On elasticity and swelling

ON ELASTICITY AND SWELLING

E. J. VAN DE KRAATS

0 1 CD

P1250 5248

C10034

70943

ON ELASTICITY AND SWELLING

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGE-SCHOOL DELFT OP GEZAG VAN DE RECTOR MAGNIFICUS DR. IR. C. J. D. M. VERHAGEN, HOOGLERAAR IN DE AFDE-LING DER TECHNISCHE NATUURKUNDE, VOOR EEN COM-MISSIE UIT DE SENAAT TE VERDEDIGEN OP WOENSDAG

29 NOVEMBER 1967 TE 16 UUR

DOOR

EDUARD JOHAN VAN DE KRAATS I A. S O S A. YcS Scheikundig ingenieur

Geboren te Apeldoorn

s#

V

1967

BIBLIOTHEEK TU Delft P 1250 5248

^

Met toestemming van de tekenaar overgenomen uit: M. Toonder, Heer Bommel en de Zwelbast.

C D . van Beelen. R. van Donselaar. J. J. M. Potters. M. A. M. Winkelen

C O N T E N T S

I. Introduction. 7 II. T h e r m o d y n a m i c a l C o n s i d e r a t i o n s . 10

1. The freely swollen gel. 10 2. The osmotic swelling e q u i l i b r i u m . 11

3. The influence of the network p a r a m e t e r s on the

swelling p r e s s u r e . 13 III. On the P r e p a r a t i o n of G e l s . 16 1. Introduction. 16 2. The c r o s s l i n k i n g r e a c t i o n . 17 3. S e v e r a l c r o s s l i n k i n g p r o c e d u r e s . 17 4 . C r o s s l i n k i n g by a m i n o l y s i s . 18 5. C r o s s l i n k i n g of poly-(p-nitrophenyl m e t h a c r y l a t e ) by hexamethylenediamine. 22 IV. On Gel C h a r a c t e r i z a t i o n P r o c e d u r e s . 25 1. Introduction. 25 2. A new swelling p r e s s u r e o s m o m e t e r . 27 3. M e a s u r e m e n t s of uniaxial c o m p r e s s i o n . 28 4. Shaping and conditioning of the g e l s . 29

V. R e s u l t s and D i s c u s s i o n . 31 1. C h a r a c t e r i z a t i o n of the p o l y m e r . 31 2. The c r o s s l i n k i n g r e a c t i o n . 34 3. Description of the g e l s . 35 4. C o m p r e s s i o n m e a s u r e m e n t s . 36 5. Swelling p r e s s u r e m e a s u r e m e n t s . 36 6. Evaluation of network p a r a m e t e r s and d i s c u s s i o n . 39

7. G e n e r a l r e m a r k s concerning swollen polymer n e t

-works on the b a s i s of the r e p o r t e d e x p e r i m e n t s . 44

Appendices 46 S u m m a r y 55 Samenvatting 57

INTRODUCTION

The t h e r m o d y n a m i c a l and m e c h a n i c a l p r o p e r t i e s of both swollen and p u r e t h r e e - d i m e n s i o n a l p o l y m e r n e t w o r k s , a s well a s the t h e o r i e s attempting to i n t e r p r e t these p r o p e r t i e s have been, and still a r e , the subjects of many d i s c u s s i o n s ( 1 , 2, 3).

A g r e a t n u m b e r of authors (4, 5, 6, 7, 8, 9) have framed, e i t h e r on the b a s i s of continuum m e c h a n i c s o r u s i n g s t a t i s t i c a l t h e r m o d y n a m i c s , t h e o r i e s d e s c r i b i n g the m e c h a n i c a l behaviour of p o l y m e r networks. The t h e o r i e s , based on s t a t i s t i c a l t h e r -modynamical concepts, all have the s a m e s t a r t i n g point, v i z . the e l a s t i c p r o p e r t i e s of a p o l y m e r network a r e supposed to o r i ginate mainly from the l o s s of conformational p o s s i b i l i t i e s ( m i c r o s t a t e s ) of a s t r e t c h e d chain (10). All t h e o r i e s compute the n u m b e r of m i c r o s t a t e s without taking into account the finite d i m e n -sions of the chains and the topological r e s t r i c t i o n s imposed by the c r o s s l i n k s , nor in any other way introduce s t r a i n dependent i n t e r m o l e c u l a r effects. N e v e r t h e l e s s the v a r i o u s authors obtain somewhat different r e s u l t s . T h e s e c o n t r o v e r s i e s a r e dealt with extensively in some r e v i e w s ( 1 , 2, 3). A r e c e n t theory (3, 11) t r i e s to reconcile the various t h e o r i e s of r u b b e r e l a s t i c i t y by m e a n s of a s e m i - e m p i r i c a l factor.

To c a l c u l a t e the m e c h a n i c a l and t h e r m o d y n a m i c a l p r o p e r t i e s of swollen p o l y m e r networks (gels) one usually combines the t h e o r i e s of r u b b e r e l a s t i c i t y with those of p o l y m e r solutions. The change of the Gibbs free energy (AGtot) caused by the diluent is a s s u m e d to c o n s i s t of a change (AGm ) caused by the p o l y m e r - s o l v e n t c o n t a c t s , s i m i l a r to a mixing p r o c e s s and a change (AG^) caused by the accompanying e l a s t i c d e f o r m a t i o n :

AG = AG + AG (1)

tot m e ^ '

Several formulae e x i s t , attempting to d e s c r i b e the change caused by the p o l y m e r - s o l v e n t c o n t a c t s . One of the m o s t widely employed is the well known F l o r y - H u g g i n s e x p r e s s i o n (12, 13), which in c a s e of a gel has the form:

AG^ = k T [ N ^ l n ( l - q - l ) + In q ' l + zN^q"'} (2) w h e r e :

N i is the n u m b e r of diluent m o l e c u l e s in the gel.

q is the degree of swelling, i. e. the r e c i p r o c a l volume f r a c -tion of the p o l y m e r in the gel,

X is the F l o r y - H u g g i n s interaction p a r a m e t e r .

8

-Using P r i n s ' (3) s u m m a r i z i n g formula, one can e x p r e s s the change of free energy due to the e l a s t i c deformation (AGg):

AGg = iAkTi/(^^ + X^ + xl - 3) - BkTi/ln X^X^\ (3) w h e r e :

A and B, for the time being, a r e unknown c o n s t a n t s , which have different values in the various t h e o r i e s .

V is the n u m b e r of chains between c r o s s l i n k s , o r r a t h e r the

number of elastically effective c h a i n s .

Xjj, X and X^ a r e the deformation r a t i o s in the direction of

the C a r t e s i a n c o o r d i n a t e s . -U^-Tiv "U-^f^et-t to lAtrWfJ»^ ttftiJUwCt A homogeneous i s o t r o p i c a l l y swollen gel is defined by: *'^'*-'^-*~

X = X = X (4)

X y z * '

A degree of swelling at which the chains a r e unstretched is obtained if the polymer molecules a r e linked together to form a t h r e e dimensional network, without changing t h e i r end to end d i s t a n c e . If this degree of swelling is denoted by q^, the product of the t h r e e deformation r a t i o s of an isotropically swollen gel with degree of swelling q, is given by:

X ^ A y \ = q/qo (5) After i n s e r t i n g (eq. 4) and (eq, 5) into (eq. 3) one finds:

AG^ = iAkTi/{3 (q/qo) 2/3 - s ] - BkTi/ln (q/qj,) (6) The total change of free e n e r g y is found by combining (eq. 1), (eq. 2) and (eq. 6):

AGtot = k T [ i A i / { 3 ( q / q o ) 2 / 3 - 3 } - Bi/ln(q/qo)+ N , l n ( l - q ' ^ ) + xN^q'^] (7) In (eq. 7) the t e r m In q"^ has been omitted since it is n e g l i -gibly s m a l l c o m p a r e d to the r e m a i n i n g t e r m s .

If one wants to know whether o r not the t h e o r i e s mentioned before d e s c r i b e the elastic isotropic swelling in a s a t i s f a c t o r y way, a method is needed, which d e t e r m i n e s the total free energy a s a function of the degree of swelling. P o s s i b l e ways to this goal a r e in p r i n c i p l e : m e a s u r e m e n t of swelling p r e s s u r e , vapour p r e s s u r e and deswelling in polymer solutions. It will be shown l a t e r how by these methods the relation between the degree of swelling and the c h e m i c a l potential of the solvent in the network can be e s t a b l i s h e d .

Most of the previous a t t e m p t s ( e . g . 3, 11, 14, 15, 16, 17) in the field of gel p r o p e r t i e s m o r e o r l e s s confirm the g e n e r a l applicability of the formulae given above. The e x p e r i m e n t s

how-e v how-e r havhow-e not bhow-ehow-en sufficihow-ently rhow-efinhow-ed to allow a dhow-ecision about the r a t h e r s m a l l differences existing between the formulae d e -rived by the v a r i o u s t h e o r e t i c i a n s . The m o s t i m p o r t a n t infor-mation obtained from these e x p e r i m e n t s is the following:

Of the v a r i o u s network p a r a m e t e r s it is c l e a r that e s p e c i a l l y X niay be a function of the degree of swelling, j u s t a s in the c a s e of concentrated p o l y m e r solutions x may be concentration dependent. In addition a v e r y m i n o r dependence of qg on the degree of swelling m a y exist, because it is known that the d i -m e n s i o n s of p o l y -m e r -molecules at l e a s t in dilute solution v a r y somewhat with the p o l y m e r concentration. More importantly qg will depend on the nature of the solvent through x» The p a r a -m e t e r s A and B a r e possibly connected to the topology of the network. The number of e l a s t i c a l l y effective c h a i n s , u, will be c o n s i d e r e d to be defined d i r e c t l y by the n u m b e r of c h e m i c a l c r o s s l i n k s . Entanglements will be c o n s i d e r e d a s topological r e s t r i c t i o n s and will be included in A and B if n e c e s s a r y ,

The aim of the p r e s e n t work is to e s t a b l i s h both in what way X depends on the degree of swelling and to d e t e r m i n e the n a -t u r e of -the cons-tan-ts A and B. To -this end swelling p r e s s u r e m e a s u r e m e n t s and u n i l a t e r a l c o m p r e s s i o n m e a s u r e m e n t s on a number of gels with a known number of c h e m i c a l c r o s s l i n k s and a high qo-value have been c a r r i e d out.

To give these e x p e r i m e n t s the needed t h e o r e t i c a l background c h a p t e r II will deal with the t h e r m o d y n a m i c s of gels and the way in which x m a y be d e t e r m i n e d .

In c h a p t e r III the p r e p a r a t i o n of the gels will be d e s c r i b e d . C h a p t e r IV will be devoted to the a p p a r a t u s needed for the e x p e r i m e n t s mentioned above.

In c h a p t e r V the r e s u l t s of these e x p e r i m e n t s and the c o n -clusions to be drawn from them will be given,

C H A P T E R I I

THERMODYNAMICAL CONSIDERATIONS

In the following the t h e r m o d y n a m i c s of swelling phenomena will only briefly be d i s c u s s e d because s e v e r a l excellent publi-cations (18, 19, 20) have a l r e a d y been devoted to this subject.

1. The freely swollen gel.

In equilibrium the c h e m i c a l potential of the diluent in both p h a s e s m u s t be equal. Any changes in the gel phase m u s t be accompanied by a change of the s a m e magnitude in the diluent p h a s e and vice v e r s a ,

T h e r e f o r e :

d M ^ J p , T , x ) = d/L<^j,(p, T) (8) w h e r e :

/Uix and fxio a r e the p a r t i a l molal Gibbs free e n e r g i e s ( c h e -m i c a l potentials) of the diluent, the s u b s c r i p t Ix r e f e r s to the gel p h a s e , 10 to the pure diluent.

X is a composition p a r a m e t e r e. g, a m o l e fraction. p is the p r e s s u r e . T is the t e m p e r a t u r e . (eq. 8) m a y be written a s : 0 A ' i ^ / 9 x ) p ^ d x + O A ' I ^ / 9 P ) ^ T ' ^ P + (9^ix/9T)^pdT = {dn^Jdp)^dp+ (^^^J^T)^dT (9) The p a r t i a l d e r i v a t i v e s a r e : (9A'ix/9T),p = - s , ^ ; (9*^10/aT)p = - 3,, (10) (9/^1,/9p)^^ = v^^; (9M,o/9p)^ = v^„ (11) w h e r e :

Six and sio a r e the p a r t i a l molal e n t r o p i e s of the diluent. Vj^jj and Vj^Q a r e the p a r t i a l molal volumes of the diluent. The influence of the t e m p e r a t u r e on the swelling equilibrium at constant p r e s s u r e , can e a s i l y be calculated from (eq. 9 and 10):

w h e r e :

Xj is the value of the composition p a r a m e t e r at swelling e q u i -l i b r i u m .

(^ lx " ^lo) T is the p a r t i a l molal heat of dilution: Ah^^. Depending on whether the sign of Ahis is positive o r n e g a -tive, the gel will i n c r e a s e o r d e c r e a s e i t s diluent content after the t e m p e r a t u r e has been r a i s e d .

The dependence of the swelling equilibrium on the p r e s s u r e at constant t e m p e r a t u r e is derived from (eq, 9 and 11):

(9'"ix/9x)pT = (vio - Vix) ( 9 P / 9 X ) T (13)

Since {diuix/öx)pj is positive (21) it is evident from (eq. 13) that when the p r e s s u r e is r a i s e d the gel will deswell somewhat if v^Q > v^^ . If v^Q < Vj^jj the r e v e r s e will o c c u r .

Using the well known Le C h a t e l i e r principle the direction of the changes mentioned above m a y of c o u r s e d i r e c t l y be p r e -dicted,

2. The osmotic swelling equilibrium.

The foregoing formulae (eq. 12 and 13) dealt with a gel which had r e a c h e d the m a x i m u m d e g r e e of swelling, at a p r e s s u r e and t e m p e r a t u r e , which w e r e supposed to be equal to the e x t e r -nal p r e s s u r e and t e m p e r a t u r e of the s u r r o u n d i n g pure diluent.

If the p r e s s u r e in both p h a s e s differs, the gel and the diluent may be in equilibrium but the gel will then not be at its m a x i -m u -m d e g r e e of swelling, a s defined above,

If the degree of swelling is l e s s than the m a x i m u m degree of swelling and the p r e s s u r e at the s a m e time would still be equal in both p h a s e s , then the c h e m i c a l potential of the pure diluent would be higher than it is in the incompletely swollen gel:

^ i o ( P o ' T ) > ^,JP,.T) (14) In o r d e r to alleviate this unbalance a p r e s s u r e difference will

a r i s e between the pure diluent ( p r e s s u r e pg) and the gel in e q u i -l i b r i u m with the di-luent.

This p r e s s u r e difference H i s the osmotic p r e s s u r e which can be derived from (eq. 9):

A«ix(Po.T)+ I (aA«ix(Po.T)/ap)dp = Aiio(Po,T) (15) If the p a r t i a l molal volume v^^ is a s s u m e d to be independent

1 2

-of the p r e s s u r e , combination -of (eq. 11 and 15) gives:

A ' l J P o ' T ) + v ^ ^ n = A^io(Po'T) (16) H e r e vix m a y be a positive a s well a s a negative n u m b e r ' ' ,

According to (eq. 14) the product v^^^ 11 h a s to be positive, which m e a n s that the osmotic swelling p r e s s u r e m a y be positive a s well as negative.

By some authors (14, 18, 21) the following a r g u m e n t i s used to show the swelling p r e s s u r e to be positive:

An unequilibrated s y s t e m of a gel surrounded by pure diluent is c o n s i d e r e d . F o r the moment equilibrium i s supposed to be attainable by r a i s i n g the p r e s s u r e in the p u r e diluent from po to Pg + n ' , thus r a i s i n g the c h e m i c a l potential of the pure liquid by an amount:

I {^^/^p)^dp = v^^U' (17) Po"^

Vio i s evidently a positive n u m b e r , the p r e s s u r e of the pure diluent t h e r e f o r e m u s t be lowered, o r which s e e m s i n c o r r e c t l y to amount to the s a m e thing: The p r e s s u r e of the gel m u s t be r a i s e d to attain equilibrium.

According to our s t a t e m e n t the p r e s s u r e of the gel m u s t e i t h e r be r a i s e d o r lowered, depending on the sign of the p a r t i a l m o lal volume of the diluent in the gel. The c h e m i c a l potentials i n -side and out-side the gel m a y be made equal by adding a t e r m v^xll to the chemical potential in the gel p h a s e , e i t h e r by l o w e r ing o r r a i s i n g the p r e s s u r e in the gel, o r by lowering the p r e s -s u r e in the pure liquid p h a -s e .

The equilibrium condition of a gel with p r e s s u r e p^ + 11 c o -existing with a pure liquid with p r e s s u r e p„ m a y be formulated by analogy with (eq. 9):

(aMix(Po)/9Tpx)dT + (aAMix/9T)p,dT + i^^,^(po)/ax)pJ dx +

{dAiu^jBx)^^dx + (9A^i,(Po)/ap)Txdp + {dAn^Jdp)j^dp =

(9/"io(Po)/9p)TdP + (ayUio(Po)/9T)pdT (18) w h e r e :

. P o ^

AMIX = ) 0/Uix/9p)dp

(9A.,^ (Pg )/9T)p^ = - s^^ (p„) ; OM^O (Po)/9T) = - s^^ (p^ ) (19)

• In the system magnesiumsulphate-water e . g . the partial molal volume of magnesiumsul-phate is negative as a result of electrostriction at low concentrations,

( ^ ' " I X ( P O ) / ^ P ) T X = ^ i x ( P o ) ' (9/"io(Po)/9p) = Vio(Po) (20) If the c o m p r e s s i b i l i t y of the gel may be neglected, which m e a n s that vix is supposed to be independent of the p r e s s u r e , the dependence of the swelling p r e s s u r e on the t e m p e r a t u r e m a y be e x p r e s s e d according to (eq, 18, 19 and 20) a s :

(a(v,^n)/aT)p^ = Si,(Po) - s^g (PQ) (21) The influence of the concentration on the swelling p r e s s u r e ,

at constant t e m p e r a t u r e and p r e s s u r e p ^ , m a y be deduced from (eq, 18):

(9A^ix(Po)/9x)pTdx + (aAMix(Po)/9x)pxdx = 0 • (22) If Vj^jj is a constant (eq, 22) may be t r a n s f o r m e d to:

^x(9lï/9^)pT = - (9^ix(Po)/9x)p^ (23) Since a c c o r d i n g to (eq, 14), (9/Uix(po)/9x)pT is always negative,

it depends on the sign of v^x , whether at i n c r e a s i n g c o n c e n t r a -tion the swelling p r e s s u r e will i n c r e a s e o r d e c r e a s e . N o r m a l l y

v^ is positive and therefore (dll/dx) j a l s o .

At constant t e m p e r a t u r e and concentration the influence on the swelling p r e s s u r e of a change in the p r e s s u r e p^ is given by:

(9/^1^ (Po)/9p)^^dp + {^A^^^ (Po)/9p)Txdp = (9A<IO (Po)/9p)^dp (24)

A s s u m i n g v^^j, to be a constant (eq. 24) m a y be converted to:

(an/ap) = v^^, /v,^ - i (25) On changing the e x t e r n a l p r e s s u r e PQ somewhat the swelling

p r e s s u r e in g e n e r a l will not change a p p r e c i a b l y b e c a u s e V^Q usually is close to vix in v e r y good approximation. Only at high e x t e r n a l p r e s s u r e of many a t m o s p h e r e s an effect can be expected.

3. The influence of the network parameters on the swelling pressure.

In the following the r e l a t i o n existing between the swelling p r e s s u r e and the Gibbs free energy a s introduced in Chapter I will be d i s c u s s e d .

The equilibrium condition of a gel with p r e s s u r e Po + 11, coexisting with pure diluent with p r e s s u r e pg has i e e n shown to be:

/.Po+ÏT

% x ( P o ' T ) + ( a A < i ^ ( P g , T ) / a p ) d p = ^ ^ g ( P g , T) (15) PrT

1 4

-The difference between the p a r t i a l molal Gibbs free e n e r g i e s is defined by:

^ix (Po' T) - M,g (Pg, T) = (9AG„//aN^)p^^ (26) On combining (eq. 15, 26 and 7) one finds:

[

OWix (Po)/9p)dp = - AkTvv^^ V ; ' q " ' ^ ' qf^' +

BkTl^v^^ V ; \ - 1 - k T { l n ( l - q " ^ ) + q"^ +Xq"^} (27) w h e r e :

Vx is the volume of the p o l y m e r network component of the gel.

(eq. 7) is differentiated a s s u m i n g A, B, x> "^ix' 1o ^"^d v to be independent of the degree of swelling q. If this is c o r r e c t t h r e e swelling p r e s s u r e m e a s u r e m e n t s suffice to evaluate all network p a r a m e t e r s * , if Vix, Vx and v a r e known. If the m e a -s u r e m e n t -s -show the a-s-sumption to be wrong, one ha-s to look for an additional type of e x p e r i m e n t .

We will only d i s c u s s the c a s e in which all network p a r a m e t e r s , X excepted, a r e c o n s t a n t s . D i r e c t m e a s u r e m e n t of the i n -fluence of the degree of swelling on x from the change in the Gibbs free e n e r g y of mixing is i m p o s s i b l e , since a change in the d e g r e e of swelling is n e c e s s a r i l y accompanied by a change in the Gibbs free e n e r g y of e l a s t i c deformation. The free e n e r g y of e l a s t i c deformation however can d i r e c t l y be m e a s u r e d in a m o s t simple way: C o m p r e s s i o n of a gel which is o r is not in contact with pure diluent can be d e s c r i b e d by (eq, 3):

AG^ = ^AkTv{Xl + X^ + Xl - 3) - BkTi/ln \ ^ ^ \ (3) F o r the sake of simplicity new deformation r a t i o s A^, A and A2 a r e defined, such that:

Ax = ( q / q o ) ' ' ^ ' ^x '^y = ( q / q o ) " ' ^ ' \ -^z = (q/qo)"'^' \ (28) F o r u n i l a t e r a l c o m p r e s s i o n at constant volume (eq. 3) with:

A^ = A^ = A"^ (29)

y z x

and (eq. 28) m a y be t r a n s f o r m e d to:

AG^ = iAkTi/{(q/qg)2/3 (A^ + 2A;1 ) - 3} - BkTi/ln(q/qg) (30) The force of c o m p r e s s i o n f is given by:

I

-1 2 / 3 -2

f = (aAGe/aL)TpN = AkTi'Lg (q/qo) (A^ - A^ ) (31) w h e r e :

Lg is the length in the x - d i r e c t i o n of the undeformed gel. On combining (eq, 31, 27 and 16) one finds:

{ n v , ^ / k T + ln(l - q-M}q + fLgV^^V;^(^^ - A " / ) " ^ + 1 =

Bz/v^^V^' - x q ' ' (32) If one plots graphically the lefthand p a r t of (eq, 32) against

the degree of swellings the slope of the function gives the F l o r y -Huggins i n t e r a c t i o n p a r a m e t e r x and the i n t e r c e p t gives (Bi^v^x Vx ). The c o m p r e s s i o n m e a s u r e m e n t s provide the product Aqg-2/3.

C H A P T E R I I I

ON THE PREPARATION OF GELS

1. Introduction.

P o l y m e r networks m a y be p r e p a r e d by one of the following m e t h o d s :

P r o c e d u r e 1: After polymerization is completed the p o l y m e r m o l e c u l e s a r e connected by a poly-functional compound. The vulcanization of r u b b e r by s u l p h u r i s a well known example of this p r o c e d u r e ,

P r o c e d u r e 2: The c r o s s l i n k s a r e introduced during p o l y m e r i -zation. T h i s m a y be accomplished by copolymerization of a bifunctional compound with a t r i - o r higher functional compound, e. g. s t y r e n e and divinylbenzene,

F o r our p u r p o s e s the p r o c e d u r e f i r s t mentioned s e e m s to be the m o r e a p p r o p r i a t e one, because our networks should p r e f e r -ably exhibit the following f e a t u r e s :

1. The distribution of c r o s s l i n k s should be r a n d o m ,

2. The total n u m b e r of chains between c r o s s l i n k s should be known.

If the c r o s s l i n k s a r e introduced during polymerization these demands o v e r l a p to a c e r t a i n extent. Both can possibly be a c c o m -plished only by a r i g o r o u s study of copolymerization reaction r a t i o s . Only v e r y s p e c i a l s y s t e m s stand a chance to lead to gels in which the c r o s s l i n k s a r e distributed at random (22),

In c a s e the chains a r e joined after the polymerization is c o m -pleted, the r e a c t i v i t y of s e g m e n t s neighbouring a c r o s s l i n k gen-e r a l l y will bgen-e influgen-encgen-ed m o s t l y by s t gen-e r i c factors and only to a m i n o r extent by inductive o r o t h e r effects. The f o r m e r i n -fluence will be diminishing rapidly when the distance between c r o s s l i n k and r e a c t i v e s e g m e n t i n c r e a s e s .

Both methods n e c e s s a r i l y only make possible the d e t e r m i n a t i o n of the amount of chemical c r o s s l i n k s * introduced. It s e e m s unlikely that a c r o s s l i n k i n g p r o c e d u r e of the second kijid can be found which p e r m i t s a s elegant a determination oi the amount of c h e m i c a l c r o s s l i n k s a s the p r o c e d u r e of the first kind to be d e s c r i b e d in this c h a p t e r .

Unlike gels of the f i r s t kind w h e r e the number of dangling ends can be e s t i m a t e d if the molecularweight ( n u m b e r - and weight-average) and the n u m b e r of c r o s s l i n k s is known, gels p r e p a r e d a c c o r d i n g to the second p r o c e d u r e allow a d e t e r m i n a t i o n of the n u m b e r of dangling ends only frorai reactivity r a t i o s . As Mukherji (23) pointed out it i s a l m o s t i m p o s s i b l e to account for them by

• In chapter V will be discussed how the number of elastically effective chains may be es-timated from the number of chemical crosslinks,

a c h e m i c a l o r physical analysis inside the gel.

In the following only c r o s s l i n k i n g of existing p o l y m e r chains will t h e r e f o r e be d i s c u s s e d .

2. The crosslinking reaction.

A c r o s s l i n k i n g reaction leading to a well defined network should have the following p r o p e r t i e s .

1. The reaction should not be accompanied appreciably by c o n c u r r e n t o r consecutive r e a c t i o n s . Such r e a c t i o n s would make the d e t e r m i n a t i o n of the n u m b e r of c h e m i c a l c r o s s l i n k s e x t r e m e l y difficult.

2. The c r o s s l i n k i n g r e a c t i o n should not be an equilibrium r e a c t i o n . Detachable c r o s s l i n k s , which a r e free to move through the s y s t e m a l t e r the topology (e. g. a s e x p r e s s e d by the definition of qg in c h a p t e r I) of the network during investigation. In such a c a s e the s y s t e m would indeed only behave a s a gel in s h o r t - t i m e s c a l e e x p e r i m e n t s . In e x p e r i m e n t s conducted over longer p e r i o d s of t i m e the s y s t e m would behave a s an e x t r e m e l y viscous solution. The time scale m a y be expanded to a sufficient extent if the r e a c t i o n is completed at a high t e m p e r a t u r e after which the s y s t e m i s cooled at such a r a t e as to prevent dissociation of c r o s s l i n k i n g bonds. The physical e x p e r i m e n t s m a y then be p e r f o r m e d at a t e m p e r a t u r e where the r e a c t i o n r a t e s a r e too s m a l l to i n t e r f e r e with the e x p e r i m e n t s .

3. Several crosslinking procedures.

C r o s s l i n k i n g m a y advantageously be p e r f o r m e d in solution. In the f i r s t place a c o m p a r a t i v e l y high qo-value m a y be expected. T h i s enables one to d e t e r m i n e m o r e a c c u r a t e l y the values of the n e t w o r k p a r a m e t e r s A and B. The t e r m c a r r y i n g B b e c o m e s a l m o s t negligable for bulk c r o s s l i n k e d g e l s . In the second place ideal mixing of c r o s s l i n k i n g agent cannot be attained o t h e r w i s e . L a s t but not l e a s t the n u m b e r of physical entanglements m a y be expected to be s m a l l a s c o m p a r e d to the n u m b e r formed when

c r o s s l i n k i n g o c c u r s in bulk. n A disadvantage i s that s y n e r e s i s m u s t be p r e v e n t e d . Because if IMA:/6'>-KX>.A^

s y n e r e s i s takes place composite networks a r e formed in which rj\/^^^bO\r^(A

qo i s a v a r i a b l e (42), «JEA* ^

The usual p r o c e d u r e is the addition of a known amount of «w/»^ , c r o s s l i n k i n g agent to a p o l y m e r solution. After gelation h a s

o c c u r r e d the amount of unused c r o s s l i n k i n g agent is d e t e r m i n e d by e x t r a c t i o n and subsequent a n a l y s i s . The amount of o n e s i d e d -l y - r e a c t e d c r o s s -l i n k i n g agent m a y be d e t e r m i n e d .inside the gel by a p p r o p r i a t e a n a l y s i s . A simple s u b s t r a c t i o n then gives the n u m b e r of c h e m i c a l c r o s s l i n k s . A l t e r n a t i v e l y one can d e t e r m i n e the efficiency of the c r o s s l i n k i n g agent by m e a s u r i n g the m i n i m a l

1 8

amount of c r o s s l i n k i n g agent needed to produce a t h r e e d i m e n -sional p o l y m e r network. If this amount for example t u r n s out to be 2 (or 4) p e r p r i m a r y molecule for a bifunctional c r o s s l i n k i n g agent, the efficiency of the c r o s s l i n k i n g is 100% (or 50%).

As p a r t of the p r e s e n t work s e v e r a l c r o s s l i n k i n g p r o c e d u r e s w e r e devised. Not a l l of these w e r e investigated thoroughly.

a. Partially hydrolyzed poly-(vinylacetate) gels. (A. 1)*

The p r o c e d u r e is a v a r i a n t of the method of Mukherji (23), who p r e p a r e d cellulose a c e t a t e gels by c r o s s l i n k i n g p a r t i a l l y hydrolyzed cellulose a c e t a t e with d i - o - a n i s i d i n e d i i s o c y a n a t e in dioxane.

P a r t i a l l y hydrolyzed'poly-(vinyl acetate) was c r o s s l i n k e d with p, p'-diisocyanatodiphenylmethane in benzene. N-methylmorpholine o r t r i e t h y l e n e d i a m i n e w e r e used a s c a t a l y s t s .

This method differs from Mukherji's in that a m o r e suitable solvent was used (isocyanates a r e r e p o r t e d to r e a c t m o r e r e a d i l y in benzene than they do in dioxane (25), m o r e o v e r the diisocyanate used is for s t e r i c r e a s o n s m o r e r e a c t i v e than M u k h e r j i ' s . F i -nally the amine ought to be another r e a c t i o n p r o m o t i n g factor.

As the c r o s s l i n k i n g efficiency was not investigated quantitatively - as Mukherji in a m o s t ingenious way did - the s u p r e m a c y of one method over the o t h e r i s a s yet not e s t a b l i s h e d .

C o n t r a r y to M u k h e r j i ' s r e m a r k the gels obtained in this way did not show s y n e r e s i s ,

R e s u l t s of swelling and c o m p r e s s i o n e x p e r i m e n t s on these gels will be published e l s e w h e r e ,

b. Partially hydrogenated poly-(methyl acrylate) gels. (A. 2)

An a t t e m p t to u s e the method d e s c r i b e d above on p a r t i a l l y hydrogenated poly-(methyl a c r y l a t e ) could not be c a r r i e d out. P a r t i a l hydrogenation of poly(methyl a c r y l a t e ) with l i t h i u m a l u -miniumhydride lead to unwanted gelformation.

c. Partially hydrolysed poly-(methyl acrylate) gels. (A. 3) C r o s s l i n k i n g of p a r t i a l l y hydrolysed poly-(methyl a c r y l a t e ) with diepoxides was investigated only superficially after it had been found that the r e a c t i o n of epoxides and carboxylic acids gives s e v e r a l reaction p r o d u c t s .

4. Crosslinking by aminolysis.

C o n s i d e r i n g the fact that m a c r o m o l e c u l a r m a t e r i a l often c o n s i s t s

* Throughout this chapter numbers preceded by A refer to the appendices, where the precise chemical procedures are to be found.

of p o l y m e r i c e s t e r s , aminolysis p r e s e n t s itself a s an e x t r e m e l y useful c r o s s l i n k i n g r e a c t i o n . The r e a c t i o n of carboxylic e s t e r s with p r i m a r y and s e c u n d a r y a m i n e s i s of the g r e a t e s t i m p o r t a n c e in the field of peptide c h e m i s t r y and has t h e r e f o r e been i n v e s t i -gated thoroughly.

The reaction of e s t e r s and s e c u n d a r y a m i n e s is r e s t r i c t e d to:

R-C' + N H - ^ R - C ' o + R - O H

\ „ • \ ^ ^

0 - R R N

If a suitable combination of e s t e r and amine is used the con-v e r s i o n m a y be q u a n ü t a t i con-v e .

S e v e r a l e x p e r i m e n t s , some aimed at different ends, u s i n g d i v e r s e combinations of r e a c t a n t s , solvents and c a t a l y s t s w e r e p e r f o r m e d . In the following a brief account of these p r e l i m i n a r y e x p e r i m e n t s will be given.

a. Crosslinking of poly-(methyl acrylate) with ethylenediamine and piperazine.

If one wants to study the behaviour of a m a c r o m o l e c u l a r s o lution during gelation e s p e c i a l l y the behaviour n e a r the g e l -ation point - one could p r e p a r e s e v e r a l gels with v a r i o u s amounts of c h e m i c a l c r o s s l i n k s . The method of d e t e r m i n i n g the amount of c h e m i c a l c r o s s l i n k s by extraction of the gel and subsequent a n a l y s i s of gel and e x t r a c t e d m a t e r i a l cannot be used in this c a s e because of the insufficient m e c h a n i c a l stability of a gel n e a r the gelation point.

One m a y think to overcome these difficulties by d e t e r m i n i n g the two r e a c t i o n r a t e c o n s t a n t s of the bifunctional c r o s s l i n k i n g agent. A p a r t from the operational difficulties of this p r o c e d u r e it is doubtful whether these " c o n s t a n t s " a r e r e a l l y c o n s t a n t s . In fact it would be s u r p r i s i n g if they w e r e . T h e r e f o r e the chances for successful application of this method s e e m to be r a t h e r s m a l l ,

A new method was devised by which it should be possible to d e t e r m i n e simultaneously the amount of u n r e a c t e d c r o s s l i n k i n g agent and of o n e - s i d e d l y - r e a c t e d c r o s s l i n k i n g agent. If these amounts and the amount of c r o s s l i n k i n g agent added originally a r e known the n u m b e r of c h e m i c a l c r o s s l i n k s m a y be found by s i m p l e s u b t r a c t i o n . Also a method of this type enables one to study a gel in statu nascendi with a known amount of c h e m i c a l c r o s s l i n k s .

The new method m a k e s use of the l a r g e difference between the b a s i c i t i e s of piperazine and its r e a c t i o n product. This dif-ference allows a d e t e r m i n a t i o n by s t r a i g h t f o r w a r d t i t r a t i o n . The b a s i c i t i e s a r e e x p r e s s e d below a s the pk^ v a l u e s :

-20-F i r s t protonation: Second protonation: HN H NH + HT — * H N H NH ©/ \ Q, ®/—S® „ 1 , - o HjN H NH + H — > • H^N H NH^ P'^b ° P r o t o n a t i o n of the half a m i d e : N H NH + H ^ - ^ R - C ^ ^ _ ^ @ pki, = 6 "^N H NHj

The difference in the b a s i c i t i e s for the g r e a t e r p a r t is caused by inductive effects.

Unfortunately the formation of a network by c r o s s l i n k i n g a poly-(methyl a c r y l a t e ) solution with piperazine u n d e r n o n - r i g o r o u s c i r c u m s t a n c e s proved to be i m p o s s i b l e .

Addition of so called bifunctional c a t a l y s t s (2-hydroxypyridine and 1 , 2 , 4 t r i a z o l e , (26) nor variation of the solvent ( 1 n i t r o -p r o -p a n e , d i m e t h y l f o r m a m i d e , a c e t o n i t r i l e and 2, 4-lutidine) could i m p r o v e t h i s .

The failure m a y be caused by s t e r i c hindrance of the s e c u n d a r y a m i n e . The e x p e r i m e n t s t h e r e f o r e w e r e r e p e a t e d with e t h y l e n e -d i a m i n e .

At f i r s t sight this m a y s e e m inconsistent with the demand that the ideal c r o s s l i n k i n g r e a c t i o n should not be accompanied by consecutive r e a c t i o n s . However the s m a l l tendency to r e a c t , exhibited by p i p e r a z i n e , in addition to the s m a l l nucleophilicity of a m i d e s r u l e s out a r e a c t i o n a s :

P p R-C" R-C' R + R-c" > ^N-R + ROH

N 0-R R-C,

^H ^0

The formation of glutimide e l e m e n t s a s d e s c r i b e d , among o t h e r s , by S c h r o d e r (27): CH CH, ' CH, CH, 1- CH, I ^ 1^ CH, I 3 c c c c I I + R - N H j > I I + 2 CHjOH C c c c O'' ^0 0 ^ ^0 . 0* ^ N ^ "'O I , I CH3 CH3 R

which is favoured because of the formation of a stable six m e m -b e r e d ring, p r o c e e d s at 200 - 230°C. Consecutive r e a c t i o n s of

t h i s type of c o u r s e do not a l t e r the n u m b e r of c h e m i c a l c r o s s -links only the s t r u c t u r e of a (very) s m a l l amount of c r o s s l i n k s i s changed. A r e a c t i o n a s : CH, CH, CH, I 3 I 3 I 3 C C H , CCH, C C H , -C=0 + C = 0 > -C=0 CH, + CHOH I I I I 3 3 NH 0 N-C-C-CH,-R CH, N-C-C-CH,-R 0 definitely is excluded.

Unfortunately ethylenediamine behaved exactly a s p i p e r a z i n e did. No gelation after heating a t 100°C for one week.

The e x p e r i m e n t s w e r e continued using hexamethylenediamine and m o r e active e s t e r s whose alcohol group exhibits an e l e c -t r o n - w i -t h d r a w i n g effec-t, -t h e r e b y causing -the carbonyl carbon a-tom to be m o r e e l e c t r o p h i l i c .

Hexamethylenediamine a s well a s ethylenediamine and p i p e r a z i n e proved to be successful c r o s s l i n k i n g agents for methyl a c r y l a t e

- p-nitrophenyl a c r y l a t e - c o p o l y m e r s (A. 4). Influence of the bifunctional c a t a l y s t s in these admittedly crude e x p e r i m e n t s could not be e s t a b l i s h e d .

In principle the n u m b e r of c r o s s l i n k s before and after gelation m a y be e s t a b l i s h e d in this way. The p r o c e d u r e however has become a tedious one, because of the acidity of the nitrophenol, which m a k e s t i t r a t i o n quite difficult. Because t h e r e i s actually no need for swelling and c o m p r e s s i o n e x p e r i m e n t s to know in what m a n n e r gelation p r o c e e d s , it was decided not to investigate this method m o r e thoroughly.

b. Ctosslinking of dinitrophenyl acrylate and acrylic acid cop-olymers by p,p'-diaminodiphenylmethane.

In o r d e r to c i r c u m v e n t t i t r a t i o n , a method of c r o s s l i n k i n g was devised which allows the d e t e r m i n a t i o n of the extent of c r o s s l i n k i n g s p e c t r o p h o t o m e t r i c a l l y .

Nitrophenolate ions have an absorption m a x i m u m at 427.5 nm. The a m i n o l y s i s of nitrophenyl e s t e r s l i b e r a t e s nitrophenol which p a r t l y d i s s o c i a t e s in protons and nitrophenolate i o n s . The d e g r e e of dissociation depends on the amine a s well a s on the nitrophenol concentration. Using the absorption of v a r i o u s a m i n e - n i t r o p h e n o l m i x t u r e s a s c a l i b r a t i o n the amount of r e a c t e d c r o s s l i n k i n g agent in a p o l y m e r solution o r a gel rnay be d e t e r m i n e d .

This method was first t r i e d out on a c o p o l y m e r s of a c r y l i c acid and 2,4 dinitrophenyl m e t h a c r y l a t e . T h e s e yield p o l y e l e c -trolyte n e t w o r k s , which will suite our p u r p o s e a s well as nonionic n e t w o r k s . The ionic ones m a y be even m o r e i n t e r e s t i n g , because they offer the possibility of studying e l e c t r o s t a t i c long range

-22-i n t e r a c t -22-i o n -22-in well def-22-ined n e t w o r k s .

Dinitrophenyl e s t e r s m a y be p r e p a r e d in a v e r y elegant way by r e a c t i n g a carboxylic acid with di-(dinitrophenyl) carbonate (A. 5) (28):

OH

NO, NO, > ^ NO,

To a dimethylformamide solution of p a r t l y (10-20%) esterified p o l y - ( a c r y l i c acid) hexamethylenediamine was added. Thorough mixingof the diamine proved i m p o s s i b l e , p a r t l y b e c a u s e the f o r m a tion of salt b r i d g e s i n t e r f e r e s with the diffusion of the diamine, p a r t -ly b e c a u s e the dinitrophenyl e s t e r s proved to be too r e a c t i v e .

T h e s e difficulties w e r e overcome by using the l e s s nucleophilic p, p' -diaminodiphenylmethane.

Unfortunately p a r t l y esterified poly-(acrylic acid) solutions, not containing c r o s s l i n k i n g agent after a long time a l s o exhibited gelation. Obviously the e s t e r groups r e a c t with the acid groups forming carboxylic acid a n h y d r i d e s :

s p OH

HC—c' /—y 0, , ^0 0, / , ^ ^ N 0 HC '0-(O/-N0j + H - 0 - C - C ' ' H _ ^ HC-C'^ ^C-CH + [ Q J

Attempts to p r e p a r e by p o l y m e r analogous substitution 100% p o l y - ( 2 , 4 - d i n i t r o p h e n y l a c r y l a t e ) proved unsuccessful, possibly because after the esterification h a s proceeded to a c e r t a i n extent the r e m a i n i n g carboxylic acid groups a r e being hindered s t e r -ically by the bulky e s t e r s .

5. Crosslinking of poly-(p-nitrophenyl methacrylate) by

hexa-methylenediamine.

a. Synthesis of monomer and polymer.

The l a s t p r e l i m i n a r y unsuccessful e x p e r i m e n t was the s y n t h e s i s and polymerization of 2,4-dinitrophenyl a c r y l a t e and m e t h a c r y l a t e .

Lebedev and Andrianova (29) have d e s c r i b e d p r e p a r a t i o n s and p r o p e r t i e s of s e v e r a l nitrophenyl a c r y l a t e s and m e t h a c r y l a t e s .

2,4-Dinitrophenyl m e t h a c r y l a t e should be an a t t r a c t i v e m o n o m e r for s e v e r a l r e a s o n s . It has no r e a c t i v e t e r t i a r y hydrogen which m a y cause chain branching during p o l y m e r i z a t i o n . F u r t h e r -m o r e the s e c u n d a r y hydrogen ato-ms a r e shielded by the -methyl and the e s t e r group. The i m p o r t a n c e of this m a y be i l l u s t r a t e d by the fission e n e r g i e s given below (30)

Resulting r a d i c a l after F i s s i o n energy a b s t r a c t i o n of a proton in k c a l / m o l . CHg - CH2. 100 (CH3)2 - CH. 89 (CH3)3 - C. 85 C g H j . 104 M o r e o v e r the m e l t i n g point of the m e t h a c r y l a t e m o n o m e r exceeds that of the a c r y l a t e by 20°C (67 - 68°C) which e a s e s the purification of the m o n o m e r .

The synthesis of the dinitrophenyl e s t e r using the p r o c e d u r e of Lebedev proved v e r y u n s a t i s f a c t o r y . Attempts (A. 6) to i m p r o v e this s y n t h e s i s did not lead to b e t t e r r e s u l t s .

P r e p a r a t i o n of the e s t e r using dinitrophenyl carbonate gave somewhat b e t t e r , but by no m e a n s s a t i s f a c t o r y y i e l d s .

P o l y m e r i z a t i o n of dinitrophenyl m e t h a c r y l a t e s c r a p e d together from the v a r i o u s a t t e m p t s to synthesize this m o n o m e r , proved to be a s difficult a s its p r e p a r a t i o n .

In o r d e r to obtain a s l i n e a r a p o l y m e r a s p o s s i b l e , pol5aner-ization was c a r r i e d out in refluxing oxygenfree benzene u s i n g l%o a z o b i s i s o b u t y r o n i t r i l e a s i n i t i a t o r . No p o l y m e r was formed, not even after benzene was r e p l a c e d by the h i g h e r boiling toluene o r t-butylbenzene. P o l y m e r i z a t i o n in bulk lead to decomposition, a s could be detected by the yellow c o l o r and phenol s m e l l of the s a m p l e obtained.

The e x p e r i m e n t s w e r e r e p e a t e d with dinitrophenyl a c r y l a t e but this lead to the s a m e r e s u l t s , with r e s p e c t to the p r e p a r a t i o n a s well a s the p o l y m e r i z a t i o n of the m o n o m e r .

The v e r y s m a l l tendency to p o l y m e r i z e m a y well be due to the dinitrophenyl group, which has a stabilizing influence on the r a d i c a l . The m e t h a c r y l a t e m o r e o v e r l a b o u r s under s t e r i c h i n -d r a n c e of the polymerization r e a c t i o n ; 1,1--disubstitute-d vinyl compounds g e n e r a l l y have v e r y high activation e n e r g i e s of p o l y -m e r i z a t i o n .

The above c o n s i d e r a t i o n s made it n e c e s s a r y to use p n i t r o -phenyl e s t e r s instead of the 2, 4-dinitro-phenyl e s t e r s , which a r e m o r e susceptible to a m i n o l y s i s . F i r s t l y , the p r e p a r a t i o n a c c o r d -ing to the slightly a l t e r e d L e b e d e v - p r o c e d u r e (A. 7) proved to be much e a s i e r . In the second place the p-nitrophenyl e s t e r s p o l y m e r i z e d m o r e readily, p r e s u m a b l y because the r a d i c a l s t a -bilization a s well a s the s t e r i c hindrance is much l e s s than is the c a s e with the dinitrophenyl e s t e r s .

P o l y m e r i z a t i o n in bulk (A. 8) of 100 g r a m pnitrophenyl m e t h -a c r y l -a t e using 114 m g -a z o b i s i s o b u t y r o n i t r i l e yielded 70 g r -a m p o l y - ( p - n i t r o p h e n y l m e t h a c r y l a t e ) . In bulk p o l y m e r i z a t i o n with such a high c o n v e r s i o n chain t r a n s f e r and branching i s often found. N e v e r t h e l e s s in this c a s e the chains m a y be a s s u m e d to be mainly l i n e a r because of the following c o n s i d e r a t i o n s :

1) As h a s been r e m a r k e d e a r l i e r the m e t h a c r y l a t e has no active t e r t i a r hydrogen; the s e c u n d a r y hydrogen is shielded by the bulky siJ^ g r o u p s .

2 4

-2) The polymerization was executed in the p a r t i a l l y molten m o n o m e r , in which the p o l y m e r i s insoluble. Because of t h e i r v e r y low mobility the p o l y m e r chains will not r e a c t r e a d i l y with each o t h e r .

b. Final preparation of suitable gels.

Gels w e r e p r e p a r e d by c r o s s l i n k i n g a 20% p o l y m e r solution in dimethylformamide with hexamethylenediamine (A, 9).

The gels did not contain e x t r a c t a b l e m a c r o m o l e c u l a r m a t e r i a l nor did they exhibit s y n e r e s i s ,

On being kept in contact with the " p u r e " diluent they slowly b e c a m e opaque and s h r i v e l e d . This is attributed to a gradually developing incompatibility of solvent and polymer a s a r e s u l t of solvent d e t e r i o r a t i o n ,

If gel and diluent w e r e r i g o r o u s l y isolated from the a t m o s p h e r e nothing of this s o r t happened; a s i m p l e r solution was to r e p l a c e the dimethylformamide by nitrobenzene.

Nitrobenzene cannot be used as a solventdiluent during c r o s s -linking. It a b s o r b s at the s a m e frequencies a s the nitrophenolate does and thus would make it quite difficult to d e t e r m i n e the amount of amine used during c r o s s l i n k i n g . M o r e o v e r the a m i n o l -y s i s is r e t a r d e d to a s u r p r i s i n g extent if nitrobenzene i s used during gelation. At room t e m p e r a t u r e gels a r e formed within two o r t h r e e hours in d i m e t h y l f o r m a m i d e . In nitrobenzene g e l -ation takes s e v e r a l d a y s .

The r e p l a c e m e n t of dimethylformamide by nitrobenzene was accomplished by i m m e r s i n g the gel for about t h r e e weeks in n i t r o b e n z e n e , during which period the i m m e r s i o n liquid was replaced e v e r y other day by p u r e nitrobenzene. After t h r e e weeks of i m m e r s i o n the gel was v e r y slowly heated to about ten d e g r e e s above the boiling point of dimethylformamide and kept at this t e m p e r a t u r e for a few h o u r s . Because the volume of the gel had to be adapted to the dimensions of the swelling p r e s s u r e o s m o m e t e r to be d e s c r i b e d in the next c h a p t e r , i t s diluent content was lowered by careful evaporation of the diluent in vacuo until the p r o p o r t i o n s d e s i r e d w e r e obtained.

ON GEL CHARACTERIZATION PROCEDURES

1. Introduction.

In c h a p t e r II it was explained that the t h e r m o d y n a m i c a l p r o p -e r t i -e s of a g-el can b-e d -e t -e r m i n -e d by m -e a s u r i n g th-e activity (i. e. the c h e m i c a l potential) of the diluent inside the gel a s a function of the d e g r e e of swelling. This can be accomplished by d e t e r m i n i n g the d e g r e e of swelling of a gel which is in e q u i -l i b r i u m with di-luent of known activity.

Of the v a r i o u s m e a s u r a b l e quantities, providing the activity of the diluent inside the gel, t h r e e a r e worth mentioning:

1. The diluent activity in a solution which is in equilibrium with the gel.

2. The vapour p r e s s u r e of the diluent contained by the gel. 3. The osmotic swelling p r e s s u r e ,

In the following the p r o c e d u r e s by which these quantities can be obtained will be d i s c u s s e d .

The method providing the quantity first mentioned i m p l i e s swelling o r deswelling of a gel in a p o l y m e r solution in the diluent. The p r o c e d u r e is a v e r y simple one, but it i s only useful a s long a s t h e r e is no doubt that i n t e r a c t i o n of gel and solute is excluded. As it is some of the r e s u l t s of Mukherji's (11,23) e x p e r i m e n t s can only be explained by interaction of p o l y m e r m o l e c u l e s and the network. A p a r t from this the a p p l i -cability of the method is limited to high d e g r e e s of swelling because the activity of the diluent outside the gel can only be lowered to a c e r t a i n , r a t h e r s m a l l , extent by the dissolved p o l -y m e r m o l e c u l e s .

Although vapour p r e s s u r e s of concentrated p o l y m e r solutions have successfully been d e t e r m i n e d , m e a s u r e m e n t s of this type on gels a p p e a r to have been only r a r e l y p e r f o r m e d (31, 32, 33)

This a p p a r e n t lack of i n t e r e s t is probable caused by the g e n e r -ally r a t h e r low p o l y m e r concentration in g e l s , only v e r y s m a l l - a l m o s t undetectable - changes in vapour p r e s s u r e s a s c o m p a r e d to that of the p u r e diluent a r e to be expected.

Methods to d e t e r m i n e the swelling p r e s s u r e a s a function of the d e g r e e of swelling, have in the p a s t been d e s c r i b e d five t i m e s (34,35, 36, 37, 14). The t h r e e o l d e r swelling p r e s s u r e o s m o -m e t e r s will not be d i s c u s s e d in f u r t h e r detail; the value of these a p p a r a t u s however is not to be thought insignificant.

T h e l a s t (14) of the two m o r e r e c e n t e x p e r i m e n t a l a r r a n g e m e n t s , which in principle a r e v e r y much the s a m e , was executed a s follows (fig. 1):

2 6

-A piece of gel (1) shaped a s a segment 2 of a s p h e r e , at its flat side is in contact , J L 1 with a r e s e r v o i r of p u r e diluent (2) from % 3 % % ^ I which it is s e p a r a t e d by a porous s t e e l ' plate (3). The r e m a i n i n g surface is c o v

e r e d by a flexible foil (4), which s e p a -r a t e s the gel f-rom a column of m e -r c u -r y (5). By m e a n s of this column a p r e s s u r e can be e x e r t e d upon the gel in such a way a s to make the determination of the r e s u l t i n g change of volume of the gel p o s s i b l e . In the a p p a r a t u s sketched above this is accomplished by e x e r t i n g p r e s s u r e through the c a p i l l a r y (6). The change of volume is determined by m e a s u r i n g the displacement of the m e r c u r y in the c a p i l l a r y ,

This p r o c e d u r e to d e t e r m i n e the activity of the diluent inside the gel no doubt is m o r e a t t r a c t i v e than the p r e c e d i n g ones, because it enables one to d e t e r m i n e the activity over a l a r g e range of d e g r e e s of swelling. Unfortunately the p r o c e d u r e d e -s c r i b e d quite likely give-s r i -s e to -some a l m o -s t uncontrollable e x p e r i m e n t a l e r r o r s , thus possibly reducing the high a c c u r a c y osmotic methods generally exhibit. This can be explained as follows. C o n t r a r y to the assumption of various authors (37, 14) it s e e m s r a t h e r optimistic to expect that swelling o r deswelling will o c c u r i s o t r o p i c a l l y in an i n s t r u m e n t of this type. Borchard (14), who tried to induce i s o t r o p i c swelling by exerting a p r e s s u r e on the pure diluent, thus lifting the piece of gel from the porous p l a t e , c o n s i d e r s the e r r o r due to anisotropy made by previous a u t h o r s to amount to 20%. If the e r r o r caused by anisotropic swelling is that l a r g e it i s by no m e a n s s u r e that B o r c h a r d wholly evaded this e r r o r by his simple p r o c e d u r e .

Anisotropy v e r y well m a y be caused only p a r t l y by the l a r g e friction coeffici-ent between porous s t e e l and gel. The foil, which s e p a r a t e s the gel and the m e r c u r y m a y have an influence which i s not to be neglected. The foil has to c o v e r the piece of gel without a wrinkle, this difficult problem b e c o m e s unsolvable if we r e m e m b e r that the s a m e foil has to c o v e r a s e r i e s of varying volumina. The foil m a y not be e l a s t i c because an e l a s t i c foil would e x e r t an e x t r a p r e s s u r e on the gel which is difficult to account for. In the a p p a r a t u s of fig. 1 a wrinkled foil was chosen thus eliminating the e x t r a p r e s s u r e p r o b l e m , but leaving an unknown amount of anisotropic swelling. This foil f u r t h e r m o r e functions a s a gasket. T h e r e f o r e it should have a c e r t a i n m e -chanical f i r m n e s s , which opposes the demand of flexibility needed to e n s u r e smooth covering of the gel.

Another s o u r c e of e r r o r s is caused by the fact that in such an a p p a r a t u s not only the c o m p r e s s i b i l i t y of the gel i s determined, but the total c o m p r e s s i b i l i t y of a p p a r a t u s , m e r c u r y , foil and -l a s t but not -l e a s t - n e a r -l y unavoidab-le a i r bubb-les.

In spite of the c o n s i d e r a t i o n s given above the r e s u l t s obtained with swelling p r e s s u r e o s m o m e t e r s rank with those obtained by

deswelling in p o l y m e r s o l u t i o n s . A p a r t from the l a r g e r range in d e g r e e s of swelling which can be investigated by o s m o m e t r y no advantage of one method above the o t h e r can be detected.

S u m m a r i z i n g , it can be stated that if a swelling p r e s s u r e o s m o m e t e r could be constructed which enables one to m e a s u r e the i s o t r o p i c c o m p r e s s i b i l i t y of a piece of gel without having to take into account a s c o r e of c o m p r e s s i b i l i t i e s of which s o m e a r e difficult to c o r r e c t for, the osmotic method would be p r e f e r -able over any o t h e r method.

2. A new swelling pressure osmometer.

In fig. 2 a swelling p r e s s u r e o s m o m e t e r i s sketched* which is based on a p r i n ciple which is different from the p r e -ceding o n e s . The a p p a r a t u s c o n s i s t s of an interchangeable swelling c h a m b e r (1) to which an upper (2) and a l o w e r p a r t (3) a r e fixed with alien s c r e w s . Between (1) and (2) a supported porous nickel foil (4)** i s placed and between (1) and (3) a platinum foil (5)***, at the c e n t e r of which a d i s p l a c e m e n t t r a n s d u c e r (6) i s fitted.

The u p p e r p a r t (2) contains a porous s t e e l disc (7) and above that a diluent c h a m b e r (8).

To the lower p a r t (3) a flexible PVC tube (9) is connected by a g l a s s tubing which s e r v e s a s viewing g l a s s (10). The flexible tube ends in an expansion v e s s e l (11). P a r t of the expansion v e s s e l , the whole tube and the l o w e r half bf the viewing glass a r e filled with m e r c u r y . The u p p e r half of the viewing g l a s s and the c o m p a r t m e n t (3) a r e filled with silicone oil.

With p a r t s (2) and (4) r e m o v e d one p l a c e s in the swelling c h a m b e r (1) which i s a cylinder of equal height and d i a m e t e r a deswollen gel of exactly the s a m e g e o m e t r y but s m a l l e r in d i m e n s i o n s . After filling the swelling c h a m b e r (the volume of which is l e s s than the volume of the freely swollen gel) with diluent, r e p l a c i n g p a r t (2) and (4) and a l s o filling the diluent r e s e r v o i r , the e x p e r i m e n t is s t a r t e d ,

The gel swells until it fills the swelling c h a m b e r completely. As the gel has the s a m e g e o m e t r y a s the swelling c h a m b e r i s o t r o p i c swelling is e n s u r e d . Because the volume of the swelling

In Appendix (A. 10) a detailed construction drawing is given.

Pore diameter: 10 fi, which is several times smaller than the pore diameter of the porous plates used in previously described apparatus.

2 8

-c h a m b e r i s l e s s than the volume of the -completely swollen gel, an osmotic p r e s s u r e will be build up. This p r e s s u r e d i s p l a c e s the thin platinum foil. The displacement i s detected by the t r a n s -d u c e r , which by a s e r v o - s y s t e m i s connecte-d with an e l e c t r i c m o t o r , which hoists up the m e r c u r y filled expansion v e s s e l until the platinum foil has r e a c h e d its original position, thus indicating equality of p r e s s u r e at both sides of the foil.*

Although the swelling p r e s s u r e itself is a l m o s t t e m p e r a t u r e independent, attention m u s t be given to t h e r m o - c o n t r o l because of the t h e r m a l expansion of the diluent, which cannot leave the gel fast enough if the t e m p e r a t u r e suddenly r i s e s . In the p r e s e n t s e t - u p the t e m p e r a t u r e was kept at 25°C t 0, 1 by wrapped around tubing through which w a t e r of constant t e m p e r a t u r e was c i r c u l a t e d .

The u l t i m a t e swelling p r e s s u r e , which is reached after about two weeks can be m e a s u r e d d i r e c t l y from the displacement of the m e r c u r y column.

To d e t e r m i n e the swelling p r e s s u r e a s a function of the degree of swelling, s e v e r a l swelling c h a m b e r s , of different volume, but all having equal height and d i a m e t e r can be u s e d .

After a swelling p r e s s u r e d e t e r m i n a t i o n is completed the gel i s removed from the swelling c h a m b e r by r e p l a c i n g the p u r e diluent (nitrobenzene in this case) in the diluent r e s e r v o i r by carbon t e t r a c h l o r i d e , which induces the gel to s h r i n k . As soon a s the gel no longer fills the swelling c h a m b e r completely, the diluent r e s e r v o i r and the nickel foil a r e removed. The gel can e a s i l y be taken out of the swelling c h a m b e r because it floats on the carbon t e t r a c h l o r i d e .

3. Measurements of uniaxial compression.

Quite a few a r t i c l e s on i n s t r u m e n t a t i o n for m e a s u r i n g the c o m p r e s s i o n of pure o r swollen p o l y m e r networks have been published. F o r our c o m p r e s s i o n m e a s u r e m e n t s the following a p p a r a t u s , which i s v e r y e a s y to o p e r a t e , has been u s e d .

fi The a p p a r a t u s * * c o n s i s t s of a p r e s s u r e IIUW^ t r a n s d u c e r (1) which can be moved by a I m i c r o m e t e r s c r e w (2), To the t r a n s d u c e r ;'l T I a teflon covered disc (3) is fitted. Below 'Lnj this disc another one with a fixed p o s i

-tion (4) is p r e s e n t . The gel, which i s

'~^ •' placed between the two d i s c s is c o m -^ p r e s s e d b y turning the m i c r o m e t e r s c r e w ,

' 1 which at the s a m e time s e r v e s to d e -,1 3 t e r m i n e the extent of c o m p r e s s i o n . The

' The accuracy of this new method to determine changes of pressure at constant volume, which was determined by means of a pressure balance proved to be 0,1 mm mercury. •• This apparatus, the two teflon covered platforms excluded, has been described by M.C.A.

force of c o m p r e s s i o n i s given by the t r a n s d u c e r .

^r\

4. Shaping and conditioning of the gels.

The applicability of both i n s t r u m e n t s , e s p e c i a l l y the swelling p r e s s u r e o s m o m e t e r , depends on the possibility of p r e p a r i n g a c y l i n d r i c a l gel of a c c u r a t e l y equal height and d i a m e t e r .

The following p r o c e d u r e s e e m e d a r a t h e r elegant one:

In a teflon container (fig. 4) fitted with a m e r c u r y lock (see appendix A. 11.) a gel is formed a c c o r d i n g to the p r o c e d u r e described in c h a p t e r III. As the gel is p r e p a r e d at 100°C one would think that if its t h e r m a l expansion is l a r g e r than that of the teflon of the container, the gel on cooling will b r e a k at the c a p i l l a r y ( a r r o w ) , because this is the weakest p a r t of the gel. If this happens, a gel with an "umbilical c o r d " is brought forth, which can e a s i l y be shaped to an a l m o s t perfect cylinder,

Unfortunately, p o s s i b l y because the t h e r m a l expansion coefficients did not differ sufficiently, the gels obtained broke along the dotted line a s shown in fig. 4, when the u p p e r p a r t of the c o n t a i n e r was taken off,

fig. 4

On the b a s i s of these e x p e r i e n c e s an improved a p p a r a t u s for p r e p a r i n g c y l i n d r i c a l gels was c o n s t r u c t e d .

The a p p a r a t u s (fig. 5) only differs from the preceding one a s far a s the upper p a r t i s c o n c e r n e d . The e s s e n c e l i e s in its t h r e e teflon p a r t s : a flat bottom plate (1), a cylindrical middle p a r t (2) of which d i a m e t e r and height a r e equal and an u p p e r p a r t (3) the bottom of which is an extension of the cylinder and the top provides a fit for the m e r c u r y lock (4). The teflon p a r t s , which a r e housed in a s t a i n l e s s s t e e l container (5), a r e p r e s s -ed together by two s p r i n g s (6).

After gelation has o c c u r r e d the three teflon p a r t s a s a whole a r e t r a n s p o r t e d into a mounted m e s s i n g cylinder (fig. 6), which in two p l a c e s , c o r r e s p o n d i n g with the p a r t i t i o n s between the teflon p a r t s (1), (2) and (3) has been sawed through. P a r t (3) is springloaded and p r e s s e s the o t h e r p a r t s against each other and against the closed end of the cylinder, A smooth cut is obtained between p a r t s (1) and (2) and between (2) and (3) with a taut steel w i r e ( d i a m e t e r 0,1 m m ) ,

3 0

-By i m m e r s i n g the cylinder, containing the piece of gel in c a r b o n t e t r a c h l o r i d e the gel s h r i n k s and can be r e -moved from the container,

RESULTS AND DISCUSSION

1. Characterization of the polymer.

In o r d e r to e s t i m a t e the n u m b e r of chains which a r e only connected at one end to the network and which therefore a r e e l a s t i c a l l y ineffective, one has to know the m o l e c u l a r weight of the constituent p r i m a r y p o l y m e r , p r e f e r a b l y the n u m b e r a v e r a g e M ^ .

Of the poly-(p-nitrophenyl m e t h a c r y l a t e ) used in our e x p e r i h i e n t s the weight a v e r a g e My/ was d e t e r m i n e d by ultracentrifugation and light s c a t t e r i n g .

a. Ultracentrifugation.

My^ was d e t e r m i n e d by two days equilibrium sedimentation (Beekman Model E Analytical Ultracentrifuge, Angular velocity w = 7,86 . 1 0 r a d / s e c . Optical r e g i s t r a t i o n by the S c h l i e r e n -method. Computation by n u m e r i c a l integration) of three solutions of the p o l y m e r in nitrobenzene (0. 248;0. 300 and 0. 500% p o l y m e r by weight.

Refraction index i n c r e m e n t (dn/dc): 0.0374 m l / g . Specific volume of the polymer (vx) : 0.719 m l / g . Mw proved to be ( 3 . 3 ± 0 . 5 ) . 10^

Considering the n a t u r e of the m o n o m e r this m o l e c u l a r weight is much higher than one would expect; even if one takes into account the polymerization p r o c e d u r e followed as d e s c r i b e d in chapter III. This p a r t i c u l a r p r o c e d u r e was chosen in o r d e r to obtain as high a m o l e c u l a r weight as possible by reducing the mobility of the p o l y m e r i z i n g c h a i n s , thus impeding chain t e r m i n a t i o n by combination or disproportionation (Trommsdorff effect).

The r e s u l t of an attempt to d e t e r m i n e the m o l e c u l a r weight of the p o l y m e r by equilibrium sedimentation in solutions of dimethylformamide (dn/dc = 0.0641 m l / g ; Vx = 0,775 m l / g ) was s t a r t l i n g indeed: Even at a v e r y low speed (3000 r . p . m . ) the m a c r o m o l e c u l a r m a t e r i a l was immediately centrifuged to the bottom of the centrifuge c e l l . This made an exact d e t e r m i n a t i o n impossible but indicated an e n o r m o u s m o l e c u l a r weight.

6. Light scattering.

Because light s c a t t e r i n g p r o v i d e s an excellent method for the d e t e r m i n a t i o n of v e r y l a r g e m o l e c u l a r weights, M\fj was d e t e r -mined by the light s c a t t e r i n g method using nitrobenzene and dimethylformamide as s o l v e n t s .

3 2

-s c a t t e r i n g level of the pure -solvent-s, make the d e t e r m i n a t i o n somewhat i n a c c u r a t e .

The e x t r e m e l y long time (up to s e v e r a l days) n e c e s s a r y for the filtration through s i n t e r e d g l a s s filters (5g, Schott & Gen Mainz, p o r e d i a m e t e r 3 - 1 , 7 /u) adds a l s o an uncertainty to the r e s u l t s . All c o n c e n t r a t i o n s were d e t e r m i n e d after filtration. In m o s t c a s e s no significant l o s s of m a c r o m o l e c u l a r m a t e r i a l was found.

0.20( -r-i

fig.7. Light scattering of poly-(p-nitrophenyl methacrylate) in nitrobenzene. The symbols have their usual meaning.

F r o m the Z i m m plots shown in fig. 7 and 8 the M^^ was found to be ( 4 . 8 ± 0 . 5 ) . 10^ in nitrobenzene and (14 ± 1.5). 10^ in d i m e t h y l f o r m a m i d e .

The Z i m m plots do not exhibit a negative second v i r i a l coeffi-cient which would constitute a proof of concentration dependent a s s o c i a t i o n . If however s m a l l c l u s t e r s of m o l e c u l e s of a constant s i z e a r e formed ( s i m i l a r to m i c e l l e s in detergent solutions) at a v e r y low concentration no negative second v i r i a l coefficient is to be expected. The fact that the Myj is three t i m e s a s l a r g e in d i -methylformamide as in nitrobenzene does indicate that there is a threefold c l u s t e r in dimethylformamide a s c o m p a r e d to n i t r o -benzene.

c. Conclusion.

The r e s u l t s given above indicate that quite likely the p o l y m e r m o l e c u l e s in dimethylformamide a r e aggregated in c l u s t e r s of about three m o l e c u l e s .

The c l u s t e r s may be aggregated in such a way that the apolar groups stick together forming a backbone from which,the polar e s t e r groups protude into the p o l a r d i m e t h y l f o r m a m i d e .

If the apolar backbone is formed by the methyl g r o u p s , the methylene s e g m e n t s cooperating or not. the p o l y m e r has to be tactic to p e r m i t the c l u s t e r formation. As the m o n o m e r is a . a - d i s u b s t i t u t e d it is possible that a s t e r e o r e g u l a r polymer is formed even by r a d i c a l p o l y m e r i z a t i o n . If only the methylene s e g m e n t s take c a r e of the backbone formation no tacticity r e -q u i r e m e n t exist.

The a r o m a t i c n a t u r e of nitrobenzene m a k e s this solvent liable to i n t e r c a l a t i o n between the e s t e r g r o u p s thus impeding the for-mation of c l u s t e r s of r e g u l a r l y a r r a n g e d c h a i n s . T h e r e f o r e the o c c u r r e n c e of stable a g g r e g a t e s in nitrobenzene is l e s s likely.

As the m o l e c u l a r weight of the p o l y m e r i s v e r y high no c o r -r e c t i o n fo-r dangling ends i s needed. M o -r e o v e -r , even if needed, such a c o r r e c t i o n could not be made exactly, because d e t e r m i

3 4

-nationof the n u m b e r a v e r a g e m o l e c u l a r weight by osmotic methods is impossible as these methods do not allow r e a s o n a b l e d e t e r m i n a -tion of m o l e c u l a r weights above 10^. Conceivable other m e t h o d s , e . g . cryoscopy have an even m o r e limited s c o p e .

2. The crosslinking reaction.

The choice of the r e a c t i o n of poly-(p-nitrophenyl m e t h a c r y l a t e ) and hexamethylenediamine in dimethylformamide for the formation of well defined three dimensional networks was - among other r e a s o n s - based on the assumption that in a dimethylformamide solution which contains nitrophenol s m a l l t r a c e s of amine can be detected. The base l i b e r a t e s nitrophenolate ions which can s p e c t r o p h o t o m e t r i c a l l y be d e t e r m i n e d . During the c r o s s l i n k i n g r e a c t i o n , the amine is used up and therefore the amount of nitrophenolate ions is reduced to a l m o s t z e r o . Of c o u r s e n i t r o p h e -nol is not a v e r y good a c i d - b a s e indicator (39), but it will suit our purpose well enough. This is i l l u s t r a t e d by fig. 9 which shows the extinctions (cell length 1 cm) of solutions of p n i t r o -phenol (0. 25 g / l ) in dimethylformamide containing v a r i o u s amounts of hexame thylene d i a m i n e .

1.6-'1

0.8-

0.4-conc of hexamethylenediamine in ti/ml J 1 1

1 2 3 4

fig. 9. The extinction of a solution of p-nitrophenol and amine as a function of the amine concentration.

Another r e a s o n for adopting this c r o s s l i n k i n g p r o c e d u r e is that the r e a c t i o n may be expected to p r o c e e d r a t h e r fast to quantitative or at l e a s t a l m o s t quantitative c o n v e r s i o n . This