Kuhn-length

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>. 

Boothroyd et al. [74] recently determined the temperature dependence of the Kuhn length for polyethylene with the aid of small-angle neutron scattering. In the temperature range between 100 and 200°C, dlnC /dT = - 1.1 x 10 3 K 1... 

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. 

Equation (22) has been confirmed by a variety of techniques including neutron scattering, dynamic light scattering, and osmotic pressured measurements [23]. As concentration increases the concentration blob decreases in size until the Kuhn length is reached and the coil displays concentrated or melt Gaussian structure. The coil accommodates concentrations between the overlap and concentrated through adjustment of the concentration blob size. 

When the temperature is increased above the 0-temperature the enhanced local viscosity at higher concentration drops. The variation is the same as observed for the macroscopic viscosity [329]. In [328] polyisoprene (PI) and PS in different solvents have also been investigated and the authors observe that the slopes of the concentration dependence of the scaled local viscosities for PS and PI have a ratio of 1.7, which matches the value of the concentration ratio either on the Kuhn length (1.6) or the persistence length (1.7) for the two polymers. 

For charged polymers, the effective bending stiffness and thus the Kuhn length is increased due to electrostatic repulsion between monomers [30-36]. This effect modifies considerably not only the PE behavior in solution but also their adsorption characteristics [37]. 

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. 

TABLE 9.1 Stiffness factor, ct, skeletal factor, s, and Kuhn length, A, for some vinyl polymers... 

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. 

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