DIELECTRIC COXSTANT AND PARTICLE SIZE STUDIESWITH CHLORINATED RUBBER SOLUTIOSS~ J. W. WILLIAMS Department of C h e m i s t r y , C n i c e r s i t y of TVisconsin, M a d i s o n , Tt’isconsin S O R M A S 11.LIZ
AND
Receiced August 1 , 1957
Quantitative studies of high molecular weight polymeric compounds are of great theoretical and technical interest. An important object of such work is to assist in the discovery of the structural plan of these molecules. It is possible that there may be found some comparatively simple method of classification. For example, we may be enabled eventually to distinguish ( 1 ) association polymers in which smaller molecular units or residues are held together t o form the aggregates through secondary valence forces, and ( 2 ) macroniolecules in which the fundamental groups are chains or fibrils of such residues which are held together by primary valence forces. Recent theoretical derelopments make it possible to estimate the size of spherical or ellipsoidal polar molecules, provided the latter are dissolved in non-polar media and provided the physical or molecular kinetic unit and the electrical molecule are identical. From dielectric constant-frequency data obtained with dilute solutions, the arerage time constants and molecular weights of zein, gliadin, and lignin have been determined. I n these cases the molecular weight values so obtained agree with figures which have resulted from the application of the classical diffusion, sedimentation, and osmotic pressure methods; in other words, the electrical arid kinetic units are identical. Data obtained in other laboratories appear to indicate that egg albumin, hemoglobin, and serum albumin molecules show similar characteristics when allowance is made for their shapes. On the other hand, the results of unpublished measurements made in this laboratory n-ith relatively dilute solutions (1 to 3 per cent) of certain other polymers (w-hydroxydecanoic acids, methyl methacrylate, rubber hydrochloride, neoprene) do not give a dispersion of ordinary dielectric constant which can be detected with our present apparatus over the wavelength range now accetsible (A = 10 111 to X = 10,000 in), although the Presented at the Fourteenth Colloid Symposium, h e l d a t Minneapolis, Minnesota, June 10-12, 1937. Present address: Department of Chemistry, Anhwei L-niversity, .inking, China. 1171
1172
S O R M A S 31. L I AND J. W. WILLIAMS
experimental data show a definite orientation contribution of the solute molecules to the dielectric constant of the s ~ l u t i o n . ~ Dilute solutions of chlorinated rubber also Lvere found not to give a dispersion of the dielectric constant over the available wave-length interval, although an effect of this kind would be expected if electrical and kinetic units are equivalent. Inasmuch as the dipole theory is restricted in exact application to dielectric constant and density data obtained with dilute solutions, the significance of results obtained at moderate concentrations may be somewhat questionable, but it was decided to experiment with solutions containing the somewhat larger amounts of chlorinated rubber as solute. Measurable dielectric constant dispersions were observed with solutions containing 3 to 7 per cent of this substance and the calculated times of relaxation appear to be independent of concentration. The Debye modification of the Clausius-Nosotti formula (2), which shon s frequency as well as temperature variation of dielectric constant, has the form
In this equation, IC1 is the molecular weight, d is the density, S is the Avogadro number, a0 is the optical polarization, p is the electric moment, w ( = 2 x v ) is the frequency, 7 is the time of relaxation or time eonstant, T is the absolute temperature, k is the Boltzmann constant, and E = E’ - ic”. The dielectric constants E’ and E” are the real part and imaginary part, respectively. The dielectric constant observed in a capacity measurement is E ’ . It varies with frequency according to the expression,
in which is the static dielectric constant, quantity, and
E,
is the corresponding optical
8 Rlr. Wilbur Bridgman of this laboratory has made a detailed study of the dielectric behavior of several of the polymeric a-hydroxydecanoic acids in dilute heneene solution. I n order to account for the d a t a i t seems necessary t o assume contributions to the polarization resulting from orientations in the electric field of recurring units which make up the several solute molecules. A report of this work will be available in the near future.
DIELECTRIC C O S S T A S T 4 N D PARTICLE SIZE
1173
The frequency v e is that frequency for which
If we wish to express the time constant in terms of the frequency v j a t which the dielectric constant-frequency or dispersion curve passes through its point of inflection we have 7
=
€-_.-.,+2 eo 2
+
1
1
2TVf
\'3
For the calculations to be niade in connection with this report, we shall use the frequency at ~vhichthe dielectric constant assumes its mean value. By remembering that it is necessary to exert a torque to rotate a spherical molecule against the inner friction of a medium in which it is suspended, the time of relaxation of such a molecule may be expressed in terms of its radius, r, to give the important result,
The symbol will be used to designate the time of relaxation of a spherical molecule. In deriving this equation the assumption has been made that the inner friction of the medium can be expressed in terms of v, its ordinary or macroscopic coefficient of viscosity. Thus, for the molecular weight, M, of a spherical solute, we h a w
n-here I.'is the partial specific volunie of the molecule in solution. If the molecule has the shape of an ellipsoid of revolution m-ith long axis a and short axis b ( b / n = p ) , and the rotation is about the long axis in a medium of viscosity 7, the relaxation t h e becomes (4) 4rab27 4 __
(1 -
7=---'
kT
1
+ (1 - 2 p 2 ) p2, 4-
P4)
(5)
In
Further,
hab2 3
MI.' N
I t is the present purpose to attempt to demonstrate the use of the dipole theory in particle size determinations by calculations made by using the observations of frequency variations of dielectric constant of solutions
1174
XORMAK hf. LI A S D J. W. WILLIAMS
of chlorinated rubber in non-polar solvents. Studies were made with solutions of five samples of chlorinated rubber prepared by us and three samples of commercial chlorinated rubber ( T ~ r n e s i t ) . The ~ chlorine contents of the specimens varied between those corresponding t o the trichloro and to the tetrachloro derivatives. PREPARATION AKD PURIFICATION OF MATERIALS
I
I n the experimental work benzene and carbon tetrachloride were used as solvents. Each was subjected to careful and rigorous purification by following procedures given by Keissberger and Proskauer ( 5 ) . As a test of the purity of the liquids used the boiling points, refractive indices, and densities were determined and compared with data of the International Critical Tables. The chlorinated rubber was prepared by direct chlorination of acetoiieextracted pale crepe r ~ b b e r . ~ Purified chlorine gas x a s passed into a warm solution of the pale crepe rubber in carbon tetrachloride. This solution of chlorinated rubber was then poured into hot water which had been made slightly alkaline by the addition of sodium carbonate, and the chlorinated rubber was precipitated out in white sheets. The product F a s then redissolved in carbon tetrachloride and reprecipitated from hot neutral water. It was dried in air between filter papers and over calcium chloride in a desiccator, rinsed with alcohol, and dried i n vacuo. EXPERIMESTAL
I n the majority of cases the dielectric constant3 were obtained by determining the capacity of a calibrated fixed cell or the capacity difference between rotor positionq of a variable cell by means of either of two asseniblies of apparatus for the hetcrodyne beat method of measurement. The first one, used with but slight modification, has been dcscribed in the literature (3). The cell is calibrated by finding its capacity in air and in benzene, the standard liquid, and from this calibration the dielectric constant of the solution is obtained from a .ingle condenser reading. The second apparatus consisted of three distinct circuits, an electron coupled standard oscillator, a detector, and n variable oscillator containing standard precision condenser arid dielectric cell coiinected in parallel. Similar arrangements for dielectric constant mca-urements are described in a recent laboratory innnual (1). -1gaiii purified benzene was uqed as liquid of knoxm dielectric constant for thc calibration. On tn.0 occasions samples of Torilesit nere presented t o us by the Hercules Pov-der Company of Tyilmington, Delan-are. 5 This material n a s supplied with the conipliments of the B. F. Goodrich Company through Dr IT F. Busse of the Physical Research Laboratory.
,
1175
DIELECTRIC COSSTANT AND PARTICLE SIZE
Additional dielectric constant measurements were made a t wave lengths X = 10 m t o X = 100 m by using a resonance apparatus and a t X = 1000 m to X = 8500 m with a special radio frequency bridge. The resonance point
was established b y means of a voltmeter circuit containing a duplex diode TABLE 1 P h y s i c a l and analytical data for chlorinated rubber solutions COSCESTRlTION ( G R A V E PER 1 100 CC. O F SOLYEXT) I
EXFT. KO.
SCEBTASCE I S V E E T I O A T E D
EOLVEXT
,
10
1
11 12 13 14
1 1
Benzene Carbon tetrachloride Chlorinated rubber I Chlorinated rubber I Chlorinated rubber I Chlorinated rubber I1 Chlorinated rubber I1 Chlorinated rubber I1 Chlorinated rubber I1 Chlorinated rubber I11 Chlorinated rubber IV Chlorinated rubber V
CClr CC14 CaHe CCl, CCla CsHa CeHa CeHe
CaHs C6Ha
'
1
I
2.236 2.122 2.132 2.128 2.217 2.134
,
3 9012 2 5341 5.3635 4.9101 1.2865 3 8456 2 247 2 253 4.1265 5.5594 1 2.250 4.1668 2 247 2 9298 I 2 243
!
'
0.8737 1.5839 1.5843 1.5812 0.8972 1.5816
61.28 61.28 61.28 66.13 66.13 66.13 66.13 60.32 59.56 58.98
0.8906 0.8919 0,8980 0.8923
TABLE l a Dielectric constant data f o r chlorinated rubber solutions
,
I
EXPT. SO.'
1
1 2 5 6 . 7 8 9 10 11 12 13 14
600 m
2 273 2 236
360m !
1
2 2 2 2
273 236 303 272 336
2.335
2.328 2.334 2.360
2.322
2.322
1
1 1
1
i
1562 m
2 273 2 237 2 302 2 271 2 336 2 307 2.261 2.325 2.334 2.357 2.343 2.321
~
' ,
78.1 m
2 273 2 236 2 300 2 268 2 331 2 303 2.262 2.324 2.332 2.351 2.340 2.319
~
'
, I
39.1 m
2 273 2 238 2 292 2 266 2 330 2 298 2,259 2.322 2.329
i
1
17.4 m
2.273 2.234 2.284 2.263 2.326 1 2.281 2.257 2.316 2.325
2.273 2.236 2.271 2.259 2.323 2.265 2,262 2 313 2.321
26 m
~
i I
'
* The experiment numbers refer to correspondin triode tube. The position of balance in the bridge was observed with the aid of an oscillating detector and a tn-0-stage amplifier of conventional design. These additional data w r e always consistent with the yalues obtained n-ith the heterodyne beat method at thc intermediate wave
,
1176
NORMA9 11. LI AKD J . W. WILLIAMS
TABLE 2 Physical and anal!/tical data ,for Tornesit solutions -
EXPT.
I'
so.
I
15 16 17 18 19 20 21 22 23 24 I 25 26 27 1 28 29 I 30 31 32
'
-~
PER CEST SUBBThKCE IS?EJTIG.4TEU
DESSITF
C11Y SOLUTE ___
Imported Imported Imported Imported Imported Domestic Domestic Domestic Domestic Domestic Domestic Domestic Domestic Domestic Domestic Domestic Domestic Domestic
Tornesit Tornesit Tornesit Tornesit Tornesit Tornesit Tornesit Tornesit Tornesit Tornesit Tornesit Torilesit Tornesit Tornesit Toinesit Tornrsit Torncsit Toinesit
1 ,5854 1 ,5848 1 ,5845 0.8809 0.8806 1 ,5844
I I I I I I I I I
1 ,5849 0.8826 0.8858 0.8957 0.8968 0.9069 1 ,5846
I1
I1 I1 I1
0.8906 0.8952
65.75 65.75 65.75 65.75 65.75 64.53 64.53 64.53 64.53 64.53 64.53 64.53 64.53 64.53 64.14 64.14 64,14 64.14
T.4BLE 2 s Dielectric constant data .for Tornesit solutions 600 m
EXPT. S O .
15 16 17 18 19 20 21 22 23 2-1 25 26 27 28 29 30 31 32
156 ? m
330 in I
2 297 I
2.272 2.316
,
2.271 2.314
1
2.277 2.287 2.302
, I
2.342 2.381
I
I 1 l
~
I
2.316 2.325 2.314
l 1
2 2 2 2 2 2 2 2 2 2 2 2 2
270 276 286 300 316 330 3-11 351 380 267 316 325 344
1
l
' I
2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2
297 278 271 314 297 268 272 284 300 316 328 339 348 378 266 315 323 3-11
1
1 ~
1 1 1
1 I
78.1 m
'
26 m
2.294 2 275 2 269 2 315 2 294 2 264 2 269 2 279
1
'
2.283 2.264 2.264 2.315 2,294 2 258 2,260 2.272 2.298 2.309 2.319 2.329 2.337 2.357 2.258 2.308 2.316 2.332
2 315 2 327 2 336 2.345 2 373 2 265 2 313 2.321 2 339
1
I
I
1
1
1
'
, I
I I
174m
2 277 2.262 2 258 2 312 2 294 2 256 2 256 2 266 2 298 2 305 2 314 2 323 2 330 2 350 2 255 2 306 2 314 2 327
DIELECTRIC C O S S T A S T A S D PARTICLE SIZE
1177
lengths, and they serve as an excellent check upon the results to be presented in the tables which follow. The partial specific volume of the chlorinated rubber was observed pycnometrically a t 25"C., the calculation being made according t o the formula,
where T.' is the partial specific volume, u: is the weight of the solvent in the pycnometer, 1 is the weight of the solution, h is the weight of the chlorinated rubber, and do is the density of the solvent. The concentration of the solution was determined by evaporating known volumes of the solution in an oven a t 90°C. and weighing the residues. The refractive indices were measured with a Pulfrich refractometer. Relative viscosities were determined by visconieters of the Ostwald type. All such measurements were made in a thermostat regulated t o 25°C. i 0.01". The results of the experimental n-ork, physicochemical and analytical, are presented in tables 1 and 2 . The dielectric constant data are accurate to about f 0.1 per cent. Such a degree of accuracy is required in view of the small actual change in the dielectric constant of the chlorinated rubber solutions which is to be expected. CALCULATIONS
In any monodisperse system the dielectric constant may be expressed as a function of the frequency by equation 2. Since in many of the experiments harmonics of a fundamental frequency are used, the frequency
2 may be replaced by nvo,where
TL is an integer and vo is the funda2n mental frequency. Thus equation 2 may be written in the form,
v or
E'
= a€,
r2 -
+ eo
CLE'X~
(2a)
in which
Equation 2a has three constants to be evaluated, a, EO, and E,. Ordinarily this is accomplished by the method of least squares, but here the calculations can be simplified because there are independent means by n-hich the quantities €0 and E, may be approximated. The dielectric constant at infinite frequency E , is obtained in the following manner. For the non-polar solvents the square of the refractive index is equal to the
1178
KORNAX hi. LI AXD J . W. WILLIAMS
dielectric constant at infinite frequency, except for the small difference due to infra-red absorption. For carbon tetrachloride, nh = 2.122, and the difference between this value and the observed dielectric constant for the liquid ( e = 2.236) is 0.114. Since the solutions investigated were TABLE 3 T i m e of relaxation data for chlorinated rubber and Tornesit i
SOLUTE
e,-e ~
Chlorinated rubber I I n CC14... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i'
In C&s.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chlorinated rubber I1
................................
I n CC14.. I n CeH6.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
fl .
