Pier Luca Palla

Theory and Monte Carlo simulations for the stretching of flexible and semiflexible single polymer chains under external fields

Recent developments of microscopic mechanical experiments allow the manipulation of individual polymer molecules in two main ways: uniform stretching by external forces and non-uniform stretching by external fields. Many results can be thereby obtained for specific kinds of polymers and specific geometries. In this work, we describe the non-uniform stretching of a single, non-branched polymer molecule by an external field (e.g., fluid in uniform motion, or uniform electric field) by a universal physical framework, which leads to general conclusions on different types of polymers. We derive analytical results both for the freely-jointed chain and the worm-like chain models based on classical statistical mechanics. Moreover, we provide a Monte Carlo numerical analysis of the mechanical properties of flexible and semiflexible polymers anchored at one end. The simulations confirm the analytical achievements, and moreover allow to study the situations where the theory cannot provide explicit and useful results. In all cases, we evaluate the average conformation of the polymer and its fluctuation statistics as a function of the chain length, bending rigidity, and field strength.

Elasticity of flexible and semiflexible polymers with extensible bonds in the Gibbs and Helmholtz ensembles

Stretching experiments on single molecules of arbitrary length opened the way for studying the statistical mechanics of small systems. In many cases in which the thermodynamic limit is not satisfied, different macroscopic boundary conditions, corresponding to different statistical mechanics ensembles, yield different force-displacement curves. We formulate analytical expressions and develop Monte Carlo simulations to quantitatively evaluate the difference between the Helmholtz and the Gibbs ensembles for a wide range of polymer models of biological relevance. We consider generalizations of the freely jointed chain and of the worm-like chain models with extensible bonds. In all cases we show that the convergence to the thermodynamic limit upon increasing contour length is described by a suitable power law and a specific scaling exponent, characteristic of each model.

Molecular dynamics of ionic self-diffusion at an MgO grain boundary

AbstractThe characterization of self-diffusion in MgO grain boundaries is a materials science problem of general interest, being relevant to the stability and reactivity of MgO layers in artificial nanostructures as well as to the understanding of mass transport and morphological evolution in polycrystalline metal oxides which are employed in many technological applications. In addition, atomic transport in MgO is a key factor to describe the rheology of the Earth’s lower mantle. In this work, we tackle the problem using a classical molecular dynamics model and finite-temperature simulations. To this purpose, we first design a stable grain boundary structure, which is meant to be representative of general internal interfaces in nanocrystalline MgO. The Mg and O self-diffusion coefficients along this grain boundary are then determined as a function of temperature by calculating the mean-square ionic displacement in the boundary region. Two different diffusion regimes at low and high temperature are identified, allowing to obtain the relevant activation enthalpies for migration from the temperature dependance of the diffusion coefficients. Our results prove that Mg diffusion along MgO grain boundaries is sufficiently fast to explain the recently reported development of MgO hollow structures during repeated hydrogen sorption cycles in Mg/MgO nanoparticles.

Response to “Comment on ‘Elasticity of flexible and semiflexible polymers with extensible bonds in the Gibbs and Helmholtz ensembles”’ [J. Chem. Phys. 138, 157101 (2013)]

Two different statistical ensembles can be considered for extending a single polymer chain: the Gibbs (or isotensional) ensemble characterized by a deterministic force applied to the free end of the chain (the other being fixed in a given reference frame), and the Helmholtz (or isometric) ensemble obtained with both the ends of the polymers tethered at two different points of the space. When the thermodynamic limit is satisfied (the number of monomers approaches infinity) these ensembles are equivalent from the thermodynamic point of view: it means that the constitutive equations (vector force-extension relations) assume the same mathematical form in both isotensional and isometric conditions. Equivalently, the Helmholtz and Gibbs free energies are linked by a Legendre transform. We explain that this general result is coherent with some “forms of inequivalence” observed by defining different average values of force and position vectors. However, this fact does not indicate thermodynamic inequivalence as l...