arXiv subjects

Marcus Müller

Publications and source records attributed to Marcus Müller.

23 records · Page 2Linked to original sources

arXiv2011

Three-phase coexistence with sequence partitioning in symmetric random block copolymers

We inquire about the possible coexistence of macroscopic and microstructured phases in random Q-block copolymers built of incompatible monomer types A and B with equal average concentrations. In our microscopic model, one block comprises M identical monomers. The block-type sequence distribution is Markovian and characterized by the correlation λ. Upon increasing the incompatibility χ (by decreasing temperature) in the disordered state, the known ordered phases form: for λ > λ_c, two coexisting macroscopic A- and B-rich phases, for λ < λ_c, a microstructured (lamellar) phase with wave number k(λ). In addition, we find a fourth region in the λ-χ plane where these three phases coexist, with different, non-Markovian sequence distributions (fractionation). Fractionation is revealed by our analytically derived multiphase free energy, which explicitly accounts for the exchange of individual sequences between the coexisting phases. The three-phase region is reached, either, from the macroscopic phases, via a third lamellar phase that is rich in alternating sequences, or, starting from the lamellar state, via two additional homogeneous, homopolymer-enriched phases. These incipient phases emerge with zero volume fraction. The four regions of the phase diagram meet in a multicritical point (λ_c, χ_c), at which A-B segregation vanishes. The analytical method, which for the lamellar phase assumes weak segregation, thus proves reliable particularly in the vicinity of (λ_c, χ_c). For random triblock copolymers, Q=3, we find the character of this point and the critical exponents to change substantially with the number M of monomers per block. The results for Q=3 in the continuous-chain limit M -> \infty are compared to numerical self-consistent field theory (SCFT), which is accurate at larger segregation.

cond-mat.soft↗

arXiv2011

Statics of polymer droplets on deformable surfaces

The equilibrium properties of polymer droplets on a soft deformable surface are investigated by molecular dynamics simulations of a bead-spring model. The surface consists of a polymer brush with irreversibly end-tethered linear homopolymer chains onto a flat solid substrate. We tune the softness of the surface by varying the grafting density. Droplets are comprised of bead-spring polymers of various chain lengths. First, both systems, brush and polymer liquid, are studied independently in order to determine their static and dynamic properties. In particular, using a numerical implementation of an AFM experiment, we measure the shear modulus of the brush surface and compare the results to theoretical predictions. Then, we study the wetting behavior of polymer droplets with different contact angles and on substrates that differ in softness. Density profiles reveal, under certain conditions, the formation of a wetting ridge beneath the three-phase contact line. Cap-shaped droplets and cylindrical droplets are also compared to estimate the effect of the line tension with respect to the droplet size. Finally, the results of the simulations are compared to a phenomenological free-energy calculation that accounts for the surface tensions and the compliance of the soft substrate. Depending on the surface/drop compatibility, surface softness and drop size, a transition between two regimes is observed: from one where the drop surface energy balances the adhesion with the surface, which is the classical Young-Dupré wetting regime, to another one where a coupling occurs between adhesion, droplet and surface elastic energies.

cond-mat.soft↗

arXiv2010

Main phase transition in lipid bilayers: phase coexistence and line tension in a soft, solvent-free, coarse-grained model

We devise a soft, solvent-free, coarse-grained model for lipid bilayer membranes. The non-bonded interactions take the form of a weighted-density functional which allows us to describe the thermodynamics of self-assembly and packing effects of the coarse-grained beads in terms of a density expansion of the equation of state and the weighting functions that regularize the microscopic bead densities, respectively. Identifying the length and energy scales via the bilayer thickness and the thermal energy scale, kT, the model qualitatively reproduces key characteristics (e.g., bending rigidity, area per lipid molecules, and compressibility) of lipid membranes. We employ this model to study the main phase transition between the liquid and the gel phase of the bilayer membrane. We accurately locate the phase coexistence using free energy calculations and also obtain estimates for the bare and the thermodynamic line tension.

cond-mat.soft↗

arXiv2008

Generating multi-chain configurations of an inhomogeneous melt from the knowledge of single-chain properties

Mean-field techniques provide a rather accurate description of single-chain conformations in spatially inhomogeneous polymer systems containing interfaces or surfaces. Intermolecular correlations, however, are not described by the mean-field approach and information about the distribution of distance between different molecules is lost. Based on the knowledge of the exact equilibrium single-chain properties in contact with solid substrates, we generate multi-chain configurations that serve as nearly equilibrated starting configurations for molecular dynamics simulations by utilizing the packing algorithm of Auhl and co-workers [J. Chem. Phys. 119, 12718 (2003)] for spatially inhomogeneous systems, i.e., a thin polymer film confined between two solid substrates. The single-chain conformations are packed into the thin film conserving the single-chain properties and simultaneously minimizing local fluctuations of the density. The extent to which enforcing the near-incompressibility of a dense polymer liquid during the packing process is able to re-establish intermolecular correlations is investigated by monitoring intermolecular correlation functions and the structure function of density fluctuations as a function of the distance from the confining solid substrates.

cond-mat.soft↗

arXiv1999

Monte Carlo investigations of phase transitions: status and perspectives

Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies of Ising models are discussed, as well as the extension to models of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms, even the scaling functions describing the crossover from the Ising universality class to the mean-field behavior with increasing interaction range can be described. Additionally, the issue of finite-size scaling in Ising models above the marginal dimension (d*=4) is discussed.

cond-mat.stat-mech↗