Universal interrelation between measures of particle and polymer size

Abstract

The characterization of many objects involves the determination of a basic set of particle size measures derived mainly from scattering and transport property measurements. For polymers, these basic properties include the radius of gyration R, hydrodynamic radius R, intrinsic viscosity [η], and sedimentation coefficient S, and for conductive particles, the electric polarizability tensor α and self-capacity C. It is often found that hydrodynamic measurements of size deviate from each other and from geometric estimates of particle size when the particle or polymer shape is complex, a phenomenon that greatly complicates both nanoparticle and polymer characterizations. The present work explores a general quantitative relation between α, C, and R for nanoparticles and polymers of general shape and the corresponding properties η, R, and R using a hydrodynamic-electrostatic property interrelation.

Single-Chain Conformation of Poly(α-olefins) in Dilute Solutions at the Crossover between Linear and Bottlebrush Architectures

“…In the limit of long polymer chains, υ g = 0.5 at the θ condition, where the solvent is poor enough such that the effects of the excluded volume expansion are canceled, and υ g = 0.59 for polymer chains in good solvent, where they acquire the ideal random coil conformation. Intermediate values (υ g = 0.535) are predicted for wormlike chains and larger values for rigid rodlike chains [υ g = (6.1/ L rod ) 4 + (0.49/ L rod –0.033 ), where L rod is the length of the rod in the range 10 < L rod < 1900]. , …”

“…In the limit of long polymer chains, υ g = 0.5 at the θ condition, where the solvent is poor enough such that the effects of the excluded volume expansion are canceled, 3 ), where L rod is the length of the rod in the range 10 < L rod < 1900]. 6,7 It is frequently assumed that exponents in eq 1 follow the relationships υ g = υ h = (υ iv + 1)/3. However, experimental observations reveal discrepancies between the values of the effective exponents, 5 which has been interpreted as a hydrodynamic draining effect.…”

Structure–Dilute Solution Property Relationships of Comblike Macromolecules in a Good Solvent

“…The computation of these values from structural information is still an area of active research. 15,16 The above arguments do not account for changes in these scaling relationships caused by the presence of branches. A quantitative method to explore these changes is through contraction factors (g i ), the ratio of branched to linear dilute solution properties.…”

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

“…76,77 In general, the shape anisotropy depends on polymer topology, chain stiffness, and polymer excluded volume interactions. 30,49,64,93,94 The model of ellipsoidal chains graed to a spherical particle in a perpendicular orientation is intended to describe graed chains that do not have a strongly attractive interaction with the surface, and in the case of the presence of such attractive interactions, e.g., when a polymer becomes bound to the substrate, we can simply modify the model so that the length of the ellipsoid of revolution along its symmetry axis (quantied by the largest eigenvalue of the radius of gyration tensor of the ellipsoid, L 3 ) is made smaller than in the transverse direction (quantied by the smallest eigenvalue of the radius of gyration tensor of the ellipsoid, L 3 ), i.e., the bound polymer is then modeled by an oblate ellipsoid of revolution. Fig.…”

“…76,77 In general, the shape anisotropy depends on polymer topology, chain stiffness, and polymer excluded volume interactions. 30,49,64,93,94…”