A study of the reaction between titanium tetrachloride and ethylene glycol : the dielectric constant of
tetraethoxytitanium at radio frequencies and low temperatures, the specific conductivity of
monochlorotriethoxytitanium
by William Hodgson
A THESIS Submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree
of Master of Science in Chemistry
Montana State University
© Copyright by William Hodgson (1949)
Abstract:
Part I A slightly yellow, viscous, polymer-like compound was prepared by reacting ethylene glycol
with titanium tetrachloride. A method of purification by precipitation of the compound from a solution
in ethyl alcohol with dry diethyl ether was tried.
An analysis of the product of the reaction indicates the presence of 21.98 percent titanium, 16.53
percent ohlorine, 5.34 percent hydrogen, 26.92 percent carbon and 29.23 percent oxygen. The
empirical formulae calculated from these data are TiClH12C5O4 based on one Ti atom, or C6H15O5
based on 6 carbon atoms.
The molecular weight determined by the freezing point method is 30. This value is too low to be
correct.
The conductivity of a solution of the product of the reaction between ethylene glycol and titanium
tetrachloride was measured. A. concentration of four grams of solute in 1000 grams of ethylene glycol
exhibited a specific conductivity of 10.9 x 10^-5 reciprocal ohms. Bxe specific conductivity was found
to decrease linearly with increasing dilution. The values obtained for the solution of the compound
were compared with values for a solution of HCl and a solution of TiCl(OC2H5)3 in glycol and found
to be more like TiCl(OC2H5)3.
This compound is decomposed rapidly by heat and slowly with time, with a subsequent loss of
chlorine. A second compound which is similar in behavior was made by reacting
monochlorotriethoxytitanlum with ethylene glycol. Its properties were not tested since it was also
decomposed by heat end with time.
The apparatus used for analysis is described and an attempt made to explain the experimental results.
Part II.
Tetraethoxytitanium has been prepared and purified. The behavior of the dielectric constant of the pure
liquid was studied at frequencies ranging from 30 to 100 megacycles, and at temperatures from -54°C
to 25°C.
The dielectric constant did not decrease with increasing frequency within the range of measurements,
and, therefore does not exhibit anomalous dispersion at those temperatures end frequencies.
Monochlorotriethoxytltenium was prepared end en attempt made to measure the dielectric constant at
1000 cycles end 25°C. It was found, however, that monochlorotriethoxytltenium conducts electricity
and the dielectric constant was not measurable with the equipment available.
The specific conductivity of pure monochlorotriethoxytltenium was measured at 25°C and found to be
1.34 x 10^-6 mhos.
A discussion of the difficulties involved in the use of a Q meter is presented.
The apparatus used for measurements is described. p e rt I.
A STUDY OJP TUB REACTION BETWEEN TITANIUM TETRACHLORIDE AND
ETHYLENE OLYCOL
P e r t JLL THE DIELECTRIC CONSTANT OE TEfBABTHOXYTITANIUM AT RADIO JPREqUENCIES
AwD JjOW TEMPERA TUBBS. THE SPECIFIC CONDUCTIVITY OF MONOCHJjOROTR LEIHOXYT ITANIUM
By
WILLIAM ^ODOSON
A THESIS
S n N m ltte d to t h e O re d u p te F r c u l t y
In
p p r t l e l f u l f i l l m e n t o f th e r e q u ir e m e n ts
f o r th e d e g r e e o f
M a s te r o f S c ie n c e In C h e m is try
pt
M ontpnc S t r t e C o lle g e
A p p ro v ed :
H e rd , M p jo r D e p p rtm e n t
^pn, ^ r / ^ u p ^ e D i v i s i o n
Iiogem pn, M ontrnp
A u gust 19^9
2
T /3 LE 0 £ CONTENTS
m s i.
£4.
I.
/B ST R A C T .............................................................................................................................
U
WTROBUCTIOiS...............................................................
5
REACTION OS' TITANIUM TE TEACELORI BE WITH ETHYLENE OLYCOL. . . .
8
ANALYSIS O i ISE COMPOUND........................................................................................
9
F o r T itr n iu m ...................................................................................................................
9
i o r C h l o r i n e ...................................................................................................................
9
II.
III.
IV.
F o r C p rh o n rn d H y d ro g e n . ...............................................................
10
MOLECULAR WElGrHT DETERMINATION.........................................................................
12
CONDUCTIVITY !EASV-REM1.NTS....................................................................
Ih
V II.
OTHER COMPOUNDS MADE.................................................................................................
18
V III.
DISCUSSION O i THE EXPERIMENTAL RESU LTS......................................................
20
IX.
SUMMARY...................................................................................................................................
22
V.
V I.
PART £ .
X.
ABSTRACT..............................................................................................................................
23
X I.
INTRODUCTION.....................................................................................................................
24
X II.
LITERATURE SURVEY...........................................................................................................
26
X III.
THEORETICAL D ISC U SSIO N .............................................................................................
27
XIV.
PREPARATION O i Tffu COMPOUNDS..............................................................................
42
XV.
MEASUREMENT O i THE DIELECTRIC CONSTANT OF TETRAETHOXYTITANIUM AT VARYING TEMPERATURES AND FREQUENCIES............................................
4]
(a )
A p p p ra tu e n e e d f o r m e r s u r e m e n t s ..........................................................
43
(b )
M ethods o f C s l c u l p t i o n ..................................................................................
47
(c)
D i f f i c u l t i e s e n c o u n t e r e d ........................................................................
60
9 3 2 2 J
- 3 -
XV.
( C o n tin u e d )
(d )
D i e le c tr i c c o n s tp n t o f te tr r e th o x y tite n iu m e t
v a r y i n g f r e q u e n c y and t e m p e r a t u r e .................................. ....
.
60
SPECIFIC CONDUCTIVITY OF MONOCHItiROTRIjMtOXITITASIUM
AT 2 5 °C ........................................................................................................................
72
X V II.
DISCUSSION OP EXrjBRIyiMTAL R ESU LTS....................................................
73
XVI T I.
SUMMARY.......................................................................................................................
74
XIX.
ACKJOWLBDUtMBi TS....................................................................................................
75
XX.
LITERATURE CITED AND CONSULTED..............................................................
76
XVI.
mm
mm
S s-Jlr I !•
ABSTRACT
A s l i g h t l y y e l l o w , v i s c o u s , p o ly m e r - I Ik e compound wee p r e p e r e d by
r e e c t l n g e th y l e n e g l y c o l w ith t l t e n l u m t e t r e c h l o r l d e . A m ethod o f p u r i f i ­
c a t i o n by p r e c i p i t a t i o n o f t h e compound from e s o l u t i o n I n e t h y l a lc o h o l
w i t h d r y d i e t h y l e t h e r w as t r i e d .
An a n a l y s i s o f t h e p r o d u c t o f t h e r e a c t i o n i n d i c a t e s t h e p r e s e n c e
2 1 .9 8 p e r c e n t t i t a n i u m , 1 6 .5 3 p e r c e n t c h l o r i n e , 5 , 3k p e r c e n t h y d r o g e n ,
2 6 .9 2 p e r c e n t c r f b o n and 2 9 .2 3 p e r c e n t o x y g e n . The e m p i r i c a l f o rm u la e
c a l c u l a t e d fro m t h e s e d a t a a r e TiClHjgCgOif. b a s e d o n one T i a to m , o r
C gH jgO ^TiC l b a s e d on 6 c a r b o n a to m s .
The m o le c u la r w e i g h t d e te r m in e d by t h e f r e e z i n g p o i n t m eth o d i s 30 .
T h is v a l u e i s to o low t o b e c o r r e c t .
The c o n d u c t i v i t y o f a s o l u t i o n o f t h e p r o d u c t o f t h e r e a c t i o n b e tw e en
e t h y l e n e g l y c o l an d t i t a n i u m t e t r a c h l o r i d e w as m e a s u re d . A c o n c e n t r a t i o n
o f f o u r gram s o f s o l u t e i n 1000 gram s o f e t h y l e n e g l y c o l e x h i b i t e d e.
s p e c i f i c c o n d u c t i v i t y o f 1 0 .9 x 10~5 r e c i p r o c a l ohm s. The s p e c i f i c con­
d u c t i v i t y w as fo u n d t o d e c r e a s e l i n e a r l y w i t h i n c r e a s i n g d i l u t i o n .
The
v a l u e s o b t a i n e d f o r t h e s o l u t i o n o f t h e compound w e re com pared w i t h v a lu e s
f o r a s o l u t i o n o f HCl and a s o l u t i o n o f T iC l(O C gH g)^ I n g l y c o l a n d fo u n d
to b e m ore l i k e T lC l(O C g H g )^ .
T h is compound i s decom posed r a p i d l y by h e a t and s lo w ly w i t h tim e ,
w i t h a s u b s e q u e n t l o s s o f c h l o r i n e . A se c o n d compound w h ic h i s s i m i l a r
i n b e h a v i o r was made by r e a c t i n g m o n o c h lo ro t r i e t h o x y t i t a n i u m w i t h e th y l e n e
g ly c o l.
I t s p r o p e r t i e s w e re n o t t e s t e d s i n c e i t was a l s o decom posed by
h e a t and w i t h tim e .
The a p p a r a t u s u s e d f o r a n a l y s i s i s d e s c r i b e d and an a t t e m p t made to
e x p la in th e e x p e rim e n ta l r e s u l t s .
II.
INTRODUCTION
Tn t h e c o u rF e o f en I n v e s t i g a t i o n b y C ro w e ^ ^ on th e d i e l e c t r i c p r o p e r ­
t i e s o f pome e s t e r s o f t l t p n i u m t e t r a c h l o r i d e , t h e r e r c t i o n o f t h i s compound
w ith <ome p o ly h y d ro x y r l c o h o l s v e s c o n s i d e r e d .
> v isc o u s , re s in o u s m e te ris l
wps p r o d u c e d w h ic h on s n e l y s l e w as shown to b e n o n h o m o ^en eo u s.
s u l t i n g th e l i t e r a t u r e ,
Upon con­
i t was fo u n d t h a t p r a c t i c a l l y n o t h i n g i s r e p o r t e d
on t h e c h e m i s tr y o f t h e r e a c t i o n s o f m e t a l h a l i d e s and p o ly h y d ro x y s l c o h o l s .
U a r d in e r an d B i e l o u e s ^ * ^ h a v e p r o p o s e d t h e f o l l o w i n g r e a c t i o n s , a lth o u g h
t h e y h a v e e s t a b l i s h e d no p r o o f t h a t t h e s e a r e th e a c t u a l r e a c t i o n s :
I.
T iC lil + RHOCH2 Ch 2OH -----------^ T i - OCH2 4
Cl
2HC1
CH2OH-ClH
and on f u r t h e r h e a t i n g !
?.
/ OCH2
T l ^ - OCHo
/ ^ o p l
Cl
CH2OH-ClH
.OCH2
4 HOCH2CH9OH ------------- » T l - C C H 0
4 H9O 4 HOCH9CH9C l
2
/
'-O O H 2
2
Cl
CH2OH
The w a t e r w as s u p p o s e d to r e a c t c h e m i c a l ly w i t h th e c h l o r i n e to fo rm a
h y d r o x y e s t e r and t h e f r e e d h y d ro g e n c h l o r i d e m ig h t h a v e c o n v e r t e d more
g ly c o l to c h lo r h y d r ln .
The r e a c t i o n p ro d u c e d ? co m p lex m ix tu r e o f com pounds,
none o f w h ic h w e re i s o l a t e d o r i d e n t i f i e d b y t h o s e w o r k e r s .
I t seem s p r o b a b l e t h a t t h e p r o d u c t m ig h t b e o f c o n s i d e r a b l e i n t e r e s t
and im p o r ta n c e s i n c e t h e n a t u r e o f th e r e a c t i o n and t h e p r o p e r t i e s o f th e
p r o d u c t i n d i c a t e d t h e p o s s i b i l i t y o f e p o ly m e r f o r m a t i o n .
f o r m a ti o n i s p o s s i b l e ,
p ro p e rtie s .
I f p o ly m e r
t h e s e m ig h t e x h i b i t some v e r y u n u s u a l and v a l u a b l e
Up t o t h e p r e s e n t tim e no m a c ro m o le c u le s c o n t a i n i n g t i t a n i u m
have been re p o rte d .
* m ore th o ro u g h s tu d y o f th e r e e c t l o n o f th e m ethod o f p u r i f i c a t i o n
pnd o f th e p r o d u c t o r p r o d u c t s o b t a i n e d a p p e e r e d t o be o f c o n s i d e r a b l e
v e lu e .
A c o m p a ris o n o f t h e m ethod u s e d by Crow e, pnd t h a t u s e d b y S r r d i n e r
rn d B i e l o u s s f o r r e a c t i n g th e g l y c o l end t i t a n i u m t e t r a c h l o r i d e
in d ic a te d
t h a t t h e r e a c t i o n c a r r i e d o u t by Crowe was s i m i l a r to th e f i r s t s ta g e o f
t h e S a r d i n e r and B i e l o u e s r e a c t i o n .
E l i m i n a t i o n o f t h e s e c o n d s ta g e s h o u ld
make t h e r e a c t i o n l e s s c o m p le x , and t h e s e p a r a t i o n o f t h e t i t a n i u m
g l y c o l a t e p r o d u c t s h o u ld n o t b e to o d i f f i c u l t .
I d e n t i f i c a t i o n o f th e
compound s h o u ld f o ll o w fro m a c o m p le te a n a l y s i s and a d e t e r m i n a t i o n o f i t s
m o le c u la r w e i g h t.
S i m p l i f i c a t i o n o f t h e r e a c t i o n p r o d u c t s s h o u ld r e s u l t b y t h e u s e o f
m o n o c h l o r o t r i e t h o x y t I t a n i u m and e t h y l e n e g l y c o l , o r o f monoc h l o r o t r i e t h o x y t Itanixim and mono sodium g l y c o l a t e .
A p o s s i b l e r e a c t i o n b e tw e e n a o n o c h lo r o -
t r i e t h o x y t i t a n l u i n and mono sodium g l y c o l a t e i s :
HOCH2 CH2ONa
+
C lT i(O C 2H5 ) 3 ---------- - HOCH2 CH2 OTi(OC 2H5) 3
+
HaCl
w h e r e a s , w i t h th e m o n o c h l o r o t r i e t h o x y t i t e n i u m and th e e th y l e n e g l y c o l , t h e
r e a c t i o n may p r o c e e d a s f o l l o w s :
C lT l(O C 2H5 )3
4
CH2 OHCH2O H ----------- C2H5OH
+
T iC l(O C 2H5 ) 2OCH2CH2OH
w i t h t h e e t h y l a l c o h o l s p l i t t i n g o f f r a t h e r th a n th e h i g h l y n e g a t i v e c h l o r i n e
a to m .
The p ro b le m s in t h i s f i r s t p a r t w i l l b e t
(1 )
to f i n d th e r e a c t i o n w h ic h w i l l g iv e th e same p r o d u c t o r p r o d u c t s
e a c h tim e ,
(2 )
t o d e te r m in e a r e l i a b l e m ethod o f i s o l a t i o n and p u r i f i c a t i o n o f
p r o d u c t , and
- 7 (3 )
t o d e te r m in e th e s t r u c t u r e u s i n g e n e l y t l c e l , m o le c u la r w e ig h t.
c o n d u c t i v i t y end o t h e r d e t e on t h e p h y c i c e l p r o p e r t i e s .
- 8 III.
REACTION OJT TITANIUM TETRACHLORIDE WITH ETHYLExfR JLYCOL
The p r o c e d u r e u s e d wee e s s e n t l p l l y t h e t o f Crow e, e x c e p t t h e t th e
tita n iu m
t e t r e c h l o r l d e wee d i s s o l v e d i n b e n z e n e ,
d i r e c t l y t o th e g l y c o l .
In d e t a i l ,
it
i n s t e a d o f b e in g added
i s ae fo llo w s .
E i g h t g rains o f
e t h y l e n e g l y c o l w e re ad d ed d ro p w le e fro m e d r o p p in g f u n n e l t o e s o l u t i o n
o f f i v e m i l l i l i t e r s o f t i t a n i u m t e t r a c h l o r i d e d i s s o l v e d i n f o r t y to f i f t y
m i l l i l i t e r s o f d r y b e n z e n e i n p s m a ll t h r e e n e c k f l a s k .
e q u ip p e d w i t h » m e c h a n ic a l s t i r r e r ,
The f l a s k was
a d e l i v e r y t u b e , and a n o u t l e t tu b e
l e a d i n g i n t o a s o l u t i o n o f sodium h y d r o x id e .
B en zen e made s good medium
i n w h ic h t o c a r r y o u t t h e r e a c t i o n s i n c e I t r e a c t s w i t h n e i t h e r o f t h e
r e a c t a n t s , and t h e p r o d u c t was i n s o l u b l e i n i t .
The p r o d u c t o f t h e r e a c t i o n was s e p a r a t e d fro m t h e b e n z e n e by f i l ­
t r a t i o n a n d h e a te d w i t h e n o i l b a t h t o 125-130°C a t re d u c e d p r e s s u r e f o r
a b o u t te n to f i f t e e n h o u r s .
The d a r k brow n s o l i d r e s i d u e w as d i s s o l v e d
i n d r y e t h y l a l c o h o l and p r e c i p i t a t e d a s a w h ite s o l i d by a d d i t i o n o f
a n h y d ro u s d i e t h y l e t h e r .
A f te r d ry in g in a d e s ic c a to r a t a p r e s s u r e o f
20 mm o f m e rc u ry f o r two to t h r e e h o u r s a t a n c o lo r e d s o l i d re m a in e d .
T h is p r o d u c t w as o n l y s l i g h t l y s o l u b l e i n e t h y l e n e g l y c o l and e t h y l a lc o h o l
and I n s o l u b l e I n b e n z e n e , h e x a n e , c y c lo h e x a n e , c a rb o n t e t r a c h l o r i d e end
a c e to n e .
I t was fo u n d t h a t r a p i d d e c o m p o s itio n to o k p l a c e on f u r t h e r
h e a t i n g t o IOO0 C.
A f t e r c o n tin u e d d r y i n g i n a d e s i c c a t o r a t 20 mm Hg.
p r e s s u r e f o r f i f t e e n t o tw e n ty h o u r s , t h e r e s i d u e was a n a ly z e d .
- 9 IV.
AiA lY StS £ ? COMPOUND
To
an ? I y z e
f o r tltp n lu m , th e
bam ple
w as i g n i t e d o v e r a M eker b u r n e r ,
and t h e t i t a n i u m c a l c u l a t e d on t n e b a s i s o f t i t a n i u m d i o x i d e .
t h e a n a l y s i s o f t h e com pound f o r t i t a n i u m ,
R e s u lts o f
i n t h i s m an n er, show ed t h e t an
i n c r e a s e fro m ? 2 .b 6 v T l t o 3 0 . 9 5 j T i r e s u l t e d fro m h e a t i n g I n a n o v en a t
o
190 C f o r 2 - 3 h o u r s .
The r e m a in d e r o f t h e compound w as k e p t i n e
d e s i c c a t o r ova.r p h o s p h o r u s p e n t o x i d e .
The t i t a n i u m c o n t e n t a f t e r two
m o n th s w as 2 2 . 63 $ and a f t e r t e n m o n th s 2 5 . 26 $ .
The a n a l y s i s f o r c h l o r i n e was c a r r i e d o u t in t h e m an n er d e s c r i b e d by
C row e.
A sam p le w as w e ig h e d i n t o a s m a ll ro u n d b o tto m f l a s k f i t t e d w ith a
r e f lu x c o n d en ser.
A volum e o f a l c o h o l e q u a l i n m i l l i l i t e r s
to 157 x
w e ig h t o f sa m p le , and a w e ig h t o f sodium e q u a l In g ram s t o 1 9 .5 * w e ig h t
o f s a m p le , w e re a d d e d t o t h e f l a s k .
sodium h a d a l l r e a c t e d .
a lc o h o l d i s t i l l e d o f f .
The m ix tu r e w as r e f l u x e d u n t i l th e
F o r t y m i l l i l i t e r s o f w a t e r w e re a d d e d and th e
The s o l u t i o n w as a c i d i f i e d w i t h d i l u t e n i t r i c a c i d
end e n o u g h s i l v e r n i t r a t e w as ad d ed t o p r e c i p i t a t e a l l o f t h e c h l o r i d e .
The s o l u t i o n w as t h e n made b a s i c w ith c o n c e n t r a t e d ammonium h y d r o x id e , and
th e t i t a n i u m h y d r o x id e f i l t e r e d o f f .
n itric
The f i l t r a t e w as made a c i d w ith
a c i d and t h e s i l v e r c h l o r i d e c o a g u la te d by d i g e s t i o n .
The s i l v e r
c h l o r i d e p r e c i p i t a t e w as t h e n p o u re d i n t o e gooch c r u c i b l e , d r i e d , and
w e ig h e d .
The p e r c e n t c h l o r i d e was c a l c u l a t e d on t h e b a s i s o f s i l v e r
c h l o r i d e and was fo u n d to b e 1 6 .5 3 end 1 7 .1 1 i n two d i f f e r e n t s a m p le s .
To e s t a b l i s h t h e e m p i r i c a l f o r m u la , i t was n e c e s s a r y to a n a ly z e f o r
c a rb o n and h y d r o g e n .
T h e re i s no r e l i a b l e end s im p le m ethod t o a n a ly z e
f o r o x y g e n , so t h e am ount p r e s e n t w as o b t a i n e d by s u b t r a c t i n g th e t o t a l
/
A
10 p e r c e n t p ^ e o f T l , C, H pad C l fro m 100 p e r c e n t .
The spmpI e
wps
b u r n e d I n e n e t a o s p h e r e o f o x y g en i n e, c o m b u s tio n tu b e
su c h PR t h r t shown I n f i g u r e I .
F ig u re I
As shown I n t h e f i g u r e , th e c o m b u s tio n tu b e c o n ta i n e d fro m l e f t to
r i g h t , 2 e p l r p l s o f c o p p e r o x i d e , t h e p o r c e l a i n b o s t c o n t a i n i n g th e
s e m p le , 2 b o p t s c o n t a i n i n g m o le c u la r s i l v e r t o r e p c t w i t h t h e c h l o r i d e ,
c o p p e r s p i r e I end w i r e , and f i n a l l y e re d u c e d c o p p e r s p i r a l .
The d r y in g
tu b e shown j u s t t o t h e r i g h t o f t h e c o m b u s tio n tu b e c o n ta i n e d c o n c e n tr a ­
t e d s u l f u r i c a c i d t o d i s s o l v e t h e w e t e r fro m th e c o m b u s tio n , a n d t h e p o t a s h
b u lb c o n ta i n e d a
s o l u t i o n o f p o ta s s iu m h y d r o x id e t o r e a c t w i t h th e
c a r b o n d i o x i d e fro m t h e c o m b u s tio n .
The tu b e and H2 SOj4., an d t h e b u lb and
KOH w e re w e ig h e d b e f o r e an d a f t e r th e e x p e r im e n t.
CO2 w e re t h e i n c r e a s e i n w e ig h t i n e a c h c a s e .
was c a l c u l a t e d on t h e b a s i s o f w a t e r .
The w e i g h ts o f H2O and
The p e r c e n t o f h y d ro g e n
The p e r c e n t o f c a r b o n w as c a l c u l a ­
t e d on t h e b a s i s o f c a r b o n d i o x i d e .
R e s u lts o f th e a n a ly s is g a v e :
2 1 .9 8 ^ t i t a n i u m , 1 6 .5 3 ^ c h l o r i n e ,
2 6 .9 2 % c a r b o n , 5 . 3 UC h y d r o g e n , and by s u b t r a c t i o n , 2 9 .2 3 $ o x y g e n .
- 11The e n p l y s i s i n d i c e t e d s n e m p i r i c a l f o rm u la o f e i t h e r TICIC^H120U b?se<i
on o n e T l ato m , o r C gK ^O jjT iC l b a s e d on 6 c a rb o n a to m s .
- 12V.
MOLRCULAB WBICHT DBTBRMIWATION
I n o r d e r to f i n d t h e r e t u e l f o r a m ie o f t h e compound u n d e r i n v e s t i g a ­
t i o n t h e m o le c u le r w e ig h t s h o u ld b e d e te r m i n e d .
S in c e t h e compound i s
s o l u b l e i n e t h y l e n e g l y c o l end t h e f r e e z i n g p o i n t o f e th y l e n e g l y c o l i s
- 1 5 ° C , t h i s e p p e p re d to b e e c o n v e n ie n t s o l v e n t to u s e f o r m o le c u lp r w e ig h t
d e t e r m i n a t i o n s by f r e e z i n g p o i n t d e p r e s s i o n m eth o d .
The m o ls l f r e e z i n g
p o i n t c o n s t a n t f o r e t h y l e n e g l y c o l wee o b t a i n e d u s i n g r n e q u a t i o n w hich
msy b e fo u n d i n pny b e e i c p h y s i c a l c h e m i s tr y b o o k .
The e q u a t i o n i s :
Mp x A t x Wj
& -
io o u x w2
w h e re K f , wg, W1 , M2 e n d A t e r e t h e m o le l f r e e z i n g c o n s t e n t ,
o f s o l u t e end s o l v e n t ,
t h e w e ig h t
t h e m o le c u la r w e ig h t o f t h e s o l u t e en d t h e f r e e z i n g
p o i n t lo w e r i n g , r e s p e c t i v e l y .
T e b le I g i v e s t h e d e t s pnd r e s u l t s f o r th e m o ls l f r e e z i n g p o i n t c o n s t e n t d e te r m i n e t i o n u s i n g d io x p n e e s
p
s o lu te .
The m o le c u la r w e ig h t o f
t h e t i t a n i u m g l y c o l ? t e wns c e l c u l e t e d , u s i n g th e same e q u a t i o n , end t h e
moI p I f r e e z i n g p o i n t c o n s t a n t g iv e n i n T s b le I .
TABLE X.
D e t e r m in a t io n o f t h e M o le l E r e e z i n r P o i n t C o n s ta n t &£ E th y le n e . C ly c o l
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w t. o f
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.8 6 7 8
2 4 .9 0 8 7
2 .4 4
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2
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2 4 .5 3 3 6
2 .1 4
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- 13 T e b le I I g i v e s t h e d e t e end r e s u l t s o f t h e m o le c u la r w e ig h t d e te r m in a ­
tio n .
TABLE I I .
E e t e r m l n s t i o n si£. I M
:
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T ria l
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.1 0 9
3 2 .4 7 9
.3 7
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.5 8
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3 0 .0 3
The v s I u e o f 30 i s to o low to b e t h e m o le c u la r w e ig h t o f t h i s com­
pound.
T h is low m o l e c u l a r w e ig h t may be
fo llo w in g :
(2)
(l)
p
r e s u l t o f any o r a l l o f th e
d i s s o c i a t i o n o r r e a c t i o n o f t h e compound w i t h g l y c o l ;
a s s o c i a t i o n o f d lo x e n e and g l y c o l c a u s i n g an i n c o r r e c t f r e e z i n g
p o in t c o n s ta n t;
(])
I m p u r i t i e s i n t h e compound and g l y c o l .
:
1
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t
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14 VI.
CONDUCTIVITY
C o n d u c t i v i t y m e a s u re m e n ts w e re made t o c h e c k d i s s o c i a t i o n o f th e com­
po u n d .
D i s s o c i a t i o n w as i n d i c a t e d s i n c e a n a q u e o u s o r e t h y l e n e g l y c o l
s o l u t i o n o f t h e com pound g av e an a c i d t e s t w i t h l i t m u s .
I t seem ed m ost
p r o b a b l e t h a t c h l o r i d e io n d i s s o c i a t e d fro m th e r e s t o f t h e m o le c u le , th e
c h lo rid e
io n r e s u l t i n g fro m one o r b o th o f t h e f o ll o w i n g s o u r c e s .
I t m ig h t
be a t t a c h e d to T i atom b y a p a r t i a l i o n i c b o n d , o r i t m ig h t b e bound to a
g l y c o l g ro u p a s m o l e c u l a r H C l.
A c o m p a ris o n h a s b e e n made b e tw e e n t h e s p e c i f i c c o n d u c t i v i t y o f a
s o l u t i o n o f th e compound i n e t h y l e n e g l y c o l , a s o l u t i o n o f HCl a n d a s o l u ­
t i o n o f monoc h l o r o t r i e t h o x y t i t a n i u m
i n th e same s o l v e n t .
The v a l u e s o f
c o n c e n t r a t i o n and c o n d u c t i v i t y f o r h y d r o c h l o r i c a c i d s o l u t i o n i n g l y c o l
a r e much l a r g e r t h e n f o r t h e compound b e c a u s e t h e c o n c e n t r a t i o n o f io n s
was much g r e a t e r i n t h e f o rm e r s o l u t i o n s ; w h e r e a s , t h e c o n c e n t r a t i o n and
c o n d u c t i v i t y o f t h e mo no c h lo ro t r Ie th o x y t i t a n Ium com pared f a v o r a b l y in
m a g n itu d e .
and 3
The r e s u l t s a r e r e c o r d e d i n T a b le I I I and shown i n F i g u r e s 2
— 15 **
W JLE I I I .
C o n c e n t r a t i o n o f S o l u t i o n s & £ T lte n iu m p y P O lr .lS , # y 4 C h l p r i dg.
^ n n r h l o r o t r i e t h o x y t l t z n l T a l a C -ly .c .Q l ££& C o r T S S r s a d l a S S P S C l f l S
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; c o m p a ris o n o f t h e r e s u l t s f o r t l t e n l u m g l y c o l e t e e n d HCl I s mede
In F i g u r e 2 , w h e r e e s , I n F ig u r e J t h e c o m p a ris o n i s b e tw e e n t h e m o n o c h lo ro trie th o x y tite n iu m
s o l u t i o n znd t h e t i t e n Ium g l y c o l e t e s o l u t i o n .
I t s h o u ld be n o t e d t h a t th e s p e c i f i c c o n d u c t i v i t y o f t h e h y d ro g e n
c h l o r i d e s o l u t i o n end t i t e n i u m g l y c o l e t e s o l u t i o n w e re d i v i d e d by t e n to
PI low e c o m p a ris o n o f t h e s l o p e s o f t h e c u r v e s i n f i g u r e 2 .
1
The c o n c e n t r a t i o n i s i n gram s o f s o l u t e p e r 1000 gram s o f s o l v e n t .
CONCENTRATIONS OE SOLUTIONS OF TITANIUM GrLYCOLATE AND HYDROGEN CHLORIDE
IN ETHYLENE GLYCOL PLOTTED AGAINST SPECIFIC CONDUCTIVITY AT 25°C
C o n c e n t r a ti o n i n gram s s o l u t e / 1000 g ram s s o l v e n t
Z aanSM
1 0 .0
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CONCENTRATIONS Of SOLUTIONS OF TITANIUM OLYCOLATE AND MONOCHLOROTRIETHOXYTITANIUM
IN ETHYLENE OLYCOL PLOTTED AOAINST SPECIFIC CONDUCTIVITY OF THE SOLUTIONS AT 25°C
C o n c e n t r e t i o a i n g ram s s o l u t e /1 0 0 0 g ram s s o l v e n t
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- 18V II.
OTHER COMPQUaPS MftPB
ftt t h i s p o i n t i t w se d e c id e d t h a t b e c a u s e o f th e c o m p le x ity , th e p r o b ­
lem s h o u ld be s t ta c k e d fro m a d i f f e r e n t a n » l e .
I f l e s s c o m p le x compounds
o f e t h y l e n e g l y c o l a n d t i t a n i u m o f d e f i n i t e l y Icnown s t r u c t u r e c o u ld be m ade,
and t h e i r p r o p e r t i e s d e te r m in e d , a c o m p a ris o n m ig h t b e p o s s i b l e b e tw e e n
t h e s e com pounds an d t h e compound j u s t d e s c r i b e d .
I t was h o p e d t h a t com­
p o u n d s m ade by r e a c t i n g m o n o c h lo ro t r i e t h o x y t i t a n i u m w i t h g l y c o l o r sodium
g l y c o l a t e w ould f i t
th a t d e s c rip tio n .
T h u s, com pounds w e re p r e p a r e d a s f o l l o w s :
m o n o c h lo ro trie th o x y tita n iu m
a s o l u t i o n o f t e n gram s o f
i n g l y c o l w as added to f o u r g ram s o f mono-
aodium g l y c o l a t e i n a e m a il ro u n d b o tto m f l a s k e q u ip p e d w i t h a r e f l u x c o n ­
d e n ser.
Mo r e a c t i o n to o k p l a c e a t room t e m p e r a t u r e ,
so th e r e a c t a n t s w ere
h e a t e d u s i n g a w a t e r b a t h u n t i l a, w h i t e p r e c i p i t a t e a p p e a r e d i n t h e f l a s k .
T h ie o c c u r r e d a t a te m p e r a t u r e o f a b o u t 80 ° C .
The r e a c t i o n f l a s k and
c o n t e n t s w e re h e a t e d f o r a b o u t o n e - h a l f h o u r and t h e n a llo w e d to c o o l.
l i q u i d w as d e c a n te d o f f and d i s t i l l e d
t a i n th e d e s ir e d p r o d u c t.
a t re d u c e d p r e s s u r e .
The
I t d id n o t con­
The s o l i d r e s i d u e i n t h e r e a c t i o n f l a s k was
s o l u b l e i n w a t e r , and e t h y l a l c o h o l , and. i n s o l u b l e i n b e n z e n e , h e x a n e ,
c a rb o n t e t r a c h l o r i d e ,
c h lo rid e .
a c e to n e and c y c lo h e x a n e .
I t t a s t e d l i k e sodium
The p ro b le m o f s e p a r a t i o n o f th e compound from t h e s a l t w as n o t
s o lv e d s a t i s f a c t o r i l y .
The sodium c h l o r i d e w as n o t e n t i r e l y i n s o l u b l e i n
e th y l a lc o h o l.
W a te r w as u s e d f i n a l l y , b u t h y d r o l y s i s to o k p l a c e in th e
w a te r s o lu tio n .
T h is w as i n d i c a t e d b y t h e a n a l y s i s f o r t i t a n i u m w hich
w as to o h i g h f o r t h e compound e x p e c t e d .
— 19 —
W ith t h e I d e a i n m ind o f f i n d i n g a p r o c e s s w h ic h p ro d u c e d a p r o d u c t
w h ic h w o u ld be e e r i l y p u r i f i e d ,
tlte n lu m
t h e r e a c t i o n b e tw e e n m o n o c h l o r o tr le t h o s y -
end e th y l e n e g l y c o l wes t r i e d .
T h e re i s e p o s s i b i l i t y
t h a t th e
r e a c t i o n c o u ld b e r e p r e s e n t e d b y t h e e q u a ti o n s
HOCH2 CH2OK
C lT l(O C 2H5 ) 3 ---------- ►HOCH2 CH2OTi ( OC2H5 ) 3
+
+
HCl
H ow ever, w i t h t h e h i g h l y n e g a t i v e c h l o r i n e atom t h e r e a c t i o n m ig h t a ls o
p r o c e e d a s m e n tio n e d e a r l i e r ,
T iC l(O C 2 E5 ) )
+
i, e .,
HOCH2 CH2O E ---------- - T iC l(O C 2H5 ) 2 OCH2CH2OH
f
C2H5OH
F o r t h e r e a c t i o n 2 .8 5 gram s o f e t h y l e n e g l y c o l w ere ad d ed to 10 g ram s o f
m o n o c h lo ro t r i e t h o x y t i t a n i u m
r e f lu x c o n d en ser.
i n a s m a ll ro u n d b o tto m f l a s k f i t t e d w i t h a
T h e re w as no e v o l u t i o n o f h e a t , o r o t h e r i n d i c a t i o n o f
f r e a c t i o n , to t h e f l a s k and r e a c t a n t s w e re h e a t e d t o a b o u t 7 5 0 when th e
l iq u i d began to r e f l u x .
h o u r s and t h e v o l a t i l e
R e f lu x in g was c o n tin u e d f o r two and o n e - h a l f
s u b s ta n c e d i s t i l l e d
o ff.
The o d o r and a b o i l i n g p o i n t i n d i c a t e d t h e v o l a t i l e s u b s ta n c e was
e t h y l a l c o h o l , w h ic h i n t u r n i n d i c a t e d t h a t t h e s e c o n d p o s s i b i l i t y shown
a b o v e to o k p l a c e .
The r e s i d u e w as a v e r y v i s c o u s , c l e a r , c o l o r l e s s l i a u i d
w h ic h s o l i d i f i e d when t h e p r e s s u r e w as r e d u c e d i n t h e f l a s k .
s o l i d w as Uow dered an d i t w as fo u n d to b e s o l u b l e i n e t h y l
The w h ite
a l c o h o l end
e th y l e n e g l y c o l , b u t n o t s o l u b l e i n b e n z e n e , h e x e n e , c a rb o n t e t r a c h l o r i d e ,
a c e to n e o r c y c lo h e x a n e .
The p r o d u c t w as decom posed by h e a t .
t i e s a re s im i la r to th o se o f th e tita n iu m
p ro d u c t.
I t s p ro p er­
t e t r a c h l o r i d e e th y l e n e g l y c o l
20 VIII.
DISCUSSION C£ BKFSEIHSfrITAL RESULTS
Oood p g re e m s n t was o b t a i n e d b e tw e e n d i f f e r e n t sem p lee i n th e a n e l y e l e
o f t h e compound d e s c r i b e d i n S e c t i o n IV f o r t i t a n i u m .
th e p ro d u c t i s q u i te u n ifo rm .
T h is i n d i c a t e d t h a t
R e p e a te d a t t e m p t s r t m aking t h e compound,
p ro d u ce d s l i g h t l y d i f f e r e n t r e s u l t s in each c a s e .
T h a t w o u ld seem to i n ­
d i c a t e s e v e r a l c o n c u r r e n t r e a c t i o n s o r s te p w is e r e a c t i o n s .
T h e re i s a p o s s i b i l i t y t h a t w i t h t h e m u l t i p l e a l c o h o l g r o u p s a t t a c h e d
t o p c e n t r a l a to m , t h e t i t a n i u m g l y c o l a t e compound i s s i m i l a r to th e
a c e ta ls .
When a c e t a l s c o n t a i n i n g p r im a r y a l c o h o l g ro u p s a r e d i s s o l v e d in
o t h e r p r im a r y a l c o h o l s ,
it
is p o s s ib le t h a t th e r e w i l l be an exchange o f
t h o s e a l c o h o l g ro u p s w i t h th e s o l v e n t w h ic h te n d s to w a rd a n e q u i l i b r i u m .
As a n e x a m p le :
, OCH1
HO — OCHs o I u t io n
^OCHgCH 3
j. CH-OH
3
T h e re i s no p r o o f t h a t th e ab o v e ty p e o f r e a c t i o n t a k e s p l a c e w ith th e
t i t a n i u m com pound.
H ow ever i t h a s b e e n d e m o n s tra te d w i t h t h e r e a c t i o n o f
m o n o c h lo ro t r i e t h o x y t i ta-nium w ith g l y c o l ,
t h a t one o r m ore e t h y l g ro u p s on
t h e m o le c u le h a v e b e e n r e p l a c e d b y t h e g l y c o l .
The a n a l y t i c a l d a te and
e m p i r i c a l fo rm u la f o r t h e p r o d u c t o f t h e r e a c t i o n o f t i t a n i u m
te tra c h lo rid e
w i t h g l y c o l i n d i c a t e s t h a t f o r one t i t a n i u m ato m , t h e ty p e s o f s t r u c t u r e s
shown b e lo w a r e p o s s i b l e .
or
X
- 21 One I s shown h e r e e s e u n i t o f e p o ly m e r , w h ere t h e f r e e b o n d s e r e e c t u e l l y
e t t e c h e d to o t h e r c a rb o n atom s o f in c o m p le t e ly d raw n g l y c o l m o le c u le s .
The c o n d u c t i v i t y d a t- ' g i v e s e v id e n c e t h a t t h e s e s t r u c t u r e s e r e m ore p r o b a b l e
th a n t h o s e p o s s i b l e
i f t h e e m p i r i c a l fo rm u la i s b a s e d on s i x c a rb o n a to m s,
t h a t i s , C ^ H ^ O ^ T iC l w h e re th e s t r u c t u r e may b e r e p r e s e n t e d b y :
HCl
HOCH2 CH2O
CH2O
OCH,
KCl
HOCH2 CHgO'
'OC2H5
E 5 C2O -
w i t h t h e c h l o r i n e p r e s e n t a s m o le c u la r h y d ro g e n c h l o r i d e .
p r o b a b l e , t h i s s t r u c t u r e c o u ld a l s o b e p o s s i b l e ,
tiv ity
OCH2
A lth o u g h l e s s
s i n c e th e s p e c i f i c co nduc­
o f b o t h th e compound and HCl v a r y l i n e a r l y w i t h t h e c o n c e n t r a t i o n .
I f t h i s tita n iu m
th e re is a p o s s ib ility
g l y c o l a t e compound d o e s b e h a v e s i m i l a r t o th e a c e t a l s ,
t h a t t h e two s t r u c t u r e s shown a b o v e , an d o t h e r s .
w e re i n e q u i l i b r i u m when t h e e t h e r w as a d d ed to p r e c i p i t a t e t h e compound.
I f t h a t w as th e c a s e , p r e c i p i t a t i o n d o e s n o t p u r i f y th e com pound.
F u r th e r
w ork i s r e q u i r e d to d e te r m in e t h i s c o n c l u s i v e l y .
The compound made b y r e a c t i n g a o n o c h lo r o t r i e t h o x y t i t a n i u m w ith e th y l e n e
g l y c o l b e h a v e s i n much th e same m an n er and t h e r e i s a. s t r o n g p r o b a b i l i t y
th a t i t
i s t h e same t y p e o f co m p le x m i x t u r e .
22
XX,
1.
-
SUMMARY
A p o ly m e r - 1 Ik e compound w s p r e p a r e d b y r e a c t i n g t i t a n i u m
c h l o r i d e w i t h e t h y l e n e - jl y c o l,
te tra ­
P r e c i p l t e t i o n b y d r y d i e t h y l e t h e r w as
n o t n ro v e n to b e # m eth o d o f p u r i f i c e t l o n .
2.
A n e l y s is o f t h e compound ^ lv e e p o s s i b l e e m p i r i c a l f o r m u l a e :
TlC IC 5H12 Oi, o r CgH15 O5 T iC l.
3.
C o n d u c tiv ity d e ta
i n d i c a t e e p o s s i b i l i t y o f m o le c u la r h y d r o g e n c h l o r i d e
o r m ore p r o b a b ly c h l o r i n e bound by p a r t i a l i o n i c bond t o t i t a n i u m .
Zi.
D i f f i c u l t y i s e x p e r ie n c e d
i n d e te r m i n in g t h e c o r r e c t s t r u c t u r a l
fo rm u la b e c a u s e th e c o r r e c t v a lu e f o r t h e m o le c u la r w e ig h t was n o t
d e te r m i n e d .
5.
M ethods o f p r e p a r a t i o n *nd p u r i f i c a t i o n o f com pounds o f n o n o c h lo r o t r i e t h o x y t i t e n i u m w e re t r i e d .
Compounds p r e p a r e d h a v e p r o p e r t i e s w h ic h
a re s im ila r to th o s e o f th e p ro d u c ts o f th e r e a c ti o n o f tita n iu m
t e t r a c h l o r i d e and g l y c o l .
6.
I t i s s u g g e s te d t h * t a u b s e c u e n t i n v e s t i g a t i o n b e made o n com pounds o f
a l e s s co m p lex n a t u r e l i k e t h e m o n o c h l o r o tr ie t h o x y tI ta n i u m - sodium
g l y c o l e t e p r o d u c t w i t h t h e p o s s i b i l i t y o f c o r r e l a t i n g t h e d a ta on
t h o s e r e a c t i o n s and t h a t o f t h e r e a c t i o n o f t i t a n i u m t e t r a c h l o r i d e
and e t h y l e n e g l y c o l .
- 23 ££X l I I .
5.
ABSTRACT
T e t r p e t h o x y t i t s n i i u n h s s b e e n p r e p s r e d end p u r i f i e d .
B ie b e h e v io r o f
t h e d i e l e c t r i c c o n s t s n t o f t h e p u r e l i q u i d w es s t u d i e d s t f r e q u e n c i e s
r s n g l n ^ fro m 30 t o 100 m e g a c y c le s , rn d s t te m p e r s t u r e s fro m -5 h °C to 25°C .
The d i e l e c t r i c c o n s t s n t d i d n o t d e c r e e s e w ith i n c r e a s i n g f r e q u e n c y
w i t h i n t h e r a n g e o f m e a s u re m e n ts , e n d , t h e r e f o r e d o e s n o t e x h i b i t an o m alo u s
d i s p e r s i o n e t t h o s e te m p e r a t u r e s r n d f r e q u e n c i e s .
M o n o c h lo r o tr ie th o x y titf in lu m w as p r e p a r e d and e n a tt e m p t made to
m e a s u re t h e d i e l e c t r i c c o n s t a n t a t 1000 c y c l e s and 2 5°C .
I t was fo u n d ,
h o w e v e r, t h a t m o n o c h l o r o tr ie t h o x y tI ta n i u m c o n d u c ts e l e c t r i c i t y and th e
d i e l e c t r i c c o n s t a n t w as n o t m e a s u r a b le w i t h t h e e q u ip m e n t a v a i l a b l e .
The s p e c i f i c c o n d u c t i v i t y o f p u r e m o n o c h l o r o tr ie t h o x y tI ta n i u m was
m e a s u re d p t 2 $°C a n d fo u n d t o be I . 34 x 10" ° m hos.
A d i s c u s s i o n o f t h e d i f f i c u l t i e s in v o lv e d i n t h e u s e o f a Q m e te r
is p re s e n te d .
Tlie a p p a r a t u s u s e d f o r m e a su re m e n ts i s d e s c r i b e d .
- P U -
ii.
INTRODUCTION
^ n o rap lo u s d i s p e r s i o n , th e d e c r e a s e o f th e d i e l e c t r i c c o n s t a n t o f
p o l e r l i q u i d s w ith i n c r e p a l n g f r e q u e n c y , h e e "been n e e d f o r raeny y e s r s to
e e s t s t i n d e t e r m i n a t i o n o f t h e p h y s i c a l s t r u c t u r e o f m o le c u le s end t h e i r
e ls e .
R e c e n tl y , h o w e v e r. I t h e s becom e I n c r e a s i n g l y I m p o r ta n t i n e l e c t r i ­
c a l e n g i n e e r i n g l a b o r a t o r i e s a s a m eans o f d e te r m i n in g th e b e s t u s e o f
each d i e l e c t r i c o r in s u la tin g m a te ria l.
I n many c a s e s t h e d i e l e c t r i c
d a t a may be t h e d e c i d i n g f a c t o r i n d e te r m i n in g w h ic h m a t e r i a l I s b e s t f o r
d i e l e c t r ic o r In s u la tio n u se .
f o r e x a m p le , m a t e r i a l s w h ich e x h i b i t
a n o m a lo u s d i s p e r s i o n a t low f r e q u e n c i e s w ould n o t b e s a t i s f a c t o r y f o r
d ie le c tric s
i n e l e c t r i c a l e q u ip m e n t u n l e s s t h e r e g i o n o f a n o m a lo u s d i s ­
p e r s i o n c o u ld b e a v o id e d b y p r o p e r c h o ic e o f t e m p e r a tu r e o r f r e q u e n c y .
A t t h e p r e s e n t tim e a n e x t e n s i v e s tu d y o f t h e d i e l e c t r i c p r o p e r t i e s
o f e s t e r s o f t i t a n i u m c o n t a i n i n g o r g a n i c g ro u p s I s b e i n g c a r r i e d o u t i n
t h is la b o ra to ry .
As a p a r t o f t h i s
s tu d y , m e a su re m e n ts a r e b e in g made to
d e te r m in e th e e f f e c t on t h e d i e l e c t r i c c o n s t a n t o f i n c r e a s i n g t h e f r e q u e n c y .
The com pounds a v a i l a b l e i n p u r e s t a t e f o r su c h e s tu d y a r e t e t r e e t h o x y t I ta n iu m , m o n o c h l o r o t r i e t h o x y t i t a n l u m , t e t r a p r o p o x y t i t a n i u m
b u to x y tita n iu m .
and t e t r e -
f o r t h e p r e s e n t w o rk , an o u t l i n e o f th e D ebye t h e o r y o f
a n o m a lo u s d i s p e r s i o n w i l l be p r e s e n t e d , d e t a i l s o f th e u s e o f a Q m e te r
w i l l b e d i s c u s s e d and m e a s u re m e n ts made on t e t r s e t h o x y t i t a n i u m
a re p re ­
s e n te d .
The m e a s u re m e n ts w e re made on a Q, m e te r , ty p e IfOA w h ic h h a s a
f r e q u e n c y r a n g e o f 30—200 me.
Z'
S in c e t h e com pounds u n d e r c o n s i d e r a t i o n a r e
—
p o lp r , v le c o u e l i q u i d s ,
25
“
th e y s h o u ld e x h i b i t p n o n p lo u s d i s p e r s i o n w i t h i n t h e
fre q u e n c y rsn g e o f th e Q m e te r.
— p6 —
XII.
LITERATURE SUEVEif
He c o n c lu d e d
t i i e t t h e e f f e c t w h ic h h e o b s e rv e d wee c e n s e d by c e r t e i n g ro u p s i n th e
m o le c u le s , f o r e x e m p le , OH o r NHg.
He b e s e d h i e c o n c lu s i o n s o n e x p e rim e n t
t e l r e s u l t s o b t a i n e d b y m e e a u re m e n ts on g l e r ^ e num ber o f com pounds.
I n 1917 Debye
( 6)
p r e s e n t e d a t h e o r y i n w h ic h h e g a v e a d e t a i l e d
e n e l y s i s o f en om eloue d i s p e r s i o n .
T h is t h e o r y c o r r e l a t e d t h e a c t u a l
s t r u c t u r e o f m o le c u le s w i t h t h e d i s p e r s i o n d i s c o v e r e d b y B r u d e .
I t hes
^ lv e n a n e a r l y c o m p le te an d s i m p l i f i e d p i c t u r e w h ich h e s s i d e d i n th e
u n d e r s t a n d i n g o f t h e c o n c e p t o f co m p le x d i e l e c t r i c c o n s t a n t s and d i e l e c ­
tric
lo s s .
O n c le y end W i l l i a m s ^ '* h a v e t e s t e d t h e Debye t h e o r y u s In ^ d i l u t e
n o n -a q u e o u s s o l u t i o n s and fo u n d t h a t a lt h o u g h t h e t h e o r y w as b a s i c a l l y
s o u n d , c o r r e c t i o n s w e re n e c e s s a r y t o c o r r e l a t e t h e e x p e r i m e n t a l w ith th e
c a lc u la te d r e s u l t s .
K irkw ood a n d F u o s s ^ ^ , on t h e o t h e r h a n d , p r o p o s e d
a t h e o r y f o r a n o m a lo u s d i s p e r s i o n i n p o ly m e rs w h ic h h a g b e e n v e r i f i e d by
S m y th ^ ^ .
D ebye
(?)
M aIsch^ ^
h a s made c o r r e c t i o n s f o r a s s o c i a t e d l i q u i d s and
h a s made a c o r r e c t i o n f o r p u r e l i q u i d s b a s e d on a q u a s i -
c r y s t a l l i n e c o n c e p t.
M easurem ents o f a n o m a lo u s d i s p e r s i o n a n d d i e l e c t r i c
(1 9 )
l o s s i n i n d u s t r i a l m a t e r i a l s h a v e b e e n made by l a g e r and B a k e r
and
Zno \
Sm ythx
and o t h e r s u s i n g th e K irkw ood and F u o ss e q u a t i o n s , o r an
a d a p t a t i o n o f th e Debye e q u a t i o n .
- 27X IIT .
TH^QFgTICAL DISCUSSION
r He t h e o r y o f p/aoniplous d i s p e r s i o n h e e b e e n t h o r o u ^ a l y t r e a t e d by
D ebye
'
end o t h e r s so t h a t a d e t a i l e d d e r i v a t i o n w i l l n o t b e g iv e n
h e re .
H ow ever, e few p o i n t s o f i n t e r e s t c o n c e r n in g p u r e l i q u i d s , th e
ty p e p r e s e n t l y u n d e r i n v e s t i g a t i o n e n d e g e n e r a l o u t l i n e o f t h e t h e o r y ,
w i l l be c o n s id e re d .
A c c o rd in g to D e b y e , a n o r i e n t a t i o n p o l a r i s a t i o n r e s u l t s when en
e le c tric fie ld
« b le to o r i e n t .
i s a p p l i e d t o eny m a t e r i e l c o n t a i n i n g d i p o l e s t h a t a r e
T h is p o l a r i s a t i o n
i s i n a d d i t i o n to th e p o l a r i z a t i o n due
to t h e d i s p l a c e m e n t o f e l e c t r o n s o r ^ to m s .
The e x i s t e n c e o f t h i s
o r i e n t a t i o n p o l a r i z a t i o n i s due to th e te n d e n c y o f t h e d i p o l e s to a l i g n
t h e m s e lv e s w i t h t h e f i e l d ,
and i t s f o r m a ti o n i s o p p o se d by t h e th e r m a l
m o tio n o f t h e m o le c u le s , o r i n t e r n a l f r i c t i o n c a u se d by m o le c u la r
b o m b a rd m e n ts, w h ic h t e n d s to k e e p t h e d i p o l e s ra n d o m ly o r i e n t e d .
IRiis
o r i e n t a t i o n p o l a r i z a t i o n i s t h e r e f o r e d e p e n d e n t on t h e t e m p e r a t u r e i n two
w ays.
F i r s t , a lo w e r t e m p e r a tu r e w i l l a llo w a n i n c r e a s e i n t h e p o l a r i z a ­
t i o n b e c a u s e t h e t h e r m a l m o tio n i s l e s s .
S eco n d , a lo w e r t e m p e r a t u r e w i l l
r e s u l t i n s d e c r e a s e i n t h e p o l a r i z a t i o n d u e to i n c r e a s e d i n t e r n a l f r i c ­
t i o n o r v i s c o s i t y b e c a u s e o f t h e s t r o n g e r f o r c e s o f a t t r a c t i o n b e tw e e n t h e
m o le c u le s .
T h ese two e f f e c t s w i l l v a r y a c c o r d in g t o th e n a t u r e o f th e
liq u id under in v e s tig a tio n .
p o la riz a tio n w ill,
At room t e m p e r a t u r e , h o w e v e r, t h e o r i e n t a t i o n
in g e n e r a l, be g r e a t e r th a n a t h ig h e r te m p e ra tu re s
b e c a u s e t h e th e r m a l m o tio n o f t h e m o le c u le s i n t e r f e r e s l e s s w i t h o r i e n t a ­
tio n .
- 28 The o r i e n t a t i o n p o l a r i z a t i o n ? l s o d e p e n d s on t h e f r e q u e n c y .
because e f i n i t e
T h is i s
tim e i s n e c e s s a r y f o r th e m o le c u le s t o becom e o r i e n t e d ,
and t h e y c o n t r i b u t e to t h e p o l a r i z a t i o n o n ly when th e f r e q u e n c y i s low
en o u g h to p e r m it o r i e n t a t i o n b e f o r e th e f i e l d
is re v e rse d .
?n o u t l i n e o f D e b y e 's t h e o r y o f an o m alo u s d i s p e r s i o n i n p o l a r l i q u i d s
i s p r e s e n t e d b e lo w .
f i r s t c o n s i d e r e s p h e r i c a l s u r f a c e draw n I n a l i q u i d , an d ta k e th e
c e n t e r o f t h i s s p h e r e a s t h e o r i g i n o f a s y s te m o f p o l a r c o o r d i n a t e s .
ITnder t h e i n f l u e n c e o f a n a l t e r n a t i n g e l e c t r i c f i e l d
th e d i s t r i b u t i o n
f u n c t i o n o f th e e l e c t r i c moments d e p e n d s u p o n t h e p o l a r a n g le
b e tw e e n th e f i e l d and t h e d i p o l e , and u p o n t im e .
I?,
The num ber o f m o le c u le s
w h ic h h a v e t h e i r m om ents i n th e d i r e c t i o n o f a s o l i d a n g le S n
tim e w i l l b e f d A , w h e re f i s t h e d i s t r i b u t i o n f u n c t i o n ,
a t a g iv en
f tim e i n t e r v a l
<5 t i p c h o s e n su c h t h a t a l l m om ents i n t h e s o l i d a n g le a t tim e t « 0 h a v e
moved o u t o f th e s o l i d a n g l e , y e t h=-ve n o t moved m ore th a n e few d e g r e e s .
The num ber o f m o le c u le s w hose m om ents h » v e e n t e r e d d A
in te rv a l
i n tim e
6 t i s g i v e n b y th e e q u a t i o n :
dA s A 1 4 A g
(I)
d t
i s t h e c o n t r i b u t i o n due t o r o t a t i o n s p ro d u c e d by t h e im p re s s e d
<*t
w h ere
fie ld ,
and A g i s t h e c o n t r i b u t i o n d u e t o r o t a t i o n s p ro d u c e d by B ro w n i»n
m ovem ent.
C o n s id e r t h e c o n t r i b u t i o n due t o B ro w n ia n movement f i r s t .
V is u a liz e
a s e c o n d s o l i d a n g le d A* w hose a x i s l a k e s an a n g le 6 w i t h t h e a x i s o f
dA
.
The num ber o f m o le c u le s w hose moments a r e i n d A
a t tim e t - O a r e
- 29 fd /i
.
^ e e j?i ju r e 4 .
fig u re b
Now s u p p o s e F c e r t a i n p r o b a b i l i t y f u n c t i o n W e x i s t s ,
n r o b p b ility th e t
f
d A at t •
The t o t a l num ber o f m o le c u le s w hose m om ents h a v e e n te r e d
S t.
m o le c u le w hose moment i s i n d / l
su c h t h ? t tfd/t g iv e s th e
p t tim e t * O w i l l b e I n
- 30 d / l d u e t o B rovm ipn novem ent i s » lv e n b y t h e e q u p ti o n i
Ag - -fd n
f
J s 'd
a
(2)
1WdA.
The i n t e g r a t i o n i e c a r r i e d o u t o v e r t h e s u r f n e e o f t h e s p h e r e o f u n i t
tvd i u s
w h ile d A i s c o n s t a n t .
F a c to r in g dn. o u t o f th e e x p re s s io n i t
ie
seen t h e t i
^ 2 = dA
J f ' d /l V
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The f u n c t i o n f ' i s e x p e n d e d f b o u t i t s v s Iu e r t dfl
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S in c e th e moments c e n move o n ly 8 few d e g r e e s i n tim e
i s s m e ll*
end
(3 )
r f t , t h e e a g le ©
^ i e t h e r e f o r e e V o s w e l l so t h e t t h e f o u r t h end
h i g h e r te r m s o f t h e e x p a n s io n msy b e n e g l e c t e d .
we c e n e x p r e s s t h e l n t e g r r l i n e a u r t i o n ( 2 )
J f 1W dA ' - f J m f i 1 +
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The f i r s t l n t e g r r l o n t h e r i g h t r i d e o f t h e e q u a t i o n i s e q u a l to
u n i t y , t h e se c o n d i n t e g r a l r e p r e s e n t s th e m ean v a l u e , 6
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d i n g to th e tim e i n t e r v a l
£ t,
sq u a re v a lu e , £
T hese i n t e g r a l s a r e e v a l u a t e d u s i n g s p h e r i c a l
trig o n o m e try .
, of € .
and t h e th ir d , i n t e g r a l r e p r e s e n t s th e m em
The c o s i n e th eo rm o f s p h e r i c a l t r i g o n o m e t r y i s ex p an d ed
u s i n g t h e s i n e m d c o s in e s e r i e s fro m g e n e r a l t r i g o n o m e t r y ,
v a lu e s o f ® i t
f o r s m a ll
is w ritte n as :
2
Cos I?
r
Cos h? -f
i X jian sto n o f t h e v a l u e O
9 s i n 'O Cos ^
cog O r f
. . .
= 1? ^ ^ f o r c o s I? * u s i n g t h e T a y lo r s
s e r i e s g iv e s :
I
Cos I ? 1 s
Cos ^
-
6 s i n 1?
_
£ 2
—
co sh ? 4 . . .
- 31
£ I r not# pxn ^ n d ed i n pow er* o f Q .
£
w h e re t h e c o e f f i c i e n t s
z
c< e
+ /3 6 2
+
. . .
in v o lv e f u n c t i o n s o f a? and <f> i m p l i c i t l y .
Thg
e x p l i c i t fo rm o f th e c o e f f i c i e n t * o f t h i s e x p a n s io n may b e o b t a i n e d by sub­
s titu tin g
in t h e l a s t w r i t t e n e x p a n s io n f o r c o s a? 1 a n d th e n by c o m p a rin g
t h e two e x p a n s io n s f o r c o s fS *.
a l l d i r e c t i o n s an d g i v e s
s
I
w h e re
.
S i
4
CO, O
s i n i?
G 2 i s t h e m ean s q u a r e v e lu e o f 0
©
€
The e x p r e s s i o n o b t a i n e d i s a v e ra g e d o v e r
=
/
and is
/ B 2Vf e l n 6 d 6 d ^
i s e v a l u a t e d in a s i m i l a r m an n er g i v i n g
C2 =
€ 2W d n t - J s L
and f i n a l l y
Zf1I n
s f t 4 j
61
4
- 0
s i n i?
g iv in g f o r A y
A - e d A -M
SO S-I?.
sln i?
-i£
+
"55$
I n t h i s e q u a t i o n we s e e t h a t i f f i s in d e p e n d e n t o f \ 3
t h e B row nian
m ovem ent c a n h a v e no e f f e c t on t h e d i s t r i b u t i o n f u n c t i o n .
ITor th e d e t e r m i n a t i o n o f t h e A p
h a v e e n t e r e d d / i i n tim e
t h e num ber o f m o le c u le s w hose m om ents
<ft due to a c t i o n o f t h e im p re s s e d f i e l d , we t a k e
i n t o a c c o u n t t h e t o r q u e on a g iv e n m o le c u le t e n d i n g t o t u r n i t
d i r e c t i o n o f th e f i e l d .
in th e
H ie t o r q u e may be r e p r e s e n t e d by t h e e q u a ti o n
M - - yUjj* s i n
- 12 w h e re yM I s th e e l e c t r i c moment end F I s th e f o r c e o f th e f i e l d
end th e
n e » e t i v e sl% n t pices s c c o u n t o f th e f ? c t th f- t t h e t o r q u e e c t s o p p o s i t e to
th e d i r e c t i o n o f I n c r e a s i n g
I? .
P t o r q u e d u e t o r n i n n e r f r i c t l o n e l f o r c e r e s u l t i n g fro m m o le c u la r
Im p a c ts en d p r o p o r tio n ? ? ! to t h e e n g u l e r v e l o c i t y , w o u ld j u s t b s le n c e th e
c o n s t e n t l y im p r e s s e d t o r q u e .
u - f
* J
W h e re i/
is
p
We e x p r e s s t h i s by th e e q u a ti o n
i^L
dt
c o n s t e n t m eem irin g t h e i n n e r f r i c t i o n o f th e l i q u i d .
I f Applied t o t h e c * s e w h ere t h e t o r q u e i s n o t c o n s t e n t i t
t h e t t h e r c c e l e r e t i o n e f f e c t i s n e g lig ib le .
In rn I n te r v a l
Ie im p lie d
/ 1 th e
m olecule w i l l t u r n t h r o u g h th e engle
Cf-Sf =
<^t - y ~
How d e te r m in e t h e num ber o f m o le c u le s w h ic h e n t e r a s o l i d e a g le co n ­
s is tin g o f p s trip
e x te n d in g b e tw e e n
I?
end ^
The num ber o f n o l e c u l e s w hose moments j r s s
in tp rv e l
+ ' d #
e ro u n d th e s p h e r e .
th r o u g h t h e c i r c l e
= /
in
e ft is
2 TTf s in d c f l ? -
2 rt i
\
Fnc t h r o u g h
t? -
d rJ
i n th e seme
2 TT f —p
eft
—
^
e f t Cin-Or
cT t i s
s i n rO
f
1J T
s ^n ^ )
S u b t r e c t i n g th e s e c o n d e x p r e s s i o n fro m t h e f i r s t
^ l “
^Sr
S u b s titu tin g e x p re s s io n s d e riv e d f o r ^ ^
?nd A g i n e q u a t i o n ( I ) ,
re m e m b e rin g
dA =
(6)
^271 f * / <ft s i n i ? ) d'O'
2 77 g i n -#
dO
rn d
^
- 33one O b tp ln s
A l hzSr"
d t *" B ln
sin lj^ r f r
Tr
-
' ) ]
F o r p s p e c i e l c ^ s e when t h e f i e l d F I s c o n s t p u t , th e n th e M pxw ell B o l t z mpnn e x p r e s s i o n
f — /e
I f p
-u /k f
F c o s t7 /k T
s o l u t i o n o f th e d I f f e r e n t l e l e o u r t i o n I f
e n e rg y o f t h e m o le c u le s ,
= 0.
yu i s t h e e l e c t r i c m om ent, I
U
i s t h e p o t e n t ip
i s th e f i e l d
in te n ­
s i t y , k i s th e B o ltz m e n n c o n s t a n t , T i s th e p b s o l u t e te m p e r p tu r e end e i s
th e e x p o n e n tle l.
S in c e th e t o r q u e
'I — —
i e l n zZ^ — —
i t mpy b e s e e n t h e t t h e M eaw ell B o ltz m e n n e x p r e s s i o n i s e s o l u t i o n o f th e
d i f f e r e n t i a l e o u e tio n f o r th e c o n d itio n
~ O p ro v id in g
JLl - M
b it
- f
T h is e q u a t i o n e x p r e s s e s t h e r e l a t i o n w h ic h e x i s t s b e tw e e n t h e m a g n itu d e
o f th e B ro w n ian f o r c e o f t h i s a n g le and th e te m p e r a tu r e and f r i c t i o n
c o n s t a n t o f t h e m o le c u le s .
a
from ( 6 ) i n
S u b s titu tin g
<8 ,
t„,
( ? ) o n e o b t a i n s th e f i n a l d i f f e r e n t i a l e q u a t i o n n e c e s s a r y to
d e te r m in e t h e d i s t r i b u t i o n f u n c t i o n f a s a f u n c t i o n o f t an d t h e a n g l e #
/
-------S'/ it!?
J t
s in
(kT
*44
SzV
-
)
F o r a p o l a r l i q u i d u n d e r t h e i n f l u e n c e o f h ig h f r e q u e n c y , th e
i n t e r n a l f o r c e may b e e x p r e s s e d b y t h e r e a l p a r t o f F = F e
, so t h a t
I
th e to rq u e on e m olecule I s
Mr
- yUS^e W
S l n yI?
where F Is the I n te n s ity o f the f i e l d , W i s 2 TTf where f i s the frequency.
The d is tr ib u tio n fu n c tio n must be
J—
2 T -d t =
- 2_
s im ?
p.
I
s o lu tio n o f ( 9 ) , which cen be w ritten
f
s in
I
„
l ^
IK
I I
(ig )
IcT
where T i s the time o f r e ls x p tlo n fo r the liq u id and is equal to
A s o lu tio n i s f
/ / 2kT.
where B i s an a rb itra ry
I +
c o n sta n t, can be shown by s u b s titu tin g t h is s o lu tio n in equation (9 ) pro­
v id in g B
I -
iw r
f = Al I -
Oms
I - iw r
- ^ f 2,
cos#
For la rg e v a lu es o f w r the fu n c tio n becomes c o n sta n t.
occurs where w T l s n early u n ity .
( 11 )
The tr a n s itio n
The mean moment o f the m olecules i s a lso
complex and i s g iv en by the equation!
e*
me
A*2’
' ■■ .
IkT
"
I + iw r ”
JiL2
IkT
Fne
I + iw r
( 12 )
which w i l l be trea ted in more d e t a il la t e r .
The meaning o f the complex moment i s th a t th ere i s a d iffe r e n c e In phase
between the moment and the in te r n a l fo r c e .
I f the phase angle Is f , the
above equation may be w r itte n :
-
3 - 3kT
(13)
where tan f = wT
I t i s w e ll known th at the d iffe r e n c e in phase between f i e l d in t e n s it y and
p o la r iz a tio n is always accompanied by energy adsorption ,
/ r a r e s u lt o f a
f i n i t e r e la x a tio n time we encounter ab sorption as w e ll as d is p e r sio n .
This phenomenon w i l l be considered la t e r .
The ^enerFl formula fo r the p o lp r I z e M llty wee shown "by Behye
to b e :
cC
w h e re
°
-
M2
i 8 th e p o l p r i z e b l l i t y d u e to d i s t o r t i o n end •£ -—
3kT
o rie n ta tio n .
i s t h e t due to
The meen moment wes shown to be
”
=
( ccO
*
+
(li,)
T h te e q u e t i o n msy b e o b t a i n e d by e d d ittg th e meen moment due to d i s t o r t i o n
t o t h s t c e l e u l e t e d f o r th e e x p r e s s i o n f o r th e meen moment d u e to o r i e n t a ­
tio n
/ e
' C o s ^ Z k T xtcosiy d/1
f i e i' c o s f / k T
dn
i s th e num ber o f m o le c u le s c o n f in e d to t h e s o l i d
mo =
w h e re Ae
F c o e ^ /ltT
s n * le d / I a c c o r d in g t o S o ltz m e n n 's le w , e n d yW c o s a? i s t h e com ponent o f
th e moment o f e m o le c u le i n th e d i r e c t i o n o f t h e f i e l d .
__
The e x p r e s s i o n
u 2 -i
i s i n t e g r a t e d ov-^r M l d i r e c t i o n s end m0i s fo u n d t o be
.
F o r high
f r e q u e n c i e s th e moment o f e p o l e r l i q u i d w i l l b e co m p le x end e f u n c t i o n o f
t h e f r e q u e n c y e s shown i n e q u a ti o n ( 1 2 ) .
B ie meen moment d u e t o o r i e n t s —
t io n th e n i s
Z
3kT
raU )
S u b s titu tin g th p t
vfI ue
I -
JL
iw r
(15)
o f th e p o l p r l z e b l l i t y due to d r i e n t e t i o n
i
it?IkT
U)
I
i t
iw r
w i t h e a u e t i o n ( 1*0 , t h e to t e l meen moment i s shown t o be
12
« (* • ♦
m d th e t o t ? ! p o l r r i z e b l l i t y
oC(w)
• 1 + L f )
= oC0 +
j!il
( 16 )
*
*
.
-L ^
'" U b s tlt u t i n » t h i s i n t h e e o u r t l o n f o r moI p r p o l a r i s a t i o n e s d e r i v e d by
M o s s o t t l w h ere I I s / v o g a d r o 'e n u m b er, <<the p o l s r l z e b i l i t y , G th e d i e l e c t r i c
c o n p t f n t , M th e m o l e c u l a r w e ig h t and d th e d e n s i t y o f t h e s u b s t a n c e .
t h e m o la r p o l a r i z a t i o n i s r e l a t e d to t h e d i e l e c t r i c c o n s t a n t by th e
C la u m lu e M o s s o t t i e o u - t l o n and i s t h e sum o f two te r m s .
The f i r s t i s
p a r t o f t h e p o l a r i z a t i o n due t o e l e c t r o n i c and a to m ic m o tio n s w i t h i n t h e
m o le c u le a l s o c a l l e d d i s t o r t i o n .
d i e l e c t r i c s w h e th e r p o l a r o r n o t .
i s th e
T h is p o l a r i z a t i o n i s p r e s e n t i n a l l
The second, term
a r t due to o r i e n t a t i o n o f d i p o le s ,
y
i s th e e l e c t r i c moment o f t h e
m o le c u le , k I s B o ltz m a n n 's c o n s t a n t , T i s t h e a b s o l u t e t e m p e r a t u r e «nd
T
i s t h e r e l a x a t i o n tim e f o r th e m o le c u le s .
A ssum ing M o s s o t t i 1r h y p o t h e s i s t o h o l d , we w i l l c o n s i d e r t h e connec­
t i o n b e tw e e n d i s p e r s i o n a n d a b s o r p t i o n .
I f t h e e q u a ti o n
(18)
is
s o lv e d f o r € one f i n d s :
- V I n s t e p d o f c h p r s c t e r l z l n * th e l i q u i d by <<„ e n d
e o n s tp n ts
end
^ ^ e re u se d .
3kT
, two d i e l e c t r i c
They p r e d e f i n e d by s e t t i n g H a l t s on
e q u a t i o n ( 18 ) w hen w * oo end w % o .
- I
M
r
k v IicCo
(w = oo)
Ji
d
=
ik 17 Ii f 0^ 0 +
3
V 0
f 2
( 20 )
- I
+
2
-tL J
3kT/
(w s O )
€ 0 t h e o p t l c p l d i e l e c t r i c c o n s t a n t , w i l l d e n o te t h e v ? lu e f o r € p t h ig h
f r e q u e n c y , end i s e q u r l to n 2 , w h e re n I s t h e in d e x o f r e f a c t i o n ,
w i l l be th e s t a t i s t i c s ! d i e l e c t r i c c o n s ta n t e t w a 0 .
end
U s in g t h e s e d e f i n i ­
t i o n s we d e f i n e P ( w)
H
d
(w)
t
- 1
1_
4
I + Iw T I
Cl + 2
„
€o - I
~ €n + 2
£o + 2
The d i e l e c t r i c c o n s t e n t e a e f u n c t i o n o f w i s th e n e x p r e s s e d :
4-
iw r
^l + 2
€
€0 + 2
=
<1 + 2
( 21)
+ 2
B u t, s c c o r d l n g to t h e f o r m e l t h e o r y o f t h e p r o p p g p ti o n o f l i g h t f o r e co m p le x
d i e l e c t r i c c o n s ta n t
€ =
r pnd
r 2 (I -
i K)2
( 22)
k p r e r e e l q u p n t l t i e s b e in g t h e o r d i n a r y in d e x o f r e f r a c t i o n , end
t h e p b s o r p t i o n in d e x , r e s p e c t i v e l y .
x —
The v e r i a b l e
+ 2
Co ^ 2
I e i n t r o d u c e d to p r e s e n t r pe e f u n c t i o n o f t h e f r e q u e n c y .
( 5 ) mpy b e shown t o b e e q u i v s l e n t to
The e q u p tio n
— 3® **
G1 + €0
?
1
rZ = 2
(2 3 )
I + x2
In th e i n t e r v a l x - O fro m r 2 =
x
-I
XeCO,
-f
Xt
t h e s q u a r e o f t h e r e f r a c t i v e in d e x ren%e
to r ? s € Q ,
The e b e o r r t i o n in d e x K h e a
p
maximum v a lu e f o r f r e q u e n c y w » iv e n b y th e
fo rm u la
______
WT=
t h e maximum v a lu e i s
2■ 1 / 4 ^
^l + 2
(24)
^ max
K -K
W[ + W0
(2 5 )
A t t h e c o r r e s p o n d in g f re q u e n c y
r2 =
i
(26)
F o r a c t u a l e x p e r im e n ts on a d s o r p t i o n , t h e r e s u l t s a r e o f t e n g iv e n i n te rm s
o f a p h a s e a n g le $ .
t h e c o n d e n s e r i s Ve
d i e l e c t r i c c o n s ta n t
I f t h e p o t e n t i a l d i f f e r e n c e b e tw e e n t h e p l a t e s o f
w h e re V i s v o l t a g e o r p o t e n t i a l d if f e r e n c e ,
€ i s co m plex ? n d i s shown a s
11
£ = €
11
£
i s c a lle d th e d i e l e c t r i c lo s s o r d i s s i p a t i v e f a c t o r ,
th e c h a r g e on one o f t h e p l a t e s ( o m i t t i n g c o n s t a n t s ) w i l l b e l
Q=
( 6 * -
i e " )
Velw t
th e p h a s e a n g le c a n b e d e f i n e d b y t h e e q u a t i o n :
Tan $
=
S
~~r
th e
- 39 G oing b p c k t o e q u a t i o n s ( $ ) Fnd ( 6 ) i t c p n b e s e e n t h e t :
Ii J+ /f ^ .p r j f
€o + 2
,
( f i
-
(27)
% )
(28)
B olton*"2 ) h s s shown t h e t by u s i n g O n s a g e r 1S e q u a t i o n :
( C l - C q )
(2 Cl +
C0 )
c irc le ,
o2
= I n s M"
Z 1 ( C 0 + 2)
P
,
I I
th e lo c u s o f p o i n ts o f ( € ' , € " )
w ith
p
(2 9 )
p a ra m e te r w r i e n e a r ly
i d e n t i c a l w i t h e c i r c l e g i v e n b y Debye w i t h th e l o c u s o f p o i n t s o f
( £ * , e ' ' ) and a p a r a m e t e r X.
T h e refo re X r w r
and t h e e q u a t i o n s f o r t h e
r e e l and Im a g in e r y p e r t o f t h e d i e l e c t r i c c o n s t a n t a r e :
(TO)
e ' = < = /^ l
€°
I 4* W2 T 2
11
6 =
(Cl - S o ) " /
I + w ^ rz
(T D
The d i e l e c t r i c l o s s f a c t o r v a r i e s w i t h t h e f r e q u e n c y a s shown I n e q u a t i o n
31.
At b o t h h i g h w h e re w »-^: and low f r e q u e n c i e s w h ere w « 3: t h e l o s s f a c t o r
a p p ro a c h e s s e r o .
I t h a s a maximum v a l u e when w =
T h is e q u a ti o n p r e d i c t s how t h e d i e l e c t r i c
w h e re
6
=
( ^ 1- ^ 0 )
l o s e w i l l d e p e n d on t h e s t a t i s ­
t i c a l an d o p t i c a l d i e l e c t r i c c o n s t a n t s .
F o r p u r e l i q u i d s , D ebye h a s shown t h a t t h e m o le c u le s a r e I n f l u e n c e d
b y two k i n d s o f f o r c e s .
F irs t,
th e m o le c u le s a r e e x p o s e d t o th e u s u a l
c o u p le due t o t h e e x t e r n a l f i e l d end s e c o n d , t h e r e e x i s t s a p o t e n t i a l
e n e rg y w h ic h a c t s to h o l d t h e m o le c u le s i n t h e i r I n s t a n t a n e o u s p o s i t i o n s
fix e d by th e ir surroundings.
Debye mssuaes th e t fo r p o t e n t ia l energy,
the sim ple approximation u « - E cos 6 where 6 |g the angle between the
a x is o f th e permanent e l e c t r i c moment end the instan taneous a x is fix e d by
the surroundings.
He has derived eq u ation s fo r the average moment in the
d ir e c tio n o f the f i e l d stren g th F where:
—
M2 JPelw t/?kT
(B z 0 )
I + J jl £
2 kT
. S f
=
^
F8w t Z 3
I-L x
I +
( B » i)
2 1
where 3 -
( z f
=
the in te r n a l f r ic t io n , where 7 i s the
inner f r i c t i o n constant fo r the liq u id , and B i s the b in din g energy.
So
th a t fo r a pure liq u id th e p o la r iz a tio n becomes
P (w) =
€ €+
I
2
I t i s seen that the tr a n s itio n from the ease o f th a t o f fr e e d ip o le s
to stro n g ly bound d ip o le s can be performed by rep la cin g the thermal energy
kT by the much la r g er energy ^ where B i s th e binding energy.
I t fo llo w s
then from th e formula fo r d i e le c t r i c lo s s e s and fo r d is p e r sio n e f f e c t th at
we have a t the same time a dim inishin g o f the d ip o le a c tio n to be observed
both in the d ie le c t r i c con stan t I t s e l f and in the lo s s e s .
energy i s a c tin g ju s t -i S i f the constant ^ -
The binding
8 rr>p* had been dim inished
and th is can be in terp reted by saying e it h e r that the v is c o s it y 7 i s le e s
than normal or th at the m olecular radius i s sm aller than would be expected .
—
I 1
X—
The d i p o l e moment o f t h e p u r e t e t r r e t h o x y t lte n lu m c e n be e x p e c te d
to b e l e s s f o r t h e p u r e l i q u i d t h e n t h e t f o r d i l u t e s o l u t i o n s .
o r l e n t e t l o n moment o f t e t r e e t h o x y t l t e n l u m
S in c e t h e
l a c e n s e d by r o t a t i o n o f t h e
e t h y l -;rour> s-bout th e c a r b o n oxygen b o n d . I t mpy b e t h a t no d e f i n i t e tim e
o f r e l » x p t l o n c a n be e x p e c t e d .
F o r m o n o c h l o r o t r l e t h o x y t l t n n l u m , on th e
o t h e r h a n d , w i t h th e T l - C l b o n d e r i g i d o n e , m g r e e t e r d i e l e c t r i c c o n s t a n t ,
e l e c t r i c m om ent, d i e l e c t r i c l o s s , t h a n t h a t f o r t e t r e e t h o x y t l t e n l u m m ig h t
be e x p e c te d .
— 42 —
XIV.
FBBPIRATIOH 0 £ COMPOUNDS
T a tr e e th o x y tlte n iu m
T h is compound was p r e p a r e d a c c o r d in g t o B i s c h o f f e n d A d k in s ^ ^ h y
t h e r e a c t i o n T lC l ^1 f hUpOCgH^ ---------- » - 7 1 ( 0 0 4 d e s c r i b e d by C row e.
m o is tu re ,
UNeOl.
The p r o c e d u r e i s
I f t h e p u r e l i q u i d i s a llo w e d t o come i n c o n t a c t w ith
i t h y d r o ly z e s fo rm in g t h e h y d r a t e d o x id e and e t h y l a l c o h o l .
lo n g e d e x p o s u r e to s i r ,
P ro ­
e v e n d r y s i r , p r o d u c e s p c h a n g e i n c o l o r from
c o l o r l e s s to y e ll o w , t o o r a n g e end f i n a l l y r e d .
D i s t i l l a t i o n a t re d u c e d
p r e s s u r e , u s i n g d e c o l o r i z i n g c h a r c o a l i n t h e C ls s s o n f l a s k , rem oves th e
c o lo r.
Monoc h l o r o t r l e t h o x y t i t a n i u m
(T lC l(O C gE g)^
T h is compound was p r e p a r e d a c c o r d in g t o J e n n in g s , W ardlsw and W a y ^ ^
by th e r e a c tio n s
Tl(O CgSg)U + CH3COCl ----------►T iC l(O C 2H g)^ + CH3 COOC2Hg
an d i s a l s o d e s c r i b e d b y C row e.
Ium .
An e n s l y s i e geve 2 1 .8 6 and 2 1 . 8 ?£ t i t s n -
% e t h e o r e t i c a l v a lu e i s 21.92% .
The c h l o r i n e a n a l y s i s i n d i c a t e s
1 6 . 37 » whereas t h e t h e o r e t i c a l v a lu e i s 1 6 . 23 %.
— 43 —
M .-
SUR^IEMT 0£
DIELECTRIC CORSTfWT Q l TETRfETHOXYTITf RIUM £T
VfRYIHO TEWRRf.CURES MD EREQim CIBS
The d i e l e c t r i c co n e t e n t o f p u r e Ti(O CgH li)^ h e e b e e n d e te r m in e d e t
f r e o u e n c i e e v p ry in ,^ by i n t e r v a l s o f 5 m e g a c y c le s , fro m 30 to 100 mega­
c y c l e s and t e m p e r a t u r e s r a n g i n g from 2 ^ ° C to -5 4 ° C .
fi d i s c u s s i o n o f t h e
d i f f i c u l t i e s e n c o u n te r e d i s g iv e n a n d m a th e m a tic a l e q u a t i o n s u s e d i n c a l c u ­
la tio n s d is c u s s e d .
(a)
f tvsa r e t u s U sed f o r
tea s u re m e n ts
The i n s t r u m e n t u s e d f o r m e a su re m e n ts o f t h e d i e l e c t r i c c o n s t a n t s
w as a Q m e te r ty p e 170A m a n u f a c tu r e d b y t h e B o o n to n R ad io C o r p o r a t i o n .
s c h e m a tic d ia g ra m o f t h e c i r c u i t ^
i s shown i n f i g u r e 5 .
A
The c i r c u i t
c o n s t a n t s a r e l i s t e d by num ber i n T a b le IV b e lo w .
T e b Ie I I .
C i r c u i t C o n s t a n ts f o r Q M e te r Tvoe 170-A
! R p sistora
i I . 24000/Uw
: 2 . 1000 a W
: 3.
1000 A |w
: 4 . 1000 a Iw
: 5 « 3 m e g .n i/ 3w
: 6 . 7500 n p o t 3w
: 7.
2 00 A Pot 3»
s 8.
i 9.
:10.
ill.
:12 .
ill.
il4 .
ti5 .
il6 .
il7 .
il8.
i! 9 .
:2 0 .
1000 A pot 3«
20000 A Dual Pot 8w
200 A p ot 3»
15000 A |w
24000 A |w
24000 A |w
40000niow
1200 n |w
25000 AlOw
3500A20w
0.8A2W
20000 nPot Iw
51%l/3*
I.
2.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Pp^Ldppsftrs
20 /Y f zero temp.
240 n t mica
2 k 0 r f t mice
240 yM/'f mica
510 [ t p t mica
510 P p f mica
240 p p f nica
Q, Tuning, A ir
Tubes
I . TVp ® 9002
2,
3,
4.
5.
6.
7.
Type
Type
Type
Type
TVpe
OS-VM-955
Q-VM-955
VR-105-30
VR-105-30
5 W 4M azda 4 7 -(6 v )
bpf.)
4/> f . ) E le c t r o ly t ic
4/M f.)
Osc. Tuning, A ir
Cx . Test Condenser
Inductors
I.
2.
3.
4.
5.
Lx .
Osc.
Osc.
Osc.
Pwr.
Pwr.
Orid
Coupling
P la te
Choke
T ransf.
Test C oil
;
1
t
:
1
1
i
i
i
I
t
1
i
:
t
t
:
:
I
t
:
_L
3
Q C o n d e n s e r U n it
O s c i l l a t o r U n iT
/?i7
- vv*a»Ciciri ■
2 3 0 V.
P ow er U n it
SCHEMATIC DRAWIKU OF Ov METER CIRCUIT
The C; v o l t m e t e r I s c a l i b r a t e d d i r e c t l y
I n Q fro m 8 0 t o 3 0 0 .
Ih e
" M u l t ip l y Q b y " m e te r I s c a l i b r a t e d fro m x I to x b-, h e n c e t h e t o t a l r a n g e
I s from 80 t o 1 2 0 0 .
The a c c u r a c y o f t h e d i r e c t r e a d i n g m e a su re m e n ts o f
c i r c u i t Q, ( f o r Q. v o l t m e t e r r e a d i n g s b e tw e e n 100 and 3 0 0 ) i s a p p r o x im a te ly
p l u s o r m in u s 103 up to 100 me. and d e c r e a s e s w ith i n c r e a s i n g f r e q u e n c y .
■Tie r a n g e o f t h e c a p a c i t a n c e o f th e Q c o n d e n s e r i s 1 1 -6 0
i n u n i t p o f /^yuf.
/'/■f c a l i b r a t e d
A c c u ra c y i s g e n e r a l l y f 2> on c a p a c i t a n c e r e a d i n g s .
The
p o w er s u p p ly i s a s e l f c o n t a i n e d d u e l v o l t a g e t r a n s f o r m e r w i t h a c h a n g e ­
o v e r s w itc h w h ic h p r o v i d e s o p e r a t i o n on e i t h e r 1 1 0 -1 2 0 v o l t s ,
o r 2 2 0 - 2b0 v o l t s ,
$ 0 -6 0 c y c l e s .
120 v o l t s f o r t h i s w o rk .
50-60 c y c l e s
The s w i tc h i s s e t f o r o p e r a t i o n a t 1 1 0 -
T h is in s t r u m e n t i s t h e b e s t a v a i l a b l e o f i t s
ty p e and i s r e a s o n a b l y a c c u r a t e f o r t h i s w o rk .
The c e l l u s e d i s shown i n f i g u r e 6 .
w i t h a c o o l i n g s y s te m d r i l l e d
th e c o n d e n se r.
rig id ly
I t c o n s is ts o f a b ra s s ja c k e t
i n th e j a c k e t w a l l s .
Two b r a s s p l a t e s form
The l a r g e r p l a t e i s t h e h i g h p o t e n t i a l and i s f a s t e n e d
to t h e c e l l w i t h a c e ra m ic i n s u l a t o r .
A b rass s tr ip
i n a b a n a n a p l u g c o n n e c ts i t t o th e % m e t e r t e r m i n a l .
te rm in a tin g
The s m a l l e r p l a t e
i s f a s t e n e d t o a V e r n ie r c a l i p e r w h ic h i n t u r n i s f a s t e n e d t o t h e c e l l
d ire c tly .
A b a n a n a p l u g c o n n e c ts th e c e l l t o th e g ro u n d p o t e n t i a l .
V a r i a t i o n o f t h e c a l i p e r r e a d i n g s g i v e s a c o r r e s p o n d in g c h a n g e i n th e
c e l l c a p a c ita n c e .
F o r t h i s w o rk , t h e c a l i p e r w as h e l d r i g i d w ith t a p e .
The c e l l i s c o v e r e d w i t h a m ach in ed p i e c e o f b r a s s w h ic h f i t s
m in im iz e s c o n t a c t w i t h m o is t a i r .
s n u g ly and
— 46
w ater c ir c u la tio n
c ir c u la tio n
o u t le t s
CROSS SSCTTON VIEW OS THE CELL USES EOR MEASURING DIELECTRIC
CONSTANTS OE LIQUIDS AT RADIO FREQUENCIES
F ig u re 6
V
—hy —
Two t y p e s o f in d u c tr -a c e c o l l s w e re u s e d .
7.
B ie s e p r e shown I n f i g u r e
The f i r s t ty p e msde c o n s i s t e d o f e p l a c e o f t
In ch c o p p e r t u h ln ^ "bent
I n t h e s h e p e o f s h o r s e s h o e pad s h i e l d e d w i t h c o p p e r s h e e t b e n t to fo rm e
c y lin d e r.
One end w ss s e e l e d w ith e p i e c e o f c o p p e r end t h e o t h e r w ith
I n c i t e , th r o u g h w h ic h t h e c o l l t e r m l n e l s p a s s e d .
The o t h e r ty p e wes rasde
fro m c o e x l e l c a b l e o f 3 /8 In c h o u t e r d i a m e t e r w hich w as s h o r t e d w ith
c o p p e r p l a t e e t one e n d .
The n a t u r e o f t h e c o n s t r u c t i o n o f t h e c a b le p r o ­
d u c e d an i n h e r e n t s h i e l d i n g , q u i t e s u f f i c i e n t f o r t h i s p u r p o s e .
w e re made v p r y tn g i n l e n g t h ,
m e g a c y c le s .
S ix c o i l s
to c o v e r t h e r a n g e o f f r e q u e n c y fro m 30-120
The t h r e e l o n g e r c o l l s c o v e r i n g th e r a n g e fro m 30 to 80 me,
w e re o f t h e f i r s t ty p e d e s c r i b e d a b o v e , b e c a u s e a t t h o s e f r e q u e n c i e s t h o s e
c o l i e g a v e t h e h i g h e s t Q.
c a b l e s f o r t h e r? n g e
85
C o n v e r s e ly , t h e t h r e e c e l l s made from c o a x i a l
to 120 me g av e t h e h i g h e s t v a l u e s o f
q.
The
a b s o l u t e v a l u e s o f i n d u c t a n c e f o r t h e c o i l s w ere n o t d e te r m i n e d .
Tne pump w h ic h was u s e d t o f o r c e t h e r e f r i g e r a n t t h r o u g h t h e c e l l
w as a standard C h e v r o le t o i l pump w h ic h w as po w ered b y e l / 3 h o rs e p o w e r
m o to r .
I t g av e v e r y s a t i s f a c t o r y r e s u l t s e v e n e t t e m p e r a t u r e s below
-5 0 °C .
The r e f r i g e r a n t w as a. m ix tu r e o f a c e t o n e and d r y i c e w h ic h p r o v e d to
b e th e l e a s t v i s c o u s l i q u i d a t t e m p e r a t u r e s to - 70 °C .
(b )
M ethods o f C a l c u l a t i o n
A c c o rd in g to B r o t h e r t o n ^ ,
i n a- p r a c t i c a l c a p a c i t o r ,
su c h a s t h e
c e l l u s e d f o r m e a s u re m e n ts , t h e c a p a c i t a n c e form s a s e r i e s c i r c u i t w i t h
th e in d u c ta n c e .
> s im p le d ia g ra m o f t h e c i r c u i t i s shown I n f i g u r e 8 .
48 -
CFUSS SECTION VIEW OF THE TYPES OF COILS USED WITH THE Q METER
F ig u re 7
- 49 -
Lead ln d u c tp n c e (L )
E q u t v p le n t p p r e l l e l r e s l s t e n c e
c o r r e s p o n d in g t o c o n d u c te n c e o f
d ie le c tric
Lepd B e s l s t e n c e
r
I d e e l C e p a c ite n c e (C _)
fig u re 8
The Im p ed an ce o f t h i s c i r c u i t w i l l h e :
z = r +
'
1
+ lv L
w h ere r i s t h e l e a d r e s i s t a n c e , g i s t h e c o n d u c ta n c e o f t h e d i e l e c t r i c , w I s
2 n f w h e re f
i s t h e f r e q u e n c y , Cg i s t h e i d e a l o r a c t u a l c a p a c i t a n c e , L i s
th e in d u c ta n c e .
I n p r a c t i c e g ' i a much s m a l l e r th a n V2Cp ^ and th e e q u a t i o n
re d u c e s to :
Z = r +
+ i f = l _ f wLj
The p o s i t i v e r e a c t a n c e f o r th e i n d u c t a n c e ^
re d u c e s th e n e g a tiv e
r e s i s t a n c e a p p e a r in g a c r o s s t h e t e r m i n a l s b y th e am ount e q u a l t o wL.
e ffe c t of th is
i n d u c t i v e e le m e n t i s ,
c a p a c ita n c e a s th e fre q u e n c y r i s e s .
The
t h e r e f o r e , to i n c r e a s e t h e a p p a r e n t
- =IO Che r e a c t a n c e
meR e u re d f o r th e c i r c u i t , p t t h e t e r m i n a l s ,
Ie
- xCe = “ xCp + xI,
s i n c e i n t h e r a n g e b e lo w th e r e s o n a n c e f r e q u e n c y th e c a p a c i t i v e r e a c t a n c e
i s n e g a tiv e in s ig n .
Xr
i s e q u a l to
^
>
Xn
an d X7 = wL
s —I —
w h e re Ca r e p r e s e n t s t h e i d e a l o r a c t u a l c a p a c i t a n c e and Ce t h e e f f e c t i v e
o r m e a su re d c a p a c i t a n c e .
So t h a t t h e e q u a t i o n c a n b e w r i t t e n :
—
I
%
—
I
+
wL
wCe
wCa
M u lt i p l y i n g th r o u g h b y wCe an d wCa i t becom es t
- wCa - - wCe + wCa wCe wL
T h is e q u a t i o n c a n b e r e a r r a n g e d to b ecom e:
Ca — Ce
CaCe
“ I + Lwz Ce
To u s e t h i s e q u a t i o n to f i n d t h e a c t u a l c a p a c i t a n c e , t h e I n d u c ta n c e
s ra s t f i r s t b e c a l c u l a t e d b y some o t h e r m ea n s.
S in c e t h e r e a r e two unknow ns,
two e q u a t i o n s a r e n e c e s s a r y t o o b t a i n t h e i n d u c t a n c e .
Two s e t s o f c o n d i­
t i o n s f o r t h e same e q u a t i o n may s u f f i c e , p r o v i d i n g t h e unknow ns re m a in
c o n s ta n t o v e r th e ran g e c h o se n .
I f m e a s u re m e n ts a r e t a k e n a t two d i f f e r ­
e n t f r e q u e n c i e s , w h ic h we w i l l d e s i g n a t e a s f ^ and f ^ ,
t h e two e q u a t i o n s
w ill be:
Ca -
Cei
I 4 Ce1Jw1Z
Ca s
------P — ,
I I* CegliWg^"
- 51 o r re p rrp n ^ in " !
Cs
^^ — Ce^ + Cs % O
CsCog
lM p ' ■■ CQp + Cs s O
d i v i d i n g Tjy Ce we o b t s l n s
Ce^
- Ce^
4 - 1 .0
Ce^ Iwp* — Cep
■+ I — 0
^
^
* Ce
!Hxe s o l u t i o n o f L may b e o b t a i n e d u s i n g d e t e r m i n a n t s t h u s :
— Ce^
I
- Ce2
I
I- s»
■...... — .... .. ............ .... .
I _
C e^i
— Ce^
Ce2^2
— Cep
Ce? - C e i ________
CepCeiWg^ - CepCe^wi^
Cep - Cei
;
~
Ce2Ce1 4 Ti 2 Cf2 - f ^ )
I _
w h ere f i s t h e f r e q u e n c y .
The e x a c t v a l u e f o r L c a n n o t b e o b t a i n e d u s i n g
t h i s e q u a t i o n , s i n c e i t a p p e a r s t h a t t h e in d u c ta n c e o f t h e c e l l and l e a d s
d o es v ^ ry w ith th e fre q u e n c y .
o f in d u c t a n c e i s r e d u c e d .
H ow ever, i f
s h o r t l e a d s = re u s e d t h e am ount
The in d u c ta n c e u s e d in t h e s e m e a su re m e n ts w»e
o b t a i n e d by c a l c u l a t i n g v a l u e s f o r a d i f f e r e n c e o f f i v e m e g a c y c le s , fro m
30 to 120 m e g a c y c le s , t h e n o b t a i n i n g v a l u e s f o r a d i f f e r e n c e o f 10 mega­
c y c l e s o v e r t h e same r a n g e .
R e p e a tin g t h e p r o c e s s u s i n g a d i f f e r e n c e o f
15 * 2 0 , 2 5 » 30 snd. on u p to 90 m e g a c y c le s , end th e n a v e r a g in g a l l o f t h e
v a l u e s g a v e a r e s u l t o f a p p r o x im a te ly 5 x 10“ ® h e n r i e s .
T h is v a l u e , when
- 52u p e d In t h e e q u a t i o n f o r p c t u s l c e p p c t t p n c e , gpve r e s u l t s f o r Cg w h ich
w e re i n f e l r p » re e m e n t.
T 'p h le s Vt VI end V II » iv e t h e d a t e end r e s u l t s
o f th e c s lc u lf ltlo n o f th e s e tu p I c a p a c ita n c e f o r th e d i e l e c t r i c s , a i r ,
b e n z e n e a n d h e x e n e o v e r t h e re n ^ e o f f r e q u e n c i e s fro m 3 0 -1 0 0 m e g a c y c le s
a t 25°C .
The r e s u l t s p r e shown p l o t t e d a g a i n s t f r e q u e n c y i n f i g u r e 9 .
- 53 TAbLW V,
Actual Crmecltence o f the C e ll w ith g.lr rs the D ie le c t r ic
— L-----------------------£»—
I ______________ Ca
10” 8
1 3 .3 1 6
31
13.6 6 1
3 .7 9 x 10 '
35
1 3 .8 2 5
4 .8 4
13 .3 7 7
40
1 4 .0 1 8
6 .3 2
1 3 .4 2 3
45
1 3 .8 0 9
7 .9 9
1 3 .0 8 7
50
1 3 .9 4 3
9 .8 7
1 3 .0 4 5
55
1 4 .3 3 2
1 1 .9 4
1 3 .2 0 2
60
1 4 .4 9 8
1 4 .2 1
1 3 .1 4 4
65
1 4 .1 1 0
16.68
1 2 .6 2 4
70
1 4 .4 8 0
1 9 .3 5
1 2 .7 0 1
75
1 4 .7 1 4
2 2 .2 1
80
1 5 .0 9 3
2 5 .2 7
12.676
85
1 5 .4 9 5
2 8 .5 2
12.690
75
1 4 .3 8 3
2 2 .2 1
1 2 .4 0 2
80
1 4 .6 8 1
2 5 .2 7
1 2 .3 8 4
85
1 5 .0 3 2
2 8 .5 2
1 2 .3 7 8
90
1 5 .5 6 1
3 1 .9 8
1 2 .4 6 1
95
1 5 .9 3 6
3 5 .6 3
90
1 4 .6 7 9
3 1 .9 8
1 1 .8 8 9
95
1 5 .2 5 8
3 5 .6 3
1 1 .9 9 7
100
1 5 .7 2 5
3 9 .4 8
12.000
5 X
5 x IO *8
5 x IO *8
1 2 .6 4 7
1 2 .4 1 2
— $4 —
T A bL E I I .
A a to f-I C ^ ccltf-T ice
_____£_____ ________
q£
i h e C e l l w ith B enzene ^
G*...........
J^ g , D i e l e c t r i c
J,
5 x 1 0-8
Ca
31
1 9 .4 5 9
3 .7 9 x IO^
35
1 9 .6 7 9
4 .8 4
1 8 .7 8 5
ho
2 0 .0 2 5
6.32
1 8 .8 3 3
45
1 9 .8 1 5
7 .9 9
I 8 . 36 I
50
20.3 1 6
9 .8 7
1 8 .4 6 4
55
2 0 .8 0 0
1 1 .9 4
1 8 .5 0 2
65
2 0 .8 5 3
1 6 .6 8
70
2 1 .6 7 6
1 9 .3 5
1 7 .9 1 8
75
2 2 .W
2 2 .2 1
1 7 .9 6 3
80
2 3 .3 1 6
2 5 .2 7
1 8 .0 1 0
85
2 4 .3 0 3
2 8 .5 2
1 8 .0 4 8
1 8 .7 6 7
6o
5 x 10-8
1 7 .7 6 4
2 2 .2 1
75
80
22 .6 6 0
2 5 .2 7
1 7 .6 1 6
85
2 3 .6 9 3
2 8 .5 2
1 7 .7 0 9
90
2 4 .8 6 4
3 1 .9 8
1 7 .7 9 0
95
26.2 2 1
3 5 .6 3
90
2 3 .5 4 9
3 1 .9 8
1 7 .1 0 8
95
2 4 .9 5 8
3 5 .6 3
1 7 .2 7 7
100
2 6 .4 9 6
3 9 .4 8
1 7 .3 9 7
5 x IQ -8
1 7 .8 7 3
- 55 T A B ia V I I .
Actual C enecitpace o f the C e ll w ith Hexene ee the D ie le c tr ic
- C e -
___ L_____
31
1 7 .7 9 0
5
35
1 7 .8 6 7
4 .8 4
1 7 .1 2 7
40
1 8 .2 7 3
6 .3 2
1 7 .2 7 6
45
1 8 .1 0 5
7 .9 9
1 6 .8 8 4
50
1 8 .5 6 9
9 .8 7
1 7 .0 1 1
55
1 9 .0 0 7
1 1 .9 4
1 7 .0 7 0
6o
1 9 .4 4 2
1 4 .2 1
1 7 .0 6 7
65
1 8 .9 5 2
16.68
70
1 9 .7 7 8
1 9 .3 5
16.601
75
20.313
2 2 .2 1
1 6 .5 7 4
80
2 1 .0 5 7
2 5 .2 7
I6.63I
85
22.012
28.52
1 6 .7 5 3
75
1 9 .5 9 7
22.21
16.395
80
2 0 .3 7 7
2 5 .2 7
1 6 .2 0 4
85
2 1 .3 5 9
2 8 .5 2
1 6 .3 7 2
90
22.322
3 1 .9 8
95
2 3 .4 6 5
3 5 .6 3
1 6 .5 4 8
90
2 1 .2 9 2
3 1 .9 8
1 5 .8 8 4
95
2 2 .4 3 3
3 5 .6 3
16.028
100
2 3 .6 3 4
3 9 .4 8
16.116
x
io*8
5 x IO "8
5 x IO"8
. Ga
1 7 .2 1 0
16.365
1 6 .4 5 1
ACTUAL CAPACITANCE OP A IR , BENZENE, AND HEXANE PLOTTED AGAINST
FREQUENCY IN MEGACYCLES AT 2 5 ° C
20
O
A ir
?
B enzene
•
H exane
?
©
A c tu a l C a p a c ita n c e
17
9
-
9
<9
'
—O
18
0
'
'
I
VJX
CA
I
O
O
O
O
13
O
O
— O
■O--------O
-o—
O
11
10
I
30
bo
I
I
I
I
b5
50
55
50
I
I
,1
65
70
F re q u e n c y
I
75
80
I ■ I
85
90
I
I
95
100
- 57The c e l l c o n s t a n t w es o b t p ln e d I n t h e f o ll o w i n g m p n n er:
The t o t p l c a p a c i t a n c e o f t h e c e l l w i t h t h e d i e l e c t r i c w i l l "be e q u a l to
t h e eum o f t h e l e a d c a p a c i t a n c e and t h e p r o d u c t o f th e d i e l e c t r i c con­
s t a n t o f t h e d i e l e c t r i c and t h e c a p a c i t a n c e b e tw e e n t h e two p l a t e s an d
t h e _ ;la te s and c e l l .
I f a i r i s t h e d i e l e c t r i c , Cp = C0+ £s C.
c a lle d th e c e l l c o n s ta n t.
C I s a ls o
I f a n o n - p o l a r l i q u i d o f known d i e l e c t r i c
c o n s ta n t I s p la c e d in th e c e l l ,
th e t o t a l c a p a c i t a n c e becom es e q u a l to
t h e sum o f t h e l e a d c a p a c i t a n c e and t h e p r o d u c t o f th e d i e l e c t r i c c o n s t a n t
o f th e known l i q u i d a n d t h e c e l l c o n s t a n t .
T hus:
Cx = C0+ €xC .
I f th e
e q u a t i o n f o r t h e c a p a c i t a n c e o f t h e c e l l w i t h a i r Ie s u b t r a c t e d fro m t h e
e q u a t i o n f o r t h e c a p a c i t a n c e o f t h e c e l l w i t h th e known l i q u i d i t i s
Ca
and
x =
w i t h a d i e l e c t r i c c o n s t a n t o f 2 .2 7 3
(Cr -
C,+e*c)
C
U s in g p u r e b e n z e n e
25 °C , th e c e l l c o n s t a n t was c a l c u ­
l a t e d o v e r t h e ra n g e o f f r e q u e n c i e s fro m 3 0 -1 0 0 me.
The r e s u l t s o f th e
c a l c u l a t i o n a r e shown i n T a b le V I I I an d e r e shown p l o t t e d a g a i n s t f r e q u e n c y
in F ig u re 1 0 .
A g a in t h e v a l u e s a r e n o t e x a c t l y c o n s t a n t , b u t a r e I n c l o s e a g re e m e n t
i n m ost c a s e s .
The e v e r? ;e v a lu e is h .1 9
— 5® ~
TABLE V I I I .
C e l l C o n s ta n t
f
"W
~TT
"IT"
“ SB
I
4.282
31
18.767
13.316
35
18.785
13.377
4.248
40
18.833
13.423
4.250
45
18.361
13.087
4.143
50
18.464
13.045
4.257
55
18.502
13.202
4.163
65
17.764
12.624
4.038
70
17.918
12.701
4.099
75
17.963
12.64?
4.176
80
18.010
12.676
4.190
65
18.048
12.690
75
______
80
17.616
12.384
4.110
85
17.709
12.378
4.188
90
17.790
12.461
4.186
95
17.873
12.412
4.290
90
17.108
11.889
4.100
95
17.277
11.997
4.148
100
17.397
12.000
4.240
2.273
VU
Cg
i s p c t u p l c e p e c i t e n c e o f B enzene
i s p c tu e l c e p e c ite n c e o f p i r
2.273
I
4.209
C e l l C o n s te n t
CELL CONSTANT PLOTTED AGA INST EBEOTTENCY IN MEGACYCLES
65
70
F re q u e n c y
- 60 (c)
D i f f i c u l t i e s E n c o u n te r e d
When t h i s w ork wee b e g u n t h e Q m e te r h e d j u s t e r r I v e d from th e f a c t o r y
end v e r y l i t t l e
wee known o f I t s l i m i t a t i o n s .
T h e re w e re no c o i l s eve 11-
e b l e w h ic h w o u ld g iv e e am?I I enou^x I n d u c ta n c e f o r t h i s w o rk , so t h a t a l l
t h e c o i l s h a d t o b e m ade.
I t was fo u n d t h a t c o p p e r t u b i n g o f $ In ch
d i a m e te r g a v e h i g h % m e te r r e a d i n g s o v e r t h e ra n g e o f f r e q u e n c i e s u s e d .
The Q. v a l u e s , h o w e v e r, d e c r e a s e d w ith i n c r e a s i n g f r e q u e n c y .
C a lc u la tio n s
b a s e d on r e a d i n g s o b t a i n e d f o r c a p a c i t a n c e o f th e c e l l w i t h d i e l e c t r i c
u s i n g u n s h i e l d e d c o i l s d i d n o t show good a g re e m e n t.
The d e v i a t i o n w as
th o u g h t t o b e c a u s e d b y a c a p a c i t a n c e b e tw e e n th e u n s h i e l d e d c o i l and t h e
c e ll.
H ow ever, th e d e v i a t i o n s p e r s i s t e d e v e n a f t e r s h i e l d i n g t h e c o l l s .
The i n d u c t a n c e , p r e v i o u s l y c a l c u l a t e d u s i n g th e e q u a t i o n d e r i v e d on p a g e
U ? w i t h a f r e q u e n c y d i f f e r e n c e o f 5 m e g a c y c le s o n l y , was r e c a l c u l a t e d i n
t h e m an n er d e s c r i b e d on p a g e h 8 .
T h is seem ed to b r i n g t h e v a lu e s w i t h i n
th e r a n g e o f e x p e r i m e n t a l e r r o r .
The c u r v e s shown i n F i g u r e 9 w e re draw n
t o show t h e e f f e c t f o r e a c h c o i l u s e d .
No e x p l a n a t i o n h » s b e e n fo u n d f o r
t h i s d e v i a t i o n from w h a t s h o u ld b e a c o n ti n u o u s s t r a i g h t l i n e o r a sm ooth
c u rv e .
I t w as th o u g h t t h a t t h e d e v i a t i o n m ig h t b e due t o
th e ty p e o f c o i l
u s e d , b u t c o i l s made fro m c o a x i a l c a b l e w h ic h a r e i n h e r e n t l y s h ie l d e d
made no d i f f e r e n c e .
I t i s p o s s ib le t h a t th e in te r n a l le a d s , th a t i s ,
th o se w ith in th e in s tru m e n t a re th e c a u s e , b u t t h a t p o s s i b i l i t y h as n o t
b e e n i n v e s t i g a t e d th o r o u g h l y a s y e t .
(d )
D i e l e c t r i c C o n s ta n t o f T ita n iu m T e t r a e t h v l a t e in. t h e ra n g e o f f r e ­
q u e n c ie s fro m 10 t o 95 m e g a c y c le s a t v a r i o u s t e m p e r a t u r e s
The d i e l e c t r i c c o n s t a n t i s c a l c u l a t e d u s i n g t h e e q u a t i o n :
— 6l —
c x - c S +€PC
C
6
X
g i v e n oa p rg e 57.
E e e u l t e o b t a i n e d f o r c & l c u l r t i o n s u s i n g d s t s o b t a i n e d e t 25°C a r e
g iv e n in T e b le IX, and shown p l o t t e d a g a i n s t f r e q u e n c y i n F i g u r e 1 1 .
The r e s u l t s a t 25 ®C i n d i c a t e t h a t a n o m a lo u s d i s p e r s i o n d o e s n o t a p p e a r
w i t h i n t h e f r e q u e n c y r a n g e 30-100 m e g a c y c le s a t t h a t t e m p e r a t u r e .
I t w as fo u n d t h a t t h e compound becom es v e ry v i s c o u s a t low te m p e ra ­
t u r e s by C row e.
I t i s e known f a c t t h a t f o r l i q u i d s e x h i b i t i n g a h ig h
v i s c o s i t y , t h e a n o m a lo u s d i s p e r s i o n o c c u r s a t lo w e r f r e q u e n c i e s t h a n i n
a l i q u i d o f lo w e r v i s c o s i t y .
K e e p in g t h a t i n m ind, m e a su re m e n ts w ere
made a t t e m p e r a t u r e s o f 6 °C , -3 0 ° C , - 4 3 0C and - 5 4 ° C , u s i n g th e c o o li n g
a p p e r a tu s d e s c r i b e d on p a g e 4 7 .
The te m p e r a t u r e v a r i a t i o n was
t I0 at
6 °C and i ?°C a t lo w e r t e m p e r a t u r e s .
R e s u l t s o f t h e c a l c u l a t i o n s a r e g i v e n in T a b le s X, X I, X II and
X III.
The r e s u l t s a r e shown p l o t t e d a g a i n s t f r e q u e n c y i n F i g u r e s 1 2 ,
1 3 , 14 and 1 5 .
F ig u r e 15 show s a d e f i n i t e d e c r e a s e o f t h e d i e l e c t r i c
c o n s t a n t u n t i l t h e f r e q u e n c y 55 me w as r e a c h e d a t w h ic h f r e q u e n c y i t
i n c r e a s e s s h a r p l y u n t i l t h e v a lu e o b t a i n e d a t o t h e r t e m p e r a t u r e s i s a g a i n
m a in ta in e d .
I f t h e d e c r e a s e shown was an o m alo u s d i s p e r s i o n , o c c u r r i n g
a t t h a t low f r e q u e n c y a t - 5 4 ° C , i t s h o u ld a l s o a p p a r e n t l y a p p e a r a t a
h ig h e r fre q u e n c y a t
3° C .
•o f u r t h e r m e a s u re m e n ts w ere p o s s i b l e , h o w e v e r, d u e to f a i l u r e o f
t h e c i r c u l a t i n g s y s te m .
- 62 -
TfBia
U
-
D i e l e c t r i c C o n s ta n t o f Tl(O C ^H ^)^ P t ?^°C
_____
f .......
c Ti
T T "
~T ~
4 .1 9 3
e Ti
I
31
2 4 .8 0 3
1 3 .3 1 6
35
2 4 .9 4 6
1 3 .3 7 7
3.759
40
2 4 .9 6 7
1 3 .4 2 3
3 .7 5 3
45
2 4 .4 7 3
1 3 .0 8 7
3 .7 1 5
50
2 4 .6 4 3
1 3 .0 4 5
3 .7 6 6
55
2 4 .6 9 8
1 3 .2 0 2
3*742
65
2 3 .9 7 8
1 2 .6 2 4
3 .7 0 6
70
2 4 .1 1 6
1 2 .7 0 1
75
2 4 .2 1 ?
1 2 .6 4 ?
3 .7 5 9
75
2 3 .8 5 1
1 2 .4 0 2
3 .7 3 0
50
2 3 .9 9 0
1 2 .3 8 4
3 .7 6 8
65
2 4 .2 1 3
1 2 .3 7 8
3 .8 2 3
90
2 3 .6 4 9
1 1 .8 8 9
3 .8 0 5
95
2 4 .0 0 3
1 1 .9 9 7
3 .8 6 3
4 .1 9 3
C«p^ f Ctttal cap p clten ce o f te tr s e th o s y tltp n lu a
I
3 .7 4 0
3 .7 2 3
D i e l e c t r i c C o n e ts n t
DIELECTRIC CONSTANT O f TETRAETHOXITITANIUM PLOTTED AGAINST FREQUENCY IN MEGACYCLES AT
F requ en cy
25° C
- 64 TfBLE I .
D i e l e c t r i c C o n s ta n t s i t T i ( QCgffg)>t e t 6 ° C
f
Ct i
~~cr~
~TT~
£i
31
25 .0 3 2
1 3 .3 1 6
4 .1 9 3
I
35
2 5 .1 3 5
13.377
3 .8 0 4
40
2 5 .1 8 2
13.623
3 .8 0 4
45
2 4 .5 7 3
13.0 8 7
3 .7 3 9
50
26.7 0 2
13.045
3 .7 8 0
55
2 6 .7 2 3
13.202
3 .7 4 8
65
2 4 .1 5 1
1 2 .6 2 4
3 .7 4 9
70
2 4 .6 1 8
1 2 .7 0 1
75
2 4 .6 6 2
1 2 .6 4 ?
3 .8 1 3
75
2 3 .9 2 6
1 2 .4 0 2
3 .7 4 8
80
2 4 .0 6 6
1 2 .3 8 4
3 .7 8 1
85
2 4 .2 3 6
1 2 .3 7 8
3 .6 2 8
90
2 3 .5 9 6
1 1 .8 8 9
3 .7 9 2
95
2 3 .9 8 5
1 1 .9 9 7
3 .8 5 9
4 .1 9 3
I
. .
g T l ...
3 .7 9 4
3 .7 9 4
— 65 *»
TABUS X I.
D i e l e c t r i c C o n s tM it o f TiCOCgH^)i, e t -1 0 °C
f
----------c— r -
c Ti
€a
e Hi
31
2 4 .8 1 6
1 3 .3 1 6
35
2 4 .9 4 9
1 3 .3 7 7
3.7 6 0
Uo
2 4 .6 6 8
1 3 .4 2 3
3.7 3 0
L5
2 4 .6 1 0
1 3 .0 8 7
3 .7 4 8
50
2 4 .6 5 0
1 3 .0 4 5
3 .7 6 3
55
2 4 .7 1 4
13.2 02
3 -7 4 6
65
2 4 .0 1 3
1 2 .6 2 4
3 .7 1 ?
70
2 4 .2 0 9
1 2 .7 0 1
75
2 4 .3 8 8
12*647
3 .8 0 0
75
2 3 .8 7 3
1 2 .4 0 2
3 .7 3 7
60
2 4 .0 7 1
1 2 .3 8 4
3 .7 3 7
65
2 4 .3 4 2
12.3 78
3 .8 5 3
90
23.883
1 1 .8 8 9
3 .8 6 0
95
2 4 .2 9 1
1 1 .9 9 7
3 .9 3 2
4 .1 9 3
4 .1 9 3
I
I
3 .7 4 3
3 .7 4 5
- 66 —
TABLSi X I I .
D i e l e c t r i c C o n s ta n t o f T l ( O C ^ ) 1, e t - 4 l° C
f
tiT i
31
2 4 .6 1 4
35
r
1 3 .3 1 6
c
4 .1 9 3
....
£ a.........
I
3 .6 9 9
1 3 .3 7 7
——— -
Uo
2 4 .7 2 2
1 3 .4 2 3
3 .6 9 5
L5
2 4 .2 9 3
1 3 .0 8 ?
3 .6 7 3
50
2 4 .4 7 3
1 3 .0 4 5
3 .7 2 5
55
2 4 .^ 9 3
1 3 .2 0 2
3 .6 9 3
65
2 3 .8 4 1
1 2 .6 2 4
3 .6 7 5
70
2 4 .0 5 7
1 2 .7 0 1
75
2 1 .1 6 4
1 2 .6 4 ?
75
2 3 -7 3 3
1 2 .4 0 2
3 .7 0 2
80
2 3 .9 2 0
1 2 .3 8 4
3 .7 5 1
85
2 4 .2 8 2
1 2 .3 7 8
3 .8 3 9
90
2 3 .7 0 0
1 1 .8 8 9
3 .8 1 7
95
2 4 .0 2 4
1 1 .9 9 7
3 .8 6 8
4 .1 9 3
I
3 .7 0 8
—
67
table
—
xin .
D i e l e c t r i c C o n s ta n t o f Tl(O C *H^)% a t - eM 0 C
f
C$ i
—
cI —
:
C
A
eSi
31
2 4 .6 2 8
1 3 .3 1 6
35
2 4 .6 9 5
13.377
3 .6 9 9
UO
2 4 .6 9 8
13.423
3 .6 8 9
U5
2 4 .1 5 3
1 3 .0 6 7
3 .6 3 9
50
2 3 .3 2 4
13.0 4 5
3 .4 5 1
55
23*414
13 .2 0 2
3 .4 3 5
65
23.8 6 5
1 2 .6 2 4
3 .6 0 6
70
2 4 .0 1 5
12 .7 0 1
75
2 4 .1 5 1
1 2 .6 4 7
3 .7 4 4
75
2 3 .6 6 9
1 2 .4 0 2
3 . 68 ?
80
2 3 .8 8 2
1 2 .3 8 4
3*742
65
2 4 .1 2 1
1 2 .3 7 6
3 .8 0 1
90
2 3 .7 2 1
1 1 .6 8 9
3 .8 2 2
95
2 4 .1 3 3
1 1 .9 9 7
3 .8 9 4
4 .1 9 3
4 .1 9 3
I
I
3 -6 9 8
3 .6 9 8
DIELECTRIC CONSTANT OE TETRAETHOXYTITANIUM PLOTTED AGAINST FREQUENCY IN MEGACYCLES AT 6°C
5 .0
4 .5
4 .0
-Q--------O-------- Q-------- O---------—
D i e l e c t r i c C o n s ta n t
o — 0 ------ O--------- q --------O-
3-5
3 .0 &
2 .5
2 .0
1 .5
1.0
_
0 .5
30
35
^5
^3
F requ en cy
si
si
9^
i&r
DIELECTRIC CONSTANT OE TETRAETHOXYTITANIUM PLOTTED AGAINST FREQUENCY IN MEGACYCLES AT - 3 0 ° C
O— O
2.C -
Frequency
D i e l e c t r i c C o n s ta n t
DIELECTRIC CONSTANT OE TETRAETKOXYTITANIUM PLOTTED AGAINST FREQUENCY IN MEGACYCLES AT
F requency
C
D i e l e c t r i c C o n s ta n t
DIELECTRIC CONSTANT OE TETRAETHOXYTITANIUM PLOTTED AGAINST FREQUENCY IN MEGACYCLES AT
l.5 _
85
F requ en cy
90
C
- 72 XVI.
SPECIFIC CONDUCTIVITY OF MOflOCHLQROTRI“STHOXYTI T / NIUM U
24°C
i n a t t e m p t was made to m e a su re t h e c a p a c i t a n c e a n d c a l c u l a t e t h e
d i e l e c t r i c c o n s t a n t o f monoc h l o r o t r i e t h o xyt i t a n ium a t a f r e q u e n c y o f 1000
c y c l e s a t 2 5 ° C on a 0 . R. c a p a c i t a n c e b r i d g e , a s w e l l a s » t h ig h f r e ­
q u e n c ie s .
The c a p a c i t a n c e o f t h e c e l l , w i t h m o n o c h l o r o t r i e t h o x y t i t a n i u i a
sa th e d i e l e c t r i c ,
c o u ld n o t b e m e a s u re d on th e b r i d g e a t t h a t f r e q u e n c y ,
a lt h o u g h t h e d i e l e c t r i c c o n s t a n t a p p e a r e d t o b e a b o u t 8 to 1 0 , a s shown
b y an a p p ro x im a te m ea su rem e n t a t h . 6 me on th e i n s t r u m e n t u se d b y C row e.
V ery few p u r e l i q u i d s e n d ,
conduct e l e c t r i c i t y .
g e n e r a l l y o n l y th o s e w h ich a r e i o n i c ,
T h is c o n d u c ta n c e a p p e a r s to b e t h e r e a s o n f o r t h e
i n a b i l i t y to o b ta in c a p a c ita n c e r e a d in g s .
The s p e c i f i c c o n d u c t i v i t y o f p u r e a o n o c h l o r o t r l e t h o x y t i t a n i u m a t
? 5 0 C w ar 1 . 4 x ! O '6 m hos, m e a s u re d w i t h a. W h e a ts to n e B r id g e a t IOOO
c y c le s /s e c .
T h is i s a b o u t t h e same mm t h a t o f p u r e w a t e r .
- 73 -
m i.
DISCUSSION OF EXFSIIHENTAL RESULTS
A lth o u g h t h e r e s u l t s f o r t h e d i e l e c t r i c c o n s t a n t show d e v i a t i o n s fro m
o c o n s t e n t v p l u e o v e r t h e r e n g e o f f r e q u e n c y , no sn o m p lo u e d i s p e r s i o n
in d ic p te d f o r c e r t a i n .
wpb
The v a lu e s f o r t h e d i e l e c t r i c c o n s t e n t e t -$ k °C
mpy h a v e shown t h e s t a r t o f t h e d i s p e r s i o n e f f e c t e t a b o u t 55 m e g s c y c le s ,
b u t th e r e s u l t s a r e s t i l l
somewhat d o u b t f u l .
The c a p a c i t a n c e c h a n g e w ith e a c h d i f f e r e n t c o i l l e a v e s some d o u b t i n
r e g a r d to t h e r e l i a b i l i t y o f t h e d a t e .
Q ie v a lu e s a t v a r i o u s f r e q u e n c i e s ,
f o r a s i n g l e c o i l f a l l on a s t r a i g h t l i n e , b u t f o r d i f f e r e n t c o i l s , a t t h e
seme f r e q u e n c y , th e c a p a c i t a n c e was d i f f e r e n t and t h e d i f f e r e n c e v a r i e d
f o r each d i e l e c t r i c u se d .
A f t e r c o n s i d e r a b l e s tu d y o f t h i s p ro b le m , i t
a p p e a r s t h a t c o i l s and e x t e r n a l l e a d s a r e p r o b a b ly n o t t h e c a u s e , b u t
r e s id u a l c o n s ta n t r e s i s ta n c e , c a p a c ita n c e ,
s tr u m e n t may b e th e c a u s e .
and in d u c ta n c e w i t h i n t h e i n ­
r h e v a r i a t i o n ho w ev er i s s m a ll and a lm o s t
w i t h i n t h e e x p e c te d p r e c i s i o n o f t h e i n s t r u m e n t .
The f r e q u e n c y a t w h ic h a n o m alo u s d i s p e r s i o n w i l l becom e e v i d e n t i s
r e l a t e d t o t h e tim e o f r e l a x a t i o n f o r t h e l i q u i d by t h e e q u a t i o n w $ » .
S o lv in g t h i s r e l a t i o n s h i p f o r T u s i n g t h e v a lu e o f 95 m e g a c y c le s f o r t h e
fre q u e n c y ,
i t c a n be s e e n t h a t T c a n n o t e x c e e d 1 .6 8 x 10“ ^ s e c o n d s .
M o n o c h lo r o tr i e t h o x y ti t e n i u m , f o r w h ic h a p a r t i a l i o n i c bond b e tw e e n
t h e c h l o r i n e an d t i t a n i u m atom h a s b e e n p r o p o s e d , d o e s c o n d u c t e l e c t r i ­
c ity .
The s p e c i f i c c o n d u c t i v i t y m e a s u re m e n ts i n d i c a t e t h a t th e compound
h a s a b o u t t h e same c o n d u c t i v i t y t h a t p u r e w a t e r e x h i b i t s .
I t w as f o r t h a t r e a s o n t h a t t h e a t t e m p t to m ea su re t h e d i e l e c t r i c
c o n s t a n t w as n o t s u c c e s s f u l on th e i n s t r u m e n t s a v a i l a b l e .
X Y III.
1.
SI) M it RY
T e t r p .e th o x y t Itp n iu m Wp p p r e p a r e d end p u r i f i e d end t h e d i e l e c t r i c c o n s t r u t o f th e p u r e l i q u i d w rs s tu d i e d
e t f r e q u e n c i e s r e n t i n g from 30-
100 m e g a c y c le e e n d r t t e m p e r a t u r e s fro m - 50°0 to 2 $°C .
2.
r^ ie d i e l e c t r i c c o n s t a n t d o e s n o t d e c r e a s e w ith i n c r e a s i n g f r e q u e n c y
w i t h i n t h e ra n g e o f m e a su re m e n ts and t h e r e f o r e d o e s n o t e x h i b i t
a n o m a lo u s d i s p e r s i o n a t t h o s e t e m p e r a t u r e s and f r e q u e n c i e s .
3.
h.
T t h e tim e o f r e l a x a t i o n c a n n o t e x c e e d 1 .6 8 x IO- ^ s e c .
M o n o c h lo r o tr i e t h o x y tl t e n i u m was p r e p a r e d end p u r i f i e d and an a tte m p t
mode to m e a su re t h e d i e l e c t r i c c o n s t a n t a t a f r e q u e n c y o f 1030 c y c l e s
m d a t e m p e r a t u r e o f ? 5° C .
e le c tric ity
5.
'o n o r h l o r o t r i e t h o x y t i t - n i u m c o n d u c ts
-nd t h e d i e l e c t r i c c o n s t a n t was n o t o b t a i n e d .
% e s p e c i f i c c o n d u c t i v i t y o f p u r e monoc h l o r o t r l e t h o x y t l t a n i v a was
m e a s u re d a t ?5°C -n d fo u n d to be I .
6.
* d is c u s s io n o f th e d i f f i c u l t i e s
u s e o f a Q, m e te r i s p r e s e n t e d .
X 10“ ^ r e c i p r o c a l ohm s.
in v o lv e d in t h e c a l i b r a t i o n and
- 75 XIX.
ACKHOWLBDlMENT
The p u t h o r w is h e s to tp k e t h i s o p p o r t u n i t y to e x p r e s s h i s s l n c e r e s t
p p p r e c l p t i o n pnd t h i n k s to B r . C h r r l e s JST. Cpu>5h l p n f o r h i s p e r s o n e l
g u id p n c e pnd. i n s p i r a t i o n d u r in g t h i s r e s e a r c h , to M r, R. C. S e i h e l o f th e
R l e c t r i c p l E n g i n e e r in g D e p a r tm e n t, end t o t h e o t h e r m em bers o f t h e Chem­
i s t r y D e p a rtm e n t f o r t h e i r many h e l p f u l s u g g e s t i o n s .
He a l s o w is h e s to
th a n k t h e R e s e a rc h C o r p o r a t i o n o f New Y ork f o r m aking t h i s I n v e s t i g a t i o n
p o s s i b l e th r o u g h p g r a n t .
— 76 —
M-
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I r o u p s " , M. S. T h e s i s , M o n tan a S t a t e C ol­
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, % % Si™,uEraaTY Ummies
3 1762 10014337 7
93228
N3T8
H669
c o p .2
DATE
H o d g so n , W illia m
A s tu d y o f th e r e a c ti o n
b e tw e e n t i t a n i u m t e t r a ­
c h l o r i d e and e t h y l e n e
g ly c o l
ISSUED TO
a -
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