Calculation of relative monomer reactivities in irreversible copolycondensation of complex systems

CALCULATION OF RELATIVE MONOMER REACTIVITIES IN IRREVERSIBLE COPOLYCONDENSATION OF COMPLEX SYSTEMS* V. Z. NIKONOV, L. :B. SOKOLOV, G. V. BABUR, Y r . V. SHARIKOV

and YE. A. YEMEL1-N Synthetic Resin Research Institute, Vladimir

(Received 29 March 1968)

THE relative reactivity of monomers, as characterized by the ratio of propagation rate constar~ts, is of considerable practical importance. The knowledge of these values m a k e s it possible to produce polymers with a certain composition, to obtain the absolute propagation rate constants in a simple manner, to identify the monomer distribution along the chain, and also to establish the mechanism of polymer formation. Considerable advances were made in this direction during copolymerization studies. So far, we know the copolymerization constants (relative reactivities) of more than 2000 combinations involving several hundreds of monomer [I]. As regards the copolycondensation, wider aspects of studies deal chiefly with the synthesis of polycondensed copolymers and their physical properties; for example, more than 500 copolymer systems have been described for copolyamides [2, 3]. The quantitative studies of copolycondensation are only just beginning [4], and the number of monomer systems with known copolycondensation constants (under defined conditions) is not more than 20 [5]. The basis of the calculation of copolycondensation (CPN) constants, involving also heterogeneous conditions, is an equation containing the copolymer composition [6, 7]: A/Ao=(B/Bo)~ , (l) in which A0, B 0 are the initial concentrations of the monomers, A and B those at the end of the process. The e,bove equation is identical with that of Wall [8] which takes into consideration two stages of chain propagation during copolymerization; this equation is the sequence to the Walling [9] equation without any further assumptions and covers the sequential copolymerization of 3 components. Although eqn. (1) will satisfactorily describe the experimental data in a number of cases in heterogeneous systems [10, 11], the CPC constants obtained from it do not characterize the * Vysokomol. soyod. A l l : No. 4, 739-749, 1969. 836

Calculation of relative monomer reuctivities

837

reactivities owing to a series of complications connected with the heterogeneity of the process; the equation also does not take into accolmt the reactivity differences between the groups of each monomer. The use of this equation in the kinetic range of a homogeneous process is limited to cases where the monomers have the same constant reactivity of fuctional groups, which is rarely encountered in practice. ~onomers with dependant functional groups (reactive centres), i.e. tAvose with reactive centres of activities varying during the process, are at present of the greatest interest. Such monomers are those of the aromatic series (diamines, dicarboxylic acids, diisocyanates and others), and also bifunctional compounds of the aliphatic series with a number of C-atoms less than 8 [12]. It is quite obvious that a determination of the true reactivities of such complex monomer systems during CPC in homogeneous or heterogeneous conditions will be impossible, unless the different reactivities of the functional groups and their changes during the process are accounted for. A full, quantitative account of such reactivities will greatly complicate studies, even in the simplest cases, such as the reactions of diisocyanates with alcohols, and this can be accomplished only b y means of a computer [13]. The calculation of the CPC process [5] (interbipolycondensation, i.e. the CPC of two monomers with a third, "binding" condensing reagent, e.g. two diamines and an acid dichloride; an interbipolycondensatioa will be, according to [14], a polycondensation of two monomers, say two amino acids, capable of condensing individually) was carried out b y means of an electronic computer "Razdan-2" for one of the most commomly used types of monomer, having dependant reactive centres (functional groups). Differential equation of the copolymer composition. The main problem of the CPC theory is the establishment of the copolymer composition (reaction products) as a function of the initial mixture composition. We shall now examine the course of an irreversible interbipolycondensation (IBPC) in wich the participating monomers have dependant reactive centres. The general scheme of copolycondensing two monomers, a i - - l ~ l - - a 1 and b ~ - - R ~ - - b i with a t h i r d (inter-component), % - - R 0 - - c 1, has the following form: n (ai--Ri--al)-{-m (hi--Re--b1) ~- (m~-n) (C 1 - ]~0--ei) --~ --> a2 - - R 1 [ "~R1RoR2 ~ ]m + n-- 2 - -

R2--b2R2b2

The above scheme is followed b y IBPC processes of two diols with acid dichlorides, a diol and diamine with diisocyanates, two diamines with bis-ketenes, etc. The reactivity changes of the monomers during the process, and the process scheme, can be illustrated b y means of the following 8 equations:

ai--Ri--ai~ci--Ro--Ci -~ a~--l~i--Ro--%, k~

bi--l~2--biA-ci--Ro--C 1 ---+ b2--R2--1~o--C2,

(a) (b)

838

V. Z. NIKONOV et al.

~Rl--a~-ci--Ro-- %

~s

c 2 - - R o - - R 1 ~',

(c)

~ R2--b2-~- Cl--Ro--cl k.> %__Ro__Rs ~ '

(d)

a1--Rl--ax+ NRo--C 2 --~ ~Ro--Rl--a2,

(e)

bl--R2--bl + ~Ro--Cs

~Ri--ai~-

k.

NRo-R2-bs,

(f)

k7

(g)

~ R o - - % --. ~ R o - - R 1 ~ ,

N R2--b2--~- ,'~Ro-- c2 -~

~Ro--Rs--.

(h)

Reactions (a) and (b), giving the start of polymer chain formation, will take place only as a result of participation of monomers, while dimers, trimers .... oligomers and the polymer will participate in subsequent stages; all the products having groups a s will be symbolized for this reason by ~ R l - - a s, all those with b 2 groups as ~ R s - - b s, and those with % groups b y ~ R o - - % . By assuming that the reaction of monomer groups is a second-order chemical kinetic equation, which was observed to be the case in the majority of polycondensations [2, 5], we shall write a system of differential equations which describes the above process scheme:

-

d[a~3

d--t- = k~ [a0 [c~+k~ [ar] [cs] ;

dgb~] dt

d [a~] = dt

- - k~

(2)

[bl] [Cl]+k a [b~] [c2] ;

(3)

[c,l ;

(4)

-- d---/- = ks [b2] [%]+k4 [b2] [c~]--ks [bd [%] --ks [b~][cl] ;

(5)

-- - -

k 3 [a2] [C1]-~-~ 7 [a2] [C2]--~ 5 [al] [OL]--[~l] [al]

d [b2] d [c~ dt

----~___

k 1 [al] [Cl]'~-~ s [bl] [cl]-~-]63 [a2] [cl]-~-k4[bs] [Cl];

(6)

d [os] --]Q [all [cl]-~-~ 2 [bl] [Cl]'~-]C 3 [a2] [Cl]'~-k 4 [b~] [ol] dt --ks [ar] [c2]--ke [bl] [%]--k7 [a2] [c2]--ks [b2] [c2] •

(7)

The system of equations (2)-(7) contains 8 reaction rate constants which can be expressed in the form of the ratios r1~]61/]~2, ~'2~]~3/]g4, 9"3~]~2/]~4, r4~-ks/ks, r~=kT/ks, re-----ks~ks, rT=kl/k5, and one of the constants (e.g. k4), which is here the standardizing multiplication factor of the system of equations, will transform ratios (rl-rT) into the respective reaction rate constants.

Calculation of relative monomer reaetivities

839

We can introduce the theory of proportionality of the reaction rate constants, belonging to the first and second groups of an inter-component with different groups of comonomers, i.e. k l ~ - a ' . k s , k2---a'.k6, k 3 = a ' . k 7 and k d - = a ' . k s, which makes rx----ra, r ~ r a , ra-~r6, and rv=a. The equation system (2)-(7) will then be determined b y values r~, r2, r3, ~ and k 4, and can be transformed into:

In1]

dt

~- {rl"ra

d []31] dt

g [a~] dt

[al] [cJ~-a'rl"ra [al] [%]}'k4;

-~- {ra [b~ [Cl]-~-~.r a [bl] [c2]}.k 4 ;

(8) (9)

= {r2 [a2] [Cl]-~-~'r2 [a2j [%]--~'ra'rl [ar] [%]--r3rl [al] [Cl]}'k4 ; (10)

d [b~] dt -- {~ [b2] [c2]-~[52] [Cl]--a'r3 [51] [c2]--r3 [bl] [Cl]}']~4 ;

(11)

d [ca] dt -- {~'l'r3 [al] [Cl]~-r3 [51] [Cl]~-?'2 [a2] [el]-~-[b2] [cl]} ]~4;

(12)

d [%] - dt = {rl'r3 [&l] [Cl]-~-1"3 [bl] [Cl]-4-r2 [a2] [cl]~-[b2] [cl] - - ~ . r l . r 3 [al] [c2]--~.r 3 [bl] [c2]--g.r 2 [a2] [c2]--~ [b2] [c2]}.k4.

(13)

The possibility of using such a proportionality follows from the validity and foundation of the Sven-Scott correlation equations [15] when used under IBPC conditions with monomers having dependant groups with the same initial reactivity, and was confirmed b y the experimental data contained in Table 1, for example. The information given in Table 1 shows that the proportionality of the 1st and 2nd groups of the rate constants for the bifunctional compounds remained practically unchanged on changing from one reagent to another. Despite the simplification, the above system of differential equations also cannot be integrated analytically, or transformed into an expression li~king the molar concentrations of the monomers with the composition of the mixture at the start. The system of differential equations was numerically solved b y the R u n g e - K u t t method as modified b y ~erson, with an automatic selection of the integration series [20]. (All the calculations on the "Razdan-2" computer were carried out b y ~ . N. Ushakova). We calculated the concentration of the uureacted monomer groups at the moment of the complete conversion to reactive inter-component groups taken in insufficient amounts, thus determining the conversion degree (7)of the mono-

840

V . Z . NIXONOV et al.

TABLE 1.

EFFECT

OF THE

TYPE

RATIO

Bifunctional compound

OF

AND

ACTIVITY

OF T H E

SOME BIFUNCTIONAL

Order of rate constant, 1.- mole -1"

Reagent

•see-1

REAGENT

ON THE

RATE

COI~STANT

COMPOUNDS

Ratio of 1st to 2nd group constants

Reaction conditions

Referenco$

I

Isophthalic acid dichloride

Adiline Water Butanol Butanol

m-Phenylenediisocyanate

4,4'-Diphenylmethanediisocyanato

Ethanol Ethanol Butanol

lO s 10-4. 10-1 1

10-~ 10-1 1

10 13" 10 8"4

3.2 2.8 2.9

T H F , 25°C T H F , 30°C Toluene, 25°C Ditto, 40°C in t h e presence of t r i e t h ylamine

Toluene, 30°C Ditto, 30°C ~ 40°C in the presence of tricthylamine

[16]

[17]

[17, 18] [19]

[18] [17, 18]

T H F = tetrahydrofuran. * Determined by experiment. Similar calculation of the 1st and 2nd group reaction rate constants [16]. The reaction rate of the isophthalic acid dichloride with water was determined from the concentration changes of water during the process (Fischer titration).

mers a t k n o w n k4- , ~-, r l - , r 2- a n d ra-vMues , and starting conditions off t = 0 , [a°] : 2 [RI°], In°]=0, [b°]----2[R°], [b°]=0, [ c ° ] : 2 7 [ R ° + R ° ] , [ c ° ] : 0 , in which [a°], [a°], [bl°], etc. are t h e concentrations o f the respective m o n o m e r groups expressed as m o l a r fractions, [R°], R °] the m o l a r concentrations of comonomers, and y is the t o t a l degree of m o n o m e r conversion in the IBPC. T h e given starting conditions m e a n a n equivalence of the groups before reaction. The results o f the numerical i n t e g r a t i o n o f the s y s t e m o f differential e q u a t i o n s (8)-(13) gave the g r o u p concentrations present in t h e reaction m i x t u r e a n d the m o l a r c o n t e n t of m o n o m e r R 1 (eJfter reaction w i t h one or two groups), present in the reaction products; this is expressed as: " [,2°1--[al] /IR, = [ a 0 ] _ [ a l ] + [ b 0 ] _ [ b l ] ' in which a I a n d b I are t h e concentrations o f c o m o n o m e r groups a t the m o m e n t o f e x h a u s t i o n o f groups f r o m the i n t e r - c o m p o n e n t . T h e molar c o n t e n t of m o n o m e r R 1 reacting with two groups is given for comparison o f results in some cases: r

[al°]-[al]-[~2]

/2R1----in0] -- [al] -- [a2] + [b °] - - [51] - - [be]"

Calculation

o f relat, i v e m o n o m e r

reactivities

841

T h e / l ~ , above does not take into account amounts of the monomers in reactions with one group, and the monomer amounts at the chain ends, or on the ends of oligomeric products, are left out altogether. Furthermore, the calculation of/~R, considers as reacted only those monomer molecules having reacted with the second group; we therefore must expect a larger effect of the reactivities of the second groups in this case. The analysis of the obtained data shows t h a t changes of a and of k4 did not affect the product composition at various values of r 1, r e and ra, and at different degrees of conversion, or the monomer ratios present in the starting mixture.

[ l

'1!

Z

/

/-! " •

t-

, ~j/

.---..=7 ,"

I,

~,,'~"/"

//y

~

r,; ,,,<

/I/

~ t~7"

/, ,' ,2"

•~ "~

I-I , ' , ~

IY,

,

,

,

I V

,

,

,

~ 0"8

"~04 ~

#.~

0

I

I

I

I

0.2

0.¢

0.8

0'8

d

I

f.O

g

0-2

04

I

!

0.5

O'#

/,0

MolarfractLon f71in pro~ucta#~1 and ~zR~ 1~1G. 1. ]_r._fluenee of t,he degree o f conversion and the eopolyeondensat, ion eonstant, s on t,he (~al) product, eomloositiol'), and (/~R1,) composit, ion as a flm.et,ion of t,he start, ing

mixt,ure composit,ion. a - - r l : 1 0 ; r2, r 3 : l . b--rl, r s : l ; r~=10, c - - r i , r 2 = l ; r 3 : =10. d--r~--r3=lO. The number on the curves denot,es the degree of conversion. 1,1'--0.1; 2,2'--0.5, 3,3"--0.9. The absence of an effect b y k4 on the product composition is not unexpected since k 4 is a constant factor present in all the right-hand sides of the equations

842

V.Z. NZKONOV et at.

in our ease; it remains after integration and cancels out when inserting into the molar fraction equation (/~R1)" The independence of composition from ~ means that the reactivity difference of the inter-component groups does not affect the reaction product composition. Changes of rl, r~, and r 3 have a larger effect on composition, and also the monomer conversion, the latter effect being shown in Fig. 1 (on the molar content of monomer R1). The results show the product composition (as /~1 and /~a,,) to differ from the composition of the starting mixture at low degrees of conversion, while there is practically coincidence between the mixtures at a large degree of conversion (~0.9). Figure 1 also shows the composition of products at rl and r 2 equalling 1, while r S changes, to be the same as the composition of the starting mixture. There is also a qualitatively differing effect of r 2 on product composition, calculated on the basis of a reacted single monomer group R 1 (/IR,), and also on the same monomer, b u t reacted with two groups (/IR,). The product composition will be independent of r 2 where rl and rs equal 1 in the first c~se; in the second case r 2 will have the same influenceon product composition as rl. The absence of any effect of the felt, tire reactivities of second monomer groups (r2) and of the first, R 1 with respect to its other group (rs), observed for r~= 1, on product composition /~R, (only this value being considered in future because of its greater practical importance) is apparently because an r 1 value differing from unity will cause all 3 constants to have an effect on product composition. The latter is illustrated b y the information given in Table 2. It is worth while noting that the product composition at low conversion is fairly similar to that calculated from eqn. (1) where the CPC constant fl equals r 1 and the degree of conversion is doubled, as can be seen from Table 3. The need for doubling the degree of conversion is due to the preferential formation of a trimer at low conversion (see below), in which 1 mole of the intercomponent is utilized for 2 moles of comonomers. It is therefore possible at low conversions, while studying the product composition, to determine the relative reactivities of the first-group monomers. That of second group monomer reactivities, r2 ~nd rs, is made difficult b y their effect on the product composition, and also would require greater accuracy of analysis because of their relatively small effect on product composition at any degree of conversion. The product composition will therefore be determined at low conversion efficieneies b y the relative reaetivities of the first-group monomers; this is quite obvious, because they mainly react first under these conditions. The product composition at larger degrees of conversion will be primarily determined b y the first group monomer reactivities, b u t will start to depend at larger degrees of conversion on the relative reactivity of the second groups (r~), and t h a t of the first-group monomer R 2 towards the second group (rs), while

C a l c u l a t i o n of r e l a t i v e m o n o m e r r e a c t i v i t i e s

843

T A B L E 2, C A L C U L A T I O N DATA ON PRODUCT COMPOSITION AT D I F F E R E N T D E G R E E S OF CONVERSION AND W I T H ALL 3 CONSTANTS C H A N G I N G

M o l a r f r a c t i o n R~ in r e a c t i o n p r o d u c t s (/~1~1) M o l a r fraction in starting mixture

rl = 5 r2= 5 r3= 5

r 3 = 10

rl = 10 r ~ = 10

r3=5

! %=10

I

r 2 = 10

72----5

r3=5

r3=lO

r3=5

r3=10

0.3882 0.6278 0.7618 0.8412 0.8922 0.9275 0.9531 0.9725 0.8977 1.0000

0-3948 0-6327 0.7643 0"8424 0.8928 0.9278 0.9532 0.9725 0-9877 1.0000

0.4133 0.6461 0"7715 0.8462 0.8978 0.9288 0.9538 0.9738 0"9877 1.0000

0"1166 0"2393 0"3661 0"4938 0"6181 0"7339 0"8349 0.9145 0'9681 1'0000 I

0-1261 0.2657 0.4171 0.5699 0"7070 0.8150 0.8913 0.9423 0.9765 1.00001

0"1187 0"2486 0"3866 0.5265 0.6591 0.7749 0.8664 0.93O9 0.9729 1.0000

0-1000 0.2000 0.3000 0.4000 0"5000 0.6000 0.7003 0.8010 0.9015 1.0000

0-1000 0.2000 0.3000 0.4003 0-5008 0.6023 0.7073 0.8207 0-9251 1.0000

0"1000 0-2000 0-3000 0"4000 0"5000 0"6001 0"7010 0"8060 0-9093 1-0000

D e g r e e o f c o n v e r s i o n 0"1 0.1 0.2 0.3 0"4 0.5 0.6 0.7 0.8 0.9 1.0

0.2910 0.4953 0.6371 0.7380 0.8121 0"8684 0.9123 0.9475 0.9762 1.0000

0.2974 0.5021 0.6422 0.7414 0.8143 0.8698 0.9132 0.9479 0.9762 1.0000

0.2924 0.4971 0.6385 0'7390 0.8128 0.8688 0.9126 0.9476 0.9762 1.0000

0.2907 0.4951 0"6370 0.7380 0.8121 0.8684 0.9124 0.9475 0.9762 1.0000

0.3910 0'6297 0.7627 0.8416 0.8925 0.9275 0.9531 0.9725 0.9877 1.0000

D e g r e e o f c o n v e r s i o n 0.5 0.1 0.2 0.3 0.4 0.5 0.6 0-7 0.8 0.9 1.0

0.1240 0.2549 0-3894 0-5215 0.6438 0-7499 0.8371 0.9058 0"9589 1-0000

0.1164 0.2383 0.3635 0.4886 0-6091 0-7197 0"8156 0.8938 0.9542 1"0000

0.1258 0.2634 0.4086 0"5494 0.6733 0.7745 0.8538 0.9151 0.9627 1-0000

0.1185 0.2471 0.3820 0.5161 0.6405 0.7484 0"8365 0.9056 0.9589 1.0000

0.1243 0.2566, 0.3945 i 0.5324 0-6627 0.7766 0.8869 0.9310 0.9729 1.0000

Dogroo of c o n v o r s i o n 0.9 0.1 0.2 0"3 0-4 0.5 0.6 0.7 0.8 0"9 1.0

0.I000 0-2000 0-3000 0-4003 0.5008 0.6020 0.7047 0.8085 0-9091 l-e000

0"1000 0.2000 0.3000 0-4000 0-5000 0"6000 0-7003 0.8009 0.9014 1.0000

0.1000 0.2000 0.3000 0.4003 0.5008 0.6022 0.7072 0.8194 0.9222 1.0000

0.1000 0.2000 0.3000 0.4000 0"5000 0"6001 0.7010 0.8056 0.9084 1-0000

0.1000 0.2000 0.3000 0.4003 0.5008 0.6020 0.7049 0.8092 0-9101 1.0000

844

V.Z.

NlXONOV et a l .

TABLE 3. COMPARISON Or PRODUCT COMPOSITION CALCULATED ACCORDING TO EQUATION (1) WITH THAT rOUND BY SOLVING DIFFERENTIAL EQUATION SYSTEM (8)-(13) M o l a r f r a c t i o n R~ i n r e a c t i o n p r o d u c t s / q ~ l Molar fraction R1 in t h e original mixture

according to Shtraikhman-Best equation

rl=5

rl~5

B=5 7=0"1

0.1 0.2 0-3 0.4 0"5 0"6 0.7 0.8 0.9 1.0

f o u n d b y s o l v i n g differential e q u a t i o n s y s t e m (8)-(13)

0.3235 0.5262 0.6605 0.7544 0.8233 0.8752 0.9169 0-9501 0.9773 1.0000

p=5 7=0"2

0.2885 0.4926 0-6351 0'7367 0.8114 0.8679 0-9121 0.9474 0-9761 1.0000

p=lO 7=0"1

0.4608 0"6765 0.7895 0.8571 0.9016 0"9330 0'9563 0.9742 0"9885 1"0000

B=10 7=0.2

0"3850 0.6256 0.7608 0.8408 0.8921 0.9274 0-9531 0.9726 0.9878 1.0000

r l = 10

rl = 10

~'2=5

ru=r 3

:1 7=0.1

=10 7=0"1

~,=0.1

r a = 10 7=0"1

0.2936 0.4968 0.6378 0.7383 0.8123 0.8685 0.9124 0.9475 0.9762 1.0000

0"2907 0'4951 0"6370 0-7379 0-8121 0-8684 0-9124 0-9475 0"9762 1-0000

0.3953 0.6311 0.7631 0.8418 0.8925 0.9276 0.9532 0.9725 0.9878 1.0000

0.3882 0.6278 0.7618 0.8412 0.8922 0.9275 0.9532 0.9725 0.9878 1-0000

there is a general trend for the product composition to be similar to that of the original mixture. Finally, the copolymer composition at large degrees of conversion will correspond with that of the starting mixture, because the comonomers are fully converted to reaction products. To simplify the explanations we shall now examine the case of a homopolycondensation of monomers a l - - R l - - a 1 and cl--Ro--C 1, having groups with varying reactivity during a 100% conversion of component c~--R0--c 1, which is taken in deficient amount. The reaction products, in this case will be: %--RI--Ro--RI--a2 a2--R1--R0--R1--Ro--RI--% a~--R1--Ro--R1--R0--R1--Ro--Rx--a~

a2-- [ ~ l - - R o ] n - - ~ l - - a

2

The number of moles of components R 1 and R o in the reaction products will be: -MR,+ x, ~---

[al°]-I- [c°]- [al] 2

(14)

in which [a°], [c~ are the concentrations of the monomer groups R 1 before the

Calculation of relative monomer reactivities

845

reaction, while [ar] is the concentration of the first monomer groups R 1 at the end of the process. The material balance with respect to group concentrations can be written as: [C 0] = [a°l] -- [all -- [a2] ,

(15)

in which [as] is the concentration of second groups of monomer R x at the end of the process (after 100% conversion of R 0 monomer groups); [a2]=0 at the start. By solving eqn. (14) and (15), we get:

M~° +1%--

2 [c°] + [as] 2

(16)

The total amount of reaction products a2--[R1--R0]n--Rl--a 2 in moles equals the terminal group concentration in the products, divided by 2, i.e.

[a~] Ma'--[R1R°in--Raa'-- 2

(17)

B y dividing the total number of moles of components R l a n d R 0 (M~I+I~o) by the total number of moles of products, we get the average number of monomer units present in the reaction products:

NR~+~.-- 2 [c°]+[a2] [a2]

(18)

This average number can be found for IBPC by-the same method and equals:

-2 [c °] + [a2] + [b2] -ATR,+r,.+ ~. = [a2] +[b2]

(19)

0.6 0"4~ r

i

6

9

12

15

f8 R

FIG. 2. Product composition (aRt) as a function of avorago mol. wt. (avorage number of units in product, ~7): /--at rl and rs=10; r3=5; 2--r~--rs=5; 3--r~ and rs= 10; r~=5. The average number of monomer u_nits is more suitable for use because it is the customary name used with oligomers. Where ZV~-3, the reaction product is a trimer, ZV=4 represents a totramer, etc.

~46

V . z . ~TIKONOVet

al.

Finally, it must be clearly shown that the term of products equivalent to the average number of units covers the mixture of products of general formula [R1R0]nR1, in which n = 1, 2. 3 . . . The tool. wt. of the products (average number of monomer units), calculated according to eqn. (18) or (19), is linked with the conversion efficiency of the process and will depend on the relative reactivity of the monomer groups, as well as the mechanism of the process; formulae (18) and (19) embrace the concentrations of the second groups of monomers which were calculated on the basis of their mechanism and the varying group reactivity. The distribution of the components in the chain can be characterized in a simpler form by a product composition as a function of their tool. wt. By extending the conclusion of Beste [7] on the independence of component distribution to the case of IBPC, one can show the monomer distribution in the chain of a high tool. wt. copolymer to be identical with that of the monomers in products obtained when using insufficient inter-component to its complete conversion. By calculating the tool. wt. according to eqn. (19) by inserting [a,] and [b2], found on solving the equations, and by plotting the graphs of product composition and different conversion efficiencies against their tool. wt., we get a curve characterizing the monomer distribution in the chain. Figure 2 shows the product composition as a function of mol. wt. at certain values of rl, r,, r 3, and a 0.3 mole concentration of R 1 in the original mixture. This Figure also shows t h a t the monomer distribution in the chain is characterized by a fair number of short sequences of monotypical chain elements (larger deviation of composition at low mol. wt.), and a small number of long sequences. The same picture also applies to other values of the copolycondensation constants. Figure 2 shows at the same time that the largest deviations from the composition of the original mixture will be found in the range of low tool. wts.; the copolymer composition equals t h a t of the original mixture at large tool. wts. These deviations will depend to a large extent, under heterogeneous conditions, on the varying reactivity of the monomer groups, especially in the kinetic range of the reaction, and also where the process begins in the kinetic and terminates in the diffusion range; this is valid also where the mechanism of the processes is different. CONCLUSIONS

(1) The product composition was calculated f o r : a n interbipolycondensation of components with t~unctional groups having varying reactivities. (2) The copolycondensation of such monomers was found n o t to depend on t h e r a t i o of reaction rate constant~ of the first and second groups of the intercomponent (when assuming proportionality in reactions with the ~monomer groups), but on the relative reactivities of the first and second-groups Of the

Calculation of relative monomer reactivities

847

m o n o m e r s , a n d on the conversion efficiency. The relative reaction of the first g r o u p m o n o m e r s h a d the largest effect on p r o d u c t composition. (3) The largest d e v i a t i o n in p r o d u c t c o m p o s i t i o n from t h a t of the original m i x t u r e occurred a t low tool. wts. of the products. T h e c o p o l y m e r c o m p o s i t i o n equalled t h a t of the original m i x t u r e at larger mol. wts. The chain d i s t r i b u t i o n of the c o m p o n e n t s was characterized b y a large n u m b e r o f short m o n o t y p i c a l chain sequences. Translated by K. A. ALLEN REFERENCES

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