Stiffness and excluded‐volume effects in polymer chains

Contrast dependence of scattering profiles for poly(ethylene glycol) in water: Investigation by small-angle neutron scattering with 3He spin filter and small-angle x-ray scattering

The small-angle neutron scattering (SANS) and small-angle x-ray scattering (SAXS) measurements were performed for deuterated and non-deuterated poly(ethylene glycol) (d-PEG and h-PEG, respectively) in D2O and a D2O/H2O mixed solvent (Mix) to compare the scattering profiles. To determine the coherent scattering intensity of SANS, a 3He spin filter was utilized. The scattering profiles determined by the SANS measurements were analyzed in terms of the wormlike chain model with touched beads along the contour of the chain. However, the SAXS profiles were not explained by the same model with uniform beads but with beads each consisting of a core and a shell having different electron densities. To explore the chain thickness determined from the SANS profile, the scattering intensities for different combinations of d-PEG/D2O, d-PEG/Mix, h-PEG/D2O, and h-PEG/Mix were also examined.

Structural analysis of micrometer-long gold nanowires using a wormlike chain model and their rheological properties

The recent growing interest in the applications of gold nanowires (AuNWs) as flexible materials has raised the fundamental issue of how their mechanical properties are related to their morphology. In this work, to address this issue, the systematic synthesis of AuNWs, their structural analysis, and their rheological investigation were demonstrated. The structural analysis of AuNWs was performed based on TEM observations and light-scattering experiments. From these observations, it was found that the length of AuNWs varies from nanometer to micrometer depending on the reaction time while a constant width of 1.6 nm is maintained. On the basis of static light-scattering experiments and a wormlike chain model, the structural parameters of AuNWs during their growth were successfully obtained. When the contour length of AuNWs reached around 5 μm, the AuNW solution showed non-Newtonian behavior and appeared to behave as a gel. Dynamic viscoelasticity measurements indicated that such viscous behavior is responsible for entanglement between AuNWs. It is concluded that AuNWs are analogous with conventional polymers in terms of both their structure and their rheological behavior.

Scattering function of semiflexible polymer chains under good solvent conditions

Using the pruned-enriched Rosenbluth Monte Carlo algorithm, the scattering functions of semiflexible macromolecules in dilute solution under good solvent conditions are estimated both in d = 2 and d = 3 dimensions, considering also the effect of stretching forces. Using self-avoiding walks of up to N = 25,600 steps on the square and simple cubic lattices, variable chain stiffness is modeled by introducing an energy penalty ε(b) for chain bending; varying q(b) = exp (-ε(b)∕k(B)T) from q(b) = 1 (completely flexible chains) to q(b) = 0.005, the persistence length can be varied over two orders of magnitude. For unstretched semiflexible chains, we test the applicability of the Kratky-Porod worm-like chain model to describe the scattering function and discuss methods for extracting persistence length estimates from scattering. While in d = 2 the direct crossover from rod-like chains to self-avoiding walks invalidates the Kratky-Porod description, it holds in d = 3 for stiff chains if the number of Kuhn segments n(K) does not exceed a limiting value n(K)(*) (which depends on the persistence length). For stretched chains, the Pincus blob size enters as a further characteristic length scale. The anisotropy of the scattering is well described by the modified Debye function, if the actual observed chain extension <X> (end-to-end distance in the direction of the force) as well as the corresponding longitudinal and transverse linear dimensions <X(2)> - <X>(2), <R(g,⊥)(2)> are used.

Asymmetrical-flow field-flow fractionation with on-line multiangle light scattering detection. 1. Application to wormlike chain analysis of weakly stiff polymer chains

Four samples of hyaluronan in the sodium form, ranging in weight-average molecular weight, M(w), from 6.67 x 10(5) to 4.23 x 10(6) were investigated by asymmetrical-flow field-flow fractionation coupled to multiangle light scattering (FlFFF-MALS) in 0.2 M aqueous NaCl at 25 degrees C. M(w) and z-average radii of gyration, R(G)(z)(), obtained via FlFFF-MALS showed a good agreement with the results obtained by conventional static light scattering. Furthermore, the molecular weight dependence of the radius of gyration for sodium hyaluronan obtained via FlFFF-MALS was analyzed on the basis of the Kratky-Porod model for unperturbed wormlike chains combined with the Yamakawa theory for radius expansion factor, and a sufficiently good agreement was observed between the theoretical prediction and experimental data. These results show the potential usage of FlFFF-MALS regarding size separation and molecular characterization even for weakly stiff chains.

Evaluation of chain stiffness of partially oxidized polyguluronate

The chain stiffness of macromolecules is considered critical in their design and applications. This study utilizes polyguluronate derived from alginate, a typical polysaccharide widely utilized in many biomedical applications, as a model macromolecule to investigate how the chain stiffness can be tightly regulated by partial oxidation. Alginate has a backbone of inherently rigid alpha-L-guluronate (i.e., polyguluronate) and more flexible beta-D-mannuronate. The chain stiffness of the polyguluronate was specifically studied in this paper, as this component plays a critical role in the formation of alginate hydrogels with divalent cations and is the dominant factor in determining the chain stiffness of alginate. We have utilized size-exclusion chromatography, equipped with refractive index, viscosity, and light-scattering detectors, to determine the intrinsic viscosity and the weight-average molecular weight of each fraction of samples. The chain stiffness of partially oxidized polyguluronate was then evaluated from the exponent of the Mark-Houwink equation and the persistence length. We have found that partial oxidation can be used to tightly regulate the steric hindrance and stiffness of the polyguluronate backbone. This approach to control the chain stiffness of inherently rigid polysaccharides by partial oxidation may find many applications in biomedical utilization of these materials.