arXiv subjects

M. Mueller

Publications and source records attributed to M. Mueller.

101 records · Page 6Linked to original sources

arXiv1998

Intrinsic profiles and capillary waves at homopolymer interfaces: a Monte Carlo study

A popular concept which describes the structure of polymer interfaces by ``intrinsic profiles'' centered around a two dimensional surface, the ``local interface position'', is tested by extensive Monte Carlo simulations of interfaces between demixed homopolymer phases in symmetric binary (AB) homopolymer blends, using the bond fluctuation model. The simulations are done in an LxLxD geometry. The interface is forced to run parallel to the LxL planes by imposing periodic boundary conditions in these directions and fixed boundary conditions in the D direction, with one side favoring A and the other side favoring B. Intrinsic profiles are calculated as a function of the ``coarse graining length'' B by splitting the system into columns of size BxBxD and averaging in each column over profiles relative to the local interface position. The results are compared to predictions of the self-consistent field theory. It is shown that the coarse graining length can be chosen such that the interfacial width matches that of the self-consistent field profiles, and that for this choice of B the ``intrinsic'' profiles compare well with the theoretical predictions.

cond-mat.soft↗

arXiv1998

Wetting and Capillary Condensation in Symmetric Polymer Blends: A comparison between Monte Carlo Simulations and Self-Consistent Field Calculations

We present a quantitative comparison between extensive Monte Carlo simulations and self-consistent field calculations on the phase diagram and wetting behavior of a symmetric, binary (AB) polymer blend confined into a film. The flat walls attract one component via a short range interaction. The critical point of the confined blend is shifted to lower temperatures and higher concentrations of the component with the lower surface free energy. The binodals close the the critical point are flattened compared to the bulk and exhibit a convex curvature at intermediate temperatures -- a signature of the wetting transition in the semi-infinite system. Investigating the spectrum of capillary fluctuation of the interface bound to the wall, we find evidence for a position dependence of the interfacial tension. This goes along with a distortion of the interfacial profile from its bulk shape. Using an extended ensemble in which the monomer-wall interaction is a stochastic variable, we accurately measure the difference between the surface energies of the components, and determine the location of the wetting transition via the Young equation. The Flory-Huggins parameter at which the strong first order wetting transition occurs is independent of chain length and grows quadratically with the integrated wall-monomer interaction strength. We estimate the location of the prewetting line. The prewetting manifests itself in a triple point in the phase diagram of very thick films and causes spinodal dewetting of ultrathin layers slightly above the wetting transition. We investigate the early stage of dewetting via dynamic Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv1998

Topological effects in ring polymers: A computer simulation study

Unconcatenated, unknotted polymer rings in the melt are subject to strong interactions with neighboring chains due to the presence of topological constraints. We study this by computer simulation using the bond-fluctuation algorithm for chains with up to N=512 statistical segments at a volume fraction Φ=0.5 and show that rings in the melt are more compact than gaussian chains. A careful finite size analysis of the average ring size R \propto N^ν yields an exponent ν\approx 0.39 \pm 0.03 in agreement with a Flory-like argument for the topologica interactions. We show (using the same algorithm) that the dynamics of molten rings is similar to that of linear chains of the same mass, confirming recent experimental findings. The diffusion constant varies effectively as D_{N} \propto N^{-1.22(3) and is slightly higher than that of corresponding linear chains. For the ring sizes considered (up to 256 statistical segments) we find only one characteristic time scale τ_{ee} \propto N^{2.0(2); this is shown by the collapse of several mean-square displacements and correlation functions onto corresponding master curves. Because of the shrunken state of the chain, this scaling is not compatible with simple Rouse motion. It applies for all sizes of ring studied and no sign of a crossover to any entangled regime is found.

cond-mat.stat-mech↗

arXiv1998

Collectivity, Phase Transitions and Exceptional Points in Open Quantum Systems

Phase transitions in open quantum systems, which are associated with the formation of collective states of a large width and of trapped states with rather small widths, are related to exceptional points of the Hamiltonian. Exceptional points are the singularities of the spectrum and eigenfunctions, when they are considered as functions of a coupling parameter. In the present paper this parameter is the coupling strength to the continuum. It is shown that the positions of the exceptional points (their accumulation point in the thermodynamical limit) depend on the particular type and energy dependence of the coupling to the continuum in the same way as the transition point of the corresponding phase transition.

quant-ph↗

arXiv1998

Phase transitions in open quantum systems

We consider the behaviour of open quantum systems in dependence on the coupling to one decay channel by introducing the coupling parameter $α$ being proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place which creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled e.g. for a picket fence with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the generic case of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the reorganization of the spectrum occurs at the critical value $α_{crit}$ of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.

quant-ph↗

arXiv1998

Monte Carlo simulations of interfaces in polymer blends

We review recent simulation studies of interfaces between immiscible homopolymer phases. Special emphasis is given to the presentation of efficient simulation techniques and powerful methods of data analysis, such as the analysis of capillary wave spectra. Possible reasons for polymer incompatibility and ways to relate model dependent interaction parameters to an effective Flory Huggins parameter are discussed. Various interfaces are then considered and characterised with respect to their microscopic structure and thermodynamic properties. In particular, interfaces between homopolymers of equal or disparate stiffness are studied, interfaces containing diblock copolymers, and interfaces confined in thin films. The results are related to the phase behaviour of ternary homopolymer/copolymer systems, and to wetting transitions in thin films.

cond-mat.soft↗

arXiv1998

Calculation of the Phase Behavior of Lipids

The self-assembly of monoacyl lipids in solution is studied employing a model in which the lipid's hydrocarbon tail is described within the Rotational Isomeric State framework and is attached to a simple hydrophilic head. Mean-field theory is employed, and the necessary partition function of a single lipid is obtained via a partial enumeration over a large sample of molecular conformations. The influence of the lipid architecture on the transition between the lamellar and inverted-hexagonal phases is calculated, and qualitative agreement with experiment is found.

cond-mat.stat-mech↗

arXiv1997

Interfaces in partly compatible polymer mixtures: A Monte Carlo simulation approach

The structure of polymer coils near interfaces between coexisting phases of symmetrical polymer mixtures (AB) is discussed, as well as the structure of symmetric diblock copolymers of the same chain length N adsorbed at the interface. The problem is studied by Monte Carlo simulations of the bond fluctuation model on the simple cubic lattice, using massively parallel computers (CRAY T3D). While homopolymer coils in the strong segregation limit are oriented parallel to the interface, the diblocks form ``dumbbells'' oriented perpendicular to the interface. However, in the dilute case (``mushroom regime'' rather than ``brush regime''), the diblocks are only weakly stretched. Distribution functions for monomers at the chain ends and in the center of the polymer are obtained, and a comparison to the self consistent field theory is made.

cond-mat.soft↗

arXiv1997

Diblock copolymers at a homopolymer-homopolymer-interface: a Monte Carlo simulation

The properties of diluted symmetric A-B diblock copolymers at the interface between A and B homopolymer phases are studied by means of Monte Carlo (MC) simulations of the bond fluctuation model. We calculate segment density profiles as well as orientational properties of segments, of A and B blocks, and of the whole chain. Our data support the picture of oriented ``dumbbells'', which consist of mildly perturbed A and B Gaussian coils. The results are compared to a self consistent field theory (SCFT) for single copolymer chains at a homopolymer interface. We also discuss the number of interaction contacts between monomers, which provide a measure for the ``active surface'' of copolymers or homopolymers close to the interface.

physics.chem-ph↗

arXiv1996

Chain length dependence of the polymer-solvent critical point parameters

We report grand canonical Monte Carlo simulations of the critical point properties of homopolymers within the Bond Fluctuation model. By employing Configurational Bias Monte Carlo methods, chain lengths of up to N=60 monomers could be studied. For each chain length investigated, the critical point parameters were determined by matching the ordering operator distribution function to its universal fixed-point Ising form. Histogram reweighting methods were employed to increase the efficiency of this procedure. The results indicate that the scaling of the critical temperature with chain length is relatively well described by Flory theory, i.e. Θ-T_c\sim N^{-0.5}. The critical volume fraction, on the other hand, was found to scale like ϕ_c\sim N^{-0.37}, in clear disagreement with the Flory theory prediction ϕ_c\sim N^{-0.5}, but in good agreement with experiment. Measurements of the chain length dependence of the end-to-end distance indicate that the chains are not collapsed at the critical point.

cond-mat↗

arXiv1994

Concentration and energy fluctuations in a critical polymer mixture

A semi-grand-canonical Monte Carlo algorithm is employed in conjunction with the bond fluctuation model to investigate the critical properties of an asymmetric binary (AB) polymer mixture. By applying the equal peak-weight criterion to the concentration distribution, the coexistence curve separating the A-rich and B-rich phases is identified as a function of temperature and chemical potential. To locate the critical point of the model, the cumulant intersection method is used. The accuracy of this approach for determining the critical parameters of fluids is assessed. Attention is then focused on the joint distribution function of the critical concentration and energy, which is analysed using a mixed-field finite-size-scaling theory that takes due account of the lack of symmetry between the coexisting phases. The essential Ising character of the binary polymer critical point is confirmed by mapping the critical scaling operator distributions onto independently known forms appropriate to the 3D Ising universality class. In the process, estimates are obtained for the field mixing parameters of the model which are compared both with those yielded by a previous method, and with the predictions of a mean field calculation.

cond-mat↗