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Machine learning is an important tool in the study of the phase behavior from molecular simulations. In this work, we use un-supervised machine learning methods to study the phase behavior of two off-lattice models, a binary Lennard-Jones (LJ) mixture and the Widom–Rowlinson (WR) non-additive hard-sphere mixture. The majority of previous work has focused on lattice models, such as the 2D Ising model, where the values of the spins are used as the feature vector that is input into the machine learning algorithm, with considerable success. For these two off-lattice models, we find that the choice of the feature vector is crucial to the ability of the algorithm to predict a phase transition, and this depends on the particular model system being studied. We consider two feature vectors, one where the elements are distances of the particles of a given species from a probe (distance-based feature) and one where the elements are +1 if there is an excess of particles of the same species within a cut-off distance and −1 otherwise (affinity-based feature). We use principal component analysis and t-distributed stochastic neighbor embedding to investigate the phase behavior at a critical composition. We find that the choice of the feature vector is the key to the success of the unsupervised machine learning algorithm in predicting the phase behavior, and the sophistication of the machine learning algorithm is of secondary importance. In the case of the LJ mixture, both feature vectors are adequate to accurately predict the critical point, but in the case of the WR mixture, the affinity-based feature vector provides accurate estimates of the critical point, but the distance-based feature vector does not provide a clear signature of the phase transition. The study suggests that physical insight into the choice of input features is an important aspect for implementing machine learning methods. 

Polyelectrolyte solutions have been proposed as a method to improve the efficiency of lithium-ion batteries by increasing the cation transference number because the polymer self-diffusion coefficient is much lower than that of the counterion. However, this is not necessarily true for the polymer mobility. In some cases, negative transference numbers have been reported, which implies that the lithium ions are transporting to the same electrode as the anion, behavior that is often attributed to a binding of counterions to the polyion. We use a simple model where we bind some counterions to the polymer via harmonic springs to investigate this phenomenon. We find that both the number of bound counterions and the strength of their binding alter the transference number, and, in some cases, the transference number is negative. We also investigate how the transference number depends on the Manning parameter, the ratio of the Bjerrum length to charge separation along the chain. By altering the Manning parameter, the transference number can almost be doubled, which suggests that charge spacing could be a way to increase the transference number of polyelectrolyte solutions. 

Polyelectrolyte solutions are of considerable scientific and practical importance. One of the most widely studied polymer is polystyrene sulfonate (PSS), which has a hydrophobic backbone with pendant charged groups. A polycation with similar chemical structure is poly(vinyl benzyltri methyl) ammonium (PVBTMA). In this work, we develop coarse-grained (CG) models for PSS and PVBTMA with explicit CG water and with sodium and chloride counterions, respectively. We benchmark the CG models via a comparison with atomistic simulations for single chains. We find that the choice of the topology and the partial charge distribution of the CG model, both play a crucial role in the ability of the CG model to reproduce results from atomistic simulations. There are dramatic consequences, e.g., collapse of polyions, with injudicious choices of the local charge distribution. The polyanions and polycations exhibit a similar conformational and dynamical behavior, suggesting that the sign of the polyion charge does not play a significant role.