If these additional criteria are met, a polymerization is proposed to be named controlled. It can also be regarded as controlled if side reactions occur but only to an extent which does not considerably disturb the control of the molecular structure of the polymer chain.

In the past decade many new polymerization mechanisms for the formation of controlled polymer structures have emerged and have been named "living", such as cationic, ring-opening metathesis, group transfer, and radical polymerizations.(2) The two terms living and controlled have been considerably confused (not to say abused) by many authors due to the lack of agreed definitions. Very often the lack of control (shown by broad MWD) is equalled with chain-breaking reactions, i.e. a non-living process. In addition, new terms such as quasiliving, pseudoliving, apparently living, "living", and immortal, have led to increasing confusion. Thus, we first will repeat/extend exisiting definitions of these terms. Then we will give a more detailed discussion and examples.

DEFINITIONS:

1. Living polymerization is a chain polymerization without irreversible chain breaking reactions, i.e. transfer and termination.

2. Living polymerization may include:
- slow initiation,
- reversible formation of species with various activities and lifetimes,
- reversible formation of inactive (dormant) species (reversible deactivation),
- reversible transfer (in some cases).
Living polymerization must not include:
- irreversible deactivation (i.e., termination),
- irreversible transfer.

3. Controlled polymerization is a synthetic method to prepare polymers which are well-defined with respect to:

- topology (e.g., linear, star-shaped, comb-shaped, dendritic, cyclic),
- terminal functionality,
- composition and arrangement of comonomers (e.g., statistical, periodic, block, graft, gradient),
(a) have molecular weights predetermined by the ratio of concentrations of reacted monomer to introduced initiator, as well as unimodal and narrow molecular weight distribution.

4. Controlled polymerization may include transfer and termination but at a proportion low enough not to significantly affect the control of molecular properties given in definition 3. This means the rate of these side reactions should be low enough in comparison with propagation rate to reach a given synthetic goal.

In addition, the following features should be fulfilled:
a) the time of mixing reagents should be short compared to the half-life of the polymerization
b) the rate of initiation should be at least comparable to that of propagation
c) the rate of exchange between various active species should be faster than that of propagation of the fastest species
d) the rate of depropagation should be low in comparison to that of propagation.

5. Living polymerizations are controlled if conditions 4 are fulfilled. Controlled polymerizations are living if irreversible transfer and termination is below the detection limit using currently available instrumentation. It is suggested to determine the contribution of transfer and termination reactions in controlled polymerizations (e.g., by working at higher molecular weights or variable temperatures) to distinguish them from living polymerizations.

6. The term controlled is preferred to apparently living or "living" (with quotation marks) used to indicate synthesis of well-defined polymers under conditions in which chain breaking reactions undoubtedly occur, like in radical polymerization.

DISCUSSION AND EXAMPLES:

In order to clarify points stated above we discuss some of them in more detail below, giving examples.
1 & 2. The term "irreversible" is important.
(a) Reversible termination (better: reversible deactivation) is a process where active species are in a dynamic equilibrium with inactive (dormant) species. These equilibria are part of nearly all modem controlled polymerizations, like cationic, group transfer, and radical polymerizations where the dormant species (P) are covalent and the active ones (P*) can be ions, ion pairs, or radicals,(4-6)

(b) Reversible transfer can be a bimolecular reaction between a dormant and an active polymer chain which only differ in their degree of polymerization (degenerative transfer, i.e. equilibrium constant K=1),(6)

3a. We discussed macromolecular control in terms of topology, functionahties and composition but refrain from discussing stereochemical microstructure. Control of the stereochemistry means, e.g., control of tacticity of polypropylene or of the various isomers in isoprene polymerization. It is best reached in coordination polymerization, and to a lesser extent in anionic polymerization. Most polymers obtained in other chain-growth processes exhibit none or poor stereocontrol. Since this is not always the synthetic aim, polymerizations without sterocontrol may still be named controlled.

3b. In case of reversible transfer with an added transfer agent the degree of polymerization is given by the ratio of the concentration of reacted monomer to that of initiator and transfer agent.

In case of very slow initiation (see 4b below) full conversion of initiator cannot be reached and DP_n will be higher than the ratio of concentrations of reacted monomer to introduced initiator.

For many reasons, it is experimentally difficult to reach and to experimentally determine the polydispersity index given by the Poisson distribution (M_w/M_n approx. equal 1/DP_n). It is not possible to define a limit where MWD should be named "narrow". The limit depends on the difficulty of the particular synthetic task. A value of M_w/M_n £ 1.1 may be agreed on for anionic polymerization whereas M_w/M_n £ 1.2 or 1.3 may be agreed on for other polymerization mechanisms.

4. In some systems relatively well-defined polymers can be prepared in spite of the presence of side reactions. Usually the effect of chain breaking reactions becomes more significant with the chain length. Therefore, some identical initiating/catalytic systems provide well-defined polymers with M_n < 10,000 but fail entirely for polymers with Mn > 100,000. Thus, the former can be considered as controlled whereas the latter not, although the only difference between them is the initiator concentration. In order to systematize such systems, we proposed a ranking which is based on the simple kinetic parameters such as ratios of transfer and termination rate constants to that of propagation.(10) See also point 5 for more details.

(a) If the time needed for mixing the reagents (monomer, initiator, catalysts), t_mix, is not short compared to the half-life of the polymerization, t_1/2, the MWD will not be given by the mechanism of polymerization but by the hydrodynamics of mixing. If t_mix > t_1/2, very broad MWDĵs can result. Sometimes these systems have been called non-living whereas they are uncontrolled.

(b) If the ratio of rate constants of polymerization and initiation is k_p/k_i < DP_n/4, the effect of initiation on DP_n and MWD is negligible.(11) If k_p/k_i >> DP_n, the maximum polydispersity index is M_w/M_n = 1.35.(12)

(c) For equilibria between active and dormant species (see 1a), the rate of deactivation should be much higher than the rate of polymerization, R_deact >> R_p. The polydispersity index at full conversion is given as M_w/M_n = 1 + 1/b, where b is proportional to the ratio of the rate constants of deactivation and propagation, k_deact/k_p, and further depends on the mechanism of exchange.(6,13,14) If deactivation is slow, very broad MWD is observed. Here again, many such systems have been called non-living whereas they are uncontrolled.
In many processes we find equilibria between species of different activity, e.g., between free ions and ion pairs in anionic polymerization. The polydispersity index depends on the relative reactivities, the proportion of the species and rates of exchange.(13)

(d) If the rate of depropagation becomes comparable to that of propagation full conversion cannot be reached, x_max = 1 - 1/(K_p[M]₀ or [M]_eq = 1/K_p, where K_p is the equilibrium constant of polymerization. Thus we need K_p [M] >> 1. For styrene at 25 ^oC, K_p = 5x10⁶ mol/L, and this prerequisite is fulfilled. However, for a-methylstyrene at 25^oC, K_p = 0.8 mol/L and it is necessary to work at low temperature and/or high monomer concentration in order to have a controlled polymerization. Moreover, at prolonged standing of the polymerizing system, the chains will redistribute and finally lead to a most probable distribution (M_w/M_n = 2) in a time which is proportional to DP_n² over the rate constant of depolymerization, k_d.(11)

5. Irreversible chain breaking reactions result in deactivated chains the proportion of which progressively increases with conversion and chain length. Let us calculate the effects of (pseudo)unimolecular termination and transfer to monomer for [M]0 = 1 mol/L and [I]₀ = 10^-3 mol/L, assuming fast initiation. If the ratios of termination/monomer transfer to propagation rate constant are k_t/k_p =10^-3 mol/L and k_trM/k_p = 10^-3, respectively, approximately 20% of chains are deactivated when polymers with polymerization degree DP_n = 200 are targeted. However, at DP_n = 500, 50% of chains are deactivated by transfer and 70% by termination. For the ratios of rate constants 10^-4, approximately 2% of chains are deactivated when polymers with DP_n = 200 are targeted. At the stage of DP_n = 500, 5% of chains are deactivated, whereas at the stage of DP_n = 900, 10% of chains are deactivated by transfer and 20% by termination. At the very end of the polymerization, the rate of termination does not change but propagation slows down leading to the rapid increase of proportion of the deactivated chains, e.g. 50% at 99% monomer conversion or at DP_n = 990. Such analysis helps to define some limits for the synthesis of well-defined systems including functional polymers and block copolymers.e.g. (15)

6. According to the above definitions, systems like controlled radical polymerization(10) cannot be called living because two radicals always terminate by coupling or disproportionation. Since chain breaking reactions are detected and quantitatively determined it was proposed to name these systems as apparently living or "living" (quotation marks refer to systems which were called living although chain breaking reactions were detected)(16,17) or controlled.(5)

CONCLUSIONS

Quantitative initiation and fast exchange are additional requirements for the synthesis of well- defined polymers. Slow initiation and slow exchange broaden polydispersities significantly, sometimes above values found in conventional systems, even if the proportion of terminated chains is low. Thus, polydispersities cannot be used as the only criterion of livingness. Additionally, the time effect is important, termination will continue even after all monomer is consumed and polymers with polydispersities M_w/M_n < 1. I may contain more than half of chains deactivated and fail to efficiently produce block copolymers.

In summary, the terms living and controlled polymerizations should be carefully distinguished. It is proposed to use the term controlled rather than living for polymerization systems which provide well-defined polymers but are not completely free of termination or transfer, like radical polymerizations. Since many researchers are used to the term living, the combination controlled/"living" may be used for a transition period

REFERENCES

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