This chapter discusses the kinetic features of the formation of polymer networks. In accordance with the general kinetic principle, a different approach to polymerization, polycondensation and cross-linking processes is required as methods for their formation.

9.1. POLYMERIZATION PROCESSES

9.1.1. THREE-DIMENSIONAL RADICAL POLYMERIZATION

We showed above that at the initial stage of three-dimensional polymerization there is a high probability of an ineffective cyclization reaction, or intrachain cross-linking.

A. Matsumoto provides the following simplified, but quite visual scheme for the three-dimensional (co)polymerization of oligomers containing two double bonds:

1. Growth of linear chains carrying pendant double bonds.

2. Primary intramolecular cyclization.

3. Intermolecular cross-linking of chains.

4. Intramolecular cross-linking (secondary cyclization) in branched macromolecules.

Reactions (3) and (4) lead to the formation of microgel particles.

The qualitative picture is clear. Quantitative results were obtained using computer modeling methods. In particular, Yu. M. Sivergin showed that the intrachain cross-linking reaction occurs already with a chain length R p* 3-5, which casts doubt on the hypothesis of A. A. Berlin about the formation of long chains of p-polymer with P„ = 10 3 -10 4 units, each unit containing a suspended double bond.

Estimating the consumption of suspended functional groups can serve as a test for the cyclization reaction: their conversion will be higher, the more intense the process of intrachain cross-linking occurs. Figure 11.123 shows

Dependence of the conversion of pendant double bonds (x) on the depth of conversion along the monomer at the initial concentration of 1,4-divinylbenzene 5 (/), 2 (2), 1 (3) and 0.5 mol/l (4 ) (data from O. Okay et al.) Corresponding data for the radical polymerization of 1,4-divinylbenzene in toluene solution. As can be seen, when extrapolating the curves of the relative conversion of suspended double bonds to zero along the total depth of transformation on the ordinate axis, the larger the value cut off, the more diluted the system is.

The likelihood of cyclization depends largely on the molecular structure of the reactants and the flexibility of the resulting chain. An example is the data shown in Figure 11.124. In contrast to the homopolymerization of methyl methacrylate (curve 6), in the process of three-dimensional copolymerization the molecular weight increases (curves 1-5), demonstrating a tendency to reach the gel point, and the nature of the growth depends on the nature of the comonomer. In the case of relatively short chains (curves 4 and 5) the value of the critical conversion is especially large, but the value extrapolated to zero yield Mw relatively small. This may be due to the fact that the primary cyclization reaction plays a significant and predominant role. In the case of long chains (curves 1 And 2) Secondary cyclization and cross-linking, leading to intensive branching, become important. This appears to be reflected in the “zero” values M and „ naturally increasing with the length of the cross-linking comonomer.

Change in the molecular weight of polymethyl methacrylate depending on the chain length of the comonomers - polyethylene glycol dimethacrylate. The concentration of the latter is 1 mol. %. Polymerization conditions: 50°C, monomer/1,4-dioxane = 1/4, initiator concentration (azoisobutyronitrile) 0.04 mol/l (data from A. Matsumoto et al.). Number of oxyethylene units:

23 (1), 9 (2), 1 (3), 3 (4) and 2 (5); (6) - homopolymerization of methyl methacrylate.

However, the intramolecular cross-linking process is not limited to the low conversion region. As N. Wesslau showed using the example of the copolymerization reaction of styrene with various dimethacrylates, the probability of cyclization increases with the depth of conversion, reaching a limiting value of approximately 10%, and this value varies depending on the molecular structure of the cross-linking agent within a wide range (0.11- 0.63).

W. P. Schröder and W. Oppeman used computer modeling to find that a significant proportion of the cross-linking comonomer is concentrated in small-sized cycles (Fig. 11.125, curve 1), what does the curve indicate? 2, showing that the rings contain a minor portion of monofunctional monomer. The reactivity of the crosslinking agent plays a significant role in this case: the higher it is, the lower the degree of intrachain crosslinking.

The secondary cyclization reaction serves as a prerequisite for the formation of a microgel. A striking example of the microgel mechanism of three-dimensional radical polymerization is the polymerization reaction of oligoester acrylates, studied in detail in the works of G.V. Korolev and described in his reviews and monographs.

Dependence of the proportion of mono- and bifunctional comonomers contained in the cycles on the reactivity of the latter (mixture composition - 16:1; modeling method - Monte Carlo) (data from U. P. Schroder, W. Oppemann):

1 - cross-linking reagent; 2 - monomer.

The formation of a microgel as a result of intramolecular cross-linking leads to v-syneresis—the displacement of low-molecular-weight components of the reaction system, comonomers, and initiator from the volume of the microgel particle, essentially to phase separation. This

Changing bimolecular termination constants (A) simple (b) during the polymerization of diethylene glycol dimethacrylate (data from E. Andrzejewska)

Changing the number (1) and size ( 2 ) microgel particles in the process of radical polymerization of trioxyethylene glycol dimethacrylates (a) and bis(triethylene glycol) phthalate (b) (data from G.V. Korolev et al.), the process is auto-accelerated: a drop in the local concentration of the oligomer in the volume of the microgel particle increases the likelihood of an intrachain reaction cross-linking, an increase in cross-link density enhances microsyneresis. Added to this is the gel effect: the mobility of macroradicals in the network drops sharply, their lifetime increases, and the length of the kinetic chain of suspended functional groups also increases. In this way, already at small conversion depths, an extremely heterogeneous structure of the reaction system is formed: microgel particles with an almost limiting conversion value in the medium of an unreacted oligomer.

The manifestation of the gel effect is illustrated in Figure II. 126a, which shows how the value of the bimolecular termination constant changes during the photopolymerization of diethylene glycol dimethacrylate. As you can see, the termination constant drops almost from the very beginning of the process. At the same time, the growth constant retains its value up to a depth of approximately 50% (Fig. 11.1266), after which a decrease in both constants is observed. According to Korolev, starting from a certain moment, which is considered as the first gel point, all emerging active chains react with the double bonds of microgel particles, new particles are not formed, and the polymerization process is realized as an increase in their size.

Indeed, using the method of static light scattering it was shown that with the depth of transformation the number of particles (iV) decreases, and their sizes (R) grow (Fig. 11.127). This stage of the reaction corresponds to a plateau on the curve of the change in the cutoff constant (see Fig. II. 126a). In Table II. Figure 19 presents data from L. Rey et al. on the size of microgel particles obtained by the dynamic light scattering method during the copolymerization of tetraethoxyethylated bisphenol A dimethacrylate (according to the authors’ nomenclature D121) with styrene or divinylbenzene.

In both cases, at the initial stage of polymerization, the formation of microgel particles and an increase in their average size are observed. Starting from a certain moment, there is

Table 11.19

Kinetics of microgel formation up to the gel point during three-dimensional copolymerization of the D121 oligomer according to dynamic light scattering data: v - volume fraction, d- diameter

Comonomer		With/, nm	1st faction		2nd faction		3rd faction
						c1, nm		cl. nm
Divin and forehead ii- angry

large-scale fraction, which indicates the development of the process of particle fusion.

Microgel particles have a gradient structure. As was shown by the EPR method, protons located inside the particle are characterized by low mobility. The reactivity of internal and peripheral double bonds differs by orders of magnitude (Fig. 11.128), i.e., due to diffusion restrictions, internal functional groups are practically unable to react. Moreover, the presence of “trapped” radicals was noted inside the particles. The state of the polymer has a decisive influence on their concentration. As can be seen from the data shown in Figure 11.129, a significant amount of radicals accumulate in the glassy polymer obtained by polymerization of ethylene glycol dimethacrylate (points 1 ), while the highly elastic state (polyethylene glycol-600 dimethacrylate) contributes to their death, significantly reducing the concentration value (points 2).

Kinetics of the reaction of Hg-II acetate with suspended double bonds of 1,4-divinylbenzene microgel (data from J. C. Hiller and W. Funke)

Concentration of frozen radicals in network polymers based on diethylene glycol dimethacrylates (1) and polyethylene glycol-600 (2) (data from Y. Zhang et al.)

Thus, as a result of radical polymerization of oligoether acrylates, a polymer with a heterogeneous supramolecular structure is formed. But this mechanism is also inherent in other systems, because it is based on a general pattern: at the initial stage, a dilute solution of sufficiently long chains is formed.

When studying the process of polymerization of oligoester acrylates using the EPR method, it was shown that the intergranular space is inhomogeneous. It consists of microvolumes, in each of which the polymerization process occurs locally. The resulting structures are characterized by different levels of cross-linking, different degrees of cyclization, and different connectivity of nodes. Accordingly, each of these microvolumes is characterized by different glass transition temperatures T s due to the different mobility of the elements of their own structure. “Freezing” of mobility due to glass transition is another significant factor that determines both the kinetics of the process at deep stages and the final structure.

The formation of a heterogeneous supramolecular structure during the copolymerization of styrene and divinylbenzene is demonstrated by broadband dielectric spectroscopy data. Two relaxation peaks, characterizing the microgel and the unreacted medium, merge as the reaction progresses, forming a wide relaxation region, indicating the presence of a wide distribution of structural elements over the glass transition temperature.

A relief picture of the morphological structure of copolymers of the D121 oligomer with styrene or divinylbenzene, obtained by L. Rey et al. using atomic force microscopy, is shown in Figure 11.130. It is obvious that the high degree of supramolecular heterogeneity reflects an equally large scatter in the characteristics of the local architecture of the polymer network.

The general picture of the formation of a network polymer by radical polymerization is represented by the following:

Relief of the morphological structure of copolymers of oligomer D121 with styrene (a) and diviylbenzene (b) (data from L. Rey et al.)

computer simulation results (see Figures 11.131 and 11.132). In the first of them, black dots indicate radicals, light gray polymer. Areas colored in dark gray contain "trapped" radicals. The empty space contains the unreacted monomer. The second shows the kinetics of diallyl isophthalate polymerization. A feature of monoallylic monomers is that they polymerize at low rates and form oligomeric products. Therefore, the 3D polymerization process usually does not result in the formation of a macrogel, but is limited to microgel particles.

Scheme for the formation of a network polymer by radical polymerization (data from J. B. Hutchison and K. S. Anseth):

A- the initial state; b- formation of microgel particles; With- the beginning of their merger; g-e- formation of a structurally heterogeneous macrogel.

Dynamics of development of the three-dimensional polymer structure of diallyl isophthalate (data from Yu. M. Sivergin, S. M. Usmanov, etc.

The influence of the cobalt porphyrin complex on the kinetics of polymerization of ethylene glycol dimethacrylate (data from S.V. Kurmaz, V.P. Roshchupkin):

Co 2 "P 10 3: 0 (1), 0.6 (2) and 3 mol/l (3). DAK = 6.4 10 1 mol/l, 60°C.

Figure 11.133 shows how, in the presence of cobalt porphyrin complexes (Co 2+ P), the kinetics of the three-dimensional polymerization process changes: the gel effect not only weakens, but also shifts towards higher conversions, indicating the absence of a microgel.

The fact is that during radical polymerization, these complexes not only serve as reversible termination agents (see Section 6.2.1), but can catalyze the chain transfer reaction according to the scheme:

Effective transfer constant k tr /k p of the order of 10 3, whereas for ordinary agents such as mercaptans this value is of the order of unity. It is this circumstance that determines the high efficiency of porphyrin complexes. The network polymers formed in their presence

Conditions that ensure the production of SRP (filled icons refer to network polymers, empty ones - to SRP; different types of points - to different complexes;

dotted lines indicate a 10% deviation from the dividing line) (data from N. M. V. Smeets et al.)

have a much more uniform supramolecular structure than shown in the above figures.

Previously (see section 7.1.2.5) the use of a chain transfer reaction for the synthesis of SRP by (co)-polymerization of polyfunctional monomers was discussed. It is obvious that cobalt porphyrin complexes are very effective in this regard. Figure 11.134 shows the conditions that ensure the production of PSA: as follows from the data presented, the chain transfer frequency k,.C, where C is the concentration of the catalytic complex, must be 85 times higher than the proportion of the cross-linking comonomer.

• Smirnov, B. R. Reports of the USSR Academy of Sciences / B. R. Smirnov, I. M. Belgovsky, G. V. Ponomarev [and others]. 254, 127 (1980).

Classical chemical kinetics considers reactions under idealized conditions, uncomplicated by processes of heat and mass transfer, diffusion, etc. With radical bulk polymerization, these processes can be neglected only at the initial stage of the reaction, when the viscosity of the reaction mass increases slightly.

From an examination of the kinetic curve (Fig. 3.3), it is obvious that 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 their termination reactions increases: as a result, after a certain period of time, the number of formed radicals will be equal to the number of disappearing macroradicals and the system passes from the non-stationary state (section I on the kinetic curve 1 in Fig. 3.3) to stationary (section II), characterized by a constant concentration of radicals in the system (c/[ R* /dt= 0), as well as the constant rate of the chain growth reaction. Section III of the kinetic curve of chain polymerization is the decay of the reaction; it can be due to several reasons - the main ones are the exhaustion 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. However, its absence does not mean that in this case stationarity in the concentration of growing radicals is not achieved. It may turn out that stationarity in growing macroradicals exists throughout the entire process, and the rate observed in the experiment changes due to changes in the monomer concentration: this can be verified if for any moment of time we divide the rate by the concentration of the reagent, presenting equation (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 stationary area; 2 - without stationary area

For a system polymerizing by a radical mechanism, the so-called quasi-stationary state is also possible. Let's imagine that at some point in time t in the system the rates of reactions of formation and death of radicals are equal, i.e. a stationary state was established. At a moment in time t 2 the rate of formation of initiating radicals decreased, which led to a 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 a stationary state can again be achieved in the system, but at a lower concentration of radicals. If the transition from the first stationary state to the second occurs quite smoothly, then the reaction system will constantly “adjust” to changes in the concentration of active centers and in practice we can assume that the stationary state is maintained all the time.

The establishment of a steady state in the system means that

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

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

In the 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 the mass is proportional to the monomer concentration to the first power and the initiator concentration to the 0.5 power.

Using data characterizing the process in a stationary state, one can only find the constant kn. From the cast-

th below 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 k p And k Q is not possible, therefore, to find them, data on the kinetics of polymerization in a non-stationary state are used, which are necessary to determine the average lifespan of a growing radical, i.e.

In the case of stationary 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

Necessary 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 ). Typically, t values ​​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 k 0 . For some monomers these values ​​are given in table. 3.7 along with the activation energies calculated using the Arrhenius equation.

Table 3.7

Kinetic parameters of radical polymerization of some monomers

* Per 1 mole of polymerizing monomer. ** Per mole of growing radicals.

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

Polymer chain growth rate w p is the number of monomer molecules attached to the growing polymer radicals per unit time. Open circuit 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 added to the growing radical before its cessation of existence.

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

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 experimentally. 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 as follows:

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 the event of a circuit break due to disproportionation v = X, and during recombination 2v = X.

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

To break 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 from equations (3.22) and (3.23) it follows that the molecular weight of the resulting polymer is inversely proportional to the square root of the initiator concentration. Consequently, by changing the concentration of the initiator, the length of the resulting macromolecules can be controlled.

Analysis of the kinetic equation of radical polymerization also makes it possible to evaluate the effect of temperature on the overall rate of the process and the size of the resulting chains. With increasing 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 paragraph 3.1 .2)) the temperature coefficients of the reactions of initiation, growth and chain termination are different: with increasing temperature, the rate of initiation increases to a greater extent than the rates of growth and chain termination.

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

Therefore, increasing the initiation rate leads to an increase in the overall polymerization rate. At the same time, an increase in the initiation rate also leads to an increase in the rates of chain growth and termination (see equations (3.8) and (3.13)): the rate of chain termination increases to a greater extent with increasing temperature - .
The value of Kp for most monomers is 10 2 ... 10 4 l/(mol?s).
The chain termination reaction is carried out in different ways depending on the nature of the macroradical, its size and structure, viscosity of the medium, temperature, composition of the reaction medium, etc.
Most often, termination occurs due to the connection of two macroradicals with each other. This termination process is called recombination (combination) of macroradicals:

Disproportionation of macroradicals - two macromolecules are formed, one of which has a double bond in the final link.

Kinetic polymerization rate equation
To derive the equation, we use the principle of a stationary state, the essence of which is as follows: in the reaction system, at some point in time, active centers (free radicals) are formed, giving rise to a chain reaction. At the same time, as a result of chain termination, active centers (in the case of radical polymerization, macroradicals) begin to disappear. The concentration of radicals increases with time, which also leads to an increase in the rate of chain termination. After a certain period of time, the number of disappearing macroradicals will be equal to the number of formed radicals. A constant, stationary concentration of growing radicals will be established in the system.
At the moment the stationary state is established, the rate of chain initiation will be equal to the rate of circuit breakage:
V in = V o.
Therefore, K in = K 0 2.
From this equation we find the concentration of macroradicals

The reaction rate (V p) in the steady state is equal to the chain growth rate (V p):

Substituting the expression into the chain growth rate equation, we obtain:

The resulting equation yields the most important rule, which is a consequence of bimolecular chain termination during radical polymerization and serves as a characteristic feature of the process that allows us to distinguish the radical mechanism of polymerization from the ionic one. In ionic processes this rule is not observed.
The rate of polymerization is proportional to the square root of the initiator concentration (“square root rule”).
It should be noted that the proportionality of the polymerization rate to the monomer concentration to the first power is not always observed. As a rule, this value is slightly greater than unity, which is associated with the participation of the monomer at the initiation stage and in the chain transfer reaction.
The rate of polymerization can be assessed by determining the change in any parameter of the system: density, refractive index, viscosity, light absorption, heat release, etc. The conversion can be controlled by chemical methods by the number of unreacted double bonds, iodometric or bromometric titration, etc.
With increasing temperature, the rate of polymerization increases, and the molecular weight of the polymer decreases. Pressure generally increases the rate and extent of polymerization. Thus, an increase in pressure by 1000 times compared to atmospheric pressure leads to an increase in the rate of initiated polymerization of styrene by an order of magnitude, and the degree of polymerization by a factor of two. The higher the initiator concentration, the higher the polymerization rate, but the lower the molecular weight of the resulting polymer. It has been established that with increasing monomer concentration, the rate of polymerization increases and the average degree of polymerization increases.
experimental part
Operating procedure:
1) carrying out radical polymerization of styrene at various concentrations of initiator;
2) determination of the polymer yield in samples of the reaction mixture by the refractometric method;
3) constructing kinetic curves of polymerization, determining the rate of the process and assessing the order of the reaction according to the initiator.
Working method
5 g of styrene are placed in test tubes with polished stoppers. Then they add samples of the initiator, weighed on a watch glass accurate to the fourth decimal place, in an amount of 0.2; 0.4; 0.6; 0.8 and 1.0% (by weight of monomer). The prepared solutions are thermostated at 70 °C. 10 minutes after the start of thermostatting, samples of the reaction mixture are taken from each test tube using a syringe with a long needle to determine the polymer yield by the refractometric method. Subsequent samples are taken from the tubes every 10 minutes. The refractometric method for determining the yield of a polymer is based on the change in the refractive index of the reaction mixture during polymerization. Before measuring the refractive index, the refractometer is thermostated at 20 °C for 10–15 min.
At least 5 samples are taken for each initiator concentration at a given temperature. The time after which the polymer yield is determined depends on the polymerization rate of the monomer; it is chosen in such a way that the degree of monomer conversion in the last sample does not exceed 15%.
By measuring the refractive index in the samples of the reaction mixture, determine the yield of polymer (x) at the time of sampling using data on the dependence of n 20 from the output of the polymer. The obtained values ​​are entered into table 1.
Table 1. Initial and experimental data

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

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, during 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 laws 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 recombination or by disproportionation.

To derive the general kinetic equation of polymerization without taking into account chain transfer reactions, certain 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) principle of a quasi-stationary state with respect to a growing radical. The steady state of sequential reactions is that the concentration of intermediate products is constant. And the time to establish a steady state is much less than the reaction time.

Intermediate particles are R ∙ , their concentration is constant.

During polymerization, the rate of change in the concentration of radicals quickly becomes zero (the rate of formation 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 feature

The 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 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 synthesis, has a V-shaped form (Fig. 2.3).

In a chain reaction there is an initial stage when the concentration of radicals increases from zero to “average” - this is the non-stationary phase of the reaction (2). As the concentration of radicals increases, the rate of their death increases. When the rates of formation of radicals and their death become close, a quasi-stationary phase of the reaction begins; in this phase, the concentration of radicals can be considered constant (3).

Conversion

Towards the end of the reaction when exhausted

monomer,

source of formation of new radicals -

% 100

their concentration quickly drops to

zero, and the reaction again becomes non-

stationary nature (4, 5). If the length

activity of non-stationary reaction phases

significantly less than the duration

phases with a constant concentration of radi-

Rice. 2.3. Kinetic curve

chain radical

polymerization-

feces, then we apply to such a reaction the

tions: 1 – process inhibition;

tod of a quasi-stationary state.

2 – acceleration of polymerization (speed

Kinetic description of the re-

growth increases with time); 3 – hundred

polymerization shares represent co-

national period (speed of political

merization

constant

Vin);

fight the system of differential equations

4 – slowdown of polymerization due to

considerations regarding the consumption of starting materials and

carefully with decreasing concentration

accumulation of intermediate and final

monomer; 5 - termination of the reaction

due to lack of monomer

products that are listed below

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

1. Initiation, as already indicated, occurs 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

nogo center.

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

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

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

ciation 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 occurs with the smallest constant, i.e. k and there will be descriptions

be based on 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 polymerization. In fact, some of them are used unproductively and are lost as a result of adverse reactions (see “cage 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 – initiation efficiency – the proportion of primary radicals, which

is spent on initiating 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 monomer disappearance:

D[M] = k,		[M]

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

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

V r = − d [ M ]	K r [ R∙ ] [ M ],

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

The activation energy for chain growth is low, 20...35 kJ/mol (this is several times less than the activation energy for initiation by peroxide initiators), so chain growth depends little on temperature.

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

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

where k o is the circuit break 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.

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

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

IN in accordance with the third assumption, for the stationary stage, when the rates of formation and disappearance of free radicals are equal:

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

		ki and f [I]

Substituting this value into equation (2.100), we get

V рп V р = − 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 radical polymerization process.

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

k = kp		ki and f

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

V рп = 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 national to 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, allowing one to distinguish the radical mechanism of polymerization from the ionic one, where this rule is not observed.

The equation is valid for radical polymerization up to degrees 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 to the first power is not always observed. As a rule, this value is slightly greater than unity, which is associated with the participation of the monomer at the initiation stage and in chain transfer reactions.

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

V рп = 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
inhabitant; T – 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 activation energies, respectively, of initiation reactions,

growth and breakage.

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 poly-

What is very important is the number average molecular weight (Mn) of the resulting products, which 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 ]			kp[M]
				ko [R∙] 2			ko [R∙]

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

into equation (2.111), we get:

kp[M]

kp[M]

f ki [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.

The kinetics of radical polymerization is generally very complex; the point is that she heterogeneous; the kinetic characteristics of the system change quite significantly with increasing process depth. The reason, first of all, is that with an increase in the degree of monomer conversion, the viscosity of the system usually increases significantly and the diffusion rate of large molecules decreases (gel effect, see below). In addition, as the polymer accumulates, the likelihood of chain transfer to the polymer increases, complicating the picture.

However, when low degrees of monomer conversion(not higher than 10%) the kinetics of the process is quite simple; On its basis, quite definite conclusions can be drawn. Next, this option will be considered - kinetics at shallow process depths(it can be called the elementary kinetics of radical polymerization).

Let us first consider the simplest case, when chain transfer reactions can be neglected; This case is real if there are no impurities in the reaction mixture to which transfer can occur and if the monomer is not allylic (then chain transfer reactions to the monomer can be neglected). In this case, we can assume that only initiation, chain growth, and chain termination reactions occur.

where v and is the initiation rate, [I] is the concentration of the initiator, k and is the initiation rate constant, f is the efficiency of the initiator (p. 15); the 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 vр is the chain growth rate, kр is the chain growth rate constant, [M] is the monomer concentration, and is the concentration of radicals (“living” chains).

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

Open circuit speed expressed by the equation:

where v o is the chain break rate, k o is the chain break rate constant

This equation reflects that termination occurs during interaction two radicals (“living” chains) (p. 16).

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

The chain growth rate equation involves the 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 condition of quasi-stationarity; at the initial stages of the process (at shallow depths) it works well. With this 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 = v o, i.e.:

Thus , 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:

Thus, 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 not difficult to understand and purely qualitatively, because 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; Let's limit ourselves to this type of transmission.

As already indicated, transferring the circuit to the regulator does not affect speed process. Medium degree of polymerization(P r) in this case is equal (to a first approximation) to the ratio of the chain growth rate to sum of speeds break and transmission of the chain (since during transmission they break 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 progress and results of polymerization are influenced by a number of other factors, which are discussed below.

Effect of temperature. A.In the most common polymerization option with the participation of initiators an increase in temperature leads to increase polymerization rates decrease molecular weight of the polymer. The increase in speed needs no comment; the decrease in molecular weight is due to the fact that with increasing temperature the rate of initiation increases to a greater extent than the rate of chain growth(because initiation has a higher activation energy). Consequently, according to the condition of quasi-stationarity, 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 decreases.

B. When photochemical initiation with increasing 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 remains virtually unchanged, while the rate of chain growth increases.

Other consequences of increasing temperature (for all polymerization options): 1) increasing temperature 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 moves left; in other words, the role of reactions grows depolymerization. All this does not allow radical polymerization to be carried out with any efficiency at temperatures above 120 o C.

Effect of pressure. Effect of pressure (P) on speed any chemical reaction is expressed by the Evans–Polyani 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 growthΔV ≠< 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, therefore, 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, when a transition state is formed, the volume increases. Consequently, with increasing pressure, the initiation rate, and hence the speed open circuit(according to the condition of quasi-stationarity) decreases. Thus, growing ratio v p /v o , i.e. . polymer molecular weight.

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

Influence of process depth(degree of 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 approximately 10%) process speed and molecular weight of the polymer practically do not change. However, as the depth of the process increases, it is observed an increase in both the speed of the process and the molecular weight of the polymer. This may seem unexpected at first glance, because... with increasing degree of monomer conversion, its concentration decreases, which, according to the above kinetic equations (p. 24), should lead to a decrease in both speed and molecular weight. However, here the kinetics are completely different; in particular, the quasi-stationary condition does not apply. The fact is that as polymer macromolecules accumulate, they quickly the viscosity of the system increases(polymer solutions, as is known, have extremely high viscosity, and the higher their concentration and the molecular weight of the polymer, the higher their viscosity). An increase in viscosity leads to a sharp decrease mobility large particles, in particular, "living chains", and, therefore, 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 maintained over a fairly wide range of system viscosity, so that the rate of chain growth does not change. A sharp increase in the v p /v o ratio 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 quasi-stationarity condition is not met.

The changes discussed above 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 also lose 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 during block polymerization (polymerization of pure monomer); It also manifests itself to a sufficient extent during polymerization in fairly 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 falls out of solution, then the viscosity changes little during the process; in this case, the gel effect is not observed, the speed of the process 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 uniformly with increasing process depth.

These specific initiators are di- or polyperoxides and iniferters.

The first of them contain two or more peroxide groups in the 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 chain termination occurs upon interaction with another “living” chain (indicated in the scheme 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; the situation may repeat itself later. Thus, as the process proceeds, the size of macromolecules is constantly growing.

Iniferters – peculiar connections that are not only initiators, but also actively participate in the processes transfers 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– transmission, Ter mination - open circuit). 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 inferter is S-benzyl-N,N-diethyldithiourea (19). In its presence the following reactions occur:

Iniferter (19) decomposes to form active radical (20) and inactive radical (21). Radical (20) initiates the growth of the polymer chain. A growing “living” 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 increasing conversion depth.

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 ordinary initiators; this has a positive effect on their technical properties.

Effect 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 the start of polymerization linear 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 practically 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.

The preliminary orientation of the monomer molecules can be achieved, for example, during polymerization in inclusion compounds (clathrates), when the 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 patterns described above were examined using examples of polymerization one monomer (homopolymerization). But, as is known, it is widely used 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, there are several problems here.

1) Opportunity copolymerization - will units of both (or three) polymers be included in the polymer chain, or will each monomer be polymerized separately and a mixture of homopolymers will be formed?

2) The relationship between the composition copolymer and composition taken for the process mixtures of monomers. What is meant here is differential copolymer composition, i.e. its composition At the moment(if we take the integral composition, i.e. the composition of the entire mass of the copolymer, then it is clear that at a large depth of the process it will approximately coincide with the composition of the mixture of monomers, however, at different depths of the process 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 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 monomer mixture. This means that during the polymerization process, monomers are not consumed in the same proportion as they were taken; one of them is consumed faster than the other, and must be added as the reaction progresses to maintain a constant composition of the monomer mixture. From here 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 a copolymer macromolecule, i.e. stages chain growth during copolymerization (because the copolymer macromolecule is formed precisely at this stage).

Let us 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 “its 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 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 difficult-to-determine concentrations of radicals. They can be eliminated from the equation by introducing quasi-stationary condition: concentrations both types radicals (~A and ~B) permanent; as in homopolymerization, the quasi-stationary condition is satisfied only at shallow process depths. It follows from this condition that the rates of mutual transformation of both types of radicals are the same. Since such transformations occur via reactions 2 and 4, then:
This equation is called Mayo-Lewis equations(sometimes called Mayo's 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(constant r 1 – for radical ~A, constant r 2 – for 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) 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 copolymerization constants also allows one to judge the structure of the resulting copolymer, as well as the possibility or impossibility of copolymerization itself.

Let us consider the main options for copolymerization, determined by the values ​​of copolymerization constants. It is convenient to present 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 monomer mixture.

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 strangers monomer, i.e. we can talk about an increased tendency of monomers to copolymerize.

A) Copolymer composition. Differential copolymer composition enriched with the monomer that is low in the 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: for [A]<< [B] D < 1, следовательно, d[A]/d[B] < , а при [B] << [A] D >1 and d[A]/d[B] > . Curve 2 intersects the azeotrope line, i.e. at some one In the ratio of monomers, polymerization is azeotropic. This ratio is easy to calculate, because in this case D = 1; from here:

B) Copolymer structure. Since each radical preferentially attaches to to someone else's monomer, in the copolymer there is a tendency towards 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 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 itself polymerize, but can form a copolymer with a 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 a “foreign” one. It means that one monomer is more active than the other during copolymerization, because reacts more easily than others both radicals. Therefore, when 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 r 1 > 1, r 2< 1 и 3’’ для r 1 < 1, r 2 >1). Azeotropic polymerization is not possible here.

The structure of copolymer macromolecules 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 monomers towards both radicals is 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 radical ~A▪ and the radical ~B▪). In this case, the ability of each monomer to enter the polymer chain does not depend on the nature of the radical, which he encounters and is determined simply probability clashes with each of the radicals. Therefore, the structure of the copolymer will be purely statistical (K M ~ 1). This case is called perfect copolymerization- not at all because in this case a copolymer with ideal properties is formed (rather the opposite), 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 o 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 “own” monomer; the system has a reduced tendency to copolymerize. Concerning composition copolymer, then it must be impoverished the monomer that few in a monomer mixture. This picture is exactly the opposite of that observed for option 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 be formed 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 noticeably with changes in reaction conditions, in particular, with changes in temperature. For example, when copolymerizing 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 giving the values ​​of constants, it is necessary to indicate the conditions.