Chain radius of gyration

The following physical quantities are calculated mean square end-to-end distance, correlations between internal points of a chain, radius of gyration, second and third virial coefficient, and so on. The parameters for this model are the area S of the equivalent Brownian chain, the two-body interaction b with dimension Ld 4 (eventually the three-body interaction c with dimension L2d 6), and, for a monodisperse sample, the chain concentration C. The swelling of... 

A sketch of a polymer brush is shown in Fig. 1. We call a the graft density or the number of grafted chains per unit area of the surface. Each chain has N monomers. In a dilute solution the chain radius of gyration, R, is for Gaussian chains in a 0 solvent... 

Quantitative Behaviour of a Finite Chain Radius of Gyration.63... 

The B network, on the other hand (94), appeared to deviate significantly from the affine. As illustrated in Figure 9.24 (94) the chain radius of gyration... 

We will start our discussion with the grafting to approach, which may be characterized as the simplest. Depending on the nature of the surface of the porous membrane that we want to decorate with a brush, we must choose an end-functionalized polymer chain (or a highly asymmetric block copolymer of an amphipathic nature) that may strongly adsorb from its functionalized part on the inner surface. Then in principle we may use the same method as for the case of a flat surface, i.e., dip the membrane in a solution that contains these polymers and then wait for the full formation of the brush. However, it has been shown [21] that self-assembly inside the pores is prohibited when the ratio of pore diameter to chain radius of gyration... 

EWIF has been used to study the adsorption of poly(methylmethacrylate) (PMMA) onto sapphire. Polymer molecular weights are 120,000 and 600,000 and some chains have been labelled with anthracene chromophores to allow fluorescence excitation by the optical evanescent wave. The surface excess is measured to be 1.47 mg/m. Moreover, the first moment of the monomer distribution, , can be evaluated. The observed value = 73A, is comparable to the chain radius of gyration, in good agreement with the theoretical models. The determination of higher moments of the distribution is not accessible with the present system. It would require the use of chains with molecular weights in the range 10 -10. ... 

The width of the adsorbed polymer layer is also consistent with the chain radius of gyration which can be calculated using the well-known formula Rf = a(V7). Taking N 1200 and a = 2.52 A for the PMMA chain, we obtain Rq = 173 A. If the profile is assumed to be a step function of width Rq one than expects < z > = Rq/ = 86 A which is very close to our experimental finding of 73 8 A. 

Quantitative discrepancies remain between the observed and predicted precursor film profiles which may reveal either an incorrect description of the long-range interactions by simple van der Waals terms or an anomalous viscosity for liquid thicknesses smaller than the chain radius of gyration. Complementary experiments and analysis are presently underway to test these problems. 

The dimensions of alginate chains (radius of gyration and intrinsic viscosity) in aqueous solutions depend on the external salt concentration the expansion is directly related to the persistence length Lp and to the thickening performance of the polymer. The relative extension of the three types of blocks increases in the following order ... 

---