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 present a scaling formula for size-dependent viscosity coefficients for proteins, polymers, and fluorescent dyes diffusing in complex liquids. The formula was used to analyze the mobilities of probes of different sizes in HeLa and Swiss 3T3 mammalian cells. This analysis unveils in the cytoplasm two length scales: (i) the correlation length ξ (approximately 5 nm in HeLa and 7 nm in Swiss 3T3 cells) and (ii) the limiting length scale that marks the crossover between nano- and macroscale viscosity (approximately 86 nm in HeLa and 30 nm in Swiss 3T3 cells). During motion, probes smaller than ξ experienced matrix viscosity: η(matrix) ≈ 2.0 mPa·s for HeLa and 0.88 mPa·s for Swiss 3T3 cells. Probes much larger than the limiting length scale experienced macroscopic viscosity, η(macro) ≈ 4.4 × 10(-2) and 2.4 × 10(-2) Pa·s for HeLa and Swiss 3T3 cells, respectively. Our results are persistent for the lengths scales from 0.14 nm to a few hundred nanometers.
We measured the viscosity of poly(ethylene glycol) (PEG 6000, 12,000, 20,000) in water using capillary electrophoresis and fluorescence correlation spectroscopy with nanoscopic probes of different diameters (from 1.7 to 114 nm). For a probe of diameter smaller than the radius of gyration of PEG (e.g. rhodamine B or lyzozyme) the measured nanoviscosity was orders of magnitude smaller than the macroviscosity. For sizes equal to (or larger than) the polymer radius of gyration, macroscopic value of viscosity was measured. A mathematical relation for macro and nanoviscosity was found as a function of PEG radius of gyration, R(g), correlation length in semi-dilute solution, xi, and probe size, R. For R < R(g), the nanoviscosity (normalized by water viscosity) is given by exp(b(R/xi)a), and for R > R(g), both nano and macroviscosity follow the same curve, exp(b(R/xi)a), where a and b are two constants close to unity. This mathematical relation was shown to equally well describe rhodamine (of size 1.7 nm) in PEG 20,000 and the macroviscosity of PEG 8,000,000, whose radius of gyration exceeds 200 nm. Additionally, for the smallest probes (rhodamine B and lysozyme) we have verified, using capillary electrophoresis and fluorescence correlation spectroscopy, that the Stokes-Einstein (SE) relation holds, providing that we use a size-dependent viscosity in the formula. The SE relation is correct even in PEG solutions of very high viscosity (three orders of magnitude larger than that of water).
Although water is the chief component of living cells, food, and personal care products, the supramolecular components make their viscosity larger than that of water by several orders of magnitude. Using fluorescence correlation spectroscopy (FCS), photon correlation spectroscopy (PCS), NMR, and rheology data, we show how the viscosity changes from the value for water at the molecular scale to the large macroviscosity. We determined the viscosity experienced by nanoprobes (of sizes from 0.28 to 190 nm) in aqueous micellar solution of hexaethylene-glycol-monododecyl-ether (in a range of concentration from 0.1% w/w to 35% w/w) and identified a clear crossover at the length scale of 17 +/- 2 nm (slightly larger than persistence length of micelles) at which viscosity acquires its macroscopic value. The sharp dependence of the viscosity coefficients on the size of the probe in the nanoregime has important consequences for diffusion-limited reactions in crowded environments (e.g., living cells).
Translational diffusion of a small charged tracer sphere in isotropic and nematic suspensions of long and thin charged rods is investigated as a function of ionic strength and rod concentration. A theory for the diffusive properties of a small sphere is developed, where both (screened) hydrodynamic interactions and charge interactions between the tracer sphere and the rod network are analyzed. Hydrodynamic interactions are formulated in terms of the hydrodynamic screening length. As yet, there are no independent theoretical predictions for the hydrodynamic screening length for rod networks. Experimental tracer-diffusion data are presented for various ionic strengths as a function of the rod concentration, both in the isotropic and nematic states. Orientational order parameters are measured for the same ionic strengths as a function of the rod concentration. The hydrodynamic screening length is determined from these experimental data and scaling relations obtained from the above mentioned theory. For the isotropic networks, a master curve is found for the hydrodynamic screening length as a function of the rod concentration. For the nematic networks the screening length turns out to be a very sensitive function of the orientational order parameter.
We have reanalyzed our former static small-angle x-ray scattering and photon correlation spectroscopy results on dense solutions of charged spherical apoferritin proteins using theories recently developed for studies of colloids. The static structure factors S(q), and the small-wave-number collective diffusion coefficient D(c) determined from those experiments are interpreted now in terms of a theoretical scheme based on a Derjaguin-Landau-Verwey-Overbeek-type continuum model of charged colloidal spheres. This scheme accounts, in an approximate way, for many-body hydrodynamic interactions. Stokesian dynamics computer simulations of the hydrodynamic function have been performed for the first time for dense charge-stabilized dispersions to assess the accuracy of the theoretical scheme. We show that the continuum model allows for a consistent description of all experimental results, and that the effective particle charge is dependent upon the protein concentration relative to the added salt concentration. In addition, we discuss the consequences of small ions dynamics for the collective protein diffusion within the framework of the coupled-mode theory.
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