Cross-linking patterns and their images in swollen and deformed gels

Using the theory of elasticity of polymer gels we show that large-scale cross-link density patterns written into the structure of the network in the melt state, can be revealed upon swelling by monitoring the monomer density patterns. We find that while isotropic deformations in good solvent yield magnified images of the original pattern, anisotropic deformations distort the image (both types of deformation yield affinely stretched images in $\theta$ solvents). We show that in ordinary solids with spatially inhomogeneous profile of the shear modulus, isotropic stretching leads to distorted density image of this profile under isotropic deformation. Using simple physical arguments we demonstrate that the different response to isotropic stretching stems from fundamental differences between the theory of elasticity of solids and that of gels. Possible tests of our predictions and some potential applications are discussed.Comment: 16 pages, 3 figure

From complexation of oppositely charged polyelectrolytes to supramolecular bottlebrushes and gels.

We develop a scaling model of coacervates formed by oppositely charged polyelectrolytes. The intramolecular electrostatic interactions in dilute polyanion or polycation solutions are characterized by the so-called electrostatic blobs, D- or D+ respectively. Polyelectrolyte sections of electrostatic blob size repel neighboring sections of the same chain with electrostatic energy on the order of thermal energy kT. Conformations of polyanion or polycation chains in their respective dilute solutions with no added salt can be described as stretched arrays of their corresponding electrostatic blobs of size D- or D+. The structure of a coacervate formed upon mixing polyanion and polycation solutions depends on the electrostatic attraction between oppositely charged polyelectrolytes balanced by the short-range repulsion. In the symmetric case with D- = D+ = De the coacervate is a dense packing of these electrostatic blobs with neighboring oppositely charged blobs of size De attracting each other with energy on order kT. This attraction is stabilized by short-range non-electrostatic repulsion with energy on the same order kT between all chain sections of size De. Please click Additional Files below to see the full abstract

Molecular structure of bottlebrush polymers in melts

Bottlebrushes are fascinating macromolecules that display an intriguing combination of molecular and particulate features having vital implications in both living and synthetic systems, such as cartilage and ultrasoft elastomers. However, the progress in practical applications is impeded by the lack of knowledge about the hierarchic organization of both individual bottlebrushes and their assemblies. We delineate fundamental correlations between molecular architecture, mesoscopic conformation, and macroscopic properties of polymer melts. Numerical simulations corroborate theoretical predictions for the effect of grafting density and side-chain length on the dimensions and rigidity of bottlebrushes, which effectively behave as a melt of flexible filaments. These findings provide quantitative guidelines for the design of novel materials that allow architectural tuning of their properties in a broad range without changing chemical composition

Molecular structure of bottlebrush polymers in melts

Bottlebrushes are fascinating macromolecules that display an intriguing combination of molecular and particulate features having vital implications in both living and synthetic systems, such as cartilage and ultrasoft elastomers. However, the progress in practical applications is impeded by the lack of knowledge about the hierarchic organization of both individual bottlebrushes and their assemblies. We delineate fundamental correlations between molecular architecture, mesoscopic conformation, and macroscopic properties of polymer melts. Numerical simulations corroborate theoretical predictions for the effect of grafting density and side-chain length on the dimensions and rigidity of bottlebrushes, which effectively behave as a melt of flexible filaments. These findings provide quantitative guidelines for the design of novel materials that allow architectural tuning of their properties in a broad range without changing chemical composition

Bond Tension in Tethered Macromolecules

The paper presents scaling analysis of mechanical tension generated in densely branched macromolecules tethered to a solid substrate with a short linker. Steric repulsion between branches results in z-fold amplification of tension in the linker, where z is the number of chain-like arms. At large z ~ 100–1000, the generated tension may exceed the strength of covalent bonds and sever the linker. Two types of molecular architectures were considered: polymer stars and polymer “bottlebrushes” tethered to a solid substrate. Depending on the grafting density, one distinguishes the so-called mushroom, loose grafting, and dense grafting regimes. In isolated (mushroom) and loosely tethered bottlebrushes, the linker tension is by a factor of z smaller than the tension in a tethered star with the same number of arms z. In densely tethered stars, the effect of interchain distance (d) and number of arms (z) on the magnitude of linker tension is given by f ≅ f0z3/2(b/d) for stars in a solvent environment and f ≅ f0z2 (b/d)2 for dry stars, where b is the Kuhn length and f0 ≅ kBT/b is intrinsic bond tension. These relations are also valid for tethered bottlebrushes with long side chains. However, unlike molecular stars, bottlebrushes demonstrate variation of tension along the backbone f ≅ f0s z1/2 / d as a function of distance s from the free end of the backbone. In dense brushes (d≅bz) with z ≅ 1000, the backbone tension increases from f ≅ f0 = 1 pN at the free end of the backbone (s ≅ b) to its maximum f ≅ zf0 ≅ 1 nN at the linker to the substrate (s ≅ zb)

Hopping Diffusion of Nanoparticles in Polymer Matrices

We propose a hopping mechanism for diffusion of large nonsticky nanoparticles subjected to topological constraints in both unentangled and entangled polymer solids (networks and gels) and entangled polymer liquids (melts and solutions). Probe particles with size larger than the mesh size ax of unentangled polymer networks or tube diameter ae of entangled polymer liquids are trapped by the network or entanglement cells. At long time scales, however, these particles can diffuse by overcoming free energy barrier between neighboring confinement cells. The terminal particle diffusion coefficient dominated by this hopping diffusion is appreciable for particles with size moderately larger than the network mesh size ax or tube diameter ae. Much larger particles in polymer solids will be permanently trapped by local network cells, whereas they can still move in polymer liquids by waiting for entanglement cells to rearrange on the relaxation time scales of these liquids. Hopping diffusion in entangled polymer liquids and networks has a weaker dependence on particle size than that in unentangled networks as entanglements can slide along chains under polymer deformation. The proposed novel hopping model enables understanding the motion of large nanoparticles in polymeric nanocomposites and the transport of nano drug carriers in complex biological gels such as mucus

Mobility of Nonsticky Nanoparticles in Polymer Liquids

We use scaling theory to derive the time dependence of the mean-square displacement 〈Δr2〉 of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (〈Δr2 (t)〉 ~ t) with diffusion coefficient similar to that in pure solvent. The motion of particles of intermediate size (ξ τe) large particles (d > a) are trapped by entanglement mesh and to move further they have to wait for the surrounding polymer chains to relax at the reptation time scale τrep. At longer times t > τrep, the motion of such large particles (d > a) is diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer liquids. Our predictions are in agreement with the results of experiments and computer simulations

Enhanced nanochannel translocation and localization of genomic DNA molecules using three-dimensional nanofunnels

The ability to precisely control the transport of single DNA molecules through a nanoscale channel is critical to DNA sequencing and mapping technologies that are currently under development. Here we show how the electrokinetically driven introduction of DNA molecules into a nanochannel is facilitated by incorporating a three-dimensional nanofunnel at the nanochannel entrance. Individual DNA molecules are imaged as they attempt to overcome the entropic barrier to nanochannel entry through nanofunnels with various shapes. Theoretical modeling of this behavior reveals the pushing and pulling forces that result in up to a 30-fold reduction in the threshold electric field needed to initiate nanochannel entry. In some cases, DNA molecules are stably trapped and axially positioned within a nanofunnel at sub-threshold electric field strengths, suggesting the utility of nanofunnels as force spectroscopy tools. These applications illustrate the benefit of finely tuning nanoscale conduit geometries, which can be designed using the theoretical model developed here.Forcing a DNA molecule into a nanoscale channel requires overcoming the free energy barrier associated with confinement. Here, the authors show that DNA injected through a funnel-shaped entrance more efficiently enters the nanochannel, thanks to facilitating forces generated by the nanofunnel geometry

Amplification of Tension in Branched Macromolecules

We propose a method for the design of branched macromolecules that are capable of building up high tension (~nN) in their covalent bonds without applying an external force. The tension is self-generated due to repulsion between branches and depends on the molecular architecture leading to amplification and focusing of tension in specific bonds. The simplest architecture is a pom-pom composed of a linear spacer and two z-arm stars at its ends resulting in z-fold tension amplification. Adsorption of those macromolecules on a substrate results in further increase in tension as compared to molecules in solution