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Implications of Philippoff flow curves for the determination of intrinsic viscosity of high polymer nitrocelluloses
I M P L I C A T I O N S OF P H I L I P P O F F F L O W CURVES F O R T H E D E T E R M I N A T I O N OF I N T R I N S I C VISCOSITY OF HIGH POLYMER NITROCELLULOSES 1 Carl M. Conrad and Hilda M. Ziifle Southern Regional Research Laboratory,~ New Orleans, Louisiana Received January 28, 1952
INTRODUCTION Recently, a study was undertaken (1) in which the technique of Krieble and Whitwell (3,4) for intrinsic viscosity of high polymer, nonNewtonian solutions was to be applied to a series of raw cotton samples. However, it was found that when the logarithms of the reduced viscosity counterparts 3 were plotted against the concentrations, the results all lay on curves. This finding was contrary to the experience of Krieble and Whitwell, for whom these plots had proven to be linear within the range of concentration studied. A second, though less noticeable deviation was found in the behavior of the z vs. concentration plots which differed in curvature from those observed by Krieble and Whitwell. After a careful examination of the techniques failed to disclose any obvious experimental sources of error, recourse was taken to an independent source of data for comparison. For this purpose, the extensive and very complete set of flow curves, published by Philippoff and Hess (6) seemed appropriate. These curves were obtained by them from a highmolecular-weight ([s~ = 40) cellulose nitrate in butyl acetate. As can be seen from their Fig. 2, they covered a range of stresses from 1 to over 10,000 dynes/sq, cm.; a range of rates of flow from 0.01 to 100,000 sec.-~; and concentrations of 0.05, 0.10, 0.25, 0.50, and 1.00 g./dl. The present report deals with the results of the study of these curves and their relation to certain types of viscosity treatments. MATERIAL AND
METHODS
Unfortunately, for the purpose of the present study, none of the original data had been published by Philippoff and Hess, but only the 1 Condensed from a paper of the same title presented at the Annual Meeting of the Society of Rheology, Chicago, Illinois, October 24-27, 1951. 2 One of the laboratories of the Bureau of Agricultural and Industrial Chemistry, Agricultural Research Administration, U. S. Department of Agriculture. The "reduced viscosity counterpart" is defined by (~-/v0-1)/c; cf. Ref. (3).
227
228
CARL M. CONRAD AND H I L D A M .
ZIIFI~E
chart. In order to obtain necessary data to compute viscosities, a photographic negative of the figure was placed on the stage of a micro comparator; the points of intersection of the curves with the grid lines were then read off and evaluated in relation to the logarithmic scale. From the known values of the logarithmic scales the quotie~lts of the shearing stresses, P, to the rates of shear, V, were determined. It is estimated that the precision of the viscosities, based on the curves and on a series of replicate readings with the comparator, was of the order of 0.2%. It can be easily shown that the slopes of the logarithmic flow curves of Philippoff and Hess are equivalent to the z of Krieble and Whitwell (3). In order to apply the Krieble and Whitwell technique it is necessary to know the z values corresponding to the viscosities. For this purpose a fivefold photostatic enlargement of Philippoff and Hess's flow curves was prepared. This was carefully examined by applying a straightedge at the outer grid lines and found to be free from detectable spherical curvature. The slopes were read off the curves at one-eighth intervals of the abscissal grid spaces with the aid of a prismatic tangent meter similar to that described by Richards and Roope (7). The precision, based upon repeated readings, was determined at high and low slopes, and on the basis of three readings each was found to be of the order of 3.5 and 1.7%, respectively. In the presentation of shear-sensitive data, both constant rate of shear (velocity gradient) and constant shearir/g stress were used as reference points. ]:~ESULTS
The Derived Data
The solvent viscosity, based on 12 separate readings distributed along the entire curve, averaged 0.00740 poise, with a standard deviation of
2.8%. The mean measured values of z are shown in Fig. 1, as a function of the shearing stress, P, and in Fig. 2 as a function of the ra~e of shear, V, in both cases on logarithmic coordinates. In Fig. 1 it is seen that the z values lie moderately uniformly about their individual modal points, the curve for 0.05 g./dl, being the most skew. One important feature of the curves is that as the concentration increases the modes are displaced in the direction of increasing shearing stresses. As will be evident later this leads to seemingly erratic curvature in functions depending on the value of z. Although it is not certain that the differences are outside the limits of experimental error, it is evident that the curves fail to return to the shearing stress axis at the higher stress values.
PHILIPPOFF
FLOW
CURVES
i
0.50
I
I0
I0 z
229
tOO
O
I0 ~
I0 4
IO s
P, DYNES/OM.~
FIG. 1. Slope, z, for the different concentration curves, represented as a function of P. The circles show the mean of three observations; some circles at low z values were omitted in order to avoid overlapping and confusion.
In Fig. 2, curves similar to those of Fig. 1 are observed, except that here they all appear to have a common mode. The apparent failure at low concentrations may or may not be within the limits of experimental error. This more nearly common modality of the z curves leads to more nearly linear curves when based on constant rates of shear.
Relation of Z to Concentration F i g u r e 3 shows t h e r e l a t i o n of z, d e r i v e d f r o m Figs. 1 a n d 2, to c o n c e n t r a t i o n . T h e large v a r i a b i l i t y of slope i n each of these sets of curves is
!
! o~
Z 5
11
2: I _ _ i 0 "2
I0"
I0 2
iO z
tO*
103
106
I0 7
V, SEC - I
FIG. 2. Slope, z, for the different concentrations (indicated by the numbers), represented as a function of V. The circles show the means of three observations.
230
CARL M. CONRAD AND HILDA M. ZIIFLE
immediately evident. It is seen that the curves based on shearing stress are more variable than those based on constant rate of shear; this, of course, is traced back to the greater displacement of modes in Fig. 1 than in Fig. 2.
Relation of Reduced Viscosity Counterpart to Concentration The more i m p o r t a n t objective lay in finding an explanation for the curvature with concentration of reduced viscosity counterpart (1). Accordingly, reduced viscosity counterparts were computed form the Philippoff and Hess viscosities, using only the three lowest concentrations because it was believed these included the maximum concentrations t h a t would be accepted in ordinary practice. The results were computed both
P=516 ~ V "IO 0
,///
I , '"
Z
/is
~'31.6 ,"
• V'IO00
i, Fg'l
/,// /Y/
J
//
,
0
.I
.2 .3 .4 CONGENTRATION, G . / D L
I
-,qo
.5
.6
FIG. 3. Relation of z to concentration at constant shearing stresses, P, (smooth curves) and at constant rates of shear, V (broken curves), for cellulose nitrate in butyl acetate ~derived from figure of Philippoff and Hess (6)].
for different constant shearing stresses, P, and for constant rates of shear, V, and are shown in Fig. 4. It is seen that the curves of Fig. 4 display a rather wide range of position and slope. At a shearing stress of P = 100 and in the vicinity of constant rate of shear, V = I00 the curves are praeically linear. Again, between P = 316 and I000 a change in the sign of curvature occurs. At other positions of constant P or V the lines are distinctly curvilinear. In general, the curves at normal constant rates of shear, V, are less curvilinear than are those at normal constant shearing stresses, P. Except for the essentially linear plots it is evident that considerable uncertainty
231
P ~ I L i P P ( ) F F FLOW CURVES
must exist concerning the value of the intercepts on the zero-concentration axis. I t is possible, though b y no means certain, t h a t all the curves would have a constant intercept if the measurements were carried to a sufficiently low concentration.
Relation of Reduced Apparent Viscosity to Concentration It seemed of special interest in the present study to examine the type of curves t h a t would be obtained according to more conventional methods. For this purpose reduced apparent viscosities were computed at both constant shearing stresses and constant rates of shear, without reference to the z value. The data were plotted both according to Martin's and
?=o! f
P. IO0
I°4
/~ •/ /
~ -7~.
,o'
J
IO 0
ooo
~,,~oo
.|
.2
,3
GONGENTRATION,G./DL.
FIG. 4. Relation of reduced viscosity counterpart (log scale) to concentration at different constant shearing stresses, P (smooth curves), and at constant rates of shear, V (broken curves) [derived from figure of Phflippoff and Hess (6)]. Huggins' procedures. To conserve space only those plotted according to the Huggins' procedure are reproduced here, as Fig. 5. These curves at constant shearing stresses are the typical Philippoff eighth-power ones, used by him for concentration extrapolations (5). Intercepts could not b e reliably determined from the limited data available until the stresses exceed 100 dynes/sq, cm., or the rates of shear several hundred reciprocal seconds. The plots at constant rate of shear are similar to those at constant shearing stress, though displaying less prominent changes of curvature. There is considerable evidence t h a t the lower limbs, i.e., at the lower concentrations, of these curves are linear
232
CARL M. CONRAD AND HILDA i~¢I. ZIIFLE
for both constant shearing stresses and constant rates of shear. Again, the wide divergence of intercepts indicates the failure of the technique as ordinarily employed, if applied to very high-polymer celluloses showing pronounced shear effects. According to Martin's plot, the curves at shearing stresses of P = i00 or more showed quite linear limbs at concentrations of 0.25 g./dl, or less, bug curved limbs at lower stresses. At constant rates of shear, linear limbs did not appear below i000 see. -~. For both constant shearing stresses and constant rates of shear the intercepts apparently differed widely depending on the particular values of P or V chosen. Based on 240 220
I
200
,V-=u,J -
180
iso ~.
140
/
-I
~-I00
1
120
/
,~v.,oolo
/
f //"
I00
~
/I /
8o
J i
/ ~ .1000
6O
../ff~3162
40
/
.~.-
/
,o
~-
0
~
•I
.2
~---'-1-~
.3 .4 .5 .6 .7 CONCENTRATION , G./DL
,o,ooo , .8
.9
FIG. 5. Relation of reduced apparent viscosity to concentration at different constant shearing stresses, P (smooth curves), and constant rates of she~r, V (broken curves), for cellulose nitrate in butyl acetate [derived from figure of Philippoff and Hess (6)].
recent findings f r o m several different sources (8,9) including our own observations with cellulose nitrate in ethyl acetate, it is believed that the apparent linearity of some of these curves at the lower concentrations is an artifact, which can be disclosed by observations at still lower concentrations where the curves near the zero concentration axis suddenly turn down. DISCUSSION
One of the interesting features of the present study is the relation of the slopes of the logarithmic flow curves to rate of shear, shearing stress, and concentration of polymer. These slopes derived from sigmoid-type flow curves, rise from a minimum of 1, reach a maximum, and then recede
PHILIPPOFF
FLOW
CURVES
233
again to, or near 1. The curves appear to be essentially symmetrical, the small amount of skewness observed, for instance, in the 0.05 g./dl. concentration, and the failure to return to 1 at the highest stress values being, perhaps, within the observational errors. It is clearly evident from Fig. 1 that the z curves do not have a common mode with log shearing stress. The mode shifts progressively toward the higher stress values as the concentration increases. To the noncoincidence of modes on this basis can be ascribed entirely the peculiar behavior of both the relation of z to concentration and the relation of reduced viscosity counterpart to concentration. From Fig. 2 it is apparent that the z curves are much more nearly unimodal when plotted against log rate of shear (velocity gradient). For this reason, in the present study at least, the relations of z and of the derived viscosity functions to concentration are much less influenced by the particular value chosen. In both constant shearing stress and constant rate of shear there appear to be unique combinations which give straight-line plots, but such combinations seem to be the exception rather than the rule. While Philippoff has shown the wide conformity among different high-polymer substances to the type of flow curves displayed by cellulose nitrate in butyl acetate, it is by no means certain that the results observed in the present study can be carried over bodily to cellulose dissolved in cupriethylenediamine or other solvents. There is evidence that the non-Newtonian behavior of cellulose nitrate is approximately twice as great for the same shearing stresses and concentrations as of cellulose in cupriethylenediamine solutions. A series of curves of a high degree of polymerization (D.P.) cellulose in this solvent and in euprammonium similar to those supplied by Philippoff and Hess for cellulose nitrate in butyl acetate would be needed. A very interesting result of the present study is the lack of common intercepts at zero concentration of the reduced viscosity, already noted for euprammonium and eupriethylenediamine solvents (2). A common intercept might be found if observations were made at still lower concentrations, but observational errors do not make it appear promising to strive in this direction. On the other hand, consideration of plausible rotatory diffusion constants shows that a true shear dependence of the intrinsic viscosities for the systems investigated might well become measurable. While the present data may indicate a moderate advantage of rate of shear as a basis for common reference of non-Newlonian viscosity data, much more work is needed to show how far the relationships shown by cellulose nitrate in butyl acetate can be extended to other systems.
234
CARL M. CONRAD AND ttlLDA M. ZIIFLE SUMMARY AND CONCLUSIONS
As a result of an analytical study of flow curves of cellulose nitrate in butyl acetate at different concentrations, published by Philippoff and Hess, it is concluded that: 1. The value of the slope, z, of the logarithmic flow curves, representing the relation of log rate of shear to log shearing stress, increases with increasing log shearing stress or log rate of shear from approximately 1, which is normal for Newtonian solutions, to a maximum and then recedes ~gain nearly symmetrically to or near 1 at the higher stresses or rates of shear. 2. When the z slopes are plotted against log shearing stress the modes of the curves for the different concentrations are not coincident, but progress with increasing concentration to higher shear stresses and with increasing amplitude. On the other hand when the z slopes are plotted against log rate of shear the modes are more nearly coincident, the deviations being perhaps within the limits of experimental error; the amplitudes increase with concentration in this case also. 3. Insofar as the z modes do no coincide for different concentrations, the relation of z and of derived viscosity quantities to concentration assumes widely different curvilinear configurations, depending on the experimental conditions of stress and rate of shear under which observations are made. 4. I n conformity with earlier studies of cuprammonium and cupriethylenediamine solutions of cellulose, it is found for cellulose nitrate in butyl acetate, also, that t h e intercepts of reduced viscoisty at zero concentration (intrinsic viscosities) vary widely with the constant velocity gradient used, and in the present series also with the constant shearing stress employed. This follows regardless of whether the dati~ ure plotted according to Martin's or the Huggins' scheme. 5. While it has been shown by Philippoff that the type of flow curves here considered are quite general among solutions of different types of high-polymer substances, there are many details to be verified concerning degree of conformity and magnitude before the present results csn be carried over to other systems. REFERENCES 1. CONRAD,C. IV[..~D Rvsc~, R. A., Some Viscometrie Studies of Cellulose in Cotton in Relation to Mechanical Processing. Paper presented before See. 15 of the XIIth International Congress of Pure and Applied Chemistry, New York, 1~. Y., Sept. 10-13, 1951. 2. CONRAD,C. M., TRI~P, V. W., AXD MANES, T. J. Phys. & Colloid Chem. 55, 1474-91 (1951).
PHILIPPOFF FLOW CURVES 3. 4. 5. 6. 7. 8. 9.
235
KRIEBLE, J. G., AND ~VItITWELL,J. C., Textile Research J. 19, 253-8 (1949). KRIEBLE, J. G. AND WHITWELL, J. C., Textile Research J. 19, 556-62 (1949). PEIUPPOFF, W., Viskosit~t der Kolloide, T. Steinkopff, Dresden and Leipzig, 1942. PHILI•POFF, W. AND HESS, K., Z. physik. Chem. B31, 237-55 (1935). I~IC~ARDS,O. W., ~WD I~OOPE, P. M., Science 71, 290-1 (1930). STRE~TER, D. J., A~TDBORER, R. F., Ind. Eng. Chem. 43, 1790-97 (1951). WEISSBEItG, S. G., SIMHA, R., AND ~:~OTttMAN,S., J. Research Natl. Bur. Standards 47, 298-314 (1951).
INTRODUCTION Recently, a study was undertaken (1) in which the technique of Krieble and Whitwell (3,4) for intrinsic viscosity of high polymer, nonNewtonian solutions was to be applied to a series of raw cotton samples. However, it was found that when the logarithms of the reduced viscosity counterparts 3 were plotted against the concentrations, the results all lay on curves. This finding was contrary to the experience of Krieble and Whitwell, for whom these plots had proven to be linear within the range of concentration studied. A second, though less noticeable deviation was found in the behavior of the z vs. concentration plots which differed in curvature from those observed by Krieble and Whitwell. After a careful examination of the techniques failed to disclose any obvious experimental sources of error, recourse was taken to an independent source of data for comparison. For this purpose, the extensive and very complete set of flow curves, published by Philippoff and Hess (6) seemed appropriate. These curves were obtained by them from a highmolecular-weight ([s~ = 40) cellulose nitrate in butyl acetate. As can be seen from their Fig. 2, they covered a range of stresses from 1 to over 10,000 dynes/sq, cm.; a range of rates of flow from 0.01 to 100,000 sec.-~; and concentrations of 0.05, 0.10, 0.25, 0.50, and 1.00 g./dl. The present report deals with the results of the study of these curves and their relation to certain types of viscosity treatments. MATERIAL AND
METHODS
Unfortunately, for the purpose of the present study, none of the original data had been published by Philippoff and Hess, but only the 1 Condensed from a paper of the same title presented at the Annual Meeting of the Society of Rheology, Chicago, Illinois, October 24-27, 1951. 2 One of the laboratories of the Bureau of Agricultural and Industrial Chemistry, Agricultural Research Administration, U. S. Department of Agriculture. The "reduced viscosity counterpart" is defined by (~-/v0-1)/c; cf. Ref. (3).
227
228
CARL M. CONRAD AND H I L D A M .
ZIIFI~E
chart. In order to obtain necessary data to compute viscosities, a photographic negative of the figure was placed on the stage of a micro comparator; the points of intersection of the curves with the grid lines were then read off and evaluated in relation to the logarithmic scale. From the known values of the logarithmic scales the quotie~lts of the shearing stresses, P, to the rates of shear, V, were determined. It is estimated that the precision of the viscosities, based on the curves and on a series of replicate readings with the comparator, was of the order of 0.2%. It can be easily shown that the slopes of the logarithmic flow curves of Philippoff and Hess are equivalent to the z of Krieble and Whitwell (3). In order to apply the Krieble and Whitwell technique it is necessary to know the z values corresponding to the viscosities. For this purpose a fivefold photostatic enlargement of Philippoff and Hess's flow curves was prepared. This was carefully examined by applying a straightedge at the outer grid lines and found to be free from detectable spherical curvature. The slopes were read off the curves at one-eighth intervals of the abscissal grid spaces with the aid of a prismatic tangent meter similar to that described by Richards and Roope (7). The precision, based upon repeated readings, was determined at high and low slopes, and on the basis of three readings each was found to be of the order of 3.5 and 1.7%, respectively. In the presentation of shear-sensitive data, both constant rate of shear (velocity gradient) and constant shearir/g stress were used as reference points. ]:~ESULTS
The Derived Data
The solvent viscosity, based on 12 separate readings distributed along the entire curve, averaged 0.00740 poise, with a standard deviation of
2.8%. The mean measured values of z are shown in Fig. 1, as a function of the shearing stress, P, and in Fig. 2 as a function of the ra~e of shear, V, in both cases on logarithmic coordinates. In Fig. 1 it is seen that the z values lie moderately uniformly about their individual modal points, the curve for 0.05 g./dl, being the most skew. One important feature of the curves is that as the concentration increases the modes are displaced in the direction of increasing shearing stresses. As will be evident later this leads to seemingly erratic curvature in functions depending on the value of z. Although it is not certain that the differences are outside the limits of experimental error, it is evident that the curves fail to return to the shearing stress axis at the higher stress values.
PHILIPPOFF
FLOW
CURVES
i
0.50
I
I0
I0 z
229
tOO
O
I0 ~
I0 4
IO s
P, DYNES/OM.~
FIG. 1. Slope, z, for the different concentration curves, represented as a function of P. The circles show the mean of three observations; some circles at low z values were omitted in order to avoid overlapping and confusion.
In Fig. 2, curves similar to those of Fig. 1 are observed, except that here they all appear to have a common mode. The apparent failure at low concentrations may or may not be within the limits of experimental error. This more nearly common modality of the z curves leads to more nearly linear curves when based on constant rates of shear.
Relation of Z to Concentration F i g u r e 3 shows t h e r e l a t i o n of z, d e r i v e d f r o m Figs. 1 a n d 2, to c o n c e n t r a t i o n . T h e large v a r i a b i l i t y of slope i n each of these sets of curves is
!
! o~
Z 5
11
2: I _ _ i 0 "2
I0"
I0 2
iO z
tO*
103
106
I0 7
V, SEC - I
FIG. 2. Slope, z, for the different concentrations (indicated by the numbers), represented as a function of V. The circles show the means of three observations.
230
CARL M. CONRAD AND HILDA M. ZIIFLE
immediately evident. It is seen that the curves based on shearing stress are more variable than those based on constant rate of shear; this, of course, is traced back to the greater displacement of modes in Fig. 1 than in Fig. 2.
Relation of Reduced Viscosity Counterpart to Concentration The more i m p o r t a n t objective lay in finding an explanation for the curvature with concentration of reduced viscosity counterpart (1). Accordingly, reduced viscosity counterparts were computed form the Philippoff and Hess viscosities, using only the three lowest concentrations because it was believed these included the maximum concentrations t h a t would be accepted in ordinary practice. The results were computed both
P=516 ~ V "IO 0
,///
I , '"
Z
/is
~'31.6 ,"
• V'IO00
i, Fg'l
/,// /Y/
J
//
,
0
.I
.2 .3 .4 CONGENTRATION, G . / D L
I
-,qo
.5
.6
FIG. 3. Relation of z to concentration at constant shearing stresses, P, (smooth curves) and at constant rates of shear, V (broken curves), for cellulose nitrate in butyl acetate ~derived from figure of Philippoff and Hess (6)].
for different constant shearing stresses, P, and for constant rates of shear, V, and are shown in Fig. 4. It is seen that the curves of Fig. 4 display a rather wide range of position and slope. At a shearing stress of P = 100 and in the vicinity of constant rate of shear, V = I00 the curves are praeically linear. Again, between P = 316 and I000 a change in the sign of curvature occurs. At other positions of constant P or V the lines are distinctly curvilinear. In general, the curves at normal constant rates of shear, V, are less curvilinear than are those at normal constant shearing stresses, P. Except for the essentially linear plots it is evident that considerable uncertainty
231
P ~ I L i P P ( ) F F FLOW CURVES
must exist concerning the value of the intercepts on the zero-concentration axis. I t is possible, though b y no means certain, t h a t all the curves would have a constant intercept if the measurements were carried to a sufficiently low concentration.
Relation of Reduced Apparent Viscosity to Concentration It seemed of special interest in the present study to examine the type of curves t h a t would be obtained according to more conventional methods. For this purpose reduced apparent viscosities were computed at both constant shearing stresses and constant rates of shear, without reference to the z value. The data were plotted both according to Martin's and
?=o! f
P. IO0
I°4
/~ •/ /
~ -7~.
,o'
J
IO 0
ooo
~,,~oo
.|
.2
,3
GONGENTRATION,G./DL.
FIG. 4. Relation of reduced viscosity counterpart (log scale) to concentration at different constant shearing stresses, P (smooth curves), and at constant rates of shear, V (broken curves) [derived from figure of Phflippoff and Hess (6)]. Huggins' procedures. To conserve space only those plotted according to the Huggins' procedure are reproduced here, as Fig. 5. These curves at constant shearing stresses are the typical Philippoff eighth-power ones, used by him for concentration extrapolations (5). Intercepts could not b e reliably determined from the limited data available until the stresses exceed 100 dynes/sq, cm., or the rates of shear several hundred reciprocal seconds. The plots at constant rate of shear are similar to those at constant shearing stress, though displaying less prominent changes of curvature. There is considerable evidence t h a t the lower limbs, i.e., at the lower concentrations, of these curves are linear
232
CARL M. CONRAD AND HILDA i~¢I. ZIIFLE
for both constant shearing stresses and constant rates of shear. Again, the wide divergence of intercepts indicates the failure of the technique as ordinarily employed, if applied to very high-polymer celluloses showing pronounced shear effects. According to Martin's plot, the curves at shearing stresses of P = i00 or more showed quite linear limbs at concentrations of 0.25 g./dl, or less, bug curved limbs at lower stresses. At constant rates of shear, linear limbs did not appear below i000 see. -~. For both constant shearing stresses and constant rates of shear the intercepts apparently differed widely depending on the particular values of P or V chosen. Based on 240 220
I
200
,V-=u,J -
180
iso ~.
140
/
-I
~-I00
1
120
/
,~v.,oolo
/
f //"
I00
~
/I /
8o
J i
/ ~ .1000
6O
../ff~3162
40
/
.~.-
/
,o
~-
0
~
•I
.2
~---'-1-~
.3 .4 .5 .6 .7 CONCENTRATION , G./DL
,o,ooo , .8
.9
FIG. 5. Relation of reduced apparent viscosity to concentration at different constant shearing stresses, P (smooth curves), and constant rates of she~r, V (broken curves), for cellulose nitrate in butyl acetate [derived from figure of Philippoff and Hess (6)].
recent findings f r o m several different sources (8,9) including our own observations with cellulose nitrate in ethyl acetate, it is believed that the apparent linearity of some of these curves at the lower concentrations is an artifact, which can be disclosed by observations at still lower concentrations where the curves near the zero concentration axis suddenly turn down. DISCUSSION
One of the interesting features of the present study is the relation of the slopes of the logarithmic flow curves to rate of shear, shearing stress, and concentration of polymer. These slopes derived from sigmoid-type flow curves, rise from a minimum of 1, reach a maximum, and then recede
PHILIPPOFF
FLOW
CURVES
233
again to, or near 1. The curves appear to be essentially symmetrical, the small amount of skewness observed, for instance, in the 0.05 g./dl. concentration, and the failure to return to 1 at the highest stress values being, perhaps, within the observational errors. It is clearly evident from Fig. 1 that the z curves do not have a common mode with log shearing stress. The mode shifts progressively toward the higher stress values as the concentration increases. To the noncoincidence of modes on this basis can be ascribed entirely the peculiar behavior of both the relation of z to concentration and the relation of reduced viscosity counterpart to concentration. From Fig. 2 it is apparent that the z curves are much more nearly unimodal when plotted against log rate of shear (velocity gradient). For this reason, in the present study at least, the relations of z and of the derived viscosity functions to concentration are much less influenced by the particular value chosen. In both constant shearing stress and constant rate of shear there appear to be unique combinations which give straight-line plots, but such combinations seem to be the exception rather than the rule. While Philippoff has shown the wide conformity among different high-polymer substances to the type of flow curves displayed by cellulose nitrate in butyl acetate, it is by no means certain that the results observed in the present study can be carried over bodily to cellulose dissolved in cupriethylenediamine or other solvents. There is evidence that the non-Newtonian behavior of cellulose nitrate is approximately twice as great for the same shearing stresses and concentrations as of cellulose in cupriethylenediamine solutions. A series of curves of a high degree of polymerization (D.P.) cellulose in this solvent and in euprammonium similar to those supplied by Philippoff and Hess for cellulose nitrate in butyl acetate would be needed. A very interesting result of the present study is the lack of common intercepts at zero concentration of the reduced viscosity, already noted for euprammonium and eupriethylenediamine solvents (2). A common intercept might be found if observations were made at still lower concentrations, but observational errors do not make it appear promising to strive in this direction. On the other hand, consideration of plausible rotatory diffusion constants shows that a true shear dependence of the intrinsic viscosities for the systems investigated might well become measurable. While the present data may indicate a moderate advantage of rate of shear as a basis for common reference of non-Newlonian viscosity data, much more work is needed to show how far the relationships shown by cellulose nitrate in butyl acetate can be extended to other systems.
234
CARL M. CONRAD AND ttlLDA M. ZIIFLE SUMMARY AND CONCLUSIONS
As a result of an analytical study of flow curves of cellulose nitrate in butyl acetate at different concentrations, published by Philippoff and Hess, it is concluded that: 1. The value of the slope, z, of the logarithmic flow curves, representing the relation of log rate of shear to log shearing stress, increases with increasing log shearing stress or log rate of shear from approximately 1, which is normal for Newtonian solutions, to a maximum and then recedes ~gain nearly symmetrically to or near 1 at the higher stresses or rates of shear. 2. When the z slopes are plotted against log shearing stress the modes of the curves for the different concentrations are not coincident, but progress with increasing concentration to higher shear stresses and with increasing amplitude. On the other hand when the z slopes are plotted against log rate of shear the modes are more nearly coincident, the deviations being perhaps within the limits of experimental error; the amplitudes increase with concentration in this case also. 3. Insofar as the z modes do no coincide for different concentrations, the relation of z and of derived viscosity quantities to concentration assumes widely different curvilinear configurations, depending on the experimental conditions of stress and rate of shear under which observations are made. 4. I n conformity with earlier studies of cuprammonium and cupriethylenediamine solutions of cellulose, it is found for cellulose nitrate in butyl acetate, also, that t h e intercepts of reduced viscoisty at zero concentration (intrinsic viscosities) vary widely with the constant velocity gradient used, and in the present series also with the constant shearing stress employed. This follows regardless of whether the dati~ ure plotted according to Martin's or the Huggins' scheme. 5. While it has been shown by Philippoff that the type of flow curves here considered are quite general among solutions of different types of high-polymer substances, there are many details to be verified concerning degree of conformity and magnitude before the present results csn be carried over to other systems. REFERENCES 1. CONRAD,C. IV[..~D Rvsc~, R. A., Some Viscometrie Studies of Cellulose in Cotton in Relation to Mechanical Processing. Paper presented before See. 15 of the XIIth International Congress of Pure and Applied Chemistry, New York, 1~. Y., Sept. 10-13, 1951. 2. CONRAD,C. M., TRI~P, V. W., AXD MANES, T. J. Phys. & Colloid Chem. 55, 1474-91 (1951).
PHILIPPOFF FLOW CURVES 3. 4. 5. 6. 7. 8. 9.
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KRIEBLE, J. G., AND ~VItITWELL,J. C., Textile Research J. 19, 253-8 (1949). KRIEBLE, J. G. AND WHITWELL, J. C., Textile Research J. 19, 556-62 (1949). PEIUPPOFF, W., Viskosit~t der Kolloide, T. Steinkopff, Dresden and Leipzig, 1942. PHILI•POFF, W. AND HESS, K., Z. physik. Chem. B31, 237-55 (1935). I~IC~ARDS,O. W., ~WD I~OOPE, P. M., Science 71, 290-1 (1930). STRE~TER, D. J., A~TDBORER, R. F., Ind. Eng. Chem. 43, 1790-97 (1951). WEISSBEItG, S. G., SIMHA, R., AND ~:~OTttMAN,S., J. Research Natl. Bur. Standards 47, 298-314 (1951).