The dynamic structure factor for molecular chains with variable stiffness in a dilute solution is investigated. In the limit of small scattering vectors q only the overall translational motion of the macromolecules contributes to the dynamic structure factor. The translational diffusion coefficient D exhibits a chain length dependence D∼1/√L for flexible chains and D∼ln L/L+const/L for rodlike chains. For flexible chains there is an intermediate scattering vector regime in which the decay rate or spectral linewidth of the dynamic structure factor is proportional to q3 indicating that stretching modes are dominant. Such an intermediate scattering vector regime cannot be observed for semiflexible or rodlike chains. At large scattering vectors q/2p≳1.5, where 1/2p is the persistence length of the macromolecules, the chain stiffness becomes important for any kind of molecules, i.e., even for very flexible ones. The dynamic structure factor and the decay rate are compared with experimental results of quasielastic neutron and light scattering experiments on different natural and synthetic macromolecules. These experimental results are in good agreement with the theoretical predictions. Furthermore, we determine the persistence length of F-actin from a dynamic light scattering experiment.

The partition functions of discrete as well as continuous stiff molecular chains are calculated using the maximum entropy principle. The chain is described by mass points, and their connectivity is taken into account by harmonic constraints (flexible segments) in addition to the bending restrictions. For comparison and as a test of the formalism the freely rotating chain as well as the Kratky–Porod wormlike chain (rigid segments) are reexamined treating the bending restrictions as constraints. It is shown that the second moments for the chain of flexible segments agree exactly with those known from the freely rotating chain for the discrete as well as the continuous chain and for all stiffnesses. Moreover, the Green’s function for the continuous chain is determined, which allows to obtain any desired two point distribution function. The influence of various bending restrictions on equilibrium properties is discussed. Furthermore, a comparison to other existing models, especially the Harris and Hearst model, is given and the validity of the various models is examined.

We present in-depth studies of the size tunability and the self-assembly behavior of Janus cylinders possessing a phase segregation into two hemicylinders. The cylinders are prepared by cross-linking the lamella-cylinder morphology of a polystyrene-block-polybutadiene-block-poly(methyl methacrylate) block terpolymer. The length of the Janus cylinders can be adjusted by both the amplitude and the duration of a sonication treatment from the micro- to the nanometer length. The corona segregation into a biphasic particle is evidenced by selective staining of the PS domains with RuO(4) and subsequent imaging. The self-assembly behavior of these facial amphiphiles on different length scales is investigated combining dynamic light scattering (DLS), small-angle neutron scattering (SANS), and imaging procedures. Cryogenic transmission electron microscopy images of the Janus cylinders in THF, which is a good solvent for both blocks, exhibit unimolecularly dissolved Janus cylinders with a core-corona structure. These results are corroborated by SANS measurements. Supramolecular aggregation takes place in acetone, which is a nonsolvent for polystyrene, leading to the observation of fiber-like aggregates. The length of these fibers depends on the concentration of the solution. A critical aggregation concentration is found, under which unimolecularly dissolved Janus cylinders exist. The fibers are composed of 2-4 Janus cylinders, shielding the inner insoluble polystyrene hemicylinder against the solvent. Herein, the SANS data reveal a core-shell structure of the aggregates. Upon deposition of the Janus cylinders from more concentrated solution, a second type of superstructure is formed on a significantly larger length scale. The Janus cylinders form fibrillar networks, in which the pore size depends on the concentration and deposition time of the sample.

We report on the unexpected finding of nanoscale fibers with a diameter down to 25 nm that emerge from a polymer solution during a standard spin-coating process. The fiber formation relies upon the Raleigh-Taylor instability of the spin-coated liquid film that arises due to a competition of the centrifugal force and the Laplace force induced by the surface curvature. This procedure offers an attractive alternative to electrospinning for the efficient, simple, and nozzle-free fabrication of nanoscale fibers from a variety of polymer solutions.Polymer nanofibers are attractive building blocks for functional nanoscale devices. They are promising candidates for various applications, including filtration, protective clothing, polymer batteries, and sensors.1-4 Furthermore, their high surface-to-volume ratio renders them attractive as catalyst supports as well as in drug delivery and tissue engineering. [5][6][7][8] Electrospinning, one of the most established fiber fabrication methods, has attracted much attention due to the ease by which fibers with diameters ranging from 10 nm to 10 µm can be produced from natural or synthetic materials. [9][10][11] However, this method requires a dc voltage in the kV range and high fiber production rates are difficult to achieve because only a single fiber emerges from the nozzle of the pipet holding the polymer solution. 12 Here, we report a simple but efficient procedure enabling the parallel fabrication of a multitude of polymer fibers with regular morphology and diameters as small as 25 nm. It involves the application of drops of a polymer solution onto a standard spin coater, followed by fast rotation of the chuck, without the need of a mechanical constriction. The fiber formation relies upon the instability of the spin-coated liquid film that arises due to a competition of the centrifugal force and the Laplace force induced by the surface curvature. This Rayleigh-Taylor instability triggers the formation of thin liquid jets emerging from the outward driven polymer solution, yielding solid nanofibers after evaporation of the solvent. In addition to being simple, the spinning procedure offers several technologically relevant advantages, including the absence of the need of a mechanical constriction and the ability to yield hollow polymer beads, and is applicable to different types of polymers.We have focused on the formation of nanofibers made of poly-(methylmethacrylate) (PMMA), which can be regarded as a prototype system for other polymers. In the centrifugal spinning experiments, an aliquot of a PMMA polymer solution was placed in the middle of the chuck of a spincoater, which was then rotated at a speed of at least 3000 rotations per minute (rpm) for a few seconds ( Figure S1 Supporting Information). The typical volume and concentration of the applied PMMA solution was 2 mL and 5 wt% in chlorobenzene, respectively, with polymer molecular weights of the order of 10 4 kg/mol. After spinning, PMMA nanofibers were collected at the edge of the spin-coater. Their diamete...

The dynamics of a free-draining chain of variable stiffness in a dilute solution is investigated. The chain is considered as a differentiable space curve with stretching and bending elasticity. Second moments, like the mean square end-to-end distance, the radius of gyration, and the pair correlation function of the equilibrium distribution exactly agree with those of the well-known Kratky–Porod wormlike chain. The equation of motion of the chain is derived and solved by a normal mode analysis. In the limit of a flexible chain the model exhibits the well-known Rouse dynamics, whereas in the rod limit the eigenfunctions correspond to bending motion only. In addition, the rotational motion in the latter limit is naturally obtained within the model. The relaxation times obtained by the model are compared with experimental transient birefringence and dynamic light scattering data. In addition, electric dichroism measurements are interpreted in terms of the model. All of these experiments are in good agreement with the theoretical predictions.

We present a complete analysis of the structure of polyethylene (PE) nanoparticles synthesized and stabilized in water under very mild conditions (15°C, 40 atm) by a nickel-catalyzed polymerization in aqueous solution. Combining cryogenic transmission electron microscopy (cryo-TEM) with X-ray scattering, we demonstrate that this new synthetic route leads to a stable dispersion of individual PE nanoparticles with a narrow size distribution. Most of the semicrystalline particles have a hexagonal shape (lateral size 25 nm, thickness 9 nm) and exhibit the habit of a truncated lozenge. The combination of cryo-TEM and small-angle X-ray scattering demonstrates that the particles consist of a single crystalline lamella sandwiched between two thin amorphous polymer layers ("nanohamburgers"). Hence, these nanocrystals that comprise only ca. 14 chains present the smallest single crystals of PE ever reported. The very small thickness of the crystalline lamella (6.3 nm) is related to the extreme undercooling (more than 100°C) that is due to the low temperature at which the polymerization takes place. This strong undercooling cannot be achieved by any other method so far. Dispersions of polyethylene nanocrystals may have a high potential for a further understanding of polymer crystallization as well as for materials science as, e.g., for the fabrication of extremely thin crystalline layers.Polyethylene (PE) is a commodity polymer that has become ubiquitous over the past several decades because of its low price and good mechanical properties. 1 Hence, the number of applications of the material is huge and many millions of tons are produced worldwide annually. However, PE has hardly played any role in the field of nanotechnology. This is due to the problem that PE is produced either by free radical polymerization under high pressure and temperature or with metal-organic catalysts working exclusively under strictly water-free conditions. Polymer nanoparticles and their composites with inorganic compounds, however, are very often produced in aqueous systems. 2 Recently, it was demonstrated that ethylene can be polymerized in aqueous systems in a catalytic fashion by Ni(II) complexes. [3][4][5][6] By virtue of this novel synthesis, long chains of polyethylene can be generated in a well-controlled environment and at ambient temperature. Thus, it could be shown that aqueous PE dispersions can be produced. This novel way of polymerization hence opens the way for the creation of nanostructures made from PE. Up to now, the particles synthesized in this way were semicrystalline and for the largest part consisted of stacks of several crystalline lamellae. 6

Imaging of individual protein molecules at the single amino acid level has so far not been possible due to the incompatibility of proteins with the vacuum environment necessary for high-resolution scanning probe microscopy. Here we demonstrate electrospray ion beam deposition of selectively folded and unfolded cytochrome c protein ions on atomically defined solid surfaces in ultrahigh vacuum (10(-10) mbar) and achieve unprecedented resolution with scanning tunneling microscopy. On the surface folded proteins are found to retain their three-dimensional structure. Unfolded proteins are observed as extended polymer strands displaying submolecular features with resolution at the amino acid level. On weakly interacting surfaces, unfolded proteins refold into flat, irregular patches composed of individual molecules. This suggests the possibility of two-dimensionally confined folding of peptides of an appropriate sequence into regular two-dimensional structures as a new approach toward functional molecular surface coatings.

We study the normal and lateral effective critical Casimir forces acting on a spherical colloid immersed in a critical binary solvent and close to a chemically structured substrate with alternating adsorption preference. We calculate the universal scaling function for the corresponding potential and compare our results with recent experimental data [Soyka F., Zvyagolskaya O., Hertlein C., Helden L., and Bechinger C., Phys. Rev. Lett., 101, 208301 (2008)]. The experimental potentials are properly captured by our predictions only by accounting for geometrical details of the substrate pattern for which, according to our theory, critical Casimir forces turn out to be a sensitive probe. Introduction. -The confinement of a fluctuating medium generates effective forces acting on its boundaries. A particularly interesting realization of this general principle is provided by the confinement of concentration fluctuations of a binary liquid mixture upon approaching a critical demixing point at temperature T = T c in its bulk phase diagram [1]. Generically, the confining surfaces preferentially adsorb one of the two components of the binary liquid. This amounts to the presence of effective, symmetry-breaking surface fields favoring either positive [(+)] or negative [(−)] values of the scalar order parameter φ which is the difference between the local concentrations of the two species. The extension of the spatial region in the direction normal to the surfaces, within which the local structural properties of the fluid deviate from the bulk ones, is given by the bulk correlation length ξ , which diverges upon approaching the critical point as ξ (t → 0) = ξ