Ordered Fluids and Liquid Crystals

Ordered Fluids and Liquid Crystals Downloaded from pubs.acs.org by UNIV OF MASSACHUSETTS AMHERST on 05/24/18. For personal use only.

20 Order and Structure in Concentrated Polymer Solutions and Gels JAN HERMANS, JR. Department of Biochemistry, University of North Carolina, Chapel Hill, N. C.

Viscometric

data demonstrate

-γ-benzyl-L-glutamate

are

that concentrated solutions of poly ordered.

The

concentration

above which ordering occurs is that predicted At high concentrations

the elastic modulus

by Flory's

of carboxy methyl

-cellulose solutions varies as the square of the concentration. ther, G = 0 below the gel point.

theoretical curves derived by assuming and the network thus formed follows and phase separation crystals demonstrate to side-by-side

that the number of inter to the

Flory's

data on suspensions

concentration,

theory of

Flow and elastic

that these particles

aggregation.

Fur

These results can be fitted with

-particle links per molecule is proportional and is deformed as a rubber.

limit theory.

gelation

measurements

of cellulose

have a strong

micro tendency

A model is constructed in

this behavior gives rise to linear aggregates with few

which

cross-links.

C e v e r a l studies were done d u r i n g the past few years a t A m e r i c a n V i s c o s e Research a n d Development C o . , M a r c u s H o o k , P a . , to investigate the i n t e r a c t i o n s b e t w e e n m a c r o m o l e c u l e s i n c o n c e n t r a t e d solutions a n d i n gels. T h e s e were s t u d i e d b y m e a s u r i n g t h e i r m e c h a n i c a l p r o p e r t i e s — i . e . , flow b e havior and elasticity. T h e results of experiments w i t h different colloids d e m o n s t r a t e some of t h e w a y s i n w h i c h macromolecules of v a r i o u s sizes, shapes, a n d surface properties m a y i n t e r a c t to f o r m , i n some cases, ordered solutions s i m i l a r t o l i q u i d c r y s t a l s a n d , i n o t h e r cases, t h r e e - d i m e n s i o n a l n e t w o r k s w i t h t h e properties of a s o l i d a n d h o w t h e order or t h e s t r u c t u r e present determines t h e m e c h a n i c a l properties. Order in Concentrated

Polypeptide

Solutions

T h e p o s s i b i l i t y of the occurrence of phase s e p a r a t i o n or o r d e r i n g i n solutions of r i g i d r o d l i k e p a r t i c l e s has been i n v e s t i g a t e d t h e o r e t i c a l l y b y Onsager (17) a n d F l o r y (15).

F l o r y showed t h a t c o n c e n t r a t e d solutions of 282

20.

HERMANS

Polymer Solutions

283

and Gels

r o d l i k e particles s h o u l d show phase s e p a r a t i o n even i n the absence of i n t e r actions between rods.

T h i s result follows f r o m a n elegant a p p l i c a t i o n of

t h e l a t t i c e m o d e l for p o l y m e r solutions.

I f t h e v o l u m e f r a c t i o n , φ, of t h e

rods i n t h e s o l u t i o n is h i g h enough, a n ordered phase, w i t h t h e molecules p r e d o m i n a n t l y i n p a r a l l e l o r i e n t a t i o n , has a higher e n t r o p y t h a n a n isotropic s o l u t i o n of t h e same c o n c e n t r a t i o n , i n w h i c h t h e molecules are r a n d o m l y Ordered Fluids and Liquid Crystals Downloaded from pubs.acs.org by UNIV OF MASSACHUSETTS AMHERST on 05/24/18. For personal use only.

oriented.

A s a result, phase separation i n t o a disordered s o l u t i o n of v o l

u m e f r a c t i o n φ* a n d a n ordered s o l u t i o n of v o l u m e f r a c t i o n a . A t t h e same t i m e , t h e n u m b e r of l i n k s per molecule i n t h e n e t w o r k increases f r o m t h e m i n i m u m n u m b e r of 1/2 at a . T h e l i n k s necessary t o a d d t h e molecules t o t h e n e t w o r k d o n o t c o n t r i b u t e t o t h e e l a s t i c i t y . R a t h e r , w e m u s t o b t a i n a n expression f o r t h e r e m a i n i n g n u m b e r of l i n k s (called cross l i n k s ) w h i c h is g i v e n b y gy

c


c

N=

(l/2)(a -2a )fW N

c

g

c

0

(5)

o

E x p r e s s i o n s f o r a , t h e a of t h e gel f r a c t i o n , a n d W as a f u n c t i o n of a h a v e been d e r i v e d b y F l o r y (4; 5, C h a p . 9). 3. M o d u l u s of E l a s t i c i t y . I t is assumed t h a t these gels are d e f o r m e d a c c o r d i n g t o t h e t h e o r y of r u b b e r e l a s t i c i t y , w h i c h tells us t h a t t h e shear m o d u l u s is g i v e n (£, C h a p . 11) b y g

g

(6)

G = NckT

1

1

mol.

_

1

1

•

wt.

Ο ·

4 6 , 0 0 0

• •

1 0 0 , 0 0 0

a

Δ Α 3 7 0 . 0 0 0

_

Δ

0

0

-

0 0

Δ

io

1

o α

8

Δ

°

0

s Δ

°

/

o

_

-

/ A

/

*l

/

/ L

/

·

°

A

•

•

-

·

m

— !

/

ί

' / !( 01

"

'

! ι 03

:•. 0-5

·· i i 07

ι 09

• II

« 1-3

15

log c Courtesy Journal

Figure 5.

of C o l l o i d

Science

Values of shear modulus for three samples of carboxymethylcellulose as a function of concentration {grams per 100 ml.)

Open and filled symbols represent measurements with slightly different equipment Gel points obtained by fitting curves of Figure 4 to these data Best fitting curve drawn for experiments on sample of highest molecular weight (12)

20.

Polymer Solutions

HERMANS

and Gels

289

C o m b i n i n g E q u a t i o n s 2, 5, a n d 6, we c a n w r i t e (5) G = (RT/2JMK)

F(a)

where M is t h e m o l e c u l a r w e i g h t , a n d F(a) is a k n o w n f u n c t i o n of a.

(7) Since

a is p r o p o r t i o n a l to C., the c u r v e of log F(a) as a f u n c t i o n of l o g a s h o w n i n


F i g u r e 4 is a t h e o r e t i c a l c u r v e of l o g G as a f u n c t i o n of C., except for a d j u s t able h o r i z o n t a l a n d v e r t i c a l displacements. C o m p a r i s o n w i t h E x p e r i m e n t . W e h a v e measured the e l a s t i c i t y of three samples of c a r b o x y m e t h y l c e l l u l o s e of different m o l e c u l a r weight as a f u n c t i o n of the c o n c e n t r a t i o n (12), b y a p p l y i n g a shear stress to the gel a n d o b s e r v i n g t h e shear. T h e shear reached a constant v a l u e i n about 30 m i n u t e s a n d c o u l d be f u l l y recovered b y r e m o v i n g the stress at t h i s or at considerably l a t e r t i m e s . F u r t h e r m o r e , t h e shear was f o u n d to be p r o p o r t i o n a l to t h e stress ( F i g u r e 5). F o r the sample of highest m o l e c u l a r w e i g h t we h a v e d r a w n t h e t h e o r e t i c a l c u r v e of F i g u r e 4, w h i c h describes t h e d a t a w e l l . F u r t h e r , gel p o i n t s c a n be d e t e r m i n e d (dashed lines i n F i g u r e 5), a n d these change a p p r o x i m a t e l y w i t h the m o l e c u l a r weight a c c o r d i n g to E q u a t i o n 4. T h e slope of the curves at h i g h v a l u e s of c becomes closely e q u a l to 2, as is r e q u i r e d b y a s s u m p t i o n 1 t h a t the n u m b e r of l i n k s per p a r t i c l e is p r o p o r t i o n a l t o t h e c o n c e n t r a t i o n . A t h i g h concentrations t h e n u m b e r of l i n k s is m u c h larger t h a n the n u m b e r of particles, a n d a l l l i n k s c a n be c o u n t e d as cross-links. T h e n u m b e r of cross-links a n d therefore the m o d ulus w i l l t h e n v a r y as c . T h u s our a s s u m p t i o n 1 has been verified i n d e p e n d e n t l y of a s s u m p t i o n 2 r e g a r d i n g the s t r u c t u r e of the n e t w o r k . 2

Phase Separation Suspensions

and Ordering

of Cellulose

in

Microcrystals

T h e t h i r d s y s t e m i n v e s t i g a t e d consisted of solutions of r i g i d r o d l i k e particles capable of f o r m i n g i n t e r m o l e c u l a r l i n k s , so t h a t at h i g h enough concentrations i n f i n i t e n e t w o r k s are present a n d the solutions are gels (1, 10). C e l l u l o s e m i c r o c r y s t a l s h a v e v a r y i n g dimensions i n the neighborhood of 0.4 m i c r o n l o n g b y 0.04 m i c r o n t h i c k , as is e v i d e n t f r o m electron m i c r o graphs (18) ( F i g u r e 6). W e present first the a v a i l a b l e i n f o r m a t i o n w h i c h suggests t h e w a y i n w h i c h these particles t e n d to aggregate a n d secondly, the elastic a n d flow properties of the gels w h i c h are f o r m e d because of t h i s aggregation. Cellulose m i c r o c r y s t a l s c a n be suspended i n d i l u t e s o l u t i o n . T u r b i d i t y measurements suggest t h a t the particles are not h i g h l y associated i n t h e absence of a d d e d salt. I n t h e presence of a l o w salt c o n c e n t r a t i o n , large aggregates are f o r m e d , as was s h o w n b y a s t u d y of l i g h t s c a t t e r i n g b y suspensions of r a m i e m i c r o c r y s t a l s (15). W h e n the salt c o n c e n t r a t i o n is f u r t h e r increased, the m i c r o c r y s t a l s p r e c i p i t a t e . Since the m i c r o c r y s t a l s


290

ORDERED

FLUIDS A N DLIQUID

C o u r t e s y J o u r n a l of P o l y m e r

Figure 6.

CRYSTALS

Science

Electron micrograph of wood cellulose microcrystals 25,000 X

c a r r y a l o w negative charge (2), o w i n g t o t h e presence of i o n i z e d c a r b o x y l groups, t h i s b e h a v i o r is t y p i c a l of a l y o p h o b i c c o l l o i d (21). E . G . Scalco a n d t h e a u t h o r h a v e s t u d i e d t h e p r e c i p i t a t i o n i n d e t a i l . S o m e s i m p l e experiments were done, w h i c h consisted of b r i n g i n g t h e salt c o n c e n t r a t i o n of m i c r o c r y s t a l suspensions of different c o n c e n t r a t i o n t o v a r i o u s values, c e n t r i f u g i n g t h e solutions a t a p p r o x i m a t e l y 2,000 g t o separate t h e phases, a n d subsequently a n a l y z i n g t h e v o l u m e a n d c o n c e n t r a t i o n of each of t h e phases. T h e results o b t a i n e d were complex. Thus, t h e c o m p o s i t i o n of t h e p r e c i p i t a t e a n d t h e s u p e r n a t a n t phases depends n o t o n l y o n t h e salt c o n c e n t r a t i o n b u t also o n t h e c o n c e n t r a t i o n of m i c r o c r y s t a l s i n t h e suspension o r gel t o w h i c h t h e salt was a d d e d . ( T h e results g i v e n below represent selected d a t a w h i c h i l l u s t r a t e t h e t r e n d s observed.) F u r t h e r m o r e , no fewer t h a n three different k i n d s of p r e c i p i t a t e were o b t a i n e d . T o cause phase s e p a r a t i o n i n a suspension o r a gel of cellulose m i c r o crystals, the salt c o n c e n t r a t i o n m u s t exceed a c e r t a i n v a l u e . T h i s m i n i m u m v a l u e is s h o w n i n F i g u r e 7 as a f u n c t i o n of t h e c o n c e n t r a t i o n (solid c u r v e ) . W h e n t h i s v a l u e of the salt c o n c e n t r a t i o n is exceeded, suspensions of 0 . 7 5 % o r higher separate i n t o a m o r e c o n c e n t r a t e d g e l a n d a d i l u t e suspension of concentrations a p p r o x i m a t e l y those expected if F i g u r e 7 were

20.

HERMANS

Polymer Solutions

291

and Gels

a phase d i a g r a m . H o w e v e r , i n more d i l u t e suspensions, t w o precipitates are n o t e d , L a n d L , w h i c h differ i n cellulose c o n c e n t r a t i o n . H e n c e t h e y settle a t different rates a n d f o r m layers of different o p a c i t y . F i g u r e 8 shows t h e v o l u m e s of t h e p r e c i p i t a t e d phases as a f u n c t i o n of N a C l m o l a r i t y for a series of different i n i t i a l cellulose concentrations. ( T h e dense p r e c i p i t a t e , L , is t h e one of smallest volume.) I n F i g u r e 7 are curves s h o w i n g t h e t r e n d of t h e v a r i a t i o n of t h e c o n c e n t r a t i o n of phases L a n d L w i t h t h e increase of t h e i n t e r a c t i o n between particles as t h e ionic s t r e n g t h is m a d e larger. A t h i g h i o n i c s t r e n g t h t h e d i s t i n c t i o n between L2 a n d L disappears. 2

3

3


2

3

3

A test f o r birefringence of t h e v a r i o u s phases revealed t h a t L is n o t biréfringent w h i l e L is. T h u s i t w o u l d appear t h a t i n L t h e r o d l i k e p a r 2

3

2

0.5

1.0

1.5 8.1

CONCENTRATION OF PHASE (%) Figure 7. Minimum value of salt concentration needed to cause phase separation in suspensions of cellulose microcrystals of varying concentration Also indicated are approximate concentrations of L and L 3 , obtained when salt is added to dilute suspensions. Concentration of precipitate obtainable by applying a high shear rate to a gel containing salt is indicated (8.1%) 2

292

ORDERED FLUIDS AND LIQUID CRYSTALS

t i d e s h a v e aggregated i n a r a n d o m m a n n e r ; i n L i n a m o r e n e a r l y p a r a l l e l m a n n e r . I t is reasonable t h a t t h e p a r a l l e l arrangement produces a denser phase. F i n a l l y , i t w a s observed t h a t phases L a n d L c a n b e resuspended w h e n t h e salt is r e m o v e d b y w a s h i n g a n d d i l u t i n g t h e precipitates w i t h d i s t i l l e d water. H o w e v e r , i n t h e presence of a h i g h salt c o n c e n t r a t i o n t h e precipitates c a n be changed i n t o y e t another f o r m w h i c h cannot be r e d i s 3


2

3

solved. W h e n t h e gellike precipitates ( L o r L ) are subjected t o h i g h shear rates i n a p i s t o n - t y p e glass tissue grinder, a dense, g r a i n y p r e c i p i t a t e 2

61

I0"

3

·

4

I0"

1

3

Figure 8.

I0" Molarity

10"'

2

NaCl

1

Volume of precipitate obtained on adding NaCl to 5 ml. of suspensions of microcrystals of different concentrations

For lowest concentrations there is a region in which the precipitate consists of two layers; lower curve is volume of lower layer ( L ) , and upper curve is volume of total precipitate ( L 2 + L ) 3

3

is f o r m e d , w h i c h resembles cellulose powder. (Its c o n c e n t r a t i o n w a s d e t e r m i n e d t o b e 8 . 1 % , i n d i c a t i n g t h e c o n t i n u e d presence of m u c h solvent.) W e believe t h a t b y t h e h i g h shear stresses w h i c h are a p p l i e d , t h e m i c r o crystals are forced i n t o positions where a great m a n y a d d i t i o n a l b o n d s of t h e t y p e responsible f o r t h e f o r m a t i o n of t h e precipitates a n d gels c a n b e f o r m e d . W e suggest t h a t t h e surfaces of t h e m i c r o c r y s t a l s manage t o r e f o r m i n p a r t t h e stable cellulose c r y s t a l s t r u c t u r e since t h i s w o u l d also e x p l a i n t h e t e n d e n c y s h o w n b y t h e particles t o assume p a r a l l e l orientations. Elasticity

and Flow of Gels of Cellulose

Microcrystals

T h e e l a s t i c i t y of a series of gels of different concentrations w a s i n v e s t i g a t e d i n a n a t t e m p t t o o b t a i n i n f o r m a t i o n about t h e s t r u c t u r e of t h e


20.

HERMANS

-0.4

Polymer

-0.2

Solutions

0

0.2 log c Courtesy

Figure 9.

293

and Gels

0.4

0.6

J o u r n a l of A p p l i e d P o l y m e r

0.8 Science

Values of shear modulus of gels of wood cellulose microcrystals Log-log plot. Line drawn tofitdata, has slope of 3.5 (11)

p a r t i c l e n e t w o r k (8) ( F i g u r e 9 ) . T h e d a t a i n t h i s log-log p l o t c a n be f i t t e d w i t h a s t r a i g h t l i n e of slope 3.5, a n d t h e existence of a g e l p o i n t is n o t i n evidence, m u c h i n contrast t o w h a t was f o u n d f o r c a r b o x y m e t h y l c e l l u l o s e ( C M C ) gels. O n e m u s t o b v i o u s l y a s k w h i c h of t h e three assumptions w i t h w h i c h t h e b e h a v i o r of the C M C gels c o u l d be e x p l a i n e d has t o be a l t e r e d . I n t h e first place, t h e a s s u m p t i o n a b o u t t h e e l a s t i c i t y of t h e n e t w o r k h a s t o be s o m e w h a t m o d i f i e d since the i n d i v i d u a l m i c r o c r y s t a l s are m u c h stiffer t h a n t h e i n d i v i d u a l C M C molecules. T h e d e f o r m a t i o n of t h e former requires elastic energy w h i l e i n d e f o r m i n g r a n d o m l y coiled macromolecules t h e e n t r o p y changes. W e h a v e been able t o show (11) t h a t f o r a n e t w o r k of stiff rods, G = (3 π Ε α / 2 0 b) N (l/η) 4

(8)

c

where E is t h e elastic m o d u l u s of cellulose (3 X 1 0 ) , a is t h e r a d i u s a n d b is the l e n g t h of t h e segments of r o d between l i n k s , N is t h e n u m b e r of cross l i n k s p e r u n i t of v o l u m e , a n d η is t h e n u m b e r of rods between c r o s s - l i n k s . u

c

294

ORDERED

FLUIDS A N DLIQUID CRYSTALS

O n t h e other h a n d , w h e n t h e n u m b e r of l i n k s per r o d is n o t s m a l l , t h e m o d u l u s s h o u l d a p p r o a c h Ed, where d is the v o l u m e f r a c t i o n of the cellulose (14) : (9)

G — Ed

F r o m the values of the m o d u l i observed, i t is e v i d e n t t h a t t h i s l i m i t is far f r o m reached i n t h e c o n c e n t r a t i o n range s t u d i e d . W e r e i t possible t o describe t h e r e a c t i o n l i n k i n g t h e rods as a b i m o l e c u l a r e q u i l i b r i u m , N /N s h o u l d be p r o p o r t i o n a l t o c. F u r t h e r m o r e , N /N = 1/2 a t t h e g e l p o i n t (see above). Since o u r measurements cover a 30-fold c o n c e n t r a t i o n range, N /No s h o u l d be greater t h a n 15 a t the highest concentrations s t u d i e d , a n d t h e m o d u l u s s h o u l d be e q u a l t o t h e v a l u e g i v e n b y E q u a t i o n 9. I t w o u l d therefore appear t h a t the first of o u r three a s s u m p t i o n s , t h e one r e g a r d i n g t h e v a r i a t i o n of the n u m b e r of cross-links w i t h the c o n c e n t r a t i o n , m u s t be modified.


c

c

0

0

c

Courtesy

Journa

of A p p l i e d P o l y m e r

Science

Figure 10. Model for networks of cellulose microcrystals formed by almost parallel aggregation of rodlike particles A. B.

Gel in which aggregates are oriented at random Gel in which aggregates have a nearly parallel orientation from a shearing motion applied before gel allowed to set (8)

W e h a v e been able t o c o n s t r u c t a m o d e l , p a r t l y based o n t h e i n f o r m a t i o n o b t a i n e d above, t o e x p l a i n t h e observed m e c h a n i c a l b e h a v i o r . S i n c e

20.

Polymer Solutions

HERMANS


I6OO1

295

and Gels

τ

ο

0.5

1.0

1.5

2.0

2.5

gradient (sec ) -1

Courtesy

Figure 11.

Journal

of A p p l i e d P o l y m e r

Science

Flow curves of gels of cotton cellulose microcrystals of different concen trations (10)

Note determination of two values of yield stress for each gel, low one after low shear rate applied, high one after gel sheared at shear rate of 80 seer , prior to measurement of yield stress 1

t h e tendency t o p a r a l l e l aggregation b y the m i c r o c r y s t a l s is so strong, there is o b v i o u s l y a t e n d e n c y f o r t h e f o r m a t i o n of l o n g strands c o n t a i n i n g m a n y particles. F o r a n infinite n e t w o r k t o be f o r m e d , these strands m u s t be cross-linked. W e e n v i s i o n the f o r m a t i o n of the cross-links as t a k i n g place b y the b r a n c h i n g a n d r e j o i n i n g of different sheaf l i k e aggregates t h r o u g h o u t the s o l u t i o n ( F i g u r e 10, A). Because of t h e large size of t h e p r i m a r y a g gregates, t h e n u m b e r of cross-links needed t o f o r m a n infinite n e t w o r k is s m a l l a n d c a n increase a great m a n y t i m e s before i t becomes e q u a l t o t h e n u m b e r of m i c r o c r y s t a l s . A l s o , almost every cross-link w i l l be a n " a c t i v e " cross-link. I t w o u l d be desirable t o h a v e t h e n u m b e r of cross-links s t i l l p r o p o r t i o n a l t o c . I n t h a t case, (l/η) ~ N /N w i l l v a r y asC.,a n d t h e m o d u l u s , w h i c h is p r o p o r t i o n a l t o b o t h N a n d ( l / η ) w i l l v a r y as c (cf. 2

c

0

3

c

E q u a t i o n 8). T h e p r e d i c t e d v a r i a t i o n of G w i t h c is close t o t h a t observed e x p e r i m e n t a l l y (G p r o p o r t i o n a l t o c - ). 3

5

F i n a l l y , the m o d e l s h o w n i n F i g u r e 10 c a n e x p l a i n a n o d d aspect of t h e flow b e h a v i o r n o t e d earlier (#). F i g u r e 11 shows a series of flow curves of gels of c o t t o n cellulose m i c r o c r y s t a l s . T h e p e c u l i a r feature of these d a t a is the i r r e g u l a r i t y a t a gradient (shear rate) of a p p r o x i m a t e l y 0.5 s e c . I f - 1

296

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one applies a shear rate below 0.5 s e c . " to the gel for some t i m e a n d t h e n increases i t to a v a l u e greater t h a n 0.5 s e c . , t h e shear stress measured i n creases w i t h t i m e t o reach a steady v a l u e as s h o w n . C o n v e r s e l y , after a shear rate greater t h a n 0.5 s e c . is a p p l i e d , t h e n lowered below t h i s v a l u e , t h e shear stress g r a d u a l l y decreases to t h e v a l u e s s h o w n . H o w e v e r , if the c r i t i c a l v a l u e of 0.5 s e c . is n o t passed u p o n going f r o m one shear rate t o another, t h e measured stresses i n s t a n t a n e o u s l y h a v e t h e i r final v a l u e . A l s o , t w o v a l u e s of t h e y i e l d stress were o b t a i n e d , as s h o w n i n F i g u r e 1 1 ; t h e l o w e r one, w h i c h lies at the e x t r a p o l a t i o n of the c u r v e to zero shear rate, is f o u n d if t h e gel is b r o u g h t to rest after a p p l i c a t i o n of a shear rate below 0.5 s e c . w h i l e t h e h i g h e r one is f o u n d after a p p l i c a t i o n of a shear rate of 80 sec . 1

-1

- 1


- 1

- 1

- 1

O u r e x p l a n a t i o n of these results is t h a t u n d e r the influence of the shear i n g m o t i o n , t h e particles assume a p a r a l l e l arrangement, w h i c h is r e t a i n e d w h e n t h e shearing m o t i o n is s t o p p e d . [ T h i s is also suggested b y t h e o b s e r v a t i o n of birefringence i n gels of m i c r o c r y s t a l s p l a c e d between m i c r o scope cover glasses (16).] I n t e r m s of o u r m o d e l , t h e r e s u l t i n g n e t w o r k m a y be d e p i c t e d as s h o w n i n F i g u r e 10, B. I t is reasonable t h a t m o r e cross-links w o u l d be present a n d t h a t t h e y i e l d stress w o u l d consequently be h i g h e r w h e n t h e rods are p r e d o m i n a n t l y p a r a l l e l .

Conclusions W e felt i t i m p o r t a n t to o b t a i n d a t a o n the p a r t i c l e n e t w o r k i n order t o u n d e r s t a n d t h e flow of gels q u a n t i t a t i v e l y . I t is clear, however, t h a t t h i s is s t i l l impossible because a n adequate t h e o r y going m u c h b e y o n d t h e ideas expressed b y G o o d e v e (7) has n o t been developed. T h e flow p r o p erties of gels v a r y c o n s i d e r a b l y ; f u r t h e r m o r e , some gels become t e m p o r a r i l y l i q u i d u p o n t h e a p p l i c a t i o n of shear, a n d others become t h i c k e r . Q u a n t i t a t i v e l y e x p l a i n i n g these v a r i o u s t y p e s of b e h a v i o r o n the basis of t h e p a r t i c l e n e t w o r k m o d e l does n o t appear easy. N e v e r t h e l e s s , t h e i n f o r m a t i o n o b t a i n e d here s h o u l d be of some a i d , i n t h a t t h e m o d e l is n o w m u c h m o r e closely defined. W e h a v e been able to collect considerable i n f o r m a t i o n a b o u t the i n t e r actions w h i c h cause t h e f o r m a t i o n of i n f i n i t e n e t w o r k s of particles i n gels of cellulose m i c r o c r y s t a l s . O u r findings about the m a n n e r of l i n k i n g of the rods w o u l d appear t o be p e c u l i a r to t h i s m a t e r i a l . T h e f o l l o w i n g a r g u m e n t suggests t h a t t h i s is perhaps n o t t r u e . I f c o l l o i d a l particles i n t e r a c t w e a k l y , t h e y w i l l n o t f o r m a gel. H o w e v e r , if t h e y i n t e r a c t s t r o n g l y , t h e y w i l l p r e c i p i t a t e . T h u s , each g e l - f o r m i n g m a t e r i a l m u s t h a v e p e c u l i a r properties, a l l o w i n g i t to escape either extreme. I n m a n y cases, t h i s m a y m e a n t h a t l i n e a r aggregation is easy, b u t t h a t c r o s s - l i n k i n g of the l i n e a r aggregates is less p r o b a b l e .

20.

HERMANS


Literature

Polymer Solutions and Gels

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Cited

(1) Battista, Ο. Α., Smith, P. Α., Ind Eng. Chem. 54, 20 (1962). (2) Edelson, M . R., Hermans, J., J. Polymer Sci. C2, 145 (1963). (3) Ferry, J. D., Advan. Protein Chem. 4, 1 (1948). (4) Flory, P. J., J. Am. Chem. Soc. 63, 3083, 3091 (1941). (5) Flory, P. J., "Principles of Polymer Chemistry," Cornell University Press, Ithaca, Ν. Y., 1953. (6) Flory, P. J., Proc. Roy. Soc. (London) A234, 73 (1956). (7) Goodeve, C. F., Trans. Faraday Soc. 35, 342 (1939). (8) Hermans, J., J. Appl. Polymer Sci. 9, 1973 (1965). (9) Hermans, J. J. Colloid Sci. 17, 638 (1962). (10) Hermans, J., J. Polymer Sci. C2, 129 (1963). (11) Ibid., A2, 4931 (1964). (12) Ibid., A3, 1859 (1965). (13) Hermans, J. J., in "Flow Properties of Disperse Systems," p. 61, North Holland, Amsterdam, 1953. (14) Litt, M . , J. Colloid Sci. 16, 297 (1961). (15) Marchessault, R. H., Koch, M . J., Yang, J. T., J. Colloid Sci. 16, 345 (1961). (16) Marchessault, R. H., Morehead, F. F., Walters, Ν. M., Nature 184, 632 (1959). (17) Onsager, L., Ann. Ν. Y. Acad. Sci. 56, 627 (1949). (18) Ranby, B. G., Discussions Faraday Soc. 11, 158 (1951). (19) Robinson, C., Ward, J. C., Beevers, R. B., Ibid., 25, 29 (1958). (20) Ward, A. G., Saunders, P. R., in "Rheology," F. R. Eirich, ed., Vol. II, p. 313, Academic Press, New York, 1958. (21) Verwey, E . J . W., Overbeek, J . Th. C., "Theory of the Stability of Lyophobic Colloids," Elsevier, Amsterdam, 1948. RECEIVED February 11, 1966.

Ordered Fluids and Liquid Crystals

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