Kuhn length/chain

An experimental test of the scaling model requires a selective variation of the two scaling variables of the model, i.e. the lateral chain distance and the chain stiffness. The Kuhn length /K depends on temperature via the characteristic ratio Cw the lateral chain distance s can be varied via the volume fraction 4>. 

Finally, a further unsolved problem should be mentioned. If we compare the plateau moduli of different polymer melts and relate them to the Kuhn length and to the density, this relation can also be adequately described with the scaling model, if an exponent a near 3 is chosen [73]. It is not known why this exponent is different if the contour length density is varied by dilution in concentrated solution or by selecting polymer chains of different volume. 

A rep < 1, Des < 1, the nucleation dynamics is stochastic in nature as a critical fluctuation in one, or more, order parameters is required for the development of a nucleus. For DeYep > 1, Des < 1 the chains become more uniformly oriented in the flow direction but the conformation remains unaffected. Hence a thermally activated fluctuation in the conformation can be sufficient for the development of a nucleus. For a number of polymers, for example PET and PEEK, the Kuhn length is larger than the distance between two entanglements. For this class of polymers, the nucleation dynamics is very similar to the phase transition observed in liquid crystalline polymers under quiescent [8], and flow conditions [21]. In fast flows, Derep > 1, Des > 1, A > A (T), one reaches the condition where the chains are fully oriented and the chain conformation becomes similar to that of the crystalline state. Critical fluctuations in the orientation and conformation of the chain are therefore no longer needed, as these requirements are fulfilled, in a more deterministic manner, by the applied flow field. Hence, an increase of the parameters Deiep, Des and A results into a shift of the nucleation dynamics from a stochastic to a more deterministic process, resulting into an increase of the nucleation rate. 

This result may be compared with Eq. (9.7), from which it follows that the persistence length is equal to half the length of a statistical chain element or Kuhn length ap = i A. This representation of the wormlike chain is of particular importance for the description of stiff polymers. 

Note that the Kuhn length is comparable to the persistence length lp, which is an alternative measure of the chain stiffness (see Sect. 3.2). For DNA (more generally, chains with worm-like elasticity), l = 2lp. 

Fig. 3.6. Dependences of the chain size (gyration radius) on the inverse temperature calculated through Monte Carlo simulations. (Top) A semiflexible chain with contour length L/a = 512 and Kuhn length l/a 20, and (bottom,) a flexible chain (l/a 2) with the same contour length. The error bars represent the standard deviations. The insets show snapshots of (a) coil states and (b) folded states...

Kuhn was the first to point out that the dimensions of a chain with given persistence p may always be described as if it were completely flexible (see (5.1.1)) by grouping a number of monomer units together into statistical chain elements (s.c.e.) or Kuhn segments. The number a of bonds in such an s.c.e. is the larger the stlffer the chain. The basic idea is that such s.c.e. s may be considered as orlentatlonally independent they are then independent subsystems as defined in sec. 1.3.6. The real chain of N bonds is now modelled as an equivalent ideal chain of = N/a s.c.e. s and the Kuhn length becomes bt (where a > 1, b > 1). Then (r ) = vdilch equals = 6pN(, provided that a... 

Note that. In a sense, the polyelectrolyte behaves now as If it were an "ideal" (Gaussian) chain with a relatively small number of Kuhn lengths. This coil size Is determined by the local stiffness, but not by long-range excluded volume. Should q Increase even furher (approaching L), then the wormlike chain would be better described by a slightly curved rod (as expressed by (5.2.21)) than by a random-flight chain. 

The average span descriptor, calculated as the average value of conformational changes and denoted by R, is used to describe long chain molecules, such as macromolecules, polymers, and proteins, and is related to the Kuhn length (see below). 

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