Ternary azeotropy in free radical copolymerization

European Polymer Journal, 1968. Vol. 4, pp. 413-417. Pergamon Press. Printed in England.

TERNARY AZEOTROPY IN FREE RADICAL COPOLYMERIZATION W. RING Untersuchungsabteilungder ChemischeWerk Hals AG Marl, Kxs. Recldinghausen,Germany (Received

13

November

1967)

A b s t r a c t - - T h e k n o w n laws o f c o p o l y m e r i z a t i o n kinetics in principle allow ternary azeotropes in free radical copolymerization even if the three m o n o m e r s do n o t f o r m binary azeotropes. T h e necessary b u t insufficient c o n d i t i o n r13 > 1; r32 > 1; rt, > 1 or rl2 > 1; r , > 1; r31 > 1, however, disagrees with

Q-e s c h e m e

o f Alfrey a n d Price.

THE PROBLEMof the existence of ternary azeotropes in free radical copolymerization has been discussed, m Subsequent computer calculations(*) on the basis of reactivity ratios tabulated by Young ~3) have resulted in a considerable number of ternary azeotropes which are to be expected according to the fundamental equations of copolymerization kinetics. It may, therefore, be justified to regard the experimental proof which is still lacking as a matter requiring analytical accuracy and effort rather than a question of fundamental uncertainty. The calculations by Wittmer et al. (2~ have indicated ternary azeotropes only in ternary mixtures where the respective two-component systems exhibit at least one binary azeotrope. Ternary azeotropes were not found when, in the system under consideration, binary azeotropes did not exist. The object of this paper is to discuss the question whether, from the point of view of copolymerization kinetics, the existence of at least one binary azeotrope is a necessary (although not sufficient) condition for ternary azeotropy. DISCUSSION ON THE BASIS OF GENERAL COPOLYMERIZATION THEORY Walling and Briggs have derived equations for ternary and higher azeotropes."' The equation Nven for three-component systems, as corrected later, C5) is as follows:

(1

-

-

~)'[M1] +

s12"[Ms]

+ s~'[3/3] =0

s , ~ ' [ M d + (1 -- ~..) • [M,] + s,'[31/3] = 0

413

(1)

414

W. KING

A =

A1

I

Sol

S31

Sin

1

S32

$x3

Sz3

1

$31

1

$21

S~I

I

S21

[

1

1

&2

S~.o

I

1

l

s.~

1

sin

s~

1

S,t - -

I

$31

A2 =

$39

An =

1

I

r,~ 4: 0.

It follows from Eqn. (1) that ternary azeotropes exist only if all the determinants have the same sign (positive or negative), and if A/A, > 1. The determinants can be written: A

=

1 - - s~2" s2~ -- s ~ - s3~ - - s~ • s3t + s~2" s~" s3~ + s~s • s~t" s3~

(2a)

A1 = I -- s , " s32 + s~l (s~, -- I) + s,x ( s , -- 1)

(2b)

As =

(2c)

1 - - s~ "s~ + s~, (s~ - - 1) + s ~ (s~ - - 0

A3 = 1 -- s , " s~ + s13 (s~ - - I) + s,~ (sl, - - 1).

(2d)

We shall assume the following reactivity ratio products: rt2 " r21 =

I. a

- i . e . s~2 " S21 =

a

1. rln" rnl = - i.e. sin" snl = b b 1.

r.~ • rn2 ----- - i . e . $ ~ • s ~ c

=

(3)

c.

In the case of free radical copolymerization without binary azeotropes: a> and

I;

b~

1;

c>

1

r~ < 1; r~ > 1 i.e. sa > 1; sk~ < 1.

(4a) (4b)

Let us first consider Eqn. (2). F a v o u r a b l e conditions for the same (positive) sign for all determinants A, are: At:

s~ " s,~ < I s3~ > 1 l s~>l

A2:

s~>l

mutually contradictory according to Eqn. (4b)

J

S13 " S3x <

contradictory to Eqn. (3) and (4a)

1

contradictory to Eqn. (4a)

} mutually contradictory according to Eqn. (4b)

Sta > I

Ternary Azeotropy A3:

s12"su

415

< I

contradictor)' to Eqn. (4a)

sl., > 1 l sol > 1

mutually contradictory according to Eqn. (4b)

J

Favourable conditions for positive signs of the determinants A, agreeing with (4) require sufficiently large values either of each of sty, sz~, and s31, or of each of s~3, s3,, and s21. A minimum requirement is sx2 > 1 ; s2s > 1 ; s3~ > 1 (or vice versa). The same criterion holds with respect to a positive sign of A.* Combinations of r,~-values, selected according to these requirements, can easily be found to meet formally with azeotropic conditions. Ternary azeotropes, however, cannot be expected if. for example, sta > 1 ; s23 > 1 ; s3t < 1. We can thus state that copolymerization kinetics, in principle, allow ternary azeotropes even if the three monomers are not capable of forming binary azeotropes. It is interesting to note that the conditions stated above imply a pronounced tendency towards sequences of the type --(M1-M~-M3),

--

representing a higher order of alternation, but at the same time, do not favour sequences of the opposite order. DISCUSSION ON T H E BASIS OF T H E Q--e SCHEME The statements made above need further discussion in terms of more restrictive assumptions than those underlying the general copolymerization theory. The condition sl~ > 1; s23 > 1; s31 < 1

(5)

or st, • s.,, " s~x > 1 combined with (4b) leads to rla'r3='r21

>

rls

---- r12

rx='r~a'ral

(6)

which contradicts " rsz

"r21

• r=3

•

r31

(7)

as proposed by Ham.(e) Since Eqn. (7) follows directly from the Q-e scheme (L 7) the inequality (6) disagrees with the latter. This can easily be shown by substitution of the Alfrey and Price (8) relation: r,,

--

Q, Q,

•

exp { -- e, (e, -- e,)}

into (6). It should be mentioned that disagreement with Eqn. (7) is not a necessary consequence, if at least one binary azeotrope is allowed in the three-component system under consideration. In this case, (5) need not to apply. Most of the monomer systems • A negative sign of all determinants will not be observed under these conditions.

416

W. RING

which, according to Wittmer, are able to form ternary azeotropes, deviate substantially from Eqn. (7). The limited adequacy of (7) has already been pointed out by M a y o m and Jenkins. ~g' To summarize, we state that the necessary but insufficient condition for ternary azeotropes (in the case o f no binary azeotropic composition) following from general copolymerization kinetics and expressed by(5) is in contradiction with the Q-e scheme o f Alfrey and Price. The adequacy o f the latter has been proved in m a n y and disproved in a n u m b e r o f other cases. The existence o f ternary azeotropes o f m o n o m e r systems not capable o f forming binary azeotropes m a y be expected along parallel lines. Azeotropy should be found only in cases where the Q-e scheme is not adequate to describe the actual copolymerization behaviour,*~- and where M a y o ' s //-factor deviates substantially from unity. The additional condition expressed by (4b), however, seriously restricts possibilities, thereby reducing the chance o f finding threec o m p o n e n t systems not capable o f forming a binary, but able to form a ternary azeotrope. * rtk = 0 is included from the discussion. I" It should be noted that the "patterns" of Bamford and Jenkins Ct°. m do not exclude the condition (5) in the case of

REFERENCES (1) w. Ring, Vortragstagung "Neue Erkenntnisse und Ergebnisse auf dem Gehiet der Copolymeren und Polymergemische" Bad Nauheim, 21.4.1966. Makromalek. Chem. 101, 145 (1967). (2) P, Wittmer, F. Hafner and H. Gerrens, Makramolek. Chem. 104, 101 (1967). (3) L. J. Young, 3".Palym. ScL 54, 411 (1961), (4) C. Wailing and E. R. Briggs, J. Am. chem. Sac. 67, 1774 (1945). (5) W. Ring, Dechema-,~,[anagr. 49, "/5 (1964). (6) G. E. Ham, 3". Palym. Sci. 2A, 4181 (1964). (7) F. R. Mayo, 3. Palym. ScL 2A, 4207 (1964). (8) T. Alfrey Jr. and C. C. Price, J. Palym. Sci. 2, 101 (1947). (9) A. D. Jenkins, Eurap. Palym. J. 1, 17"/(1965). (10) C. H. Bamford, A. D. Jenkins and R. Johnston, Trans. Faraday Sac. 58, 418 (1959). (11) C. H. Bamford and A. D. Jenkins, J. Palym. S¢i. 59, 149 (1961); Trans. Faraday Sac. 59, 530 (1963). R~sum&--Les lois classiques de la cin&ique des ¢opolym~risations permettent en principe de pr6voir l'existence d'az~otropes ternaires dans les copolym~risations i'adicalaires m~me si les trois monomc~res utilis~s ae forment pas d'az~otropes binaires. Cependant la condition n&:essaire, mais non sufflsante: r~3> l;r3z> 1 ; r n > 1 Ot] e n c o r e

rt~.> 1 ; r 2 3 > 1 ; r ~ t > I,

est en d~saccord avec le schema Q--e de Alfrey et Price. Sommarlo--Le leggi note delle cinetiche di copolimerizzazione rendono teoricamente possibili azeotropi temari nella copolimerizzazione per radicali liberi anche se i tre moaomeri non formano azeotropi binari. D'altra parte, le condizioni necessarie, ma non sufficienti rt3 > 1, ran >

oppure

I ; r2t >

1

rtz > 1;ran > 1;rat > 1

non sono in accordo con Io "Q-e-scheme" di Alfrey e Price.

Ternary Azeotropy

417

Ztk~ mmenfassung--Die bekannten kopolymerisafionskinetischen Gesetzm~il3igkeiten erlauben tem~ire Azeotrope bei der radikalischen Copolymerisation grunds~tzlich auch dann, wenn die drei Monomeren nicht zur Bildung bin~rer Azeotrope beffthigt shad. Die notwendige abet nicht hinreichende Bedingung rta > 1;ra.. > 1;rzt > 1 oder rl, > 1; rzs > I; r3t > 1 steht jedoch im Widerspruch zum Q-e Schema yon Afrey und Price.