Molecular-weight dependence

4 Molecular Weight Dependence Because the Rouse model describes the static conformation of a polymer chain in the theta condition, we expect that the model can also describe the dynamics. However, this expectation is wrong. [Pg.234]

In the Rouse model, the relaxation time Ti of the first mode is proportional to (Eq. 3.136). The experimentally observed exponent for a polymer chain in a theta solvent is 3/2. The discrepancy also exists in the molecular weight dependence of Dq. Experimentally, we observe Dq (Section 3.2.7) in the theta solvent. In the Rouse model (Eq. 3.160), Dq The model fails to give the correct exponent. The shortcoming of the model is ascribed to the neglect of hydrodynamic interactions. In the following subsection, we take into account the hydrodynamic interactions. In Section 4.3, we will see an example in which the Rouse model can describe the motion of polymer chains correctly. [Pg.234]

A scaling analysis [95-97] provides the temperature and molecular weight dependence... [Pg.70]

There are three major aspects of polymer viscosity discussed in this chapter. First, we shall consider the fact that most bulk polymers display shear-dependent viscosity that is, this property does not have a single value but varies with the shearing forces responsible for the flow. Second, the molecular weight dependence of polymer viscosity is examined. We may correctly expect a... [Pg.75]

Our approach in this chapter is to alternate between experimental results and theoretical models to acquire familiarity with both the phenomena and the theories proposed to explain them. We shall consider a model for viscous flow due to Eyring which is based on the migration of vacancies or holes in the liquid. A theory developed by Debye will give a first view of the molecular weight dependence of viscosity an equation derived by Bueche will extend that view. Finally, a model for the snakelike wiggling of a polymer chain through an array of other molecules, due to deGennes, Doi, and Edwards, will be taken up. [Pg.76]

The Molecular Weight Dependence of Viscosity Experimental Aspects... [Pg.103]

In connection with a discussion of the Eyring theory, we remarked that Newtonian viscosity is proportional to the relaxation time [Eqs. (2.29) and (2.31)]. What is needed, therefore, is an examination of the nature of the proportionality between the two. At least the molecular weight dependence of that proportionality must be examined to reach a conclusion as to the prediction of the reptation model of the molecular weight dependence of viscosity. [Pg.124]

Evaluate the relaxation time associated with each of these molecular weights and verify that the molecular weight dependence of r corresponds to the value given in Sec. 2.13. [Pg.197]

An extra amount of free volume is associated with chain ends, which are capable of wagging in a way that is not possible in the middle of a chain. Accordingly, as molecular weight decreases, Vj- increases, which, in turn, decreases Tg. The following expression has been found to describe this molecular weight dependence ... [Pg.255]

In any application of a copolymer the rate of formation of the product, its molecular weight, and the uniformity of its composition during manufacture are also important considerations. While the composition of a copolymer depends only on the relative rates of the various propagation steps, the rate of formation and the molecular weight depend on the initiation and termination rates as well. We shall not discuss these points in any detail, but merely indicate that the situation parallels the presentation of these items for homopolymers as given in Chap. 6. The following can be shown ... [Pg.470]

The viscosity of a polymer solution is one of its most distinctive properties. Only a minimum amount of research is needed to establish the fact that [77] increases with M for those polymers which interact with the solvent to form a random coil in solution. In the next section we shall consider the theoretical foundations for the molecular weight dependence of [77], but for now we approach this topic from a purely empirical point of view. [Pg.604]

Such a coil is said to be nondraining, since the interior of its domain is unaffected by the flow. We anticipate using Eq. (1.58) to describe the molecular weight dependence of In view of this, we replace rg by (rg ) and attach a subscript 0 to the latter as a reminder that, under 0 conditions, solvent and excluded-volume effects cancel to give a true value. With these ideas in mind, the volume fraction of the nondraining coil is written... [Pg.609]

The emphasis in the foregoing analysis was explaining the range of exponents which describe the dependence of [r ] on M. In this section we retreat a bit from this objective and reexamine Eqs. (9.40) and (9.44) without regard to the molecular weight dependence of the individual factors ... [Pg.610]

Next we shall examine the molecular weight dependence of the coil expansion factor a to see if the latter can explain the observations of a s greater than 0.5. [Pg.617]

We begin by writing the volume of the spherical coil domain as = (4/3)7rr, where r = a(r ). For simplicity we temporarily write this as r = aro we return to below to introduce the molecular weight dependence... [Pg.618]

Our primary objective in undertaking this examination of the coil expansion factor was to see whether the molecular weight dependence of a could account for the fact that the Mark-Houwink a coefficient is generally greater than 0.5 for T 0. More precisely, it is generally observed that 0.5 < a < 0.8. This objective is met by combining Eqs. (9.55) and (9.68) ... [Pg.620]

The intrinsic viscosity of poly(7-benzyl-L-glutamate) (Mq = 219) shows such a strong molecular weight dependence in dimethyl formamide that the polymer was suspected to exist as a helix which approximates a prolate ellipsoid of revolution in its hydrodynamic behaviorf ... [Pg.652]

Experimental values of X have been tabulated for a number of polymer-solvent systems (4,12). Unfortunately, they often turn out to be concentration and molecular weight dependent, reducing their practical utility. The Flory-Huggins theory quahtatively predicts several phenomena observed in solutions of polymers, including molecular weight effects, but it rarely provides a good quantitative fit of data. Considerable work has been done subsequentiy to modify and improve the theory (15,16). [Pg.435]

In which X is the average monomer interpenetration distance, L is the contour length of interdiffused chains and n(t) is the number of chains diffused at time t. The time and molecular weight dependence of these molecular properties are given in Table 1. [Pg.376]

Thus, fracture occurs by first straining the chains to a critical draw ratio X and storing mechanical energy G (X — 1). The chains relax by Rouse retraction and disentangle if the energy released is sufficient to relax them to the critically connected state corresponding to the percolation threshold. Since Xc (M/Mc) /, we expect the molecular weight dependence of fracture to behave approximately as... [Pg.389]

The hydrophobized polymers demonstrated higher activity than unmodified polymers. The molecular weight dependency on the activity was also found. In particular, MA-CDA-5K-A (MW 5,000) hydrophobized with 10 mol% aniline induced both cytokines remarkably higher than unmodified MA-CDA and modified MA-CDA with different molecular weights. [Pg.186]

In Eq. (12), the fourth term results from the increased volume available to the ends of the polymer chains on melting and the fifth term results mainly from the requirement that the ends of the molecules should stay out of the crystallites. Both terms are entropy terms giving the molecular weight dependence of the formation of bundle-like nucleus. Thus, the net transition rate J can be determined by the following equations ... [Pg.308]

Figure 18 Molecular weight dependencies of the phase transition temperature (T,) from orthorhombic to hexagonal phase and the melting temperature Tm) of the hexagonal phase of PE. O = phase transition from orthorhombic to hexagonal phase A A = melting of the hexagonal phase. (From Ref. 131.)...

Fig. 8 (a) Effects of varying the amino acid at fourth position in ELP[V8X2]. (b) Extrapolation of transition temperature for other ratios of Val Xaa. (a) and (b) Reprinted from [24] with permission from American Chemical Society, copyright 1993 (c) Molecular weight dependence of transition temperature. Reprinted from [23] with permission from Elsevier, copyright 2002... [Pg.79]

Fig. 12. Molecular weight dependences of the normalized chain relaxation time, tJTs, for linear polymers ( ), branched fractions ( ), and branched feed polymer (+). (Reproduced with permission from [88]. Copyright 2001 American Chemical Society.)...

$Fig. 12. Molecular weight dependences of the normalized chain relaxation time, tJTs, for linear polymers ( ), branched fractions ( ), and branched feed polymer (+). (Reproduced with permission from [88]. Copyright 2001 American Chemical Society.)...$

The viscosity average molecular weight depends on the nature of the intrinsic viscosity-molecular weight relationship in each particular case, as represented by the exponent a of the empirical relationship (52), or (55). However, it is not very sensitive to the value of a over the range of concern. For polymers having the most probable distribution to be discussed in the next chapter, it may be shown, for example, that... [Pg.313]

Rymden, R. Stilbs, P. (1985b). Concentration and molecular weight dependence of counterion self-diffusion in aqueous poly(acrylic acid) solutions. Journal of Physical Chemistry, 89, 3502-5. [Pg.88]

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