Monte Carlo Prediction of the Structure Factor of Polyethylene in Good and ϑ-Solvents

Screening lengths and osmotic compressibility of flexible polyelectrolytes in excess salt solutions

We report results of small angle neutron scattering measurements made on sodium polystyrene sulfonate in aqueous salt solutions. The correlation length (ξ) and osmotic compressibility are measured as a function of polymer (c) and added salt (cS) concentrations, and the results are compared with scaling predictions and the random-phase approximation (RPA). In Dobrynin et al.'s scaling model the osmotic pressure consists of a counter-ion contribution and a polymer contribution. The polymer contribution is found to be two orders of magnitude smaller than expected from the scaling model, in agreement with earlier observations made on neutral polymers in good solvent condition. RPA allows the determination of single-chain dimensions in semidilute solutions at high polymer and added salt concentrations, but fails for cS≤ 2 M. The χ parameter can be modelled as the sum of an intrinsic contribution (χ0) and an electrostatic term: χ∼χ0 + K'/√cS, where χ0 > 0.5 is consistent with the hydrophobic nature of the backbone of NaPSS. The dependence of χelec∼ 1/√cS disagrees with the random-phase approximation (χelec∼ 1/cs), but agrees with the light scattering results in dilute solution and Dobrynin et al.'s scaling treatment of electrostatic excluded volume.

A Replica Exchange Molecular Dynamics Simulation of a Single Polyethylene Chain: Temperature Dependence of Structural Properties and Chain Conformational Study at the Equilibrium Melting Temperature

The conformational properties of a finite length polyethylene chain were explored over a wide range of temperatures using a replica exchange molecular dynamics simulation providing high quality simulation data representative for the equilibrium behavior of the chain molecule. The radial distribution function (RDF) and the structure factor S(q) of the chain as a function of temperature are analyzed in detail. The different characteristic peaks in the RDF and S(q) were assigned to specific distances in the chain and structural changes occurring with the temperature. In S(q), a peak characteristic for the order in the solid state was found and used to determine the equilibrium melting temperature. A detailed scaling analysis of the structure factor covering the full q range was performed according to the work of Hammouda. In the Θ region, a quantitative analysis of the full structure factor was done using the equivalent Kuhn chain, which enabled us to assign the Θ region of our chain and to demonstrate, in our particular case, the failure of the Gaussian chain approach. The chain conformational properties at the equilibrium melting temperature are discussed using conformational distribution functions, using the largest principal component of the radius of gyration and shape parameters as order parameters. We demonstrate that for the system studied here, the Landau free energy expression based on this conformational distribution information leads to erroneous conclusions concerning the thermodynamic transition behavior. Finally, we focus on the instantaneous conformational properties at the equilibrium melting temperature and give a detailed analysis of the conformational shapes using different shape parameters and a simulation snapshot. We show that the chain does not only take the lamellar rod-like and globular conformational shapes, typical of the solid and liquid states, but can also explore many other conformational states, including the toroidal conformational state. It is the first demonstration that a flexible molecule like PE can also take a toroidal conformational state, which is normally linked to stiffer chains.

Detailed Structures and Mechanism of Polymer Solvation

In the present study, we simulated a model system, PE in biphenyl, to gain the insight into the detailed solvation structures and the molecular mechanism of polymer chain solvation. Using atomistic molecular dynamics (MD) simulation, it was found that when the biphenyl is far from PE chain or in the bulk, the dihedral angle of the two rings in the solvent molecule are approximately 32 degrees. But, the dihedral angel is about 27 degrees when the biphenyls are very close to the PE chain. In the first solvation shell, the orientation angle of the biphenyl long axis to the chain segment backbone was found to be enhanced around two values: approximately 0 and approximately 60 degrees. The detailed solvation structures found here include all dyad conformations (TT, TG, TG', GT, GG, GG', G'T, G'G, and G'G') and vary as a function of the distance between PE chain and biphenyls in the first solvation shell. The closer the the solvent molecule to the PE segment, the higher the TT conformation fraction response is. The other dyad conformations such as TG, GG', etc. undergo different decreases, respectively. This study shows that the solvation even in the Theta condition makes the overall size expansion or the chain stretched. Such a cooperative change was examined here and found not due to generating or losing a conformational state but due to a change in conformational distribution. This change occurs in the middle location of the chain instead of the chain end locations.

Partitioning of a polymer into a nanoscopic protein pore obeys a simple scaling law

The dependence of the rate on polymer mass was examined for the reaction of four sulfhydryl-directed poly(ethylene glycol) reagents with cysteine residues located in the lumen of the staphylococcal alpha-hemolysin pore. The logarithms of the apparent rate constants for a particular site in the lumen were proportional to N, the number of repeat units in a polymer chain. The proportionality constant was -(a/D)(5/3), where a is the persistence length of the polymer ( approximately 3.5A) and D is the diameter of the pore. Despite some incongruencies with the assumptions of the derivation, the result suggests that the polymers partition into the lumen of the pore according to the simple scaling law of Daoud and de Gennes, c(pore)/c(solution) = exp(-N(a/D)(5/3)). Therefore, the measured reaction rates yield an estimate of the diameter of the pore and might be applied to determine the approximate dimensions of cavities within other similar proteins.

Excluded volume in the configurational distribution of a strongly-denatured protein

The configurational distribution of phosphoglycerate kinase (PGK) strongly-denatured in 4 M guanidine hydrochloride solution is investigated using small-angle neutron scattering (SANS) and Monte Carlo computer simulation. It is shown that the experimental scattering profile can be represented by a random flexible chain of spheres of excess scattering density with excluded volume interactions, the best agreement being achieved when partial sphere intersection is allowed. The radius of gyration of the chain increases by a factor of 4 on denaturation, whereas the average length of segments approximately 5 residues long increases by only approximately 10%, consistent with a picture in which the large expansion on denaturation originates primarily from increased long-range flexibility of the polypeptide chain. The results provide a description of the chain statistics from which the construction of starting points for simulation studies of folding of the protein can be envisaged.