Comb Backbone Research Articles

Temporal anomalous diffusion and drift of particles in a comb backbone with fractional Cattaneo−Christov flux

This paper investigates the temporal anomalous diffusion and drift of particles in a comb backbone. Fractional Cattaneo–Christov flux is introduced and the formulated governing equation has a Dirac delta function and mixed partial derivative which displays evolutional characteristics from parabolic (α → 0) to hyperbolic (α = 1). A solution is obtained numerically with the L1-scheme and the shifted Grünwald formula. Two completely opposite distributions are found: one is the monotonically decreasing convex distribution for the particle numbers and the other is the monotonically increasing concave distribution for the fractional order moments. The change rates of both the distributions decrease with the increase of time. Moreover, the influences of related parameters on the temporal evolution characteristics are discussed and analyzed in detail.

Primitive chain network simulations for comb-branched polymer under step shear deformations

The damping of the relaxation modulus under step shear deformation is weaker for multi-branched polymers such as comb polymers than for linear polymers. This weak damping has been related to the hierarchical relaxation, the branched arm relaxation occurring prior to the backbone relaxation and dilating the entanglement network for the backbone relaxation/contraction. A corresponding model has been proposed and favorably compared with the data for the damping function. However, the enhancement of dilation due to large deformation, known to occur for linear polymers to affect the chain contraction rate, was not considered in the model. Thus, in this paper, we investigated the dilation for a comb polymer under deformation with the aid of a 3D multichain sliplink simulation that naturally accounts for the dilation due to the constraint release through the many chain dynamics. The simulation was confirmed, to the first time, to reproduce the linear and nonlinear viscoelastic data for a comb polyisoprene (Kirkwood et al., Macromolecules 42:9592–9608, 2009). A magnitude of dilation under deformation was examined for the survival probability of the sliplinks. It turned out that the dilation for the comb backbone activated by the arm relaxation is enhanced by the deformation at short times but not at long times where the backbone relaxes and the damping function is defined. This result lends support to the conventional model.

Self-Assembly in Solution of a Reversible Comb-Shaped Supramolecular Polymer

We report a single step synthesis of a polyisobutene with a bis-urea moiety in the middle of the chain. In low polarity solvents, this polymer self-assembles by hydrogen bonding to form a combshaped polymer with a central hydrogen bonded backbone and polyisobutene arms. The comb backbone can be reversibly broken, and consequently, its length can be tuned by changing the solvent, the concentration or the temperature. Moreover, we have proved that the bulkiness of the side-chains have a strong influence on both the self-assembly pattern and the length of the backbone. Finally, the density of arms can be reduced, by simply mixing with a low molar mass bis-urea.

Double-Globular Structure of Porcine Stomach Mucin: A Small-Angle X-ray Scattering Study

We present evidence from small-angle X-ray scattering synchrotron experiments that porcine stomach mucin (MUC6) contains a double-globular comb structure. Analysis of the amino acid sequence of the peptide comb backbone indicates that the globular structure is determined by both the charge and hydrophobicity of the amino acids and the placement of the short hydrophilic carbohydrate side chains (approximately 2.5 nm). The double-globular structure is, thus, due to a block copolymer type hydrophobic polyampholyte charge instability in contrast to the random copolymer instabilities observed previously with synthetic polyelectrolytes (particularly polystyrene sulfonates). Careful filtering was required to exclude multimonomer aggregates from the X-ray measurements. A double Guinier analysis ( R g approximately 26 nm) and a double power law fit are consistent with two globules per chain in low salt conditions. The average radius of the globules is approximately 10 nm in salt- free condition (double Guinier fit) and the average distance of intrachain separation of the globules is 48 nm. The addition of salt causes a significant decrease in the radius of gyration (14 nm 100 mM NaCl) of the chains and is attributed to the contraction of the glycosylated peptide spacer between the two globules (the globular size continues to be approximately 10 nm and the globule separation is then 18 nm). Without salt, the scaling of the semidilute mesh size (xi) as a function of the mucin concentration (c) is xi approximately c (-0.45)compared with xi approximately c (-0.28) in high salt conditions, highlighting the globular nature of the chains. In contrast, hydrophilic flexible polyelectrolytes have a stronger concentration dependence of xi when excess salt is added.

Surface adsorption of comb polymers by Monte Carlo simulations

This paper reports off-lattice Monte Carlo simulations of highly-branched comb homopolymers weakly adsorbed on a flat, featureless surface showing only covolume and dispersion interactions with the adsorbate. A minimal coarse-grained model, described by hard spheres connected by harmonic springs, was employed. The interaction energy of the adsorbed combs and linear chains is first discussed as a function of the molecular mass and of the number of beads in contact with the surface. The molecular size is then investigated as a function of backbone length and branching density at a fixed arm size. The apparent swelling exponents of the adsorbed combs are larger than those of the corresponding linear chains, and much larger than that of the free molecules. This result indicates a surface-induced stiffening of the comb backbone, further studied through the persistence length lpers. It is found that lpers increases upon adsorption over the free-molecule value, more so the larger is the branching density. Finally, the thickness of the adsorbed layer, the surface-induced molecular anisotropy and the molecular aspect ratio are investigated as a function of branching density and molecular mass.

Thermal and viscoelastic structure–property relationships of model comb-like poly(n-butyl methacrylate)

A range of comb polymers of poly(n-butyl methacrylate), where the degree of polymerization (DP) of both the backbone and branches was controlled using RAFT-mediated free-radical polymerization, was synthesized using the method of Vosloo et al. [Macromolecules 2004;37: 2371]. Individual architectural parameters (branch length, branch number and DP of the comb backbone) of these relatively monodisperse samples were systematically varied in order to study the impact of each structural parameter on the thermal and rheological properties of the resulting comb polymers. Differential scanning calorimetry showed lower glass transition temperatures for the comb polymers compared to the original linear backbones. There were negligible differences in glass transition temperatures between comb polymers containing branches of different lengths, and between comb polymers containing backbones of narrow and of broad molecular weight distributions. These observations suggest that because the comb polymers are very tightly spaced, the branches act in the same way as long chain polyBMA. Viscoelastic properties of the comb polymers were investigated using dynamic mechanical analysis, using time–temperature superposition to extend the rheological data over a wide frequency range. Major differences in the viscoelastic responses of the original linear backbones and the comb polymers were observed, which were explained in terms of arm retraction/relaxation leading to tube dilation. All comb polymers showed viscoelastic responses that are characteristic of combs, but differences in responses due to changes in branch length and branch number were difficult to detect. This was mainly due to the relatively high number of branches, whose retractions occurred over a broad frequency range, and thus dominated the observed changes in moduli, thereby possibly masking subtle differences in responses.

Inhomogeneous superconductivity in comb-shaped Josephson junction networks

We show that some of the Josephson couplings of junctions arranged to form an inhomogeneous network undergo a non-perturbative renormalization provided that the network's connectivity is pertinently chosen. As a result, the zero-voltage Josephson critical currents Ic turn out to be enhanced along directions selected by the network's topology. This renormalization effect is possible only on graphs whose adjacency matrix admits a hidden spectrum (i.e. a set of localized states disappearing in the thermodynamic limit). We provide a theoretical and experimental study of this effect by comparing the superconducting behaviour of a comb-shaped Josephson junction network and a linear chain made with the same junctions: we show that the Josephson critical currents of the junctions located on the comb's backbone are bigger than those of the junctions located on the chain. Our theoretical analysis, based on a discrete version of the Bogoliubov–de Gennes equation, leads to results which are in good quantitative agreement with experimental results.

Topology-induced confined superfluidity in inhomogeneous arrays

We report a study of the zero-temperature phase diagram of the Bose-Hubbard model on topologically inhomogeneous arrays. We show that the usual Mott-insulator and superfluid domains, in the paradigmatic case of the comb lattice, are separated by regions where the superfluid behavior of the bosonic system is confined along the comb backbone. The existence of such confined superfluidity, arising from topological inhomogeneity, is proved by different analytical and numerical techniques which we extend to the case of inhomogeneous arrays. We also discuss the relevance of our results to real systems exhibiting macroscopic phase coherence, such as coupled Bose condensates and Josephson arrays.

Size and persistence length of molecular bottle-brushes by Monte Carlo simulations.

Single-chain simulations of densely branched comb polymers, or "molecular bottle-brushes" with side-chains attached to every (or every second) backbone monomer, were carried out by off-lattice Monte Carlo technique. A coarse-grained model, described by hard spheres connected by harmonic springs, was employed. Backbone lengths of up to 100 units were considered, and compared with the corresponding linear chains. The backbone molecular size was investigated as a function of its length at fixed arm size, and as a function of the arm size at fixed backbone length. The apparent swelling exponents obtained by a power-law fit were found to be larger than those for the corresponding linear polymers, indicative of stiffening of the comb backbone. The probability distribution function for the backbone end-to-end distance was also investigated for different backbone lengths and arm sizes. Analysis of this function yielded the critical exponents, which revealed an increase in the swelling exponent consistent with values found from the molecular size. The apparent persistence length of the backbone was also determined, and was found to increase with increasing branching density. Finally, the static structure factors of the whole bottle-brushes and of their backbones are discussed, which provides another consistent estimate of the swelling exponents.