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Register a new userPhase transitions in solvent dependent polymer adsorption in three dimensions
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We consider the phase diagram of self-avoiding walks (SAW) on the simple cubic lattice subject to surface and bulk interactions, modeling an adsorbing surface and variable solvent quality for a polymer in dilute solution, respectively. We simulate SAWs at specific interaction strengths to focus on locating certain transitions and their critical behavior. By collating these new results with previous results we sketch the complete phase diagram and show how the adsorption transition is affected by changing the bulk interaction strength. This expands on recent work considering how adsorption is affected by solvent quality. We demonstrate that changes in the adsorption crossover exponent coincide with phase boundaries.
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Advanced chain-growth computer simulation methodologies have been employed for a systematic statistical analysis of the critical behavior of a polymer adsorbing at a substrate. We use finitesize scaling techniques to investigate the solvent-quality dependence of critical exponents, critical temperature, and the structure of the phase diagram. Our study covers all solvent effects from the limit of super-self-avoiding walks, characterized by effective monomer-monomer repulsion, to poor solvent conditions that enable the formation of compact polymer structures. The results significantly benefit from taking into account corrections to scaling.
We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular proteins, upon adding suitable local interactions. Our algorithm can easily be equipped with such interactions, but we study here mainly the flexible homopolymer case where each conformation is generated with uniform probability. We argue that the algorithm is ergodic and has dynamical exponent z=0. We then use it to study polymers of size up to 64^3 = 262144 monomers. Results are presented for the effective interaction between end points, and the interaction with the boundaries of the system.
We show that near a second order phase transition in a two-component elastic medium of size L in two dimensions, where the local elastic deformation-order parameter couplings can break the inversion symmetry of the order parameter, the elastic modulii diverges with the variance of the local displacement fluctuations scaling as $[ln(L/a_0)]^{2/3}$ and the local displacement correlation function scaling as $[ln(r/a_0)]^{2/3}$ for weak inversion-asymmetryThe elastic constants can also vanish for system size exceeding a non-universal value, making the system unstable for strong asymmetry, where a 0 is a small-scale cut-off. We show that the elastic deformation-order parameter couplings can make the phase transition first order, when the elastic modulii do not diverge, but shows a jump proportional to the jump in the order parameter, across the transition temperature. For a bulk system, the elastic stiffness does not diverge for weak asymmetry, but can vanish across a second order transition giving instability for strong asymmetry, or displays jumps across a first order transition. In-vitro experiments on binary fluids embedded in a polymerized network, magnetic colloidal crystals or magnetic crystals could test these predictions.
We consider the thermodynamic behavior of local fluctuations occurring in a stable or metastable bulk phase. For a system with three or more phases, a simple analysis based on classical nucleation theory predicts that small fluctuations always resemble the phase having the lowest surface tension with the surrounding bulk phase, regardless of the relative chemical potentials of the phases. We also identify the conditions at which a fluctuation may convert to a different phase as its size increases, referred to here as a fluctuation phase transition (FPT). We demonstrate these phenonena in simulations of a two dimensional lattice model by evaluating the free energy surface that describes the thermodynamic properties of a fluctuation as a function of its size and phase composition. We show that a FPT can occur in the fluctuations of either a stable or metastable bulk phase and that the transition is first-order. We also find that the FPT is bracketed by well-defined spinodals, which place limits on the size of fluctuations of distinct phases. Furthermore, when the FPT occurs in a metastable bulk phase, we show that the superposition of the FPT on the nucleation process results in two-step nucleation (TSN). We identify distinct regimes of TSN based on the nucleation pathway in the free energy surface, and correlate these regimes to the phase diagram of the bulk system. Our results clarify the origin of TSN, and elucidate a wide variety of phenomena associated with TSN, including the Ostwald step rule.
Driven diffusive systems constitute paradigmatic models of nonequilibrium physics. Among them, a driven lattice gas known as the asymmetric simple exclusion process (ASEP) is the most prominent example for which many intriguing exact results have been obtained. After summarizing key findings, including the mapping of the ASEP to quantum spin chains, we discuss the recently introduced Brownian asymmetric simple exclusion process (BASEP) as a related class of driven diffusive system with continuous space dynamics. In the BASEP, driven Brownian motion of hardcore-interacting particles through one-dimensional periodic potentials is considered. We study whether current-density relations of the BASEP can be considered as generic for arbitrary periodic potentials and whether repulsive particle interactions other than hardcore lead to similar results. Our findings suggest that shapes of current-density relations are generic for single-well periodic potentials and can always be attributed to the interplay of a barrier reduction, blocking and exchange symmetry effect. This implies that in general up to five different phases of nonequilibrium steady states are possible for such potentials. The phases can occur in systems coupled to particle reservoirs, where the bulk density is the order parameter. For multiple-well periodic potentials, more complex current-density relations are possible and more phases can appear. Taking a repulsive Yukawa potential as an example, we show that the effects of barrier reduction and blocking on the current are also present. The exchange symmetry effect requires hardcore interactions and we demonstrate that it can still be identified when hardcore interactions are combined with weak Yukawa interactions.
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