Models pearl necklace model

Kirkwood and Riseman (1948) did not encounter this problem, because they used the bead-rod or, in other words, pearl-necklace model of macromolecule (Kramers 1946), in which A is a number of Kuhn s stiff segments, so that N present the length of the macromolecule. 

Parameter values were chosen so that Ub models a stiff covalent bond, whereas the repulsive portion of ii j, approximates a hard sphere potential of diameter au, which was set equal to the bond length a so that the chain becomes the familiar pearl necklace model. 

The conformation parameter a (=A/Af, where Af is A of a hypothetical chain with free internal rotation) for cellulose and its derivatives lies between 2.8-7.5 2 119,120) and the characteristic ratio ( = A2Mb//2, where Ax is the asymptotic value of A at infinite molecular weight, Mb is the mean molecular weight per skeletal bond, and / the mean bond length) is in the range 19-115. These unexpectedly large values of a and Cffi suggest that the molecules of cellulose and its derivatives behave as semi-flexible or even inflexible chains. For inflexible polymers, analysis of dilute solution properties by the pearl necklace model becomes theoretically inadequate. Thus, the applicability of this model to cellulose and its derivatives in solution should be carefully examined. 

The bond lei h b entering in this expression ould not be confused with the c c bond length. We are using an idealized pearl necklace model, and b may be several times larger than the c — c bond length. 

A pearl necklace model in which the polypeptide chain forms the string of the necklace and the surfactant molecules form micelle-like clusters along the polypeptide chain, which passes through the micellar clusters in a a-helical conformation. In contrast to the rod-like particle model, this model assumes that the polypeptide chain is flexible. 

The pearl necklace model for the BSA-dodecylsulphate complexes is very different from the model used to interpret the neutron diffraction data for the complexes formed between the deuterated bifunctional enzyme N-5 -phosphoribosylanthranilate/indole-3-glycerol-phosphate... 

Application of the concept of partial shielding by Debye and Bueche, and, independently, by Brinkman,to the pearl-necklace model gave, for viscosity and sedimentation. 

Two early theoretical models to rationalize this result were pursued the porous-sphere model of Debye and Bueche [1948], in which spherical beads representing the monomers are distributed uniformly in a spherical volume, and the more realistic pearl necklace model, proposed by Kuhn and Kuhn [1943], in which the beads are linked together by infinitely thin linkages. For each of these models, the principal challenge was to describe the flow of solvent around and within the volume occupied... 

T. G. F. Schoon Pearl necklace model of spherical structural units (f)... 

Several coarse-grained geometrical models other than the skeletal chain model are being used to predict how various physical quantities depend on the chain length, the polymer concentration, and so forth, and to perform computer simulations. Figure 1.6 illustrates a bead-stick model (a), a bead-spring model (b), and a pearl-necklace model (c). 

In the pearl-necklace model, the beads (pearls) are always in contact with the two adjacent beads. This model is essentially a bead-stick model with the stick length equal to the bead diameter. The bead always has a positive diameter. As in the bead-stick model, we can restrict the bond angle and the dihedral angle. 

Suppose a polymer chain consisting of N spheres of diameter b (pearl-necklace model see Fig. 1.34). We consider the dilute solution limit in which each chain is isolated from the other chains in the solution. When the chain dimension is R, these N spheres are contained in a cube of volume close to R, but no other spheres... 

Kirkwood-Riseman Theory (1948) This theory is based on a model in which the chain consists of a sequence of monomer units. When a polymer molecule is placed in a fluid of surrounding medium (solvent molecules), the flow is perturbed by the resistance offered by each polymer unit. This model is known as the pearl string (or pearl necklace) model, where each monomer unit is a bead (see Figure 8.5). The emphasis of the Kirkwood-Riseman theory is on the hydrodynamic resistance of the indivdual beads. When the individual resistance is summed, we obtain the resistance of the whole molecule. 

This theory has been partially confirmed by sedimentation experiment (Langevin and Rondelez, 1978). The value of the slope so far found was —0.50 0.10. We now have some evidence to believe that in the semidilute range of polymer solution the solvent is forced through in orderly fashion around the blob of radius C but still cannot penetrate the interior of the blob. Note that this theory is reminiscent of the pearl necklace model and the hydrodynamic equivalent sphere. 

Abstract This introductory chapter provides a brief (textbook-like) survey of important facts concerning the conformational and dynamic behavior of polymer chains in dilute solutions. The effect of polymer-solvent interactions on the behavior of polymer solutions is reviewed. The physical meanings of the terms good, 9-, and poor thermodynamic quality of the solvent are discussed in detail. Basic assumptions of the Kuhn model, which describes the conformational behavior of ideal flexible chains, are outlined first. Then, the correction terms due to finite bond angles and excluded volume of structural units are introduced, and their role is discussed. Special attention is paid to the conformational behavior of polyelectrolytes. The pearl necklace model, which predicts the cascade of conformational transitions of quenched polymer chains (i.e., of those with fixed position of charges on the chain) in solvents with deteriorating solvent quality, is described and discussed in detail. The incomplete (up-to-date) knowledge of the behavior of annealed (i.e., weak) polyelectrolytes and some characteristics of semiflexible chains are addressed at the end of the chapter. 

Keywords Ideal polymer chain Realistic polymer chain Chain conformations Solvent quality Quenched polyelectrolyte Annealed polyelectrolyte Pearl necklace model Persistence length... 

The pearl necklace model (Fig. 1.3[b]) is a somewhat more useful model, although it is strictly athermal but, by a proper choice of the ration h/ between the radius h of the excluded volume sphere around each bead and the bond length I, one can ensure automatically that chains cannot cross each other if they respect excluded volume restrictions (no spheres are allowed to overlap apart, possibly, from subsequent ones if one chooses l l[Pg.12]

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