Kinetics of polymerization. Kinetics of radical polymerization Kinetics of radical polymerization
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 depth of the process. 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 rate of diffusion of large molecules decreases (gel effect, see below). In addition, as the polymer accumulates, the probability of chain transfer to the polymer increases, complicating the picture.
However, when small degrees of monomer conversion(not higher than 10%) the kinetics of the process is quite simple; on its basis, quite certain conclusions can be drawn. Further, this variant will be considered, i.e., the kinetics at small depths of the process(it can be called the elementary kinetics of radical polymerization).
Let us first consider the simplest case, when chain transfer reactions can be neglected; such a case is real if there are no impurities in the reaction mixture that can be transferred and if the monomer is not allylic (then the reactions of chain transfer to the monomer can be neglected). In this case, we can assume that only the reactions of chain initiation, growth, and termination occur.
where v i is the initiation rate, [I] is the initiator concentration, k i is the initiation rate constant, f is the initiator efficiency (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 admission 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:
 |
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 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. Thus, 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 monomer conversion 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 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 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.
Polymerization
Polymerization- this is a process for obtaining high-molecular compounds, in which the growth of a molecular chain occurs as a result of the sequential attachment of molecules of a low-molecular substance (monomer) to the active center localized at its end:
M i M* + M M i+1 M* etc.
where M i is a chain with a length of i links; M* -- active center; M is a monomer molecule
According to the number of monomers involved in polymerization, there are homopolymerization(one monomer) and copolymerization(two or more monomers).
Depending on the chemical nature of the active centers involved in the formation of molecular chains (radical or ion), there are radical and ionic polymerization.
Radical polymerization
Radical polymerization always proceeds by a chain mechanism. The functions of active intermediates in radical polymerization are performed by free radicals. Common monomers that undergo radical polymerization include: ethylene, vinyl chloride, vinyl acetate, vinylidene chloride, tetrafluoroethylene, acrylonitrile, methacrylonitrile, methyl acrylate, methyl methacrylate, styrene, butadiene, chloroprene, and other monomers. Radical polymerization usually involves several elementary chemical steps: initiation, chain growth, chain termination, and: chain transfer. Mandatory stages are chain initiation and growth.
Initiation. Initiation consists in the creation of free radicals in the reaction system capable of starting reaction chains. The most common method of initiating polymerization is based on carrying out thermal homolytic decomposition of unstable substances in the monomer medium - initiators. Various types of peroxides are widely used as initiators: dialkyl peroxides (peroxide di- tert-butyl), hydroperoxides (cumyl hydroperoxide), perethers ( tert-butylperbenzoate), acyl peroxide (benzoyl peroxide), etc. Peroxides, for example, when heated, decompose according to the polymerization scheme monomer styrene copolymer
In addition to peroxides, azo compounds are widely used as initiators, of which 2,2"-azobisisobutyronitrile (AIBN) is the most widely used:
Radical polymerization initiators are usually not distinguished by their selective action with respect to various monomers, therefore the choice of the initiator is most often determined by the temperature at which the desired rate of free radical generation can be achieved in each particular case. So, AIBN is used at 50--70 ° C, benzoyl peroxide at 80--95 ° C, and peroxide tert-butyl at 120--140°C. The activation energy of initiation is usually close to the energy of the bond that breaks during the decay of the initiators. and ranges from 105 to 175 kJ/mol. The radical formed during the decay of the initiator molecule attaches to the double bond of the monomer and starts the reaction chain:
R * + CH 2 \u003d CHX R--CH 2 -CHX *
Redox systems can be used to initiate radical polymerization at room or low temperature. The oxidation-reduction reaction is carried out in a medium containing the monomer. Polymerization is caused by free radicals formed as reaction intermediates. You can pick up oxidizer-reductant pairs that are soluble in water (hydrogen peroxide - ferrous sulfate; sodium persulfate - sodium thiosulfate, etc.) or in organic solvents (organic peroxides - amines; organic peroxides - organic salts of ferrous iron, etc. .). Accordingly, radical polymerization can be initiated in both aqueous and organic media.
A typical example of a redox reaction in an aqueous medium is the interaction of hydrogen peroxide with ferrous ions:
Fe +2 + H 2 O 2 Fe +3 + OH - + HO *
The HO radical, when attached to the monomer molecule, initiates radical polymerization.
An example of a redox reaction that initiates radical polymerization in organic media is the interaction of benzoyl peroxide with methylaniline:
Photochemical initiation Radical polymerization is based on the formation of free radicals as a result of the homolytic breaking of chemical bonds when a quantum of initiating radiation is absorbed by a monomer or specially introduced photoinitiators or photosensitizers.
At radiation-chemical initiation Radical polymerization uses high-energy radiation (rays, fast electrons, particles, neutrons, etc.). The activation energy of photochemical and radiation-chemical initiation is close to zero. A feature of the last two methods of initiation is the ability to instantly turn on and off the irradiating radiation, which is important in some research work.
chain growth. Chain growth is carried out by successive addition of monomer molecules to radicals resulting from initiation, for example:
C 6 H 5 -C (O) -O-CH 2 -CHX * + CH 2 \u003d CHX
C 6 H 5 -C (O) -O-CH 2 -CHX-CH 2 -CHX *
C 6 H 5 -C (O) -O-CH 2 -CHX-CH 2 -CHX + CH 2 \u003d CHX *
C 6 H 5 -C (O) -O-CH 2 -CHX-CH 2 -CHX-CH 2 -CHX *
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .
C 6 H 5 -C (O) -O- (CH 2 -CHX) n -CH 2 -CHX * + CH 2 \u003d CHX
C 6 H 5 -C (O) -O- (CH 2 -CHX) n + 1 -CH 2 -CHX *, etc.
where k p is the chain growth rate constant.
The development of a kinetic chain is accompanied by the formation of a material chain. The activation energies of chain propagation reactions are in the range of 12–40 kJ/mol.
The rate constants and activation energy of chain growth primarily depend on the nature of the monomer. Solvents that are not prone to specific interaction with monomer molecules and growing radicals do not affect the reaction of radical polymerization growth.
An exact quantum-chemical calculation of the activation energies of the addition of radicals to the double bonds of monomers is difficult in most cases. However, the use of the semi-empirical Evans-Polyani-Semenov Rule, according to which the activation energy E a is related to the heat effect of an elementary reaction Q by the relation E a \u003d A - Q (where A and are constant values for similar series), allows you to. In many cases, evaluate E a and predict its change in a series of monomers of the same type.
The activation energy of the addition of a monomer to a radical is the lower, i.e., the more active the monomer, the higher the conjugation energy in the radical, which results from the addition of this monomer to the original radical. On the contrary, the activation energy of the addition of a radical to a double bond is the lower, i.e., the reactivity of the radical is the higher, the lower its conjugation energy. Thus, the reactivity in the series of monomers and their corresponding radicals change antibatically. For example, the reactivity in the series of vinyl monomers with substituents
C 6 H 5, -CH \u003d CH 2, -COCH 3, -CN, -COOR, CR, -OCOCH 3, -OR
decreases from left to right. The reactivity of the corresponding radicals decreases from right to left. Therefore, the higher the reactivity of the monomer, the higher the activation energy of the chain propagation reaction, i.e., the lower the rate of its radical polymerization.
In the above brief qualitative consideration, polar and spatial effects are not taken into account, which in a number of cases have a significant effect on the activation energies of radical processes. The theory that considers the reactivity of monomers and radicals only taking into account conjugation energies and does not take into account polar and spatial effects is called theory of ideal radical reactivity.
chain break. Reactions that limit kinetic and activation chains are called termination reactions. Termination leads to the disappearance of active radicals in the system or to their replacement by low-active radicals that are unable to attach monomer molecules. Chain termination during radical polymerization mainly occurs when two growing radicals interact as a result of their recombination:
~CH 2 -CHX* + ~CH 2 -CHX* ~CH 2 -CHX-CHX-CH 2 ~
or disproportionation:
~CH 2 -CHX* + ~CH 2 -CHX* ~CH 2 -CH 2 X + ~CH=CHX
The chain termination reaction includes translational diffusion of macroradicals with the formation of a combined coil, mutual approach of active terminal units due to segmental diffusion inside the combined coil, and direct chemical interaction of reaction centers with the formation of "dead" macromolecules.
The termination activation energy does not exceed 6 kJ/mol and is mainly determined by the activation energy of mutual diffusion of radicals.
Chain termination can occur at any length of the growing macroradical. Therefore, during polymerization, macromolecules of different lengths (different degree of polymerization). This explains the polymolecularity of synthetic polymers, which is described by the corresponding molecular weight distributions.
Chains can also be terminated during the interaction of radicals with inhibitors. Inhibitors can be used inactive stable free radicals, such as diphenylpicrylhydrazyl, N-oxide radicals, which themselves do not initiate polymerization, but recombine or disproportionate with growing radicals. Substances can also serve as inhibitors, the molecules of which, interacting with active radicals, saturate their free valences, and themselves turn into inactive radicals. The latter include quinones (for example, benzoquinone, duroquinone), aromatic di- and trinitro compounds (dinitrobenzene, trinitrobenzene), molecular oxygen, sulfur, etc. Inhibitors can also be compounds of metals of variable valence (salts of ferric iron, divalent copper, etc.) , which break growing chains due to redox reactions. Often, inhibitors are introduced into the monomer to prevent their premature polymerization. Therefore, before polymerization, each monomer must be thoroughly purified from impurities and the added inhibitor.
chain transfer. The limitation of material chains during polymerization can occur not only by termination reaction, but also as a result of chain transfer reactions, which are very characteristic of radical polymerization. When a chain is transferred, an atom or a group of atoms is detached from a molecule by a growing radical ( circuit transmitter). As a result, the radical is converted into a valence-saturated molecule and a new radical is formed that is capable of continuing the kinetic chain. Thus, during transfer reactions, the material chain breaks, but the kinetic chain does not.
The chain transfer can be carried out through the monomer molecules. For example, in the case of vinyl acetate
~R * + CH2 \u003d CH-OCOCH 3 ~RH + CH 2 \u003d CH-OCOCH 2 *
where k M is the rate constant of chain transfer to the monomer.
In this case, the growing radical, instead of joining at the double bond of the vinyl acetate molecule, can tear off one of the hydrogen atoms of the acetyl group, saturating its free valency and converting the monomer molecule into an active radical. The latter can react with another monomer molecule, starting the growth of a new macromolecule:
CH2 \u003d CH-OSOCH 2 * + CH 2 \u003d CH-OCOCH 3 CH 2 \u003d CH-OCOCH 2 -CH 2 -CH * -OCOCH 3
The ability of monomer molecules to participate in the chain transfer reaction is usually characterized by self-transfer constant C M equal to the ratio of the chain transfer rate constant to the monomer. (k M) to the chain growth rate constant (k P), i.e. C M = k M /k P . For most vinyl monomers that do not contain mobile groups or atoms, k M< In the presence of a solvent, solvent molecules can play the role of a chain transfer agent, for example, in the case of toluene ~ CH 2 -CHX * + C 6 H 5 CH 3 ~ CH 2 -CH 2 X + C 6 H 5 CH 2 * where k S is the rate constant of the circuit. The interaction of the growing radical with the chain transfer molecule leads to the cessation of the growth of this material chain, i.e., reduces the molecular weight of the resulting polymer. The ability of solvents to participate in chain transfer during radical polymerization of a given monomer is characterized by the transfer constant C S = k S /k P (Table 1). Chain transfer reactions are widely used in the synthesis of polymers to control their molecular weights. To reduce the molecular weight of the synthesized polymer, transmitters with values of C S > 10 -3 are usually used, which are called regulators, for example ~CH 2 --CHX + CC1 4 ~CH 2 --CHXCI + CC1 3 * Table 1. Chain transfer constants in the radical polymerization of styrene at 60°C. Kinetics of radical polymerization. The rate of initiation in the presence of initiators that decompose upon heating under conditions under which decomposition occurs by a non-chain mechanism can be expressed by the equation V in = k in [I] (1.1) where [I] is the concentration of the initiator; k in -- rate constant of initiation. The chain growth rate is expressed by the equation where k ip is the rate constant of the addition of the monomer to the radical with the degree of polymerization n = i; -- concentration of radicals with degree of polymerization i; [M] -- monomer concentration. In the formation of polymers of high molecular weight, with a good approximation, it can be assumed that k p does not depend on the degree of polymerization of the radical (practically, starting from the degree of polymerization n = 3-4). Then the expression for v p is simplified: where is the concentration of all growing radicals. The rate of disappearance of radicals as a result of recombination and disproportionation is described by the equation D[R]/dt = k 0 [R] 2 where k 0 is the termination rate constant (assuming that the reactivity of radicals in termination reactions does not depend on their degree of polymerization). The total polymerization rate, equal to the rate of disappearance of the monomer in the system, provided that the degree of polymerization of the resulting polymer is sufficiently high and the monomer is consumed only for polymerization, is identical to the chain growth rate, i.e. D[M]/dt v p = k p [R][M] (1.2) If there is no inhibitor in the system, active radicals disappear as a result of their recombination or disproportionation. In this case, the change in the concentration of radicals is described by the equation D[R]/dt = v in - k 0 [R] 2 The concentration of radicals [R], which is difficult to measure by direct experiments, can be excluded from equation (1.2), assuming that the rate of formation of radicals is equal to the rate of their disappearance ( quasi-stationarity condition), i.e., d[R]/dt = 0. In the case of radical polymerization, this condition is usually practically satisfied within a few seconds after the start of the reaction. That's why v in \u003d k 0 [R] 2 [R] = (v in / k 0) 1/2 And -d[M]/dt = k p (v in / k 0) 1/2 [M] (1.3) Thus, the rate of radical polymerization is of the first order in terms of monomer concentration and of the order of 0.5 in terms of initiator concentration, which, as a rule, is observed experimentally. Degree of polymerization. From the kinetic data, the degree of polymerization P n of the resulting polymer can be calculated. It is equal to the ratio of the number of monomer molecules included in the composition of polymer chains during polymerization to the number of formed material chains. If polymerization proceeds under conditions of quasi-stationarity in the absence of an inhibitor, then at a sufficiently small depth of transformation, when there is still little polymer in the system and, therefore, the rate of chain transfer to the polymer and the consumption of the monomer can be neglected P n \u003d v p / v 0 + v lane (1.4) where v 0 is the rate of bimolecular chain termination; v lane \u003d (k M [M] + k S [S] x [R] - the sum of the chain transfer rates to the monomer and solvent. When two radicals recombine, one material chain is formed, i.e., the average doubling of Р n occurs, therefore, in the denominator of equation (1.4), before the term corresponding to termination by recombination, it is necessary to put the factor S. In addition, assuming that the proportion of polymer radicals terminating by the disproportionation mechanism is equal, and the proportion of radicals dying during recombination is equal to 1-, the equation for P n takes the form Then for the reciprocal of P n , we get: Expressing the radical concentration in terms of the polymerization rate v p = k P [R] [M] and using the constants C M and C S , we finally get: The resulting equation relates the number average degree of polymerization to the reaction rate, chain transfer constants, and monomer and transfer agent concentrations. From equation (1.5) it follows that the maximum number average degree of polymerization of the resulting polymer, achievable at a given temperature, in the absence of other transfer agents, is determined by the reaction of chain transfer to the monomer, i.e. P n max C M -1. The equations derived above are valid for radical polymerization at low degrees of monomer-to-polymer conversion (not exceeding 10%). At large conversion depths, deviations are observed associated with an increase in the viscosity of the reaction medium with an increase in the concentration of the polymer dissolved in it, which slows down the diffusion of macroradicals and sharply reduces the likelihood of their recombination or disproportionation. As a result, the effective termination rate constant decreases significantly. The concentration of radicals in the system increases, and the rate of polymerization increases. This phenomenon is called gel effect. If a polymer is formed during radical polymerization that is insoluble or swells to a limited extent in the reaction medium, then the effects associated with diffusion inhibition of the bimolecular termination reaction appear already starting from very small transformation depths. Institute of High Technology Physics KINETICS OF RADICAL POLYMERIZATION OF STYRENE Performer ____________ ___________ student gr.4GM12 Head ____________ ___________ L.I. Bondaletova Tomsk - 2011 Theoretical part
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). AT 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. AT 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. 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. AT this equation includes the concentration of the radical, which is very difficult to determine. AT 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 inhabitant; 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.
Ministry of Education and Science of the Russian Federation
Federal State Budgetary Educational Institution
higher professional education
"NATIONAL RESEARCH
TOMSK POLYTECHNICAL UNIVERSITY»
sch
Direction - Chemical technology
Department - Technologies of organic substances and polymeric materials
Lab Report
in the discipline "Innovative development of chemical technology"
(signature) (date) Maksyakova A.V.
(signature) (date)
Objective: determine the rate of radical polymerization of styrene at various concentrations of the initiator and evaluate the order of the reaction according to the initiator.
Reagents: styrene, azo-bis-isobutyric acid dinitrile, petroleum ether or hexane.
Cutlery and utensils: refractometer, thermostats for 20 and 70 0 C, test tubes with ground stoppers with a capacity of 20 ... watch glass.
Polymers can be synthesized either from low molecular weight compounds (monomers) or from high molecular weight compounds (polymers).
An example of a reaction for the synthesis of polymers from low molecular weight compounds is chain polymerization and stepwise polycondensation. During the polymerization of monomers, macromolecules are formed as a result of the opening of unsaturated bonds in alkenes or the breaking of chemical bonds in cyclic compounds. In both cases, the chemical backbone of the monomer and the repeating unit is the same.
In the process of stepwise polycondensation, bi- and polyfunctional compounds react with each other. The reaction proceeds stepwise with a gradual increase in the molecular weight of the polymer.
Polymerization is understood as a chain reaction, during which monomer molecules are sequentially attached to the active center located at the end of the growing chain.
Depending on the nature of the active center, ionic and radical polymerizations are distinguished. The general scheme of polymerization, regardless of the nature of the active sites, can be represented as follows:
Polymerization is caused by primary active centers formed from specially introduced compounds: initiators in radical polymerization and catalysts in ionic polymerization, or as a result of physical action on the system, for example, by irradiating the monomer.
Radical polymerization is a chain reaction that proceeds through the formation of free radicals.
The reaction is one of the main reactions for obtaining macromolecular compounds.
In the simplest case, the scheme of radical polymerization includes three stages, which correspond to the following elementary reactions: initiation, chain growth, and chain termination. In the case of chemical initiation, this scheme can be represented as follows.
where Kras, Kin, Kr, Krek, Kdis are the rate constants for the decomposition of the initiator (In), polymerization initiation, chain growth and termination by recombination and disproportionation, respectively.
The course of radical polymerization depends on the presence of even an insignificant amount of impurities in the system, and sometimes on the material of the reactor and its shape. Impurities can react with the growing macromolecule, stopping or slowing down the polymerization process.
Initiation of radical polymerization
is the process of formation of free-radical centers R . Due to the presence of unpaired electrons in outer orbits, they are characterized by electrophilic properties, the ability to attack electron pairs - and even - bonds of the monomer and convert it into a free radical:
Free radicals can result from the action on systems physical factors: as a result of thermal exposure (thermal initiation), under the action of light (photoinitiation), radioactive irradiation (radiation initiation), as well as purely chemical means - during the homolytic decomposition of compounds with relatively low binding energies or as a result of redox processes.
In industrial conditions, the most commonly used method is chemical initiation, in which substances (initiators) are used that easily decompose with the formation of free radicals. These include peroxides, hydroperoxides, azo and diazo compounds, and redox systems.
The initiation process is characterized by two successive reactions: the decomposition of the initiator (In) with the formation of free radicals R and the interaction of the radical with the monomer (M) with the formation of an active center of the free radical type RM . The limiting reaction is the stage of decomposition of the initiator.
The rate of initiation can be described by the formula:
,
where is the initiator concentration.
The radicals formed during the decay of the initiators can recombine in the short period of time when they are in the "cage" formed by the molecules of the monomer and the solvent, i.e. did not have time to disperse. This effect is called cell effect or primary recombination.
chain growth
in radical polymerization, it consists in the sequential attachment of monomer molecules to the active center (primary radical), which continues until the growing chain retains the properties of a free radical. The rate of the polymer chain growth reaction depends on the reactivity of the monomer and the activity of the growing polymer radical and is determined by the expression:
V p = K p [M].
The value of Kp for most monomers is 10 2 ... 10 4 l/(mol?s).
The chain termination reaction proceeds in different ways, depending on the nature of the macroradical, its size and structure, the viscosity of the medium, the temperature, the composition of the reaction medium, and so on.
Most often, the 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, from a certain 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 chain termination rate. 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 steady state is established, the rate of chain initiation will be equal to the rate of chain termination:
V in \u003d V about.
Therefore, K in \u003d K 0 2.
From this equation we find the concentration of macroradicals
The reaction rate (V p) in the stationary state is equal to the chain growth rate (V p):
Substituting the expression into the chain growth rate equation, we obtain:
The most important rule follows from the resulting equation, which 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. In ionic processes, this rule is not respected.
The rate of polymerization is proportional to the square root of the initiator concentration (the "square root rule").
It should be noted that proportionality of the polymerization rate to the monomer concentration in the first degree 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 the chain transfer reaction.
The polymerization rate can be estimated by determining the change in any system parameter: density, refractive index, viscosity, light absorption, heat release, etc. The conversion can be controlled by chemical methods by the number of unreacted double bonds by iodometric or brommetric titration, etc.
With an increase in temperature, the rate of polymerization increases, and the molecular weight of the polymer decreases. Pressure generally increases the rate and degree of polymerization. Thus, an increase in pressure by a factor of 1000 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 an increase in the monomer concentration, the rate of polymerization increases and the average degree of polymerization increases.
experimental part
Operating procedure:
1) conducting radical polymerization of styrene at various concentrations of the initiator;
2) determination of the polymer yield in samples of the reaction mixture by the refractometric method;
3) construction of polymerization kinetic curves, determination of the process rate and evaluation of the reaction order with respect to the initiator.
Method of work
Place 5 g of styrene into test tubes with ground stoppers. Then they make a sample of the initiator, weighed on the watch glass to within the fourth decimal place, in the amount of 0.2; 0.4; 0.6; 0.8 and 1.0% (by weight of the monomer). The prepared solutions are thermostated at 70 °C. 10 minutes after the start of thermostating, samples of the reaction mixture are taken from each test tube using a syringe with a long needle to determine the yield of the polymer by the refractometric method. Subsequent samples are taken from the test tubes every 10 minutes. The refractometric method for determining the polymer yield 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 in table 1.
Table 1. Initial and experimental data
2. 3. 5. Kinetics of radical polymerization
