A Low Shear, High Temperature Rotational Viscometer - Advances in

9 A Low Shear, H i g h Temperature Rotational Viscometer T h e Viscosity of Ultrahigh Molecular Weight Polyethylene H. L. WAGNER

Downloaded by UNIV OF SYDNEY on November 8, 2016 | http://pubs.acs.org Publication Date: June 1, 1983 | doi: 10.1021/ba-1983-0203.ch009

National Bureau of Standards, Polymer Science and Standards Division, Washington, D C 20234

J. G. D I L L O N Food and Drug Administration, Office of Medical Devices, Silver Spring, MD 20910

To obtain accurate measurements of the limiting viscosity number of solutions of ultrahigh molecular weight polyethylene (UHMWPE), a low shear floating-rotor viscometer of the Zimm—Crothers type was developed to measure viscosities at elevated temperatures (135 °C) and essentially zero shear rate. The zero shear rate measurements for a set of UHMWPE samples were compared with viscosity measurements at moderate and high shear rates (up to 2000 s-1) carried out in a capillary viscometer. The limiting viscosity number of UHMWPE depends, as expected, on shear rate, and the higher shear rate data could not be extrapolated to yield the correct zero-shear rate viscosities.

JL

H E SIMPLEST A N D MOST C O N V E N I E N T T E C H N I Q U E

available

for

the

d e t e r m i n a t i o n o f t h e relative size o f p o l y m e r m o l e c u l e s is the m e a s u r e m e n t o f its d i l u t e s o l u t i o n v i s c o s i t y . T h e c l a s s i c a l t e c h n i q u e s o f m o l e c u l a r w e i g h t m e a s u r e m e n t s u c h as l i g h t s c a t t e r i n g o r o s m o m e t r y , as w e l l as s i z e e x c l u s i o n c h r o m a t o g r a p h y ( S E C ) , a r e e i t h e r too d i f f i c u l t or i m p o s s i b l e w i t h p o l y m e r s o f m o l e c u l a r w e i g h t greater t h a n about a m i l l i o n , a l t h o u g h t h e y are q u i t e s u i t a b l e for t y p i c a l c o m mercially available high-volume polymers with molecular weights i n the h u n d r e d thousand range. D i l u t e solution viscosity measurements may be made on ultrahigh molecular weight polymers but by a techT h i s chapter not subject to U . S . copyright P u b l i s h e d 1983 A m e r i c a n C h e m i c a l Society

Craver; Polymer Characterization Advances in Chemistry; American Chemical Society: Washington, DC, 1983.

POLYMER CHARACTERIZATION

166


n i q u e q u i t e different f r o m that u s e d for l o w e r m o l e c u l a r w e i g h t p o l y m e r s . F o r the latter, the use o f a c a p i l l a r y v i s c o m e t e r w i t h shear rates o f the order o f a f e w t h o u s a n d r e c i p r o c a l seconds is satisfactory b e c a u s e the v i s c o s i t y is i n d e p e n d e n t o f shear rate. T h i s r e l a t i o n s h i p is far f r o m the case w i t h the u l t r a h i g h m o l e c u l a r w e i g h t p o l y m e r s . T h e n o n - N e w t o n i a n b e h a v i o r o f t h e s e p o l y m e r s is w e l l r e c o g n i z e d i n t h e l i t e r a t u r e as a p r o b l e m t h a t m u s t b e d e a l t w i t h i f a c c u r a t e m e a s u r e m e n t s o f t h e l i m i t i n g v i s c o s i t y n u m b e r are to b e m a d e . A s the s h e a r rate i n c r e a s e s , t h e s h a p e a n d o r i e n t a t i o n o f t h e m o l e c u l e c h a n g e s u f f i c i e n t l y so t h a t t h e s h e a r stress i s n o l o n g e r p r o p o r t i o n a l t o t h e shear rate. I n F i g u r e 1, t h e d a t a o b t a i n e d i n a m u l t i b u l b c a p i l l a r y v i s c o m e t e r , i n w h i c h t h e flow at s e v e r a l s h e a r rates m a y b e m e a s u r e d , a r e s h o w n for u l t r a h i g h m o l e c u l a r w e i g h t p o l y e t h y l e n e ( U H M W P E ) . T h e d e p e n d e n c e o n s h e a r rate i s a p p a r e n t a n d e x p l a i n s , i n p a r t , w h y i t i s so d i f f i c u l t to o b t a i n g o o d i n t e r l a b o r a t o r y a g r e e m e n t . N o t o n l y d o e s t h e s h e a r rate v a r y as t h e i n v e r s e c u b e o f t h e r a d i u s o f t h e c a p i l l a r y , b u t t h e s h e a r rate is a l s o a f u n c t i o n o f t h e flow r a t e , w h i c h w i l l v a r y w i t h the sample. F o r T D N A , of m o l e c u l a r w e i g h t of about 10 , viscosities m e a s u r e d at d i f f e r e n t s h e a r rates m a y d i f f e r b y as m u c h as a f a c t o r o f t w o ( I ) . S i m i l a r b e h a v i o r h a s b e e n f o u n d for p o l y s t y r e n e (2) a n d exm e t h y l p o l y s t y r e n e s (3) o f u p to 1.4 x 1 0 i n m o l e c u l a r w e i g h t . 8

2

7

10

1

0

'

1

•

.01

.02

.03

1

1

.04

.05

CONCENTRATION, g/dL Figure 1. Viscosity number as a function of shear rate for a sample of UHMWPE in decalin at 135 °C in a multibulb capillary viscometer.



9.

WAGNER AND DILLON

Ultrahigh

Molecular

Weight Polyethylene

167

B e c a u s e c a p i l l a r y v i s c o m e t e r s are n o t u s u a l l y d e s i g n e d to p r o v i d e a c o n s t a n t o r v e r y l o w s h e a r r a t e , v i s c o s i t y d a t a for s h e a r r a t e - s e n s i t i v e materials m u s t be o b t a i n e d i n a v i s c o m e t e r w h e r e the effect of shear rate is m i n i m a l or n o n e x i s t e n t . T h e Z i m m - C r o t h e r s floating-rotor l o w shear v i s c o m e t e r , a l t h o u g h u s e d m o s t l y for b i o l o g i c a l m o l e c u l e s s u c h as D N A ( I ) , a l s o h a s f o u n d a p p l i c a t i o n f o r h i g h m o l e c u l a r w e i g h t s y n t h e t i c p o l y m e r s (3). I n t h i s v i s c o m e t e r at t h e l o w s h e a r rates o f a f e w r e c i p r o c a l s e c o n d s , t h e v i s c o s i t y i s i n d e p e n d e n t o f s h e a r r a t e , so t h a t t h e m e a s u r e d v i s c o s i t y is e s s e n t i a l l y t h e z e r o - s h e a r rate v i s c o s i t y . A n o t h e r i m p o r t a n t advantage is that t h e d e g r a d a t i o n d u e to shear, w h i c h c a n r e d u c e t h e v i s c o s i t y s u b s t a n t i a l l y , i s v e r y u n l i k e l y at t h e s e l o w shear rates. T h i s d e g r a d a t i o n is s o m e t i m e s o b s e r v e d i n a c a p i l l a r y v i s c o m e t e r d u r i n g a m e a s u r e m e n t w h e n t h e f l o w t i m e d e c r e a s e s as the s a m p l e is r e c y c l e d t h r o u g h the v i s c o m e t e r . In the past, the v i s c o s i t y of U H M W P E was m e a s u r e d i n c a p i l l a r y v i s c o m e t e r s at 1 3 5 ° C i n d e c a l i n at a s i n g l e c o n c e n t r a t i o n o f 0 . 0 5 % (4). It i s a s s u m e d n o t o n l y t h a t t h i s d a t u m m a y b e e x t r a p o l a t e d t o z e r o concentration u s i n g the same viscosity—concentration relationships f o u n d for l o w e r m o l e c u l a r w e i g h t p o l y m e r s , b u t also that s u c h a n e x t r a p o l a t i o n w i l l y i e l d a z e r o - s h e a r rate l i m i t i n g v i s c o s i t y n u m b e r . H o w e v e r , f o r m o l e c u l a r w e i g h t s o f t h e o r d e r o f 1 x 1 0 to 10 x 1 0 , w h i c h w e b e l i e v e i s t h e r a n g e o f m o l e c u l a r w e i g h t s for U H M W P E , a n d l i m i t i n g v i s c o s i t y n u m b e r s o f a b o u t 4 0 , a c o n c e n t r a t i o n as h i g h as 0 . 0 5 % i s i n t h e s e m i d i l u t e r a n g e (5). T h e v i s c o s i t y n u m b e r i s n o l o n g e r e x p e c t e d to b e l i n e a r w i t h c o n c e n t r a t i o n i n t h i s r a n g e , a n d c o n s e q u e n t l y , t h e v i s c o s i t y — c o n c e n t r a t i o n r e l a t i o n s h i p s f o u n d for l o w e r m o l e c u l a r w e i g h t p o l y e t h y l e n e s c a n n o t b e e x p e c t e d to h o l d . F i g u r e 2 s h o w s o u r r e s u l t s for t w o d i f f e r e n t U H M W P E s , o n e at t h e h i g h e r e n d o f t h e m o l e c u l a r w e i g h t r a n g e , t h e o t h e r at t h e l o w e r . T h e s t r a i g h t l i n e indicates the result obtained m a k i n g the just m e n t i o n e d assumptions and gives a n i d e a o f the p o s s i b l e error. A l t h o u g h the e r r o r is not too l a r g e for t h e l o w e r m o l e c u l a r w e i g h t s a m p l e , i t is q u i t e s e r i o u s f o r t h e h i g h e r one. 6

6

T h e l i m i t i n g v i s c o s i t y n u m b e r is u s e d as a n i n d i c a t o r o f r e l a t i v e b u t not absolute m o l e c u l a r weights because the presently available parameters for t h e e m p i r i c a l M a r k - H o u w i n k r e l a t i o n for p o l y e t h y l ene were obtained from data o n l o w e r m o l e c u l a r w e i g h t polymers. B o t h e x p e r i m e n t a n d theory demonstrate that these parameters do not a p p l y n e c e s s a r i l y to p o l y m e r s i n t h e u l t r a h i g h m o l e c u l a r w e i g h t r a n g e (6, 7). In the process o f c h a r a c t e r i z i n g U H M W P E for s u r g i c a l i m p l a n t s , w e assembled a l o w shear viscometer of the Z i m m — C r o t h e r s type. T h i s v i s c o m e t e r has s o m e u n i q u e features, the p r i n c i p a l one b e i n g its h i g h t e m p e r a t u r e c a p a b i l i t y , a necessary r e q u i r e m e n t for p o l y e t h y l -


168



Ε

0.02

0.04

0.06

0.08

0.10

Concentration, g/dL Figure 2. Viscosity number as a function of concentration for samples of UHMWPE in decalin at 135 °C. The same Ubbelohde viscometer was used for all measurements. Shear rate is variable and depends on flow rate. The straight lines are those used for extrapolation to limiting viscosity number, assuming viscosity —concentration relationships ob served for lower molecular weight poly ethylenes. e n e m e a s u r e m e n t s b e c a u s e t h i s p o l y m e r i s i n s o l u b l e at r o o m t e m p e r ature.

High Temperature, how Shear Viscometer T h e c o n s t r u c t i o n o f this v i s c o m e t e r is b a s e d o n the o r i g i n a l d e s i g n o f the floating-rotor v i s c o m e t e r first d e s c r i b e d b y Z i m m a n d C r o t h e r s (8). T h e d r i v e s y s t e m f o r t h e r o t o r i s s i m i l a r to o n e d e s c r i b e d e l s e w h e r e (9). T h e e s s e n t i a l f e a t u r e s o f t h e v i s c o m e t e r a r e s h o w n i n F i g u r e 3. S o l v e n t or s o l u t i o n is p l a c e d b e t w e e n a n i n n e r glass c y l i n d e r , the r o t o r , a n d a f i x e d o u t e r g l a s s c y l i n d e r , t h e stator. T h e r o t o r floats f r e e l y i n t h e l i q u i d a n d i s c e n t e r e d w i t h i n t h e stator b y s u r f a c e f o r c e s ; i t i s s u b j e c t to a c o n s t a n t t o r q u e p r o d u c e d b y t h e i n t e r a c t i o n o f a c y l i n d e r of a l u m i n u m i n s e r t e d into the rotor a n d four s u r r o u n d i n g solenoids. T h e apparatus operates o n the p r i n c i p l e of an electromagnetic i n d u c t i o n m o t o r . T h e r e a r e n o m e c h a n i c a l d e v i c e s a t t a c h e d to t h e r o t o r ,


9.

WAGNER AND DILLON

Ultrahigh

Molecular

Weight Polyethylene

169

w h i c h is supported b y buoyancy. U n l i k e the Couette viscometer, a l l t h e e n e r g y l o s s o c c u r s i n t h e l i q u i d , m a k i n g p o s s i b l e m e a s u r e m e n t s at l o w viscosities w i t h g o o d p r e c i s i o n . Therefore, the s p e e d o f the rotor is i n v e r s e l y p r o p o r t i o n a l t o t h e v i s c o s i t y o f t h e l i q u i d . A resistive-capacitance circuit splits the current f e d the solenoids i n t o t w o l e g s t h a t a r e e q u a l b u t 90° o u t o f p h a s e . E a c h l e g e n e r g i z e s a p a i r o f o p p o s i t e s o l e n o i d s so that adjacent s o l e n o i d s are o u t o f p h a s e . T o r q u e o n the rotor is p r o d u c e d b y e d d y currents i n d u c e d i n t h e a l u m i n u m a n d is h e l d constant b y a n adjustable constant current supply. T h e constant current s u p p l y is based o n a K e p c o b i p o l a r operat i o n a l a m p l i f i e r c a p a b l e o f s u p p l y i n g 1.5 A at 7 5 V . T h e c i r c u i t u s e d i s the o n e d e s c r i b e d b y t h e m a n u f a c t u r e r o f t h e u n i t f o r o p e r a t i o n at constant current. T h e reference for the a m p l i f i e r is a p r e c i s i o n 6 0 - H z oscillator s t a b i l i z e d for b o t h frequency a n d a m p l i t u d e to better t h a n 0 . 1 % . T h e root m e a n square v a l u e o f the c u r r e n t for the e n t i r e c i r c u i t is s t a b i l i z e d t o b e t t e r t h a n 0 . 1 % .


1

T o m i n i m i z e t h e t e n d e n c y t o w o b b l e at l o w v e l o c i t i e s , t h e r o t o r a n d s t a t o r are f a b r i c a t e d f r o m u n i f o r m b o r e g l a s s t u b i n g , a b o u t 3 0 m m i n d i a m e t e r w i t h a 1 - m m gap b e t w e e n t h e m for t h e l i q u i d . T h e t o p Certain commercial equipment, instruments, or materials are identified in this chapter to specify the experimental procedure. In no case does such identification imply recommendation by the National Bureau of Standards, nor does it imply that the material or equipment identified is necessarily the best for the purpose. 1

Figure 3. The high-temperature,

low shear viscometer,

schematic.




170

e d g e o f the glass rotor is p o l i s h e d a n d free of n i c k s , a n d the b o t t o m is r o u n d e d as s y m m e t r i c a l l y as p o s s i b l e . T h e a l u m i n u m i n s e r t , w h i c h m u s t also b e s y m m e t r i c a l to r e d u c e w o b b l e , is m a c h i n e d c a r e f u l l y to f i t t h e g l a s s r o t o r at 1 3 5 ° C . T h e t o t a l w e i g h t of the rotor is a d j u s t e d b y d r i l l i n g the p r o p e r size h o l e t h r o u g h the center of the a l u m i n u m . B e c a u s e the rotor is s u s p e n d e d b y b u o y a n c y , the size of the h o l e r e q u i r e d d e p e n d s o n the density of the s o l v e n t . T h e l e n g t h o f t h e i n s e r t s h o u l d b e s u c h as to b e w i t h i n t h e c o n f i n e s o f t h e m a g n e t i c field o f t h e s o l e n o i d s . T o a v o i d s h a t t e r i n g t h e g l a s s , t h e g l a s s a n d a l u m i n u m are h e a t e d s e p a r a t e l y i n a 150 ° C o v e n a n d t h e n a s s e m b l e d a n d p u t i n t o t h e stator i n t h e b a t h . T h i s p r o c e d u r e is n e c e s s a r y b e c a u s e o f t h e d i f f e r e n c e i n t h e rate o f e x p a n s i o n o f t h e two materials. T h e e n t i r e a p p a r a t u s i s b o l t e d r i g i d l y to a f r a m e i m m e r s e d i n t h e h i g h t e m p e r a t u r e o i l b a t h . T h i s r i g i d m o u n t i n g w a s n e c e s s a r y to a c h i e v e g o o d r e p r o d u c i b i l i t y . T h e b a t h w a s fitted w i t h a c o v e r so t h a t measurements c o u l d be made under a blanket of argon. Solvent readi n g s a r e r e p r o d u c i b l e to a b o u t 1% f r o m d a y to d a y , e v e n t h o u g h t h e b a t h is c o o l e d o v e r n i g h t a n d r e h e a t e d o n the m o r n i n g o f a r u n . T h e rotation t i m e , or p e r i o d , is d e t e r m i n e d b y d i r e c t i n g a laser b e a m onto the rotor w h i c h has b e e n c o a t e d w i t h a w i d e b a n d o f c h r o m i u m , e x c e p t for t w o v e r t i c a l c l e a r w i n d o w s a f e w m i l l i m e t e r s w i d e a n d 180° a p a r t . D u r i n g r o t a t i o n , t h e b e a m p a s s e s t h r o u g h t h e s e w i n d o w s a n d impinges on the photocell, w h i c h , i n conjunction w i t h a S c h m i d t t r i g g e r a s s e m b l y , starts a c o u n t e r - t i m e r to m e a s u r e t h e p e r i o d o f t h e rotor. T h e r e l a t i v e v i s c o s i t y i s e q u a l to t h e r a t i o o f t h e t i m e p e r c y c l e f o r t h e s o l u t i o n , o r t h e p e r i o d , to t h a t for t h e s o l v e n t at t h e s a m e t o r q u e o r current. S a m p l e i s i n t r o d u c e d i n t o t h e s i d e a r m o f t h e stator b y m e a n s o f a f u n n e l . F o r p o l y o l e f i n s , t h e f u n n e l m u s t b e h e a t e d to p r e v e n t c o o l i n g of the hot solution a n d p r e c i p i t a t i o n of the p o l y m e r . T h e height of the rotor is t h e n a d j u s t e d b y a d d i n g or w i t h d r a w i n g l i q u i d after it has b e e n floated. T h e c e n t e r i n g e f f e c t is a c h i e v e d b y t h e s u r f a c e t e n s i o n o f t h e m e n i s c u s . A s p o i n t e d o u t b y Z i m m (1), t h e s h a p e o f t h e m e n i s c u s is c r u c i a l for t h i s c e n t e r i n g ; surface forces act to c e n t e r t h e i n n e r r o t o r i f t h e l i q u i d s u r f a c e r i s e s u p f r o m its r i m to t h e w a l l o f t h e stator. T h e o p t i m u m h e i g h t o f t h e r o t o r i s d e t e r m i n e d b y t h e h e i g h t at w h i c h the m a g n e t i c c o u p l i n g is a m a x i m u m , that is, w h e r e the p e r i o d is s h o r t e s t for a g i v e n c u r r e n t . A t t h i s h e i g h t , t h e r o t o r s p e e d is c h a n g i n g v e r y s l o w l y w i t h h e i g h t , so t h a t s m a l l e r r o r s i n h e i g h t w i l l l e a d to m i n i m a l error i n the period. Measurement

Procedure

A l t h o u g h the data for o n l y one v a l u e of the t o r q u e , or the c u r r e n t , w e r e finally u s e d , t h e p e r i o d w a s d e t e r m i n e d f o r a r a n g e o f c u r r e n t


9.

WAGNER AND DILLON

Ultrahigh

Molecular

Weight Polyethylene

171

v a l u e s f r o m 3 0 to 1 5 0 m A at 1 0 - m A i n t e r v a l s . T h e p e r i o d s w e r e f i r s t d e t e r m i n e d for the s o l v e n t , t h e n for the s o l u t i o n . T h e r e l a t i v e v i s c o s ity i s t h e r a t i o o f t h e p e r i o d f o r t h e s o l u t i o n to t h a t o f t h e s o l v e n t at a g i v e n t o r q u e o r c u r r e n t s e t t i n g . T h e l i m i t i n g v i s c o s i t y n u m b e r t h e n is calculated i n the customary w a y by plotting the viscosity n u m b e r (Vrei — l)/

A Low Shear, High Temperature Rotational Viscometer - Advances in

Recommend Documents