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This notation is simplified still further by defining the
ratio of constants
which is called the chain transfer constant for the monomer in question
tc molecule RX.
1 1 [RX]
J- = = + I CRX -------------------
Vu V all RX [M]
It is apparent from this expression that the larger the sum of chain
transfer term: becomes, the smaller will be v
The magnitude of the individual terms in the summation depends on
both th< specific chain transfer constants and the concentrations of the
reactants undei consideration. The former are characteristics of the
system and hence quantitie: over which we have little control; the latter
can often be adjusted to study ã particular effect. For example, chain
transfer constants are generally obtainec under conditions of low
conversion to polymer where the concentration î polymer is low enough to
ignore the transfer to polymer. We shall return belov to the case of high
conversions where this is not true.
If an experimental system is investigated in which only one molecule
i: significantly involved in transfer, then the chain transfer constant
material is particularly easy to obtain. If we assume that species SX is
the only molecule to which transfer occurs, Eq. (6.88) becomes
+ csx I
vu V sx [M]
This suggests that polymerizations should be conducted at different
ratios of [SX]/[M] and the molecular weight measured for each. Equation
(6.89) shows that a plot of l/t>tr versus [SX]/[M] should be a straight
line of slope ^sx • Figure 6.8 shows this type of plot for the
polymerization of styrene at 100°C in the presence of four different
solvents. The fact that all show a common intercept as required by Eq.
(6.89) shows that the rate of initiation is unaffected
by the nature of the solvent. The following example
examines chain transfer
constants evaluated in this situation.
Estimate the chain transfer constants for styrene to isopropylbenzene,
ethyl-benzene, toluene, and benzene from the data presented in Fig. 6.8.
Figure 6.8 Effect of chain transfer to solvent according to Eq. (6.89)
for polystyrene at 100°C. Solvents used were ethyl benzene (•),
isopropylbenzene (o), toluene (ë), and benzene (°). [Data from R. A.
Gregg and F. R. Mayo, Discuss. Faraday Soc. 2:328 (1947).]
Addition or Chain-Growth Polymerization
on the relative magnitude of these constants in terms of the structure
of the solvent molecules.
The chain transfer constants are given by Eq. (6.89) as the slopes of
the lines in Fig. 6.8. These are estimated to be as follow:
SX /-c3H7 C2H5 CH3 H
Csx X 104 2.08 1.38 0.55 0.16
The relative magnitudes of these constants are consistent with the
general rule that benzylic hydrogens are more readily abstracted than
those attached directly to the ring. The reactivity of the benzylic
hydrogens themselves follows the order tertiary > secondary > primary,
which is a well-established order in organic chemistry. The benzylic
radical resulting from hydrogen abstraction is resonance stabilized. For
toluene, as an example,
In certain commercial processes it is essential to regulate the
molecular weight of the addition polymer either for ease of processing or
because low moleculai weight products are desirable for particular
applications such as lubricants oi plasticizers. In such cases the
solvent or chain transfer agent is chosen and its concentration selected
to produce the desired value of vtr. Certain mercaptans have especially
large chain transfer constants for many common monomers and are
especially useful for molecular weight regulation. For example, styrene
has a chain transfer constant to "-butyl mercaptan equal to 21 at 60°C.
This is about 107 times larger than the chain transfer constant to
benzene at the same temperature.
Chain transfer to initiator or monomer cannot always be ignored. It
may be possible, however, to evaluate the transfer constants to these
substances by investigating a polymerization without added solvent or in
the presence of a solvent for which Csx is known to be negligibly small.
In this case the transfer constants CIX and CMX can be determined from
experiments in which vtI (via
Mn and nn) and Rp are measured. The following steps outline a procedure
for accomplishing this:
1. By Eqs. (6.14), (6.24), and (6.33),
1 _ Rt ktRp
i7 RP kp [M]
2. Solving Eq. (6.26) for [IX], we have