Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Kuhn chain

In the diaryl-substituted polysilane, the global dimensions are approximated by a wormlike chain model with a persistence length of 100 A. Thus, for the highest molecular weight studied, LIq — 100, and the chain dimensions are similar to those of a flexible-model Kuhn chain with bond lengths IkOf —200 A, that is,... [Pg.410]

The first model (Kuhn chain) is built up by planar segments of limited conjugation length which are separated by defects, e.g. cis double bonds. The second concept of a worm-like chain (Porod-Kratky chain) visualizes a continuous... [Pg.128]

Figure 11.3 Schematic drawings of a worm-like polymer chain (with continuous flexibility) and a Kuhn chain (with rigid links joined at hinges that allow free rotation about the angle between the links). The length of the links has been chosen so that the contour length and mean-square end-to-end length of the Kuhn chain are the same as those of the worm-like chain. (From Donald and Windle 1992, with permission from Cambridge University Press.)... Figure 11.3 Schematic drawings of a worm-like polymer chain (with continuous flexibility) and a Kuhn chain (with rigid links joined at hinges that allow free rotation about the angle between the links). The length of the links has been chosen so that the contour length and mean-square end-to-end length of the Kuhn chain are the same as those of the worm-like chain. (From Donald and Windle 1992, with permission from Cambridge University Press.)...
However, the freely jointed Kuhn chain is the most idealised model for a real macromolecule therefore, there exist several corrections taking into account specific features of the polymer structure. Thus, for chains in which LJA<10, condition (11.30) no longer holds. The modified condition is written as follows [94] ... [Pg.314]

Taking into account that the effects of short-range ordering, e.g., of fixed valence angles and hindrance of internal rotation [3, 4], do not change the shape of the distribution function and the correlation Rg-N but increase Ro, that can be interpreted in terms of increase of a statistical length of an equivalent Kuhn chain segment [5]. [Pg.279]

Second, the Kuhn chain has the same contour length as the real chain,... [Pg.612]

Figure 2.9 Kuhn chain model a real chain conformation of No bonds with bond length a is mapped into a freely jointed chain of N steps, each of length . Figure 2.9 Kuhn chain model a real chain conformation of No bonds with bond length a is mapped into a freely jointed chain of N steps, each of length .
This conclusion therefore suggests that we could build an equivalent freely jointed chain, without compromising the Afo-dependence of the polymer size given by Equation 2.20, by defining an effective bond length, which is renormalized by incorporating the consequences of Coo. Such a model is the Kuhn chain model and is the basis of all coarse-grained models of polymer chains. [Pg.26]

The Kuhn parameters N and are related to the number of actual skeletal bonds and bond length by requiring that both Kuhn and real chains have the same chain length L at full extension. For the Kuhn chain, L = Nt since the model chain is freely jointed. For the real chain of the type discussed in Section 2.1, L = Noacos(6/2), where (180 - 9) is the bond angle. Therefore,... [Pg.26]

Also the mean square end-to-end distance for the Kuhn chain (being a freely jointed chain) is... [Pg.26]

In the rest of the book, we shall use N to denote interchangeably the number of Kuhn segments, the degree of polymerization of the chain, and chain length. By using the same symbol R to denote the various measures of the polymer radius, one of the main results of the Kuhn chain model is the universal law. [Pg.27]

Figure 2.11 Relation between tensile force and chain extension for the freely jointed Kuhn chain (FJC) (Equation 2.49) and the Gaussian chain (G) (Equation 2.47). The vertical dashed line represents the fully extended state. Figure 2.11 Relation between tensile force and chain extension for the freely jointed Kuhn chain (FJC) (Equation 2.49) and the Gaussian chain (G) (Equation 2.47). The vertical dashed line represents the fully extended state.
Figure 2.12 Sketches of a wormlike chain, (a) Freely rotating Kuhn chain, (b) Space curve representation R(s) is the position vector of the segment at the contour variable s u(s) and 9u(s)/9s are the local tangent and curvature, respectively. Figure 2.12 Sketches of a wormlike chain, (a) Freely rotating Kuhn chain, (b) Space curve representation R(s) is the position vector of the segment at the contour variable s u(s) and 9u(s)/9s are the local tangent and curvature, respectively.
Although the polymer chains must possess chemical specificity in order to express their unique functions in various macromolecular processes, they exhibit certain universal behavior at larger length scales. By parametrizing the chemical details at the monomeric level, we have described various coarsegrained models, namely the Kuhn chain, Gaussian chain, and the wormlike Kratky-Porod chain. Chain stiffness is captured by the persistence length parameter. [Pg.44]

The system of Eqs. 99 and 100 is an exact representation of segment dynamics in a system of many entangled Kuhn chains. However, this system... [Pg.41]


See other pages where Kuhn chain is mentioned: [Pg.336]    [Pg.616]    [Pg.398]    [Pg.19]    [Pg.507]    [Pg.182]    [Pg.312]    [Pg.313]    [Pg.313]    [Pg.76]    [Pg.137]    [Pg.142]    [Pg.279]    [Pg.348]    [Pg.396]    [Pg.25]    [Pg.26]    [Pg.31]    [Pg.31]    [Pg.33]    [Pg.35]    [Pg.102]   
See also in sourсe #XX -- [ Pg.128 ]

See also in sourсe #XX -- [ Pg.19 ]

See also in sourсe #XX -- [ Pg.312 , Pg.313 , Pg.314 ]

See also in sourсe #XX -- [ Pg.142 ]




SEARCH



Kuhn Chain Model

Kuhn chain segment length

Kuhn length/chain

Polymer chain structure Kuhn length

© 2024 chempedia.info