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Kinetics of graft copolymerization in homogeneous and heterogeneous media
2060
V.A. DANIELYAN
(2) It is shown that in the copolymerization of ethylene and propylene in the presence of the unstable catalysts VC14-A1 (C2Hs)~C1 and VOC13-A1 (i8o-C4H9)~C1 the reactivity of the monomers remains constant with time. (3) The reactivity ratios of ethylene and propylene were determined for the conditions studied. For the VC14-A1 (C2H5)2C1 system r1=3 and r2=0.073; for t h e VOC13--A1 (/80-(~4H9)2C1 s y s t e m rl----16.8 a n d r2~-0.0522.
Translated by E. O. PHILLIPS REFERENCES 1. G. NATTA, G. MAZZANTI, A. VALVASSORI and G. PAJARO, Chem. Ind. 39: 743, 1957 2. G. MAZZANTI, A. VALVASSORI, G. PAJARO, Chem. Ind. 39: 825, 1957 3. G. NATTA, G. VALASSORI, G. MAZZANTI and G. SARTORI, Chem. Ind. 40: 896, 1958 4. G. BIER, A. GUMBOLT and G. SCHLEITER, Makromol. Chem. 58: 43, 1962 5. E. JUNGHAMS, A.' GUMBOLT and G. BIER, Makromol. Chem. 58: 18, 1962 6. Yu. OBLUI, M. UKHNYAT and M. NOVAKOVSKA, Vysokomol. soyed. 7: 939, 1965 7. T. ALFREY, J. BOHRER and H. MARK, Copolimerizatsiya (Copolymerization). p. 14, Foreign Literature Publishing House, 1953 (Russian translation) 8. A. P. FIRSOV, V. I. TSVETKOVA, N. M. CHIRKOV, Vysokomol. soyed. 3: 1161, 1961 9. I.N. MESH.KOVA, G. M. BAKOVA, V. I. TSVETKOVA and N. M. CHIRKOV, Vysokomol. soyed. 3: 1516, 1961 (Translated in Polymer Science U.S.S.R., 3: 6, 1011, 1962) 10. N. GAYLORD and H. MARK, Lineinye i stereoregulyarnye polimery (Linear and Stereoregular Polymers). pp. 44, 364, Foreign Literature Publishing House, 1962 (Russian translation); V. I. TSVETKOVA, O. N. PIROGOV, D. M. LISITSYN and N. M. CHIRKOV, Vysokomol. soyed. 3: 585, 1961 (Translated in Polymer Science U.S.S.R. 3: 4, 586, 1962)
KINETICS OF GRAFT COPOLYMERIZATION IN HOMOGENEOUS AND HETEROGENEOUS MEDIA*t V. A. DANIELYAN Institute of Organic Chemistry, Armenian S.S.R. Academy of Sciences WHATEVER m e c h a n i s m o f chemical or energetic i n i t i a t i o n o f g r a f t i n g is used (except w h e n t h e m a i n p o l y m e r is itself a micro-initiator) s o m e degree o f h o m o p o l y m e r i z a t i o n o f t h e g r a f t i n g m o n o m e r is inevitable, regardless of t h e p h y s i c a l s t a t e o f t h e m e d i u m . D e t e r m i n a t i o n of t h e efficiency of grafting, J, a n d of t h e conditions affecting this m a g n i t u d e is, in t h e l a s t analysis t h e basic p r o b l e m . * Vysokomol. soyed. 8: No. 11, 1866-1870, 1966.
Communication I I I in the series "Synthesis and study of grafted elastomers".
2061
Kinetics of graft copolymerization
Under both homogeneous and heterogeneous conditions the chemical initiation of grafting can be represented b y the following kinetic scheme of elementary steps. 1) I
kdec°mp ) 2I"
2) I ' + M
--
3) I" + Pm ki2 -> Pm 4) P ' + M kp ) p. 5) P" + Pm ktfe ) P 2c Pm 6) P m + M 7) p . + p .
k~i > P" ---~t ]
decomposition of initiator initiation of homopolymerization -- attack on main polymer -- propagation -- chain transfer to main polymer
--
kil > P"
--
reinitiation
-- chain termination, inactive products 9)
Pm+Pm
~'kt*
In the last three equations kt=ktr+l%d (ktr and ktd are the rate constants of termination b y recombination and disproportionation respectively). In reactions (4)-(8) P" can also be l~mP" (grafted macroradical), which from the kinetic point of view has the same significance though the resulting products arc different. Moreover the last three, termination reactions can lead to the formation of homopolymer, graft copolymer or crosslinked products, depending on whether P', I'm or I'm t)" are involved, and on the mechanism of termination (recombination or disproportionation). The above scheme does not take into account the possibility of chain transfer through other substances (solvent, monomer, initiator etc.). I f these possibilities are taken into account the already complicated kinetics of grafting will be still further complicated. There is comparatively little published kinetic information in this field and most of this is restricted to special cases, for example references [1], [2] and [6]. Voeks [3] derived an equation for the dependence of the efficiency of grafting, 5, (Voeks used the symbol Fg) on [1V[], [Pro] and [I], which after small changes b y Mori and his collaborators [6] takes the form: ]~ri[M]
~[t)m] /ki2
]~tfp~
[Pm]2 ]¢i2ktfP~
5--kri[M]+(7(2f]Cdecomp]Ct[I]l/')[[M] ~k-~il+ ]Cp/
[ ~ ~ g J +ft,
where f is the initiator efficiency and ft is the fraction of termination by recombination contributed b y combination of Pm and Pm t)" with P',
A=
(GEP'] "][Pm]
[P']) P" ] [p']"
where A is the fraction of recombination in the total termination process. The last terms in the above relationship are included because they also lead to the formation of graft copolymer.
2062
V.A. DANIELYAI~T
Assuming t h a t f t = c o n s t , it is seen that the efficiency of grafting increases with decrease in [I] and [M] and with increase in [Pm]. The above relationship is in good qualitative agreement with the experimental data of all authors who have tested it. I t is, of course, almost impossible to make calculations by means of this equation because it contains a number of constants that are difficult to measure, and ci is found experimentally as the ratio of the weight of monomer entering the copolymer to the total quantity of monomer polymerized. The decisive factor determining ~ is the quantity
ki2[P~]
A- k~l[~+kitPm] i.e. the fraction of reaction of the initiator with the main polymer in the over-all process of creation by the initiator of active centres along the main polymer chain and initiation of homopolymerization [31. Although not all acts of activation of the main polymer lead to grafting (some degradation m a y occur) a large value offi is desirable because homopolymerization then decreases. We have derived an equation enabling fi to be determined for any concrete system of Pro, I and M. From the steady-state condition d [P'] dt = kil[I'][M] +k~i [Pro][M]--k t[P']~--o'kt [P'] [P~n]--]Ctfp[P'] [P~n]: 0
(I)
d[P~] =/c~2 [I'][Pj + ktfp[P'] [Pro]-/Cr~[Pj [M] - akt [P'] [Pro]dt - ~ k t [Pm] ~= 0.
(2)
Adding (1) and (2) we obtain
k|l[r] [iv[]÷~12 [I'][Pm] --kt [i:)']2_ 2akt [p'] [Pm] -(T2f~t[Pro]2=0 or [I'](kil[I~]÷ ]¢[2[Pro])= ]¢~([e']÷ (9-[l)m])2 , whence
[p'] + (~[Pm] / [ I°] ([]¢il[M] --~~i2 []-:)m])
q
x~ k~
k~2[ F j
kt
- a [P~] = . v ~t v
A
o.[P~].
(3)
The total rate of polymerization in the presence of the main polymer Pm is given by d [~] [P'] [M] = / ~ ' ~ / ~ [Pm] ]~p--O'kp[Pln] L~] • v=- d~=kP x/ kt ~/ A
Kinetics of graft copolymerization
2063
Multiplying and dividing the first term of the right hand part of this equation by k~/2 and the second term b y kri gives
v=/Vil [~[]/ki2 [Pm] ]gp (:rVri]CP Inserting the value offl we obtain v
= k~/
[M]-]-]~i2 [Pm]
]~ri
(4)
When [Pm]----O (also Vri-~O) we obtain the usual expression for the rate of homopolymerization, vo:
Vo-
k ,~ia ~,112[M]
(5)
Dividing (4) by (5) we obtain
V= /~il [M] +]g,2 [l:)m] V0
~/
kjl [M]
°'Vrikpkt1/2 kpkriV~/z [M]"
(6)
Taking account of the fact t h a t
kil [M] -~-ki2 [Pm]~ 1/2__
1
and also
Vri:kri [Pm] [M]
and v~1/2-= - (kil [I'] [M]) 1/2 ,
we obtain v
1
4
ePm]
Putting [Pro] ~---o~ [Pm],
[I']~-fl[I] and bl[2R1/~2 - const.,
'~il P'
we finally obtain v
1 [Pro] --- const. Vo ~/1--fi ~/~] [M]
(7)
DISCUSSION
It is seen from equation (7) that in the presence of the main polymer the rate of polymerization of the grafting monomer decreases. When [P j=--0 v = v o and fi=0. When [Pm]> 0 V/Vo< 1 and f i > 0 , fi increases with increase in [Pm] and with decrease in [I] and [M], and conversely the polymerization rate increases with
2064
V.A. D A ~ L Y A _ W
increase in [I] and [M] and with decrease in [Pm]. Thus fi is dependent on these parameters in a similar manner to the efficiency of grafting, and the rate of polymerization in the presence of the main polymer is less than the rate of homopolymerization at least up to the onset of a pronounced gel-effect. The curve of v/v o ~f([Pm]) (equation (7)) is shown in the diagram. I t bends downward because for this function the second derivative with respect to [Pm], f " ~ O . A family of curves is obtained for different values of [I] and [M], and when [I1] > [I~] > [I3] and [M1]> [Ms] > [Ma] then fil
0.$
Dependence of the ratio of the rates of polymerization of the grafting monomer in the presence and absence of the main polymer, v/vo, on the concentration of the latter, [Pm), for constant concentrations of monomer [M] and initiator IX]: 1-[Mx], [I1]; 2--[M,], [I,]; Z--[M,], [I,3 calculated (to the first approximation) from the equation a~-l/x/1--f~, where a is the intercept OA on the v/v o axis, formed b y the tangent at the point a (see d i a gram). The ratio km/ka in the Voeks-Mori equation for the efficiency of grafting can also be calculated from the value o f f i . The experimental determination of.fi involves measurement of v/v o (the dilatometric method is the most accurate) at constant [M] and [I] and different values of [ P j , construction of the curve V/Vo=f([Pj) and mathematical treatment of this curve. I t is interesting to note that Mori, in the previously cited reference [4], obtained the equation v 1 Vo
B[Pm] ' 1+--
where B and C are empirical constants for the studied polymer-monomer system.
Kinetics of graft copolymerization
2065
This equation was derived from a graph, similar to the one above, of v/v o against [ P J at [M]=const., and was compared with a theoretically derived equation. Since the initiator concentration does not enter this expression the curve was constructed on the basis of results obtained with three different initiators, and this curve bends upward. This cannot be considered to be correct for the following reasons: a) the value off/calculated by us from equation (7) is negative, which has no physical meaning, and b) when the graph of reference [4] is plotted more carefully and for the separate initiators, curves with negative curvature are obtained. Heterogeneous grafting. ~Vhen the homopolymers are incompatible phase-separation of the reaction medium occurs. Grafting takes place in the phase containing the main polymer [5]. Since the distribution of the grafted polymer with respect to chemical composition is fairly broad the fraction of the graft copolymer that is richer in the main polymer remains in the layer of the latter and the other fraction, richer in grafted chains transfers to the homopolymer layer. Moreover since the main polymer layer is the more viscous the fraction of the homopolymer formed in that layer is " t r a p p e d " there. Although the qualitative relationship between 5 and the concentrations of the reactants mentioned at the beginning of this paper is also fully applicable to heterogeneous systems, the process is complicated by change in the concentrations resulting from phase separation and mass-exchange between the layers. I f to the first approximation mass-exchange between the layers is neglected the actual concentration of the main polymer in the grafting layer, [P~]f, will be given by [Pm]f=Pm/~ where a=Vl/(Vl~-v2) (~ is the ratio of the volume of the grafting layer to the total volume of the reaction medium, and v~ and v2 are the volumes of the grafting and homopolymerization layers respectively). 0 ~ a ~ l and v ~ v 2 from [Pm]=0 up to complete occupation of the volume by the grafting layer. This can be reached by increasing [Pm] to a certain value [5], but before this [Pro]f> )[Pn,]. I f it is assumed that the initiator is distributed uniformly between the layers its concentration in relation to [Pm]~ will be less than its initial concentration. Thus conditions favourable for increase in 5 are created in the grafting layer. Homopolymerization in the second leads however to decrease in the efficiency of grafting. It m a y be added that the number of acts of chain transfer through the main polymer from homopolymer macroradicals increases in the grafting layer, since [Pn~]~>[Pm]. This again leads to further increase in 5, particularly if chain transfer by this mechanism plays a perceptible part in addition to direct attack on the polymer by the initiator. The degree of polymerization, KP, of the homopolymer in the grafting layer then decreases. This is seen spontaneously from the equation
1 1 ]{tfp[Pm]f KP--Kp m F k~ [M]
2066
V. YE. DREVAL' et al.
Thus for grafting under conditions of heterogeneity and incompatibility establishment of the optimal conditions becomes an important problem, requiring detailed study. CONCLUSIONS (1) An equation is derived for experimental determination of the ratio, f~ of the reaction of the initiator with the main polymer to the over-all process of creation b y the initiator of active centres on the main polymer and initiation of homopolymerization, in graft copolymerization. (2) The conditions affecting the value of the p a r a m e t e r fi, and the relationship between fi and the efficiency of grafting have been determined. (3) Some relationships in grafting under heterogeneous conditions when the component homopolymers are incompatible are discussed. Translated by E. O. Pm1~Ps REFERENCES 1. C. H. BAMFORD, A. D. JENKINS and E. F. T. WHITE, J. Polymer Sci. 34: 271, 1959 2. T. G. FOX, M. S. GLUCKMANN,F. GORNICK, R. K. GRAHAM and S. GRATCH, J. Polymer Sci. 37: 397, 1959 3. J. F. VOEKS, J. Polymer Sci. 18: 123, 1955 4. J. MORI, J. MINOURA and M. IMOTO, Makromol. Chem. 24: 205, 1957 5. J. SEBBAN-DANON, J. chim. phys. 58: 246, 1961 6. M. LAZAR, J. PAVLINEC, J. Polymer Sci. A2: 3197, 1964
THE NEWTOMAN VISCOSITY OF CONCENTRATED SOLUTIONS OF POLYSTYRENE AND POLYETHYLENE* t V. YE. ])REVAL', A. A. TAGER, ~¢~. S. LUTSKII and V. K. POSTI~IKOV A. M. Gorkii State University of the Urals (Received 2 August 1965)
IT HAS previously been shown b y two of us t h a t the nat ure of the solvent and its interaction with the dissolved polymer have a large effect on the Newtonian viscosity of concentrated polymer solutions [1-3]. This is seen particularly clearly when the tem pe r at ur e at which the polymer is dissolved and at which the viscosity is measured is much below the glass t e m p e r a t u r e of the polymer. I t was found t h a t curves of the concentration dependence of viscosity approach one another as the t e m p e r a t u r e is increased. These experiments were, however, conducted within * Vysokomol. soyed. 8: No. II, 1871-1874, 1966. t Communication IV in the series "Concentrated polymer solutions".
V.A. DANIELYAN
(2) It is shown that in the copolymerization of ethylene and propylene in the presence of the unstable catalysts VC14-A1 (C2Hs)~C1 and VOC13-A1 (i8o-C4H9)~C1 the reactivity of the monomers remains constant with time. (3) The reactivity ratios of ethylene and propylene were determined for the conditions studied. For the VC14-A1 (C2H5)2C1 system r1=3 and r2=0.073; for t h e VOC13--A1 (/80-(~4H9)2C1 s y s t e m rl----16.8 a n d r2~-0.0522.
Translated by E. O. PHILLIPS REFERENCES 1. G. NATTA, G. MAZZANTI, A. VALVASSORI and G. PAJARO, Chem. Ind. 39: 743, 1957 2. G. MAZZANTI, A. VALVASSORI, G. PAJARO, Chem. Ind. 39: 825, 1957 3. G. NATTA, G. VALASSORI, G. MAZZANTI and G. SARTORI, Chem. Ind. 40: 896, 1958 4. G. BIER, A. GUMBOLT and G. SCHLEITER, Makromol. Chem. 58: 43, 1962 5. E. JUNGHAMS, A.' GUMBOLT and G. BIER, Makromol. Chem. 58: 18, 1962 6. Yu. OBLUI, M. UKHNYAT and M. NOVAKOVSKA, Vysokomol. soyed. 7: 939, 1965 7. T. ALFREY, J. BOHRER and H. MARK, Copolimerizatsiya (Copolymerization). p. 14, Foreign Literature Publishing House, 1953 (Russian translation) 8. A. P. FIRSOV, V. I. TSVETKOVA, N. M. CHIRKOV, Vysokomol. soyed. 3: 1161, 1961 9. I.N. MESH.KOVA, G. M. BAKOVA, V. I. TSVETKOVA and N. M. CHIRKOV, Vysokomol. soyed. 3: 1516, 1961 (Translated in Polymer Science U.S.S.R., 3: 6, 1011, 1962) 10. N. GAYLORD and H. MARK, Lineinye i stereoregulyarnye polimery (Linear and Stereoregular Polymers). pp. 44, 364, Foreign Literature Publishing House, 1962 (Russian translation); V. I. TSVETKOVA, O. N. PIROGOV, D. M. LISITSYN and N. M. CHIRKOV, Vysokomol. soyed. 3: 585, 1961 (Translated in Polymer Science U.S.S.R. 3: 4, 586, 1962)
KINETICS OF GRAFT COPOLYMERIZATION IN HOMOGENEOUS AND HETEROGENEOUS MEDIA*t V. A. DANIELYAN Institute of Organic Chemistry, Armenian S.S.R. Academy of Sciences WHATEVER m e c h a n i s m o f chemical or energetic i n i t i a t i o n o f g r a f t i n g is used (except w h e n t h e m a i n p o l y m e r is itself a micro-initiator) s o m e degree o f h o m o p o l y m e r i z a t i o n o f t h e g r a f t i n g m o n o m e r is inevitable, regardless of t h e p h y s i c a l s t a t e o f t h e m e d i u m . D e t e r m i n a t i o n of t h e efficiency of grafting, J, a n d of t h e conditions affecting this m a g n i t u d e is, in t h e l a s t analysis t h e basic p r o b l e m . * Vysokomol. soyed. 8: No. 11, 1866-1870, 1966.
Communication I I I in the series "Synthesis and study of grafted elastomers".
2061
Kinetics of graft copolymerization
Under both homogeneous and heterogeneous conditions the chemical initiation of grafting can be represented b y the following kinetic scheme of elementary steps. 1) I
kdec°mp ) 2I"
2) I ' + M
--
3) I" + Pm ki2 -> Pm 4) P ' + M kp ) p. 5) P" + Pm ktfe ) P 2c Pm 6) P m + M 7) p . + p .
k~i > P" ---~t ]
decomposition of initiator initiation of homopolymerization -- attack on main polymer -- propagation -- chain transfer to main polymer
--
kil > P"
--
reinitiation
-- chain termination, inactive products 9)
Pm+Pm
~'kt*
In the last three equations kt=ktr+l%d (ktr and ktd are the rate constants of termination b y recombination and disproportionation respectively). In reactions (4)-(8) P" can also be l~mP" (grafted macroradical), which from the kinetic point of view has the same significance though the resulting products arc different. Moreover the last three, termination reactions can lead to the formation of homopolymer, graft copolymer or crosslinked products, depending on whether P', I'm or I'm t)" are involved, and on the mechanism of termination (recombination or disproportionation). The above scheme does not take into account the possibility of chain transfer through other substances (solvent, monomer, initiator etc.). I f these possibilities are taken into account the already complicated kinetics of grafting will be still further complicated. There is comparatively little published kinetic information in this field and most of this is restricted to special cases, for example references [1], [2] and [6]. Voeks [3] derived an equation for the dependence of the efficiency of grafting, 5, (Voeks used the symbol Fg) on [1V[], [Pro] and [I], which after small changes b y Mori and his collaborators [6] takes the form: ]~ri[M]
~[t)m] /ki2
]~tfp~
[Pm]2 ]¢i2ktfP~
5--kri[M]+(7(2f]Cdecomp]Ct[I]l/')[[M] ~k-~il+ ]Cp/
[ ~ ~ g J +ft,
where f is the initiator efficiency and ft is the fraction of termination by recombination contributed b y combination of Pm and Pm t)" with P',
A=
(GEP'] "][Pm]
[P']) P" ] [p']"
where A is the fraction of recombination in the total termination process. The last terms in the above relationship are included because they also lead to the formation of graft copolymer.
2062
V.A. DANIELYAI~T
Assuming t h a t f t = c o n s t , it is seen that the efficiency of grafting increases with decrease in [I] and [M] and with increase in [Pm]. The above relationship is in good qualitative agreement with the experimental data of all authors who have tested it. I t is, of course, almost impossible to make calculations by means of this equation because it contains a number of constants that are difficult to measure, and ci is found experimentally as the ratio of the weight of monomer entering the copolymer to the total quantity of monomer polymerized. The decisive factor determining ~ is the quantity
ki2[P~]
A- k~l[~+kitPm] i.e. the fraction of reaction of the initiator with the main polymer in the over-all process of creation by the initiator of active centres along the main polymer chain and initiation of homopolymerization [31. Although not all acts of activation of the main polymer lead to grafting (some degradation m a y occur) a large value offi is desirable because homopolymerization then decreases. We have derived an equation enabling fi to be determined for any concrete system of Pro, I and M. From the steady-state condition d [P'] dt = kil[I'][M] +k~i [Pro][M]--k t[P']~--o'kt [P'] [P~n]--]Ctfp[P'] [P~n]: 0
(I)
d[P~] =/c~2 [I'][Pj + ktfp[P'] [Pro]-/Cr~[Pj [M] - akt [P'] [Pro]dt - ~ k t [Pm] ~= 0.
(2)
Adding (1) and (2) we obtain
k|l[r] [iv[]÷~12 [I'][Pm] --kt [i:)']2_ 2akt [p'] [Pm] -(T2f~t[Pro]2=0 or [I'](kil[I~]÷ ]¢[2[Pro])= ]¢~([e']÷ (9-[l)m])2 , whence
[p'] + (~[Pm] / [ I°] ([]¢il[M] --~~i2 []-:)m])
q
x~ k~
k~2[ F j
kt
- a [P~] = . v ~t v
A
o.[P~].
(3)
The total rate of polymerization in the presence of the main polymer Pm is given by d [~] [P'] [M] = / ~ ' ~ / ~ [Pm] ]~p--O'kp[Pln] L~] • v=- d~=kP x/ kt ~/ A
Kinetics of graft copolymerization
2063
Multiplying and dividing the first term of the right hand part of this equation by k~/2 and the second term b y kri gives
v=/Vil [~[]/ki2 [Pm] ]gp (:rVri]CP Inserting the value offl we obtain v
= k~/
[M]-]-]~i2 [Pm]
]~ri
(4)
When [Pm]----O (also Vri-~O) we obtain the usual expression for the rate of homopolymerization, vo:
Vo-
k ,~ia ~,112[M]
(5)
Dividing (4) by (5) we obtain
V= /~il [M] +]g,2 [l:)m] V0
~/
kjl [M]
°'Vrikpkt1/2 kpkriV~/z [M]"
(6)
Taking account of the fact t h a t
kil [M] -~-ki2 [Pm]~ 1/2__
1
and also
Vri:kri [Pm] [M]
and v~1/2-= - (kil [I'] [M]) 1/2 ,
we obtain v
1
4
ePm]
Putting [Pro] ~---o~ [Pm],
[I']~-fl[I] and bl[2R1/~2 - const.,
'~il P'
we finally obtain v
1 [Pro] --- const. Vo ~/1--fi ~/~] [M]
(7)
DISCUSSION
It is seen from equation (7) that in the presence of the main polymer the rate of polymerization of the grafting monomer decreases. When [P j=--0 v = v o and fi=0. When [Pm]> 0 V/Vo< 1 and f i > 0 , fi increases with increase in [Pm] and with decrease in [I] and [M], and conversely the polymerization rate increases with
2064
V.A. D A ~ L Y A _ W
increase in [I] and [M] and with decrease in [Pm]. Thus fi is dependent on these parameters in a similar manner to the efficiency of grafting, and the rate of polymerization in the presence of the main polymer is less than the rate of homopolymerization at least up to the onset of a pronounced gel-effect. The curve of v/v o ~f([Pm]) (equation (7)) is shown in the diagram. I t bends downward because for this function the second derivative with respect to [Pm], f " ~ O . A family of curves is obtained for different values of [I] and [M], and when [I1] > [I~] > [I3] and [M1]> [Ms] > [Ma] then fil
0.$
Dependence of the ratio of the rates of polymerization of the grafting monomer in the presence and absence of the main polymer, v/vo, on the concentration of the latter, [Pm), for constant concentrations of monomer [M] and initiator IX]: 1-[Mx], [I1]; 2--[M,], [I,]; Z--[M,], [I,3 calculated (to the first approximation) from the equation a~-l/x/1--f~, where a is the intercept OA on the v/v o axis, formed b y the tangent at the point a (see d i a gram). The ratio km/ka in the Voeks-Mori equation for the efficiency of grafting can also be calculated from the value o f f i . The experimental determination of.fi involves measurement of v/v o (the dilatometric method is the most accurate) at constant [M] and [I] and different values of [ P j , construction of the curve V/Vo=f([Pj) and mathematical treatment of this curve. I t is interesting to note that Mori, in the previously cited reference [4], obtained the equation v 1 Vo
B[Pm] ' 1+--
where B and C are empirical constants for the studied polymer-monomer system.
Kinetics of graft copolymerization
2065
This equation was derived from a graph, similar to the one above, of v/v o against [ P J at [M]=const., and was compared with a theoretically derived equation. Since the initiator concentration does not enter this expression the curve was constructed on the basis of results obtained with three different initiators, and this curve bends upward. This cannot be considered to be correct for the following reasons: a) the value off/calculated by us from equation (7) is negative, which has no physical meaning, and b) when the graph of reference [4] is plotted more carefully and for the separate initiators, curves with negative curvature are obtained. Heterogeneous grafting. ~Vhen the homopolymers are incompatible phase-separation of the reaction medium occurs. Grafting takes place in the phase containing the main polymer [5]. Since the distribution of the grafted polymer with respect to chemical composition is fairly broad the fraction of the graft copolymer that is richer in the main polymer remains in the layer of the latter and the other fraction, richer in grafted chains transfers to the homopolymer layer. Moreover since the main polymer layer is the more viscous the fraction of the homopolymer formed in that layer is " t r a p p e d " there. Although the qualitative relationship between 5 and the concentrations of the reactants mentioned at the beginning of this paper is also fully applicable to heterogeneous systems, the process is complicated by change in the concentrations resulting from phase separation and mass-exchange between the layers. I f to the first approximation mass-exchange between the layers is neglected the actual concentration of the main polymer in the grafting layer, [P~]f, will be given by [Pm]f=Pm/~ where a=Vl/(Vl~-v2) (~ is the ratio of the volume of the grafting layer to the total volume of the reaction medium, and v~ and v2 are the volumes of the grafting and homopolymerization layers respectively). 0 ~ a ~ l and v ~ v 2 from [Pm]=0 up to complete occupation of the volume by the grafting layer. This can be reached by increasing [Pm] to a certain value [5], but before this [Pro]f> )[Pn,]. I f it is assumed that the initiator is distributed uniformly between the layers its concentration in relation to [Pm]~ will be less than its initial concentration. Thus conditions favourable for increase in 5 are created in the grafting layer. Homopolymerization in the second leads however to decrease in the efficiency of grafting. It m a y be added that the number of acts of chain transfer through the main polymer from homopolymer macroradicals increases in the grafting layer, since [Pn~]~>[Pm]. This again leads to further increase in 5, particularly if chain transfer by this mechanism plays a perceptible part in addition to direct attack on the polymer by the initiator. The degree of polymerization, KP, of the homopolymer in the grafting layer then decreases. This is seen spontaneously from the equation
1 1 ]{tfp[Pm]f KP--Kp m F k~ [M]
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V. YE. DREVAL' et al.
Thus for grafting under conditions of heterogeneity and incompatibility establishment of the optimal conditions becomes an important problem, requiring detailed study. CONCLUSIONS (1) An equation is derived for experimental determination of the ratio, f~ of the reaction of the initiator with the main polymer to the over-all process of creation b y the initiator of active centres on the main polymer and initiation of homopolymerization, in graft copolymerization. (2) The conditions affecting the value of the p a r a m e t e r fi, and the relationship between fi and the efficiency of grafting have been determined. (3) Some relationships in grafting under heterogeneous conditions when the component homopolymers are incompatible are discussed. Translated by E. O. Pm1~Ps REFERENCES 1. C. H. BAMFORD, A. D. JENKINS and E. F. T. WHITE, J. Polymer Sci. 34: 271, 1959 2. T. G. FOX, M. S. GLUCKMANN,F. GORNICK, R. K. GRAHAM and S. GRATCH, J. Polymer Sci. 37: 397, 1959 3. J. F. VOEKS, J. Polymer Sci. 18: 123, 1955 4. J. MORI, J. MINOURA and M. IMOTO, Makromol. Chem. 24: 205, 1957 5. J. SEBBAN-DANON, J. chim. phys. 58: 246, 1961 6. M. LAZAR, J. PAVLINEC, J. Polymer Sci. A2: 3197, 1964
THE NEWTOMAN VISCOSITY OF CONCENTRATED SOLUTIONS OF POLYSTYRENE AND POLYETHYLENE* t V. YE. ])REVAL', A. A. TAGER, ~¢~. S. LUTSKII and V. K. POSTI~IKOV A. M. Gorkii State University of the Urals (Received 2 August 1965)
IT HAS previously been shown b y two of us t h a t the nat ure of the solvent and its interaction with the dissolved polymer have a large effect on the Newtonian viscosity of concentrated polymer solutions [1-3]. This is seen particularly clearly when the tem pe r at ur e at which the polymer is dissolved and at which the viscosity is measured is much below the glass t e m p e r a t u r e of the polymer. I t was found t h a t curves of the concentration dependence of viscosity approach one another as the t e m p e r a t u r e is increased. These experiments were, however, conducted within * Vysokomol. soyed. 8: No. II, 1871-1874, 1966. t Communication IV in the series "Concentrated polymer solutions".