Hydrodynamic radius polymer chain

In dilute polymer solutions, hydrodynamic interactions lead to a concerted motion of tire whole polymer chain and tire surrounding solvent. The folded chains can essentially be considered as impenneable objects whose hydrodynamic radius is / / is tire gyration radius defined as... 

The length of monomer unit of MA is taken to be 0.25 nm [71]. The length of the polymer chain equal to the turn or the diameter of the protein globule is calculated taking into account the hydrodynamic size of the protein molecule via Stockes radius (Rsl). 

In contrast, the hydrodynamic radius distribution recorded for aqueous solutions of copolymers with a low grafting density is bimodal, with a contribution from small entities of = 5-30 nm, assigned to single polymer chains, and a contribution from larger particles of = 80 = 150 nm (Fig. 24b, c). The relative importance of the two populations depends on copolymer concentration the relative amount of the larger particles increases with increasing copolymer concentration. 

The solution properties of dendrigraft polybutadienes are, as in the previous cases discussed, consistent with a hard sphere morphology. The intrinsic viscosity of arborescent-poly(butadienes) levels off for the G1 and G2 polymers. Additionally, the ratio of the radius of gyration in solution (Rg) to the hydrodynamic radius (Rb) of the molecules decreases from RJRb = 1.4 to 0.8 from G1 to G2. For linear polymer chains with a coiled conformation in solution, a ratio RJRb = 1.48-1.50 is expected. For rigid spheres, in comparison, a limiting value RJRb = 0.775 is predicted. 

All factors related to the arrangement of the polymer chain in space are classified as tertiary structure. Parameters measurable directly (the radius of gyration RG, the end-to end distance h, the hydrodynamical radius RH, and the asymmetry in light scattering intensity) or indirectly (interaction parameters, the second virial coefficient A2) are related to the dimensions, such as size and shape of the polymer chain in a specific solvent under given conditions of temperature and pressure. For the exact determination of the coil size of macromolecules, it is necessary to ensure that measure-... 

The measurements from linear chains revealed two unexpected results. First, the p-parameter was found to be 16-23% lower than predicted by theory both in 6-solvents and in good solvents190 192,204-209. In other words, the hydrodynamic radius is larger than theoretically expected. Second, the p-parameter decreases for lower molecular weights the effect is more pronounced for the polymers in a 6-solvent than in a good solvent. 

Fig. 23 Angular dependence of Rayleigh ratio (Rw(q)) of segmented PNIPAM-seg-St copolymer chains in water measured from static LLS, where K is a constant, q is the scattering vector and polymer concentration (C) was 7.2 x 10-7 g/mL. The inset shows the temperature dependence of the hydrodynamic radius distribution /(Rh) determined from dynamic LLS [94]...

Figures 35 and 36 reveal that for each copolymer studied, the average aggregation number (ATagg) and average hydrodynamic radius ((%)) of polymer clusters made of collapsed and associated P(DEA-co-DMA/x) chains increase and approach corresponding constants after a certain time, indicating the for-...

Fig. 11 Temperature dependencies of the hydrodynamic radius of PNIPA-g-PEO a high molecular weight and b low molecular weight chains in water at different polymer concentrations. PEO poly(ethylene oxide). (Adapted from Ref. [44])...

The decrease in the hydrodynamic radius coincides with the first inflection point of the potentiometric titration a further and significantly smaller decrease might be assumed at the second inflection point. At pH 4 spherical structures with a maximal radius of approximately 120 nm are observed. As the contour length of the polymer chain is only 140 nm these spherical aggregates most probably do not represent simple spherical micelles. More likely vesicles are formed. At pH 10 also spherical aggregates are found, which appear to be less uniform than the ones formed under acidic conditions. at basic conditions the maximal radius was determined to be about 100 nm. 

The branched architecture has great influence on the packing of molecular chains. In general, dendrimers have smaller hydrodynamic radius and the melt and solution viscosity of a hyperbranched polymer is expected to be lower than that of a parent linear polymer. Viscosity measurements performed with a cone viscometer confirmed the decrease of viscosity of star-shape polymers compared to the respective high molecular weight arms (polymers B-R-4 and C-R-4, Tables 1 and 2). This observation is consistent with the decrease of hydrodynamic volume observed for... 

Many foods contain high-molecular weight polymers, such as proteins, pectins, and others. Often, they contribute significantly to the structure and viscosity of foods. In dilute solutions, the polymer chains are separate and the intrinsic viscosity, denoted as [ ], of a polymer in solution depends only on the dimensions of the polymer chain. Because [ ] indicates the hydrodynamic volume of the polymer molecule and is related to the molecular weight and to the radius of gyration, it reflects important molecular characteristics of a biopolymer. The concentrations of polymers used should be such that the relative viscosities of the dispersions are from about 1.2 to 2.0 to assure good accuracy and linearity of extrapolation to zero concentration (Morris and Ross-Murphy, 1981 da Silva and Rao, 1992). Intrinsic viscosity can be determined from dilute solution viscosity data as the zero concentration-limit of specific viscosity (ijsp) divided by concentration (c) ... 

When two particles, each with a radius R and containing an adsorbed surfactant or polymer layer with a hydrodynamic thickness 5, approach each other to a surface-surface separation distance h that is smaller than 25, the surfactant or polymer layers interact with each other, with two main outcomes [1] (i) the surfactant or polymer chains may overlap with each other or (ii) the surfactant or polymer layer may undergo some compression. In both cases, there will be an increase in the local segment density of the surfactant or polymer chains in the interaction region this is shown schematically in Figure 8.1. The real-hfe situation perhaps lies between the above two cases, however, with the surfactant or polymer chains undergoing some interpenetration and some compression. 

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