THECONFORMATION OF CELLULOSE TRICAPROATE
Jan., 1960
99
THE CONFORMATION OF POLYMER MOLECULES. 111. CELLULOSE TRICAPROATE] BY W. R. KRIGBAUM AND L. H. SPERLING~ Department of Chemistry, Duke University, Durham, N . C . Received J u l y 20, 1969
Cellulose tricaproate exhibits the properties characteristic of inflexible chain polymers. The intrinsic viscosity [q] decreases rapidly with temperature, and the ratio of the [q] values in different solvents is independent of molecular weight. I n thermodynamically good solvents the molecuIar expansion factor 01 remains near unity and is independent of molecular weight. Theta temperatures were determined for the tricaproate in dimethylformamide and in a dioxane-water mixed range. The Flory solvent. Light scattering measurements were performed upon six fractions spanning a thirty-fold hydrodynamic parameter 9' is still below its asymptotic limit for a degree of polymerization ( N ) , = 2600, and decreases a t lower molecular weights. The same variation has been reported for cellulose trinitrate, and this is in accord with the recent theoretical treatment of Stockmayer and Albrecht. On the other hand, the ( s 2 / N )ratio for the tricaproate becomes larger as the molecular weight is decreased, which is the reverse of the variation predicted for non-gaussian chains by Benoit and Doty, and observed experimentally for cellulose trinitrate. Under theta conditions [q] N Mlh, despite a considerable variation of both and (s?/N) with molecular weight. Due to the cancellation of these opposing variations, the exponent a in the relation [q] = K'Ma is only slightly larger than 0.5 for thermodynamically good solvents. This low value of the molecular m i g h t exponent observed in good solvents is unique, since under these conditions a = 0.7 to 0.8 for flexible chain 1.0 for the lower cellulose esters. The (>/N) ratios observed in a good solvent, 1-chloronaphthalene, polymers and a are smaller than those measured under theta conditions in dimethylformamide. This suggests that the unusual variation of (s?/N) with molecular weight observed for the tricaproate is a skeletal effect. An examination of the solvent dependence of [ q ] suggests that London dispersion forces, rather than dipole interactions, are responsible for the high barrier to rotation :&boutthe chain bonds which gives the cellulose derivatives their unique molecular properties. Thus the difference between the cellulosics and the more flexible molecules is one of degree, rather than kind.
+'
-
The study of flexible chain polymers has led to a rather satisfactory understanding of the manner in which the molecular size and hydrodynamic properties of these polymers depend upon such factors as the molecular weight, temperature and solvent power. This behavior may be summarized briefly as follows. The unperturbed mean- sq uare radius of gyration s 7 is proportional to the molecular weight 41. Thus, at a given temperature the ( s T / M ) ratio is a property of the polymer examined, and is independent of the chemical nature of the particular theta solvent chosen. As the temperature is raised the (G2/M) ratio decreases slowly, indicating a relatively small potential energy hindering rotation. In thermodynamically good solvents the average molecular - -dimensions are expanded by a factor a = (s2/so2)1/z which increases with molecular weight, a t least over the range which is accessible to study. The relation of Flory and Fox3 adequately describes the behavior of the intrinsic viscosity for these polymers [VI = 0' (Zz/M)a/*Ml/zO13
(1)
where Q' is a constant. The equation implies that for viscosities measured under Flory theta conditions the [ q ] e / M ' / 2 ratio should be independent of molecular weight. This predicted constancy has been verified4 for polystyrene and polyisobutylene down to molecular weights of the order of 10,OOG. For thermodynamically good solvents the treatment of Flory5 predicts a X O . 'so , t,hat according
-
( I ) For the grcwdirig papers of this series see W. R. Krigbauiii and I ) . li. C a r p e n t r r , T I I I R J O C R N A L99, , lltiG (1955); 62, l58fi (1458). ( 2 ) Buckeye Cellulose Corporation, Melnphis. Tenn. ( 3 ) P. J. Flory and T. G . Fox, Jr., J . A m . Chem. Soc., 73, 1904 (1951). (4) W. R. Krigbaum, L. Maridelkern and P. J. Flory, J . Polymer Sei., 9 , 381 (1952). (5) P . J. Flory, J . Cheni. P h y s . , IT, 303 (1949).
to equation 1 the exponent a in the empirical molecular weight relation [V] =
K'M5
(2)
should exhibit a maximum value of 0.8. Experience has shown that this rule also is generally obeyed. In summary, one obtains the impression that the principal factors affecting the behavior of flexible chain polymers are well in hand, and that the objective of further refinements will be limited to improved quantitative agreement. There is a second class of polymers, of which the cellulose derivatives are the best known examples, whose behavior is quite different from that outlined above. The ( $ / M ) ratio for these polymers varies with molecular weight, and only approaches an asymptotic value for molecular weights of the order of 105-106.6-7 I n thermodynaniically good solvents the molecular expansion factor Q is only slightly larger than unity, and for many of these polymers is essentially independent of molecular weight. The intrinsic viscosities of the cellulosics display large negative temperature coefficient^,*-^ reflecting the relatively high barrier to rotation about the chain bonds. For a fixed temperature, the ratio of the intrinsic viscosities in two different solvents appears to be practically independent of molecular weight, and does not correlate with the values of t,he second virial c o e % ~ i e n t ~as - ~ do ~ those of the polymers having more flexible chains. (ti) -4.XI. IIoltzcr, 11. Bcnoit and P. Doty, THISJoclth-aL, 6 8 , 624 (l!IR4). (7) M. I,. Iliirit, 8. Neivinan, 11. A . Sclirrarca arid 1'. .I. l'lory, ibid., 60, 1278 (14.56). (8) I.. hlaridclkcrn aiid f. J . l l u r y , J . A n i . Clicm. S o c . , 74, 2517 (1952). (9) P. J. Flory, 0. K. Spurr. Jr., tlnd D. K. Cariieritcr, J . f'olymer S c i . . 27, 231 (1958). (10) W. R. Moore and J. Russell. J . Colloid Sei.. 8, 243 (1953): 9 , 338 (1954).
w.R. KRIGBAUM AND L. H. SPERLING
100
Finally, for cellulose trinitrate the parameter a’ in equation 1 has been found7a1l t o decrease quite markedly as the molecular weight is lowered. From the foregoing it is clear that the essential difference between these two classes of polymers is the more inflexible molecular structure characteristic of the latter group. For these polymers the dependence of the intrinsic viscosity upon solvent power and temperature must reflect primarily variations of the unperturbed molecular dimensions. However, the origin of the forces responsible for this large hindrance potential, and the influence of the solvent upon this rotatioral barrier, require further elucidation. The fact that many of the cellulose derivatives have extremely high melting points makes the direct measurement of their unperturbed dimensions very difficult, if not impossible. The only data obtained under theta conditions are those of Mandelkern and Flory for the tributyrate and tricaprylate esterse8 Only in the latter case were they able to achieve theta conditions using a single liquid as the solvent, but unfortunately the intrinsic viscosity of this polymer does not have a large negative temperature coefficient, as do the butyrate arid lower esters. We have therefore selected the tricnproate for investigation, hoping to obtain a polymer which could be studied conveniently under theta conditions, but which still retains the properties characteristic of the molecules with strongly hindered rotation. Theta temperatures were determined by osmotic pressure and precipitation temperature measurements. We then performed a study of the molecular dimensions and hydrodyiinmic behavior of a series of fractions, both under theta conditions and in thermodynamically good solvents. Experimental Samples .-Two batches of cellulose tricaproate having a total weight of 115 g. were prepared from purified cotton linters by the method of Malm, et aZ.12 Analysis of these gave for the first C = 63.1% and H = 8.80%, and for the second C = 63.2% and H = 8.89%. These compare favorably with the theoretical triester composition, C = 63.lwO and H = 8.76%. The two saniples were individually subjected to two stages of fractionation by a rapid extraction process described elsewhere . I 3 The dioxane-water system was employed, and the initial polymer concentration was 1% in eatch case. The ( M ) v / ( M ) nratio for the whole polymer was estimated from the cumulative curve to be about 4.5, while for most of the fractions this ratio fell in the range 1.1-i.6. Viscosity.-Flow times were measured using a Ubbelohde viscometer. The solutions were filtered into the viscometer through a medium porosity sintered glass disc. Kinetic energy corrections were applied, but the effect of shear rate was not investigated. Osmometry.-Stahin osmometer^'^ were used with Type 300 regenerated cellulose mem ranes.16 Static measurements were obtained and the diffwence in height of the liquid levels was read to 0.01 mni by means of a cathetometcr. Light Scattering.-The light scattering amarntus ha8 (11) 11. 31. IIii,q?it~,D. .A. I. Goring and 6. C . RIason, Can. J . Chem., 36, 952 (1955). (12) C , J, Rlalm. ,J. TV. Mench. D. L. ICendnII a n d G. D. Hiatt, I d . Eng. Chem., 43, 084 (19.51). (18) IV. R. Kriehaiini aut1 11. Kotliar, J . I’olurner Sei., 34. 323
(i95a). ( 1 4 ) J.
V. Stabin and E. H. Iinrnergnt, ibid., 14, 209 (1954).
(15) Obtained from Sylrania Division. American Viscose Corporation, Fredericksbura, Va.
Vol. 64
been described previously.lB The solutions were clarified by filtration into the light scattering cell through ultrafine porosity sintered glass, followed by centrifugation in the cell a t 55,000 g for 30-45 minutes according to the procedure described by Dandliker and Kraut.” Comparison of the scattering curves for these solutions with those clarified by filtration alone indicated the centrifugal procedure to be definitely superior. A cross-sectional view of the temperature controlled cell holder is shown in Fig. 1. Outer glass cell A, which is filled with solvent, serves as a constant temperature bath. Magnetic stirrer I is turned by disc magnet J. The lattcr is cut in the form of a pulley, and irr belt driven by a motor attached to base K. Cell A is wrapped with blackened asbestos paper, and carries two windings of resistance wire. One of these Berves as a steady heater and the other as an intermittent heater controlled by a Sargent Model S Thermonetor. Brass top B allows the insertion of the thermistor probe and a copper-constantan thermocouple used to measure the cell temperature. Scattering cell E R i positioned by the blackened brass p!ate C which fits over Teflon cap D, and by etand H. The entire assembly is positioned on the stage of the light scattering instrument by two perpendicular bars meeting the sides of stand K . The turbidities reported are relative to a 0.5070 toluene solution of the Corncll standard polystvrene, taking for the latter 7 = 3.51 X 10-3 em.-’ a t 4358.4. and 1.36X cm.-l a t 5461 A.1‘3918-19 The reciprocal of the reduced intensity for t,he standard polyst,yrene solution was a linear function of sin2 (e/2) to wit,hin 1% from 45 to 1 2 5 O , a;d corresponded to a dissymmetry zd6,of 1.18 dz 0.01 a t 4358 A. and 1.12 =k 0.01 at 5461 A. Measurements of dn/dc were performed using a Brice-Phoenix differential refractometer calibrated with aqueous sucroFe solutions, taking for the latter dnldc = 0.1436 a t 5461 A.
Experimental Results
A. Determination of Theta TemperaturesThe two theta solvents investigated for cellulose tricaproate were dimethylformamide and a dioxanewater mixture (100 to 7 by volume). The theta temperature for the single solvent was determined by osmotic pressure measureineiits performed upon fraction D at 30, 41.6 and 53.5’. The results appear plotted as a/c us. c in Fig. 2. A membrane dissymmetry which developed during the course of these measurements introduced a fairly large uncertainty in the results obtained for the lowest concent,ration. The second virial coefficient A2 may be expressed as A, = (oz/T’l)$,l(l
-
F(S)
(3)
where 8 a i d VI are the partial specific volume of the polymer and the molar volume of the solvent, respectively. Since 1 1 2 v:misiies at the thetn temperature, from the plot of A , z’s. t (“C.) shown in the insert to Fig. 2, we obtain 8 = 314 f 1°K. After assignment of this value, the +,F(X) products shown in column four of Tsble I were calculated. These are found to be essentially independent of temperature, and t,o lead to a value of the entropy parameter, of 0.10 * 0.01. This behavior should be contrasted with the relatively large temperature dependence of F ( X ) observcd for polyisobut,vleriezo and polyst,yrenez1 in the (If,) (1956) (17) (1956). (16) ( 19.50) (19)
I). K. C:upenter and IV. R. Krigbaltm, J . Cljenl. I’JLw., 24, 1041
I
W. B. Dandliker and J. ICrarit,, J . A m . C h e m .
S o c . , 78, 2380
C. I . (‘err, Jr., and R . H. Zinrrn, J . Ciiern. Z’hr,.s.,
18, 1624
I
A. Oth, J. 0 t h and 1’. Deureux, J . Poliime?
(20) TV. R. Krighaum and P. J. Florp, J . A m . Chem. Sor., 7 6 , 177.5
(19.53). (21) W. R. Krigbaurn, ibid., ‘76, 3738 (1954).
THECONFORMATION OF CELLULOSE TRICAPROATE
Jan., 1960
101
4
vicinity of the theta temperature. Since F ( X ) is a function of X = 2(a2 - l ) , the observation that for cellulose tricaproate F ( X ) is nearly independent of temperature near theta places this polymer in the inflexible chain category.
,,B,,,
TABLE I THXR\IODk7SAJIIC PARhXETEHS FOR CELLVLOSE TRICAPROATE DETERMINED OSMOTICALLY ll. Fraction D in dimet,hylformnmide t (o c . )
10 -y ,If j n
30.0 41.6 53.5
1.36 1.31 1.29
13.
A2
1Oj
-5.8 0.5 6.5
-+
F(X1
0.103
... 0.107
Fract,ion E in dioxane--water (100:7) .------lDs
AT------.
t("C.)
10q M ) n
(I
37.1 41.3
(2,OB)
-1.9 -0.94
49.4
$1
(2.06) ( 2 ,OB)
= 0)
3.7
(t =
m)
8.5 17 46
The determination of the theta temperature for the dioxane-wa,ter system was performed both by osmometry and by precipitation temperature measurements. The osmotic measurements were complicated by partitioning of the mixed solvent across the membrane. This effect has been investigated theoretically,22-26but has not received much attention from the experimental point of view. We may expect the observed osmotic pressure to increase with time, since the compoeition of the solvent in the solution compartment will become progressively richer in the thermodynamically good solvent. However, because we do not start a t osmotic equilibrium there will be two processes going on simultaneously. It turns out that the normal approach to osmotic equilibrium by the gross transfer of solvent through the membrane is 5 to 15 times more rapid than the partitioning of the solvent. As shown by the open circles in Fig. 3, if Ah is set to a high value there is initially a rapid decrease toward osmotic equilibrium, followed by a slow rise (due to exchange of solvent) which continues for several days. We let Aho and Ah, be the equilibrium differences in heights which would be observed a t zero time (no solvent interchange) and at infinite time (a.fter completion of interchange), and designate the non-equilibrium value observed a t time t be Aht. Furthermore let Aht = Ah, - Aht and Ah0 = Ah, - Ah0 (see Fig. 3 ) . If we assume that the exchange of solvent follows the same first-order rate law as does the normal approach to equilibrium, then after a sufficient time log 6h' = log 6ho - b t
(4)
For each set of data a trial value of Ah, was assumed and the corresponding 6ht values were plotted as log Aht vs. 2. This process then was (22) (23) (24) (25) (1953). (26) (1054).
G. Gee, Trans. Faraday Soc., 40, 463, 468 (1944). F. T. Wall, J. A m . Chem. Sac., 66, 447 (1944). R. L. Scott, J . Chem. Phys., 17, 268, 279 (1949). T. Kawai, J . Chem. Soc. Japan, 26, 336, 341 (1952); 26, 6
1%'. R. Krigbaiim nrtd 1). K. Carpenter, J. Polumer Sei., 14, 241
Fig. 1 .-Diagram of the temperature controlled cell holder for light scattering (see text for discussion).
0"
i
-1
1
I
IO
20
io3c (g /mi 1, Fig. 2 . 4 s m o t i c data for cellulose tricaproate fraction D in dimethylformamide a t three temperatures.
repeated using a better approximation for Ahm until a linear relation was obtained. From the intercept of this line, which is 6h0, and the assumed value of Ahm one may calculate the value of Aha which would have been observed if no solvent exchange had taken place. Some typical results obtained for the log aht vs. t plot are illustrated in Fig. 4. Our data show that 6ho for a given solution increases quite rapidly with temperature, and that ICl is, to a first approximation, a linear function of the polymer concentration. In this connection we note that since the volume of the solvent compartment is a t least twenty times that of the solution cell, the composition on the solvent side can be assumed to be unaffected by the interchange. Figure 5 shows the values of T / C obtained a t three temperatures for fraction E in the dioxanewater mixed solvent. The filled circles correspond to values of Ah0 (no interchange). For comparison, the open circles in Fig. 5 illustrate the behavior of x / c corresponding to Ah, (complete exchange)
W. R. KRIGBAUM AND L. H. SPERLING
102
I
I
\p i
24
22
Ah (cm ),
I
I
t
Vol. 64
--
7------
2c
\ I € -
\
b
!/ /
1
I C
I i
1 10
20
30
40
time in hours. Fig. 3.-The variation of Ah with time for cellulose tricaproate in the dioxane-water mixed solvent as observed with solvent interchange ( 0 )and as calculated for no interchange (@).
1.6
c ( g /100ml)
Fig. 5.--?r/c vs. c for cellulose tricaproate fraction E in the dioxane-water mixed solvent if no interchange of solvent takes place (0)and after completion of the solvent exchange (0).
30
0
5
wt % polymer.
,
I
20
40
60
80
100
120
time (hrs ), Fig. 4.-Plot of log ahr os. time used t o eliminate the effect of solvent exchange for the osmotic data obtained a t 49.4' ,).( 41.2' ( 0 )and 37.1" ( ).
at the two temperatures. Measurements also were conducted upon this same polymer fraction in dioxane a t 35", yielding (M)= = 206,000 and A, = 7 X The lines in Fig. 5 were drawn so that the intercepts correspond to this molecular weight. The A z values obtained for the mixed solvent are shown in Part B of Table I. Upon plotting the A z values corresponding t o zero time against temperature, as shown in the insert to Fig. 5 , there is obtained 0 = 316 f 3°K. Precipitation temperature measurements were also performed for the same dioxane-water mixture. Solutions varying in concentration from 0.1 to 8% were prepared using two polymer fractions having ( M ) , values of 206,000 and 743,000. These mere sealed in small glass tubes and placed
Fig. 6.-(Above) Precipitation temperatures for = 2.06 X 106 (curve A) and 7.43 X lo5 (curve B) measured in the dioxane-water mixed solvent. The filled circles represent precipitation temperatures extrapolated to AT = m. (Below) Smoothed precipitation temperatures plotted against ( l / < M > n)l'2 for the concentrations (reading from top to bottom) 5 , 4,2 , 1 and 0.5%.
in a water-bath. The temperature was raised until all the samples were dissolved completely, and then slowly lowered (10"/hr.). The temperature was recorded at which each sample became
THECONFORMATION OF CELLULOSE TRICAPROATE
Jan., 1960
sufficiently turbid to obscure the numbers on a thermometer held behind it. The bath then was warmed slowly and the temperatures at which the solutions became clear were recorded again. This process was repeated until reproducible results were obtained. Although it was rather difficult to distinguish the point at which phase separation occurred, the difference between the precipitation and solution temperatures was usually less than 2". We have treated the data according to the procedure of Mandelkern and Flory.8 The precipitation temperatures observed for each molecular weight were plotted against concentration as shown in the upper part of Fig. 6. Smoothed values were read from these curves for several concentrations, and these were plotted against ( l/(M)n)'1% as illustrated in the lower portion of Fig. 6 . The intercepts, representing the precipitation temperature at each concentration for a polymer of infinite molecular weight, are indicated by the filled circles in the upper graph. These were extrapolated to zero concentration t o obtain 8 = 316 2 ° K . Although the close agreement between the theta values determined by the two methods is partially fortuitous, we do feel that these measurements constitute a verification of the semi-empirical procedure of Mandelkern and Flory for the treatment of precipitation temperature data for ternary systems. B. Determination of the Molecular Weight Heterogeneity.-A knowledge of the num&raverage molecular weight is required to characterize the heterogeneity of the polymer samples. This information is essential for the evaluation of the parameter a' appearing in equation 1. Newman, et a1.,2i have pointed out that for a heterogeneous polymer equation 1 becomes
*
[?I
=
a' ( ( S 2 ) 3 1 9 ) , / ( M ) ,
(5a)
whereas (.$ and (~lf), are the quantities actually measured. Thus, in terms of the experimental quantities 17
1
= (
'/w )( (i% W 1 l f )) w
(5b)
where
the evaluation of the correction factor, qz, has been discussed e l s e ~ v h e r e . ~ , ~ Nevertheless, ~-*~ a few words emphasizing the important role played by polymer heterogeneity may be in order a t this point. If one assumes a weight fraction distribution of the form j(.V) = (gh+'/h!)
h'he-u'
(7)
and ignores the small variation of the expansion factor a with molecular weight, then the correction factor becomes29
(27) S. Newman, W. R. Krigbaum, C. Laugier a n d P. J . Flory, J . Polymer Sci.. 14, 481 (1951). (28) A. R. Shultz, J . Am. Chem. Soc.. 76, 3422 (1954). (29) W.R. Krigbarim and 73. K. Carpenter, THISJOURNAL, 69, I l G G (1958).
50
103
t
i I
I
j
G
.--
2to
0
5
IO
~
F
15
~
20
io3c (g /mi Fig. 7.-Osmotic pressure data for cellulose tricaproate fractions in DMF a t 41" ( 0 )and in dioxane a t 35" ( 0 ) .
This correction amounts to 60% of the experimental value when (M)w/(M)n= 1.5, and qa = 1.95 when ( M ) w / ( M ) n= 2.0. If reliable a' values are to be obtained, the need for accurate knowledge of the polydispersity becomes more essential as the (A&/ (M)nratio increases. This remark applies particularly to the cellulosics, which are quite difficult to fractionate effectively. There is another aspect of the QQ correction which warrants our attention. If one employs the Lansing-Kramer distribution in place of equation 7, then the appropriate correction iszi q9 =
((Af)w/(M)*)I3/8
(8b)
Values calculated according to those two relations diverge rapidly as the (M)w/(M)n ratio increases. Since the precise form of the molecular weight distribution is seldom (if ever) known, this introduces an uncertainty which can only be minimized by keeping the molecular weight distribution as narrow as possible. I n the calculations which follow we have used the correction as given by equation 8a. Figure 7 shows the results obtained by osmotic pressure measurements performed upon fractions B, C and F in the theta solvent, dimethplformamide a t 41" (314"K.), and for fractions E, G and H in n thermodynamically good solvent, dioxane, a t 35". The determination of ( M ) n for fraction D was discussed in Part A. These (AI), 2nd A , values are listed in columns three and seven of Table 11. Columns four and five give ( M ) , values determined by light scattering measurements (described below) using dimethylformamide and l-chloronaphthalene as the solvents. The A2 values observed using the latter solvent appear in column eight. C. Light Scattering Measurements.-Molecular weights and dimensions were determined using three solvents : l-chloronaphthalene at 24", the dioxane-water mixture a t 63", and dimethylformamide at 41 O (theta conditions).
W. R. KRIGBAUM AND L. H. SPERLING
104
Vol. 64
solvents which have been chosen for light scattering studies have had lower refractive indices, e.g. , acetone (1.36) and ethyl acetate (1.37). Past experience has shown that clarification of the solutions becomes progressively more difficult as the refractive index of the solvent is decreased. Water, which has an unusually low refractive index (1.33), is an outstanding case in point. This suggests that the dust particles responsible for the undesired scattering have a relatively high refractive index. This reasoning led us to choose 1-chloronaphthalene (n = 1.63) as a thermodynamically good solvent for light scattering measurements. We experienced no difficulty with the clarification of these solutions. The dn/dc value measured at 24" for the 5461 A. wave length was 0.147. We were unable to perform light scattering meas0 0.5 1.0 urements at the theta temperature of the dioxanes i t (#) water mixed solvent due to phase separation at the Fig. 8.-Angular dependence of the reciprocal scattering concentration level required to achieve sufficient intensit for fraction H in 1-chloronaphthalene. Values excess scattering. As would be expected from Fig. extrapo%ted to infinite dilution are indicated by open circles. 6, viscosity measurements could be carried out for solutions of much lower concentration a t the theta I I temperature without difficulty. The light scattering measurements were therefore performed at 63". 30 L The dn/dc value observed at this temperature was 0.104 for the 5461 k. wave length. Of the three solvents investigated, this mixed IO6 K solvent had the lowest refractive index and was the most difficult to clarify. After our customary filtration and centrifugation procedure described in 20 the Experimental Section, each solution was carefully transferred to another cell and centrifuged again for 30 minutes a t 50,000 g before the measurements were performed. Dry weight analysis indicated that this procedure did not change the solution concentration by a measurable amount. IO The refractive index of dimethylformamide is 1.43, and the dnldc values measured a t 5461 and 4358 A. were 0.0478 and 0.0442, respectively. The data were plotted as Kc/R us. sin2 (0/2), where R is the reduced scattering intensity. This is illustrated in Fig. 8, in which the filled circles represent data obtained for three concentrations of IO 20 fraction H dissolved in 1-chloronaphthalene. The lo3 c (g./rnI.), intercepts represent the corresponding values at Fig. 9.-Reciprocal of the reduced scattering intensity a t zero angle, and these must be plotted against conzero angle plotted against concentration for cellulose tn- centration. Figure 9 shows the zero angle intercaproate in DMF a t 41' ( 0 )and in 1-chloronaphthalene a t cepts plotted against concentration for all of the 2 4 O (0). fractions. The intercepts of these lines were used TABLE I1 to evaluate the weight-average molecular weights, In order t o determine the z-average MOLECULAR WEIGHTDATAFOR FRACTIONS OF CELLULOSE (M),. mean-square radii of gyration, (s2),, data for TRIC.4PRoATE other angles were plotted in the same fashion as the % of 104 A~ whole 1zero angle data shown in Fig. 9, and the intercepts Frae- poly--(M)T--Diox- C1tion mer (M), DMF 1-Cl-N (M)n ane N were plotted against sin2(O/2) as illnqtrated by the A 4 2 ..... 41,700 .... .. .. . . open circles in Fig. 8. Then was deterB 5.6 61.000 .... 62,500 1.03 . . 6.5 mined in the usual fashion from the (slope/interC 2.8 70,000 (98,400)" (1.3) .. .. cept) ratio of this line. Since the concentration D 1 9 . 6 lX?.OOO 208,000 212,000 1 . 8 1 . . 8.6 dependence mas essentially linear, equivalent reE 14.4 t'08.000 (195,000)~ (-1.0) 7.0 . . F 1 2 . 1 275,000 . . 230,000 (-1.0) . . 5.0 sults could be obtained using the Zimm plot.30 G 4 0 31.5,000 352,000 .... 1 . 1 2 6.9 . . Figure 10 shows the data obtained under theta €I 1 1 . 1 743,000 1 , 4 8 0 , 0 0 0 1,310,000 1.76 3 . 0 1 . 1 conditions for fraction H in dimethylforniamide a Calculated from eq. loa. plotted in this way. Most of the cellulose derivatives have refractive (30) P. Outer. C . I. Carr and B. €1. Z m m , J. Chem. Phys., 18, 830 indices near that of the tricaproate, n = 1.47. The (1950).
/I
' I
~
9 '
(M)W
,
,
THECONFORMATION OF CELLULOSE TRICAPROATE
Jan., 1960
The depolarization correction varied from 1.03 t o
1.07 for these solvents. Fluorescence was observed at the 4358 A. wave length during the measurements upon fractions A, D and H in diniethylformamide. The fluorescent intensity was measured and an appropriate correction was applied. The corrected ( M ) , for fraction A differed by only 5% from the value determined a t the green wave length, while the corrected value for fraction H was 13% higher than that measured in l-chloronaphthalene. The ( M ) , values appear in columns four and five of Table 11. The va.lues listed for fractions A and D in dimethylformamide are those measured at the green wave length (where no fluorescence was observed). Column eight of Table I1 gives the values of the second virial coefficient Az calculated from the 1-chloronaphthalene data. The weight-average and z-average degrees of appear in polymerization, ( N ) , and columns two and three of Table 111, while column four gives the experimental (&, values. The 9' values listed in column five were calculated according t o equations 5b and 6. The values of the intrinsic viscosity required for this calculation were taken from Table IV which appears in a later section. Comparison with the value 9' = 3.2 X characteristic of randomly coiling polymers shows that the @' value exhibited by a cellulose tricaproate having ( N ) , = 2660 has not yet reached this asymptotic value.
105 1
I 25
107~C
R
15
a=o i 5
10
s J B
+
15
1 0 3 ~
Fig. 10.-Zimm plot of the data for fraction H in dimethylformamide a t the theta temperature.
erogeneities of these samples were not measured ; however, one might expect the distributions to be even broader than (M),/(A& = 2.0 as assumed by these authors, which mould augment the reported 9' values, thus further increasing the discrepancy. A recent theoretical investigation by Stockmayer and Albrecht31has shown that the Flory pirameter P appearing in the expression for the frictional constant depends to some extent upon the excluded volume. It seems quite likely that the same will be true of the parameter 9'. Since this variation arises from the departure of the chain from gausTABLE 111 MOLECULAR SIZEAND HYDRODYNAMIC PARAMETERS sian form, one would expect inflexible chains, such as the cellulosics, to exhibit a similar behavior as the molecular weight is decreased. Turning next to the molecular dimensions, we A. 1-Chloronaphthalene a t 24" have calculated the values of the molecular expansion factor CY = ([v]/[~]e)l/a appearing in column 0.24 1.01 127 5.49 424 B 124 six of Table I11 from the observed A,, ( M ) , and .87 1.09 D 420 579 12.0 175 [77] (Table IV below) through use of the relation9.49 1.03 1.05 F 466 532 162 ships2 1.40 1.05 H 2600 3710 51.5 126 [q]
B. Dimethylformamide a t 41"
A
G H
83 411 696 2920
H
2600
D
..
..
..
..
..
564 770 4400
17.0 17.8 65.5
0.60 .G2 1.47
..
301 23 1 149
.. ..
C. Dioxane-water (100:7) a t 63" 3710
56.2
1.15
1.05
138
Holtzer, et aZ.,6concluded from their observations upon cellulose trinitrate in acetone that although 9' may increase somewhat with (N),, this variation is within their experimental uncertainty. On the other hand, Hunt, et aL17reported that 9' exhibits its asymptotic value for the trinitrate in ethyl acetate only when ( N ) , > 2000. Huque, et UZ.," investigated a series of high molecular weight nitrate samples ( ( N ) , = 2200 t o 8400) in both of the solvents mentioned above. Their data for ethyl acetate confirm the conclusion of Hunt and co-workers, but they report that for acetone a' is still increasing with ( W ) , a t the highest molecular weight investigated. For their three samples of highest molecular weight a' E 4 X lo", which exceeds the asymptotic value, 3.2 X The het-
-
[?]e = 1.43 X
9' A2(&&
(9)
The @-valuesfor the tricaproate in thermodynamically good solvents are seen to be only slightly larger than unity and essentially independent of molecular weight. As mentioned previously, this behavior is exhibited by the trinitrateaf7and appears to be characteristic of inflexible molecules. The (G2)J (AT), ratios calculated through use of these CYvalues are listed in column seven of Table 111, and appear plotted against (N)w in Fig. 11. The number of repeating units in the chain was chosen as the indepelident variable in order to permit a more meaningful comparison with the published data for the trinitrate.6J-'l We observe in Fig. 11 that for both polymers ( g / N ) approaches an asymptotic value a t very high degrees of polymerization. For shorter chains the (ST,") ratio exhibits a marked solvent dependence. Since the tricaproate exhibits smaEler dimensions in the thermodynamically good solvent, 1-chloronaphthalene, than in the theta solvent, di(31) W. H. Stockmayer and A . C . Albrecht, J . Polymer Sea., 32, 215 (1958). (32) W. R. Krigbaiim, J . Polumer Sci., 18, 315 (1935).
W. R. KRIGBAUM AND L. H. SPERLING
106
60C
\
(s -.
3,
cellulose 0,b cellulose
- chloro~phlholene
tricoproate
trinitrote
(N), 400
ethyl
2oc
-
ocetote
1 .
% -
I
102
IO4
103
(N), .
.
Fi ll.-,/, plotted against , for cellufose tricaproate (filled circles) in dimethylformamide and l-chloronaphthalene and for cellulose trinitrate in ethyl acetate ( O ) 7 , (/?)I1 and in acetone (O),O ( A ) . l l
Vol. 64
upon the molecular weight dependence of the intrinsic viscosity, as will be discussed below. If this be true, the treatment of non-gaussian chains developed by Benoit and Doty is not universally applicable to inflexible polymers. The most plausible explanation for the unexpected behavior exhibited by the tricaproate involves a shifting of the population in the various rotational states as the molecular weight is increased. D. Intrinsic Viscosities.-Table 1V lists the intrinsic viscosities measured in four solvents. These appear in Fig. 12 plotted against molecular weight using the conventional log-log scale. I n order t o separate the lines, the intrinsic viscosities shown for dimethylformamide, l-chloronaphthalene and dioxane have been multiplied by the factors 2, 4 and 8, respectively. The relationships obtained are = 1.25
[?I
x
10-3
(dioxane) (loa)
((~)~)0.67
= 1.70 X 10-3 ((M)w)OJ1(l-chloronaphthalene) (lob) [ale = 2.45 X ((M)w)OJO(dimethylformamide )(lOc) [p]e
= 2.24
x
((M),)O.M
(dioxane-water) (10d)
I n fitting these points we have neglected the data for fraction A of lowest molecular weight, since these consistently fell below the lines representing the remainder of the data. TABLE IV INTRINSIC VISCOSITY DATA LIIL
Frac-
I
0
/
I
I
4.5
5.0
I
I
55
60
log (M),
Fig. 12.-Molecular weight dependence of the intrinsic viscosity for cellulose tricaproate in dioxane at 35", in 1chloronaphthalene at 24O, in dimethylformamide a t 41' and in the dioxane-water mixed solvent at 43".
tion
(how
A B C D E F G H
41,700 62,500 (98,400) 212,000 (195,000) 236,000 352,000 1,310,000
Dioxane
360
0.326 .66 .90 1.32 1.32 1.72 1.72 3.36
1-C1;N 24
.. 0.46
IlLf: 41
0.32 .60
Dioxanewater 430
0.27 .539
..
..
...
1.00
1.22
1.07
..
..
1.27 1.18 2.19
1.58 1.53 2.72
1.38 1.36 2.35
..
One immediately notices the unusually low values of the molecular weight exponent, a , in the good solvents, dioxane and l-chloronaphthalene. We recall that the corresponding a values for flexible chain polymers fall in the range 0.7-0.8, while for cellulose trinitrate and triacetate a = 0.9-1.0. For an explanation of these differences we must consider the various factors in equation 1
methylformamide, we can be certain that in this case the solvent dependence is strictly a skeletal effect. For the trinitrate (&"/N) approaches an asymp[7/]= ~ . ' ( ~ / M ) ~ / L I P / Z ~ ~ (1) totic value a t large N from below. This behavior has As mentioned above, CP' and ( g / M ) are indebeen interpreted in terms of Benoit and Doty's pendent of molecular both weight for flexible chain polytreatment of non-gaussian chains. 33 However, as mers, so that the molecular weight dependence reshown in Fig. 12, the ( $ / N ) ratios for the tricap- sides in the M1/9a3product. For cellulose derivaroate in both solvents approach an asymptotic tives, on the other hand, a3is near unity a t all molimit from above. The earliest work on cellulose lecular weights. I n the case of the trinitrate both acetate34 and nitrate36also indicated an increase of @' and ( $ / M ) increase with molecular weight, re(so2,") as N was diminished, but these results are sulting in a large molecular weight exponent, a. of doubtful validity due to inadequate clarification However, for the tricaproate the variations of these of the solutions. Nevertheless, we believe that two quantities nearly cancel, so that the factor M112 the decrease of this ratio observed for the trica- makes the principal contribution in this case. proate is real in view of its profound influence We observe that for the tricaproate in the two (33) H.Benoit and P. Doty, THISJOURNAL, 67, 958 (1953). theta solvents the exponent is 0.50, just as would (34) R. S.Stein and P. Doty, J . Am. Chem. Soc., 68,159 (1946). be expected of a flexible chain polymer. However, (35) R. AI. Badger and R. 13. Blaker, THISJOURNAL, 63, 1056 both @' and (s?/M) are varying with molecular (1949).
Jan., 1960
THECONFORMATION OF
weight over the range of these measurements. If we assume that equations 10d and 1Oc can be extrapolated t o higher molecular weights where @' would attain its asymptotic value, then from equation l we estimate 10l6(s7/N) = 85-95. Reference to Fig. 13 shows that the latter is a reasonable asymptotic value for the D M F curve. From these values we obtain an effective bond length, b = (g/N)'/2, of 22-24 A. and a limiting persistence length q as calculated according to the relation of Benoit and Doty,22of 50-55 A. For comparison, the yalues for the trinitrate are b = 35 A. and q = 117 A. Thus, although the tricaproate is more extended a t low degrees of polymerization, its dimensions in the asymptotic region are smaller than those of the trinitrate. Flory, Spurr and Carpenter9 have concluded that the large negative temperature coefficient of the intrinsic viscosity characteristic of cellulose derivatives must have its origin in skeletal effects, rather than in osmotic effects. This is illustrated quite clearly in Table V, where the viscosities for our fraction H of highest molecular weight as measured in the dioxane-water theta solvent are compared with those reported by Carpenter and Krigbaum' for a high molecular weight polystyrene in the theta solvent cyclohexane. In each case the temperature was varied over a range of approximately 20". For polystyrene the intrinsic viscosity increases with temperature almost as rapidly as a3,since the accompanying decrease in (s,2/'M) is inconsequential. The A2 value increases relatively slowly with temperature due to the concomitant decrease of the factor F ( X ) appearing in equation 3. On the other hand the A z value for the tricaproate increases much more rapidly with temperature, since F ( X ) remains near unity. However, in spite of this more rapid increase of solvent power, the skeletal effect predominates and [ q ] falls off at higher temperatures due to the rapid reduction of (sT/M).
107
CELLULOSE TRICAPROaTE
1.2
14 .
6
18.
2.-
l.2
7.4
IO4 A
Fig. 13.-Correlation of the solvent dependence of the intrinsic viscosity for cellulose nitrates,a acetates,'o tricnproate and tricaprylates with the A parameter defined in the text.
formation, and if the population of bonds in the available rotational states becomes more randomly distributed as the molecular weight is increased. We would like to obtain some information concerning the origin of the forces responsible for the high rotational barriers in these polymers. We have seen that the (ST,")ratios for both the trinitrate and the tricaproate exhibit a large solvent dependence if the molecular weight is below the asymptotic region. This is certainly n manifestation of a skeletal effect in the latter case, since the observed dimensions are smaller in a good solvent, 1-chloronaphthalene, than those measured under theta conditions in DMF. Turning to Table IT', the intrinsic viscosities listed for these two solvents fall in the same order. Furthermore, except for the [q] value for fraction H in dioxane, the ratio of the intrinsic viscosities in any two of these solvents TABLE ST is independent of molecular weight, again suggesting that the solvent dependence is predominantly TEXPER~TURE DEPEXDEUCE OF [q] due to variations of the unperturbed dimensions. Cellulose tricaproate, = I n view of these considerations we have examined 1.31 X lo6,in dioxane-water Polystyrene, (A!& = 3.20 X (100: 7 ) 106, in cyclohexane the solvent dependence of the intrinsic viscosity t("C.) 104 A ? [a1 t(0c.) 104 A~ [?I more closely, hoping to obtain thereby some insight 2 35 35 0.00 1 20 into the forces responsible for the rotational energy 43 0 0 2 20 45 .31 51 0 4 1.78 barrier. 55 .54 2 10 2 08 A1 1 2 Since the therinodynamicinteractionsareexcluded from consideration, one might look for a correlaConclusions tion between the intrinsic viscosity and some physiWe have seen that cellulose tricaproate qualifies cal constant characterizing the solvent. Let us asas an inflexible chain polymer. Its unperturbed sume that dipolar interactions are responsible for molecular dimensions decrease rapidly with tem- the skeletal effect. We should then expect some perature, and in thermody~lamicallygood solvents relationship between the intrinsic viscosity and the the molecular expansion factor a is not much larger dielectric constant of the solvent. OnsageP has than unitv and is independent of molecular weight. shown that if the dipole is imagined to lie in a cpherThe departure of 9'from its asymptotic value pro- ical cayity of radius 6 , and to be surrounded by a vides further evidence that the tricaproate chains continuous medium of dielectric constant e , then in are non-gaussian. However, the tricaproate does the medium the reaction field of the dipole is renot obey the taeatment of non-gaussian chains set duced hy the factor f forth by Benoit and Doty, since (so7N) increases f = Lb3 2 c - 2 as the molecular weight is decreased. This exceptional behavior may be explained if the hin( 3 6 ) L. Onnaprr, J . A m . Chem. Roc., 68, 1486 (193G). drance pot)ential heavily favors one rotational con-
108
W. R. KRIGBAUM AND L. H. SPERLING
Vol. 64
the opposing variation of the osmotic expansion overtakes the skeletal effect. This is indicated in Fig. 14 by the fact that the [7]8 values as calculated by Flory, Spurr and Carpenterg for the triacetate exhibit the expected negative slope. The assumption stated above implies that it should be possible to correlate both the skeletal and osmotic effects with the A parameter. I n this connection it is interesting that Moorea8found that for a given class of solvents (e.g., ketones, formates, acetates, etc.) the intrinsic viscosity of cellulose nitrate could be correlated with the cohesive energy density (c.e.d.) of the solvent. Thus, he was able to express a skeletal effect in terms of a parameter which has been used for many years as a measure of the energy change on mixing. This suggests that the A parameter and c.e.d. are interrelated. We therefore plotted A values (assuming V , = 100 cc.) for a number of liquids ggainst their c.e.d. values. A = - (n2 - 1)/(2n2 + 1) The points conformed reasonably well to a linear (Pl'h + VP1/8)3 relationship, although some systematic deviations where VI and V , are the molar volumes of solvent were apparent. I n particular, the A values of the and of a polymer segment, respectively. In order higher paraffins were somewhat low, those of the to test this relation we require viscosity data for a aromatics tended t o be high, and that for CS2 was given polymer sample in a variety of solvents. considerably above the line. In general, however, Fortunately, Moore and Russell have obtained this the deviations were not large, so that we would antype of data for cellulose acetatelo and nitrateas ticipate about the same success in predicting ensamples having different degrees of substitution in ergy changes from A values as that achieved using a wide variety of polar solvents. Figure 13 shows ce.d. log [v] plotted as a function of A. The correlation In summary, dispersion forces, rather than dipole is quite satisfactory, particularly in view of the interactions, appear to be responsible for the high wide variety and highly polar nature of these solpotential barrier to rotation in the cellulosics. vents. The dispersion forces become weaker as A Hence, the difference between these polymers and increases, hence we expect a negative slope if skeletal effects predominate. This is the case for the tri- those having more flexible chains must be one of caproate and for three nitrate esters (one not degree, rather than kind. Acknowledgment.-This investigation was supshown). However, the slope is positive for the tricaprylate datas when these are adjusted to a ported by the Allegany Ballistics Laboratory, an common temperature, and for the diacetate and establishment owned by the United States Navy triacetate (not shown) esters.1° We believe that in and operated by Hercules Powder Company, these cases the chains are more flexible, at least under Contract NOrd 10431. L. H. S. wishes to under the conditions of these measurements, so that express his appreciation to the Tennessee Eastman Corp. for a fellowship during the final year of (37) F. London, Trans. Faraday Soe., 33, 8 (1937). his graduate study. (38) W.R. Moore, J . Polymer Sez., 5 , 91 (1950); 7 , 175 (1951).
However, attempts by Moore and Russell1oto relate the intrinsic viscosity of cellulose diacetate to the dielectric constant of the solvent met with no apparent success. Hence, the type of dispersion force first treated by Londona7appears to offer the only remaining possibility. In this case the time scale of the fluctuation is too short to permit orientation of a solvent dipole, so that one must consider instead the electron polarizability of the solvent. Thus, to modify equation 11 for application to an instantaneous dipole we replace E by n2,where n is the refractive index of the solvent. Before making use of this modified version of the equation, the magnitude of the poorly-defined cavity radius b must be assigned. We have arbitrarily equated this t o the sum of the radii of a polymer segment and a solvent molecule. Since only a relative scale of values is desired, we have defined a parameter A as
