Non-extensivity of the chemical potential of polymer melts

Following Flory's ideality hypothesis the chemical potential of a test chain of length $n$ immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in $n$. We argue that an additional contribution $\delta \mu_c(n) \sim +1/\rho\sqrt{n}$ arises ($\rho$ being the monomer density) for all $\P(N)$ if $n \ll$ which can be traced back to the overall incompressibility of the solution leading to a long-range repulsion between monomers. Focusing on Flory distributed melts we obtain $\delta \mu_c(n) \approx (1- 2 n/) / \rho \sqrt{n}$ for $n \ll ^2$, hence, $\delta \mu_c(n) \approx - 1/\rho \sqrt{n}$ if $n$ is similar to the typical length of the bath $$. Similar results are obtained for monodisperse solutions. Our perturbation calculations are checked numerically by analyzing the annealed length distribution P(N) of linear equilibrium polymers generated by Monte Carlo simulation of the bond-fluctuation model. As predicted we find, e.g., the non-exponentiality parameter $K_p \equiv 1 - /p!^p$ to decay as $K_p \approx 1 / \sqrt{}$ for all moments $p$ of the distribution.Comment: 14 pages, 6 figures, submitted to EPJ

A finite excluded volume bond-fluctuation model: Static properties of dense polymer melts revisited

The classical bond-fluctuation model (BFM) is an efficient lattice Monte Carlo algorithm for coarse-grained polymer chains where each monomer occupies exclusively a certain number of lattice sites. In this paper we propose a generalization of the BFM where we relax this constraint and allow the overlap of monomers subject to a finite energy penalty \overlap. This is done to vary systematically the dimensionless compressibility $g$ of the solution in order to investigate the influence of density fluctuations in dense polymer melts on various s tatic properties at constant overall monomer density. The compressibility is obtained directly from the low-wavevector limit of the static structure fa ctor. We consider, e.g., the intrachain bond-bond correlation function, $P(s)$, of two bonds separated by $s$ monomers along the chain. It is shown that the excluded volume interactions are never fully screened for very long chains. If distances smaller than the thermal blob size are probed ($s \ll g$) the chains are swollen acc ording to the classical Fixman expansion where, e.g., $P(s) \sim g^{-1}s^{-1/2}$. More importantly, the polymers behave on larger distances ($s \gg g$) like swollen chains of incompressible blobs with P(s) \si m g^0s^{-3/2}.Comment: 46 pages, 12 figure

On the Dynamics and Disentanglement in Thin and Two-Dimensional Polymer Films

We present results from molecular dynamics simulations of strictly two-dimensional (2D) polymer melts and thin polymer films in a slit geometry of thickness of the order of the radius of gyration. We find that the dynamics of the 2D melt is qualitatively different from that of the films. The 2D monomer mean-square displacement shows a $t^{8/15}$ power law at intermediate times instead of the $t^{1/2}$ law expected from Rouse theory for nonentangled chains. In films of finite thickness, chain entanglements may occur. The impact of confinement on the entanglement length $N_\mathrm{e}$ has been analyzed by a primitive path analysis. The analysis reveals that $N_\mathrm{e}$ increases strongly with decreasing film thickness.Comment: 6 pages, 3 figures, proceedings 3rd International Workshop on Dynamics in Confinement (CONFIT 2006

Are polymer melts "ideal"?

It is commonly accepted that in concentrated solutions or melts high-molecular weight polymers display random-walk conformational properties without long-range correlations between subsequent bonds. This absence of memory means, for instance, that the bond-bond correlation function, $P(s)$, of two bonds separated by $s$ monomers along the chain should exponentially decay with $s$. Presenting numerical results and theoretical arguments for both monodisperse chains and self-assembled (essentially Flory size-distributed) equilibrium polymers we demonstrate that some long-range correlations remain due to self-interactions of the chains caused by the chain connectivity and the incompressibility of the melt. Suggesting a profound analogy with the well-known long-range velocity correlations in liquids we find, for instance, $P(s)$ to decay algebraically as $s^{-3/2}$. Our study suggests a precise method for obtaining the statistical segment length \bstar in a computer experiment.Comment: 4 pages, 3 figure

Single chain structure in thin polymer films: Corrections to Flory's and Silberberg's hypotheses

Conformational properties of polymer melts confined between two hard structureless walls are investigated by Monte Carlo simulation of the bond-fluctuation model. Parallel and perpendicular components of chain extension, bond-bond correlation function and structure factor are computed and compared with recent theoretical approaches attempting to go beyond Flory's and Silberberg's hypotheses. We demonstrate that for ultrathin films where the thickness, $H$, is smaller than the excluded volume screening length (blob size), $\xi$, the chain size parallel to the walls diverges logarithmically, $R^2/2N \approx b^2 + c \log(N)$ with $c \sim 1/H$. The corresponding bond-bond correlation function decreases like a power law, $C(s) = d/s^{\omega}$ with $s$ being the curvilinear distance between bonds and $\omega=1$. % Upon increasing the film thickness, $H$, we find -- in contrast to Flory's hypothesis -- the bulk exponent $\omega=3/2$ and, more importantly, an {\em decreasing} $d(H)$ that gives direct evidence for an {\em enhanced} self-interaction of chain segments reflected at the walls. Systematic deviations from the Kratky plateau as a function of $H$ are found for the single chain form factor parallel to the walls in agreement with the {\em non-monotonous} behaviour predicted by theory. This structure in the Kratky plateau might give rise to an erroneous estimation of the chain extension from scattering experiments. For large $H$ the deviations are linear with the wave vector, $q$, but are very weak. In contrast, for ultrathin films, $H<\xi$, very strong corrections are found (albeit logarithmic in $q$) suggesting a possible experimental verification of our results.Comment: 16 pages, 7 figures. Dedicated to L. Sch\"afer on the occasion of his 60th birthda

Coordinatively unsaturated ruthenium complexes as efficient alkyne-azide cycloaddition catalysts

The performance of 16-electron ruthenium complexes with the general formula Cp*Ru(L)X (in which L = phosphine or N-heterocyclic carbene ligand; X = Cl or OCH2CF3) was explored in azide−alkyne cycloaddition reactions that afford the 1,2,3- triazole products. The scope of the Cp*Ru(PiPr3)Cl precatalyst was investigated for terminal alkynes leading to new 1,5-disubstituted 1,2,3-triazoles in high yields. Mechanistic studies were conducted and revealed a number of proposed intermediates. Cp*Ru- (PiPr3)(η2-HCCPh)Cl was observed and characterized by 1H, 13C, and 31P NMR at temperatures between 273 and 213 K. A rare example of N,N-κ2-phosphazide complex, Cp*Ru(κ2-iPr3PN3Bn)Cl, was fully characterized, and a single-crystal X-ray diffraction structure was obtained. DFT calculations describe a complete map of the catalytic reactivity with phenylacetylene and/or benzylazide.Publisher PDFPeer reviewe

The Halogen Bond in the Design of Functional Supramolecular Materials: Recent Advances

Halogen bonding is an emerging noncovalent interaction for constructing supramolecular assemblies. Though similar to the more familiar hydrogen bonding, four primary differences between these two interactions make halogen bonding a unique tool for molecular recognition and the design of functional materials. First, halogen bonds tend to be much more directional than (single) hydrogen bonds. Second, the interaction strength scales with the polarizability of the bond-donor atom, a feature that researchers can tune through single-atom mutation. In addition, halogen bonds are hydrophobic whereas hydrogen bonds are hydrophilic. Lastly, the size of the bond-donor atom (halogen) is significantly larger than hydrogen. As a result, halogen bonding provides supramolecular chemists with design tools that cannot be easily met with other types of noncovalent interactions and opens up unprecedented possibilities in the design of smart functional materials. This Account highlights the recent advances in the design of halogen-bond-based functional materials. Each of the unique features of halogen bonding, directionality, tunable interaction strength, hydrophobicity, and large donor atom size, makes a difference. Taking advantage of the hydrophobicity, researchers have designed small-size ion transporters. The large halogen atom size provided a platform for constructing all-organic light-emitting crystals that efficiently generate triplet electrons and have a high phosphorescence quantum yield. The tunable interaction strengths provide tools for understanding light-induced macroscopic motions in photoresponsive azobenzene-containing polymers, and the directionality renders halogen bonding useful in the design on functional supramolecular liquid crystals and gel-phase materials. Although halogen bond based functional materials design is still in its infancy, we foresee a bright future for this field. We expect that materials designed based on halogen bonding could lead to applications in biomimetics, optics/photonics, functional surfaces, and photoswitchable supramolecules

Surface segregation of conformationally asymmetric polymer blends

We have generalized the Edwards' method of collective description of dense polymer systems in terms of effective potentials to polymer blends in the presence of a surface. With this method we have studied conformationally asymmetric athermic polymer blends in the presence of a hard wall to the first order in effective potentials. For polymers with the same gyration radius $R_g$ but different statistical segment lengths $l_{A}$ and $l_{B}$ the excess concentration of stiffer polymers at the surface is derived as % \delta \rho _{A}(z=0)\sim (l_{B}^{-2}-l_{A}^{-2}){\ln (}R_{g}^{2}/l_{c}^{2}{)%}, where $l_{c}$ is a local length below of which the incompressibility of the polymer blend is violated. For polymer blends differing only in degrees of polymerization the shorter polymer enriches the wall.Comment: 11 pages, 7 figures, revtex

Hierarchical Self-Assembly of Halogen-Bonded Block Copolymer Complexes into Upright Cylindrical Domains

Self-assembly of block copolymers into well-defined, ordered arrangements of chemically distinct domains is a reliable strategy for preparing tailored nanostructures. Microphase separation results from the system, minimizing repulsive interactions between dissimilar blocks and maximizing attractive interactions between similar blocks. Supramolecular methods have also achieved this separation by introducing small-molecule additives binding specifically to one block by noncovalent interactions. Here, we use halogen bonding as a supramolecular tool that directs the hierarchical self-assembly of low-molecular-weight perfluorinated molecules and diblock copolymers. Microphase separation results in a lamellar-within-cylindrical arrangement and promotes upright cylindrical alignment in films upon rapid casting and without further annealing. Such cylindrical domains with internal lamellar self-assemblies can be cleaved by solvent treatment of bulk films, resulting in separated and segmented cylindrical micelles stabilized by halogen-bond-based supramolecular crosslinks. These features, alongside the reversible nature of halogen bonding, provide a robust modular approach for nanofabricatio