Single chain radii

This has also been studied experimentally and theoretically by the Saclay group.Let us start from the good solvent side, at a fixed concentration c = and progressively reduce the excluded volume parameter i = a (1 - 2 )- When u a (athermal solvent), the scaling formulas of Chapter III hold. When v becomes much smaller than a , the single chain radius/ decreases and the overlap concentration c = N/R increases. To make this more precise, we use the Flory formula for / as a function of v [eq. (1.38)]... 

Single chains confined between two parallel purely repulsive walls with = 0 show in the simulations the crossover from three- to two-dimensional behavior more clearly than in the case of adsorption (Sec. Ill), where we saw that the scaling exponents for the diffusion constant and the relaxation time slightly exceeded their theoretical values of 1 and 2.5, respectively. In sufficiently narrow slits, D density profile in the perpendicular direction (z) across the film that the monomers are localized in the mid-plane z = Djl so that a two-dimensional SAW, cf. Eq. (24), is easily established [15] i.e., the scaling of the longitudinal component of the mean gyration radius and also the relaxation times exhibit nicely the 2 /-exponent = 3/4 (Fig. 13). 

Fig. 26 Hydrodynamic radius of a graft copolymer PVCL-g-14 single chain at low temperatures and of the particles formed above the critical solution temperature (a). Temperature dependence of the hydrodynamic radius of grafted PVCL microgel E4 (b) [181]...

Fig. 3 Dissolving kinetics (in terms of average hydrodynamic radius Rh) of collapsed single-chain PNIPAM globules, where t is the standing time after the solution temperature was quenched from 33.02 to 30.02 °C and the dashed line represents a stable average value of Rh of individual PNIPAM random coils at 30.02 °C. The weight-average molar mass (Mw) of the PNIPAM sample used is 1.08 x 107g/mol with a polydispersity index (Mw/Mn) less than 1.1 [32]...

Spherical micelles are formed where the value of surfactant packing parameter is less than 1/3 (single chain surfactants with large head group areas such as anionic surfactants). The spherical aggregates are extremely small and their radius is approximately equal to the maximum stretched out length of the surfactant molecule. 

The first two terms correspond to the combinatorial entropy terms of Eq. (1) and form the non-interacting part of the structure factor which is just a weighted average of the single-chain structure factors SA(q) and SB(q) of both blend components. SA(q) and SB(q) are characterized by the radius of gyration RgA= aA(NA/6)1/2 and RgB=aB(NB/6)1/2, where aA and aB are the statistical segment lengths of polymer A and polymer B, respectively. The last term of Eq. (4) yields the SANS determined interaction parameter %SANS ... 

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