End-to-end distribution function for dilute polymers

Modeling intra- and intermolecular correlations for linear and branched polymers using a modified test-chain self-consistent field theory

A modified test-chain self-consistent field theory (SCFT) is presented to study the intra- and intermolecular correlations of linear and branched polymers in various solutions and melts. The key to the test-chain SCFT is to break the the translational symmetry by fixing a monomer at the origin of a coordinate. This theory successfully describes the crossover from self-avoiding walk at short distances to screened random walk at long distances in a semidilute solution or melt. The calculations indicated that branching enhances the swelling of polymers in melts and influences stretching at short distances. The test-chain SCFT calculations show good agreement with experiments and classic polymer theories. We highlight that the theory presented here provides a solution to interpret the polymer conformation and behavior under various conditions within the framework of one theory.

Long polymers near wedges and cones

We perform a Monte Carlo study of N-step self-avoiding walks, attached to the corner of an impenetrable wedge in two dimensions (d=2), or the tip of an impenetrable cone in d=3, of sizes ranging up to N=10(6) steps. We find that the critical exponent γ(α), which determines the dependence of the number of available conformations on N for a cone or wedge with opening angle α, is in good agreement with the theory for d=2. We study the end-point distribution of the walks in the allowed space and find similarities to the known behavior of random walks (ideal polymers) in the same geometry. For example, the ratio between the mean square end-to-end distances of a polymer near the cone or wedge and a polymer in free space depends linearly on γ(α), as is known for ideal polymers. We show that the end-point distribution of polymers attached to a wedge does not separate into a product of angular and radial functions, as it does for ideal polymers in the same geometry. The angular dependence of the end position of polymers near the wedge differs from theoretical predictions.

Ideal polymers near scale-free surfaces

The number of allowed configurations of a polymer is reduced by the presence of a repulsive surface resulting in an entropic force between them. We develop a method to calculate the entropic force, and detailed pressure distribution, for long ideal polymers near a scale-free repulsive surface. For infinite polymers the monomer density is related to the electrostatic potential near a conducting surface of a charge placed at the point where the polymer end is held. Pressure of the polymer on the surface is then related to the charge density distribution in the electrostatic problem. We derive explicit expressions for pressure distributions and monomer densities for ideal polymers near a two- or three-dimensional wedge, and for a circular cone in three dimensions. Pressure of the polymer diverges near sharp corners in a manner resembling (but not identical to) the electric field divergence near conducting surfaces. We provide formalism for calculation of all components of the total force in situations without axial symmetry.

The conformational ensembles of α-synuclein and tau: combining single-molecule FRET and simulations

Intrinsically disordered proteins (IDPs) are increasingly recognized for their important roles in a range of biological contexts, both in normal physiological function and in a variety of devastating human diseases. However, their structural characterization by traditional biophysical methods, for the purposes of understanding their function and dysfunction, has proved challenging. Here, we investigate the model IDPs α-Synuclein (αS) and tau, that are involved in major neurodegenerative conditions including Parkinson's and Alzheimer's diseases, using excluded volume Monte Carlo simulations constrained by pairwise distance distributions from single-molecule fluorescence measurements. Using this, to our knowledge, novel approach we find that a relatively small number of intermolecular distance constraints are sufficient to accurately determine the dimensions and polymer conformational statistics of αS and tau in solution. Moreover, this method can detect local changes in αS and tau conformations that correlate with enhanced aggregation. Constrained Monte Carlo simulations produce ensembles that are in excellent agreement both with experimental measurements on αS and tau and with all-atom, explicit solvent molecular dynamics simulations of αS, with much lower configurational sampling requirements and computational expense.

Mesoscopic description of solvent effects on polymer dynamics

Solvent effects on polymer dynamics and structure are investigated using a mesoscopic solvent model that accounts for hydrodynamic interactions among the polymer beads. The simulation method combines molecular dynamics of the polymer chain, interacting with the solvent molecules through intermolecular forces, with mesoscopic multiparticle collision dynamics for the solvent molecules. Changes in the intermolecular forces between the polymer beads and mesoscopic solvent molecules are used to vary the solvent conditions from those for good to poor solvents. Polymer collapse and expansion dynamics following changes in solvent conditions are studied for homopolymer and block copolymer solutions. The frictional properties of polymers are also investigated.

Wavelet treatment of the intrachain correlation functions of homopolymers in dilute solutions

Discrete wavelets are applied to the parametrization of the intrachain two-point correlation functions of homopolymers in dilute solutions obtained from Monte Carlo simulations. Several orthogonal and biorthogonal basis sets have been investigated for use in the truncated wavelet approximation. The quality of the approximation has been assessed by calculation of the scaling exponents obtained from the des Cloizeaux ansatz for the correlation functions of homopolymers with different connectivities in a good solvent. The resulting exponents are in better agreement with those from recent renormalization group calculations as compared to the data without the wavelet denoising. We also discuss how the wavelet treatment improves the quality of data for correlation functions from simulations of homopolymers at varied solvent conditions and of heteropolymers.

The behavior of the form factor in two dimensions for linear polymers in different regimes

Off-lattice Monte Carlo simulations employing the PIVOT algorithm are used to generate ideal and excluded volume linear polymers in two dimensions. The form factor at small and large wave vectors is calculated from the resulting configurations and compared to the exact equation for ideal chains and to both scaling and renormalization group predictions for excluded volume chains. It is found that using the des Cloizeaux form for the distance distribution function in an analytic calculation of the form factor leads to close agreement with the Monte Carlo data and that simple expressions for both the small and large wave vector expansions reproduce the essential features of the form factor.

Granular polymer solution

We have measured the spectrum of fluctuations in the size of a granular polymer in a granular solvent. The system consists of a linear chain of plastic spheres immersed in a planar fluid of self-propelled balls. The time average of the end-to-end length r of the chain scales with the number of links N according to <r(2)> approximately N2nu, with nu=0.75+/-0.01. This provides an experimental test of the theoretical value nu=3 / 4 of the critical exponent for a self-avoiding random walk in two dimensions. The measured probability distribution P(r) is compared with the universal function of the scaling theory.