Microcanonical analysis of adsorption of homopolymer chain on a surface

Polymer adsorption on curved surfaces

The conformational behavior of a coarse-grained finite polymer chain near an attractive spherical surface was investigated by means of multicanonical Monte Carlo computer simulations. In a detailed analysis of canonical equilibrium data over a wide range of sphere radius and temperature, we have constructed entire phase diagrams both for nongrafted and end-grafted polymers. For the identification of the conformational phases, we have calculated several energetic and structural observables such as gyration tensor based shape parameters and their fluctuations by canonical statistical analysis. Despite the simplicity of our model, it qualitatively represents in the considered parameter range real systems that are studied in experiments. The work discussed here could have experimental implications from protein-ligand interactions to designing nanosmart materials.

First-order phase transitions in the real microcanonical ensemble

We present a simulation and data analysis technique to investigate first-order phase transitions and the associated transition barriers. The simulation technique is based on the real microcanonical ensemble where the sum of kinetic and potential energy is kept constant. The method is tested for the droplet condensation-evaporation transition in a Lennard-Jones system with up to 2048 particles at fixed density, using simple Metropolis-like sampling combined with a replica-exchange scheme. Our investigation of the microcanonical ensemble properties reveals that the associated transition barrier is significantly lower than in the canonical counterpart. Along the line of investigating the microcanonical ensemble behavior, we develop a framework for general ensemble evaluations. This framework is based on a clear separation between system-related and ensemble-related properties, which can be exploited to specifically tailor artificial ensembles suitable for first-order phase transitions.

Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations

Over the last decade flat-histogram Monte Carlo simulations, especially multi-canonical and Wang-Landau simulations, have emerged as a strong tool to study the statistical mechanics of polymer chains. These investigations have focused on coarse-grained models of polymers on the lattice and in the continuum. Phase diagrams of chains in bulk as well as chains attached to surfaces were studied, for homopolymers as well as for protein-like models. Also, aggregation behavior in solution of these models has been investigated. We will present here the theoretical background for these simulations, explain the algorithms used and discuss their performance and give an overview over the systems studied with these methods in the literature, where we will limit ourselves to studies of coarse-grained model systems. Implementations of these algorithms on parallel computers will be also briefly described. In parallel to the development of these simulation methods, the power of a micro-canonical analysis of such simulations has been recognized, and we present the current state of the art in applying the micro-canonical analysis to phase transitions in nanoscopic polymer systems.

Molecular Dynamics and Monte Carlo simulations in the microcanonical ensemble: Quantitative comparison and reweighting techniques

Molecular Dynamics (MD) and Monte Carlo (MC) simulations are the most popular simulation techniques for many-particle systems. Although they are often applied to similar systems, it is unclear to which extent one has to expect quantitative agreement of the two simulation techniques. In this work, we present a quantitative comparison of MD and MC simulations in the microcanonical ensemble. For three test examples, we study first- and second-order phase transitions with a focus on liquid-gas like transitions. We present MD analysis techniques to compensate for conservation law effects due to linear and angular momentum conservation. Additionally, we apply the weighted histogram analysis method to microcanonical histograms reweighted from MD simulations. By this means, we are able to estimate the density of states from many microcanonical simulations at various total energies. This further allows us to compute estimates of canonical expectation values.

Conformation and adsorption transition on an attractive surface of a ring polymer in solution

Ring polymers have the same critical adsorption point and crossover exponent as linear chains.

Surface adsorption of colloidal brushes at good solvents conditions

Monte Carlo simulations are presented for a minimal model of one spherical colloidal particle as it interacts with one attractive flat substrate. The colloidal particle is decorated by either 6 or 14 grafted polymer chains. The chains are always rather short, with their radius of gyration, estimated at infinite dilution in good solvent conditions, never larger than the spherical colloid diameter. Although all simulations are conducted under "good-solvent" conditions for the grafted polymer chains, we find that small changes in the polymer segment-polymer segment energetic interaction parameter can lead to significantly different scenarios. When the Lennard-Jones attraction is weak, 0.12 k(B)T, increasing the polymer length decreases the likelihood of colloidal adsorption, as expected. On the contrary, when the attraction is 0.18 k(B)T, increasing the length of the grafted polymer chains promotes the adsorption of the colloidal brush onto the surface. When the Lennard-Jones energetic parameter that describes polymer segment-polymer segment interactions is 0.15 k(B)T, as the length of the grafted polymer chains increases the probability of colloidal adsorption decreases to a minimum, and then increases. The results, explained in terms of a competition between entropic (due to the reduction in degrees of freedom available to the grafted polymer chains upon colloidal brush adsorption) and enthalpic driving forces (due to favorable colloid-surface and polymer segment-surface interactions), could be useful for controlling the circulation lifetime of liposomes within the blood stream, and optimizing solar energy harvesting by depositing colloidal particles on solid surfaces.