Segment factor

A segment factor / related M to the constant ratio between the carboxyl group and the monomer. With specific reference to pectin, a second factor (/") was later postulated to account for the degree of carboxylation.7 Subsequently, a series of pectins determined to have an anhydrogalacturo-nan content of 68-96% (/" = 0.68-0.96) did not always change the exponent of M. A CMC sample with a 0.75 degree of carboxylation, making /" = 0.25, increased the exponent by 1. 

As probes must be manufactured individually for each different tube type, the probe development is an important factor for the economic use of the method. The classical procedure of probe development is a combination of experience and experiment. The new probe design is based on the experience with already manufactured probes. For an evaluation of the new design the probe must be manufactured. If the probe design is complicated, for example due to dual exciter coil arrangement or segmented differential detector coil systems, the costs of the development can be very high. Therefore a method for the pre-calculation of the probe performance is extremely useful. 

This last result includes the factor since all segments are counted twice by the combination of Eqs. (1.53) and (1.54). The double summation also makes the two terms in the brackets equal to two times either one of them. This procedure averages over all segments fulfilling the role of center of mass therefore it is appropriate to identify the quantity evaluated by Eq. (1.59) by the symbol rg. ... 

The segmental friction factor introduced in the derivation of the Debye viscosity equation is an important quantity. It will continue to play a role in the discussion of entanglement effects in the theory of viscoelasticity in the next chapter, and again in Chap. 9 in connection with solution viscosity. Now that we have an idea of the magnitude of this parameter, let us examine the range of values it takes on. 

To the extent that the segmental friction factor f is independent of M, then Eq. (2.56) predicts a first-power dependence of viscosity on the molecular weight of the polymer in agreement with experiment. A more detailed analysis of f shows that segmental motion is easier in the neighborhood of a chain end because the wagging chain end tends to open up the structure of the melt and... 

Equation (2.56) not only enables us to understand the basis for the first-power dependence of rj on M, but also presents us with a new and important theoretical parameter, the segmental friction factor. We shall see in the next chapter that it is a quantity which can also be extracted from measurements of the viscoelasticity of polymers. 

Table 2.3 Segmental Friction Factors Ranked in Order of Decreasing Values for Polymers Compared 100°C Above Their Respective Glass Transition Temperatures...

This last factor overcounts the number of couplings, since the random placement of chain segments makes it improbable that each entanglement will involve a new molecule. Thus an entanglement may be redundant the chain might already be coupled to the original molecule. 

Since the tube friction factor measures the force needed to impart a unit velocity to the chain along the tube direction, we can think of applying this force, one segment at a time, to the diffusing chain. Since the friction factor per segment is f, Eq. (2.65) becomes... 

Although we still need to explain the use of this theory, Eq. (3.98) shows that segmental friction factors are accessible through viscoelastic studies. This fact was anticipated in the list of f values given in Table 2.3. 

Use values of the constants for polystyrene from Table 4.4 to calculate the shift factors needed to connect those segments in Fig. 4.17 measured at 96.3 and 108.7°C, with the isotherm measured at Tg = 100.0°C. Are the values reasonable ... 

We saw in Sec. 1.11 that coil dimensions are affected by interactions between chain segments and solvent. Both the coil expansion factor a defined by Eq. (1.63) and the interaction parameter x are pertinent to describing this situation. 

Rather than discuss the penetration of the flow streamlines into the molecular domain of a polymer in terms of viscosity, we shall do this for the overall friction factor of the molecule instead. The latter is a similar but somewhat simpler situation to examine. For a free-draining polymer molecule, the net friction factor f is related to the segmental friction factor by... 

Random coils. Equation (9.53) gives the Kirkwood-Riseman expression for the friction factor of a random coil. In the free-draining limit, the segmental friction factor can, in turn, be evaluated from f. In the nondraining limit the radius of gyration can be determined. We have already discussed f in Chap. 2 and (rg ) in this chapter and again in Chapter 10, so we shall not examine the information provided by D for the random coil any further. 

Prices for the different material groups (F —F ) are largely influenced by product size and shape and the quantity of production. Apart from product shape, the main price-determining factor is the performance factor K Prices for the powder, a sintered anisotropic ring, and a sintered anisotropic segment are roughly on the order of 1, 2, and 5, respectively. 

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