Number Of Available Configurations Research Articles

A method for calculating the nonequilibrium entropy of a flowing polymer melt via atomistic simulation.

Nonequilibrium thermodynamics as applied to polymeric liquids is limited by the inability to quantify the configurational entropy. There is no known experimental method to determine it rigorously. Theoretically, entropy is based entirely on the configurational microstate of the material, but for polymer liquids, the number of available configurations is immense and covers long length scales associated with the chain-like nature of the constituent molecules. In principle, however, it should be possible to calculate the entropy from a realistic molecular dynamics simulation that contains positional data for each atomic unit making up the polymer macromolecules. However, there are two challenges in calculating the entropy from an atomistic simulation: it is necessary to relate atomic positions to configurational mesostates, depending on the degree of coarse-graining assumed (if any), and then to entropy, and considerable computational resources are required to determine the three-dimensional probability distribution functions of the configurational mesostates. In this study, a method was developed to calculate nonequilibrium entropy using 3d probability distributions for a linear, entangled polyethylene melt undergoing steady-state shear and elongational flow. An approximate equation expressed in terms of second moments of the 3d distributions was also examined, which turned out to provide almost identical values of entropy as the fully 3d distributions at the mesoscopic level associated with the end-to-end vector of the polymer chains.

Synthesis of semicrystalline nanocapsular structures obtained by Thermally Induced Phase Separation in nanoconfinement.

Phase separation of a polymer solution exhibits a peculiar behavior when induced in a nanoconfinement. The energetic constraints introduce additional interactions between the polymer segments that reduce the number of available configurations. In our work, this effect is exploited in a one-step strategy called nanoconfined-Thermally Induced Phase Separation (nc-TIPS) to promote the crystallization of polymer chains into nanocapsular structures of controlled size and shell thickness. This is accomplished by performing a quench step of a low-concentrated PLLA-dioxane-water solution included in emulsions of mean droplet size <500 nm acting as nanodomains. The control of nanoconfinement conditions enables not only the production of nanocapsules with a minimum mean particle diameter of 70 nm but also the tunability of shell thickness and its crystallinity degree. The specific properties of the developed nanocapsular architectures have important implications on release mechanism and loading capability of hydrophilic and lipophilic payload compounds.

All-atom molecular dynamics simulations of an artificial sodium channel in a lipid bilayer: the effect of water solvation/desolvation of the sodium ion

All-atom molecular dynamics is used to investigate the transport of Na+ across a 1,2-dioleoyl-sn-glycero-3-phosphocholine lipid bilayer facilitated by a diazacrown hydraphile. Specifically, the free energy of Na+ passing through the bilayer is calculated using the adaptive biasing force method to study the free energy associated with the increase in Na+ transport in the presence of the hydraphile molecule. The results show that water interaction greatly influences Na+ transport through the lipid bilayer as water is pulled through the bilayer with Na+ forming a water channel. The hydraphile causes a reduction in the free energy barrier for the transport of Na+ through the head group part of the lipid bilayer since it complexes the Na+ reducing the necessity for water to be complexed and, therefore, dragged through with Na+, an energetically unfavorable process. The free energy associated with Na+ being desolvated within the bilayer is significantly decreased in the presence of the hydraphile molecule; the hydraphile increases the number of solvation states of Na+ that can be adopted, and this increase in the number of available configurations provides an entropic explanation for the success of the hydraphile.

Site–bond percolation on triangular lattices: Monte Carlo simulation and analytical approach

A generalization of the pure site and pure bond percolation problems called site–bond percolation on a triangular lattice is studied. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as S∩B and S∪B) for site–bond percolation are used. In S∩B (S∪B), two points are said to be connected if a sequence of occupied sites and (or) bonds joins them. By using finite-size scaling theory, data from S∩B and S∪B are analyzed in order to determine (i) the phase boundary between the percolating and non-percolating regions and (ii) the numerical values of the critical exponents of the phase transition occurring in the system. A theoretical approach, based on exact calculations of configurations on finite triangular cells, is applied to study the site–bond percolation on triangular lattices. The percolation processes have been monitored by following the percolation function, defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied elements. A comparison of the results obtained by these two methods has been performed and discussed.

Percolation of dimers on square lattices

A theoretical approach, based on exact calculations of configurations on finite rectangular cells, is applied to study the percolation of homonuclear dimers on square lattices. An efficient algorithm allows us to calculate the detailed structure of the configuration space for M=Lx×Ly cells, with M varying from 16 to 36. The percolation process has been monitored by following the percolation function, defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied sites. The percolation threshold has been calculated by means of two complementary methods: one based on well-known renormalization techniques and the other based on determining the inflection point of the percolation function curves. A comparison of the results obtained by these two methods has been performed. The study includes the use of finite-size scaling theory to extrapolate numerical results towards the thermodynamic limit. The effect of jamming due to dimers is also established. Finally, the critical exponents ν, β and γ have been obtained and values compared with numerical results and expected theoretical estimations. The present results show agreement and even improvement (in the case of γ) with respect to some numeric values available in the literature.

Aging and relaxation in glass-forming systems

We propose that there exists a generic class of glass-forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems exhibit patches (or clusters) of these competing states which become locally stable in the sense of having a relatively high local shear modulus. It is in between these clusters where aging, relaxation, and plasticity under strain can take place. We demonstrate explicitly that relaxation events that lead to aging occur where the local shear modulus is low (even negative) and result in an increase in the size of local patches of relative order. We examine the aging events closely from two points of view. On the one hand we show that they are very localized in real space, taking place outside the patches of relative order, and from the other point of view we show that they represent transitions from one local minimum in the potential surface to another. This picture offers a direct relation between structure and dynamics, ascribing the slowing down in glass-forming systems to the reduction in relative volume of the amorphous material which is liquidlike. While we agree with the well-known Adam-Gibbs proposition that the slowing down is due to an entropic squeeze (a dramatic decrease in the number of available configurations), we do not agree with the Adam-Gibbs (or the Volger-Fulcher) formulas that predict an infinite relaxation time at a finite temperature. Rather, we propose that generically there should be no singular crisis at any finite temperature: the relaxation time and the associated correlation length (average cluster size) increase at most superexponentially when the temperature is lowered.

The configurational entropy of two-dimensional random Penrose tilings

The configurational entropy of two-dimensional random tilings of Penrose rhombi has been calculated by two methods. Estimating the configurational degeneracy by determining the number of available configurations of each tile during physical model building gave an entropy of 0.495k per tile for a compositionally unconstrained tiling. Geometrical models based on the number of configurations around each vertex without correlations between them, gave higher values.