Polymers persistence length

Fig. 6 Schematic view of the chain structure in the semidilute concentration range. The mesh size is about equal to the effective polymer persistence length feff aod to the screening length (if no salt is added to the system).

The exponent b depends also on the polyelectrolyte linear charge density p and on the polyelectrolyte stiffness [130], which make it a nonuniversal characteristic for the used polyelectrolytes. Typically, polyelectrolytes with smaller p reveal a stronger dependence of <7 on The polyelectrolyte-sphere binding affinity was shown to decrease with the polymer persistence length and to increase with the polyelectrolyte linear charge density. Note that for complexation of polyelectrolytes of different p with the spherical dimethyl dodecylamine oxide (DMDAO) micelles, a modified dependence on the critical micelle charge density has been suggested, namely cT(. [128]. 

As discussed in the last 3 years, polysaccharides behave in solution under a worm like chain [26] the local stiffness of the chain is characterized by a persistance length (Ip) the larger Ip is, the larger the chain deviates from the gaussian behaviour in the usual molecular weight range of these natural polymers [27], This makes difficult to use the relations given in litterature for synthetic... 

A polymer coil does not only possess a structure on the atomistic scale of a few A, corresponding to the length of covalent bonds and interatomic distances characteristic of macromolecules are coils that more or less, obey Gaussian statistics and have a diameter of the order of hundreds of A (Fig. 1.2) [17]. Structures of intermediate length scales also occur e. g., characterized by the persistence length. For a simulation of a polymer melt, one should consider a box that contains many such chains that interpenetrate each other, i. e., a box with a linear dimension of several hundred A or more, in order to ensure that no artefacts occur attributable to the finite size of the simulation box or the periodic boundary conditions at the surfaces of the box. This ne-... 

For many polymers K and a values can be found in the Polymer Handbook [23]. In a recent study by Vanhee et al. [30] the universal calibration has been applied using the polystyrene (PS) calibration curve to characterize rigid rod poly(p-phenylenes) (PPP). It turned out that due to its larger persistence length, PPP with a certain mass requires a much larger volume than PS for the same molecular weight. Ron et al. employed universal calibration for the characterization of erodible copolymers [58]. 

Fig. 7 Persistence length P is plotted vs. the chain diameter D both for polymers giving Class I and for polymers giving Class II mesophases. (From ref [11], see also Table 1). Reproduced with permission from [11]. Copyright 2004 Am Chem Soc...

Geometrical and flexibility data pertaining to the same polymers are also given in Table 1, namely the persistence length and the average chain-to-chain interaxial distance D. The first five polymers in Table 1 have D values smaller than 6 A, unlike all the following polymers (i.e., no. 6 to 19 in Table 1, Class II). This is a consequence of the relatively bulky substituents carried by Class II polymer chains. For some of the polymers in Table 1 the C0o and P literature values are widely scattered or unavailable. In those cases lower-limit values of P from experimentally determined geometrical parameters, are predicted from our model by suitable interpolation and reported within parentheses. 

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