- Email: [email protected]
A study of the kinetics of phase layer separation in polymer-crystallizable plasticizer systems
PolymerScienceU.S.S.R, Vol. 25, No. 11, pp. 2674-2679, 1983 Printed in Poland
A
STUDY
OF
THE
KINETICS
OF
IN POLYMER-CRYSTALLIZABLE
0082-8950/83 $10.00+.00 © 1984 PergamonPress Ltd.
PHASE
LAYER
PLASTICIZER
SEPARATION SYSTEMS*
V. A. GOT,OVId, Y r . M. LOTME~rTS~,V,A. B. IT.'~ and 1~./7. KO~Da~ov~ All-Soviet Institute for Research on Metal Corrosion Protection
(Received 26 May 1982) The kinetics and completion of plasticizer crystallization in the cellulose nitrate2,4-dinitrotohiene system have been studied over a wide temperature-concentration range. During the phase separation process, crystallization occurs of only part of the plasticizer which is thermodynamically possible. The temperature dependence of the crystallization rate and also the degree of completion of the process has an extremal function wi~h temperature. By not taking account of the degree of completion of the crystallization process, errors arise in the determination of the concentration limits of the phase diagram. C~aYSTATm~ZATIO~'kinetics have been studied in the cellulose mtrate (C~)-2,4-dinitrotoluene (DNT) model system. The method of preparation of the plasticized system was described in [3]. We studied C ~ with a nitrogen content of 1 2 ~ and My----7-5 × 104. D N T was purified b y twice recrystallizing from ethanol. Crystallization kinetics were studied using an isothermal volume and linear dilatometer and in concentrated systems by the change in random compression modulus [5]. Specific volumes were determined in liquid, divided dilatomers. Linear dimensions were measured b y a contact method using a watch-type indicator with a graduation of 0.01 ram. The random compression modulus E was determined on a Klaper consistometer with a loading time of 10 sec. The crystalline phase content in plasticized systems was determined using resistance thermometers in a microcalorimeter [6], with a pecision of : L 3 ~ . The crystallization study was preceded b y annealing the system for 2 hr at 100 °, which was necessary for complete fusion of the plasticizer crystals and homogenisation of the system. The main emphasis at present in the study of phase separation in plasticized polymers whose low-molecular weight component is capable of crystallizing, has been the construction of phase diagrams [1-4], whilst the problems of the kinetics and completion of the crystallization process have hardly been studied. Apart from its practical value, connected with directional effects on the structure and properties of a system with a crystallizable plasticizer [1], a kinetic study presents theoretical interest i.e. from the viewpoint of explaining basic factors which determine the rate and, especially important in polymer systems, the completion of the phase separation process. * Vysokomol. soyed. A25: No. 11, 2300-2304, 1983. 2674
Phase layer separation in polymer-crystallizable plasticizer systems
2675
The latter m a y be used a~ a criterium for appraising various methods for construction of the phase composition diagrams. Figure 1 gives typical relations of the plasticizer crystallization isotherm in a plasticized polymer. The isotherms have an S-shape which is characteristic of crystallization of low and high molecular weight substances. The crystallization rate from which the magnitude of the inverse of the half --1 period of crystallization ~0.~ m a y be judged [5], appears to have an extremal function with temperature (Fig. 2). The maximum crystallization rate occurs in the 40-50 ° temperature range. The extremal dependence of the platicizer crystal in the 40-50 ° temperature range. The extremal dependence of the plasticizer crystallization rate agrees qualitatively with the conclusions of classical nucleation theory [7].
•'II~i0z 5
v.lo ,m /kg
I
b
a
z.o
7.4
2
3 I I
20
60
6"6
I00
120
200
Time ~ rnin E • 10-a, Pa
E , 10-4 Pa
d 8
~"~"
8~
1"5
e_G 0"5 6
18
30
12
3G
60
T/me ~. fO'Z,rn/n
Fzo. 1. Typical crystallization isotherms, obtained for changes in length Jl/l~ (a), specific volume V (b) and compression modulus E (e, d) during the crystallization of plasticizer from a system cpntaining 75 (a), 70 (b), 65 (c) and 60 (d) wt.% of DNT at 57.4 (1), 60 (2), 55 (3), 45 (4), 40 (5), 30 (6), 22 (7), 20 (8) and 40 (9). One of the important questions concerning phase separation in polymer systems is t h a t of its extent of completion. For this, calorimetric studies were made to determine crystalline phase content after prolonged isothermal crystallization
"26"/6
V . A . G o L o v r ~ e$ a/.
Crystallization durations of 3-12 months exceeded by an order the time for process completion, found from kinetic studies. This prompts one to consider the values of degrees of crystallinity obtained for plasticized systems a s pseudo-equilibrated, i.e. corresponding to practically complete phase separation in the given conditions. Figure 3 presents the temperature dependence of plasticizer crystal content in :NG-DNT systems and Fig. 4 gives the similar dependence for the degree of completion of crystallization, a = ~ / o ~ , where o~ is the weight fraction of crystals, corresponding to completion of the process, calculated from the composition diagram [2]. The magnitudes of ~ and o) are extremal functions of temperature, where the location of the maximum coincides with the temperature of maximum crystallization rate. In principle, the degree of completion of crystallization even when the process proceeds under optimum conditions, is essentially less than 1. One of the reasons for non-completion of crystallization is kinetic retardation d u e to the high viscosity of the polymer system. As crystallization proceeds, the quantity of plasticizer in the polymer phase decreases, causing additional retarda.tion.
log ~.'s EnTin-~ -1 0"7 -2
O'5
-3 -#
t
IO
t
i
30
I
t
50
0"3 To
I0
30
50 T °
Fro. 2 Fro. 3 Fie. 2. Relation of ~0.5to temperature for systems containing 75 (1), 70 (2), 65 (3) and 60 (4) wt.% of DNT, constructed by linear (A) and volume (B) dilatometry and from changes in compression modulus (G). F r o . 3. Relation of content of crystal-phase plasticizer, ca, to temperature for systems conraining 75 (1) and 70 (2) wt.% of DNT. These reasons are evidently not the only determining factors. Thus, it follows from the results obtained (Fig. 5) that with an initial plasticizer content of qz=0.7, crystallization proceeds up to the point when the residual plasticizer content, which has not e, ~tcred the crystalline phase, is below qz=0.6. At the same time, with initial s y s ~ m s with ~z----0"6, crystallization proceeds rather quickly. This prompts the co~clusion th~l,t the appearance of crystals of plasticizer in the bulk system causes process retardation. One reason for the similar influence of
Phase layer separation i~ polymer-crystallizable plasticizer systems
2677
the separatable crystalline phase m a y be linked with the peculiar reinforcing effect of the crystalline filler, causing limited mobility o f the p o l y m e r chains [8-10]. T h e p h e n o m e n o n of incomplete phase separation m a y be, to a certain e x t e n t , due to emergence o f i n t e r n a l stresses in the system, as a result o f crystallization. As can be seen f r o m t h e d a t a given in Fig. 1, a c o n t r a c t i o n o f specific v o l u m e is observed in the zone o f crystal growth. A t the same time, the elastic modulus o f the system is increased during crystallization, which impedes bulk r e l a x a t i o n a n d while preserving c o n t i n u i t y o f t h e system, causes internal stretching stresses to appear. The presence o f the latter, in accord with the t h e r m o d y n a m i c analysis [ 11], m u s t cause a r e d u c t i o n in t h e m o t i v e force of the crystallization process o f the
0.70.5~ ,I 0.3
lO
I 50 T
30
FIO. 4. Relation of degree of completion a of the process to temperature for systems containing 75 (1) and 70 (2) wt. % of DNT.
I
0"6 - o
8O:
~
0"4 0"2
4O I
0"4
I
0.6
FIG. 5
I 0.8
20
20
60
~I , ~. ~
FIo. 6
FIO. 5. Relation of residual concentration qres of plasticizer in the plasticized polymer phase after crystallization at 47 (1) and 20° (2), to initial plasticizer concentration q~ in the plasticized system. FIo. 6. Boundary of region of crystallization of the plasticizer, determinod by the thorm~)dynamic method (1) [2], and calculated (2) from the content of crystalline phase after thermostarting aS various temperatures, by the method described in [4]; 3--concentrational depex~donce of the glass transition temperature of tho system.
2678
V . A . GOLOVIN e~ al.
chemical potential of the plasticizer due to appearance of non-equilibrated components of the chemical potential A#~, corresponding to the equation A / ~ = P V x , where P is stress, V1 is the partial molal volume of the plasticizer. The values of stress (in MPa) are given below for the highly elastic and glassy states of the system, for different contractions of the specific volume, AV/170
.dV/Vo Highly elastic state Glassy state
0.01 0'3 30
0.05 1"5 150
0.1 3.0 300
The calculation was made from the equation, P=KAV/Vo, where K is the bulk compression modulus, A V is the volume change and V0 is the initial volume of the system. The magnitude of K was taken as 3 × 10 - n for the highly elastic state and as 3 × 10 -9 Pa [12], for the glassy state. I t is evident from the results given that even with the very small volume changes, which occur during crystallization, the stresses which develop m a y be rather large and commensurate with the magnitudes of osmotic pressure in polymer solutions Thus the relaxation properties of the polymer matrix may exhibit a decisive influence on the degree of completion and apparent degree of equilibrium of crystallizable polymer system. It is necessary to consider the above mentioned features of crystallization of plasticizers in polymer compositions when contrueting phase composition diagrams of the polymer-plasticizer system. So for example, when using calorimetric methods to determine the amount of "free" plasticizer [4] from data on the amount of plasticizer crystallizing under the conditions of the experiment the importance of errors arises due to pseudoequilibrium of the system (Fig. 6). T ~
by C. W. C ~ e
REFERENCES
1. S. P. PAPKOV, Studneobraznoye sostoyaniye polimerov (The Gel Composition of Polymers). p. 194, Khimiya, 1974; S. P. PAPKOV, Fiziko-kblmlcheskiye osnovy perera° botki rastvorov polimerow (The Physico-chemical Basis of Treatment of Polymer Solutions) Khimiya, 1972 2. V. A. GOLOVIN, Yu. M. LOTMENTSEV and V. A. ANDREYEV, Vysokomol. soyod. A18: 1073, 1976 (Translated in Polymer Sci. U.S.S.R. 18: 5, 1233, 1976) 3. V. A. GOLOVIN, Yu. M. LOTMENTSEV and R. L SHNEERSON, Vysokomol. soyed. A17: 2351, 1975 (Translated in Polymer Sci. U.S.S.R. 17: 10, 2709, 1975) 4. I. B. RABINOVICH and A. N. MOCHALOV, In: Tez. II. Yses. conf. po. termodinamikyo organicheskikh syoedinenii (Proceedings of 2nd All-Soviet Conference on the Thermodynamic of Organic Compounds). p. 66, Izd. Gor'korskun-ta, Gorkii, 1976 5. M. F. BIYKHINA, KristaUizatsiya kauchukov i rezin (Crystallization of Rubbers and Resins). p. 79, Khimiya, 1973 6. V. A. YURZHENKO, T. M. GRITSENKO, N. N. FEDOROV and I. A. POPOV, In: Noviye
metody issoledovauiya polimerov (Now Methods for Polymer Study).p. 191, Naukova Dumka, Kiev, 1975
Description of non-equilibrated polycondensation processes
2679
7. L. MANDEL'KERN, Kristallizatsiya polimerov (Crystallization of polymers), p. 237, M i r , 1966. 8. Yu. S. LIPATOV, Fizicheskaya khimiya napohaennikh polimerov (Physical Chemistry of Filled Polymers). p. 131, Iqaukova Dumka, Kiev, 1977 9. I. B. RABINOVIOH, Vysokomol. soyed. B12: 626, 1970 (Not translated in Polymer Sci.
U.S.S.R.) 10. T. A. SEREBRYANIKOVA and A. I. MAKLAKOV, Vysokomol. soyed. B21: 265, 1 9 7 9 (Not translated in Polymer Sci. U.S.S.R.) 11. P. J. FLORY, J. Amer. Chem. Soc. 78: 1O, 5222, 1956 12. D. V. VAN-KREVELEN, Svoistva i khimicheskoye stroyeniye polimerov (Properties and Chemical Structure of Polymers). p. 145, Khimiya, 1976.
Polymer Science U.S.S.R. Vol. 25, No. 11, pp. 2679-2687, 1988
Printed in Poland
0082-3950/88 $10.00 +.00 © 1984 Pergamon Press Ltd.
THE APPLICABILITY OF A STATISTICAL APPROACH TO A DESCRIPTION OF NON-EQUILIBRATED POLYCONDENSATION PROCESSES* V. I. IZtZm~,_Kand M. L. TAI Institute of Chemical Physics, U.S.S.R. Academy of Sciences Applied Mathematics and Cybernetics Research Institute, Gorky State University
(Received 26 May 1982) Based on the results of a study of self-assembly processes, conditions have been found for application of a statistical approach to the description of non-equilibrated polycondensation processes. An algorithm has been proposed for calculation of the following linear polycondensation cases: alternating copolycondensation of two monomers, the reactivity of one of which is subordinate to tl~e "neighbouring group effect", alternating copolycondensation of n monomer of type A and ~monomers of type B, t h e reactivity of monomers of type A being subordinate to the "neighbouring group effect", copolycondensation of monomers A and B, the reactivity of A being subordinate to the "neighbouring group effect" and the possibility of forming either Aa or A~ blocks, where i is any number.
T1r~ solution of a complete system of differential equations, describing the l~ineties of non-equihbrated polycondensa~ion is usually very difficult. Consequently, beginning with l~lory [1], a statistical method was developed (see bibliography to [2]), the essence of which is the use of assumptions having a statistical origin and permitting one to apply the solution of a complete set of differential equations to a system, which satisfies the concentration of certain isolated components, * Vysokomol. soyed. #-25: 1~o. 11, 2305-2311, 1983.
A
STUDY
OF
THE
KINETICS
OF
IN POLYMER-CRYSTALLIZABLE
0082-8950/83 $10.00+.00 © 1984 PergamonPress Ltd.
PHASE
LAYER
PLASTICIZER
SEPARATION SYSTEMS*
V. A. GOT,OVId, Y r . M. LOTME~rTS~,V,A. B. IT.'~ and 1~./7. KO~Da~ov~ All-Soviet Institute for Research on Metal Corrosion Protection
(Received 26 May 1982) The kinetics and completion of plasticizer crystallization in the cellulose nitrate2,4-dinitrotohiene system have been studied over a wide temperature-concentration range. During the phase separation process, crystallization occurs of only part of the plasticizer which is thermodynamically possible. The temperature dependence of the crystallization rate and also the degree of completion of the process has an extremal function wi~h temperature. By not taking account of the degree of completion of the crystallization process, errors arise in the determination of the concentration limits of the phase diagram. C~aYSTATm~ZATIO~'kinetics have been studied in the cellulose mtrate (C~)-2,4-dinitrotoluene (DNT) model system. The method of preparation of the plasticized system was described in [3]. We studied C ~ with a nitrogen content of 1 2 ~ and My----7-5 × 104. D N T was purified b y twice recrystallizing from ethanol. Crystallization kinetics were studied using an isothermal volume and linear dilatometer and in concentrated systems by the change in random compression modulus [5]. Specific volumes were determined in liquid, divided dilatomers. Linear dimensions were measured b y a contact method using a watch-type indicator with a graduation of 0.01 ram. The random compression modulus E was determined on a Klaper consistometer with a loading time of 10 sec. The crystalline phase content in plasticized systems was determined using resistance thermometers in a microcalorimeter [6], with a pecision of : L 3 ~ . The crystallization study was preceded b y annealing the system for 2 hr at 100 °, which was necessary for complete fusion of the plasticizer crystals and homogenisation of the system. The main emphasis at present in the study of phase separation in plasticized polymers whose low-molecular weight component is capable of crystallizing, has been the construction of phase diagrams [1-4], whilst the problems of the kinetics and completion of the crystallization process have hardly been studied. Apart from its practical value, connected with directional effects on the structure and properties of a system with a crystallizable plasticizer [1], a kinetic study presents theoretical interest i.e. from the viewpoint of explaining basic factors which determine the rate and, especially important in polymer systems, the completion of the phase separation process. * Vysokomol. soyed. A25: No. 11, 2300-2304, 1983. 2674
Phase layer separation in polymer-crystallizable plasticizer systems
2675
The latter m a y be used a~ a criterium for appraising various methods for construction of the phase composition diagrams. Figure 1 gives typical relations of the plasticizer crystallization isotherm in a plasticized polymer. The isotherms have an S-shape which is characteristic of crystallization of low and high molecular weight substances. The crystallization rate from which the magnitude of the inverse of the half --1 period of crystallization ~0.~ m a y be judged [5], appears to have an extremal function with temperature (Fig. 2). The maximum crystallization rate occurs in the 40-50 ° temperature range. The extremal dependence of the platicizer crystal in the 40-50 ° temperature range. The extremal dependence of the plasticizer crystallization rate agrees qualitatively with the conclusions of classical nucleation theory [7].
•'II~i0z 5
v.lo ,m /kg
I
b
a
z.o
7.4
2
3 I I
20
60
6"6
I00
120
200
Time ~ rnin E • 10-a, Pa
E , 10-4 Pa
d 8
~"~"
8~
1"5
e_G 0"5 6
18
30
12
3G
60
T/me ~. fO'Z,rn/n
Fzo. 1. Typical crystallization isotherms, obtained for changes in length Jl/l~ (a), specific volume V (b) and compression modulus E (e, d) during the crystallization of plasticizer from a system cpntaining 75 (a), 70 (b), 65 (c) and 60 (d) wt.% of DNT at 57.4 (1), 60 (2), 55 (3), 45 (4), 40 (5), 30 (6), 22 (7), 20 (8) and 40 (9). One of the important questions concerning phase separation in polymer systems is t h a t of its extent of completion. For this, calorimetric studies were made to determine crystalline phase content after prolonged isothermal crystallization
"26"/6
V . A . G o L o v r ~ e$ a/.
Crystallization durations of 3-12 months exceeded by an order the time for process completion, found from kinetic studies. This prompts one to consider the values of degrees of crystallinity obtained for plasticized systems a s pseudo-equilibrated, i.e. corresponding to practically complete phase separation in the given conditions. Figure 3 presents the temperature dependence of plasticizer crystal content in :NG-DNT systems and Fig. 4 gives the similar dependence for the degree of completion of crystallization, a = ~ / o ~ , where o~ is the weight fraction of crystals, corresponding to completion of the process, calculated from the composition diagram [2]. The magnitudes of ~ and o) are extremal functions of temperature, where the location of the maximum coincides with the temperature of maximum crystallization rate. In principle, the degree of completion of crystallization even when the process proceeds under optimum conditions, is essentially less than 1. One of the reasons for non-completion of crystallization is kinetic retardation d u e to the high viscosity of the polymer system. As crystallization proceeds, the quantity of plasticizer in the polymer phase decreases, causing additional retarda.tion.
log ~.'s EnTin-~ -1 0"7 -2
O'5
-3 -#
t
IO
t
i
30
I
t
50
0"3 To
I0
30
50 T °
Fro. 2 Fro. 3 Fie. 2. Relation of ~0.5to temperature for systems containing 75 (1), 70 (2), 65 (3) and 60 (4) wt.% of DNT, constructed by linear (A) and volume (B) dilatometry and from changes in compression modulus (G). F r o . 3. Relation of content of crystal-phase plasticizer, ca, to temperature for systems conraining 75 (1) and 70 (2) wt.% of DNT. These reasons are evidently not the only determining factors. Thus, it follows from the results obtained (Fig. 5) that with an initial plasticizer content of qz=0.7, crystallization proceeds up to the point when the residual plasticizer content, which has not e, ~tcred the crystalline phase, is below qz=0.6. At the same time, with initial s y s ~ m s with ~z----0"6, crystallization proceeds rather quickly. This prompts the co~clusion th~l,t the appearance of crystals of plasticizer in the bulk system causes process retardation. One reason for the similar influence of
Phase layer separation i~ polymer-crystallizable plasticizer systems
2677
the separatable crystalline phase m a y be linked with the peculiar reinforcing effect of the crystalline filler, causing limited mobility o f the p o l y m e r chains [8-10]. T h e p h e n o m e n o n of incomplete phase separation m a y be, to a certain e x t e n t , due to emergence o f i n t e r n a l stresses in the system, as a result o f crystallization. As can be seen f r o m t h e d a t a given in Fig. 1, a c o n t r a c t i o n o f specific v o l u m e is observed in the zone o f crystal growth. A t the same time, the elastic modulus o f the system is increased during crystallization, which impedes bulk r e l a x a t i o n a n d while preserving c o n t i n u i t y o f t h e system, causes internal stretching stresses to appear. The presence o f the latter, in accord with the t h e r m o d y n a m i c analysis [ 11], m u s t cause a r e d u c t i o n in t h e m o t i v e force of the crystallization process o f the
0.70.5~ ,I 0.3
lO
I 50 T
30
FIO. 4. Relation of degree of completion a of the process to temperature for systems containing 75 (1) and 70 (2) wt. % of DNT.
I
0"6 - o
8O:
~
0"4 0"2
4O I
0"4
I
0.6
FIG. 5
I 0.8
20
20
60
~I , ~. ~
FIo. 6
FIO. 5. Relation of residual concentration qres of plasticizer in the plasticized polymer phase after crystallization at 47 (1) and 20° (2), to initial plasticizer concentration q~ in the plasticized system. FIo. 6. Boundary of region of crystallization of the plasticizer, determinod by the thorm~)dynamic method (1) [2], and calculated (2) from the content of crystalline phase after thermostarting aS various temperatures, by the method described in [4]; 3--concentrational depex~donce of the glass transition temperature of tho system.
2678
V . A . GOLOVIN e~ al.
chemical potential of the plasticizer due to appearance of non-equilibrated components of the chemical potential A#~, corresponding to the equation A / ~ = P V x , where P is stress, V1 is the partial molal volume of the plasticizer. The values of stress (in MPa) are given below for the highly elastic and glassy states of the system, for different contractions of the specific volume, AV/170
.dV/Vo Highly elastic state Glassy state
0.01 0'3 30
0.05 1"5 150
0.1 3.0 300
The calculation was made from the equation, P=KAV/Vo, where K is the bulk compression modulus, A V is the volume change and V0 is the initial volume of the system. The magnitude of K was taken as 3 × 10 - n for the highly elastic state and as 3 × 10 -9 Pa [12], for the glassy state. I t is evident from the results given that even with the very small volume changes, which occur during crystallization, the stresses which develop m a y be rather large and commensurate with the magnitudes of osmotic pressure in polymer solutions Thus the relaxation properties of the polymer matrix may exhibit a decisive influence on the degree of completion and apparent degree of equilibrium of crystallizable polymer system. It is necessary to consider the above mentioned features of crystallization of plasticizers in polymer compositions when contrueting phase composition diagrams of the polymer-plasticizer system. So for example, when using calorimetric methods to determine the amount of "free" plasticizer [4] from data on the amount of plasticizer crystallizing under the conditions of the experiment the importance of errors arises due to pseudoequilibrium of the system (Fig. 6). T ~
by C. W. C ~ e
REFERENCES
1. S. P. PAPKOV, Studneobraznoye sostoyaniye polimerov (The Gel Composition of Polymers). p. 194, Khimiya, 1974; S. P. PAPKOV, Fiziko-kblmlcheskiye osnovy perera° botki rastvorov polimerow (The Physico-chemical Basis of Treatment of Polymer Solutions) Khimiya, 1972 2. V. A. GOLOVIN, Yu. M. LOTMENTSEV and V. A. ANDREYEV, Vysokomol. soyod. A18: 1073, 1976 (Translated in Polymer Sci. U.S.S.R. 18: 5, 1233, 1976) 3. V. A. GOLOVIN, Yu. M. LOTMENTSEV and R. L SHNEERSON, Vysokomol. soyed. A17: 2351, 1975 (Translated in Polymer Sci. U.S.S.R. 17: 10, 2709, 1975) 4. I. B. RABINOVICH and A. N. MOCHALOV, In: Tez. II. Yses. conf. po. termodinamikyo organicheskikh syoedinenii (Proceedings of 2nd All-Soviet Conference on the Thermodynamic of Organic Compounds). p. 66, Izd. Gor'korskun-ta, Gorkii, 1976 5. M. F. BIYKHINA, KristaUizatsiya kauchukov i rezin (Crystallization of Rubbers and Resins). p. 79, Khimiya, 1973 6. V. A. YURZHENKO, T. M. GRITSENKO, N. N. FEDOROV and I. A. POPOV, In: Noviye
metody issoledovauiya polimerov (Now Methods for Polymer Study).p. 191, Naukova Dumka, Kiev, 1975
Description of non-equilibrated polycondensation processes
2679
7. L. MANDEL'KERN, Kristallizatsiya polimerov (Crystallization of polymers), p. 237, M i r , 1966. 8. Yu. S. LIPATOV, Fizicheskaya khimiya napohaennikh polimerov (Physical Chemistry of Filled Polymers). p. 131, Iqaukova Dumka, Kiev, 1977 9. I. B. RABINOVIOH, Vysokomol. soyed. B12: 626, 1970 (Not translated in Polymer Sci.
U.S.S.R.) 10. T. A. SEREBRYANIKOVA and A. I. MAKLAKOV, Vysokomol. soyed. B21: 265, 1 9 7 9 (Not translated in Polymer Sci. U.S.S.R.) 11. P. J. FLORY, J. Amer. Chem. Soc. 78: 1O, 5222, 1956 12. D. V. VAN-KREVELEN, Svoistva i khimicheskoye stroyeniye polimerov (Properties and Chemical Structure of Polymers). p. 145, Khimiya, 1976.
Polymer Science U.S.S.R. Vol. 25, No. 11, pp. 2679-2687, 1988
Printed in Poland
0082-3950/88 $10.00 +.00 © 1984 Pergamon Press Ltd.
THE APPLICABILITY OF A STATISTICAL APPROACH TO A DESCRIPTION OF NON-EQUILIBRATED POLYCONDENSATION PROCESSES* V. I. IZtZm~,_Kand M. L. TAI Institute of Chemical Physics, U.S.S.R. Academy of Sciences Applied Mathematics and Cybernetics Research Institute, Gorky State University
(Received 26 May 1982) Based on the results of a study of self-assembly processes, conditions have been found for application of a statistical approach to the description of non-equilibrated polycondensation processes. An algorithm has been proposed for calculation of the following linear polycondensation cases: alternating copolycondensation of two monomers, the reactivity of one of which is subordinate to tl~e "neighbouring group effect", alternating copolycondensation of n monomer of type A and ~monomers of type B, t h e reactivity of monomers of type A being subordinate to the "neighbouring group effect", copolycondensation of monomers A and B, the reactivity of A being subordinate to the "neighbouring group effect" and the possibility of forming either Aa or A~ blocks, where i is any number.
T1r~ solution of a complete system of differential equations, describing the l~ineties of non-equihbrated polycondensa~ion is usually very difficult. Consequently, beginning with l~lory [1], a statistical method was developed (see bibliography to [2]), the essence of which is the use of assumptions having a statistical origin and permitting one to apply the solution of a complete set of differential equations to a system, which satisfies the concentration of certain isolated components, * Vysokomol. soyed. #-25: 1~o. 11, 2305-2311, 1983.