the shape of planar interfaces for phase-separated binary blends. Our SCFT results agree with MD simulations, validating both the predicted χ values and our thermodynamic integration method. Combined with atomistic simulations, our method can be applied to predict χ for new polymers from their chemical structures.

Small Activity Differences Drive Phase Separation in Active-Passive Polymer Mixtures

Recent theoretical studies found that mixtures of active and passive colloidal particles phase separate but only at very high activity ratio. The high value poses serious obstacles for experimental exploration of this phenomenon. Here we show using simulations that when the active and passive particles are polymers, the critical activity ratio decreases with the polymer length. This not only facilitates the experiments but also has implications on the DNA organization in living cell nuclei. Entropy production can be used as an accurate indicator of this nonequilibrium phase transition.

Influence of Chain Stiffness, Grafting Density and Normal Load on the Tribological and Structural Behavior of Polymer Brushes: A Nonequilibrium-Molecular-Dynamics Study

We have performed coarse-grained molecular-dynamics simulations on both flexible and semiflexible multi-bead-spring model polymer brushes in the presence of explicit solvent particles, to explore their tribological and structural behaviors. The effect of stiffness and tethering density on equilibrium-brush height is seen to be well reproduced within a Flory-type theory. After discussing the equilibrium behavior of the model brushes, we first study the shearing behavior of flexible chains at different grafting densities covering brush and mushroom regimes. Next, we focus on the effect of chain stiffness on the tribological behavior of polymer brushes. The tribological properties are interpreted by means of the simultaneously recorded density profiles. We find that the friction coefficient decreases with increasing persistence length, both in velocity and separation-dependency studies, over the stiffness range explored in this work.