UDC 541.64:547.32:547.371
RADICAL COPOLYMERIZATION OF STYRENE AND UNSATURATED GLYCIDIL ETHERS
M.A. Chernigovskaya, T.V. Raskulov
Angarsk State Technical Academy,
665835, Irkutsk region, Angarsk, st. Tchaikovsky, 60, [email protected]
Binary radical copolymerization of unsaturated glycidyl ethers (alli-glycidyl ether, vinyl glycidyl ether of ethylene glycol) with styrene in toluene was studied. The copolymerization constants and microstructure of the resulting copolymers were calculated. It has been established that the composition of the copolymers depends on the structure of the unsaturated glycidyl ether. Allyl glycidyl ether copolymers, regardless of the composition of the initial monomer mixture, are close in structure to alternating ones. When copolymerizing styrene with vinyl glycidyl ether of ethylene glycol, the latter is characterized by lower reactivity. Il. 2. Table. 3. Bibliography 14 titles
Key words: radical copolymerization; styrene; allyl glycidyl ether; vinyl glycidyl ether of ethylene glycol.
RADICAL COPOLYMERIZATION OF STYRENE AND UNSATURATED GLYCIDYL ETHERS
M.A. Chernigovskaya, T.V. Raskulova
Angarsk State Technical Academy,
60, Chaikovskogo St., 665835, Angarsk, Irkutsk Region, 665835 Russia, [email protected]
The radical copolymerization of styrene and unsaturated glycidyl ethers (allyl glycidyl ether, ethylene glycol vinyl glycidyl ether) was examined in toluene solution. The reactivity ratios and parameters of copolymer microstructure were calculated. It was found that copolymer composition depends on unsaturated glycidyl ethers structure. Copolymers of styrene and allyl-glycidyl ether have alternative structure. Ethylene glycol vinyl glycidyl ether has less reactivity than styrene in copolymerization. 2 figures. 3 tables. 14 sources.
Key words: radical copolymerization; styrene; allyl glycidyl ether; ethylene glycol vinyl glycidyl ether. INTRODUCTION
One of the promising directions is the synthesis of copolymers with active functional chemistry of high-molecular compounds being groups. As monomers
For such syntheses, epoxy compounds and, in particular, unsaturated glycidyl ethers (UGEs) are of increasing interest. Copolymers containing NGE units are of interest for theoretical studies, since the simultaneous presence of an oxirane ring and oxygen atoms in the side chain in the composition of NGE makes it possible to exhibit complex formation effects.
On the other hand, such polymers provide the broadest opportunity for directed modification by carrying out polymer-analogous reactions along oxirane rings and, therefore, open the way to the production of materials, including composites, with a predetermined valuable set of properties.
The range of NGEs used in radical copolymerization reactions is quite wide, but the most studied at present are methacrylic acid derivatives (for example, glycidyl methacrylate), allyl glycidyl ether (AGE), as well as vinyl glycidyl ethers of glycols (for example, vinyl glycidyl ether ethylene glycol (EGE)). AGE and VGE seem to be the most interesting as modifiers for industrial polymers, since due to their low reactivity they should be included in the polymers in limited quantities, without changing the overall set of properties of the base polymer.
The traditional areas of use of these compounds in copolymerization processes are discussed in detail in the works. Recently, epoxy-containing copolymers are increasingly used for the production of various nanomaterials and nanocompositions [for example, 5,6], as well as functional polymer composite materials. Therefore, the study of copolymerization processes of NGE, including AGE and VGE, with basic industrial monomers is of undoubted scientific interest.
The purpose of this work was to study the binary radical copolymerization of styrene (St) with AGE and VGE.
EXPERIMENTAL PART
For the synthesis of copolymers, we used commercial St produced by OJSC AZP (purity
99.8%) with constants: p = 0.906 g/ml, 1kip = = 145 °C, AGE (product of the company "AShsI") with constants: p = 0.962 g/ml, ^ip = 154 °C, n20 = = 1, 4330, and VGE, obtained at the Institute of Chemical Chemistry SB RAS, purified to chromatographic purity
99.9% with the following constants: p = 1.038
g/ml, ^ip = 204 °C, = 1.4310.
Copolymerization was carried out in a toluene solution at a temperature of 60°C and a tenfold excess of solvent. Azo-bis-isobutyric acid dinitrile was used as an initiator in an amount of 1 wt%. The resulting copolymers were isolated by precipitation with isobutanol, purified by reprecipitation with isobutanol from acetone, and dried to constant weight.
The composition of the resulting products was determined according to elemental analysis (C, H), functional analysis (content of epoxy groups) and IR spectroscopy. The content of epoxy groups in the copolymers was determined by back titration with hydrochloric acid according to. Relative viscosity was determined for 1% solutions in cyclohexanone at 25 °C.
THE DISCUSSION OF THE RESULTS
Depending on the composition of the initial mixture, the resulting copolymers are solid powdery or amorphous substances of white color, highly soluble in polar solvents.
The fact that copolymerization occurs in the systems studied was confirmed using turbidimetric titration data. For example, in the turbidimetric titration curves of St - VGE copolymers (Fig. 1), one inflection is observed, which indicates the formation of copolymers, and not a mixture of two homopolymers. A similar picture is observed for St-AGE copolymers.
In the IR spectra of NGE, an absorption band is observed in the region of 1620-1650 cm-1, characteristic of a double bond. The presence of an oxirane ring is confirmed by the presence of absorption bands in the spectrum in the following regions: 765 and 915 cm-1, related to asymmetric stretching vibrations of the epoxy ring; 1230 cm-1, related to symmetrical stretching vibrations of the epoxy ring; 3060 cm-1, corresponding to vibrations of the methylene group in the epoxy ring.
In the IR spectra of the copolymer, there are no absorption bands characteristic of a double bond, which confirms that the copolymerization process occurs along the vinyl or allylic groups. In the absorption regions characteristic of the oxirane ring and alkyl groups, the spectra of the copolymers are identical to the spectra of the original NGE.
Experimental data obtained as a result of studying copolymerization processes in the St - VGE and St - AGE systems are presented in table. 1.
It was assumed that the studied NGE
O 0.2 0.4 0.6 0.8 1.0
Precipitator volume, ml
Rice. 1. Dependence of the optical density of solutions of St - VGE copolymers on the volume of added precipitant (methanol). Content of VGE in the initial mixture (% mol.): 1 - 10; 2 - 25; 3 - 50
Table 1
General principles of copolymerization of St - NGE in toluene solution _(DAK1 wt.%, 60°C, 2 h)__
No. Composition of the initial mixture, % mol. Composition of the copolymer, % mol. Exit, %
St OGE St NGE
System St - AGE
1 95 5 36,36 63,64 3,7
2 90 10 55,14 44,86 12,6
3 70 30 47,16 52,84 32,4
4 50 50 92,32 7,68 20,2
5 30 70 46,73 53,27 19,8
6 10 90 60,13 39,87 19,3
System St - VGE
1 90 10 91,98 8,02 68,5
2 75 25 79,93 20,07 56,7
3 50 50 67,95 32,05 46,2
4 25 75 55,08 44,92 38,1
5 10 90 46,45 53,55 32,5
have lower reactivity in radical copolymerization than Art. This picture is indeed observed for St–VGE copolymers. They are enriched with St units throughout the studied range of initial mixtures, while the content of VGE units in the composition of the copolymers increases symbatically with its amount in the monomer mixture (Table 1).
For copolymers St - AGE observed
different picture. For any composition of the initial monomer mixture, the content of St and AGE units in the copolymers is almost the same and ranges from 40 to 64 mol.%, which indicates the formation of products close to alternating (Table 1).
As an analysis of literature data shows, AGE is characterized by processes of alternating copolymerization with quite
table 2
General principles of copolymerization of VX - NGE in toluene solution
(DAK 1% wt., 60 °C, 2 h)
Composition of the initial mixture, % mol. Composition of the copolymer, % mol. Yield, % Viscosity [G|], dl/g
VKh NGE VKH NGE
VX - AGE system
95,0 5,0 96,79 3,21 3,19 0,20
90,0 10,0 93,92 6,08 2,88 0,15
85,0 15,0 87,92 10,58 2,56 0,08
73,7 26,3 76,19 23,81 2,69 0,04
30,1 69,9 44,69 55,31 2,48 0,04
VX - VGE system
95,0 5,0 95,55 4,45 3,78 0,29
90,0 10,0 92,44 7,56 3,45 0,26
80,0 20,0 88,44 11,56 3,01 0,22
75,0 25,0 78,79 21,21 2,91 0,17
25,0 75,0 36,62 63,38 2,23 0,13
a wide range of monomers [for example, 11, 12]. This is explained by the formation of charge transfer complexes between AGE and the second comonomer, in which AGE plays the role of a donor. However, a study of the binary radical copolymerization of AGE with VC, carried out by the authors, did not reveal the formation of alternating copolymers (Table 2).
The formation of alternating copolymers during the copolymerization of AGE with St can be associated with the formation of charge transfer complexes between the epoxy group of AGE and the aromatic ring of styrene. The resulting complex then plays the role of an “individual monomer” in copolymerization, which leads to the production of products of alternating structure.
Product yields are generally decreasing
with an increase in the content of low-active monomer units in the composition of copolymers (Table 1), which is due to an increase in the concentration of NGE in the initial mixture of comonomers. Increasing the concentration of a low-active monomer increases its content in the copolymer, but reduces the total rate of chain growth and, consequently, reduces the yield of the product and its molecular weight. This reasoning is confirmed by the values of the relative viscosity of copolymer solutions (for example, St-AGE) and their dependence on the content of esters in the initial mixture (Fig. 2).
The calculation of the relative activity constants of monomers (copolymerization constants) for the studied systems was carried out using different methods. System copolymerization constants
Rice. 2 Dependence of the relative viscosity of St-AGE copolymers on the AGE content in the initial mixture
Table 3
Copolymerization constants and average block lengths of St ^^ _and NGE ^2) units in copolymers_
System M1 m1 r Li L2
System St - AGE 0.70 0.47 r1 = 0.09 1 1
0.50 0.92 r2 = 0.05 21 1
0.75 0.20 n1 = 1.13 ± 0.09 n2 = 0.22 ± 0.02 10 1
System St - VGE 0.50 0.32 9 1
St - AGE was calculated based on functional analysis data using the nonlinear least squares method in the MathCAD 11 Enterprise Edition package, which allows calculations to be carried out using any sets of experimental data. The copolymerization constants for the St-VGE system were calculated using the standard Fineman-Ross and Kelen-Tudos methods using the Mortimer and Tidwell experimental design method. The values of copolymerization constants are presented in table. 3. Based on the values of the copolymerization constants, the parameters of the microstructure of the copolymers were determined, which are also given in Table. 3.
The obtained values of the copolymerization constants confirm the previously made conclusion about the different reactivity of NGE in the processes of copolymerization with St. For the St - AGE system, the values of the calculated copolymerization constants are close to zero, which is typical for alternating copolymers. Calculation of the microstructure of these copolymers showed that, regardless of the composition of the initial mixture, almost strictly alternating products are obtained (Table 3).
The values of the relative activity constants for St - VGE copolymers indicate a lower reactivity of VGE in radical copolymerization compared to St. VGE is present in the data structure of the co-
polymers only in the form of single units, and the length of blocks of St units in copolymers naturally decreases with a decrease in the proportion of St in the original mixture.
Thus, the structure of the copolymers St and NGE can apparently be reflected by the following formula:
- // ZHPH. 1998 T. 71, No. 7. P. 1184-1188.
2. Vinyl glycidyl ethers of glycols - promising monomers for polymerization processes / L.S. Grigorieva [and others]. L.: Publishing house LTI, 1982. 9 p.
3. Raskulova T.V. Copolymerization of vinyl halides with functionally substituted vinyl monomers: dissertation... Dr. Chemistry. Sciences: 02.00.06: protected 04/21/2010: approved. 08.10.2010. Irkutsk, 2010. 315 p.
4. Pokrovskaya M.A., Raskulova T.V. Copolymerization of allyl glycidyl ether with styrene // AGTA Bulletin. 2011. No. 5. P. 87-89.
5. Surface functionalization of Si3N4 nanoparticles by graft polymerization of glycidyl methacrylate and styrene / Luo Ying // J. Appl. Polym. sci. 2006. V. 102. No. 2. P. 992.
6. Tan Chung-Sung, Kuo Ting-Wu. Synthesis of polycarbonate-silica nanocomposites from copolymerization of CO2 with allyl glycidyl ether, cyclohexene oxide, and sol-gel // J. Appl. Polym. sci. 2005. V. 98. No. 2. P. 750.
7. Formation of composites based on vinyl glycidyl ether of ethylene glycol and vinyl chloride / O.V. Lebedeva [and others] // Plastic masses. 2013. No. 9. pp. 35-39.
8. Kalinina M.S. Analysis of condensation polymers. M.: Nauka, 1983. 296 p.
9. Practical guide to determining molecular weights and molecular weight distribution of polymers / A.I. Shatenshtein [and others]. M.: Khimiya, 1964. 188 p.
10. Fractionation of polymers / ed. M. Kantova. M.: Mir, 1971. 444 p.
11. Heatley F., Lovell P.A., McDonald J. NMR studies of free-radical polymerization and copolymerization of monomers and polymers containing allyl groups // Eur. Polym. J. 2. 1993. V. 29, No. 2. R. 255.
12. Yu Qing-bo, Bai Ru-ke, Zhang Ming-Hi. Living radical copolymerization of allyl glycidyl ether with methyl acrylate in the presence of benzylimidazole-1-carbodithionate // Anhui ligong daxue xuebao. Ziran kexue ban; J. Anhui Univ. sci. and Technol. Natur. sci. 2006. V. 26, No. 3. P. 56.
13. Effect of the penultimate link in the copolymerization of vinyl chloride and unsaturated glycidyl ethers / T.V. Raskulova [et al.] // High-molecular compounds A. 2000. T. 42, No. 5. P. 744-750.
14. Tidwell P.W., Mortimer G.A. An Improved Method of Calculating Copolymerization Reactivity Ratios // J. Polym. sci. A. 1965. V. 3. P. 369.
UDC 541.64:547.32:547.371
RADICAL COPOLYMERIZATION OF STYRENE AND UNSATURATED GLYCIDIL ETHERS
M.A. Chernigovskaya, T.V. Raskulov
Angarsk State Technical Academy,
665835, Irkutsk region, Angarsk, st. Tchaikovsky, 60, [email protected]
Binary radical copolymerization of unsaturated glycidyl ethers (alli-glycidyl ether, vinyl glycidyl ether of ethylene glycol) with styrene in toluene was studied. The copolymerization constants and microstructure of the resulting copolymers were calculated. It has been established that the composition of the copolymers depends on the structure of the unsaturated glycidyl ether. Allyl glycidyl ether copolymers, regardless of the composition of the initial monomer mixture, are close in structure to alternating ones. When copolymerizing styrene with vinyl glycidyl ether of ethylene glycol, the latter is characterized by lower reactivity. Il. 2. Table. 3. Bibliography 14 titles
Key words: radical copolymerization; styrene; allyl glycidyl ether; vinyl glycidyl ether of ethylene glycol.
RADICAL COPOLYMERIZATION OF STYRENE AND UNSATURATED GLYCIDYL ETHERS
M.A. Chernigovskaya, T.V. Raskulova
Angarsk State Technical Academy,
60, Chaikovskogo St., 665835, Angarsk, Irkutsk Region, 665835 Russia, [email protected]
The radical copolymerization of styrene and unsaturated glycidyl ethers (allyl glycidyl ether, ethylene glycol vinyl glycidyl ether) was examined in toluene solution. The reactivity ratios and parameters of copolymer microstructure were calculated. It was found that copolymer composition depends on unsaturated glycidyl ethers structure. Copolymers of styrene and allyl-glycidyl ether have alternative structure. Ethylene glycol vinyl glycidyl ether has less reactivity than styrene in copolymerization. 2 figures. 3 tables. 14 sources.
Key words: radical copolymerization; styrene; allyl glycidyl ether; ethylene glycol vinyl glycidyl ether. INTRODUCTION
One of the promising directions is the synthesis of copolymers with active functional chemistry of high-molecular compounds being groups. As monomers
For such syntheses, epoxy compounds and, in particular, unsaturated glycidyl ethers (UGEs) are of increasing interest. Copolymers containing NGE units are of interest for theoretical studies, since the simultaneous presence of an oxirane ring and oxygen atoms in the side chain in the composition of NGE makes it possible to exhibit complex formation effects.
On the other hand, such polymers provide the broadest opportunity for directed modification by carrying out polymer-analogous reactions along oxirane rings and, therefore, open the way to the production of materials, including composites, with a predetermined valuable set of properties.
The range of NGEs used in radical copolymerization reactions is quite wide, but the most studied at present are methacrylic acid derivatives (for example, glycidyl methacrylate), allyl glycidyl ether (AGE), as well as vinyl glycidyl ethers of glycols (for example, vinyl glycidyl ether ethylene glycol (EGE)). AGE and VGE seem to be the most interesting as modifiers for industrial polymers, since due to their low reactivity they should be included in the polymers in limited quantities, without changing the overall set of properties of the base polymer.
The traditional areas of use of these compounds in copolymerization processes are discussed in detail in the works. Recently, epoxy-containing copolymers are increasingly used for the production of various nanomaterials and nanocompositions [for example, 5,6], as well as functional polymer composite materials. Therefore, the study of copolymerization processes of NGE, including AGE and VGE, with basic industrial monomers is of undoubted scientific interest.
The purpose of this work was to study the binary radical copolymerization of styrene (St) with AGE and VGE.
EXPERIMENTAL PART
For the synthesis of copolymers, we used commercial St produced by OJSC AZP (purity
99.8%) with constants: p = 0.906 g/ml, 1kip = = 145 °C, AGE (product of the company "AShsI") with constants: p = 0.962 g/ml, ^ip = 154 °C, n20 = = 1, 4330, and VGE, obtained at the Institute of Chemical Chemistry SB RAS, purified to chromatographic purity
99.9% with the following constants: p = 1.038
g/ml, ^ip = 204 °C, = 1.4310.
Copolymerization was carried out in a toluene solution at a temperature of 60°C and a tenfold excess of solvent. Azo-bis-isobutyric acid dinitrile was used as an initiator in an amount of 1 wt%. The resulting copolymers were isolated by precipitation with isobutanol, purified by reprecipitation with isobutanol from acetone, and dried to constant weight.
The composition of the resulting products was determined according to elemental analysis (C, H), functional analysis (content of epoxy groups) and IR spectroscopy. The content of epoxy groups in the copolymers was determined by back titration with hydrochloric acid according to. Relative viscosity was determined for 1% solutions in cyclohexanone at 25 °C.
THE DISCUSSION OF THE RESULTS
Depending on the composition of the initial mixture, the resulting copolymers are solid powdery or amorphous substances of white color, highly soluble in polar solvents.
The fact that copolymerization occurs in the systems studied was confirmed using turbidimetric titration data. For example, in the turbidimetric titration curves of St - VGE copolymers (Fig. 1), one inflection is observed, which indicates the formation of copolymers, and not a mixture of two homopolymers. A similar picture is observed for St-AGE copolymers.
In the IR spectra of NGE, an absorption band is observed in the region of 1620-1650 cm-1, characteristic of a double bond. The presence of an oxirane ring is confirmed by the presence of absorption bands in the spectrum in the following regions: 765 and 915 cm-1, related to asymmetric stretching vibrations of the epoxy ring; 1230 cm-1, related to symmetrical stretching vibrations of the epoxy ring; 3060 cm-1, corresponding to vibrations of the methylene group in the epoxy ring.
In the IR spectra of the copolymer, there are no absorption bands characteristic of a double bond, which confirms that the copolymerization process occurs along the vinyl or allylic groups. In the absorption regions characteristic of the oxirane ring and alkyl groups, the spectra of the copolymers are identical to the spectra of the original NGE.
Experimental data obtained as a result of studying copolymerization processes in the St - VGE and St - AGE systems are presented in table. 1.
It was assumed that the studied NGE
O 0.2 0.4 0.6 0.8 1.0
Precipitator volume, ml
Rice. 1. Dependence of the optical density of solutions of St - VGE copolymers on the volume of added precipitant (methanol). Content of VGE in the initial mixture (% mol.): 1 - 10; 2 - 25; 3 - 50
Table 1
General principles of copolymerization of St - NGE in toluene solution _(DAK1 wt.%, 60°C, 2 h)__
No. Composition of the initial mixture, % mol. Composition of the copolymer, % mol. Exit, %
St OGE St NGE
System St - AGE
1 95 5 36,36 63,64 3,7
2 90 10 55,14 44,86 12,6
3 70 30 47,16 52,84 32,4
4 50 50 92,32 7,68 20,2
5 30 70 46,73 53,27 19,8
6 10 90 60,13 39,87 19,3
System St - VGE
1 90 10 91,98 8,02 68,5
2 75 25 79,93 20,07 56,7
3 50 50 67,95 32,05 46,2
4 25 75 55,08 44,92 38,1
5 10 90 46,45 53,55 32,5
have lower reactivity in radical copolymerization than Art. This picture is indeed observed for St–VGE copolymers. They are enriched with St units throughout the studied range of initial mixtures, while the content of VGE units in the composition of the copolymers increases symbatically with its amount in the monomer mixture (Table 1).
For copolymers St - AGE observed
different picture. For any composition of the initial monomer mixture, the content of St and AGE units in the copolymers is almost the same and ranges from 40 to 64 mol.%, which indicates the formation of products close to alternating (Table 1).
As an analysis of literature data shows, AGE is characterized by processes of alternating copolymerization with quite
table 2
General principles of copolymerization of VX - NGE in toluene solution
(DAK 1% wt., 60 °C, 2 h)
Composition of the initial mixture, % mol. Composition of the copolymer, % mol. Yield, % Viscosity [G|], dl/g
VKh NGE VKH NGE
VX - AGE system
95,0 5,0 96,79 3,21 3,19 0,20
90,0 10,0 93,92 6,08 2,88 0,15
85,0 15,0 87,92 10,58 2,56 0,08
73,7 26,3 76,19 23,81 2,69 0,04
30,1 69,9 44,69 55,31 2,48 0,04
VX - VGE system
95,0 5,0 95,55 4,45 3,78 0,29
90,0 10,0 92,44 7,56 3,45 0,26
80,0 20,0 88,44 11,56 3,01 0,22
75,0 25,0 78,79 21,21 2,91 0,17
25,0 75,0 36,62 63,38 2,23 0,13
a wide range of monomers [for example, 11, 12]. This is explained by the formation of charge transfer complexes between AGE and the second comonomer, in which AGE plays the role of a donor. However, a study of the binary radical copolymerization of AGE with VC, carried out by the authors, did not reveal the formation of alternating copolymers (Table 2).
The formation of alternating copolymers during the copolymerization of AGE with St can be associated with the formation of charge transfer complexes between the epoxy group of AGE and the aromatic ring of styrene. The resulting complex then plays the role of an “individual monomer” in copolymerization, which leads to the production of products of alternating structure.
Product yields are generally decreasing
with an increase in the content of low-active monomer units in the composition of copolymers (Table 1), which is due to an increase in the concentration of NGE in the initial mixture of comonomers. Increasing the concentration of a low-active monomer increases its content in the copolymer, but reduces the total rate of chain growth and, consequently, reduces the yield of the product and its molecular weight. This reasoning is confirmed by the values of the relative viscosity of copolymer solutions (for example, St-AGE) and their dependence on the content of esters in the initial mixture (Fig. 2).
The calculation of the relative activity constants of monomers (copolymerization constants) for the studied systems was carried out using different methods. System copolymerization constants
Rice. 2 Dependence of the relative viscosity of St-AGE copolymers on the AGE content in the initial mixture
Table 3
Copolymerization constants and average block lengths of St ^^ _and NGE ^2) units in copolymers_
System M1 m1 r Li L2
System St - AGE 0.70 0.47 r1 = 0.09 1 1
0.50 0.92 r2 = 0.05 21 1
0.75 0.20 n1 = 1.13 ± 0.09 n2 = 0.22 ± 0.02 10 1
System St - VGE 0.50 0.32 9 1
St - AGE was calculated based on functional analysis data using the nonlinear least squares method in the MathCAD 11 Enterprise Edition package, which allows calculations to be carried out using any sets of experimental data. The copolymerization constants for the St-VGE system were calculated using the standard Fineman-Ross and Kelen-Tudos methods using the Mortimer and Tidwell experimental design method. The values of copolymerization constants are presented in table. 3. Based on the values of the copolymerization constants, the parameters of the microstructure of the copolymers were determined, which are also given in Table. 3.
The obtained values of the copolymerization constants confirm the previously made conclusion about the different reactivity of NGE in the processes of copolymerization with St. For the St - AGE system, the values of the calculated copolymerization constants are close to zero, which is typical for alternating copolymers. Calculation of the microstructure of these copolymers showed that, regardless of the composition of the initial mixture, almost strictly alternating products are obtained (Table 3).
The values of the relative activity constants for St - VGE copolymers indicate a lower reactivity of VGE in radical copolymerization compared to St. VGE is present in the data structure of the co-
polymers only in the form of single units, and the length of blocks of St units in copolymers naturally decreases with a decrease in the proportion of St in the original mixture.
Thus, the structure of the copolymers St and NGE can apparently be reflected by the following formula:
- // ZHPH. 1998 T. 71, No. 7. P. 1184-1188.
2. Vinyl glycidyl ethers of glycols - promising monomers for polymerization processes / L.S. Grigorieva [and others]. L.: Publishing house LTI, 1982. 9 p.
3. Raskulova T.V. Copolymerization of vinyl halides with functionally substituted vinyl monomers: dissertation... Dr. Chemistry. Sciences: 02.00.06: protected 04/21/2010: approved. 08.10.2010. Irkutsk, 2010. 315 p.
4. Pokrovskaya M.A., Raskulova T.V. Copolymerization of allyl glycidyl ether with styrene // AGTA Bulletin. 2011. No. 5. P. 87-89.
5. Surface functionalization of Si3N4 nanoparticles by graft polymerization of glycidyl methacrylate and styrene / Luo Ying // J. Appl. Polym. sci. 2006. V. 102. No. 2. P. 992.
6. Tan Chung-Sung, Kuo Ting-Wu. Synthesis of polycarbonate-silica nanocomposites from copolymerization of CO2 with allyl glycidyl ether, cyclohexene oxide, and sol-gel // J. Appl. Polym. sci. 2005. V. 98. No. 2. P. 750.
7. Formation of composites based on vinyl glycidyl ether of ethylene glycol and vinyl chloride / O.V. Lebedeva [and others] // Plastic masses. 2013. No. 9. pp. 35-39.
8. Kalinina M.S. Analysis of condensation polymers. M.: Nauka, 1983. 296 p.
9. Practical guide to determining molecular weights and molecular weight distribution of polymers / A.I. Shatenshtein [and others]. M.: Khimiya, 1964. 188 p.
10. Fractionation of polymers / ed. M. Kantova. M.: Mir, 1971. 444 p.
11. Heatley F., Lovell P.A., McDonald J. NMR studies of free-radical polymerization and copolymerization of monomers and polymers containing allyl groups // Eur. Polym. J. 2. 1993. V. 29, No. 2. R. 255.
12. Yu Qing-bo, Bai Ru-ke, Zhang Ming-Hi. Living radical copolymerization of allyl glycidyl ether with methyl acrylate in the presence of benzylimidazole-1-carbodithionate // Anhui ligong daxue xuebao. Ziran kexue ban; J. Anhui Univ. sci. and Technol. Natur. sci. 2006. V. 26, No. 3. P. 56.
13. Effect of the penultimate link in the copolymerization of vinyl chloride and unsaturated glycidyl ethers / T.V. Raskulova [et al.] // High-molecular compounds A. 2000. T. 42, No. 5. P. 744-750.
14. Tidwell P.W., Mortimer G.A. An Improved Method of Calculating Copolymerization Reactivity Ratios // J. Polym. sci. A. 1965. V. 3. P. 369.
n1.docx
6.2. Radical copolymerization6.2.1. Copolymerization rate
Changing the composition of the monomer mixture, as a rule, leads to a noticeable and sometimes dramatic change in the rate and degree of polymerization. This is due to changes in the effective values of the constants of all elementary reactions, and sometimes to the measurement technique.
Measuring the copolymerization rate using dilatometry. As a rule, the rate of copolymerization at the initial stage is measured by dilatometry. The contraction coefficient K in this case is usually calculated based on the linear relationship:
Where K 11 and K 22 are contraction coefficients corresponding to the homopolymerization of monomers M 1 and M 2; F 1 and F 2 are the mole fractions of monomer units in the copolymer.
However, in many cases a linear relationship is not true. Therefore, to calculate the contraction coefficient, an equation was proposed that takes into account the cross-growth reaction:
where K 12 is the contraction coefficient corresponding to the formation of an alternating copolymer; b 11, b 22 and b 12 are the relative amounts of different chemical bonds of the main chain.
Initiation speed. In copolymerization, in contrast to polymerization, the rate of initiation is determined not only by the nature and concentration of the initiator, but often also by the composition of the monomer mixture. In the case of azo compounds, for example azobisisobutyronitrile, it is usually assumed that the rate of initiation is either constant or linearly dependent on the composition of the monomer mixture. It is known that the rate constant for the decomposition of azobiisobutyronitrile depends on the nature of the solvent. In the case of mixed solvents, which include a mixture of monomers, the rate constant for the decomposition of azobiisobutyronitrile can be calculated using the formula:
Where? i is the volume fraction of the solvent, k decomposition, i is the rate constant for the decomposition of azobisisobutyronitrile in this solvent. Deviations from the linear dependence of the initiation rate on the composition of the monomer mixture are rare and, as a rule, insignificant. Significant deviations were found during the copolymerization of acrylonitrile with methyl methacrylate in a dimethylformamide solution.
In contrast to azo compounds, the linear dependence of the rate of initiation of copolymerization on the composition of the monomer mixture in the case of peroxides is rather an exception. Possible reasons for such deviations are associated with the donor-acceptor interaction of the components of the reaction mixture. It has been shown that during the copolymerization of styrene with methyl methacrylate and acrylonitrile, initiated by benzoyl peroxide, the monomers have a noticeable effect on the rate of decomposition of the latter as a result of the formation of donor-acceptor complexes:
PB... AN (MMA), PB... AN (MMA)... St
(PB - benzoyl peroxide, AN - acrylonitrile, MMA - methyl methacrylate, St - styrene).
Table 6.3 Values of initiation rate constants for the styrene - acrylonitrile system, [PB], [AIBN] = 0.001 mol/mol mixture, ѓ AN - mole fraction of acrylonitrilein a monomer mixture
| - AN Mol. shares | k in ·10 -5 , s -1 at T,°C |
|||
| 60 | 75 | 75 (AIBN) | 85 |
|
| 0,0 | 1,23 | 5,29 | 2,02 | 18,80 |
| 0,1 | 1,27 | 5,34 | 1,92 | 22,18 |
| 0,2 | 1,27 | 5,40 | 1,94 | 22,92 |
| 0,4 | 1,45 | 6,50 | 2,09 | 25,81 |
| 0,5 | 1,66 | 6,67 | 2,11 | 27,92 |
| 0,7 | 1,94 | 8,90 | 2,28 | 38,31 |
| 0,8 | 2,08 | 11,60 | 2,45 | 40,32 |
| 0,9 | 2,20 | - | 3,00 | 63,85 |
The presence of these complexes was proven by UV, IR, and NMR spectroscopy. The effects of complex formation are most pronounced in the styrene-acrylonitrile system. In table Table 6.3 presents data reflecting the influence of the composition of the monomer mixture on the values of the rate constants for the initiation of this reaction during the copolymerization of styrene with acrylonitrile initiated by benzoyl peroxide (BP) and 2,2"-azobis(isobutyro-nitrile) (AIBN).
Formal kinetic description of copolymerization. Chemical model of chain termination. The ab initio equation for the rate of radical copolymerization was first proposed by Melville and Walling, who started from the Mayo-Lewis copolymerization model. This model considers four growth reactions (equations (6.1)) and three chain termination reactions: 
The copolymerization rate equation has the form:
where [M 1 ] and [M 2 ] are the molar concentrations of monomers M 1 and M 2 in the monomer mixture; 
Options? 1 and? 2 can be easily found from homopolymerization experiments, the value of the parameter? cannot be established in independent experiments. Usually? are found by comparing the experimental dependence of the copolymerization rate on the composition of the monomer mixture with the theoretical one. Thus, in the case of copolymerization of styrene with methyl methacrylate, the experimental curve coincides with the theoretical one at? = 13 (Fig. 6.4). 
Equation (6.77) has found wide application, as a result of which extensive factual material on the value of ? has been accumulated. Analysis of these data showed that almost always? > 1, and for a number of systems there is a correlation? ~ 1/r 1 ·r 2 (Table 6.4).
This correlation was explained in terms of a chemical model of the chain termination reaction in copolymerization, taking into account the polar reactivity factor.
In the method described above for finding the quantity ?, which can be characterized as the fitted curve method, it is assumed that? = const, i.e. does not depend on the composition of the monomer mixture.
Table 6.4Correlation between?
Andr 1
·
r 2
with radical copolymerization
| Monomers | r 1 | r 2 | r 1 r 2 | ? |
| ?-Chlorostyrene - methyl acrylate | 1,21 | 0,14 | 0,16 | 147 |
| Styrene - 3,3,3-trichloropropene | 7,80 | 0,017 | 0,13 | 63 |
| Styrene - butyl acrylate | 0,75 | 0,15 | 0,114 | 35 |
| Styrene - isobutyl methacrylate | 0,55 | 0,40 | 0,22 | 21 |
| Methyl methacrylate - acrylonitrile | 1,20 | 0,15 | 0,18 | 14 |
| Styrene - methyl methacrylate | 0,52 | 0,46 | 0,23 | 13 |
| Styrene - methacrylonitrile | 0,30 | 0,16 | 0,048 | 6,7 |
| Acrylonitrile - methyl acrylate | 0,67 | 1,26 | 0,84 | 2,3 |
| Methyl methacrylate - butyl methacrylate | 0,79 | 1,27 | 1,0 | 1,1 |
Actually this is not true. If you calculate the value? separately for each monomer mixture according to the copolymerization rates (equation (6.77)), then, as a rule, a significant dependence is found? from the composition. To date, this dependence has not received an exhaustive explanation, however, the very fact of its existence indicates that the parameter? does not have a complete physical basis and should be considered as corrective. For this reason, the Melville-Walling equation, based on the chemical model of chain termination, is rarely used today.
Diffusion model of chain termination. In the 60s. XX century North proposed a diffusion model of chain termination in radical polymerization. According to this model, the rate of termination reaction is limited by the segmental mobility of the chain, which is inversely proportional to the viscosity of the solvent. This dependence was used to experimentally test the diffusion theory of chain termination. Indeed, it turned out that in many cases (but not always) the initial rate of polymerization decreases with increasing solvent viscosity. During the polymerization of methyl methacrylate and vinyl acetate, as well as during their copolymerization, the initial rate depends on the viscosity of the reaction mixtures. This kind of data indicates that the diffusion chain termination model is applicable to both radical polymerization and copolymerization.
The copolymerization rate equation taking into account the diffusion mechanism was first derived by Atherton and North:
This equation includes an effective chain termination rate constant k o, which is believed to be the same for all three chain termination reactions. Since the mobility of the chain is determined by its composition, it is initially assumed that the value of k o depends on the composition of the copolymer; the simplest form of such a dependence is:
Equations (6.78) and (6.79) made it possible to qualitatively correctly describe the dependence of the rate of copolymerization of methyl methacrylate with vinyl acetate on the composition of the monomer mixture; however, complete quantitative agreement between the theoretical and experimental curves was not achieved. Later, other equations were proposed to relate the termination rate constants in copolymerization and homopolymerization. Direct determination of k o in copolymerization and comparison of experimental and theoretical dependences of the chain termination rate constant on the composition of the monomer mixture showed that the best agreement is observed when using the equations: 
where q 1 and q 2 are the fractions of growth radicals ending in units m 1 and m 2.
The next stage in the development of the theory of copolymerization rate is associated with the spread of pulsed laser polymerization technology. If this method or another (for example, the rotating sector method) determines the rate constant of chain growth during copolymerization, then the rate of the latter can be expressed by a simple equation for the law of mass action:
where is the “average” chain growth rate constant; - total concentration of growth radicals; [M] is the total concentration of monomers. The value is naturally related to the composition of the monomer mixture, the relative activities of the monomers and the constants of elementary chain growth reactions. This relationship can be established based on different copolymerization models. Based on the end link model, i.e. Mayo-Lewis model, obtained: 
However, experimental testing of this equation by pulsed laser polymerization showed its inconsistency in many cases, in particular, in the copolymerization of styrene with methyl methacrylate (Fig. 6.5).
As a result, a hypothesis was put forward about the influence of the nature of the preterminal unit on the rate of radical copolymerization. To quantitatively characterize this effect, in addition to four copolymerization constants - relative activities of monomers in the pre-terminal link model - two new ones were introduced - relative activities of radicals:
where k 211, k 111, k 122, k 222 are the rate constants of elementary reactions (6.55).
The relative activities of radicals s 1 and s 2 show how many times the rates of growth reactions of radicals with different pre-terminal units differ. Taking into account the effect of the pre-terminal link leads to a more complex expression for the average rate constant of the chain growth reaction during copolymerization: 
Where 
From the given values of s 1 and s 2 in the caption to Fig. 6.5 it follows that the nature of the pre-terminal link can change the growth rate constant of the macroradical several times. The effect of the preterminal link, which affects only the rate of the growth reaction, but not the composition of the copolymer, is called implicit. Both effects - implicit and explicit (affecting the composition of the copolymer) - have a common nature, which will be discussed in the next section.
The radical copolymerization of active monomers with inactive ones is very specific. The first group includes monomers with ?-?-conjugation between the double bond and the substituent, the second group includes all the others. When copolymerizing such monomers, the copolymer is excessively enriched with the active monomer; small additions of the latter inhibit copolymerization. As an example, in fig. 6.6 shows the speed dependence 
Table 6.5Relative activities of monomers during styrene copolymerization (1)with acrylonitrile (2), defined within the end-end modelsand pre-terminal link, 60°C
| Wednesday | r 1 | r 2 | r 1 1 | r 2 1 | r 1 2 | r 2 2 |
| In bulk | 0,394 | 0,063 | 0,232 | 0,566 | 0,087 | 0,036 |
| In toluene | 0,423 | 0,118 | 0,242 | 0,566 | 0,109 | 0,105 |
| In acetonitrile | 0,485 | 0,081 | 0,322 | 0,621 | 0,105 | 0,052 |
copolymerization of styrene with vinyl acetate depending on the composition of the monomer mixture. Small additions of the active monomer - styrene (about 0.1%) - reduce the polymerization rate of vinyl acetate by two orders of magnitude. The reason is the low reactivity of the styrene radical, stabilized by conjugation of the sp 2 terminal carbon atom with the aromatic ring. This mechanism will be discussed in more detail below.
6.2.2. The nature of the pre-terminal link effect
The pre-terminal link model was proposed by Merz, Alfrey and Goldfinger in 1946, and they were the first to derive equation (6.50). For a long time, this model was used for the copolymerization of monomers, one of which is not capable of homopolymerization. As a result, a simplified composition equation containing only two constants (6.51) could be used to calculate relative activities. This equation was first applied to the copolymerization of styrene (1) with fumaronitrile (2). Since the latter is not capable of homopolymerization, then r 2 = r 12 = 0. It was found that r 1 = 0.072 and r 21 = 1.0, which indicates a very strong effect of the pre-terminal link. Equation (6.51) with the above values of relative activities satisfactorily described the experimental data on the composition of the copolymer.
Currently, there is an opinion that the scope of application of the pre-terminal copolymerization model in the part that describes the composition of the copolymer is significantly wider compared to what was previously thought. It is believed, in particular, that the model is widely applicable to the copolymerization of vinyl monomers. In table Figure 6.5 presents well-known data on the copolymerization constants of styrene with acrylonitrile, determined in accordance with the end- and pre-end link models. These data almost unambiguously indicate that copolymerization proceeds in accordance with the latter model. Firstly, experimental data on the triad composition of the copolymer (NMR) coincide with theoretically calculated ones only based on the model of the pre-terminal unit. Secondly, the data characterizing the effect of the pre-terminal unit are in quantitative agreement with the data of experiments on the addition of monomers to low-molecular-weight radicals simulating the last two units of the growth radical.
Currently, the nature of the explicit and implicit effects of the preterminal link is associated with two components - steric and electronic. Below are diagrams of the transition state of the growth reaction during radical (co)polymerization, where only one substituent of the pre-terminal unit X is isolated: 
Theoretical calculations show that the values of the pre-exponential factor depend mainly on the freedom of rotation around the resulting bond vi, the terminal bond V 2 and the vibrations of the transition complex as a whole v 3 (a). It turned out that during rotation around the terminal bond, a significant braking potential arises with the ecliptic (opposite each other) position of the X substituent of the preterminal unit and the CH 2 group of the joining monomer. As a result, the value of the pre-exponential factor is halved even at X = CH 3 .
The electronic component of the preterminal unit is explained by its influence on the polarity and resonance stabilization of the terminal radical. However, both effects should be quite weak, since they are transmitted through several?-bonds.
6.2.3. Effect of temperature and pressure on radical copolymerization
The effect of temperature on the rate and degree of copolymerization is similar to homopolymerization (Section 5.1.4). Exceptions may be associated with copolymerization complicated by depolymerization. The effect of temperature on the composition of the copolymer can be established based on the Arrhenius equation, the application of which to relative activities leads to the following dependencies: 
For monomers of similar structure, for example vinyl, the frequency factors differ little: to a first approximation, we can assume that =A 11 /A 12 = A 22 /A 21 = 1. Then 
Table 6.6 Values of relative activities of monomers at different temperatures and ratios of frequency factors
| Monomers | r 1, r 2 | A 11 /A 12, A 22 /A 21 |
|
| 60°C | 131°C | ||
| Styrene Methyl methacrylate | 0,520 | 0,590 | 1,06 |
| Styrene methyl acrylate | 0,747 | 0,825 | 1,31 |
| Styrene Diethyl maleate | 6,52 | 5,48 | 2,55 |
| Styrene Diethyl fumarate | 0,301 0,0697 | 0,400 0,0905 | 1,50 |
| Styrene N-chlorostyrene | 0,742 | 0,816 | 1,27 |
| Styrene Trans-stilbene | 5.17 (70°C) | 7.23 (140°C) | 34,34 |
whence it follows that with increasing temperature r 1? 1, r 2 ? 1 regardless of the initial values of relative activities. In other words, with increasing temperature, the selectivity of the addition of monomers to radicals decreases. However, this effect is small, since the difference in the activation energies of chain growth (E 11 - E 12) and (E 22 - E 21) is small. In table Table 6.6 shows the values of the relative activities of monomers at different temperatures, from which it can be seen that the theoretical concepts for monomers of the same type are justified.
Deviations are observed during the copolymerization of monomers with a different structure, for example, during the copolymerization of styrene with diethyl maleate (1,2-disubstituted monomer) and trans-stilbene (bifunctional monomer CH 2 =CH-C 6 H 4 -CH = CH 2).
The effect of pressure on the rate and degree of copolymerization is qualitatively similar to that described above for homopolymerization. The effect of pressure on relative activities can be predicted from equation (5.51). Applying it to the product of relative activities, we get:
under the assumption that = , where and is the change in volume during the formation of a transition complex from the initial monomer and radical in cross-growth reactions, i.e. activation volumes of these reactions. From Sect. 5.1.4 it follows that
An increase in pressure always leads to an increase in the product r 1 ·r 2 as a result of an increase in the values of both copolymerization constants r 1 and r 2.
Table 6.7Effect of pressure on the copolymerization of some monomers
| M 1 | M 2 | р·10 -5 , Pa | r 1 | r 2 | r 1 r 2 |
| Styrene | methyl acrylate | 1,0 3039,8 | 0,704 | 0,159 | 0,112 |
| Styrene | Acrylonitrile | 1,0 1013,2 | 0,07 | 0,37 | 0,03 |
| Acrylonitrile | Methyl methacrylate | 1,0 1013,2 | 1,34 | 0,12 | 0,16 |
| Styrene | Diethyl fumarate | 1,0 1013,2 | 0,26 | 0,06 | 0,02 |
| Styrene | Cis-1,2-dichlorethyls | 1,0 1013,2 | 195 | 0,00 | 0,00 |
Thus, pressure leads to a decrease in the selectivity of the addition of monomers to radicals. It is necessary to pay attention to the fact that the values of the copolymerization constants of sterically hindered monomers, which include 1,2-di- and more substituted ethylene, are equal to or close to zero at atmospheric pressure, at high pressure they become different from zero and (or) increase (see Table 6.7).
6.2.4. Alternate copolymerization
When copolymerizing electron-withdrawing (A) and electron-donating (D) monomers, copolymers with regular or close to regular alternation of monomer units are quite often formed.
Electron-donating monomers include monomers with a developed α-β conjugation system, monomers with substituents that increase electron density on the double bond, as well as olefins. They are divided into the following groups:
1. Ethylene and monomers with ?-?-conjugation - ?-olefins, cycloalkenes, vinylcycloalkanes, allyl monomers.
2. Monomers with?-p-conjugation - vinyl ethers, vinyl sulfides, N-vinyl amines, N-vinyl amides, vinyl halides.
3. Monomers with?-?-conjugation - vinylaromatic monomers, trans-stilbene, phenanthrene, acenaphthylene, indene, vinylpyridines, phenylacetylene, etc.
4. Monomers with?-p-?-conjugation - vinyl ethers, N-vinylcarbazole, N-vinylpyrrolidone, N-vinylsuccinimide, N-vinylphthalimide.
Electron-withdrawing monomers have substituents that remove electron density from the double bond:
1. Anhydrides and imides of unsaturated dicarboxylic acids (maleic, itaconic, etc.) and their derivatives.
2. Mono- and dicarboxylic unsaturated acids, their esters, amides, nitriles.
3. Tetrahalide substituted ethylene.
4. SO 2 is one of the strongest electron acceptors of radical copolymerization.
Alternating copolymerization of monomers belonging to different classes results from the formation of charge transfer complexes (CTCs), also called donor-acceptor (DA) complexes, between them or between a monomer of one class and a propagating radical of another. According to Mulliken's theory, the CZ wave function can be represented by a superposition of the wave functions of two limiting structures - without transfer and with complete electron transfer, the latter being unimportant. It follows from this that the Coulomb interaction does not play a significant role in the formation of bonds between the components of the complex. A characteristic sign of the formation of SCC is the appearance of a new absorption band in the visible or UV part of the spectrum. Typically, AGE is more reactive compared to monomers. The reason for this is associated with the easier polarizability of CPCs compared to monomers due to a more extensive β-electronic structure and the ability to transition to an excited ionized state. In addition to double ones, triple DA complexes of monomers are known. The former are formed between relatively strong electron donors and acceptors, for example, between maleic anhydride and styrene. The latter are formed between weak electron acceptors, such as acrylates, and strong electron donors in the presence of Lewis acids. The role of the latter is to shift the electron density toward themselves in coordination double complexes:
which leads to an increase in the electron-withdrawing properties of the acrylic monomer. In general, the process of formation of ternary DA complexes is described by the following equilibria: 
where M is acrylic monomer, D is donor monomer, X is Lewis acid. The equilibrium constants for the formation of ternary and double DA complexes of monomers are close. Thus, for the complexes acrylonitrile - ZnCl 2 - styrene, (methyl methacrylate) 2 - SnCl 4 - styrene, the equilibrium constants at room temperature are 0.062 and 0.21 l/mol, respectively. Double DA complexes are characterized by values in the range of 0.1 -0.2 l/mol.
For the first time, the hypothesis about the formation of CPC monomers and their ability to polymerize as a single kinetic particle was expressed by Bartlett and Nozaki more than 50 years ago. Alternating copolymerization was studied especially actively in the 70-80s. XX century It was found that the ability for alternating copolymerization is often associated with the thermodynamic equilibrium constant for the formation of CPC by monomers, which in the case of binary complexes has the following form: 
where , [M A ], are the equilibrium concentrations of monomers and complex; K is the equilibrium constant. As the complexation equilibrium constant increases, the ability for alternating copolymerization changes as follows:
TO
0,01
0,1 (0,1-0,15)
K> 5 - the formation of a stable complex that is not capable of polymerization, which can be isolated as an individual substance.
There are two models of copolymerization involving monomer complexes. The first of them - the Seiner and Lit model - provides for the entry of both molecules of the monomer complex into the chain, the second - the dissociation model - provides for the entry of only one of the monomers of the complex into the chain. According to the first model, it is necessary to take into account in the elementary reaction the four previously discussed growth reactions (6.1) of the terminal unit model involving free monomers and four reactions involving the complex: 
as well as the equilibrium reaction of complexation of monomers (6.93).
According to the “dissociation model” of the complex, it is also necessary to consider eight growth reactions: four involving free monomers and four involving the complex, as well as the reaction of complexation of monomers (6.93). This model can be applied to copolymerization in a solvent that forms complexes with the monomer. In this case, two complexation reactions are considered, i.e. each of the monomers with a solvent. The following are growth reactions involving monomer complexes: 
A comparison of (6.94) and (6.95) shows that they differ in the nature of the terminal units of the resulting growth radicals. This happens because, according to the “complex dissociation” model, only one of the monomers of the complex joins in the chain growth reaction, while the second plays the role of an activator.
The mechanism of alternating copolymerization is determined by which of the elementary reactions of the considered models is predominant. The mechanism was studied by three methods: based on the composition of the copolymer, the rate of copolymerization (kinetic method) and the EPR method. In the latter case, “direct” observation of radical growth at low temperatures was used, as well as the use of a spin trap.
Using the “direct” EPR method, as well as the kinetic method, it was proven that during the copolymerization of SO 2 with dimethylbutadiene, a “complex” mechanism is realized, which involves the inclusion of both monomers of the complex in the chain. In the reaction mixture, there are two types of independently growing chains, differing in the nature of the terminal link: 
Using the spin trap method, it was shown that the “complex” mechanism is also realized during the alternating copolymerization of cis-butene-2 with SO 2. In this case, one growth reaction dominates - the addition of the monomer complex to the growth radical ending with an SO 2 unit:
Kinetic methods of analysis are associated with the phenomenon of destruction of monomer complexes when diluting reaction mixtures with a solvent. When the graph of the dependence of the copolymerization rate on the composition of the monomer mixture clearly shows a maximum, its shift is recorded when the reaction mixtures are diluted with a solvent. To calculate the parameters characterizing the process, at least three series of experiments with monomer mixtures of three different compositions and knowledge of the dissociation constant of the complex (K -1) are required. Using the maximum shift method (Fig. 6.7), it was found that during the copolymerization of maleic anhydride (M 2) with vinyl phenyl ether (M 1)
k 12 / k 21 = 17.6; /k 12 = 7.51; /k21 = 0.355.
The first means that the reactivity of the vinyl phenyl ether radical is significantly higher in cross-growth reactions compared to the maleic anhydride radical. This fact corresponds to the established ideas about the “ideal” reactivity of monomers and radicals, according to which ?-?-conjugation in the latter reduces their reactivity. From the second relation it follows that complexes of monomers are preferentially added to the growth radical of maleic anhydride, and free maleic anhydride is added to the growth radical of vinyl phenyl ether. Thus, in this case, all types of cross-growth reactions (i.e., leading to the formation of an alternating copolymer) are represented - with the participation of free radicals and monomer complexes. This mechanism of alternating copolymerization is called mixed. It is also characteristic of the alternating copolymerization of maleic anhydride with allyl monomers. With alternating copolymerization of some monomers, the “maximum shift” effect is absent. This indicates that the contribution of growth reactions involving monomer complexes to the formation of an alternating copolymer chain is extremely insignificant. 
However, this result does not mean that there is no donor-acceptor interaction in the cross-growth reaction. Almost simultaneously with the hypothesis about the role of donor-acceptor comonomer complexes in alternating copolymerization, a hypothesis was put forward about donor-acceptor interaction in the reaction of electron-donating growth radicals with electron-withdrawing monomers (and vice versa). According to Walling's hypothesis, the cross-growth reaction involving the styrene radical and the maleic anhydride monomer occurs through an electron transfer step, which reduces its activation energy: 
Alternating copolymerization has distinct features compared to statistical copolymerization. These include:
Spontaneous initiation
Insensitivity to most inhibitors and chain transmitters,
High chain growth rate.
These features are clearly manifested in copolymerization with the participation of ternary donor-acceptor complexes of monomers, since in this case it is possible to compare alternating and statistical copolymerization of the same monomers. Let us consider, as an example, the copolymerization of butyl methacrylate with dimethylbutadiene. In the absence of a complexing agent, the copolymer composition curve has a weakly expressed S-shape, which indicates an insignificant alternation effect (Fig. 6.8). In the presence of (C 2 H 5) 2 AlCl, the rate and degree of copolymerization sharply increase (Fig. 6.9), and the copolymer composition curve takes on the form characteristic of the formation of a regularly alternating copolymer (equimolar composition of the copolymer, regardless of the composition of the monomer mixture). The role of (C 2 H 5) 3 AlCl is to enhance the electron-withdrawing properties of butyl methacrylate: 
Using the EPR method, it was established that in this case there is a “sequential” mechanism of alternating copolymerization, when the nature of the radical at the end of the growing chains successively changes. In this case, the donor-acceptor interaction is realized between the growth radical and the monomer.
6.2.5. Influence of the reaction environment
Contrary to the opinion that existed for quite a long time after the completion of the quantitative theory of copolymerization, the reaction medium can have a significant impact on the composition and structure of the copolymer. There are two fundamentally different mechanisms for this influence:
1. Through the formation of various types of complexes between monomers and radicals, on the one hand, and components of the reaction medium, on the other. The latter may include a solvent or specially introduced substances, most often acids or Lewis bases * (* Kabanov V. A., Zubov V. P., Semchikov Yu. D. Complex radical polymerization. M: Khimiya, 1987.).
2. Through selective solvation of growing chains by monomers - in the case when the latter have different thermodynamic affinities for the copolymer as solvents** (** Semchikov Yu. D., Smirnova L. A. Model of copolymerization taking into account the selective solvation of macroradicals // Vysokomolek. Conn. B. 1999. T. 41, No. 4. P. 634-748.).
In the first case, effects at two levels are observed. In the absence of a pronounced specific interaction between the reagents and the solvent, an insignificant effect of the latter on the relative activities of the monomers is observed. A well-known example is the copolymerization of styrene with methyl methacrylate in aromatic solvents of different polarities.
A strong effect on the composition and structure of the copolymer is observed when sufficiently strong hydrogen and coordination bonds are formed between the monomers and (or) growth radicals and the solvent or Lewis acid, which can be specially introduced into the reaction mixture as a modifier of the copolymer composition or a polymerization activator. In this case, significant changes in the composition of the copolymer and the relative activities of the monomers are observed during the copolymerization of unsaturated carboxylic acids, their amides, amines, nitriles and esters with other monomers. In this case, the rates and degrees of copolymerization often change significantly.
The reaction mixture in bulk copolymerization is a typical solution of a polymer in a mixed solvent. The properties of such solutions depend, among other things, on the thermodynamic characteristics of the mixture used as a solvent. Thus, for solutions with a positive deviation of the mixed solvent from ideality, phenomena such as selective solvation of macromolecules by one of the solvent components and cosolubility, i.e. dissolving a polymer in a mixture of solvents, each of which individually does not dissolve the polymer. Signs of a positive deviation of a liquid mixture from ideality are positive values of the excess Gibbs function of mixing components, i.e. > 0 and a convex dependence of the saturated vapor pressure above the mixture on its composition.
When copolymerizing monomer mixtures with a positive deviation from ideality, the influence of selective solvation of macroradicals and macromolecules by monomers on the composition of the copolymer and the relative activities of the monomers is often observed. Particularly significant effects were found in the copolymerization of N-vinylpyrrolidone with vinyl acetate, styrene with methacrylic acid, styrene with acrylonitrile, 2-methyl-5-vinylpyridine with vinyl acetate, less significant - for a number of other systems* (* Semchikov Yu. D. Preferential sorption of monomers and molecular weight effect in radical copolymerization // Macromol. Symp., 1996. V. 111. P. 317.). In all cases, there was a dependence of the copolymer composition on the molecular weight, which is atypical for “classical” radical copolymerization, which is explained by the dependence of the selective solvation coefficients of macroradicals on their degree of polymerization.
Thus, the influence of the environment on radical copolymerization is associated with two groups of effects. Electronic effects are associated with the redistribution of electron density in monomers and (or) radicals as a result of their formation of weak complexes with solvents, complexing agents such as Lewis acids. Concentration effects are associated with the selective solvation of propagating radicals by monomers. In all cases, the quantitative theory of copolymerization outlined above remains applicable, however, the relative activities of the monomers are effective quantities.
6.2.6. Relationship between the structure of the monomer and radical and reactivity. SchemeQ-
e
In parallel with the development of the quantitative theory of copolymerization, a quantitative Alfrey-Price scheme was developed half a century ago, relating copolymerization constants to empirical reactivity parameters. According to this scheme, the growth rate constant in radical polymerization and copolymerization is expressed by the empirical equation:
where P i and Q j are parameters taking into account the resonant one; e i and e j are polar reactivity factors. Based on (6.96), expressions for the relative activities of monomers can be easily obtained:
Next, multiplying the relative activities of monomers in (6.97) and taking the logarithm of the resulting product, we obtain:
from which it follows that the tendency to alternation during copolymerization is determined only by the difference in the values of the polar parameters of the monomers.
The Q-e scheme is widely used in copolymerization, since it allows the relative activities of monomers and, therefore, the composition and structure of the copolymer to be calculated without carrying out copolymerization, from the known Q and e values of the monomers. These values, in turn, were determined by copolymerizing monomers with known and unknown values of Q and e. Styrene was chosen as the starting monomer, which was assigned e - -0.8, Q = 1. The significance of the Q-e scheme is also that that it made it possible to classify monomers into certain groups based on the values of the parameters Q and e: active (Q > 0.5) and inactive (Q 0) and, thereby, predict the type of polymerization process in which it is advisable to use a given monomer. Quantum chemical calculations have shown that the parameters Q and e have a clear physical content; this follows from the correlations given in the next section.
Analysis of systematic data in the field of radical (co)polymerization leads to the conclusion that the reactivity of monomers and radicals in the growth reaction is determined by resonance stabilization (conjugation), the polarity of the double bond, as well as the degree of its shielding by substituents.
Steric factor. The importance of the steric factor is especially pronounced in reactions of radical addition of disubstituted ethylene. It is known that 1,1-disubstituted compounds easily polymerize and copolymerize by a radical mechanism, while 1,2-disubstituted compounds, for example maleic anhydride, are practically incapable of homopolymerization, and during copolymerization their content in the copolymer does not exceed 50%. The reasons for such different behavior of these closely related classes of unsaturated compounds can be understood by considering the stereochemistry of the chain growth reaction.
The spatial structure of organic compounds is largely determined by the type of hybridization of carbon atoms. The unsaturated atoms of the growth radical and the monomer have cp 2 hybridization. This means that the axes of p-orbitals of unsaturated atoms are perpendicular to the plane in which the β-bonds are located. The carbon atoms of the main chain of the radical form a flat zigzag; all of them, with the exception of the terminal unsaturated carbon atom, have cp 3 hybridization. From the diagram below it is clear that when a conditional tetra-substituted monomer (AB)C = C(XY) approaches “its” growth radical, a contact interaction is likely, i.e. repulsion of substituents A and B of the monomer and the carbon atom of the radical until the axes of the p-orbitals are aligned. As a result, the growth reaction cannot occur: 
A similar situation is observed when tri- and 1,2-disubstituted ethylene approaches its “own” growth radical. Thus, polymerization of tetra-, tri- and 1,2-substituted ethylene is impossible for purely steric reasons. An exception is fluorine-substituted ethylene, during the polymerization of which, due to the small radius of the substituent, steric difficulties do not arise. In contrast to polymerization, copolymerization of tetra-, tri- and 1,2-disubstituted ethylenes with mono- or 1,1-disubstituted ethylenes is possible. In this case, substituents and hydrogen atoms confront each other in the “danger zone,” which, as a rule, does not prevent the monomer and radical from approaching each other and the growth reaction occurring. However, since elementary acts of homopolymerization of a disubstituted monomer are impossible, the content of this monomer in the copolymer does not exceed 50%.
Table 6.1Copolymerization of vinyl acetate (1) with chlorinated ethylene (2)
| Monomer | r 1 | r 2 |
| Tetrachlorethylsn | 6,8 | 0 |
| Trichlorethylene | 0,66 | 0,01 |
| Cis-dichlorethylene | 6,3 | 0,018 |
| Trans-dichlorethylene | 0,99 | 0,086 |
| Vinylidene chloride | 0 | 3,6 |
| Vinyl chloride | 0,23 | 1,68 |
In table Figure 6.8 provides data illustrating the influence of the steric factor in copolymerization. Vinyl chloride and 1,2-disubstituted monomer vinylidene chloride are more active compared to vinyl acetate (r 1 > r 2). However, tri- and tetrasubstituted chloroethenes are less active, with r 1 =0, due to their inability to homopolymerize. Trans-1,2-disubstituted are less reactive compared to cis-1,2-disubstituted, which is a general rule in copolymerization.
Resonance factor. The importance of the resonance factor of reactivity or the effect of conjugation on the reactivity of monomers is most clearly manifested in radical copolymerization and polymerization. Depending on the presence or absence of conjugation of the double bond of the monomer with the unsaturated group of the substituent, all monomers are divided into active And inactive. Typical representatives of each group are presented below: 
From a comparison of the above structures it is clear that only direct α-β conjugation in the monomer makes it active in copolymerization; other types of conjugation are ineffective.
As a rule, copolymerization is advisable between monomers of the same group, because only in this case it is possible to avoid excessive differences in the composition of the copolymer from the composition of the monomer mixture. Thus, at the initial stage of copolymerization of equimolar mixtures of inactive monomers vinyl chloride and vinyl acetate and active monomers styrene and acrylonitrile, copolymers are formed, containing in the first case 69 mol.% vinyl chloride. in the second - 60 mol.% styrene. When copolymerizing equimolar mixtures of an inactive monomer with an active one - vinyl acetate with styrene - a copolymer is formed containing 98 mol.% styrene, i.e. practically a homopolymer.
Let us consider the data on the rate constants of elementary chain growth reactions (l/(mol s)) for joint and separate polymerization of vinyl acetate (1) and styrene (2) at 25°C:
| k 11 | k 22 | r 1 | r 2 | k 12 | k 11 |
| 637 | 40 | 0,04 | 55 | 15900 | 0,73 |
It can be seen that the active monomer styrene adds to the vinyl acetate radical at a rate four orders of magnitude greater than that of the inactive monomer vinyl acetate (k 12 and k 11). When comparing the resonance ability of radicals, the situation is reversed. The rate of addition of the vinyl acetate radical to its “own” monomer is three orders of magnitude higher compared to the rate of addition of the styrene radical to vinyl acetate (k 11 /k 21 = 873). A similar picture is revealed when comparing the rates of addition of styrene and vinyl acetate radicals to the styrene monomer (k 12 /k 22 =400). Thus, conjugation or resonance effect has the opposite effect on the reactivity of monomers and radicals - it increases the activity of the former and reduces the activity of the latter. It follows from this that the reactivity series of monomers and their corresponding radicals are opposite. This position is known as antibath rule.
Table 6.9Influence of the resonance factor on the value of the growth rate constant, 20-30°C
| Monomer | Q | k Р, l/(mol s) |
| Vinyl acetate | 0,026 | 1000 |
| Vinyl chloride | 0,044 | 6000 |
| N-Vinylpyrrolidone | 0,14 | 710 |
| Methyl methacrylate | 0,74 | 280 |
| Styrene | 1 | 40 |
| Butadiene-1,3 | 2,39 | 8,4 |
| Isoprene | 3,33 | 2,8 |
The influence of the resonance factor of reactivity is also very significant in relation to the rate of radical polymerization and copolymerization. From Table. 6.9 it can be seen that the rate constants of the growth reaction of a number of monomers decrease with increasing resonance parameter Q, i.e. with an increase in the efficiency of conjugation of the double bond of the monomer with the substituent. In particular, the growth rate constant of the inactive monomer vinyl acetate is two orders of magnitude greater than that of the active monomer styrene. At first glance, this result seems surprising, since, due to the antibate rule, the high activity of the monomer is compensated by the low activity of its corresponding radical, and vice versa. The point is that the effect of conjugation on the reactivity of monomers and the corresponding growth radicals is not the same in effectiveness - the activity of the monomer increases to a lesser extent compared to stabilization, i.e., a decrease in the reactivity of the radical.
The third important effect, caused by the resonance factor of reactivity, is associated with the structure of the polymer chain. Previously, the possibility of chemical isomerism of repeating sections of a chain consisting of several units was considered due to their different orientation along the chain (Section 1.1.5). Below is a diagram showing two possible directions of the growth reaction during the copolymerization of styrene: 
In the first case, the conjugation of the aromatic substituent with the resulting radical and the transition complex is realized, and therefore the monomer behaves as active. In the second case, there is no conjugation, since the unsaturated carbon atom of the radical is separated from the aromatic substituent by two α-bonds, and in this case the monomer is inactive. As a result, the first reaction turns out to be more preferable (k p >> k" p) and the addition of the radical to the monomer occurs with a probability greater than 90% according to the “head” to “tail” type.
The mechanism of action of the resonance factor of reactivity is based on the effect of stabilization, reduction of the ?-electronic energy of the transition state and radical growth due to conjugation with the substituent. Quantitatively, the resonance stabilization factor is taken into account by the parameters P, Q of the Alfrey-Price Q-e scheme and a number of quantum chemical parameters, among which the bond order P and localization energy are most often used. Of particular importance for characterizing the reactivity of unsaturated molecules is the localization energy L, the concept of which was first introduced by Ueland. As applied to the growth reaction, its physical meaning is as follows. The carbon atom of the monomer attacked by the radical changes the hybridization from sp 2 to sp 3 and is thus removed from the conjugation system. The energy required for this is called the localization energy of the monomer L? . Similar reasoning can be carried out in relation to the conjugated radical, however, the localization energy of the radical La does not have a significant effect on the relative activities of the monomers. The value of L? can be calculated as the energy of transition of the monomer to the biradical triplet state:
Let us denote the energy of the ?-electrons of the monomer E M radical by E r and the energy of the radical by ? (Coulomb integral). Then the monomer localization energy L ? turns out to be equal to:
In table Table 6.10 shows the values of various resonance parameters of monomers calculated by the quantum chemical method. They all correlate with lnQ and with each other. In Fig. 6.10 shows the correlation between L? - the most well-known quantum chemical parameter characterizing the resonance factor of reactivity, and InQ.
From the data in Fig. 6.10 and table. 6.10 it follows that as the parameter Q increases, the absolute value of the monomer localization energy decreases. This means that as the conjugation energy in a monomer increases, the energy required to activate the cleavage of its double bond decreases.
Table 6.10Empirical and calculated quantum chemical resonance parameters of the structuremonomers and radicals
| Monomer | InQ | L? | R | L? |
| CH 2 =C(CN) 2 | 3,0 | 1,598 | 0,835 | 1,414 |
| CH 2 =CH-CH=CH 2 | 0,871 | 1,644 | 0,894 | 0,828 |
| CH 2 = C (CH 3) CHO | 0,372 | - | - | - |
| CH 2 =CH-CONH 2 | 0,174 | - | - | |
| CH 2 =C(CH 3)CN | 0,113 | 1,639 | - | 0,897 |
| CH 2 = SNS 6 H 5 | 0,00 | 1,704 | 0,911 | 0,721 |
| CH 2 = CHNO | -0,163 | - | 0,910 | |
| CH 2 =C(CH 3)COOCH 3 | -0,301 | 1,737 | - | 0,691 |
| CH 2 =CH-CN | -0,511 | 1,696 | 0,913 | 0,839 |
| CH 2 =CH-COOCH 3 | -0,868 | 1,783 | 0,914 | 0,645 |
| CH 2 =CCl 2 | -1,514 | 1,832 | - | 0,867 |
| CH 2 = CHSN 2 OH | -3,04 | - | - | - |
| CH 2 =CHCl | -3,12 | 1,877 | 0,989 | 0,474 |
| CH 2 = C (CH 3) 2 | -3,41 | - | - | - |
| CH 2 =CH-OC 2 H 5 | -3,44 | 1,841 | 0,966 | 1,647 |
| CH 2 =CH-OCOCH 3 | -3,65 | 1,885 | 0,965 | 0,445 |
| CH 2 =CHF | -3,69 | - | - | - |
| CH 2 =CH 2 | -4,20 | 2,000 | 1,000 | 0,000 |
| CH 2 = CHSN 3 | -6,21 | - | - | - |
P is the bond order in the monomer, L? and L? - localization energy of the monomer and growth radical in units of P (resonance integral).
Let us consider the change in the potential energy of an approaching monomer and radical, taking into account the localization energy of the monomer L? . The bringing together of non-activated particles should lead to the emergence of repulsive forces and, consequently, an increase in potential energy (Fig. 6.11, curve 2). The approach of the radical to the activated monomer, i.e. being in a biradical state, leads to a decrease in potential energy (curve 1), which in this case changes in accordance with the Morse function. The latter describes the change in potential energy when two atoms connected by a chemical bond are separated. From fig. 6.11 it is clear that a decrease in the localization energy leads to a decrease in the activation energy of the growth reaction, because the position of the “repulsion” curve (curve 2) is practically independent of the structure of the monomer and the value of L? .
The above approach, developed by Evans and Schwartz, does not take into account the role of polar and steric factors. The reactivity of monomers and radicals, determined only by the resonance factor, is called ideal reactivity. 
Polar factor. The double bond of monomers subject to radical copolymerization is usually polarized due to the donor-acceptor action of the substituents, as is the unsaturated carbon atom of the growth radical: 
The donor-acceptor effect of substituents leads to the appearance of partial charges on the α-carbon atom of the double bond and the β-carbon atom of the terminal unit of the growth radical (unsaturated).
The influence of the polar reactivity factor is most clearly manifested in radical copolymerization, where it is responsible for the occurrence of the effect of alternation of monomer units. Price was the first to draw attention to the importance of the polar factor in copolymerization and concluded that “copolymerization proceeds most easily in binary systems in which one monomer has an excess and the other a deficiency of electrons.” For a long time, the nature of the polar effect was explained from the position of electrostatic interactions, which was later recognized as unsatisfactory. Another hypothesis, which has become widespread to date, explained the tendency to alternate units during copolymerization by electron transfer between the components of the transition complex, i.e. is a development of Walling's hypothesis: 
In the above scheme, the CH 2 =CHX monomer, for example methyl methacrylate, and the corresponding growing radical are electron acceptors, and the CH 2 =CHY monomer, for example styrene, is an electron donor. It is believed that the contribution of the ionic structure to the transition state reduces the activation energy of cross-growth; as a result, during copolymerization, a tendency to alternation of monomer units appears, however, the resulting copolymer remains statistical. The described mechanism is consistent with the data of quantum chemical calculations, according to which, with an increase in the difference between the polar parameters of the monomers |e 1 - e 2 | charge transfer between the components of the transition complex increases. 
Table 6.11Valuesgrowth reaction rate constantsAndparameterepair-substituted styrene, 60°C
Radical copolymerization is usually initiated by the same methods as radical homopolymerization. The elementary stages of radical copolymerization proceed by the same mechanisms as in homopolymerization.
Let's consider the copolymerization of two monomers. Assuming that the activity of growing radicals is determined only by the type of terminal unit, when describing the reaction kinetics, four elementary chain growth reactions should be taken into account:
Growth reactionRate of growth reaction
~R 1 + M 1 ~R 1 k 11
~R 1 + M 2 ~R 2 k 12
~R 2 + M 1 ~R 1 k 21
~R 2 + M 2 ~R 2 k 22
where M i is a monomer of i-ro type; ~R j is a macroradical ending with an M j unit, k ij is the rate constant for the addition of the M j monomer to the ~R i radical.
Kinetic processing of the given reaction scheme in a quasi-stationary approximation makes it possible to establish a connection between the composition of the copolymers and the composition of the initial mixture of monomers. In a quasi-stationary state, the concentrations of radicals ~R 1 - and ~R 2 - are constant, i.e., the rates of cross-chain growth are equal:
k 12 = k 21 (1-6)
The rates of monomer conversion during copolymerization are described by the equations
For the ratio of the rates of these reactions we obtain:
Excluding stationary concentrations of radicals from this equation and using the quasi-stationarity condition (1.6), we obtain the expression
here r 1 = k 11 /k 12 and r 2 = k 22 /k 21 - the so-called copolymerization constants. The values r 1 and r 2 represent the ratio of the rate constants of addition of “own” and “foreign” monomers to a given radical. The values of r 1 and r 2 depend on the chemical nature of the reacting monomers. At the initial stages of the transformation, when the monomer concentrations and [M 2 ] can be assumed to be constant without much error, the composition of the copolymer will be determined by the equation
where [] and are the concentrations of monomer units in the macromolecule.
The dependence of the composition of copolymers on the composition of the monomer mixture is conveniently characterized by the diagram composition of the monomer mixture - composition of the copolymer (Fig. 1.1). The shape of the resulting curves (1 - 4) depends on the values of r 1 and r 2. In this case, the following cases are possible: 1) r 1 = r 2 = 1, i.e. for all ratios of monomer concentrations in the reaction mixture, the composition of the copolymer is equal to the composition of the original mixture; 2) r 1 > 1, r 2< 1, т. е. для всех соотношений концентраций мономеров в исходной смеси сополимер обогащен звеньями M 1 ; 3) r 1 < 1, r 2 >1, i.e., for all initial ratios of monomer concentrations, the copolymer is enriched with M 2 units; 4) r 1< 1 и r 2 < 1, т. е. при малых содержаниях M 1 в исходной смеси мономеров сополимер обогащен звеньями М 1 а при больших - звеньями М 2 . В последнем случае наблюдается склонность к чередованию в сополимере звеньев M 1 и М 2 , которая тем больше, чем ближе к нулю значения r 1 и r 2 , Случай, r 1 >1 and r 2 > 1, which should correspond to the tendency for separate polymerization of monomers in the mixture, is not realized in practice.
The constants r 1 and r 2 can be determined experimentally. Knowing them makes it possible to predict the composition of the copolymer and the distribution of monomer units in the chains for any ratio of monomers in the mixture. The values of r 1 and r 2 during radical copolymerization and, consequently, the composition of the copolymer usually weakly depend on the nature of the solvent and change little with temperature.
Rice.
Table 1.2. Radical coblimerization constants for some monomers
Consideration of the constants r 1 and r 2 within the framework of the theory of ideal radical reactivity leads to the conclusion that r 1 = r 2 = 1, i.e., the rate constants for the addition of one of the monomers to both radicals are the same number of times greater than the rate constants for the addition of the other monomer to these radicals. For a number of systems this condition is well justified experimentally. In such cases, monomer units of both types are randomly located in macromolecules. However, for many systems r 1 x r 2< 1, отклонения связаны с влиянием полярных и пространственных факторов, которые обусловливают тенденцию мономерных звеньев M 1 и M 2 к чередованию в макромолекулах. В табл. 1.2 в качестве примеров приведены значения констант сополимеризации и их произведений для некоторых пар мономеров.
Scheme "Q - e". Polar factors were taken into account within the framework of a semi-empirical scheme called the “Q - e” scheme, in which it is accepted that
k 11 = P 1 Q 1 exp(-e 1 2 )
and k 12 = P 1 Q 2 exp(-e 1 e 2 )
where P and Q are parameters corresponding to the conjugation energies in the monomer and radical, according to the theory of ideal radical reactivity; e 1 and e 2 are quantities that take into account the polarization of reacting monomers and radicals.
r 1 = Q 1 /Q 2 exp(-e 1 (e 1 -e 2))
and likewise
r 2 = Q 2 /Q 1 exp(-e 2 (e 2 -e 1))
Using this scheme, it is possible to evaluate the relative reactivity of monomers and the role of polar factors for a large number of pairs of copolymerizing monomers. Styrene with values Q = 1, e = -0.8 is usually taken as the standard monomer. When styrene is copolymerized with other monomers, the latter are characterized by their Q and e values, which makes it possible to predict the behavior of these monomers in copolymerization reactions with other monomers for which Q and e values have also been established. Although the “Q-e” scheme does not yet have a complete theoretical justification, in practice she turned out to be very helpful. The Q and e values of most monomers are collected in reference literature.
Radical sonolimerization usually initiated in the same ways as radical polymerization. It is characterized by the same mechanisms of growth, chain termination and transmission.
Let's consider the copolymerization of two monomers M, and M 2. If the activity of growth radicals is determined only by the type end link then four elementary growth reactions should be taken into account:
The corresponding rates of elementary stages of chain growth can be written as
The kinetics of the chain growth reaction determines the composition of copolymers and the entire complex of their chemical and physical-mechanical properties. The model, which takes into account the influence of the terminal link on the reactivity of the active center in relation to monomer molecules and considers four elementary reactions of a growing chain with different types of terminal link (M*) with the monomer (M (), is called "end link model" copolymerization. This model was independently proposed in 1944 by American chemists F. Mayo and F. Lewis. Kinetic processing of the given scheme in a quasi-stationary approximation makes it possible to establish the relationship between composition of copolymers And composition of the initial mixture of monomers, those. an equation that describes the composition of the “instant” copolymer, as well as the composition of the copolymer formed at the initial conversions, when changes in monomer concentrations can be neglected.
Assumptions required for the conclusion copolymer composition equations(dependence of the copolymer composition on the composition of the monomer mixture) include:
- 2) reactivity of M* and M: * does not depend on R p;
- 3) quasi-stationary condition: the concentrations of M* and M* remain constant if the rates of their mutual transformation are the same, i.e. V p |2 = K r 21;
4) low conversions.
The rates of monomer conversion during copolymerization are described by the equations
where from, and t 2 - concentration of monomer units in the copolymer.
The ratio of the rates of these reactions leads to the expression
Taking into account the stationary condition for the concentrations of radicals, it is easy to obtain the following expression, which characterizes at the initial stages of the transformation, when changes in the concentrations of monomers [M,] and [M2], can be neglected, the dependence of the composition of the resulting copolymer on the composition of the monomer mixture:
Where k iV k 22- rate constant for the radical to add its monomer; kvl, k. n- rate constant for the addition of a foreign monomer by a radical; g, = k n /k l2 , r 2 = k 22 /k 2l- copolymerization constants, depending on the chemical nature of the reacting monomers.
Often, instead of concentrations, their corresponding mole fractions are used. Let us denote by /, and / 2 the mole fractions of comonomers in the mixture, and by F( And F2- mole fractions of units M ( and M 2 in the copolymer:
Then, combining expressions (5.28)-(5.30), we obtain
The dependence of the composition of copolymers on the composition of the monomer mixture is conveniently characterized by a composition diagram (Fig. 5.1). At r(> 1 and r 2 1 copolymer is enriched with Mj units (curve 1) at r x 1 and r 2 > 1 copolymer is enriched with M units; (curve 2). If r, = r 2 = 1, then the composition of the copolymer is always equal to the composition of the original mixture (direct 3).
Rice. 5.1.
If r( r ( > 1 and r 2 > 1, then there is a tendency towards separate polymerization of monomers in the mixture (curve 5). If the composition curve intersects the diagonal of the composition diagram, then at the intersection point called azeotropic, the composition of the copolymer is equal to the composition of the comonomer mixture.
The properties of binary copolymers depend on the average composition of the copolymer, its compositional heterogeneity and the distribution of monomer units in macromolecules. With the same composition, the distribution of links along the chain can be different (block, statistical, alternating or gradient). The composition of an individual macromolecule may differ from the average composition of the entire sample, which leads to compositional heterogeneity of the copolymer. A distinction is made between instantaneous and conversion heterogeneity of copolymers. Instant compositional heterogeneity arises as a result of the statistical nature of the process. Conversion compositional heterogeneity is caused by a change in the composition of the monomer mixture during copolymerization (except for azeotropic copolymerization), its contribution to the overall compositional heterogeneity is much higher than the contribution of instantaneous heterogeneity.
During copolymerization at deep stages of transformation, the composition of the monomer mixture (except in the case of azeotropic copolymerization) continuously changes during the course of the reaction: the relative content of the more active monomer decreases, and the less active one increases (Fig. 5.2).
Rice. 5.2. Dependence of the copolymer composition on the composition of the monomer mixture for cases of one-sided enrichment (curve1: r,> 1; r 2 2: r x 1; r 2 > 1)
For the same composition of the monomer mixture (Fig. 5.2, point A) products are formed with different contents of the first component: corresponding in the first case - point IN at the second point D". During the reaction, the mole fraction M will constantly change: in the first case it will decrease, in the second it will increase. At the same time, the instantaneous compositions of the resulting copolymers will change: in the first case, there will be a constant depletion of the copolymer in Mp units; in the second, an enrichment in M units. In both cases, products of different “instant” compositions accumulate, which leads to the emergence of conversion compositional heterogeneity of the resulting copolymer. However, the average composition of the final product in both cases will be the same: at 100% conversion it is equal to the composition of the monomer mixture and corresponds to the point WITH.
During copolymerization with a tendency to alternate (see Fig. 5.1, curve 4) for an arbitrary composition of the initial monomer mixture, there are two composition regions on the composition curve: one lies above the diagonal and the second lies below this diagonal. They are separated by the azeotrope point ( ), which is located at the intersection of the composition curve with the diagonal. With the exception of the azeotrope point, during copolymerization the instantaneous compositions of the copolymer change along a curve to the right. Thus, in this case, copolymerization at deep conversions leads to compositionally heterogeneous products.
An exception is the azeotropic copolymerization of a monomer mixture, during which the compositions of the copolymer and monomer mixture do not change during the reaction and remain equal to the initial composition of the monomer mixture until the monomers are completely exhausted. The invariance of the copolymer composition during azeotropic copolymerization leads to the production of homogeneous products, the compositional heterogeneity of which is minimal and is associated only with its instantaneous component. The condition for the formation of an azeotropic composition has the form
The values of G[ and g 2 can be determined experimentally. Knowing them makes it possible to predict the composition of the copolymer and the distribution of monomer units in the chains for any ratio of monomers in the mixture. Values of r, and g 2 during radical copolymerization and, therefore, the composition of the copolymer usually weakly depends on the nature of the solvent and changes very little with temperature.
The exceptions are:
- 1) phenomena associated with donor-acceptor interactions of reagents. If one of the monomers turns out to be a strong donor and the other a strong acceptor, alternating copolymers are formed (styrene - maleic anhydride, r, = 0 and g 2 = 0);
- 2) co-polymerization of ionic monomers depending on pH (acrylic acid - acrylamide, pH = 2, g, = 0.9 and g 2 = 0.25; pH = 9, g, = 0.3 and g 2 = 0, 95);
- 3) co-polymerization of the “polar monomer - non-polar monomer” pair in polar and non-polar solvents (bootstrap effect, styrene - n-butyl acrylate, g = 0.87 and g 2 = 0.19 in weight and g, = 0.73 and g 2 = 0.33 in DMF; 2-hydroxymethyl methacrylate - tert- butyl acrylate, g, = 4.35 and g 2= 0.35 in mass and g, = = 1.79 and g 2 = 0.51 in DMF);
- 4) heterophasic co-polymerization. In heterophase copolymerization, selective sorption of one of the monomers by the polymer phase can lead to a deviation from the composition characteristic of homogeneous copolymerization of the same solution (styrene - acrylonitrile: copolymerization in bulk and in emulsion; MW A - N-vinylcarbazole in benzene g, = 1 ,80 and g 2 = 0.06, in methanol g, = 0.57 and g 2 = 0,75).
Consideration of the quantities r, and g 2 within the framework of the theory of ideal radical reactivity leads to the conclusion that r, r 2 = 1, i.e. the rate constants for the addition of one of the monomers to both radicals are the same number of times greater than the rate constants for the addition of the other monomer to these radicals. There are a number of systems for which this condition is well realized experimentally. In such cases, monomer units of both types are randomly located in macromolecules. Most often, g., 1, which is associated with polar and steric effects, which determine the tendency for the alternation of monomer units M and M 2 in macromolecules. In table Table 5.12 shows the values of copolymerization constants for some pairs of monomers. Conjugation with a substituent reduces the activity of the radical to a greater extent than it increases the activity of the monomer, so a monomer that is more active in copolymerization turns out to be less active in homopolymerization.
To quantitatively characterize the reactivity of monomers in radical copolymerization, a zero-empirical
Radical copolymerization constants for some monomers
scheme Q-e, proposed in 1947 by American chemists T. Alfrey and K. Price. Within the framework of this scheme it is assumed that
Where P Q- parameters corresponding to the conjugation energies in the monomer and radical according to the theory of ideal radical reactivity. Quantities e ( And e 2 take into account the polarization of the reacting monomers. Then
Using this scheme, it was possible to evaluate the relative reactivity of monomers and the role of polar factors for a large number of pairs of copolymerizing monomers.
Was taken as the standard monomer styrene with meanings Q = 1, e= 0.8. When copolymerizing styrene with other monomers (M), the latter were characterized by their Q values and e~, which made it possible to predict the behavior of these monomers in copolymerization reactions with other monomers, for which values were also established Q And e.
For active radicals, the activity of monomers depends on resonance factors. With increase Q constant k l2 increases. For inactive radicals (styrene, butadiene), the activity of monomers depends on polarity. In table 5.13 shows the values of Qn e some monomers.
Table 5.13
ValuesQAndesome monomers
