Collapse transition of a square-lattice polymer with next nearest-neighbor interaction

Interpolating the radial distribution function in a two-dimensional fluid across a wide temperature range

Calculations of pair correlations in fluids usually require resource-intensive simulations or integral equations, while existing simple approximations lack accuracy. Here, we show that the pair correlation function for monolayer fluid-like systems can be decomposed into correlation peaks defined using Voronoi cells. Being properly normalized, these peaks exhibit a universal form, weak temperature dependence, and resemble those of an ideal gas, except for the first peak. As a result, we propose a simple and accurate approach to interpolate the pair correlation functions, suitable for molecular, colloids, and cellular fluids.

Coil-globule transition in two-dimensional polymer chains in an explicit solvent

The structure of two-dimensional polymer chains in a solvent at different temperatures is still far from being fully understood. Computer simulations of high-density macromolecular systems require the use of appropriate algorithms, and therefore the simulations were carried out using the Cooperative Motion Algorithm. The polymer model studied was exactly two-dimensional, coarse-grained and based on a triangular lattice. The theta temperature and temperature of coil-to-globule transition, and critical exponents were determined. The differences between the structure of such a disk and that of a chain in a dense polymer liquid were shown.

Structure of Strongly Adsorbed Polymer Systems: A Computer Simulation Study

The structure of very thin polymer films formed by strongly adsorbed macromolecules was studied by computer simulation. A coarse-grained model of strictly two-dimensional polymer systems was built, and its properties determined by an efficient Monte Carlo simulation algorithm. Properties of the model system were determined by means of Monte Carlo simulations with a sampling algorithm that combines Verdier-Stockmayer, pivot and reputation moves. The effects of temperature, chain length and polymer concentration on the macromolecular structure were investigated. It was shown that at low temperatures, the chain size increases with the concentration, that is, inversely with high temperatures. This behavior should be explained by the influence of inter-chain interactions.

Semianalytical solutions of Ising-like and Potts-like magnetic polymers on the Bethe lattice

We study magnetic polymers, defined as self-avoiding walks where each monomer i carries a "spin" s_{i} and interacts with its first neighbor monomers, let us say j, via a coupling constant J(s_{i},s_{j}). Ising-like [s_{i}=±1, with J(s_{i},s_{j})=ɛs_{i}s_{j}] and Potts-like [s_{i}=1,...,q, with J(s_{i},s_{j})=ɛ(s_{i})δ(s_{i},s_{j})] models are investigated. Some particular cases of these systems have recently been studied in the continuum and on regular lattices and are related to interesting applications. Here, we solve these models on Bethe lattices of branching number σ, focusing on the ferromagnetic case in zero external magnetic field. In most cases, the phase diagrams present a nonpolymerized (NP) and two polymerized phases: a paramagnetic (PP) and a ferromagnetic (FP) one. However, quite different thermodynamic properties are found depending on q in the Potts-like polymers and on whether one uses the Ising or Potts coupling in the two-state systems. For instance, for the standard Potts model [where ɛ(1)=⋯=ɛ(q)] with q=2, beyond the θ-point (where the critical and discontinuous NP-PP transition lines meet), a second tricritical point connecting a critical and a discontinuous transition line between the PP-FP phases is found in the system. A triple point where the NP-PP, NP-FP, and PP-FP first-order transition lines meet is also present in the phase diagram. For q≥3 the PP-FP transition is always discontinuous, and the scenario with the triple and θ points appears for q≤6. Interestingly, for q≥7, as well as for the Ising-like model the θ point becomes metastable and the critical NP-PP transition line ends at a critical end point (CEP), where it meets the NP-FP and PP-FP coexistence lines. Importantly, these results indicate that when q≤6 the spin ordering transition is preceded by the polymer collapse transition, whereas for q≥7 and in the Ising case these transitions happen together at the CEPs. Some interesting nonstandard Potts models are also studied, such as the lattice version of the model for epigenetic marks in the chromatin introduced by Michieletto et al. [Phys. Rev. X 6, 041047 (2016)2160-330810.1103/PhysRevX.6.041047]. In addition, the solution of the dilute Ising and dilute Potts models on the Bethe lattice are also presented here, since they are important to understand the PP-FP transitions.

Adsorption of two-dimensional polymers with two- and three-body self-interactions

Using extensive Monte Carlo simulations, we investigate the surface adsorption of self-avoiding trails on the triangular lattice with two- and three-body on-site monomer-monomer interactions. In the parameter space of two-body, three-body, and surface interaction strengths, the phase diagram displays four phases: swollen (coil), globule, crystal, and adsorbed. For small values of the surface interaction, we confirm the presence of swollen, globule, and crystal bulk phases. For sufficiently large values of the surface interaction, the system is in an adsorbed state, and the adsorption transition can be continuous or discontinuous, depending on the bulk phase. As such, the phase diagram contains a rich phase structure with transition surfaces that meet in multicritical lines joining in a single special multicritical point. The adsorbed phase displays two distinct regions with different characteristics, dominated by either single- or double-layer adsorbed ground states. Interestingly, we find that there is no finite-temperature phase transition between these two regions though rather a smooth crossover.

Exact partition function zeros of the Wako-Saitô-Muñoz-Eaton β hairpin model

I compute exact partition function zeros of β hairpins, using both analytic and numerical methods, extending previous work [J. Lee, Phys. Rev. Lett. 110, 248101 (2013)] where only a restricted class of hairpins was considered. The zeros of β hairpins with an odd number of peptide bonds are computed and the difference of the distribution of zeros from those for an even number of peptide bonds is explained in terms of additional entropy of liberating the extra bond at the turn region. Upon the introduction of a hydrophobic core in the central region of the hairpin, the zeros are distributed uniformly on two concentric circles corresponding to the hydrophobic collapse and the transition to the fully folded conformation. One of the circles dissolves as the core moves toward the turn or the tip region, which is explained in terms of the similarity of the intermediate state with the folded or unfolded states. The exact partition function zeros for a hairpin with a more complex structure of native contacts, the 16 C-terminal residues of streptococcal protein G B1, are numerically computed and their loci are closely approximated by concentric circles.

Partition function zeros and phase transitions for a square-well polymer chain

The zeros of the canonical partition functions for flexible square-well polymer chains have been approximately computed for chains up to length 256 for a range of square-well diameters. We have previously shown that such chain molecules can undergo a coil-globule and globule-crystal transition as well as a direct coil-crystal transition. Here we show that each of these transitions has a well-defined signature in the complex-plane map of the partition function zeros. The freezing transitions are characterized by nearly circular rings of uniformly spaced roots, indicative of a discontinuous transition. The collapse transition is signaled by the appearance of an elliptical horseshoe segment of roots that pinches down towards the positive real axis and defines a boundary to a root-free region of the complex plane. With increasing chain length, the root density on the circular ring and in the space adjacent to the elliptical boundary increases and the leading roots move towards the positive real axis. For finite-length chains, transition temperatures can be obtained by locating the intersection of the ellipse and/or circle of roots with the positive real axis. A finite-size scaling analysis is used to obtain transition temperatures in the long-chain (thermodynamic) limit. The collapse transition is characterized by crossover and specific-heat exponents of φ≈0.76(2) and α≈0.66(2), respectively, consistent with a second-order phase transition.

Exact partition function zeros of the Wako-Saitô-Muñoz-Eaton protein model

I compute exact partition function zeros of the Wako-Saitô-Muñoz-Eaton model for various secondary structural elements and for two proteins, 1BBL and 1I6C, by using both analytic and numerical methods. Two-state and barrierless downhill folding transitions can be distinguished by a gap in the distribution of zeros at the positive real axis.

Partition function zeros of a square-lattice homopolymer with nearest- and next-nearest-neighbor interactions

We study distributions of the partition function zeros in the complex temperature plane for a square-lattice homopolymer with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions. The dependence of distributions on the ratio of NN and NNN interaction strengths R is examined. The finite-size scaling of the zeros is performed to obtain the crossover exponent, which is shown to be independent of R within error bars, suggesting that all of these models belong to the same universality class. The transition temperatures are also computed by the zeros to obtain the phase diagram, and the results confirm that the model with stronger NNN interaction exhibits stronger effects of cooperativity.

Exact partition function zeros of a polymer on a simple cubic lattice

We study conformational transitions of a polymer on a simple-cubic lattice by calculating the zeros of the exact partition function, up to chain length 24. In the complex temperature plane, two loci of the partition function zeros are found for longer chains, suggesting the existence of both the coil-globule collapse transition and the melting-freezing transition. The locus corresponding to coil-globule transition clearly approaches the real axis as the chain length increases, and the transition temperature could be estimated by finite-size scaling. The form of the logarithmic correction to the scaling of the partition function zeros could also be obtained. The other locus does not show clear scaling behavior, but a supplementary analysis of the specific heat reveals a first-order-like pseudotransition.