1056
RICHARD M. BADGER A S D ROBERT
H.
BLAXER
(10) SORTOS, F . H., JOHSSON, A . L., ASD LAWRESCE, W.G . : J. -1m. Ceram. Soc. 27, 14964 (1944). (11) l-.isI), ~ 7 r . a u I a r I R : 1'hj.s. Colloid Chem. 52, 277-320 (1948). (12) V E L T ~ I I SRS. .S., .ISD GREES, 11.: J. -4pplied Phys. 14, 569-76 (1943).
THE ISYESTIG-ITIOS OF THE PROPERTIES OF NITROCELLULOSE IIOLECULES I S SOLUTIOS BY LIGHT-SC-4TTERISG NXTHODS. I1 EXPERIRIEST.4L
RESL-LTS .ISD
R I C H A R D RI. BADGER Gatep
ASD
ISTERPRETATIOS'
ROBERT H. BLAIlER
a i d Crellin Laboratories of Chemistvj, Cnlijornza Institute of Technology, Pasadena, Calzfornza Recezted October 7 , 1948 11LTRODCCTIOS
Techniques and instruments developed in this laboratory for the determination of the sizes and shapes of high-polymer molecules by the light-scattering method n-ere described in a prerious paper (a), which in the following will be referred t o as Paper S o . I. The present paper describes the application of these methods t o a study of a series of nitrocellulose fractions which has resulted in rather definite conclusions regarding the character of the nitrocellulose molecule in solution. The results obtained from the light-scattering measurements are correlated n-ith viscosity and diffusion data by the use of recently developed theories.
Materials The nitrocellulo,?c specimens employed in this investigation include several unfractionated commercial materials and seven fract'ions. Fractions S-4,3, 8-3.4, S-1.14, P-3.2. and 1'-4,2, all of approximately 13.4 per cent nitrogen content, u-ere proi-itled by the courtesy of Professor J. W. Williams of the University of \lTisconsin.YFractions designated as -1and B were kindly supplied by Dr. R. L. Ilitchell of Rayonnier, Inc. The solrent' used in all experiments was chemical1~-pure acetone. '('onrribution S o . 1255 from t h e Gates ant1 Crellin Laboratories of Chemistry, Califorilia Iristitule of Teclinolog>-. The investigation herein described was supported by the Bureau of 0rtln:rnce of t h c U. S.S:iv>-Departnierit and JY:E carried out under Contract S 6 - o r i 102, T:isk Order \-I,with the Officc of S a v n l Resrarch. ?Tile details of the fractionation procedure n r r described in O.S.R.D Report S o . 4123, PI3.i So. 1SS61, entitled "The Characterization arid Solubility of Fractionated Wood P u l p a i i d CCJtt(Ji1Linters Sitrocelluloses," by J. I T . Williams et al.
SIZE ASD
1057
SHAPE OF KITROCELLULOSE MOLECULES IS SOLUTIOK
Viscosity measurements The viscosity measurements were all made a t 25°C. with an Ostwald capillary viscometer according t o procedures previously described (6). '
Refractit'e-indexincrement Tl'ith each of the specimens examined the difference betn-een the refractive increment of solution and pure solvent was determined a t three concentrations TAIBLE1 Rejractiie-index increment of nitrocelliiloses of seLeral nitrogen contents i n acetoric T h e concentration c is expressed as weight fraction XITBOGEN COhTEST
hlTROCELLLXOSE DESIGXATIOX
dn/dc X 107
1 -A
10.98 11.89
Hercules 609-68-2.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hercules 2917 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
= 5461
99.8 9S.5
A. ,
X = 4318
A.
102.2 101.o
I
I
It
12
13
14
% NITROGEN
FIG.1. Refractive-index increment of nitrocellulose in acetone as a function of nitrogen content
beloIv 1 per cent, usin4 a differential refractometer. Measurements were made a t 25"C., using the 5461 A. and the 4358 mercury lines. In all cases the refractive index was found to increase linearly with concentration, within experimental error. The refractive-index increment, dnjdc, was obtained from a plot of n versus c. KOdependence of this quantity on molecular weight was observed, but a marked dependence on nitrogen content is shoun in table 1 and figure 1. The trend of dn/dc with nitrogen content is similar t o that reported by Jullander (lo), but the absolute values obtained by that investigator appear to us to be slightly low.
K.
1058
RICHARD M. BADGER AXD ROBERT H. BLAKER
Light-scattering and depolarization measurements The general procedure employed in the light-scattering measurements has been described in Paper KO. I. As as there discussed, no filtration procedure has been found a t all adequate for preparing solutions in polar solrents, and the acetone solutions Jvere consequently centrifuged for 20 min. in a held of 32,000 g, n-hich as found adequate to remove contamination of dust particles. L l l l measurenients here reported were made at approximately 25"C., u i n g the 5461 -1.mercury line. The measuiement of the 90" scattering n - 2 b made with unpolarized incident light and the absolute intensity of scattering ]vas determined by coinparison a-ith a carbon disulfide standard. In figure 2 representative plots
I
I
I
I
2
4 c.103
6
FIG.2 . Representative plots of c/i w s u s
c for four
nitrocellulose fractions
are shonn of c ' i temrts c, where c is the concentration in weight fraction and i is the intensity of scattering at 90" relative t o that of carbon disulfide. In connection n ith the 90" scattering measurements the depolarization of scattered light n as determined Ivith the incident light unpolarized. KO dependence on concentration or on molecular neight v-as observed. The average depolarization for four nitrocellulose fractions of 13.4 per cent nitrogen Tvas found t o be 0.029. I n studiei of the angular distribution of scattering the incident light \\as polarized with the plane of vibration pcrpendicular t o the plane including incident and scattered beams, since this somewhat simplifies the interpretation of the results. 1Ieasurements of the intensity of scattering relative to the intensity
SIZE AKD SHAPE OF SITROCELLCLOSE
MOLECULES I ~ YSOLL-TIOX:
f [ 1059
at 90" \yere made at a series of angles betn-een 53" and 124" in solution. Plots showing the results obtained in six fractions are shown in figure 3. The curves for fractions P 4 , 2 and for Rayonnier B are practically identical and coincide in the plot. TA%131,E 2 Dnln or( iiyli! a m t i e r i n g . I iscosi!y. a r i d dijJicsi(*ri ( ~ ,iiit,oi.ciliclose f ~ i . n c ~ t i o rin i , ~ace:one c501icticin SITROGES
SA?IPLE SO.
cnsrExr
-
ISTRISSIC VISCOSITY
A1 ,/.
DIFFTSIOS
cossr.nz, D
(R.ASDOXI C O I L )
per cent
>-4 .3 h-3 4 b - l 1-1 P-3 2 P-42
~tnyonnie;,B . . . . . . . . . . Rnyoiinicr 1. . . ..,. .....
~
0.30 1.30 2.22 2 98 6.66
13.96 13.06
14.90 21 .OO
,
1
I
60
9.400 35.000 50.000 93.000 310.000
(-1; 1.10 1.13 1.22 1.38
(1.31) 1.86
100,000 5lS.000
I
I
50
13.1s 13.36 13.44 13.41 13.12
I
I
I
I 70 80 90 100 110 0 ( A N G L E MEASURED IN SOLUTION)
120
130
FIG.3. Intensity of scattering rersus scattering angle in solution for six nitrocellulose fractions (incident light polarized). T h e scale of ordinates is the same for all curves b u t t h e origins u e shifted to prevent overlapping.
I n the concentration range 0.2-1 .O per cent no dependence of angular distrihution on concentration Ti-as found,3 a result which is in agreement Trith the observations of Stein and Doty on cellulose acetate ( l i ) . 3Ke h a r e observed a definite dependence on concentration in the case of blood type "A suhstnnce" a n d of nil osin i n ~ o r which k nil1 be repoited later
1000
RICHSRD M. BADGER ;L"D ROBERT H. BLAKER RESULTS O F MEASURERIEXTS
Though in principle direct information regarding molecular shapes should be obtainable from the shapes of the angular distribution curves, this is in practice not yet possible. The curves calculated for different molecular models differ little in shape in the angular range of practical measurement, and very high accuracy of measurement n-ould be necessary t o determine uniquely the molecular model which is applicable. Consequently the scattering curves have been characterized merely by a dissymmetry coefficient q, which is the ratio of scattered intensity a t tIyo angles-namely, a t GO" and 120"-measured in the solution. This quantity can, however, be obtained more reliably from the smoothed plot of data taken over a range of angles than from tn-o measurements alone.
SAUPLE
1 ,
UOLECULAR DI1[EXBIOS
LIGHT-SCATTERISGIOLECrLAR WEIGHTS (.!ftc)
Sphere
Rod
1
'Oil
1
d (sphere) A.
d-4,3 d-3 4
9 400
!I, 400
1'-3 2 1'-4 2
35,000 49,000 s; 000 298 000
35,000 49,000 bn, 000 312.000
1137 onnicr B R a \ O I l l l l C l -1
356,000 304 000
,370 000
s-1 1-4
1
~
0,400 35,000 50.000 93.000 319.000 400.000 518 000
,
, ~
1 (rod)
R [coil
Extend$ length
A.
4
A
sns
64b
170 630 900
1210 1690
1230
~
_
I
603 685 800 10S0 (965) 1470
(1450)
'
(11201 200s
I
_
5700
6550 0200
Cdculatecl on basis of r n n d o m coil molecule.
With the use of this dissymmetry coefficient n characteristic dimension has been calculated for three different molecular models-the sphere, the rod, and the random coil-employing methods which have previously been described in the literature and have recently been reviewed (12). The dimension calculated in the respective cases is the sphere diameter d , the rod length I , and the rootmean-square distance betn-een ends of the coil, 2/av, which we shall designate simply by R. These quantities are given in table 3. It should be mentioned that the behavior of the Rayonnier fraction B seemed t o be somewhat anomalous in regard to the low asymmetry of scattering as compared with the high molecular \\-eight and high vibcobity. The quantities calculated from the asymmetry are consequentlJ- of somen-hat doubtful significance. I n the determination of molecular n-eights from the light-scattering data not only has the Cabannes factor been applied in all cases, but for a11 escept the fraction of lowest molecular n-eight, for 11-hich the asymmetry of scattering v a s negligible, equation 1 of Paper S o . I has been corrected by multiplication of its right-hand member by a factor calculated from the disqynmetry of scattering.
SIZE XT-D SHAPE OF NITROCELLULOSE MOLECULES IN SOLUTION
1061
This factor is the ratio of the intensities of scattering at 0" and go", respectively. Since the scattering at 0" is not observed, it must be calculated from the observed dissymnietry of scattering, employing one of the probable molecular models. Mo1ecul:ir aeights calculated on the basis of three models are giyen in table 3. They clilier significantly only for the higher inolecular weights. *At wq- high niolecular n-eights the spherical niodel may have some validity, but the tn-o models of particular interest are, of course, the random coil and the rod. -1s n-ill be shown belon-, n-hen the degree of polymerization, z , is much less than 100 :he rod niodel is presumably the more nearly applicable. At higher
A
0
Frc, 4 I t m d o n i coil models. -4,one planar configuration of the polyethylene niodel : B, four of t h e sixteen p l a n a configurations of the cellulose model corresponding to the single co I1 fig u I :at !< I. (1f -4. )
molecular weights the cellulose molecule presumably assumes the characteristics of a i,andom coil. It should be pointed out, hon-ever, that the particular random coil motlrl nn which the light-scattering equations, and the viscosity and diffusion equations later to be discussed, are based does not adequately represent the cellulo+e molecule. Consequently it is not certain t o what extent these equations are applicalj!e t o cellulose and our present considerations must be regarded as tentative. X portion of the molecular model upon n-hich existing statistical considerations of the rand:m coil molecule have been based is shown in figure 41.The internal configurarion of such a chain is specified by one set of coordinates, 41,the angles Iiet~vecnsuccessive bond pairs. This model is presumably adequate for representinc the hehavior of polyethylene and other similar substances. S o w in
1062
RICHARD 11. B-IDGER -1BD ROBERT H. BL.1KER
cellulose the tn-o bonds connecting the tn-o glucoside oxygens to a given glucose ring may be approximately parallel, hut their projections are certainly far from coincident. Consequently if one represents the cellulose molecule by a qimplified model consisting of a string of osygen atoms connected by bonds representing
S.AUPLE
(DEGREE OF POLTXERIZATIOS:
3:3 7 23 1i 6 327 112~0
Rayoiinier B . ... . Rxyonnier -1 ,
1360
~
1iGO
, ,
36.:) 11 . D
11 .:I 10.8
:39 , 4 I 4‘,!. 2
z FIG.5. Plot of mid acetate.
V‘=/Z~
zeTsus
i
from light-scattering d a t a o n cellulose nitrate
the glucose rings, these bonds must each h a w an “offset,” as shon-n in figure 4B. To describe the configuration of the chain a nen- set of coordinates is required u-hich relate t o the rotation of the “kinked bonds” about axes parallel t o their extensions. The importance of the new degrees of freedom is shou-n in the figure,
SIZE ASD
SHAPE OF SITROCELLCLOSE
MOLECULES IS SOLUTIOS
1063
which presents four of the sixteen pohsihle planar configurations coneyionding to one planar configuration of the polyethylene model. -1theoretical treatment of the cellulose model must certainly be ninde before one can be quite certain that conclusions hased on btatistical consideration%of the simpler polyethylene model are valid in the case of cellulose ant1 its deli1 atires. It these conclusions are valid we should expect that R, the root-mean-quare distance betn-een ends of the molecule, \\auld increase with the square root of z, the degree of polymerization, provided that z is not too small. Xctually the calculated R z1 is found to decrease slightly uithz, as may lie been in tahle 4 and figure 3 . -in even stronger trend n a s ohserved for cellulose acetate by Stein and Doty (17). Khether this trend is due to the reasons just mentioned or results from experimental error remains to be determined. The results of the light-scattering and viscosity measurements are presented in table 2 and quantities derived from them in tables 3 and 4. For correlation n i t h these data diffusion constants are much t o be desired, but unfortunately accurate diffusion measurements on nitrocellulose fractions d o not appear t o have been made. K e consequently include approximate diffusion const ants determined in this laboratory by a rapid method (4) which may be sufficiently accurate to be of use in the follon-ing discussion. These constants show precisely the same trend n-ith molecular weight as v a s found by Jullander (10) for unfractionated material, but are about 23 per cent smaller. This difference is not unreasonable, considering that the t1i-o sets of measurements involre fractionated and unfractionated materials, respectively. DISCUSSION O F DATA
Cellulose and its derivatives have long been regarded as the typical class of substances t o which the simple Staudinger viscosity relation may be applied 11 ith reasonable accuracy. Certainly, ample data have established the approximate validity of the relation [7] z = li over a range of z approximately 100-500. which happens t o include the majority of commercial regenerated celluloses and cellulose derivatives. More recent data have estatiliShed a definite decrease in [ v ] / z at higher molecular n-eights. This is indicated liy the work of Badgley and Mark (1) and most strikingly shoun by the investigations of G r a l h ( 7 ) on celluloses of very high molecular Treight in cuprammonium. The approximate constancy of [71 x in the range mentioned might tie taken as supporting the viscosity theory based on the random coil molecular model developed by Huggins (8), except that a consequence of that theory relating t o the diffusion constant is far from being wtisfied. In cellulose and derivatives the product D E ,where D is the diffusion constant, is not constant but increases rather rapidly n ith z . This indicates a consitleiable hydrodynamic interaction of the monomer units in the molecular chain, an effect neg!ected in the Huggins theory . T-ery recently more elaborate theories of viscosity and dift'usion have heen developed by Debye and Bueche ( 3 ) and tiy Kirkwood and Riseman (11). The t n o theories predict a very similar monotonic decrease of [TI z as i increa-e-. result-
1064
RICHARD M. BA4DGER A S D ROBERT H. BLllKER
ing from the hydrodynamic interaction above mentioned. Both theories propose a relation hetneen diffusion and viscosity data, but since this relation is rather more explicit in the IGrkn-ood-Riseman theory, and is based on a more definite
molecular model, our discussion Tvill be largely restricted to that cabe. Both theories represent adequately the molecular u-eight dependence of viscosity in polystyrene, etc., but the more severe test of correlating viscosity and diffuiion data has not yet been made. In attempting to apply either theory to rellulose and its tlerivativei one meets n-ith serious difficulty. If the parameters are so chosen as t o fit the tlctrenic in [17]/z which iets in n-ith z 400, the region in which it is relatively constant i> not well represented, as will lie shown belon-. The reason for the failure of the theor- in the lon--molecular-n-eight range is obvious if one con4dw> tlw data in table 4.The statistical methods employed are only valid when 2 i h not lOCJ small, and the more restricted the rotation of groups in the molecular chain, the larger the value of x at which the theory becomes applicable. The lon cr limit of applicability may be roughly estimated as follows: The statistical treatment yields the result that for x sufficiently large, R = bz’:?, where R is the root-meansquare distance between ends of the polymer chain and the proportionality constant b is an “effective” bond length. The more restricted the rotation the greater will he the ratio of b to bo, the actual length of the monomer unit. But since it is physically impossible that R be greater than bz we may expect that the statistical method will be applicable only when boz > bz”?, or when z > S o w all measurements agree in indicating that the molecules of cellulose and its derivatives are rather stiff and at moderate molecular weights are nearly fully extended. In the case of nitrocellulose our light-scattering data yield the value b 54 8. (table 4). From x-ray data on cellulose n-e may take bo 3.1 8. Consequently we may espect the Iiirkwood-Riseman theory t o fail when x < 100, and t o predict too high values of [ 7 ] / 2 for smaller values of x . This indeed appears t o be the case. There are fen viscosity and molecular lveight data for z < 100, but esamination of all reliable data on fractionated cellulose acetate or nitrate with which n-e are familiar suggests a rather surprising fact,-namely, that [7]lx appears to have a broad maximum at x 120. S o one set of data by itself at all adequately supports this conclusion. I n some cases the measurements do not extend t o sufficiently low molecular weights so that the observed falling off of [7],’z is greater than experimental error. I n other cases the data have not been interpreted in the manner now regarded as most acceptable. However, it is rather impressive that seven sets of data, involving molecular weight determinations by four methods, all more or less strongly support the conclusion. These data are quoted in table 5 and a fen. sets are represented in figure 6. The region x < 80 would repay investigation, but this will be rather difficult, since the range of special interest i b precisely that in which molecular weight determination becomes very difficult. One can, however, make a rough estimate of the behavior to be expected in this region. When z is small the length of the stiff cellulose molecule will increase with a
-
-
-
-
SIZE A S D SHhPE O F SITIIOCELL~LOSEMOLECULES IS SOLUTIOS
1065
poxer of z Tvhich is at first nearly unity, Ilut gradually decreases with increasing z . I n this region the Simha (14) treatment of the elongated prolate ellipsoid should
be reasonably 11-ellapplicable and [ 7 ] / z may be expected t o increase n-ith a pon-er
RLFEREXCES
5 . . . . . Acetate 6 . . . . . Acetate 7 . .. . . .Icetate
Osmotic pressure Osmotic pressure Sedimentation r a t e
~
Blaker et al. Bndgley a n d Mark Sookne a n d Harris Singer, Sookne, and Harris
* These authors used a thermodynamically unacceptable function t o catrnpolnte t h e reduced osmotic pressure to zero concentration a n d t h e reported molecular n eights a r e consequently somewhat in error If t h e d a t a a r r recalculated according t o accepted practice, the values of [&z s h o n a trend i n rensonnhlc agreement n i t h other t i n t n .
r
0 BADGER AND BLAKER
a)
MOSIMANN (13) 8 SOOKNE AND HARRIS(16) ACETATE SINGER (15)
I5
0 BAOGLEY AND M A R K ( I )
p 2
FIGCRE. 6. Plot of
[ q ] / z cersus
21'2
for cellulose nitrate and acctntc
of z at first somewhat less than unity, and slowly diminishing. -1s the slight fles-
ibility of the molecule accumulates, the random coil model will eventually become applicable and Tq]/z will decrease, as is predicted by the never viscosity theories and is observed for x > 120.
1066
RICHARD M. BSDGER BXD ROBERT H. BLAKER
The approximate validity of the simple Staudinger relation over the range of molecular n-eights n-hich is of most practical interest is consequently seen to be rather accidental and results from the occurrence uithin that range of a flat maximum of [17] ' z in the transition region where the cellulose molecule loies the character of a rigid rod and gradually assumes that of a random coil. This mahimum may hare interesting consequences 11hen the Staudinger equation i q used for estimating weight-average molecular n-eights of heterogeneous materials. The viscosity and d i f h i o n data on cellulose and derivatives are inadequate for making a really satisfactory test of the Kirkxood-Riseman theory in the region in n-hich it may he expected t o be valid. J1-e nevertheless present our own data together n-ith those of other investigators on cellulose acetate, for compar-
3c
- 2c
mo
N
n
IC
ison. I n figure 7 the diffusion data are plotted. According t o the KirkwoodRiseman theory the plot of I l x iersits z1 should be a straight line. Though the data 011 nitrocellulose are admittedly not precise, they show the same trend as data on unfractionated material obtained by Jullander (10) and u-e consequently believe that the slope of the line drawn through the points can not he greatly in error. The viscosity and diffusion equations of IGrkn-ood and Riseman involve tu-o molecular parameters: b, the eff'ective bond length, and t, the frictional constant of the monomer unit. 1-alues of these constants obtained from the slopes and intercepts of the plots of figure 7 are given in the first ron- of table 6. I n the case of the nitrate the effective bond length, b, lies n-ithin the limits determined from our light-scattering measurements. I n the case of the acetate the agreement is
SIZE ASD SHAPE O F SITROCELLULOSE MOLECULES I S SOLI-TIOS
1067
less good. It seems possible to us that Stein and Doty (17) have somen-hat overestimated the asymmetry of scattering due to the presence of contamination. Certainly, to judge from the viscosities, one should expect b for the acetate t o be smaller than for the nitrate if {, the frictional constant of the monomer unit, is of the same order of magnitude. It is obviously not possible t o ohtain a unique set of parameters from the viscosity data alone, since the I
