We measured the form factor of bottle-brush macromolecules under good solvent conditions with small-angle neutron scattering and static light scattering. The systems under investigation are brushes, synthesized via the grafting-from route, built from a poly͑alkyl methacrylate͒ backbone to which poly͑n-butyl acrylate͒ side chains are densely grafted. The aim of our work is to study how the systematic variation of structural parameters such as the side chain length and backbone length change the conformation of the polymer brushes in solution. All spectra can be consistently described by a model, considering the bottle-brush polymers as flexible rods with internal density fluctuations. Parameters discussed are ͑1͒ the contour length per main chain monomer l b , ͑2͒ the fractal dimension of the side chains D s , as well as ͑3͒ the fractal dimension D, and ͑4͒ the Kuhn length k of the overall brush. l b = 0.253± 0.008 nm is found to be independent of the side chain length and equal to the value found for the bare main chain, indicating a strongly stretched conformation for the backbone due to the presence of the side chains. The fractal dimension of the side chains is determined to be D s = 1.75± 0.07 which is very close to the value of 1 / 0.588Ϸ 1.70 expected for a three-dimensional self-avoiding random walk ͑3D-SAW͒ under good solvent conditions. On larger length scales the overall brush appears to be a 3D-SAW itself ͑D = 1.64± 0.08͒ with a Kuhn-step length of k = 70± 4 nm. The value is independent of the side chain length and 46 times larger than the Kuhn length of the bare backbone ͑ k = 1.8± 0.2 nm͒. The ratio of Kuhn length to brush diameter k / d ജ 20 determines whether lyotropic behavior can be expected or not. Since longer side chains do not lead to more persistent structures, k / d decreases from 8 to 4 with increasing side chain length and lyotropic behavior becomes unlikely.

We have investigated the dynamic structure factor for single-chain relaxation in a polyethylene melt by means of molecular dynamics simulations and neutron spin echo spectroscopy. After accounting for a 20% difference in the chain self-diffusion coefficient between simulation and experiment we find a perfect quantitative agreement of the intermediate dynamic structure factor over the whole range of momentum transfer studied. Based on this quantitative agreement one can test the experimental results for deviations from standard Rouse behavior reported so far for only computer simulations of polymer melt dynamics. [S0031-9007(98)05363-0] PACS numbers: 61.25.HqThe dynamics of polymer chains in a dense melt could be supposed to pose a theoretical problem requiring a very complex and mathematically involved description. We have to describe a liquid of intertwined threads where each of them has on average excluded volume interactions with p N other threads, where N is the degree of polymerization of the chains. According to all experimental evidence so far, e.g., Refs. [1-3], however, it seems that all these complex topological interactions can be completely neglected as long as the degree of polymerization of the chains is below some critical value, the so-called entanglement molecular weight N e . For chains longer than N e the entanglements have to be taken into account [4-7] but for shorter chains the simple Rouse theory [8] is supposed to describe the chain dynamics. Computer simulations of abstract [9,10] as well as atomistic [11] polymer models, on the other hand, show systematic deviations from the Rouse behavior, which can be traced to the interactions between the chains in the melt.We will show in this paper the first detailed quantitative comparison between a molecular dynamics (MD) simulation of the melt dynamics of an atomistic polymer model and a neutron spin echo (NSE) determination of the single-chain dynamics in the same polymer melt. By establishing the quantitative agreement between simulation and experiment for the internal dynamics of the chains we can then draw conclusions about the validity or shortcom-ings of the Rouse model from the combined information of simulation and experiment.Simulations and experiments were performed on a dense polyethylene melt of n-C 100 H 202 at 509 K. Experimentally we had already obtained information on the dynamic behavior of longer chain polyethylene (PE) samples at the same temperature from neutron scattering studies [1,2], and we had validated a united atom (UA) model (CH 2 groups treated as one superatom) [12] as well as an explicit atom (EA) model [13] by simulations of shorter chain alkanes. The C 100 chains are slightly shorter than the entanglement length of PE at this temperature (N e 136 [2]) and long enough to show Gaussian chain statistics in their conformations [14], thereby making them the ideal test system for a description by the Rouse model. After equilibration for 3 ns we performed a NVT (constant number of particles, volume, and temperature) mole...

We have measured both the static and dynamic structure factors of a single dendrimer with small-angle x-ray scattering ͑SAXS͒ and neutron spin-echo spectroscopy under good solvent conditions with the aim of finding a consistent correlation between the structural properties of dendrimers and their dynamic behavior. The samples under investigation were star-burst polyamidoamine dendrimers with generations gϭ0 to 8 in dilute methanol solutions. A model independent approach employing inverse Fourier transformation and square root deconvolution methods has been used to analyze the SAXS data to obtain the pair distance distribution function p(r) and the radial excess electron density profile ⌬ (r). In addition, we formulated a model that takes both the colloidal ͑globular, compact shape with form polydispersity or fuzzy surface͒ as well as the loose, polymeric ͑self-avoiding random walk͒ character of dendrimers into account. With this model we were able to describe the spectra of all dendrimer generations consistently. Parameters discussed as a function of the dendrimer generation are, among others, the correlation length of the density fluctuations ͑blob radius͒ , the radius of gyration R g , the sphere radius R s , the form polydispersity s or analogously, the width of the fuzzy surface region 2 f . Both the model-independent approach and the model fits reveal that at least down to the third generation the dendrimers exhibit a rather compact, globular shape. These findings are in agreement with the dynamic results obtained by NSE spectroscopy which probes length scales both larger and much smaller than the dimension of a single dendrimer. The method reveals that the dynamics throughout is dominated by the center-of-mass diffusion-the internal dynamics is suppressed. The diffusion coefficients obtained are close to the values calculated from the Stokes-Einstein relation using the sphere radius R s determined from the SAXS spectra. Dynamically, the dendrimers behave like ''hard'', solid spheres.

Extensive Monte Carlo simulations are presented for bottle-brush polymers under good solvent conditions, using the bond fluctuation model on the simple cubic lattice. Varying the backbone length (from N b = 67 to N b = 259 effective monomers) as well as the side chain length (from N = 6 to N = 48), for a physically reasonable grafting density of one chain per backbone monomer, we find that the structure factor describing the total scattering from the bottle-brush provides an almost perfect match for some combinations of (N b , N) to experimental data of Rathgeber et al. [J. Chem. Phys. 2005, 122, 124904], when we adjust the length scale of the simulation to reproduce the experimental gyration radius of the bottle-brush. While in the experiment other length scales (gyration radius of side chains, backbone persistence length, scale characterizing the radial monomer density profile in the plane normal to the backbone) can be extracted only via fitting to a complicated and approximate theoretical expression derived by Pedersen and Schurtenberger, all these properties can be extracted from the simulation directly. In this way, quantitatively more reliable estimates for the persistence length and side chain gyration radius of the experimental systems can be extracted. In particular, we show that the popular assumption of a Gaussian radial monomer density profile is inaccurate, in the very good solvent regime studied by the simulation, and show that alternative forms based on scaling theory work better. We also show that the persistence length of the bottle brush in the simulation depends systematically on the backbone length and not only on the side chain length. For the cases where an explicit comparison with the experimental results (based on their evaluation within the Pedersen-Schurtenberger model) is possible, simulation and experiment are consistent with each other and some of the (rather minor) differences between simulation and experiment can be attributed to the weaker strength of excluded volume in the latter. Thus, we show that by suitable mapping between simulation and experiment on length scales of the local concentration fluctuations (here <2 nm) the analysis of experimental data can be systematically refined.

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