Persistent length

The structure of microemulsions have been studied by a variety of experimental means. Scattering experiments yield the droplet size or persistence length (3-6 nm) for nonspherical phases. Small-angle neutron scattering (SANS) [123] and x-ray scattering [124] experiments are appropriate however, the isotopic substitution of D2O for H2O... 

Complicated theories of ionic gel swelling [99, 113, 114] must inevitably take into account the real electrostatic interactions, the finite extensibility of chains, as well as the electrostatic persistence length effect. Their application is most advisable in the case of strongly charged hydrogels [114]. 

Growth rate in the mononucleation regime Growth rate in regime I, II, III, respectively Substrate length Persistence length Kinetic length... 

By definition, this is equal to the substrate, or persistence, length Lp (see Sect. 3.4.2) which by this criterion can easily take values so large that nonlinear growth should be observed for small crystals in regime I. 

The sedimentation coefficient provides a useful indicator of polysaccharide conformation and flexibility in solution, particiflarly if the dependence of on Mw is known [62]. There are two levels of approach (i) a general level in which we are delineating between overall conformation types (coil, rod, sphere) (ii) a more detailed representation where we are trying to specify particle aspect ratios in the case of rigid structures or persistence lengths for linear, flexible structures. 

If the persistence length Ip is much larger than the mean chain diameter, d, Yamakawa and Fujii gave limiting values for ai = - ln(d/2Ip) and = 0.1382. Freire and Garcia de la Torre [122] have considered further these coefficients. The factor 2Ip appears rather than Ip simply because 2Ip is equivalent to the statistical Kuhn segment length... 

The worm like chain behaviour of the pectins is developped allowing to predict the dimensions of the chain as soon as the persistence length is known. The experimental data are compared with the theoretical prediction obtained from conformational analysis. 

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... 

Then, the dimensions of a chain can be predicted whatever are the solution conditions if the intrinsic persistence length (Ip) is known Ip is a parameter reflecting the local structure and up to now, few tentatives to calculate Ip from conformational analysis exist in the litterature. 

From disaccharide analysis, few authors predict the conformation of the poly a-D galacturonan as well as the role of the charge density [35,36] they determine the persistence length Ip that will allow us to explain the behaviour in solution. 

The persistence length of pectins, in condition of charge screening (O.IM NaCl) were estimated from data as in Figure 6. 

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-... 

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