End chain

Ruths M and Granick S 1998 Rate-dependent adhesion between opposed perfluoropoly (alkyl ether) layers dependence on chain-end functionality and chain length J. Rhys. Chem. B 102 6056-63... 

The amount of branching introduced into a polymer is an additional variable that must be specified for the molecule to be fully characterized. When only a slight degree of branching is present, the concentration of junction points is sufficiently low that these may be simply related to the number of chain ends. For example, two separate linear molecules have a total of four ends. If the end of one of these linear molecules attaches itself to the middle of the other to form a T, the resulting molecule has three ends. It is easy to generalize this result. If a molecule has v branches, it has v 2 chain ends if the branching is relatively low. Branched molecules are sometimes described as either combs or... 

Structures [VIII] and [IX] are not equivalent they would not superimpose if the extended chains were overlaid. The difference has to do with the stereochemical configuration at the asymmetric carbon atom. Note that the asymmetry is more accurately described as pseudoasymmetry, since two sections of chain are bonded to these centers. Except near chain ends, which we ignore for high polymers, these chains provide local symmetry in the neighborhood of the carbon under consideration. The designations D and L or R and S are used to distinguish these structures, even though true asymmetry is absent. 

One limitation of this method that should immediately come to mind is the restriction to relatively low molecular weight polymers. This is a corollary of the fact that chain ends are inconsequential for very long chains. Hence, the sensitivity of the method decreases as the molecular weight of the polymer increases. As a general rule, molecular weights in the neighborhood of 25,000 represent the upper limit for applicability of this method. 

Condensation polymers such as polyesters and polyamides are especially well suited to this method of molecular weight determination. For one thing, the molecular weight of these polymers is usually less than for addition polymers. Even more pertinent to the method is the fact that the chain ends in these molecules consist of unreacted functional groups. Using polyamides as an example, we can readily account for the following possibilities ... 

Can branching be ruled out, since it would obviously make the number of chain ends per molecule an unknown quantity ... 

With either S or H as additives, two different kinds of chain are present A BAB. .. ABAB and A BABAB. . . ABABAA with S or B BABAB. . . ABAB with H. In these cases the total number of acid and base groups counts the total number of chain ends. There are two equivalents of total chain ends per mole of chains. Therefore, for S, [total ends] = 39.9 + 2.4 = 42.3 and... 

Note that the method of end group analysis is inapplicable to copolymers, since the presence of more than one repeat unit adds extra uncertainty as to the nature of chain ends. The above example included the remark that the molecular weights calculated in the example were average values. In the next section we shall examine this point in greater detail. 

The factor containing r increases with increasing r and reflects the fact that there are more locations to place the loose chain end within larger spherical shells, but. ... 

We desire to use the probability function derived above, so we recognize that the mass contribution of the volume element located a distance r from an axis through the center of mass is the product of the mass of a chain unit mp times the probability of a chain unit at that location as given by Eq. (1.44). For this purpose, however, it is not the distance from the chain end that matters but, rather, the distance from the center of mass. Therefore we temporarily identify the jth repeat unit as the center of mass and use the index k to count outward toward the chain ends from j. On this basis, Eq. (1.49) may be written as... 

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... 

The next step in the development of a model is to postulate a perfect network. By definition, a perfect network has no free chain ends. An actual network will contain dangling ends, but it is easier to begin with the perfect case and subsequently correct it to a more realistic picture. We define v as the number of subchains contained in this perfect network, a subchain being the portion of chain between the crosslink points. The molecular weight and degree of polymerization of the chain between crosslinks are defined to be Mj, and n, respectively. Note that these same symbols were used in the last chapter with different definitions. 

Note that as M the absolute number of chain ends per unit volume decreases, as does the chain-end correction. 

Polymer chain ends disrupt the orderly fold pattern of the crystal and tend to be excluded from the crystal and relegated to the amorphous portion of the sample. 

Before concluding this section, there is one additional thermodynamic factor to be mentioned which also has the effect of lowering. Since we shall not describe the thermodynamics of polymer solutions until Chap. 8, a quantitative treatment is inappropriate at this point. However, some relationships familiar from the behavior of low molecular weight compounds may be borrowed for qualitative discussion. The specific effect we consider is that of chain ends. The position we take is that they are foreign species from the viewpoint of crystallization. 

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 ... 

The effect of branching is to increase the number of chain ends and, therefore, free volume, which decreases Tg. Conversely, crosslinking ties together separate molecules, decreases the number of loose ends, and raises Tg. Copolymers show different effects on T, depending on the microstructure... 

Among the complications that can interfere with this conclusion is the possibility that the polymer becomes insoluble beyond a critical molecular weight or that the low molecular weight by-product molecules accumulate as the viscosity of the mixture increases and thereby shift some equilibrium to favor reactants. Note that we do not express reservations about the effect of increasing viscosity on the mobility of the polymer molecules themselves. Apparently it is not the migration of the center of mass of the molecule as a whole that determines the reactivity but, rather, the mobility of the chain ends which carry the reactive groups. 

We saw in Chap. 1 that the ratio M /M is widely used in polymer chemistry as a measure of the width of a molecular weight distribution. If the effect of chain ends is disregarded, this ratio is the same as the corresponding ratio of n values ... 

A cross-linked product with unsaturation at the chain ends does, indeed, have a higher modulus. This could be of commercial importance and indicates that industrial products might be formed by a nonequilibrium process precisely for this sort of reason. 

Reaction (5.W) is interesting inasmuch as either the AA or BB monomer must be present to produce crosslinking. Polymerization of AB with only Aj- (or Bf) introduces a single branch point, but no more, since all chain ends are mis-oriented for further incorporation of branch points. Including the AA or BB molecule reverses this. The bb unit which accomplishes this in reaction (5.W) is underscored. 

All polymer molecules have unique features of one sort or another at the level of individual repeat units. Occasional head-to-head or tail-to-tail orientations, random branching, and the distinctiveness of chain ends are all examples of such details. In this chapter we shall focus attention on two other situations which introduce variation in structure into polymers at the level of the repeat unit the presence of two different monomers or the regulation of configuration of successive repeat units. In the former case copolymers are produced, and in the latter polymers with differences in tacticity. Although the products are quite different materials, their microstructure can be discussed in very similar terms. Hence it is convenient to discuss the two topics in the same chapter. 

In writing Eqs. (7.1)-(7.4) we make the customary assumption that the kinetic constants are independent of the size of the radical and we indicate the concentration of all radicals, whatever their chain length, ending with the Mj repeat unit by the notation [Mj ], This formalism therefore assumes that only the nature of the radical chain end influences the rate constant for propagation. We refer to this as the terminal control mechanism. If we wished to consider the effect of the next-to-last repeat unit in the radical, each of these reactions and the associated rate laws would be replaced by two alternatives. Thus reaction (7. A) becomes... 

Equations (7.32) and (7.34) provide the method for evaluating the r s from thi data given. We recognize that a 12 dyad can come about from 1 adding to 1 as well as from 2 adding to 1 therefore we use half the number of 12 dyad as a measure of the number of additions of monomer 2 to chain end 1 Accordingly, by Eq. (7.30),... 

The carbon atoms carrying the substituents are not truly asymmetric, since the two chain sections-while generally of different length-are locally the same on either side of any carbon atom, except near the ends of the chain. As usual, we ignore any uniqueness associated with chain ends. 

The active-center chain end is open to front or rear attack in general hence the configuration of a repeat unit is not fixed until the next unit attaches to the growing chain. 

The probabilities of the various dyad, triad, and other sequences that we have examined have all been described by a single probability parameter p. When we used the same kind of statistics for copolymers, we called the situation one of terminal control. We are considering similar statistics here, but the idea that the stereochemistry is controlled by the terminal unit is inappropriate. The active center of the chain end governs the chemistry of the addition, but not the stereochemistry. Neither the terminal unit nor any other repeat unit considered alone has any stereochemistry. Equations (7.62) and (7.63) merely state that an addition must be of one kind or another, but that the rates are not necessarily identical. 

Polypropylene polymerized with triethyl aluminum and titanium trichloride has been found to contain various kinds of chain ends. Both terminal vinylidene unsaturation and aluminum-bound chain ends have been identified. Propose two termination reactions which can account for these observations. Do the termination reactions allow any discrimination between the monometallic and bimetallic propagation mechanisms ... 

A reaction analogous to the alkylation step of reaction (7.Q) can account for the association of an aluminum species with chain ends ... 

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