Search results for "Length"

Understanding the Multiple Length Scales Describing the Structure of Bottle-brush Polymers by Monte Carlo Simulation Methods

2011

Bottle-brush polymers contain a long flexible macromolecule as a backbone to which flexible side chains are grafted. Through the choice of the grafting density and the length of the side chains the local stiffness of this cylindrical molecular brush can be controlled, but a quantitative understanding of these phenomena is lacking. Monte Carlo simulation results are presented and discussed which address this issue, extractingmesoscopic length scales (such as the cross-sectional radius, persistence length, and contour length of these objects). Large-scale simulations of the bond fluctuation model are combined with simulations of the simple selfavoiding walk (SAW) model with flexibility contro…

Conformations and orientational ordering of semiflexible polymers in spherical confinement.

2017

Semiflexible polymers in lyotropic solution confined inside spherical nanoscopic “containers” with repulsive walls are studied by molecular dynamics simulations and density functional theory, as a first step to model confinement effects on stiff polymers inside of miniemulsions, vesicles, and cells. It is shown that the depletion effects caused by the monomer-wall repulsion depend distinctly on the radius R of the sphere. Further, nontrivial orientational effects occur when R, the persistence length ℓp, and the contour length L of the polymers are of similar magnitude. At intermediate densities, a “shell” of wall-attached chains is forming, such that the monomers belonging to those chains a…

Monte Carlo Simulations of Semi-Flexible Polymers

2005

We present Monte Carlo simulations on the phase behavior of semiflexible macromolecules. For a single chain this question is of biophysical interest given the fact that long and stiff DNA chains are typically folded up into very tight compartments. So one can ask the question how the state diagram of a semiflexible chain differs from the coilglobule behavior of a flexible macromolecule. Another effect connected with rigidity of the chains is their tendency to aggregate and form nematically ordered structures. As a consequence one has two competing phase transitions: a gas-liquid and an isotropic-nematic transition potentially giving rise to a complicated phase diagram.

Persistence Length of Cylindrical Brush Molecules Measured by Atomic Force Microscopy

2006

Mechanical properties of single cylindrical polymer brushes with polyisopropylacrylamide (PNIPAM) side chains deposited on mica were probed by atomic force microscopy. Visualization and stretching of individual molecules in aqueous solution clearly reveal the semiflexible nature of the cylindrical macromolecules. Imaging of the brushes on mica and inferring lp from a 〈R2〉 vs L plot results in an average persistence length of lp = 29 ± 3 nm, assuming the chains adopt their equilibrium conformation on the surface. Stretching experiments suggest that an exact determination of the persistence length using force extension curves is impeded by the contribution of the side-chain elasticity. Modeli…

Ejection of a Polymer Chain from a Nanopore: Theory and Computer Experiment

2010

We consider the ejection dynamics of a flexible polymer chain out of confined environment. This situation arises in different physical contexts, including a flexible synthetic polymer partially confined in a nanopore and a viral genome partially ejected from its capsid. We describe the chain release from confinement both analytically and by means of dynamic Monte Carlo simulation. We find two distinct regimes of ejection dynamics depending on whether the chain is fully or partially confined. Partially confined chains are ejected from a pore of length L and diameter D after a typical time τ ∝ L2D5/3, regardless of their contour length N. The process is driven by a constant force f ≈ 5kBT/D a…

Understanding the properties of liquid-crystalline polymers by computational modeling

2020

Abstract A topical review of recent theoretical work on the properties of lyotropic solutions and melts containing semiflexible polymers in thermal equilibrium is given, with a focus on the liquid-crystalline and smectic order of these systems in the bulk and under confinement. Starting with a discussion of single chain properties in terms of the Kratky-Porod worm-like chain model and its limitations, extensions along the lines of Onsager’s theory for the isotropic-nematic transition of solutions of hard rods are briefly reviewed. This discussion is followed by a review of recent Molecular Dynamics simulations and classical Density Functional Theory calculations. It is argued that, even in …

1978

Theoretical relations for the dependence of the z-average radius of gyration Rz as a function of the mass average molar mass Mw are derived for expanded coils, persistence coils with persistence of direction, persistence coils with persistence of direction and curvature, and for needles, all exhibiting a Schulz-distribution of their molar masses. These relations are applied to experimental data from light scattering of polystyrene in toluene and DNA-Na in aqueous NaCl-solution of 200 mol NaCl per m3 at room temperature. In the case of DNA it becomes evident that the double helix shows no important persistence of curvature and that the experimental data can be described adequately by a persi…

Determination of Calcium in Certain Fertilizers by Inductively Coupled Plasma Atomic Emission Spectrometry: Studies of Some Spectral and Interelement…

1997

Abstract Four analytical wavelengths (393.366, 396.847, 317.933, and 422.673 nm) were used to determine Ca in 2 fertilizers by inductively coupled plasma atomic emission spectroscopy (ICP-AES). Matrix effects were studied by adding to real fertilizer solutions fertilizer elements that are known or believed to interfere with Ca determination. Matrix effects were calculated by multiple linear regression. Interference was caused by S, K, or B. At 422.673 nm, the interference of B and K is a spectral effect, and at 396.847 and 317.933 nm, the interference of S and K is an interelement effect. At 393.366 nm, no linear interference was found. The best wavelength for determining Ca in fertilizers …

Iron Determination in Fertilizers by Inductively Coupled Plasma Atomic Emission Spectrometry: Study of Spectral and Interelement Effects at Different…

1996

Abstract Four analytical wavelengths of iron (238.204, 239.562, 259.940, and 240.488 nm) were tested for determination of Fe in fertilizers by inductively cou pled plasma atomic emission spectroscopy (ICP AES). Variations in measurements were caused by the changing interference pattern at different wave lengths evaluated by multiple linear regression. Thus, results obtained with different wavelengths are not comparable. Ca, P, and K were typical ele ments causing interference in almost all examined Fe wavelengths. Wavelength Fe II 238.204 nm is the best wavelength for determination of Fe in fertiliz ers by ICP-AES. Method accuracy is ± 8% at the ex amined Fe levels in fertilizers.

Determination of Boron in Fertilizers by Inductively Coupled Plasma-Atomic Emission Spectrometry: Studies of Some Spectral Interferences at Different…

1995

Abstract The most sensitive analytical wavelengths of boron cannot be used in the determination of boron in fertilizers by inductively coupled plasma-atomic emission spectrometry because of spectral interference by potassium, phosphorus, and iron. For the 4 wavelengths of boron investigated, it was noticed that, at the same wavelength, the pattern of spectral interference changes according to fertilizer composition. The spectral interference patterns at the 4 analytical boron wavelengths were studied by adding matrix elements typically found in fertilizers to real fertilizer samples. When levels of added matrix elements correlate less than 0.2 to each other, the effect of added matrix eleme…