Universal interrelation between measures of particle and polymer size

Dilute polyelectrolyte solutions: recent progress and open questions

Polyelectrolytes are a class of polymers possessing ionic groups on their repeating units. Since counterions can dissociate from the polymer backbone, polyelectrolyte chains are strongly influenced by electrostatic interactions. As a result, the physical properties of polyelectrolyte solutions are significantly different from those of electrically neutral polymers. The aim of this article is to highlight key results and some outstanding questions in the polyelectrolyte research from recent literature. We focus on the influence of electrostatics on conformational and hydrodynamic properties of polyelectrolyte chains. A compilation of experimental results from the literature reveals significant disparities with theoretical predictions. We also discuss a new class of polyelectrolytes called poly(ionic liquid)s that exhibit unique physical properties in comparison to ordinary polyelectrolytes. We conclude this review by listing some key research challenges in order to fully understand the conformation and dynamics of polyelectrolytes in solutions.

Far-Field Electrostatic Signatures of Macromolecular 3D Conformation

In solution as in vacuum, the electrostatic field distribution in the vicinity of a charged object carries information on its three-dimensional geometry. We report on an experimental study exploring the effect of molecular shape on long-range electrostatic interactions in solution. Working with DNA nanostructures carrying approximately equal amounts of total charge but each in a different three-dimensional conformation, we demonstrate that the geometry of the distribution of charge in a molecule has substantial impact on its electrical interactions. For instance, a tetrahedral structure, which is the most compact distribution of charge we tested, can create a far-field effect that is effectively identical to that of a rod-shaped molecule carrying half the amount of total structural charge. Our experiments demonstrate that escape-time electrometry (ETe) furnishes a rapid and facile method to screen and identify 3D conformations of charged biomolecules or molecular complexes in solution.

Solution properties of spherical gold nanoparticles with grafted DNA chains from simulation and theory

There has been a rapidly growing interest in the use of functionalized Au nanoparticles (NPs) as platforms in multiple applications in medicine and manufacturing. The sensing and targeting characteristics of these NPs, and the realization of precisely organized structures in manufacturing applications using such NPs, depend on the control of their surface functionalization. NP functionalization typically takes the form of polymer grafted layers, and a detailed knowledge of the chemical and structural properties of these layers is required to molecularly engineer the particle characteristics for specific applications. However, the prediction and experimental determination of these properties to enable the rational engineering of these particles is a persistent problem in the development of this class of materials. To address this situation, molecular dynamic simulations were performed based on a previously established coarse-grained single-stranded DNA (ssDNA) model to determine basic solution properties of model ssDNA-grafted NP-layers under a wide range of conditions. In particular, we emphasize the calculation of the hydrodynamic radius for ssDNA-grafted Au NPs as a function of structural parameters such as ssDNA length, NP core size, and surface coverage. We also numerically estimate the radius of gyration and the intrinsic viscosity of these NPs, which in combination with hydrodynamic radius estimates, provide valuable information about the fluctuating structure of the grafted polymer layers. We may then understand the origin of the commonly reported variation in effective NP "size" by different measurement methods, and then exploit this information in connection to material design and characterization in connection with the ever-growing number of applications utilizing polymer-grafted NPs.

Structure-dilute solution property relationships of comb-like macromolecules in a good solvent

The structural characterization of branched polymers still poses experimental challenges despite their technological potential. This lack of clarity is egregious in linear low-density polyethylene (LLDPE), a common industrial plastic. Here, we design a coarse-grain, implicit solvent molecular dynamics model for LLDPE in 1,2,4-trichlorobenzene, a canonical good solvent, that replicates all-atom simulations and experiments. We employ this model to test the relationship between the contraction factors, the ratios of branched to linear dilute solution properties. In particular, we relate the contraction factor of the radius of gyration to that of the intrinsic viscosity and the hydrodynamic radius. The contraction exponents are constant as we vary branch length and spacing in contrast to theoretical expectations. We use this observation to develop a general theory for the dilute solution properties of linear polymers with linear side-chain branches, comb-like macromolecules, in a good solvent and validate the theory by generating master curves for LLDPE.

Violation of Stokes-Einstein and Stokes-Einstein-Debye relations in polymers at the gas-supercooled liquid coexistence

Molecular dynamics simulations are performed on a system of model linear polymers to look at the violations of Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations near the mode coupling theory transition temperatureT_cat three (one higher and two lower) densities. At low temperatures, both lower density systems show stable gas-supercooled-liquid coexistence whereas the higher density system is homogeneous. We show that monomer density relaxation exhibits SE violation for all three densities, whereas molecular density relaxation shows a weak violation of the SE relation nearT_cin both lower density systems. This study identifies disparity in monomer mobility and observation of jumplike motion in the typical monomer trajectories resulting in the SE violations. In addition to the SE violation, a weak SED violation is observed in the gas-supercooled-liquid coexisting domains of the lower densities. Both lower density systems also show a decoupling of translational and rotational dynamics in this polymer system.

Communication: A comparison between the solution properties of knotted ring and star polymers

We computationally investigate the good solvent solution properties of knotted ring and star polymers by combining molecular dynamics (MD) simulation and path-integral calculations. We consider knotted rings having a minimal crossing number m c in the range, 0 ≤ m c ≤ 9, and star polymers having a range of f star arms, 2 ≤ f ≤ 20, attached to a common core monomer particle. After generating configurational ensembles of these polymers by MD, we use the path-integration program ZENO to calculate basic configurational properties, i.e., radius of gyration, hydrodynamic radius, intrinsic viscosity, as well as fluctuations in these properties. Our simulations indicate that the configurational properties of knotted rings and star polymers in solution show a similar decrease with increasing m c and f. Moreover, fluctuations in these properties also decrease with increasing topological complexity. Our findings should be helpful in polymer characterization and more generally for understanding the role of polymer topology in polymer material properties.

Knot Energy, Complexity, and Mobility of Knotted Polymers

The Coulomb energy E C is defined by the energy required to charge a conductive object and scales inversely to the self-capacity C, a basic measure of object size and shape. It is known that C is minimized for a sphere for all objects having the same volume, and that C increases as the symmetry of an object is reduced at fixed volume. Mathematically similar energy functionals have been related to the average knot crossing number 〈m〉, a natural measure of knot complexity and, correspondingly, we find E C to be directly related to 〈m〉 of knotted DNA. To establish this relation, we employ molecular dynamics simulations to generate knotted polymeric configurations having different length and stiffness, and minimum knot crossing number values m for a wide class of knot types relevant to the real DNA. We then compute E C for all these knotted polymers using the program ZENO and find that the average Coulomb energy 〈E C〉 is directly proportional to 〈m〉. Finally, we calculate estimates of the ratio of the hydrodynamic radius, radius of gyration, and the intrinsic viscosity of semi-flexible knotted polymers in comparison to the linear polymeric chains since these ratios should be useful in characterizing knotted polymers experimentally.