Relaxation spectroscopy of LC main chain polymers: Experimental and theoretical investigations

A series of thermotropic main chain polymers with extended dimethylsiloxane segments was investigated. The study of dielectric properties of polymers revealed the relationship between their ability to form a mesophase and their molecular mobility. The peculiar behaviour of dielectric α-relaxation parameters during the transition from mesomorphic to isotropic members of this polymeric series was shown. The theoretical approaches were developed for understanding macrochain dynamics of liquid crystalline polymers. The theoretical and experimental results are in good agreement.     

Two-dimensional Quantum Random Walk

We analyze several families of two-dimensional quantum random walks. The feasible region (the region where probabilities do not decay exponentially with time) grows linearly with time, as is the case with one-dimensional QRW. The limiting shape of the feasible region is, however, quite different. The limit region turns out to be an algebraic set, which we characterize as the rational image of a compact algebraic variety. We also compute the probability profile within the limit region, which is essentially a negative power of the Gaussian curvature of the same algebraic variety. Our methods are based on analysis of the space-time generating function, following the methods of Pemantle and Wilson (J. Comb. Theory, Ser. A 97(1):129–161, 2002).     

Surfactant-induced amorphous aggregation of tobacco mosaic virus coat protein: a physical methods approach

The interactions of non-ionic surfactant Triton X-100 and the coat protein of tobacco mosaic virus, which is an established model for both ordered and non-ordered protein aggregation, were studied using turbidimetry, differential scanning calorimetry, isothermal titration calorimetry, and dynamic light scattering. It was found that at the critical aggregation concentration (equal to critical micelle concentration) of 138 x 10(-6) M, Triton X-100 induces partial denaturation of tobacco mosaic virus coat protein molecules followed by protein amorphous aggregation. Protein aggregation has profound ionic strength dependence and proceeds due to hydrophobic sticking of surfactant-protein complexes (start aggregates) with initial radii of 46 nm. It has been suggested that the anionic surfactant sodium dodecyl sulfate forms mixed micelles with Triton X-100 and therefore reverses protein amorphous aggregation with release of protein molecules from the amorphous aggregates. A stoichiometric ratio of 5 was found for Triton X-100-sodium dodecyl sulfate interactions.     

Nano‐scaled intrachain ordering and dynamics in two‐dimensional orientational polymer domains1)

Statistical and local relaxation properties of two‐dimensional finite polymer systems (domains) are considered. The domains consist of a large number of semirigid chains with the finite contour length at free, half‐free and fixed boundary conditions for chain ends. The intermolecular orientational order at short distances between chains in the thick domains is similar to the order in infinite two‐dimensional systems. The correlations of orientation between sufficiently distant elements of different chains decay by the exponential law, but the effective constant of interchain interactions in the domain is proportional to the molecular weight of the chain. At the given intra‐and interchain interactions an elongtation of the chains leads to a local ordering of chains in the domain (at free boundary conditions) or, on the contrary, to the decreasing of the parameter of short‐range orientational order (at fixed and half‐free boundary conditions). Independently of type of boundary conditions the parameter of large‐range orientational order tends to zero with increasing of the chain contour length. Dynamical equations and relaxation spectrums for times of local motions are obtained. From time correlation functions of local relaxation the times of nano‐scaled mobility of chains were calculated in depending on the bending rigidity of chains, the parameter of interchain interactions, and the contour length of chains. At the given intra‐and interchain interactions an elongtation of chains forming the domain leads to to the slowing‐down of local mobility of chains in the domain. The comparison with experimental date obtained by dielectric relaxation and polarized luminescence methods on investigation of nano‐scaled mobility in the dilute melts of comb‐shaped polymers has been carried out.     

Theory of relaxation properties of two‐dimensional polymer networks, 2. Local dynamic characteristics

Using normal mode transformation obtained in Part 1 of this series^[1], the exact analytical expressions for the mean‐square displacements of junctions and non‐junction beads, the autocorrelation functions of the end‐to‐end chain vectors between neighboring junctions, and those of subchain vectors of a two‐dimensional regular network consisting of "bead and spring" Rouse chains are obtained. Contributions of intra‐ and interchain relaxation processes to the local dynamic characteristics considered are compared. The time behavior of dynamic quantities obtained is estimated for different scales of motions. The possibility of describing long‐time relaxation of a two‐dimensional network by a simplified coarse‐grained network model is demonstrated. It is shown that the local relaxation properties of a two‐dimensional polymer network (as well as a three‐dimensional network) on scales smaller than the average distance between cross‐links are very close to those of a single Rouse chain. The large‐scale collective relaxation of the polymer networks having a two‐dimensional connectivity differs considerably from that of the three‐dimensional networks.     

Theory of relaxation spectra of polymer networks with interchain friction and long-range hydrodynamic interactions

The dynamic network model taken into account the friction relative to incompressible effective viscous medium (EVM), the hydrodynamic interactions of a network with the EVM, and the interchain friction is considered. Two collective network relaxation spectra (RS) arise. The first RS corresponds to the network motion relative to immobile EVM, the EVM does not take part in this motion. The second RS includes the combined viscous motion of the network and EVM because of long-range hydrodynamic interactions. This RS is finite and narrow for infinitely large network. The symmetry of this motion is in concordance with that of incompressible EVM. The existence of interchain friction leads to the narrowing of both types of relaxation spectra.     

Molecular dynamic simulation of polymer and polymer-oxide nanoclusters

Small systems composed of 10 molecules of poly-p-xylylene or a TiO₂ cluster (rutile) surrounded by 10 molecules of poly-p-xylylene are modeled via the method of molecular dynamics. The thermodynamic characteristics, structure, and mobility of poly-p-xylylene chains in the model systems are studied in a wide temperature interval (195–995 K) and compared with the corresponding characteristics of a volume phase and an individual polymer chain. With increasing temperature, the mobility of monomer units increases; this process leads to disordering. At high temperatures, there is an evident tendency for loosening and further disintegration of an aggregate into individual chains, which adopt a Gaussian coil shape. These transitions are similar to the transitions of the folded individual molecule of poly-p-xylylene. Introduction of a TiO₂ nanoparticle into poly-p-xylylene has a strong effect on the characteristics of the system with short polymer chains, where the adhesion of poly-p-xylylene molecules on the TiO₂ surface is accompanied by disordering in the peripheral region.     

Dynamics of Polymer Networks with Strong Differences in the Viscous Characteristics of their Crosslinks and Strands

We study theoretically the relaxation properties of polymer networks, whose monomers and junction sites have different friction parameters (ζ and ζ_jun, respectively). For this, we focus on topologically regular cubic networks built from “bead‐and‐spring” Rouse chains. Setting σ = ζ_jun/ζ, we determine analytically both the eigenvalues and the eigenmodes of the model for arbitrary values of σ. This allows us to extend previous approaches (Macromolecules 2000 , 33, 6578) which were restricted by the condition σ = 3. We compute the frequency dependent storage, G′(ω), and loss, G″(ω), moduli (which for σ ≫ 3 or σ ≪ 3 display two plateaus and two maxima, respectively) and also the mean‐square displacements of the network junctions and of the beads; these turn out to obey power laws, whose validity ranges depend on σ.

     

Asymptotics of Damped Periodic Motions with Random Initial Speed

We consider motion on the circle, possibly with friction and external forces, the initial velocity being a large random variable. We prove that under various assumptions the probability law of the stopping position of the motion converges to a distribution depending only on the motion equation. Here the time of stopping is either a constant or the first time instant at which the velocity vanishes, and the initial velocity is of the form αU + β, where U is a fixed random variable and α and/or β tend to infinity.     

Thresholdless surface solitons

We report on the existence of nonlinear surface waves that, on the one hand, do not require the threshold energy flow for their excitation, and, on the other hand, extend into media at both sides of the interface at low powers, i.e., cannot be reduced to the conventional Tamm states. Such waves can be excited if the refractive index in at least one of the materials forming the interface is periodically modulated, with properly selected modulation depth and frequency. Thresholdless surface solitons can be stable in the entire existence domain.