Inhibitors are often used to reduce the rate of polymerization. In this case they are called moderators.

Retarders are substances that neutralize only a part of the radicals present in the system; they reduce the polymerization rate without completely suppressing it (Fig. 2.2, cr. 4).

IN In this case, in the course of reaction (2.85), the radical Z is formed∙ , which is able to continue chain growth, but at a slower rate, since its activity is significantly lower than that of the primary radical.

IN Unlike moderators, inhibitors mainly work with primary radicals, and moderators, as a rule, with growing macroradicals.

Retarders include telogens, disulfides (R-S-S-R), mercaptans, halocarbons - they are molecular weight regulators.

CH2+RS

It should be noted that the mechanism of action of inhibitors does not differ from the mechanism of action of inhibitors, and such a division is somewhat arbitrary. In addition, the same compound can serve as an inhibitor of the polymerization of one monomer and a moderator of another. For example, iodine completely stops the polymerization of methyl methacrylate and only slows down the polymerization of styrene.

2. 3. 5. Kinetics of radical polymerization

Kinetics is the science of the rates of chemical reactions and their mechanisms. Let us consider some kinetic regularities as applied to re-

polymerization actions by a free radical mechanism, when initiation is carried out with the help of chemical initiators (peroxides, azo compounds, etc.), and chain termination occurs when two growing macroradicals collide either by their recombination or by disproportionation.

To derive the general kinetic equation for polymerization without taking into account chain transfer reactions, some assumptions are used:

1) the reactivity of radicals does not depend on the length of the polymer chain, which is quite large;

2) the monomer is consumed mainly at the stage of chain growth, the share of its participation in the remaining stages of the process is negligible;

3) the principle of a quasi-stationary state with respect to a growing radical. The steady state of successive reactions is that the concentration of intermediate products is constant. And the time to establish a stationary state is much less than the reaction time.

Intermediate particles - R ∙ , their concentration is constant.

During polymerization, the rate of change in the concentration of radicals quickly becomes equal to zero (the rate of appearance of radicals is equal to the rate of their death), and this is equivalent to the position that the rates of initiation and termination are equal to each other (V and = V o ). It follows from one characteristic

Benefits of chain polymerization: the lifetime of the active radical is negligible. Indeed, for many polymerization reactions, it has been experimentally confirmed that the concentration of radicals increases rapidly at the initial moment of time, and then reaches a constant value.

A typical kinetic curve describing the transformation (conversion) of a monomer into a polymer as a result of polymerization, depending on the time of the synthesis, has a ò-shaped form (Fig. 2.3).

There is an initial stage in the chain reaction, when the concentration of radicals increases from zero to "average" - this is the non-stationary phase of reaction (2). With an increase in the concentration of radicals, the rate of their death increases. When the rates of formation of radicals and their destruction become close, the quasi-stationary phase of the reaction sets in; in this phase, the concentration of radicals can be considered constant (3).

Conversion

By the end of the reaction when exhausted

monomer

source of new radical formation

% 100

catch their concentration drops rapidly to

zero, and the reaction again acquires non-

stationary character (4, 5). If long-

duration of non-stationary phases of the reaction

much less than the duration

phases with a constant concentration of radio-

Rice. 2.3. Kinetic curve

chain radical

polymerization

calov, then the method is applicable to such a reaction

tions: 1 – inhibition of the process;

method of the quasi-stationary state.

2 - acceleration of polymerization (co-

Kinetic description of the re-

growth increases with time); 3 - sta-

polymerization shares are co-

tsionary period (policy rate)

merization

constant

Vin );

fight a system of differential equations

4 - slowing down of polymerization, due to

of consumption of starting materials and

with decreasing concentration

accumulation of intermediate and final

monomer; 5 - termination of the reaction

due to lack of monomer

products listed below

consideration of the individual stages of the reaction. Derivation of the equation for the individual stages of radical polymerization:

1. Initiation, as already mentioned, proceeds in two stages:

a) formation of primary radicals

b) interaction of the initiator radical with the monomer molecule, i.e. active center formation

where k and and k and , are the rate constants for the decay of the initiator and the formation of the active

center.

The decomposition of the initiator into combined radicals is characterized by a high activation energy. In this regard, most of the initiators of decomposition

are observed at a noticeable rate only at temperatures above 50 ... 70 ° C; Moreover, with increasing temperature, the decomposition rate increases sharply (the half-life decreases).

In most cases k and< k и , , поэтому лимитирующей стадией ини-

of initiation is the stage of decomposition of the initiator, since the rate of the initiation process is determined by the most energy-intensive of the two stages of the process, which proceeds with the smallest constant, i.e. k and there will be descriptions

be the following equation:

Vi = ki [ I ] .

Strictly speaking, this equation is valid only if all the radicals formed during the decomposition of the initiator are effectively used to initiate the polymerization. In fact, some of them are spent unproductively and are lost as a result of side reactions (see "cell effect"). If we denote by ƒ the fraction of radicals formed during the decomposition of the initiator, which is effectively used for the initiation reaction, then the equation for the initiation rate must be modified

Vi = ki f [ I ] ,

where ƒ is the efficiency of initiation, i.e., the fraction of primary radicals that

is spent on the initiation of radical polymerization;					[ I ] - concentration
initiator.
2. Chain growth
		kp ,
		¾¾® R 2

where k p , is the chain growth rate constant.

The rate of chain growth is equal to the rate of disappearance of the monomer:

D[M]=k,		[ M ]

				kp(n)
	R n + M ¾¾¾® R n +1
		d[M]	K n [ R∙ ] [ M ]
	the first assumption should			kp ,	K p ,	K \u003d k p (n) \u003d k p, and	from the third
	= [ R∙ ] = const .

Therefore, the chain growth rate is described by the equation:

V p = − d [ M ]	K R [ R∙ ] [ M ] ,

where [ R ∙ ] , [ M ] are the concentrations of the active center and monomer, respectively.

The activation energy of chain growth is low, it is 20...35 kJ/mol (this is several times less than the activation energy of initiation by peroxide initiators), so the chain growth does not depend much on temperature.

Chain growth is a fast reaction, which we have already noted when considering chain polymerization. k p usually has a value of the order of 104 l/(mol·s). Undoubtedly, the chain growth rate for different monomers will be different and depend on their reactivity and the activity of the growing macroradical.

3. Chain termination on the example of recombination occurs due to the bimolecular interaction of macroradicals:

where k o is the chain termination rate constant.

V=k

where [ R ∙ ] is the concentration of macroradicals.

The kinetic chain termination reaction is characterized by a low activation energy Ea = 15 ... 20 kJ/mol.

Obviously, the chain growth rate (2.100) is practically equal to the polymerization reaction rate, since the number of monomer molecules reacting with initiator radicals is negligible compared to the number of monomer molecules involved in chain growth.

IN this equation includes the concentration of the radical, which is very difficult to determine.

IN according to the third assumption, for the stationarity stage, when the rates of formation and disappearance of free radicals are equal to:

Solving this equation for [ R ∙ ] , we get:

		ki and f [I]

substituting this value into equation (2.100), we obtain

V rp V r = − d [ M ]
	K p [ M ]		ki and f [I]

where V rp is the rate of radical polymerization.

All parameters included in equation (2.105) can be determined by monitoring the process of radical polymerization.

Denoting the rate constants of the corresponding reactions by k, we get the combined constant:

k = kp		ki and f

then the rate of radical polymerization can be represented by the equation:

V rp \u003d k [ M ] 1 [ I ] 0.5.

This equation is known as square root equations» . The most important rule follows from it: the polymerization rate is directly proportional to

is the monomer concentration and the square root of the initiator concentration.

It is a consequence of bimolecular chain termination during radical polymerization and serves as a characteristic feature of the process, which makes it possible to distinguish the radical polymerization mechanism from the ionic one, where this rule is not observed.

The equation is valid for radical polymerization up to the degree of monomer conversion α = 10 ... 20%, i.e. in the early stages of the process before the onset of the “gel effect” and is characteristic of an already developed reaction, therefore, a deviation from this expression is observed at the beginning and especially at the end of the polymerization process.

The proportionality of the polymerization rate to the monomer concentration in the first power is not always observed. As a rule, this value is somewhat greater than unity, which is associated with the participation of the monomer at the stage of initiation and in chain transfer reactions.

For practical calculations at sufficiently high degrees of conversion of monomers, the following equation is used:

V rp \u003d k [ M ] 1.5 [ I ] 0.5.

The total activation energy E a for radical polymerization is determined

is divided by the Arrhenius equation:

k = Ae RT ,
where k is the overall polymerization rate constant;					A is the pre-exponential multiplier
a citizen; T is the absolute temperature; R is the universal gas constant.
Based on (2.106), the activation energy
E a =		E a and + E a p −			1 E a o ,

where E a and , E a p , E a o are the activation energies of initiation reactions, respectively,

growth and break.

The total activation energy for most polymerization reactions is ~ 80 kJ/mol.

Equation (2.107) shows what factors affect the polymerization process

rization. But knowing the dependence of V p on factors is not enough, because for polyme-

The number average molecular weight (Mn) of the products obtained is very important and can be characterized by the average degree of polymerization.

The equation for the average degree of polymerization

Using the rate constants of elementary reactions, one can represent

develop an approximate expression for the average degree of polymerization (n).

The average degree of polymerization of the resulting polymer n is determined by the ratio of the rates of growth and chain termination.

				k p [ R∙ ] [ M ]			k p [ M ]
				ko [ R∙ ] 2			ko [ R∙ ]

Substituting the value [ R ∙ ] , derived from the stationarity conditions (2.103),

into equation (2.111), we get:

k p [ M ]

k p [ M ]

f k and [ I ]

ko f ki [ I ]

reducing all reaction rate constants into a single constant, we have:

k , =

ko f ki

n=k

The degree of polymerization is inversely proportional to the square root of the initiator concentration and directly proportional to the monomer concentration.

Radical polymerization of vinyl monomers CH 2 =CHX underlies the technology for the production of various polymeric materials. The mechanism and kinetic regularities of polymerization were intensively studied in the 50s and 60s; A number of monographs have been published on this subject. Polymerization is distinguished from other chain reactions by the following two features. First, as a result of the chain process of successive attachment of monomer molecules to the growing macroradicle, the materialization of multiply repeated acts of chain continuation occurs in the form of the final product, the macromolecule. Secondly, only one type of active centers conducts a chain reaction, namely, a free-valence macroradical on carbon. The addition of the monomer CH 2 \u003d CHX to the radical R · occurs, as a rule, via the CH 2 group, so that the radical RCH 2 C · HX is formed, the subsequent addition proceeds according to the head-to-tail type, which is energetically the most favorable:

RCH 3 C HX + CH 2 \u003d CHX ® RCH 2 CHXCH 2 C HX

Attachment of another type (head to head, etc.) proceeds only to a small extent. For example, in the polymerization of vinyl acetate (300-400K), head-to-head attachment occurs in no more than 2% of cases.

Initiated polymerization of an unsaturated compound includes the following steps:

r + CH 2 \u003d CHX rCH 2 C HX (R 1 )

R 1 + M R 2

R n + M R n+1

R n + R m R n -R m

R n + R m R n H + R m-1 CH=CHX

When deriving kinetic relationships, the following 4 assumptions are usually made:

1. The case is considered when polymerization proceeds with long chains, i.e. the polymerization rate v>> v i ;

2. It is assumed that k p and k t do not depend on the length of the reacting macroradical, i.e. k p1 = k p2=... k pn , and the same for k tc and k td . This assumption seems reasonable, especially

for high-molecular radicals, since the reactivity of the radical is determined by its molecular structure near the free valence, and during homopolymerization, the structure of all macroradicals is the same and they differ only in their length.

3. The reaction is assumed to proceed in a quasi-stationary regime. This is true for experiments with v i = const and duration t>> t R , where t R = (2 k t / v i) -1/2 . At v i = 10 -8 - 10 -6 mol/l and 2 k t = 10 6 - 10 8 l/mol s, the lifetime of macroradicals R· varies in the range of 0.1-10 s, which is much shorter than the reactor warm-up period (50-200 s).

4. Termination with the participation of primary radicals formed from the initiator is usually neglected (this reaction r + R is not in the scheme), since in most cases almost all r react with the monomer, and the fraction of r reacting with macroradicals is small, because<< . При таких преположениях для скорости полимеризации v and the length of the kinetic chain v the following expressions are obtained:

v= k p[M]( v i /2 k t) 1/2 , (1)

n= v/v i = k p[M](2 k t v i) -1/2 (2)

Various peroxide compounds, azo compounds, polyarylethanes, and disulfides are used as polymerization initiators. The initiator decay mechanism is discussed in Lecture 2.

When the initiator decomposes in the condensed phase, two radicals are formed, surrounded by solvent or monomer molecules (during bulk polymerization). Some of these pairs die in the cell (enter into recombination or disproportionation reactions), and some go into the volume. If all radicals released into the bulk react with the monomer, then the rate of initiation is equal to the rate of generation of radicals: v i = 2 ek d[I]. If some of the initiator radicals released into the bulk react with macroradicals, then v i grows with [M] until it reaches 2 ek d[I]. Examples of this kind are described in the literature. The concentration of the monomer practically does not affect the release of radicals into the volume, since the recombination of radical pairs in the cell proceeds immeasurably faster than the reaction of the radical with the monomer.

Usually the initiator decays slowly, so that during the experiment v i = const. However, there are cases when a significant part of it decays during the experiment. In this case, in the quasi-stationary reaction mode, the kinetics of monomer consumption is described by the equation:

The chain propagation reaction determines both the rate of polymerization and the structure of the resulting polymer. Vinyl monomers polymerize head-to-tail (see above). Chain continuation rate constant k p is determined by the activity of the monomer and the macroradical leading the chain reaction. Below are the rate constants k p for a number of monomers:

Styrene: k p = 2.4 ´ 10 8 exp(- 37.6/RT), L/mol s;

Methyl methacrylate: k p = 2.5 ´ 10 6 exp(- 22.6/ RT), L/mol s;

Vinyl acetate: k p = 2.0 ´ 10 6 exp(- 19.6/ RT), L/mol s;

Methyl acrylate: k p = 1.1 ´ 10 6 exp(- 17.6/ RT), L/mol s;

Vinyl chloride: k p = 3.3 ´ 10 6 exp(- 36.4/ RT), L/mol s;

Acrylonitrile: k p = 2.3 ´ 10 5 exp(- 16.2/ RT), l/mol s

Accession, of course, proceeds with a decrease in entropy, the pre-exponential of 10 6 l/mol corresponds to the activation entropy D ¹ S = - 52J/(mol l). Monomers CH 2 =CHX containing a polar group (ester, nitrile, etc.) form complexes with metal ions. For example, methyl methacrylate forms 1:1 complexes with metal salts Li + , Mn 2+ , Fe 3+ , Co 2+ , Zn 2+ , acrylonitrile with metal salts Li + i , Mg + , Fe 3+ , Mn 2+ , Co 2+ , Ni 2+ . Such complexes often react faster with macroradicals. For example, methyl methacrylate reacts with k p = 2.5 ´ 10 2 L/mol s, and its complex c
ZnCl 2 - c k p = 6.1 ´ 10 2 l/mol s. Zinc chloride accelerates the polymerization of methyl methacrylate.

With an increase in temperature, the depolymerization reaction begins to play a significant role; decomposition of a macroradical into a monomer and a radical

R n R n-1 + M

Since the macroradical growth reaction is exothermic, the depolymerization reaction is endothermic and the difference E U- E p=D H 0 . With an increase in temperature, a state is reached that the rates of chain growth and depolymerization become equal: k p[M]= k U , and the polymerization rate is zero. This state corresponds to the maximum polymerization temperature equal to:

T max = (4)

For pure monomer (in bulk polymerization) T max = 583K (styrene), T max = 493K (methyl methacrylate), T max = 334K (a-methylstyrene).

Chain termination, as can be seen from the scheme, occurs as a result of the reaction between macroradicals. These radicals enter into reactions of two types, namely recombination:

2 ~ CH 2 - C XY ~CH 2 - CXY- CXY- CH 2 ~~

and disproportionation:

2~ ~ CH 2 -C XY ~~ CH 2 - CHXY + ~~ CH=CXY

The average degree of polymerization depends on the ratio between the rate constants of these two reactions:

P = k p[M] or (5)

This ratio also affects the molecular weight distribution: M w /M n = 1.5 for R · recombination and M w /M n = 2 for their disproportionation.

Rate constants k t = t tc + k td depending on the structure of the monomer vary in the range of 10 8 - 10 6 l/mol s. There is an antibatic relationship between the chain termination rate constant and the viscosity of the solvent. This indicates that the reaction between two macroradicals is limited by diffusion processes. A number of facts indicate that the translational diffusion of macroradicals in solution is not the limiting stage of chain termination during polymerization. For macroradicals with a polar group X at the end (~~ CH 2 CHX), there is an obvious symbate (if not coincidence) between k t and the reorientation frequency of the dipole group (T = 300K).

Apparently, in most cases, it is segmental mobility that limits the rate and determines the rate constant of macroradical destruction.

Classical chemical kinetics considers reactions under idealized conditions, not complicated by heat and mass transfer, diffusion, etc. In bulk radical polymerization, these processes can be neglected only at the initial stage of the reaction, when the viscosity of the reaction mass increases slightly.

From the consideration of the kinetic curve (Fig. 3.3), it is obvious that at first there is a more rapid formation of active centers - initiating radicals that give rise to polymer chains. As the number of radicals in the system increases, the proportion of reactions of their termination increases: as a result, after a certain period of time, the number of formed radicals becomes equal to the number of disappearing macroradicals and the system passes from a non-stationary state (section I on the kinetic curve 1 in fig. 3.3) into a stationary state (section II), characterized by a constant concentration of radicals in the system (c/[ R* /dt= 0), as well as a constant chain propagation reaction rate. Section III of the kinetic curve of chain polymerization - attenuation of the reaction; it can be due to several reasons - the main ones are the depletion of the monomer and initiator.

Curve 2 (see Fig. 3.3) also refers to a chain process, but there is no region of constant speed on it. However, its absence does not mean at all that stationarity with respect to the concentration of growing radicals is not achieved in this case. It may turn out that stationarity with respect to growing macroradicals exists throughout the entire process, and the experimentally observed rate changes due to a change in the monomer concentration: this can be seen if, for any moment of time, the rate is divided by the concentration of the reagent, representing Eq. (3.8) in the form

If the concentration of macroradicals R" is constant for different periods of time, then the process is stationary.

Rice. 33.

1 - with a stationarity area; 2 - without stationarity section

For a system polymerized by a radical mechanism, the so-called quasi-stationary state is also possible. Imagine that at some point in time t in the system, the rates of reactions of formation and death of radicals became equal, i.e. a stationary state has been established. At the point in time t2 the rate of formation of initiating radicals decreased, which led to the violation of stationarity, i.e. the concentration of growing radicals decreased. However, the rate of death of radicals, proportional to their concentration, will also decrease (see equation (3.13)), and the system can again reach a steady state, but at a lower concentration of radicals. If the transition from the first stationary state to the second occurs smoothly enough, then the reaction system will constantly “adjust” to the change in the concentration of active centers, and in practice we can assume that the stationary state is preserved all the time.

The establishment of a stationary state in the system means that

or, taking into account expressions (3.4) and (3.13),

The steady state polymerization rate is equal to the chain growth rate w = w p =& p [M] (see equation (3.8)); after substituting into equation (3.8) the concentration of growing radicals, from relations (3.14) we obtain

At steady state, the ratio k p k^ ,5 /ko" 5 is a constant value equal to the rate constant of the polymerization reaction k. Therefore, equation (3.15) can be represented in a simpler form:

from which, as well as from equation (3.15), it follows that the rate of radical polymerization in bulk is proportional to the concentration of the monomer to the first power and the concentration of the initiator to the power of 0.5.

With the help of data characterizing the process in a stationary state, one can only find the constant k n . Of a cast-

equation (3.24), equivalent to equations (3.15) or (3.16), after determining the overall polymerization rate w= and initiation rates calculate the ratio However

based on data only on the kinetics of stationary polymerization, determine individual constants kp And k Q fails, therefore, to find them, data on the kinetics of polymerization in the nonstationary state are used, which are necessary to determine the average lifespan of the growing radical, i.e.,

In the case of a steady flow of polymerization, t is determined by the equation

From equation (3.8) we have = w/(k^[ M]) and after substituting this relation into the last expression, we obtain

Required to calculate the ratio kp/k 0 the value of the average lifespan of the radical t is determined under conditions of non-stationary polymerization (photoinitiated) using the rotating sector method or the post-effect method (their descriptions can be found in the work). Typically, the values ​​of t lie in the range of 0.1-10 s. With known relationships kp/k®" 5 And kp/k 0 you can calculate the values ​​of individual constants kp And k0. For some monomers, these values ​​are given in table. 3.7 together with the activation energies calculated using the Arrhenius equation.

Table 3.7

Kinetic parameters of radical polymerization of some monomers

* Per 1 mol of polymerizable monomer. ** Per mole of growing radicals.

An analysis of equation (3.16) also makes it possible to estimate the effect of certain parameters of the radical polymerization process on its rate and the size of the resulting chain molecules.

Polymer chain growth rate wp is the number of monomer molecules attached to the growing polymer radicals per unit time. Circuit breaking speed w 0 is determined by the number of macroradicals that stop growing as a result of termination per unit time. Therefore, the ratio

called kinetic chain length, shows how many monomer molecules are attached to the growing radical until its existence ceases.

Taking into account equalities (3.8) and (3.13) and after appropriate transformations, equation (3.17) can be represented as

and after substitution from equation (3.14) we get

To exclude from equation (3.19) partial constants of the polymerization process, we multiply the numerator and denominator by k®" 5:

but since k p k^ 5 /k 0 = k, the expression for the length of the kinetic chain will take a simpler form:

In expression (3.20) [M] and are known from the experimental conditions, a k And k u found by experience. From equation (3.20) it follows that the length of the kinetic chain is directly proportional to the concentration of the monomer and inversely proportional to the square root of the concentration of the initiator.

To establish the relationship between the length of the kinetic chain and the rate of polymerization, we multiply the numerator and denominator of equation (3.19) by & p [M]:

Taking into account expression (3.16), the last equation can be rewritten in the following form:

From equation (3.21) it follows that the length of the kinetic chain is inversely proportional to the rate of polymerization.

The length of the kinetic chain in the absence of chain transfer reactions (see Section 3.1.4) is directly related to the average degree of polymerization of the resulting macromolecules X: in case of chain termination by disproportionation v = X, and during recombination 2v = X.

Then equations (3.20) and (3.21) can be written as follows:

To terminate the chain by disproportionation:

For recombination:

At the initial stage of the process of radical polymerization in bulk, the degree of transformation of the monomer into a polymer is small and the concentration of the monomer can be assumed to be constant; then it follows from equations (3.22) and (3.23) that the molecular weight of the resulting polymer is inversely proportional to the square root of the concentration of the initiator. Therefore, by changing the concentration of the initiator, one can control the length of the formed macromolecules.

An analysis of the kinetic equation of radical polymerization also makes it possible to estimate the effect of temperature on the overall rate of the process and the size of the resulting chains. With an increase in temperature, the rates of all three elementary stages of polymerization increase, but not to the same extent. Due to differences in the activation energy of each stage (112–170 kJ/mol at the initiation stage (see Table 3.3), 28–40 kJ/mol at the growth stage, and 0–23 kJ/mol at the termination stage (see Section 3.1 .2)) the temperature coefficients of the reactions of initiation, chain growth, and chain termination are different: with an increase in temperature, the rate of initiation increases to a greater extent than the rates of chain growth and termination.

Replacing in equation (3.15) &° ,5 0.5 by w®' 5 (equation (3.4)), we obtain

Therefore, an increase in the rate of initiation leads to an increase in the overall rate of polymerization. At the same time, an increase in the rate of initiation also leads to an increase in the rates of growth and termination of chains (see equations (3.8) and (3.13)): the rate of chain termination increases with increasing temperature to a greater extent - is the concentration of the initiator, k and is the initiation rate constant, f is the efficiency of the initiator (p. 15); factor 2 reflects the formation of two radicals from the initiator molecule (the most common option)

chain growth rate can be expressed by the equation:

where v р is the chain growth rate, k р is the chain growth rate constant, [M] is the monomer concentration, is the concentration of radicals (“living” chains).

This equation reflects the fact that any chain propagation reaction is the interaction of a radical with a monomer (p. 15). It is valid under the assumption that the growth constant k р does not depend on the value of the radical R (this assumption is correct).

Circuit breaking speed is expressed by the equation:

where v o - chain termination rate, k o - chain termination rate constant

This equation reflects the fact that the termination occurs during the interaction two radicals ("living" chains) (p. 16).

Overall polymerization rate is the rate of consumption of the monomer (– d[M]/dt) and, therefore, it is equal to the rate of chain growth

The chain growth rate equation includes a concentration of radicals, which is difficult to measure. However, the concentration of radicals can be excluded from the growth rate equation if we assume that during the process the concentration of radicals is constant. This assumption is called quasi-stationary condition; at the initial stages of the process (at shallow depths) it is performed well. With such an assumption the rate of formation of radicals is equal to the rate of their disappearance. Since radicals are formed at the initiation stage and disappear at the termination stage, the rates of these reactions are equal, i.e. v and \u003d v o, i.e.:

In this way , the polymerization rate is proportional to the monomer concentration and the square root of the initiator concentration.

(determining the molecular weight of the polymer) in the first approximation is equal to the length of the kinetic chain (p. 17), i.e. the ratio of the rates of chain growth and chain termination reactions:

In this way, the molecular weight of the polymer is proportional to the monomer concentration and inversely proportional to the square root of the initiator concentration.

Thus, an increase in the monomer concentration leads to an increase in both the rate of polymerization and the molecular weight of the polymer, while an increase in the concentration of the initiator, increasing the rate of the process, reduces the molecular weight. The latter is easy to understand and purely qualitatively, since as the concentration of the initiator increases, the concentration of growing chains also increases, which increases the probability of their meeting and chain termination.

Let us now somewhat complicate the system and take into account chain transfer reactions (except for chain transfer to a “dead” polymer, so we are still considering the kinetics at small depths of polymerization). Usually, chain transfer reactions to foreign molecules, primarily to regulators, are of the greatest importance; confine ourselves to this type of transmission.

As already mentioned, transferring the circuit to the regulator does not affect speed process. Average degree of polymerization(P r) in this case is equal (in the first approximation) to the ratio of the chain growth rate to sum of speeds breakage and transmission of the chain (because during transmission, molecular chains):

The above analysis of elementary kinetics made it possible to determine the dependence of the polymerization rate and molecular weight of the polymer on the concentration of the monomer and initiator, and for the molecular weight, also on the concentration of the regulator(if present). In addition, the course and results of polymerization are influenced by a number of other factors, which are discussed below.

The effect of temperature. A. In the most common polymerization option with the participation of initiators an increase in temperature leads to increase polymerization rate decrease molecular weight of the polymer. The increase in speed does not need comments; the decrease in molecular weight is due to the fact that with increasing temperature the initiation rate increases to a greater extent than the chain growth rate(because initiation has a higher activation energy). Consequently, according to the condition of quasi-stationarity, and the rate of chain termination increases faster than the growth rate, i.e., the ratio v p / v o decreases, and, consequently, the molecular weight.

B. When photochemical initiation with rising temperature both the rate of the process and the molecular weight of the polymer increase. This is due to the fact that with increasing temperature, the rate of photochemical initiation practically does not change, while the chain growth rate increases.

Other consequences of temperature increase (for all polymerization options): 1) temperature increase reduces the regularity of the structure of polymer macromolecules, because at the same time, the probability of articulation of elementary links according to the “tail to tail” and “head to head” schemes increases (p. 16); 2) Polymerization of vinyl monomers (and dienes) - reaction exothermic(see below); Therefore, as the temperature rises, the equilibrium monomer Û polymer shifts to the left; in other words, the role of reactions grows depolymerization. All this does not allow any effective radical polymerization at temperatures above 120 o C.

Influence of pressure. Effect of pressure (P) on speed any A chemical reaction is expressed by the Evans–Polanyi equation:

where k is the reaction rate constant, ΔV ≠ is the change in volume during the formation of an activated complex (transition state) from reacting particles.

During radical polymerization at the stage chain growth∆V≠< 0, т.к. реакции роста цепи – bimolecular, and in such reactions the volume decreases during the formation of the transition state; therefore, with increasing pressure, the speed chain growth(and, consequently, polymerization in general) increases. On the contrary, for the reaction initiationΔV ≠ > 0, because here the limiting stage is the decay of the initiator monomolecular reaction, and in such reactions, the formation of a transition state increases the volume. Consequently, with increasing pressure, the rate of initiation, and hence the rate open circuit(according to the condition of quasi-stationarity) decreases. In this way, growing ratio v p / v o , i.e. . polymer molecular weight.

Polymerization at high pressures (about 1000 atm.) Is used for ethylene (high-pressure polyethylene is formed).

Influence of process depth(monomer conversion).

The influence of this factor is the most complex and strongly depends on other conditions of the process.

A. In most cases, when small process depths (up to about 10%) process rate and polymer molecular weight practically do not change. However, with an increase in the depth of the process, an increase in both the rate of the process and the molecular weight of the polymer. This may seem unexpected at first glance, because as the degree of conversion of the monomer increases, its concentration decreases, which, according to the above kinetic equations (p. 24), should lead to a decrease in both the rate and molecular weight. However, here the kinetics is completely different; in particular, the quasi-stationarity condition does not apply. The fact is that as the accumulation of polymer macromolecules rapidly system viscosity increases(solutions of polymers, as is known, have an exceptionally high viscosity, and the greater, the higher their concentration and the molecular weight of the polymer). The increase in viscosity leads to a sharp decrease mobility large particles, in particular, "living chains", and hence the probabilities their meetings, i.e. open circuit(chain termination becomes a diffusion-controlled process). At the same time, the mobility of small particles (monomer molecules) is retained in a fairly wide range of system viscosities, so that the chain growth rate does not change. A sharp increase in the ratio v p /v o leads to a significant increase in the molecular weight of the polymer. The rate of decomposition of the initiator, as a monomolecular reaction, does not depend on viscosity, i.e. the rate of formation of radicals is higher than the rate of their disappearance, the concentration of radicals increases, and the condition of quasi-stationarity is not met.

The above changes associated with an increase in viscosity are called gel effect(sometimes also called the Tromsdorff effect). With a further increase in the depth of the process, the viscosity can increase so much that small particles lose their mobility; this leads to a slowdown in the chain growth reaction, and then to its complete stop, i.e. to stop polymerization. The gel effect is especially pronounced in block polymerization (pure monomer polymerization); it also manifests itself to a sufficient degree during polymerization in sufficiently concentrated solutions.

B. If polymerization is carried out in highly dilute solutions and polymers with a relatively low molecular weight are formed, or if the resulting polymer precipitates out of solution, then the viscosity changes little during the process; in this case, the gel effect is not observed, the process rate and the molecular weight of the polymer change little.

In relatively recent times, polymerization processes in the presence of specific initiators have been studied; wherein the molecular weight of the polymer increases relatively evenly with increasing depth of the process.

These specific initiators are di- or polyperoxides and iniferters.

The first of these contain two or more peroxide groups per molecule. When using these initiators, the process proceeds as follows (using the example of an initiator with two peroxide groups):

After the decomposition of such a bis-peroxide, radicals are formed, one of which (16) contains a peroxide group. Radical (16) initiates the growth of the polymer chain; then the chain is terminated upon interaction with another "live" chain (indicated in the diagram as R~) and a "dead" polymer is formed (17). This polymer contains a labile peroxide group; under the conditions of the process, this group decomposes, forming a polymer radical (18), which begins to “complete” by reacting with monomer molecules; then the situation may repeat itself. Thus, as the process proceeds, the size of macromolecules is constantly growing.

Iniferters - peculiar compounds that are not only initiators, but also actively participate in the processes transmission chains and cliff chains; hence their name, combined from some of the letters of the English names of these reactions ( ini tiation - initiation, Trans fer- transfer, Ter mination - chain break). The main feature of these initiators is that during decomposition they form two radicals, of which only one active, and second - inactive– it cannot initiate the growth of the polymer chain.

One such iniferter is S-benzyl-N,N-diethyldithiocarbamide (19). In its presence, the following reactions occur:

Iniferter (19) breaks up to form active radical (20) and inactive radical (21). Radical (20) initiates the growth of the polymer chain. A growing "live" chain can: A) transfer the chain to the initiator; B) terminate by recombination with an inactive radical (21); such a recombination is quite probable, because inactive radicals can accumulate in a fairly significant concentration. Both during transfer and upon termination, the “live” chain turns into the same “dead” polymer (22), which contains labile terminal units ~CH 2 -CH(X)-S(C=S)-NEt 2 ; these links easily dissociate into radicals by the reaction of reverse recombination, and the "dead" polymer "comes to life" again and is capable of further growth. Therefore, here, too, the molecular weight increases with an increase in the depth of conversion.

Polymerization processes in the presence of polyperoxides and iniferters make it possible to obtain polymers with lower degree of polydispersity than processes in the presence of conventional initiators; this has a positive effect on their technical properties.

Influence of preliminary orientation of monomer molecules. It is known that the collision of reacting particles will be effective if they are oriented in a certain way. If the monomer molecules before polymerization linearly oriented relative to each other:

then the chain growth rate should increase significantly, because in each growth reaction, the radical is oriented exactly to the “head” of the monomer, and almost every collision between the radical and the monomer will be effective (the value of the factor A in the Arrhenius equation increases). The rate of chain termination does not increase, so that not only the rate of polymerization increases, but also the molecular weight of the polymer.

Preliminary orientation of monomer molecules can be achieved, for example, during polymerization in inclusion compounds (clathrates), when monomer molecules are linearly oriented in the crystal channels of the “host” compound. Other options are solid-state polymerization of single crystals of some monomers or polymerization in monomolecular layers at the interface; these options will be discussed later, in the section "Practical ways to carry out polymerization"

Radical copolymerization

All the regularities described above were considered on the examples of polymerization one monomer (homopolymerization). But, as you know, it is widely used and copolymerization– joint polymerization of two or three monomers. It is carried out to obtain polymers with a wider range of properties, to obtain materials with predetermined properties, as well as in basic research to determine the reactivity of monomers. The copolymerization products are copolymers.

Basically the mechanism of radical copolymerization is quite similar to the mechanism of radical homopolymerization. However, several problems arise here.

1) Possibility copolymerization - whether links of both (or three) polymers will be included in the polymer chain, or each monomer will be polymerized separately and a mixture of homopolymers is formed.

2) The ratio between the composition copolymer and the composition taken for the process mixtures of monomers. Here it means differential copolymer composition, i.e. its composition Currently(if we take the integral composition, i.e. the composition of the entire mass of the copolymer, it is clear that at a large process depth it approximately coincides with the composition of the monomer mixture, however, at different process depths, macromolecules with different ratios of monomer units can be formed).

If the differential composition of the copolymer matches with the composition of the monomer mixture taken for polymerization, then the copolymerization is called azeotropic. Unfortunately, cases of azeotropic copolymerization are quite rare; in most cases, the differential composition of the copolymer is different on the composition of the mixture of monomers. This means that in the process of polymerization the monomers are not consumed in the proportion in which they are taken; one of them is consumed faster than the other, and during the course of the reaction it must be added to maintain a constant composition of the mixture of monomers. From this it is clear how important it is not only quality, but also quantitative solution to this problem.

3) The nature of the structure of the resulting copolymer, i.e. whether a random, alternating, or block copolymer is formed (see pages 7-8).

The solution to all these problems follows from the analysis kinetics formation of the copolymer macromolecule, i.e. stages chain growth during copolymerization (because the copolymer macromolecule is formed precisely at this stage).

Consider the simplest case of copolymerization two monomers, conventionally designating them as A and B. The stage of chain growth in this case, in contrast to homopolymerization, includes elementary reactions of not one, but four types: indeed, in the course of growth, “living” chains of two types are formed - with a terminal radical unit of the monomer A [~A, say, ~CH 2 –CH(X)] and with a terminal radical unit of the monomer B [~B, say ~CH 2 –CH(Y) ] and each of them can attach to “own” and “foreign” monomer:

The differential composition of the copolymer depends on the ratio of the rates of these four reactions, the rate constants of which are denoted as k 11 ...k 21 .

Monomer A is included in the composition of the copolymer according to reactions 1) and 4); therefore, the rate of consumption of this monomer is equal to the sum of the rates of these reactions:

This equation includes hard-to-determine concentrations of radicals. They can be eliminated from the equation by introducing quasi-stationarity condition: concentration both types radicals (~A and ~B ) constant; as in homopolymerization, the condition of quasi-stationarity is satisfied only at small depths of the process. It follows from this condition that the rates of mutual transformation of both types of radicals are the same. Since such transformations occur according to reactions 2 and 4, then:
This equation is called Mayo-Lewis equations(sometimes called the Mayo equation). This equation reflects the dependence of the differential composition of the copolymer on the composition of the monomer mixture and on the values ​​of r 1 and r 2 . The parameters r 1 and r 2 are called copolymerization constants. The physical meaning of these constants follows from their definition: each of them expresses comparative activity of each of the radicals in relation to "own" and "foreign" monomer(the constant r 1 is for the radical ~A , the constant r 2 is for the radical ~B ). If the radical is more easily attached to “its own” monomer than to “foreign”, r i > 1, if it is easier to “foreign”, r i< 1. Иначе говоря, константы сополимеризации характеризуют comparative reactivity of monomers.

The left side of the Mayo-Lewis equation is the differential composition of the copolymer. On the right side, two factors can be distinguished: 1) the composition of the monomer mixture [A]/[B]; 2) a factor that includes the copolymerization constants r 1 [A] + [B]/r 2 [B] + [A] = D (we denote it by the symbol D). It is easy to see that for D=1 d[A]/d[B] = [A]/[B], i.e. copolymerization is azeotropic. As mentioned above, cases of azeotropic copolymerization are rather rare; in most cases, D ≠ 1. Thus, the factor D is the factor that determines the difference between the differential composition of the copolymer and the composition of the monomer mixture. If D > 1, then the copolymer is enriched in monomer A compared to the original mixture (i.e., monomer A is consumed in a larger proportion than monomer B). At D< 1, напротив, быстрее расходуется мономер В.

The value of the factor D is completely determined by the values ​​of the copolymerization constants; therefore it is copolymerization constants determine the ratio of the differential composition of the copolymer and the composition of the mixture of monomers taken for the reaction.

Knowing the values ​​of the copolymerization constants also makes it possible to judge the structure of the resulting copolymer, as well as the possibility or impossibility of the copolymerization itself.

Let us consider the main variants of copolymerization determined by the values ​​of the copolymerization constants. It is convenient to represent them graphically in the form of curves of the dependence of the differential composition of the copolymer on the composition of the mixture of monomers taken for the reaction (Fig. 3).

Rice. 3. Dependence of the differential composition of the copolymer on the composition of the mixture of monomers.

1. r 1 = r 2 = 1. In this case, d[A]/d[B] = [A]/[B], i.e. at any composition of a mixture of monomers occurs azeotropic copolymerization. This is a rare option. Graphically, it is expressed by a dotted line 1 - azeotrope line. An example of such a system is the copolymerization of tetrafluoroethylene with chlorotrifluoroethylene at 60 0 C.

2.r1< 1, r 2 < 1 . Both constants are less than one. This means that each radical preferentially reacts with stranger monomer, i.e. one can speak of an increased propensity of monomers to copolymerization.

BUT) composition of the copolymer. Differential composition of the copolymer enriched with that monomer, which is low in a mixture of monomers(curve 2 in Fig. 3). This is easy to deduce from the analysis of the factor D in the Mayo-Lewis equation: with [A]<< [B] D < 1, следовательно, d[A]/d[B] < , а при [B] << [A] D >1 and d[A]/d[B] > . Curve 2 crosses the azeotrope line, i.e. at some one ratio of monomers polymerization is azeotropic. This ratio is easy to calculate, because in this case D = 1; from here:

B) The structure of the copolymer. Since each radical preferentially attaches to someone else's monomer, the copolymer tends to alternation. If the copolymerization constants are not much less than unity, this trend is not very pronounced, and the copolymer is closer to random than to alternating [microheterogeneity coefficient K M (p. 7) is closer to 1 than to 2]. But the smaller the value of the constants, the more the polymer structure approaches the alternating one. The limiting case is an infinitesimal value of both constants (r 1 → 0, r 2 → 0); this means that each radical reacts only with a "foreign" monomer, in other words, each of the monomers separately does not polymerize, but together they form a copolymer. Naturally, such a copolymer has a strictly alternating structure. An example of such a system is the pair: 1,2-diphenylethylene - maleic anhydride. There are also known cases when one of the constants is infinitesimal and the other has a finite value; in such cases, only one of the monomers does not polymerize itself, but can form a copolymer with the second partner. An example of such a system is styrene-maleic anhydride.

3. r 1 > 1, r 2< 1 или r 1 < 1, r 2 > 1 . One of the constants is greater than one, the other is less than one, i.e. one of the monomers reacts more easily with “its own” monomer, and the second with “alien” one. It means that one of the monomers is more active than the other during copolymerization, because responds more easily to others both radicals. Therefore, at any composition of the monomer mixture, the differential composition of the copolymer is enriched with units of the more active monomer (in Fig. 3, curves 3' for r1 > 1, r2< 1 и 3’’ для r 1 < 1, r 2 >one). Azeotropic polymerization is not possible here.

The structure of macromolecules of the copolymer in this variant is closest to statistical. A special (and not so rare) case: r 1 × r 2 = 1, i.e. r 1 = 1/r 2, while the values ​​of the constants are not much more or less than one. This means that the comparative activity of the monomers with respect to both radicals the same(for example, at r 1 = 2, r 2 = 0.5, monomer A is 2 times more active than monomer B in reactions with both the ~A▪ radical and the ~B▪ radical). In this case, the ability of each monomer to enter the polymer chain does not depend on the nature of the radical, with which it encounters and is determined simply probability collisions with each of the radicals. Therefore, the structure of the copolymer will be purely statistical (K M ~ 1). This case is called perfect copolymerization- by no means because in this case a copolymer with ideal properties is formed (rather vice versa), but by analogy with the concept of an ideal gas, where, as is known, the distribution of particles is completely statistical. The most famous examples of such copolymerization include the copolymerization of butadiene with styrene at 60°C (r 1 = 1.39, r 2 = 0.78). In the general case, the option “one constant is greater than one, the other is less” is perhaps the most common.

4. r 1 > 1, r 2 > 1. Both constants are greater than one; each of the radicals preferentially reacts with "its" monomer; the system has a reduced tendency to copolymerize. Concerning composition copolymer, then it must be depleted the monomer that few in a monomer mixture. This picture is directly opposite to that observed for the variant r 1< 1, r 2 < 1, а на рис. 3 была бы представлена кривой, зеркально подобной кривой 2. Но этот вариант copolymerization rare; one can only mention the copolymerization of butadiene with isoprene at 50 ° C (r 1 = 1.38, r 2 = 2.05), where the constants are only slightly greater than unity. But, unfortunately, there are cases when both constants are infinitely large (r 1 →¥, r 2 ®¥); in this case, copolymerization simply does not occur, each of the monomers polymerizes separately and a mixture of two homopolymers is formed (for example, a pair: butadiene - acrylic acid). A very useful option would be where the constants would have a large, but final size; in this case would form block copolymers; Unfortunately, no such cases have yet been found.

The term "copolymerization constants" should not be taken too literally: their values ​​for a given monomer can change markedly with changes in reaction conditions, in particular with changes in temperature. For example, during the copolymerization of acrylonitrile with methyl acrylate at 50 o C, r 1 = 1.50, r 2 = 0.84, and at 80 o C, r 1 = 0.50, r 2 = 0.71. Therefore, when citing the values ​​of constants, it is necessary to specify the conditions.

Theoretical and practical information about the influence of various factors on radical polymerization, namely the conversion of the monomer and, accordingly, the yield of the polymer, its molecular parameters (molecular weight, polydispersity and MWD) can be obtained by studying the patterns of development of this process in time, that is, its kinetics . Of the three main elementary stages - initiation, growth and chain termination - the slowest and most energy-intensive is initiation. To start it, an activation energy of 84-126 kJ/mol is required, which is 3-4 times higher than the activation energy of the chain growth stage and almost 10 times the activation energy of the termination stage.

The initiator is characterized by efficiency. Let us consider in more detail the stage of decomposition of the initiator into radicals.

The initiator decomposes into two radicals, which can give rise to two kinetic chains. However, the radical pair is surrounded by molecules of the environment, which create a dense environment, called the cell. The density of the medium prevents the rapid diffusion separation of the radical pair, so some of the radicals perish by recombination without escaping into the bulk.

The initiation efficiency (probability of chain nucleation) is expressed by the following equation:

The inhibitory method is used to determine δ. It is especially important to take into account δ in media with low molecular mobility, where the yield of radicals from the cell is low. This is well illustrated by the following example. When moving from liquid ethylbenzene with high molecular mobility to polystyrene with extremely low molecular mobility, the initiation efficiency decreases by a factor of 20: from 0.6 to 0.03.

The overall rate of radical polymerization V is equal to the rate of consumption of the monomer M during its interaction with the growing radical.

Based on the law of mass action, the rate of each elementary reaction v of the polymerization process can be represented by the following equations:

where v and and k and, v p and k p , v 0 and k o - the rate and rate constant of the reactions of initiation, just and chain termination, respectively; [I], [M*], [R], [M] - concentrations of the initiator, radicals, growing radicals and monomer, respectively.

Since the number of monomer molecules participating in the reaction with the primary radical during initiation is very small compared to the number of monomer molecules participating in chain growth (the initiator is usually introduced in an amount of up to 1% of the monomer mass), the monomer concentration can be considered constant, and then

During radical polymerization, a stationary mode of the process is established a few seconds after the start of the reaction: radicals appear upon initiation and disappear at the same rate upon termination, that is, vu = vo and d/dt = 0. Then [M*] = (k and /ko) 1/2 [I] 1/2 and the equation for the overall polymerization rate becomes:

Equation (9) is valid in the initial stage of polymerization, when the monomer conversion and polymer yield are low (10-15%).

The molecular weight of the polymer, as well as the degree of polymerization n, is determined by the length of the kinetic chain, which depends on the ratio of the rates of chain termination and growth reactions

The more v p compared to v o , the more monomer molecules have time to join the growing radical before chain termination, the longer the chain. Taking into account equation (9) and the stationarity condition of the process, we obtain

The physical meaning of equations (9) and (11) is as follows. The molecular weight of the polymer and the rate of radical polymerization are directly dependent on the concentration of the monomer, an increase in which causes an acceleration of the process and an increase in the length of chain molecules. Similarly, the rate and molecular weight of a polymer is affected by an increase in pressure, as compression brings the reacting molecules closer together, facilitating the polymerization process.

With an increase in the concentration of the initiator in the system, the number of radicals increases. These radicals react with a large number of monomer molecules, thereby increasing the rate of their transformation into macroradicals, that is, the rate of polymerization. But an increase in the concentration of radicals contributes to an increase in the probability of their collision, that is, an increase in the rate of termination of the polymerization chain. This leads to a decrease in the molecular weight of the polymer.

Similarly, the kinetics of radical polymerization is affected by temperature. Typically, the rate of polymerization increases by a factor of 2-3 with a temperature increase of 10°C. An increase in temperature facilitates the decomposition of the initiator into radicals, at the same time, the mobility of all particles of the system - molecules and radicals - increases, therefore, the probability of particle collision increases. This leads to an increase in the rates of chain propagation and termination reactions. Thus, with an increase in temperature, the overall rate of polymerization always increases, while the molecular weight of the polymer decreases, and the proportion of low molecular weight fractions increases. An increase in temperature simultaneously contributes to the formation of branched macromolecules, a violation of the chemical regularity of the construction of the polymer chain, since the probability of monomers entering the chain according to the “head-to-head” or “tail-to-tail” principle increases.

The rate of polymerization and the molecular weight of the polymer are significantly affected by various impurities and atmospheric oxygen, and oxygen, depending on the nature of the monomer and polymerization conditions, can accelerate or slow down polymerization. Oxygen slows down the photopolymerization of vinyl acetate, but accelerates the photopolymerization of styrene, inhibits the polymerization of vinyl chloride initiated by benzoyl peroxide, which proceeds in a nitrogen or argon atmosphere with good polymer yield and high molecular weight. Therefore, to obtain polymers, monomers of high purity (~ 99%) are used and the technological process is carried out in an inert gas atmosphere.

To this day, most modern synthetic polymers are obtained by the method of radical polymerization. Despite the obvious advantages of this method over ionic polymerization (mild synthesis conditions, a wide range of monomers, etc.), its significant drawback is that it does not allow one to obtain narrowly dispersed homo- and copolymers with a given molecular weight and structure.

Intensive research around the world over the past decade has shown that these problems can be solved using non-traditional radical processes, united by the common name "pseudo-living radical polymerization". In these processes, macromolecules arising from the target monomer interact with specially introduced stable additives - agents of reversible chain transfer. The resulting macromolecules are able to "revive" and regenerate propagating radicals, which can again participate in the chain propagation reaction up to the next act of its limitation by termination or transfer. In such processes, the quadratic termination of macroradicals, which is characteristic of classical radical polymerization, ceases to play a significant role. Repeatedly repeating stages of chain restriction (termination) and “revitalization” of chains ensure the successive growth of macromolecules during polymerization and a decrease in the MWD width. The most common reversible chain transfer agents (RPCs) are sulfur-containing compounds of the general formula

where Z is a stabilizing group, Y is a leaving group.

They allow the controlled synthesis of polymers and copolymers to be carried out in practice already now. At the same time, the scientific theoretical interpretation of the RAFT mechanism during polymerization requires reflection.