Dynamics of a Spreading Nanodroplet: A Molecular Dynamic Simulation

The spreading of polymer nanodroplets upon a sudden change from partial to complete wetting on an ideally flat and structureless solid substrate has been studied by molecular dynamic simulations using a coarse‐grained bead‐spring model of flexible macromolecules. Tanner's law for the growth of the lateral droplet radius {R(t) ∝ t^0.1} is found to hold as long as the droplet does not disintegrate into individually moving chains. The data for the contact angle θ following from Tanner's law correspond to a dependence on time {θ(t) ∝ t^−0.3}. Our analysis of the mean square displacements of the polymer centers of mass reveals several dynamic regimes during the process of spreading. PACS numbers: 68.10.Gw, 05.70.Ln, 61.20.Ja, 8.45.Gd.

Molecular dynamics results for the average mean square displacement of all polymer chains plotted vs. time for a broad range of values for ε_wall.     

Interfaces between coexisting phases in polymer mixtures: What can we learn from Monte Carlo simulations?

Symmetric binary polymer mixtures are studied by Monte Carlo simulation of the bond fluctuation model, considering both interfaces between coexisting bulk phases and interfaces confined in thin films. It is found that the critical behavior of interfacial tension and width is compatible with that of the Ising model, as expected from the universality principle. In the strong segregation limit, only qualitative but not quantitative agreement with the self-consistent field (SCF) theory is found. It is argued that the SCF theory requires but for the short chains studied (N = 32 effective monomer units per chain), the limit is only reached for close to unity. Also, the effective χ-parameter decreases in the interface. It is shown that the interfacial width w does not increase by the adsorption of block copolymers as long as their areal density is still dilute (“mushroom” regime). But a broadening of interfaces does occur for thin films confined between walls at distance D, due to fluctuations that lead to for short-range forces, in agreement with experiment.     

Interfaces in polymer blends

We investigate the structure and thermodynamics of interfaces in dense polymer blends using Monte Carlo (MC) simulations and self‐consistent field (SCF) calculations. For structurally symmetric blends we find quantitative agreement between the MC simulations and the SCF calculations for excess quantities of the interface (e.g., interfacial tension or enrichment of copolymers at the interface). However, a quantitative comparison between profiles across the interface in the MC simulations and the SCF calculations has to take due account of capillary waves. While the profiles in the SCF calculations correspond to intrinsic profiles of a perfectly flat interface the local interfacial position fluctuates in the MC simulations. We test this concept by extensive Monte Carlo simulations and study the cross‐over between “intrinsic” fluctuations which build up the local profile and capillary waves on long (lateral) length scales. Properties of structurally asymmetric blends are exemplified by investigating polymers of different stiffness. At high incompatibilities the interfacial width is not much larger than the persistence length of the stiffer component. In this limit we find deviations from the predictions of the Gaussian chain model: while the Gaussian chain model yields an increase of the interfacial width upon increasing the persistence length, no such increase is found in the MC simulations. Using a partial enumeration technique, however, we can account for the details of the chain architecture on all length scales in the SCF calculations and achieve good agreement with the MC simulations. In blends containing diblock copolymers we investigate the enrichment of copolymers at the interface and the concomitant reduction of the interfacial tension. At weak segregation the addition of copolymers leads to compatibilization. At high incompatibilities, the homopolymer‐rich phase can accommodate only a small fraction of copolymer before the copolymer forms a lamellar phase. The analysis of interfacial fluctuations yields an estimate for the bending rigidity of the interface. The latter quantity is important for the formation of a polymeric microemulsion at intermediate segregation and the consequences for the phase diagram are discussed.     

Novel initiators for oxazoline polymerization: generation of polydiacetylene-polyoxazoline networks

A series of bolaform polyoxazolines (POZO) with 1,3-diacetylene cores ((POZO)_m-(CH₂)_n-C≡C-C≡C-(CH₂)_n-(POZO)_m) were synthesized by the living polymerization of 2-methyl-1,3-oxazolines initiated by triflate esters derived from bis(ω-hydroxyalkyl)-1,3-diacetylenes. The chain length of the alkylspacers within the diacetylene core as well as the length of the attached polyoxazoline chains was varied between n = 1 and 4; m = 5, 10 and 15. The thermally induced 1,4-addition process yielding polydiacetylenes (PDA) was studied leading to highly conjugated POZO-PDA hybrid materials.     

Monte Carlo simulation studies of the interfaces between polymeric and other solids as models for fiber-matrix interactions in advanced composite materials

As a coarse-grained model for dense amorphous polymer systems interacting with solid walls (i.e., the fiber surface in a composite), the bond fluctuation model of flexible polymer chains confined between two repulsive surfaces is studied by extensive Monte Carlo simulations. Choosing a potential for the length of an effective bond that favors rather long bonds, the full temperature region from ordinary polymer melts down to the glass transition is accessible. It is shown that in the supercooled state near the glass transition an “interphase” forms near the walls, where the structure of the melt is influenced by the surface. This “interphase” already shows up in static properties, but also has an effect on monomer mobilities and the corresponding relaxation behavior of the polymer matrix. The thickness of the interphase is extracted from monomer density oscillations near the walls and is found to be strongly temperature dependent. It is ultimately larger than the gyration radius of the polymer chains. Effects of shear deformation on this model are simulated by choosing asymmetric jump rates near the moving wall (large jump rate in the direction of motion, and a small rate against it). It is studied how this dynamic perturbation propagates into the bulk of the polymer matrix.     

Monte Carlo methods for polymer chains in two - dimensional geometries (polymers at surfaces and interfaces)

Coarse-grained models of polymers at interfaces can be defined such that their treatment by Monte Carlo simulation is most convenient and efficient for the problem at hand. This simulation strategy is briefly illustrated with three examples: (1) The orientational ordering of rigid rod-like polymers grafted to a surface, where “table methods” can be used, applying a fine discretization of the angles describing rod orientation. (2) Surface enrichment of one species in a polymer blend is treated by a semi-grand-canonical technique. (3) The number of configurations and structure of a star polymer attached with its center to a wall is studied by a “growth technique” generalizing simple sampling methods.     

Monte Carlo simulation in polymer physics: Some recent developments

The computer simulation of macromolecular materials has to deal with phenomena on length scales from 1Å to 100Å, as well as with time scales ranging over many orders of magnitude, and thus still presents a challenge. With suitably coarse-grained models which disregard detailed information on chemical structure nevertheless collective phenomena can be described, such as unmixing of polymer blends, mesophase ordering of block-copolymer melts, “blob formation” in semidilute solutions, etc. Simulations of such models provide a sensitive test of approximate theories and give valuable hints for experiments.     

Transverse optical patterns for ultra‐low‐light‐level all‐optical switching

We review recent theoretical and experimental efforts toward developing an all‐optical switch based on transverse optical patterns. Transverse optical patterns are formed when counterpropagating laser beams interact with a nonlinear medium. A perturbation, in the form of a weak switch beam injected into the nonlinear medium, controls the orientation of the generated patterns. Each state of the pattern orientation is associated with a state of the switch. That is, information is stored in the orientation state. A realization of this switch using a warm rubidium vapor shows that it can be actuated by as few as 600 ± 40 photons with a response time of 5 µs. Models of nonlinear optical interactions in semiconductor quantum wells and microresonators suggest these systems are also suitable for use as fast all‐optical switches using this same conceptual design, albeit at higher switching powers.