Relation between viscosity and direct current conductivity in polyvinyl chlorid

Kallweit, J.-H.

English

NASA Technical Reports Server

UARl RESEARCH REPORT NO. 20 Y 6 5 - 2 4 2 9 2  
> V I  
4 879YP c i c 
INASA CR OR TMZ OR AD NUMB<RR) 
r" CODE1 
THE RELATIONSHIP BETWEEN THE VISCOSITY AND THE 
DC-CONDUCTIVITY IN POLWINYLCHLORIDE 
kATEGORY1 
by 
Juerg- Heinri c h Ka I lweit 
This research was supported partially by the 
National Aeronautics and Space Administration 
Grant NsG-381 
UNIVERSITY OF ALABAMA RESEARCH I N S T I l U  TE 
HUNTSVILLE, ALABAMA 
I I  
G i i  
= E  - -  
March 1965 
https://ntrs.nasa.gov/search.jsp?R=19650014691 2020-03-17T00:03:44+00:00Z
1 
n 
THE RELATIONSHIP BETWEEN THE VISCOSITY 
AND THE DC-CONDUCTIVITY IN POLYVINYLCHLORIDP 
by 
Juerg -He inr ich Kal lwe it ** 
Problem 
% 
p f 2 9 / L  
It is common assumption that the dc-conductivity (T in high- 
polymers mainly depends on the sample viscosity q because both the 
viscosity and conductivity show a similar strong temperature depen- 
dence. In accordance with Waldens' rule, it is written 
0 1 ( 3 - -  'I 
To check this relation, the same samples of PolyvinylchloridC(PVC) 
with varied plasticizer content (Palatinol AH = Dioctylphthalate) 
were used to measure the viscosity and dc-conductivity as function 
of time and temperature. 
. 
This research was supported partially by the National Aeronautics and 
Space Administration Grant NsG-381. 
9; 
-1.-1. ""Research Institute, University of Alabama, P. 0. Box 1 2 4 7 ,  Huntsville, 
A 1  ab ama . 
t 
2 
PART I 
Experiments 
Samples with a thickness of 0.06 cm were cut from the following 
mat er i a 1 : 
Table I 
Sample No. PVC Vinoflex 332 Plasticizer Palatinol AH 
and Symbol Percent by weight -t 0.5% Stabilizator 
Percent by weight 
100 0 
* 
B A  92 8 
c -I- 84 16 
D O  74 26 
E O  
F V  
63 
50 
37 
50 
The viscosity r) was obtained from the results of a creep experiment. 
The measurements were done in accordance with the experiment described 
by Becker in 1 1 .  A rod-shaped sample was fixed at the upper end in 
perpendicular position and charged with a load at the time t = 0. For 
small deformations, a tensile strength so results, which is constant 
with respect to time. The relative change in the sample length E (t) . 
was measured as function of time, The differentation of the compliance 
J with respect to the time 
gives formally the equation for Newton's flow 
3 
v(t) can be called also the Trouton-viscosity of the sample ( 2 1 .  @ 
can be written 
The differentat ion was obtained by graphical methods. From equation@ 
follows that 9 must be a function of the time. The viscosity of high- 
polymers can be considered to be a criterion for the "friction force" 
between the position-changing segments of the molecular chains during 
stress, The decreasing possibility for position changes in stress 
direction leads to increasing the viscosity as function of the load 
period. To eliminate this time dependence as well as possible, only 
the r(-values obtained three seconds after load charging were used for 
the comparison with the values of the specific dc-conductivity. Figure I 
shows the temperature dependence of the viscosity obtained after'three 
with the plasticizer content as parameter. 
The experimental device for the determination of the specific dc- 
conductivity is described in 
vacuum of about 10 Torr during the measurement. The applied voltage 
of 1000 volt was identical with an electrical field strength of 16.7 
[KV/cm.] All samples were heat treated, before each change of the measuring 
temperature, for one hour at a temperature 30 C above the respective 
second-order transition temperature. Afterwards they were cooled down 
slowly (or heated up slowly) until the desired sample temperature was 
reached. 
effects in the sample due to former charging. Polarization effects 
are the reason for the strong time dependence of the conductivity in 
I3  1 , The samples were again placed in 
- 4  
0 
This procedure was necessary t o  el.iminate all polarization 
5 
With S toke ' s  l a w  for t h e  f a c t o r  f 
f =  6 . r ~ ~ .  0 r = r ad ius  of t h e  ion  wi th  supposed s p h e r i c a l  
shape 
0 
@ o = z ' q g c -  
and 
I 
V c = concen t r a t ion  
E q a charge u n i t  
Z 0 valency; Z is supposed t o  be 1 i n  t h i s  
paper 
follows 
= cons t  c (T)  
Because 0 a l s o  con ta ins  t h e  temperature-dependent concen t r a t ion  c (T) , 
t h e  product  u q should be temperature  independent.  F igure  IV shows 
t h a t  t h e  expected r e l a t i o n s h i p  was not observed a t  a l l .  There a r e  two 
p o s s i b l e  explana t ions :  (1) Stoke ' s  law is a too  rough approximation 
i n  t h e  case of the  t e s t e d  highpolymers; (2) The v i s c o s i t y  i n  S t o k e ' s  
law i s  not  i d e n t i c a l  wi th  t h e  v i s c o s i t y  7 obta ined  by r e t a r d a t i o n  
experiments ,  which may be c a l l e d  "macroviscosity." But an e f f e c t i v e  
l o c a l  v i s c o e i t y  ' (microviscos i ty)  must  be used i n  connect ion wi th  
S t o k e ' s  law. Only i n  t h e  case  o f  f l u i d s  'I i s  a good approximation 
f o r  q'. 
A t  f i r s t  i t  was necessary  t o  check whether o r  no t  any r e l a t i o n s h i p  
between U and 7 could be found, It is known from d i e l e c t r i c  measure- 
ments on FVC [ 6 ]  t h a t  t h e  maximum of t h e  l o s s  tangent  was always 
n e a r l y  t h e  same when t h e  v i s c o s i t y  'I of t h e  sample i s  t h e  same g iven  
va lue .  It made no d i f f e r e n c e  whether t h e  magnitude of was due t o  
t h e  tempera ture  o r  whether it was due t o  t h e  p l a s t i c i z e r  used.  There- 
f o r e ,  i t  was checked as t o  which r e l a t i o n s h i p  between * and 7 e x i s t s  
6 
when equal magnitudes of u are considered, which can be due to tempera- 
ture or due to plasticizer variation. The shape of the plot of lg a 
over lg 9 seemed to indicate a hyperbola (Figure V ) ,  Afterwards, lgq 
was plotted as function of the product lg( u q). The graphic repre- 
sentation (Figure V I )  gives the desired possibility for the derivation 
of  the relationship between u end 9. 
lg q - m l g o  9 + const. 
or 
m- 1 
0 9 = const. 4 
for the samples A, B, and C. The tan of the slope angle m must be 
derived with the help of the above plot. 
PART I1 
Discus s ion 
The experimental results described in Part I seemed to show that 
it is problematic to use the viscosity values obtained by retardation 
experiments in connection with Stoke's formula in (-9. It was asked 
which results would be formally obtained when the magnitude of the 
viscosity in formula (1.1) 
of the effective local viscosity 9' 
would be considered to be the magnitude 
9' should have the dimension of a viscosity. 
are given in Table TI. Because m is neatly one, the values for q' 
are unexpectedly low; but it: has been shown by Ferry 
The numerical results 
7 1 that: the 
7 
orde r  of t h e  e f f e c t i v e  l o c a l  v i s c o s i t y  f o r  small  fo re ign  molecules may 
be of t h e  c a l c u l a t e d  o rde r .  S t  is fur thermore i n t e r e s t i n g  t o  n o t e  t h a t  
t h e  compensation law 
c e s s  i n  t h e  system PVC/Plast ic izer .  
81 1 9  1 seems t o  hold f o r  t h e  conduc t iv i ty  pro- 
(See F igure  V I S ) .  Pormultr @ , 
w r i t t e n  now as  
(2 f -  6 * n s r e r ? '  
would g ive  f o r  t h e  equat ion  i n  
@ n r  
~ 
@ 
2 
o(T) Q'(T) c(T) 
The graph i n  Figure VI11 shows t h a t  now t h e  expected r e l a t i o n s h i p  is 
obta ined .  This  r e s u l t  i nd ica t ed  con t inua t ion  of t h e  formal tes t :  by 
L 
w r i t i n g  f o r  t h e  median d r i f t  v e l o c i t y  v 
and f o r  t h e  conduc t iv i ty  
2 1 @ u -  c q / 6 * 1 r * r  q / valency z - 1 
where t h e  mob i l i t y  be of t h e  ions is given by 
F i n a l l y ,  t h e  express ion  f o r  t h e  d i f f u s i o n  c o e f f i c i e n t  D would be 
@ D - KT/6 r 9 r ? '  
because t h e  r e l a t i o n s h i p  between t h e  e l e c t r i c a l  and mechanical d e f i n i -  
t i o n  f o r  t h e  mob i l i t y  i s  
r e s u l t s  f o r  t h e  samples A, B ,  C and some va lues  f o r  D. 
could  n o t  be  done without  another  assumption f o r  t h e  r a d i u s  r of t h e  
ions .  
be  small molecules.  Under t h i s  assumption, two p o s s i b l e  va lues  were 
be - q bmech, Table SI1 g ives  t h e  numerical  
The c a l c u l a t i o n  
The kind of t h e  ions  is not known, bu t  most probably they  w i l l  
8 , 
chosen f o r  t h e  unknown rad ius  r : 
r = 1 * loo7 cm 
r = 5 * 1 0  cm 
The va lues  f o r  sample D were added t o  show t h a t  t h e  non l inea r  p l o t s  i n  
F igure  V I  do not  g ive  s e n s i b l e  va lues .  
- 7  
The crude approximations do not  a l low d e t a i l e d  d i scuss ion  of t h e  
r e s u l t  summarized i n  Table TIT.. But t h i s  r e s u l t  seems t o  i n d i c a t e  t h a t  
t h e  va lues  f o r  t h e  ion  v e l o c i t y ,  concen t r a t ion ,  and t h e  d i f f u s i o n  coef -  
f i c i e n t  a r e  of a range,  which could be  a more-or-less f a i r  approximation 
of t h e  a c t u a l  va lues .  The expected temperature  dependence of t h e  mob i l i t y  
of t h e  s i n g l e  samples was obtained.  B u t  i t  i s  d i f f i c u l t  t o  understand 
t h a t  t he  mob i l i t y  d id  not  increase  with inc reas ing  p l a s t i c i z e r  con ten t .  
The common assumption is t h a t  the inc rease  of t he  c o n d u c t i v i t y  w i t h  
h ighe r  p l a s t i c i z e r  conten t  is c h i e f l y  due t o  t h e  g r e a t e r  i o n - m o b i l i t y .  
Here i t  would t u r n  out  t h a t  t h e  ion concen t r a t ion  i s  t h e  dominating 
f a c t o r ,  The va lues  f o r  t h e  d i f f u s i o n  c o e f f i c i e n t  do not  d i f f e r  markedly 
from t h e  va lues  of Luther and Meyer, who measured t h e  d i f f u s i o n  c o e f f i -  
c i e n t  of p l a s t i c i z e r  i n  PVC 
b 1 . 2  10'' cm sec-'1 and by Meyer D = 1.4 * 10 Icm2 sec-lj 
I101 , For sample C a t  343'K was measured 
2 -11 
Although i t  cannot be s a i d  t h a t  p l a s t i c i z e r  molecules a r e  r e spons ib l e  f o r  
t h e  charge t r a n s p o r t ,  t h e  low order  of t h e  d i f f u s i o n  c o e f f i c i e n t  may 
i n d i c a t e  t h a t  molecules as charge c a r r i e r s  are migra t ing  under t h e  f o r c e  
of t h e  app l i ed  e l e c t r i c a l  f i e l d .  
The c a l c u l a t e d  va lues  f o r  D and can be  used t o  check whether 
or n o t  v a l u e s  a r e  obta ined  f o r  the jump d i s t a n c e  d of t h e  i o n s ,  which 
9 
I 
, 
a r e  of t h e  same o rde r  as va lues  known from l i t e r a t u r e .  Foss and Danhaueer 
@ evalua ted  t h e  jump d i s t a n c e  i n  PPN accord ing  t o  t h e  r e a c t i o n  r a t e  
theory  from t h e  i so thermal  f i e l d  dependence a8 about 200 A; Amborski I121 
measured f o r  Mylar a t  130°C,69 A. 
o u t  p l a s t i c i z e r  would be f o r  t he  assumed ion  r a d i u s  r = 1 10 , iden- 
t i c a l  t o  127 A (See I12 1 ); but t h i s  fair agreement should not be  over- 
valued because D = vd t u r n s  o u t ,  according t o  t h e  approximations used 
in t h i s  pape r ,  t o  be  independent from any s p e c i f i c  sample. 
0 
0 
The va lues  i n  t h e  case  of PVC with- 
- 7  
0 
- 
O t h e r  types  of highpolymer m a t e r i a l  must be t e s t e d  b e f o r e  any 
s t a t emen t s  can be  made. The de termina t ion  of t h e  f r e e  volume should 
be  added t o  t h e  v i s c o s i t y  measurements, and t h e  dc-conduct iv i ty  should 
be  measured a s  func t ion  of temperature and e l e c t r i c  f i e l d  s t r e n g t h  . 
Samples wi th  v a r i e d  p l a s t i c i z e r  con ten t  and c r y s t a l l i n i t y  should be  
checked. The unders tanding  of t h e  dc -conduc t iv i ty  i n  highpolymers 
depends on t h e  exac t  knowledge of t h e  mob i l i t y  of t h e  charge c a r r i e r s .  
10 
ACKNOWLEDGEMENT 
The author would like to thank Dr. G. W. Becker, Physikalisch- 
Technische Bundesanstalt, Braundschweig, Germany, for the measurement 
of the viscosity and for many valuable discussions. 
The samples are courtesy of Dr. Wuerstlin, Badische Anilin und 
Sodafabrik, Ludwigshafen, Germany. 
The experiments were done in the Physikalisches Institut, 
Technische Hochschule, Braunschweig, Germany. I would like to thank 
the director, Professor Dr. Cario. 
This was partially funded by the National Aeronautics and Space 
Administration under NsG-381. 
11 
REFERENCES 
1. G .  W. Becker, Kolloid-Zeitschrift und Zeitschrift fuer Polymere, 
166 (1959) p. 4. 
2. F. H .  Mueller und C. Engelter, Kolloid-Zeitschrift und Zeitechrift 
fuer Polymere, 186 (1962) p. 36. 
3. J. H. Kallweit, Kunststoffe, 47 (1957) p .  651. 
4. J. H. Kallweit, Kolloid Zeitschrift und Zeitschrift fuer Polymere, 
188 (1963) p. 97. 
5 .  F. Wuerstlin, Kunststoff-Technik, 11 (1941) p .  269, 
6. J. M. Davies, R. F. Miller, and W. Busse, J. Amere Chem. SOC., 63 
(1941) p. 361. 
7. John D. Ferry, Viscoelastic Properties of Polymere, John Wiley 61 
Sons, New York, 1962. 
8. R. W. Warfield and M. C. Petree, Die Makromolekulare Chemie, 5 8  
(1962) p .  139. 
9. P. Ruetschi, 2. f .  Phys. Chem., 14 (1958) P O  277. 
10. H .  Meyer, Dissertation Braunschweig, (1958). 
11. R. A .  Foss and Walter Danhauser, J. of Appl. Polym. Sci., V o l .  7 ,  
(1963) p .  1015. 
12 
SYNOPSIS 
I n  gene ra l ,  i t  has  been said t h a t  t h e  dc-conduct iv i ty  u is pro- 
p o r t i o n a l  t o  t h e  inverse  v i s c o s i t y  q . But t h e  r e l a t i o n  o * q = cons t  
has  not been proven i n  the  case  of t h e  system Polyvinylchlorid?Dioctyl- 
p h t h a l a e  The experimental  results can be descr ibed  by 
m - 
u ‘I m-l = cons t  
i f  t h e  p l a s t i c i z e r  conten t  is not t oo  h igh ,  The ion  mob i l i t y  seems t o  
depend on a l o c a l  e f f e c t i v e  v i s c o s i t y ,  which d i f f e r s  from t h a t  v i s c o s i t y  
which is der ived  from r e t a r d a t i o n  experiments,  
1 
I I j 3.2 10l2 ! 
I I 
I 4.3 10-4 2 . 1  10'2 1 
323 I 309 I 3.9 
I 
333 I 300 
f 
i 
B 293 341 
303 1 330 
313 1 319 
I I 
I 5 * 0  ' lo1O I 1 323 1 309 i 2.0 . 10-3 
333 I 300 1 '3 .5  . j 1 
I I I 
! 1.17 i I 7.90 ' lo1 5.75 ' 
1 I 
1 I 
7.3 8 1.3  1 0 ~ 3  
9.5 . 10-4 1.9 1012 ' ' 6.15 10' 5.85 10" 
1.3  , 3.1 l o l l  I ; 1 4.64 10' ' 6.03 loo2 
I 
. I  
6.99 
I 
I  3.55 ' lo1 
i I I 
I 
TABLE SI 
n 0 
d I S  
O O O d d O  
d d d d d d  
O 2 2 5 s s  d . . . . . .  
N r J h l N r J r n  l m m u  
d d d d d d  N N N  
0 0 0 0 0 0 1 ~ 0 0  
A A r n I j h d  r J 0 0 I j  
d d d d d d l 2 s E :  
d d d d d d  d d  
I 
I 
. . . . . .  . . .  
c o u \ D u o u  N a r J  . . . .  1 . . .  
_. - -_- 
0 0 0 0 0 0  l o o m  
d d d d d d  N h l d  
1 1 1 1 I l  I l l 1  
0 0 0 0 0 0  
. . . . . .  I . . .  
m 
I 
5 
hl 
m 
0 . . . .  
m m m m  d 
- -  . - 
0 0 0 0  
d d d d  
0 
d 
I 
d 
0 
t d '  
I 
V 
al 
m 
m 
I 
d 
0 
. . . . . .  . . . .  
h \ D O l n  
h l m m \ D  
. . . .  
_ _  - .  . 
. I ! .  . . . . . . .  . . . .  
r n h l c u b  
0 0 m l n u  
m * \ D o 3  
. . . .  
. . . . . .  I . . .  
rn 
I 
u 
al 
m 
E u 
. . . . . . . .  
n I 
d 
0 
E u 
0 
~' 
d 
- H  
H 
H 
w 
I4 
F9 
2 
.- 
n 
0 
I 
E u 
I . . . . . . . .  . . . .  . . . . . .  
\ D h c o 0 0 0 0 \ D 0  
u u u * l n m d l n  
. . . . . . . .  
U 
7 
I 
u 
al 
v) 
d d 0 0  
d d d d  
I l l 1  
0 0 0 0  
d d d d  . . . .  
d o 0  
I h l h l h l  
I l l  
1 0 0 0  
d d d  
I 1 . . . . . . . .  
q ; P  0 0 0 0 0 0 0 0  P P P P P P 
l b O  d d d d d d d  
I A r t A  . . . . . .  . [  . . . . . . . .  . . . .  
c o m o m l n d  
m \ o o Q ) m u l d h l o  . . . . . .  . . .  
m u 3 m d d d l d h l m  
. -  . . 
n 
d 
I 
l n l n l n l n  
I l l 1  
0 0 0 0  
d d d d  . . . .  
\ D a \ D m  
N U N *  
* m b m  
. . . .  
. . . . . .  I . . .  o d d o r l o (  o b o u m m  h l h l h  . . . . . . . . . .  E , u ,  
.. - . . .  ..... ._ - . . .  
h 
I 
0 
d 
4 
0 
ln 
n 
E u 
u 
13 
CAPTIONS TO FIGURES , 
Fipure I: 
Log Viscosity Vs. Reciprocal Temperature For the System PVC/DOP, 
The Plasticizer Content fs Parameter. 
Figure 11: 
The Polarization Voltage as Function of Temperature. The 
Plasticizer Content f e  Parameter; Charging Time Is 600 Seconds. 
Figure 111: 
Log Specific Conductivity Vs. Reciprocal Temperature For the 
System PVC/DOP. The Plasticizer Content 1s Parameter. 
FiPure IV: 
Log (Specific Conductivity Times Viscosit3) Vs. Temperature. 
Figure V: 
Log Specific Conductivity Vs. Log Viscosity. 
Figure VI: 
Log Viscosity Vs. Log (Specific conductivity Times Viscosity) 
With the Plasticizer Content a s  Parameter, 
Figure VII: 
Log (Specific Resistance) Vs. Activation Energy. 
Firrure VIII: 
Log Specific (Conductivity Times Effective Viscoaity)Vs. 
Temperature, 
0. 
1000 
- 1000 
500 
1000 
500 
1000 
500 
1000 
500 
~ 1000 
500 
0 
A 
I I I I I I I I I I I 
-+\+ 
C '+ 
\+ 
, l';\7/ I 
- 
I I I 
E 
I I I I I I I I I I I 
0 50 - T  bC] eo0 
2 
b 
lg a 
2 
I 
1 
0 
- 1  
-2 
-3 
3 
2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 
1000 -
T [a] 
* . 
8 
c 
W 
t 
h 0. co 
0 
+ 
1 1  
IO 
9 
8 
I, 
B 
7 
6 
c 
‘g P 
1 
3 
2 
1 
0 
0 
7 
- A U  I 
. 
I 
m 
I I I I I I 
0 - N 
I c 
0- 
cn - 


The relationship between the viscosity and the dc-conductivity in polyvinylchloride

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