Predicting Flory-Huggins χ from Simulations

Wetting Phenomena: Line Tension and Gravitational Effect

An apparent contact angle is formed when a droplet is deposited on a solid substrate. Young's law has been employed to describe the equilibrium contact angle. Often in experiments, the equilibrium contact angle deviates from Young's law and depends on the volume of the droplet, known as the line tension effect. However, the physical origin of the line tension is quite controversial. Especially, the sign and the quantity of the line tension spanning 6 orders of magnitude are unsolved problems. Here, we quantify the line energy in terms of physical parameters and demonstrate that both positive and negative line tensions exist. The results are quantitatively compared with existing experiments as well as with previous theories.

Wetting and Contact-Angle Hysteresis: Density Asymmetry and van der Waals Force

A droplet depositing on a solid substrate leads to the wetting phenomenon, such as dew on plant leaves. On an ideally smooth substrate, the classic Young's law has been employed to describe the wetting effect. However, no real substrate is ideally smooth at the microscale. Given this fact, we introduce a surface composition concept to scrutinize the wetting mechanism via considering the liquid-gas density asymmetry and the fluid-solid van der Waals interaction. The current concept enables one to comprehend counterintuitive phenomenon of contact-angle hysteresis on a smooth substrate and increase of contact angle with temperature as well as gas bubble wetting.

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).

Data-Driven Imputation of Miscibility of Aqueous Solutions via Graph-Regularized Logistic Matrix Factorization

Aqueous, two-phase systems (ATPSs) may form upon mixing two solutions of independently water-soluble compounds. Many separation, purification, and extraction processes rely on ATPSs. Predicting the miscibility of solutions can accelerate and reduce the cost of the discovery of new ATPSs for these applications. Whereas previous machine learning approaches to ATPS prediction used physicochemical properties of each solute as a descriptor, in this work, we show how to impute missing miscibility outcomes directly from an incomplete collection of pairwise miscibility experiments. We use graph-regularized logistic matrix factorization (GR-LMF) to learn a latent vector of each solution from (i) the observed entries in the pairwise miscibility matrix and (ii) a graph where each node is a solution and edges are relationships indicating the general category of the solute (i.e., polymer, surfactant, salt, protein). For an experimental data set of the pairwise miscibility of 68 solutions from Peacock et al. [ACS Appl. Mater. Interfaces 2021, 13, 11449-11460], we find that GR-LMF more accurately predicts missing (im)miscibility outcomes of pairs of solutions than ordinary logistic matrix factorization and random forest classifiers that use physicochemical features of the solutes. GR-LMF obviates the need for features of the solutions and solutions to impute missing miscibility outcomes, but it cannot predict the miscibility of a new solution without some observations of its miscibility with other solutions in the training data set.

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.

Prediction of small-molecule compound solubility in organic solvents by machine learning algorithms

Rapid solvent selection is of great significance in chemistry. However, solubility prediction remains a crucial challenge. This study aimed to develop machine learning models that can accurately predict compound solubility in organic solvents. A dataset containing 5081 experimental temperature and solubility data of compounds in organic solvents was extracted and standardized. Molecular fingerprints were selected to characterize structural features. lightGBM was compared with deep learning and traditional machine learning (PLS, Ridge regression, kNN, DT, ET, RF, SVM) to develop models for predicting solubility in organic solvents at different temperatures. Compared to other models, lightGBM exhibited significantly better overall generalization (logS  ± 0.20). For unseen solutes, our model gave a prediction accuracy (logS  ± 0.59) close to the expected noise level of experimental solubility data. lightGBM revealed the physicochemical relationship between solubility and structural features. Our method enables rapid solvent screening in chemistry and may be applied to solubility prediction in other solvents.

Development of Coarse-Grained Models for Poly(4-vinylphenol) and Poly(2-vinylpyridine): Polymer Chemistries with Hydrogen Bonding

In this paper, we identify the modifications needed in a recently developed generic coarse-grained (CG) model that captured directional interactions in polymers to specifically represent two exemplary hydrogen bonding polymer chemistries-poly(4-vinylphenol) and poly(2-vinylpyridine). We use atomistically observed monomer-level structures (e.g., bond, angle and torsion distribution) and chain structures (e.g., end-to-end distance distribution and persistence length) of poly(4-vinylphenol) and poly(2-vinylpyridine) in an explicitly represented good solvent (tetrahydrofuran) to identify the appropriate modifications in the generic CG model in implicit solvent. For both chemistries, the modified CG model is developed based on atomistic simulations of a single 24-mer chain. This modified CG model is then used to simulate longer (36-mer) and shorter (18-mer and 12-mer) chain lengths and compared against the corresponding atomistic simulation results. We find that with one to two simple modifications (e.g., incorporating intra-chain attraction, torsional constraint) to the generic CG model, we are able to reproduce atomistically observed bond, angle and torsion distributions, persistence length, and end-to-end distance distribution for chain lengths ranging from 12 to 36 monomers. We also show that this modified CG model, meant to reproduce atomistic structure, does not reproduce atomistically observed chain relaxation and hydrogen bond dynamics, as expected. Simulations with the modified CG model have significantly faster chain relaxation than atomistic simulations and slower decorrelation of formed hydrogen bonds than in atomistic simulations, with no apparent dependence on chain length.

Sorption Characteristics of Polymer Brushes in Equilibrium with Solvent Vapors

While polymer brushes in contact with liquids have been researched intensively, the characteristics of brushes in equilibrium with vapors have been largely unexplored, despite their relevance for many applications, including sensors and smart adhesives. Here, we use molecular dynamics simulations to show that solvent and polymer density distributions for brushes exposed to vapors are qualitatively different from those of brushes exposed to liquids. Polymer density profiles for vapor-solvated brushes decay more sharply than for liquid-solvated brushes. Moreover, adsorption layers of enhanced solvent density are formed at the brush–vapor interface. Interestingly and despite all of these effects, we find that solvent sorption in the brush is described rather well with a simple mean-field Flory–Huggins model that incorporates an entropic penalty for stretching of the brush polymers, provided that parameters such as the polymer–solvent interaction parameter, grafting density, and relative vapor pressure are varied individually.

Multiple approaches for achieving drug solubility: an in silico perspective

Discovering new therapeutically active molecules is the ultimate destination in pharmaceutical research and development. Most drugs discovered are lipophilic and, hence, exhibit poor aqueous solubility, resulting in low bioavailability. Thus, there is a need to use various solubility enhancement techniques. Computational approaches enable the analysis of drug-carrier interactions or the numerous conformational changes in the carrier matrix that might establish an appropriate balance between cohesive and adhesive stability in a formulation. In this review, we discuss research approaches that provided molecular insight into drugs and their modifiers to unravel their solubility, stability, and bioavailability.

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

Polymer science has been driven by ever-increasing molecular complexity, as polymer synthesis expands an already-vast palette of chemical and architectural parameter space. Copolymers represent a key example, where simple homopolymers have given rise to random, alternating, gradient, and block copolymers. Polymer physics has provided the insight needed to explore this monomer sequence parameter space. The future of polymer science, however, must contend with further increases in monomer precision, as this class of macromolecules moves ever closer to the sequence-monodisperse polymers that are the workhorses of biology. The advent of sequence-defined polymers gives rise to opportunities for material design, with increasing levels of chemical information being incorporated into long-chain molecules; however, this also raises questions that polymer physics must address. What properties uniquely emerge from sequence-definition? Is this circumstance-dependent? How do we define and think about sequence dispersity? How do we think about a hierarchy of sequence effects? Are more sophisticated characterization methods, as well as theoretical and computational tools, needed to understand this class of macromolecules? The answers to these questions touch on many difficult scientific challenges, setting the stage for a rich future for sequence-defined polymers in polymer physics.

Significance of thermodynamic interaction parameters in guiding the optimization of polymer:nonfullerene solar cells

Polymer solar cells (PSCs) based on polymer donors and nonfullerene small molecule acceptors are a very attractive technology for solar energy conversion, and their performance is heavily determined by film morphology. It is of considerable interest to reveal instructive morphology-performance relationships of these blends. This feature article discusses the recent advances in analysing the morphology formation of nonfullerene PSCs with an effective polymer thermodynamic quantity, i.e., Flory-Huggins interaction parameter χ. In particular, guidelines of high and low χ systems are summarized. The fundamental understanding of χ and its correlations to film morphology and photovoltaic device parameters is of utmost relevance for providing essential material design criteria, establishing suitable morphology processing guidelines, and thus advancing the practical applications of PSCs based on nonfullerene acceptors.

Photovoltaic Blend Microstructure for High Efficiency Post-Fullerene Solar Cells. To Tilt or Not To Tilt?

Achieving efficient polymer solar cells (PSCs) requires a structurally optimal donor-acceptor heterojunction morphology. Here we report the combined experimental and theoretical characterization of a benzodithiophene-benzothiadiazole donor polymer series (PBTZF4-R; R = alkyl substituent) blended with the non-fullerene acceptor ITIC-Th and analyze the effects of substituent dimensions on blend morphology, charge transport, carrier dynamics, and PSC metrics. Varying substituent dimensions has a pronounced effect on the blend morphology with a direct link between domain purity, to some extent domain dimensions, and charge generation and collection. The polymer with the smallest alkyl substituent yields the highest PSC power conversion efficiency (PCE, 11%), reflecting relatively small, high-purity domains and possibly benefiting from "matched" donor polymer-small molecule acceptor orientations. The distinctive morphologies arising from the substituents are investigated using molecular dynamics (MD) simulations which reveal that substituent dimensions dictate a well-defined set of polymer conformations, in turn driving chain aggregation and, ultimately, the various film morphologies and mixing with acceptor small molecules. A straightforward energetic parameter explains the experimental polymer domain morphological trends, hence PCE, and suggests strategies for substituent selection to optimize PSC materials morphologies.

Wetting of Polymer Brushes by Polymeric Nanodroplets

End-anchoring polymers to a solid surface to form so-called polymer brushes is a versatile method to prepare robust functional coatings. We show, using molecular dynamics simulations, that these coatings display rich wetting behavior. Depending on the interaction between the brushes and the polymeric droplets as well as on the self-affinity of the brush, we can distinguish between three wetting states: mixing, complete wetting, and partial wetting. We find that transitions between these states are largely captured by enthalpic arguments, while deviations to these can be attributed to the negative excess interfacial entropy for the brush droplet system. Interestingly, we observe that the contact angle strongly increases when the softness of the brush is increased, which is opposite to the case of drops on soft elastomers. Hence, the Young to Neumann transition owing to softness is not universal but depends on the nature of the substrate.

Diffusion in Lamellae, Cylinders, and Double Gyroid Block Copolymer Nanostructures

We study transport of penetrants through nanoscale morphologies motivated by common block copolymer morphologies, using confined random walks and coarse-grained simulations. Diffusion through randomly oriented grains is 1/3 for cylinder and 2/3 for lamellar morphologies versus an unconstrained (homopolymer) system, as previously understood. Diffusion in the double gyroid structure depends on the volume fraction and is 0.47-0.55 through the minority phase at 30-50 vol % and 0.73-0.80 through the majority at 50-70 vol %. Thus, among randomly oriented standard minority phase structures with no grain boundary effects, lamellae is preferable for transport.