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Rheokinetics of radical polymerization
Polymer Science U.S.S.R. Vol. 22, lqo. 9, I)P. 2296-2804, 1980
0082-8950/80/092296-09507.5010
lh,inted in Poland
0 1981 PergamonPrea Ltd.
RHEOKINETICS OF RADICAL POLYMERIZATION* S. G. KVLICHlXH~¢ and A. YA. M ~ x ~ Scientific Industrial Association "Plastics"
(Received 9 August !979) Kinetic mechanisms and rheological properties of polymerization systems were examined and concrete mathematical ratios describing the increase in the viscosity of reaction masses during radical polymerization, derived. The conclusions drawn were confirmed b y experimental results of radical polymerization of methyl methaerylate and styrene available in the literature.
TH~ formation of polymer molecules is accompanied by ~ considerable increase in the viscosity of the reaction medium, the range of viscosity variation normally representing several decimal orders of magnitude. The type of viscosity variation influencing polymerization a n d technical apparatus used is determined by t h e mechanism and specific properties of a given reaction. However, unfortunately, the few investigations devoted to the variation of rheological properties of polymerizing masses are only restricted to recording the dependence of viscosity over a period of time t/(t) or on the degree of conversion of t/(fl). The existence o f a relation between the type of viscosity increase of the reaction medium and kinetic regularities of particular reactions enables the specific variation of main kinetic factors to be observed: temperature, composition of the reaction medium, reagent concentration and phase condition of the system. This approach requires a quantitative link to be established between the mechanism and reaction kinetics of polymerization and the type of viscosity increase. This program was implemented and experimentally confirmed for ionic polymerization with a constant number of active centres of macromolecular extension [1, 2]. This study seeks to develop the rheokinetie approach to a widely used class of reaction of radical polymerization and to verify experimentally theoretical results using experimental data available in the literature concerning the type of viscosity increase in typical reactions of radical polymerization, which forms the basis for a general methodological approach to the viscometrie analysis of radical polymerization. This approach is based on a combination of well-known kinetic mechanisms. of polymerization and existing views about general rules governing rheological properties of polymer solutions (reaction masses). This combined approach enabled us to obtain new results concerning viscosity increase in polymerizatiorr and the effect of main process parameters. * Vysokomol. soyed. A 2 2 : N o , 9, 2093-2100, 1980. 2296
Rheokinetics of radical polymerization
229~
t
An increase in the viscosity of the reaction medium in polymerization is determined both by the increase in molecular weight of the polymer formed and the increase of its content in the polymerization mass. ~Iechanisms governing the variation of molecular weight and polymer concentration in the reaction system depend on kinetics and the mechanism of polymerization [3]. The reaction mass should generally be regarded as a solution of the polymer formed in t h e initial monomer and solvents used. The viscosity of this solution is a function of average chain length of the polymer formed (z~) and its concentration ~: ~ = f (N, ~). The weight fraction of the polymer formed in the reaction system is equal to the degree of monomer conversion, i.e. ~ - ~ f l : ([~I]o--~I]/[1VI]0), where [M]0 is the initial and [1~], the current concentration of the monomer. In m a n y cases, during thermal initiation, in particular, the current concentration of the initiator [1] is expressed as follows: [I]~-[I]o exp (--k~t), (1) where [I]o is the initial concentration of the initiator, ki, rate constant of initiation, t, time. The viscosity of a single-phase polyme.r solution such as homogeneous reaction masses, m a y be described by the formula:
y-.~KflbN a,
(2)
where K, a and b are constants, ~V, degree of polymerization. I n radical processes without considering chain transfer and combination termination, variations of the numerical average degree of polymerization _h~ and conversion fl are described by formulae [4, 5]: =_
[M]ofl [i]d l _ e _ ~ t ) 2 4Y]CP.... ~. -~l~, tLl (*-e j,
(3)
(4)
where kp and kt are constants of chain propagation and termination, respectively, f is the efficiency of the initiator. Formulae m a y then be derived which characterize viscosity variations of t h e reaction mass when selecting as independent argument the degree of conversion fl or time t
q-~ K fl' L[i]o(l__~_,,,ij or
where
ktkt K,-~K[M]~.
(6)
:2298
S.O. KULICHIKHIN and A. YA. }ffAT.~r~l
Therefore, when constants of elementary reactions and theological properties o f polymer solutions in the monomer or in the solvent used are known, the use o f formula (6) makes it possible to give a full rheological description of the viscosity variation of reaction media in radical polymerization. The formulae derived m a y be simplified considerably. Expanding in series t h e functions contained in these formulae and being restricted to linear components (when fl<
t/=Ofl b, -where O - ~ K 1
~/2fkl-*[I]o*
(7)
-- ctmstant.
I f we consider viscosity variation over a period of time, we m a y write r/= 01t~,
(8)
• where
These formulae give a fairly simple description of viscosity increase at the initial stages of radical polymerization and enable a quantitative evaluation to be made of the role of major factors: kinetic constants and initiator concentration. I t is natural t h a t t h e y do not apply t o advanced stages of conversion, w h e n auto-acceleration takes place, which is dependent on the formation of a gelfraction and kinetic constants show a consequent variation. Let us examine the consequences that follow from the regularities derived in relation to the role of initiator concentration [I]0 and the temperature of isothermal polymerization T. The value of [I]0 forms part of constant 8 and 8z in formulae (7) and (8) and if its effect is expressed simply formulae (8) and (7) m a y be written as:
,l=6'[]];*"f
(9)
,1= oi[I]o eb-.)?,
(1 O)
w h e r e 8' and 01 are constants, the physical significances of which are easily established from the formulae described. Therefore, when fl=const ~ [ I ] ~ *~ and when t = c o n s t t/~[I]o~(b-a), where i n d e x a characterizes the effect of molecular weight on the viscosity of the polymer solution in a given solvent, or the monomer itseff and b is the effect of concentration. Reaction temperature has a variable effect on the yield and molecular weight ~ f the polymer formed. I f we compare viscosity with a constant degree of conver-
Rheokineties of radical polymerization
2299
sion and bear in mind that values of K1, kp, kt and ki in formula (7) may be presented as exponential functions of temperature, it appears that ~ exp [E~~ a (Ep-- ½Et-- ½Ei)/RT],
(11)
where E, is the activation energy of viscous flow, El, Ep and Et is the activation energy of chain initiation, growth and termination, respectively. An "effective" activation energy of viscosity increase may be derived with an arbitrary value of fl----const. When plotting the dependence of v/(fl)on T in coordinates log v/-T-1 when fl-~const activation energy is determined as follows:
E~:E,+a(Ep--½Et--½E1)
(12)
When comparing temperature dependences of fl values corresponding to isoviscous states of the reaction mass, and plotting them in coordinates In fl-T -1 (when ~----const) the formula for the "effective" activation energy takes the form: E~=--
E,+a(Ep-- ½Et-- ½El) b
(13)
When studying the temperature dependence of the visosity for a fixed time of polymerization t----const (i.e. with the dependence of In tI-T -1 when t----const) activation energy is determined as
Et----E~+(a-~b) (Ep--½E,)-}-½(b--a)Ei
(14)
The temperature dependence of the time during which a given level of viscosity is achieved (y*~eonst) for a case which is most important practically, is determined by the "effective" activation energy calculated from: E;--
E,w}-(a~-b ) (Ep--½Et)-}-½(b--a)Ei b
(15)
These results show that the empirical approach of calculating the activation energy of rheokinetic processes proposed previously [6] is, in general, incorrect. Therefore, the concept of activation energy becomes ambiguous dependent on the conditions of comparison and the significance of the values, the temperaCure dependence of which have been considered. Formulae and ratios derived allow for experimental verification and this will be dealt with later. Few experimental studies have been carried out giving results of the variation of rheological properties of reaction media during radical polymerization. Information in the literature is practically limited to polymerization of methacrylic acid esters (see e.g. former studies [7, 8])and styrene [9]. Main experimental results concerning the formation of PMMA [7, 8] and PS [9] will be described below. In every case we are dealing with bulk polymerization, i.e. a process taking place in the monomer itself. With polymerization in a solvent a polymer solution in a solvent mixture should be considered, the mixture consisting of a
2300
S. G. KuLIeH~HI~¢ and A. YA. MAL~r~
low molecular weight liquid and the initial monomer; it should be borne in mind that the composition of this mixture varies continuously during polymerization because of the depletion of the monomer. In the studies cited experimental results are shown in the form of a dependence of the highest l~ew~onian viscosity of the polymerizing mass on the degree of conversion ~(fl). We will first deal with the effect of [I]0 and temperature on the increase of viscpsity, which enables numerical values of indices a and b to be determined and compared with values obtained with independent investigations into theological properties of polymer solutions in their monomers. Parameters a and b determine the dependence of the viscosity of the reaction mass on time, degree of conversion, initial concentration of the initiator and the temperature of isothermal polymerization (formulae (7-15)). Therefore, an independent determination of these values from various experiments and their comparison serves as a criterion of the validity of theoretical results obtained. Values of a and b are determined from rheoldnetie results b y plotting dependences ~([I]0 ) with fl=const and ~/(fl) with [I]0=eonst in double logarithmic coordinates. Figure 1 shows dependences of ~(fl) for radical polymerizatioir of methyl methacrylate (plotted using experimental results [8]) and Fig 2,
log~ [poise]
//i
tog V [poise]
2,0
--
0
4
1.0
l I'I
,
o
I
tO9P [~.%] FIG. 1
1'3
1.2
1.6
toS P [ ~ ~] FIQ. 2
FIO. 1. Dependence of the viscosity of the reaction mass in radical polymerization of methyl methacrylato on the degree of conversion with benzoyl peroxide concentrations of 0.02 (1);: 0.05 (2); 0-075 (3); 0.1 (d) and 0.15 wt~.~/o (5); 50%
FIG. 2. Dependence of the viscosity of the reaction mass on the degroo of conversion ir~ radical polymerization of styrene at 100%
Rheokinetics of radical polymerization
2301
for radical polymerization of styrene (according to results obtained in another paper [9]). Straight lines correspond to the concentration dependence of viscosity c with exponent b which is 12.8 for PMMA and 5.5 for PS. These values coincide in practice with results of independent investigations of rheological properties of P]VIMA solutions in methyl methacrylate [10] and PS in styrene Ill].
l°9 '2 [poise] log M
0
q-
6"2 3
5.6 l
-2
1
o
I
-I
to9 fI1o E ote °/oi
2"8
Fro. 3
3"0 T'I xlOa FIG. 4
FIG. 3, Dependence of the viscosity.of the reaction mass in radical polymerization of m e t h y l m e t h a c r y l a t e on t h e initial concentration of the initiator ( T ~ 5 0 ° ; fl=16~o). ~2G. 4. Dependence of t_he molecular weight of PMMA orr the temperature of polymerization;
[I]o=O.2 wt.%. Index a was determined by plotting the dependence ~([I]o) with fl=const for PM:MA, which" is based on the use of formula (9) (Fig. 3, experimental results from a previous study [8]). This relation conforms to exponential relation t/~ [I]~z'7, which corresponds to a=3.4. This is in very satisfactory agreement with the conventional "universal" value of index a in.the dependence of melts and concentrated solutions of polymers on their molecular weight [12]. Let us now examine the temperature dependence of the viscosity increaseduring radical polymerization using effective activation energy values according to formulae (12) and (13). The temperature dependence of the viscosity w i t h an arbitrary constant degree of conversion is determined by activation energies of viscous flow, chain initiation, growth and termination. The combination o f temperature dependences of these constants determines the molecular weight variation of the polymer formed on changing polymerization temperature; the activation energy of the process may be described as follows:
E~-~Ep--~Et--½Ei
S. G. KUmCHIKHn~ and A. YA. MAL~TN
2302
In the formation of PMM~ initiated by benzoyl peroxide this value determined using experimental data [8] is 1!.5 keal/mole (Fig. 4), which is in satisfactory agreement with results in the literature (Ei--30 kcal/mole, Ep--½Et--4-5-5 keM/mole [5]). The value of Ep determined by plotting In ~-T -z (Fig. 5) is 34 keal/mole. This value satisfies formula (12) when a-~3.4 and the activation energy of viscous flow E,----5-6 kcal/mole. The latter value corresponds to experimental results derived for an average composition region of PMMA solu~i'~ fO-~ poise
4-
3log
[poi~../].
z /]]
logp [wt.°/o]
-
I'#
-
1"3
,JZ/l/;l
3
t
2"8
I
3"0 r -', ZOa,K FIG. 5
/
I
8.Z 12
1G
20/~, w~ %
FIG. 6
F i e . 5. Dependence of the viscosity of the reaction mass with ~ = c o n s t = 1 8 % and the degree of conversion with e = c o n s t = 5 × l0 s Poise on the temperature of polymerization of methyl methaerylate, [I]0=0.2 w~.%. F I e . 6. Dependence of the viscosity of the reaction mass on the degree of conversion of m e t h y l methacrylate with benzoyl peroxide concentrations of 0.02 (•); 0.05 (2); 0.075 (3); 0.1 (4); 0.15 w~.% (a). Broken lines represent calculated results.
Rheokinetics of radical polymerization
2303
tions in the monomer [10]. A study of the variation of the degree of conversion on changing temperature (Fig. 5) in order to achieve a constant level of viscosity, gives the value of E~=2.5-3 kcal/mole, which corresponds to formula (13) with a--~3.4 and b : 1 3 . Analysis gives parameters a and b, which agree with values obtained from independent rheological measurements, and confirm the validity of theoretical assumptions concerning the variation of viscosity during radical polymerization. However, formulae (7) and (8) allow for the a p r i o r i quantitative calculation of viscosity variation over a period of time, or according to the degree of conversion at different temperatures. This calculation was carried out for radical bulk polymerization of methyl methacrylate with different concentrations of benzyol peroxide, the initiator. Viscosity variation during polymerization may be calculated with known constants of elementary reactions and rheological dependences of the viscosity of a polymer solution in the monomer on concentration and molecular weight. Results in the literature [10, 13] enabled this relation to be determined for PM_M~ solutions in methyl methacrylate log ~]~--32.0+ 12.8 log fl+3-4 log M
(16)
Kinetic constants of polymerization of methyl methacrylate at 50 ° are kp/k~ --~0-084 [14], f----0.9 [5],/~1=0-7 × 10 -e sec -1 (in a former study [4] ki values were given at 60 ° and the activation energy calculated, in order to derive ki at 50°). Results of calculation and their comparison with experimental dependences are shown in Fig. 6. These data suggest satisfactory agreement with theoretical and experimental dependences of 0])fl. Some deviation with high [I]o values may be due to radical recombination of the initiator and a small reduction off. The agreement of well-known experimental results and theoretical equations proposed indicates that the rheokinetie method developed for analysing viscosity variation in radical polymerization gives an accurate interpretation of the main processes and enables a quantitative prediction to be made of the viscosity increase in homogeneous polymerization, in relation to: initiator concentration, temperature and time, based on general laws relating the viscosity of polymer solutions. The equations derived also enable the "reciprocal problem" to be solved, namely, determining kinetic constants of polymerization based on experimental dependences of viscosity variation. Translated by E. SEMERE REFERENCES 1. S. G. KUL1CHIKHIN, S. L. IVANOVA, M. A. KORCHAGINA and A. Ya. MALKIN, Dokl. A N S S S R 243: 700, 1978 2. A. Ya. ~ N , S. G. KULICHIKHIN, S. L. IVANOVA and M. A. KORCHAGINA,
Vysokomol. soyed. 21: 2112, 1979 (Not translated in Polymer Sci. U.S.S.R.) 3. S. Ya. FRENKEL', Vvedeniye v statistieheskuyu teoriyu polimerizatsii (Introduction into the Statistical Theory of Polymerization). Izd. "Nauka", 1965
23O4
V. I. V~.'T.~GREN' ~t a~.
4. A1. AI. BERLIN, S. A. V0L'FSON and N. S. YENIKOLOPYAN, glnetika polimeriza. tsionnykh protsessov (Kinetics of Polymerization Processes). Izd. "Khimiya", 1978 5. Kh. S. BAGDASAR'YAN, Teoriya radikal'noi polimerizatsii, Izd. "Nauka", 1966 6. Yu. S. CHERKINSKH, Vysokomol. soyed. A19: 459, 1977 (Translated in Polymer Sei. U.S.S.R. 19: 3, 524, 1977) 7. A. V. RYABOV, D. N. YEMEL'YANOV and M. A. CHEKUSHINA, Trudy po kblmii i khim. tekhonlogfi, 3, 122, 1965 8. D. N. YEMEL'YANOV, Doktorskaya dissertatsiya (Doctor's Degree). MGU, 1979 9. S. A. GORODINSKAYA, N. V. ANDRIASYAN and Yu. I. TROKHI~, Vestnik Kiyevskogo politekhn, in-ta, seriya khimich, mashinostroyeniya i tekhnologiya, No. 11, 32, 1974 10. L. I. MYASNIKOVA, Kandidatskaya dissertatsiya (Post-graduate Thesis), Gor'kii un-t., 1974 1t. I. JOSHIAKI and J. L. WHITE, J. Appl. Polymer Sci. 18: 2997, 1974 12. G. V. VINOGRADOV and A. Ya. MALKIN, Reologiya polimerov (Rheology of Polymers), Izd. "IChimiya", 1975 13. A. V. RYABOV, D. N. YEMEL'YANOV, L V. C H E K M O D A Y E V A , V. A. ROSLYAK0VA and N. A. SHABALINA, Vysokomol. soyed. B12: 192, 1970 (Not translated in Polymer Sci. U.S.S.R.) 14. N. A. PLATE and A. G. PONOMARENKO, Vysokomol. soyed. AI6: 2635, 1974 (Trans. lated in Polymer Sei. U.S.S.R. 16: 12, 3067, 1974)
Polymer Science U.S.S.R. Vol. 22,1~o. 9, pp. 2304-2309, 1980
Printed in Poland
0032-3950/80/092304-06507.50/0
0
1981 PergamonPress Ltd..
EFFECT OF THERMAL MOTION ON CONFORMATION REGULARITY OF MACROMOLECULES IN AMORPHOUS REGIONS OF POLYMERS* V. I. VETTEGBE~¢', L. S. TITEICKOV, YU. V. ZWLE~C]~V, V. V. ZHIZHEI~'KOV a n d YE. A. YEGOROV A. I. Ioffe Physico-Technieal Institute, U.S.S.R. Academy of Soiences Moscow Textile Institute
(Received 16 August 1979) A study was made of the dependence of the integral coefficient of absorption on temperature for a number of I R bands corresponding to regular molecular sections of isotactic polypropylene, polyethylene terephthalate and polycaprolactam. Enthalpy and entropy values were found for the loss of conformation regularity of molecules for * Vysokomol. soyed..~22: No. 9, 2101-2104, 1980.
0082-8950/80/092296-09507.5010
lh,inted in Poland
0 1981 PergamonPrea Ltd.
RHEOKINETICS OF RADICAL POLYMERIZATION* S. G. KVLICHlXH~¢ and A. YA. M ~ x ~ Scientific Industrial Association "Plastics"
(Received 9 August !979) Kinetic mechanisms and rheological properties of polymerization systems were examined and concrete mathematical ratios describing the increase in the viscosity of reaction masses during radical polymerization, derived. The conclusions drawn were confirmed b y experimental results of radical polymerization of methyl methaerylate and styrene available in the literature.
TH~ formation of polymer molecules is accompanied by ~ considerable increase in the viscosity of the reaction medium, the range of viscosity variation normally representing several decimal orders of magnitude. The type of viscosity variation influencing polymerization a n d technical apparatus used is determined by t h e mechanism and specific properties of a given reaction. However, unfortunately, the few investigations devoted to the variation of rheological properties of polymerizing masses are only restricted to recording the dependence of viscosity over a period of time t/(t) or on the degree of conversion of t/(fl). The existence o f a relation between the type of viscosity increase of the reaction medium and kinetic regularities of particular reactions enables the specific variation of main kinetic factors to be observed: temperature, composition of the reaction medium, reagent concentration and phase condition of the system. This approach requires a quantitative link to be established between the mechanism and reaction kinetics of polymerization and the type of viscosity increase. This program was implemented and experimentally confirmed for ionic polymerization with a constant number of active centres of macromolecular extension [1, 2]. This study seeks to develop the rheokinetie approach to a widely used class of reaction of radical polymerization and to verify experimentally theoretical results using experimental data available in the literature concerning the type of viscosity increase in typical reactions of radical polymerization, which forms the basis for a general methodological approach to the viscometrie analysis of radical polymerization. This approach is based on a combination of well-known kinetic mechanisms. of polymerization and existing views about general rules governing rheological properties of polymer solutions (reaction masses). This combined approach enabled us to obtain new results concerning viscosity increase in polymerizatiorr and the effect of main process parameters. * Vysokomol. soyed. A 2 2 : N o , 9, 2093-2100, 1980. 2296
Rheokinetics of radical polymerization
229~
t
An increase in the viscosity of the reaction medium in polymerization is determined both by the increase in molecular weight of the polymer formed and the increase of its content in the polymerization mass. ~Iechanisms governing the variation of molecular weight and polymer concentration in the reaction system depend on kinetics and the mechanism of polymerization [3]. The reaction mass should generally be regarded as a solution of the polymer formed in t h e initial monomer and solvents used. The viscosity of this solution is a function of average chain length of the polymer formed (z~) and its concentration ~: ~ = f (N, ~). The weight fraction of the polymer formed in the reaction system is equal to the degree of monomer conversion, i.e. ~ - ~ f l : ([~I]o--~I]/[1VI]0), where [M]0 is the initial and [1~], the current concentration of the monomer. In m a n y cases, during thermal initiation, in particular, the current concentration of the initiator [1] is expressed as follows: [I]~-[I]o exp (--k~t), (1) where [I]o is the initial concentration of the initiator, ki, rate constant of initiation, t, time. The viscosity of a single-phase polyme.r solution such as homogeneous reaction masses, m a y be described by the formula:
y-.~KflbN a,
(2)
where K, a and b are constants, ~V, degree of polymerization. I n radical processes without considering chain transfer and combination termination, variations of the numerical average degree of polymerization _h~ and conversion fl are described by formulae [4, 5]: =_
[M]ofl [i]d l _ e _ ~ t ) 2 4Y]CP.... ~. -~l~, tLl (*-e j,
(3)
(4)
where kp and kt are constants of chain propagation and termination, respectively, f is the efficiency of the initiator. Formulae m a y then be derived which characterize viscosity variations of t h e reaction mass when selecting as independent argument the degree of conversion fl or time t
q-~ K fl' L[i]o(l__~_,,,ij or
where
ktkt K,-~K[M]~.
(6)
:2298
S.O. KULICHIKHIN and A. YA. }ffAT.~r~l
Therefore, when constants of elementary reactions and theological properties o f polymer solutions in the monomer or in the solvent used are known, the use o f formula (6) makes it possible to give a full rheological description of the viscosity variation of reaction media in radical polymerization. The formulae derived m a y be simplified considerably. Expanding in series t h e functions contained in these formulae and being restricted to linear components (when fl<
t/=Ofl b, -where O - ~ K 1
~/2fkl-*[I]o*
(7)
-- ctmstant.
I f we consider viscosity variation over a period of time, we m a y write r/= 01t~,
(8)
• where
These formulae give a fairly simple description of viscosity increase at the initial stages of radical polymerization and enable a quantitative evaluation to be made of the role of major factors: kinetic constants and initiator concentration. I t is natural t h a t t h e y do not apply t o advanced stages of conversion, w h e n auto-acceleration takes place, which is dependent on the formation of a gelfraction and kinetic constants show a consequent variation. Let us examine the consequences that follow from the regularities derived in relation to the role of initiator concentration [I]0 and the temperature of isothermal polymerization T. The value of [I]0 forms part of constant 8 and 8z in formulae (7) and (8) and if its effect is expressed simply formulae (8) and (7) m a y be written as:
,l=6'[]];*"f
(9)
,1= oi[I]o eb-.)?,
(1 O)
w h e r e 8' and 01 are constants, the physical significances of which are easily established from the formulae described. Therefore, when fl=const ~ [ I ] ~ *~ and when t = c o n s t t/~[I]o~(b-a), where i n d e x a characterizes the effect of molecular weight on the viscosity of the polymer solution in a given solvent, or the monomer itseff and b is the effect of concentration. Reaction temperature has a variable effect on the yield and molecular weight ~ f the polymer formed. I f we compare viscosity with a constant degree of conver-
Rheokineties of radical polymerization
2299
sion and bear in mind that values of K1, kp, kt and ki in formula (7) may be presented as exponential functions of temperature, it appears that ~ exp [E~~ a (Ep-- ½Et-- ½Ei)/RT],
(11)
where E, is the activation energy of viscous flow, El, Ep and Et is the activation energy of chain initiation, growth and termination, respectively. An "effective" activation energy of viscosity increase may be derived with an arbitrary value of fl----const. When plotting the dependence of v/(fl)on T in coordinates log v/-T-1 when fl-~const activation energy is determined as follows:
E~:E,+a(Ep--½Et--½E1)
(12)
When comparing temperature dependences of fl values corresponding to isoviscous states of the reaction mass, and plotting them in coordinates In fl-T -1 (when ~----const) the formula for the "effective" activation energy takes the form: E~=--
E,+a(Ep-- ½Et-- ½El) b
(13)
When studying the temperature dependence of the visosity for a fixed time of polymerization t----const (i.e. with the dependence of In tI-T -1 when t----const) activation energy is determined as
Et----E~+(a-~b) (Ep--½E,)-}-½(b--a)Ei
(14)
The temperature dependence of the time during which a given level of viscosity is achieved (y*~eonst) for a case which is most important practically, is determined by the "effective" activation energy calculated from: E;--
E,w}-(a~-b ) (Ep--½Et)-}-½(b--a)Ei b
(15)
These results show that the empirical approach of calculating the activation energy of rheokinetic processes proposed previously [6] is, in general, incorrect. Therefore, the concept of activation energy becomes ambiguous dependent on the conditions of comparison and the significance of the values, the temperaCure dependence of which have been considered. Formulae and ratios derived allow for experimental verification and this will be dealt with later. Few experimental studies have been carried out giving results of the variation of rheological properties of reaction media during radical polymerization. Information in the literature is practically limited to polymerization of methacrylic acid esters (see e.g. former studies [7, 8])and styrene [9]. Main experimental results concerning the formation of PMMA [7, 8] and PS [9] will be described below. In every case we are dealing with bulk polymerization, i.e. a process taking place in the monomer itself. With polymerization in a solvent a polymer solution in a solvent mixture should be considered, the mixture consisting of a
2300
S. G. KuLIeH~HI~¢ and A. YA. MAL~r~
low molecular weight liquid and the initial monomer; it should be borne in mind that the composition of this mixture varies continuously during polymerization because of the depletion of the monomer. In the studies cited experimental results are shown in the form of a dependence of the highest l~ew~onian viscosity of the polymerizing mass on the degree of conversion ~(fl). We will first deal with the effect of [I]0 and temperature on the increase of viscpsity, which enables numerical values of indices a and b to be determined and compared with values obtained with independent investigations into theological properties of polymer solutions in their monomers. Parameters a and b determine the dependence of the viscosity of the reaction mass on time, degree of conversion, initial concentration of the initiator and the temperature of isothermal polymerization (formulae (7-15)). Therefore, an independent determination of these values from various experiments and their comparison serves as a criterion of the validity of theoretical results obtained. Values of a and b are determined from rheoldnetie results b y plotting dependences ~([I]0 ) with fl=const and ~/(fl) with [I]0=eonst in double logarithmic coordinates. Figure 1 shows dependences of ~(fl) for radical polymerizatioir of methyl methacrylate (plotted using experimental results [8]) and Fig 2,
log~ [poise]
//i
tog V [poise]
2,0
--
0
4
1.0
l I'I
,
o
I
tO9P [~.%] FIG. 1
1'3
1.2
1.6
toS P [ ~ ~] FIQ. 2
FIO. 1. Dependence of the viscosity of the reaction mass in radical polymerization of methyl methacrylato on the degree of conversion with benzoyl peroxide concentrations of 0.02 (1);: 0.05 (2); 0-075 (3); 0.1 (d) and 0.15 wt~.~/o (5); 50%
FIG. 2. Dependence of the viscosity of the reaction mass on the degroo of conversion ir~ radical polymerization of styrene at 100%
Rheokinetics of radical polymerization
2301
for radical polymerization of styrene (according to results obtained in another paper [9]). Straight lines correspond to the concentration dependence of viscosity c with exponent b which is 12.8 for PMMA and 5.5 for PS. These values coincide in practice with results of independent investigations of rheological properties of P]VIMA solutions in methyl methacrylate [10] and PS in styrene Ill].
l°9 '2 [poise] log M
0
q-
6"2 3
5.6 l
-2
1
o
I
-I
to9 fI1o E ote °/oi
2"8
Fro. 3
3"0 T'I xlOa FIG. 4
FIG. 3, Dependence of the viscosity.of the reaction mass in radical polymerization of m e t h y l m e t h a c r y l a t e on t h e initial concentration of the initiator ( T ~ 5 0 ° ; fl=16~o). ~2G. 4. Dependence of t_he molecular weight of PMMA orr the temperature of polymerization;
[I]o=O.2 wt.%. Index a was determined by plotting the dependence ~([I]o) with fl=const for PM:MA, which" is based on the use of formula (9) (Fig. 3, experimental results from a previous study [8]). This relation conforms to exponential relation t/~ [I]~z'7, which corresponds to a=3.4. This is in very satisfactory agreement with the conventional "universal" value of index a in.the dependence of melts and concentrated solutions of polymers on their molecular weight [12]. Let us now examine the temperature dependence of the viscosity increaseduring radical polymerization using effective activation energy values according to formulae (12) and (13). The temperature dependence of the viscosity w i t h an arbitrary constant degree of conversion is determined by activation energies of viscous flow, chain initiation, growth and termination. The combination o f temperature dependences of these constants determines the molecular weight variation of the polymer formed on changing polymerization temperature; the activation energy of the process may be described as follows:
E~-~Ep--~Et--½Ei
S. G. KUmCHIKHn~ and A. YA. MAL~TN
2302
In the formation of PMM~ initiated by benzoyl peroxide this value determined using experimental data [8] is 1!.5 keal/mole (Fig. 4), which is in satisfactory agreement with results in the literature (Ei--30 kcal/mole, Ep--½Et--4-5-5 keM/mole [5]). The value of Ep determined by plotting In ~-T -z (Fig. 5) is 34 keal/mole. This value satisfies formula (12) when a-~3.4 and the activation energy of viscous flow E,----5-6 kcal/mole. The latter value corresponds to experimental results derived for an average composition region of PMMA solu~i'~ fO-~ poise
4-
3log
[poi~../].
z /]]
logp [wt.°/o]
-
I'#
-
1"3
,JZ/l/;l
3
t
2"8
I
3"0 r -', ZOa,K FIG. 5
/
I
8.Z 12
1G
20/~, w~ %
FIG. 6
F i e . 5. Dependence of the viscosity of the reaction mass with ~ = c o n s t = 1 8 % and the degree of conversion with e = c o n s t = 5 × l0 s Poise on the temperature of polymerization of methyl methaerylate, [I]0=0.2 w~.%. F I e . 6. Dependence of the viscosity of the reaction mass on the degree of conversion of m e t h y l methacrylate with benzoyl peroxide concentrations of 0.02 (•); 0.05 (2); 0.075 (3); 0.1 (4); 0.15 w~.% (a). Broken lines represent calculated results.
Rheokinetics of radical polymerization
2303
tions in the monomer [10]. A study of the variation of the degree of conversion on changing temperature (Fig. 5) in order to achieve a constant level of viscosity, gives the value of E~=2.5-3 kcal/mole, which corresponds to formula (13) with a--~3.4 and b : 1 3 . Analysis gives parameters a and b, which agree with values obtained from independent rheological measurements, and confirm the validity of theoretical assumptions concerning the variation of viscosity during radical polymerization. However, formulae (7) and (8) allow for the a p r i o r i quantitative calculation of viscosity variation over a period of time, or according to the degree of conversion at different temperatures. This calculation was carried out for radical bulk polymerization of methyl methacrylate with different concentrations of benzyol peroxide, the initiator. Viscosity variation during polymerization may be calculated with known constants of elementary reactions and rheological dependences of the viscosity of a polymer solution in the monomer on concentration and molecular weight. Results in the literature [10, 13] enabled this relation to be determined for PM_M~ solutions in methyl methacrylate log ~]~--32.0+ 12.8 log fl+3-4 log M
(16)
Kinetic constants of polymerization of methyl methacrylate at 50 ° are kp/k~ --~0-084 [14], f----0.9 [5],/~1=0-7 × 10 -e sec -1 (in a former study [4] ki values were given at 60 ° and the activation energy calculated, in order to derive ki at 50°). Results of calculation and their comparison with experimental dependences are shown in Fig. 6. These data suggest satisfactory agreement with theoretical and experimental dependences of 0])fl. Some deviation with high [I]o values may be due to radical recombination of the initiator and a small reduction off. The agreement of well-known experimental results and theoretical equations proposed indicates that the rheokinetie method developed for analysing viscosity variation in radical polymerization gives an accurate interpretation of the main processes and enables a quantitative prediction to be made of the viscosity increase in homogeneous polymerization, in relation to: initiator concentration, temperature and time, based on general laws relating the viscosity of polymer solutions. The equations derived also enable the "reciprocal problem" to be solved, namely, determining kinetic constants of polymerization based on experimental dependences of viscosity variation. Translated by E. SEMERE REFERENCES 1. S. G. KUL1CHIKHIN, S. L. IVANOVA, M. A. KORCHAGINA and A. Ya. MALKIN, Dokl. A N S S S R 243: 700, 1978 2. A. Ya. ~ N , S. G. KULICHIKHIN, S. L. IVANOVA and M. A. KORCHAGINA,
Vysokomol. soyed. 21: 2112, 1979 (Not translated in Polymer Sci. U.S.S.R.) 3. S. Ya. FRENKEL', Vvedeniye v statistieheskuyu teoriyu polimerizatsii (Introduction into the Statistical Theory of Polymerization). Izd. "Nauka", 1965
23O4
V. I. V~.'T.~GREN' ~t a~.
4. A1. AI. BERLIN, S. A. V0L'FSON and N. S. YENIKOLOPYAN, glnetika polimeriza. tsionnykh protsessov (Kinetics of Polymerization Processes). Izd. "Khimiya", 1978 5. Kh. S. BAGDASAR'YAN, Teoriya radikal'noi polimerizatsii, Izd. "Nauka", 1966 6. Yu. S. CHERKINSKH, Vysokomol. soyed. A19: 459, 1977 (Translated in Polymer Sei. U.S.S.R. 19: 3, 524, 1977) 7. A. V. RYABOV, D. N. YEMEL'YANOV and M. A. CHEKUSHINA, Trudy po kblmii i khim. tekhonlogfi, 3, 122, 1965 8. D. N. YEMEL'YANOV, Doktorskaya dissertatsiya (Doctor's Degree). MGU, 1979 9. S. A. GORODINSKAYA, N. V. ANDRIASYAN and Yu. I. TROKHI~, Vestnik Kiyevskogo politekhn, in-ta, seriya khimich, mashinostroyeniya i tekhnologiya, No. 11, 32, 1974 10. L. I. MYASNIKOVA, Kandidatskaya dissertatsiya (Post-graduate Thesis), Gor'kii un-t., 1974 1t. I. JOSHIAKI and J. L. WHITE, J. Appl. Polymer Sci. 18: 2997, 1974 12. G. V. VINOGRADOV and A. Ya. MALKIN, Reologiya polimerov (Rheology of Polymers), Izd. "IChimiya", 1975 13. A. V. RYABOV, D. N. YEMEL'YANOV, L V. C H E K M O D A Y E V A , V. A. ROSLYAK0VA and N. A. SHABALINA, Vysokomol. soyed. B12: 192, 1970 (Not translated in Polymer Sci. U.S.S.R.) 14. N. A. PLATE and A. G. PONOMARENKO, Vysokomol. soyed. AI6: 2635, 1974 (Trans. lated in Polymer Sei. U.S.S.R. 16: 12, 3067, 1974)
Polymer Science U.S.S.R. Vol. 22,1~o. 9, pp. 2304-2309, 1980
Printed in Poland
0032-3950/80/092304-06507.50/0
0
1981 PergamonPress Ltd..
EFFECT OF THERMAL MOTION ON CONFORMATION REGULARITY OF MACROMOLECULES IN AMORPHOUS REGIONS OF POLYMERS* V. I. VETTEGBE~¢', L. S. TITEICKOV, YU. V. ZWLE~C]~V, V. V. ZHIZHEI~'KOV a n d YE. A. YEGOROV A. I. Ioffe Physico-Technieal Institute, U.S.S.R. Academy of Soiences Moscow Textile Institute
(Received 16 August 1979) A study was made of the dependence of the integral coefficient of absorption on temperature for a number of I R bands corresponding to regular molecular sections of isotactic polypropylene, polyethylene terephthalate and polycaprolactam. Enthalpy and entropy values were found for the loss of conformation regularity of molecules for * Vysokomol. soyed..~22: No. 9, 2101-2104, 1980.