Role of Velocity Gradient in Determining the Cuprammonium Fluidity of Cellulose CARL M. CONRAD .4gricultural Rlarketing Service, United States Department of Agriculture, Washington, D. C.
supply pressure (either positive or negative) was adjusted by means of a stopcock until a slow steady stream of bubbles escaped. The superimposed pressure was measured by means of a water manometer inserted in a 4-liter bottle contained in the supply air line. The composition of the cuprammonium reagent corresponded to the specifications of the Committee on Viscosity of Cellulose of the AMERICAN CHEMICAL SOCIETY (1). It was found to have a fluidity at 25’ C. of 82.25 rhes. This composition was used in preference to that of a solution, such as that of T. A. P. P. I. (28), containing only 15 grams of copper per liter because, as reported by Conrad ( 6 ) , it dissolved raw cotton cellulose much more readily. Before solution in the cuprammonium reagent the cotton was purified by extraction for 4 hours with 95 per cent ethyl alcohol in a large Soxhlet apparatus. Ethyl alcohol was found to be a much more inclusive solvent for the heterogeneous waxy constituents than carbon tetrachloride, benzene, or even a 50-50 alcohol-benzene mixture. Also the alcohol removes residual sugars and other substances, not removed by carbon tetrachloride or benzene. KO bleaching was employed because of its possible damaging effect on the sample and because of the absence of lignin in cotton fiber. There was no evidence that the fractional per cent of pectic substance remaining on the fiber interfered with the solution of the
IN
ATTEMPTIKG to apply certain routine methods for determining the fluidity of raw cotton cellulose, as a measure of its textile quality, serious difficulties were encountered. These were due to the anomalous behavior of the solutions, which was much more pronounced in the case of native cotton cellulose than in many “finished” cottons, rayons, and other cellulose derivatives. The literature dealing with the routine measurement of the cuprammonium fluidity or viscosity of cellulose generally recognizes the anomalous nature of the solutions. Thus, Clibbens and Geake (5) so outlined their technique that failure to obey the Poiseuille law was made evident, but they did not indicate any alternate procedure in case of deviation. I n 1929, the Committee on Viscosity of Cellulose of the AMERICANCHEMICAL SOCIETY (1) recognized the “plastic” behavior of cuprammonium solutions of cellulose but questioned the practical significance of such effects. I n 1932 the Fabrics Research Committee ( 7 ) ,recognizing the “instrument effect”, gave detailed and exacting specifications for the construction of capillary viscometers, hoping in this way to reduce the ‘‘ lastic” effect to a minimum. Keither the T. A. P. P. I. (287 method for determination of cuprammonium fluidity of cellulose, nor the new tentative method adopted by Committee D-13 of the American Society for Testing Materials (2) attempts any adjustments for the non-h-ewtonian flow. The requirements for treating the viscosity of anomalous solutions have been extensively studied in Europe by a number of investigators. The literature has been adequately summarized for cellulose by Philippoff (16). However, while a sat’isfactory theoretical ground seems to have been laid, the necessary dures are not readily adaptable for routine applications. for this reason or through lack of knowledge of the new developments, little or no attempt seems to have been made t o take advantage of them.
8%;:;
It is the purpose of the present paper to describe experiments in which a n attempt is made to adapt some of the new techniques for routine or commercial use.
Apparatus and General Procedure
A-
For the fluidity determinations viscometers were employed which were similar to the consistometers described by Herschel and Bulkley (11). The parts, general arrangement, and dimensions are shown in Figure I. The burets were graduated at 5-ml. intervals and designed to deliver four, or in a few cases, five successive 5-ml. quantities during a complete discharge. A series of capillaries was used, all of which had a length of 2.50 * 0.02 cm., an outer diameter of 0.7 cm., and an inner radius varying between the limits of 0.0702 and 0.0737 cm. In the final calibration, the capillary radius was determined accurately by means of mercury. The mean heads, h, of the burets were computed for each 5-ml. portion discharged, by mean? of MeisPnPr’s approximation formula : SECTION OF TIP
where hl and hg are the initial and final distances between the level of the column and the lower tip of the capillary. The mean heads were converted into pressures, in grams per square centimeter, by multiplication with the density of the cuprammonium hydroxide solution used-namely, 0.974-no account being taken of the slight increase in density that results from the solute. In some of the determinations the hydrostatic reduced or augmented, externally, by means of a ! ~ ~ ~ bling arrangement in which an escape of air was provided from a comparatively large glass tube (7 mm. in inner diameter) through the desired head of water in a tall glass cylinder. The
FIGURE1. b
526
%
DIMENSIONS O F BURET VISCOMETERS
P a R T S AXD
A . Plan of buret, showing position of the six etched rings ~ Enlarged W O E S section through lower end B. C . Stopcock assembly for insertion t o ring a t top
D. Calibrated capillary and rubber tube assembly E. F.
Weighted spring SRmple tranafei tube
August 15, 1941
ANALYTICAL EDITION
527
Concentration Corrections Since the fluidities were expressed in terms of 0.5 per cent solutions, it was necessary to make a second adjustment of all observed fluidity values for small deviations of concentration. This was necessitated by smal! variations in capacities of the burets as well as variations in cellulose content of samples. The most convenient method for interpolating fluidity for different concentrations was found to be that based on a formula published by Farrow and Neale (8): FOR KINETICENERGY LOSSES FIGURE 2. ADDITIONCORRECTIOXS 111
+
A / C = B/log q r (3) A and B are empirical constants, C is the concentration of the cellulose in grams per 100 ml. of solvent, and qr is the relative viscosity of the solution. A plot of 1/C against l/log qr should give a straight line. Farrow and Keale confirmed that the linearity of such a plot was approximately realized in practice, and that B had a value of about 11. The Fabrics Research Committee ( 7 ) re-examined the concentration viscosity relationship and found rather good linearity of the curves. However, they found a somewhat smaller value for B, this varying between 5 and 10, the more highly viscous samples having the higher values. The writer recomputed some data given by Staudinger and Sorkin (27) for gel solutions of nitrocellulose of different degrees of polymerization in butyl acetate and found that here, too, a plot of l / C against l/log qr gave practically straight lines and a value of B varying between about 4 and 10. In the small region of l / C between 1.5 and 2.5, within which all interpolations would fall, the curves may be taken as linear without appreciable error. For use, an arbitary value of B = 10 was adopted and a table of corrections prepared for deviations of concentration from 0.5 per cent. 1
relation t o fluidity without kinetic energy correction and time of discharge for 5-ml. portions of solutions
cellulose or the results. However, the cellulose content of the sample was determined and used for concentration adjustments. In reparation for the determination a weighed portion of the qampt, sufficient to give an approximately 0.5 per cent solution, was introduced by means of the sample tube (Figure 1, F ) into the buret, together with a small spring weight (Figure 1, E ) to promote agitation later. The buret was then flushed out with approximately 3 volumes of purified nitrogen, evacuated to a pressure of about 5 cm. of mercury, and again refilled with pure nitrogen to eliminate oxygen as completely as possible. Without disconnecting, the cuprammonium hydroxide solution was introduced until the buret, which was in an inclining position, was approximately two-thirds full. Care was taken that all of the sample was wet by the reagent, whereupon it was given a vigorous shaking. The buret was then completely filled with the solvent and placed in an enclosed, light-tight, rotating box and allowed to turn end-over-end overnight a t the rate of about 2 revolutions per minute. Next morning the burets were placed in a closefitting glass jacket in a thermostat bath, controlled at 25’ * 0.1” C., and allowed to stand 20 minutes for the attainment of equilibrium temperature. The time required for the discharge of the 5-ml. volumes was then determined with a “split second” stop watch. The results for 0.5 gram of cellulose per 100 ml. of solution are expressed for textile purposes in terms of fluidity rather than of viscosity, since, as pointed out by Clibbens and Geake ( 5 ) ,the relation between fluidity and loss of strength is nearly linear, and the practical range of the absolute fluidity scale is much more convenient for textile celluloses than is that of the viscosity scale.
Kinetic Energy Corrections Corrections were made in all cases for kinetic energy losses. This mas done by first computing the fluidity without kinetic energy correction and then adding the correction. The corrections were approximate and were taken from a chart such as is shown in Figure 2, based on the evaluation, for convenient values of observed fluidities, F,, and times of f l o ~t , of the usual expression for kinetic energy correction:
Here, F, is the corrected fluidity, ?n is the kinetic energy coefficient, usually taken as 1.12, d is the density of the liquid, V is the volume of liquid discharged in t seconds, and L is the length of the capillary. When the differences between F , and F , are plotted in logarithmic coordinates against the uncorrected or observed fluidities for different observed times of flow, a series of straight lines results from which addition corrections can be read off by inspection.
Demonstration of Anomalous Behavior of Solutions of Raw Cotton Cellulose The anomalous behavior of the solutions may best be show1 by three different methods of treating the data from two solutions of cotton cellulose, and, for comparison, a mineral oil and an aqueous 71 per cent solution of glycerol. According to the first procedure, the fluidity is computed for each ring interval of the viscometer according to the formula of Clibbens and Geake: F , = c/t (4) in which F , is the observed fluidity in rhes, before correction for kinetic energy, C is the viscometer constant for a particular ring interval and already adjusted for density of the cuprammonium solvent, and t is the time in seconds for discharge between rings. According to the second procedure the raw data are treated according to Bingham’s plasticity method (4, p. 323) employing the formula: TI
In this formula F , is really Bingham’s “mobility” value, although for purposes of comparison it will be referred t o as “fluidity”, t has the same significance as above, C is a constant having a different numerical value from that of Equation 4, V is the volume in milliliters of solution delivered between two successive rings, P is the total computed pressure causing flow, and y is the “back pressure” or yield value. (There may be some question as to whether the term “mobility” is strictly applicable in the case of solutions of cellulose, since the back pressure, y, is only apparent and unreal. When y is equal to the capillary rise the values calculated by this formula are exactly comparable to those computed with the aid of Equation 4.) The value of y is found by a graphical method as the intercept on the P axis when B!t is plotted
By reference to Table I it will be seen that the fluidity of the mineral oil and the glycerol solution was practically constant, regardless of ring interval (pressure) or method of treating the raw data-i. e., the solutions showed Newtonian flow. However, the two cotton solutions exhibited different fluidities, depending on the method of treatment of the data and, for two of the methods, on the ring interval of the viscometer. The variation with ring interval, depending as i t does on applied pressure, is shown especially in the results obtained by the Clibbens and Geake formula, where the total decrease from upper to lower ring interval amounted for the two cotton solutions to about 45 per cent of the average fluidity value.
06
5
$
,
4
2
s38 w
voi. 13, N ~ a.
INDUSTRIAL AND ENGINEERING CHEMISTRY
528
2
a I
0 0
5
IO
15
25
20
HYDROSTATIC PRESSURE,
30
35
GM./CM?
FIGURE3. RATE OF FLOW-PRESSURE CURVESFOR “TRUE” AND AXOMALOUS LIQUIDS 1.
2. 3. 4.
Approximately 71 per cent aqueous glycerol (“true” solution) Mineral oil (“true” liquid) 0.5 per cent cuprammonium solution of cotton cellulose 293 (anomalous solution) 0.5 per cent cuprammonium solution of cotton cellulose 295 (anomalous solution) 0
against P. Such plots are shown in Figure 3 for a “true” liquid and solution, and two anomalous solutions. Whereas the curves for the “true” liquids when extended pass almost through the origin, the curves for the two cotton solutions (anomalous) when extended intersect the abscissa at nearly 9 grams per square centimeter. [Theoretically, even for liquids that obey the Poiseuille law the curves should pass through a point on the pressure axis slightly to the right of the origin, owing t o the influence of surface tension. According to Herschel and Bulkley (11) this will be a t 4y COS e p=, where y is the surface tension of the solution, e is the OD angle ofcontact of the liquid with the surface, g is the gravitational constant, and D is the outer diameter of the capillary. Taking cos e equal to 0.5 and D as 0.7 cm., the surface tension correction was about 0.20 gram per square centimeter in the viscometers described above. ] The third method of treating the data, the velocity gradient method, will be described subsequently but the data are included here for comparison. The results, corrected for kinetic energy losses and variations of concentrations, are summarized in the last three columns of Table I.
VELOCITY
GRADIENT, S E C - ’
FIGURE 4. RELaTION O F FLUIDITY O F “TRUE” AND .%NOMALOUS LIQUIDS AND SOLUTIONS TO MEAS VELOCITY GRADIEXT 0. Approximately 71 per cent aqueous glycerol (“true” solution)
0 . Mineral oil (“true” liquid) @.
e,
0.5 per cent cuprammonium solution of cotton cellulose 29 3 (anonialous solution) 0.5 per cent cuprammonium solution of cotton cellulose 295 (anomalous solution)
The fluidities for the two cottons by Binaham’s ulasticitv formula are naturally larger than those by t h e Clibbens a& formula, but rather uniform, except for the lowest ring intervals. Figure 3 shows that the points for the lower pressures on the two cotton curves fall well above the straight-line portion of the curves. I n some cases no three of the four sets of observations could legitimately be fitted to a straight line, SO that the yield value, y, was uncertain. Superimposition of a small air pressure on the solutions during flow was tried with a view to bringing the points higher and, therefore, more nearly on the straight-line portion of the curve. TABLE I. FLUIDITIES OF MINERAL OIL, AQUEOUS71 PERCEXTGLYCEROL, .ISD 0.5 However, this not only greatly inPERCENTCOTTOX CELLULOSE creased the kinetic energy correction, Sample and viscometer Mean Mean Fluidity b y Method of: Rate of Velocity Ring Mean Clibbens Bingham’s Capillary Velocity but changed the yield value and, in Pressure Flow Gradient and Geake plasticityh gradientc Radius= Interval some cases, resulted in turbulent flow Nl, G./sq. c m . .1fl./aec. Sec.-l Rhes Rhea Rhes for the highest ring interval. Ifinera1 oil, 0-5 25,54 0.315 731 3.04 8.01 3.04 R = 0.0721 cm. 5-10 20.94 0.236 595 3.05 :?,OS 3.05 On the other hand the fluidities of 0.208 10-15 16.37 469 3.07 3.07 3.07 0.148 15-20 11.86 331 3.00 3.00 3.00 the two cotton solutions by the velocity AV. 532 3.04 3.04 3.04 gradient method, while much lower, 35.66 0.625 1430 4.47 4.47 4.42 Glycerol 0-5 are as uniform for the different ring 0.538 1241 4.69 29.31 4.69 4.66 (appror. 71’-Z), 6-10 intervals for a given cotton, as are R = 0.0722 cm. 10-15 23.19 0.427 982 4.65 4.65 4.65 15-20 16.90 0.314 724 4.66 4.66 4.71 those for the mineral oil and glycerol 20-2,; 10.54 0 196 448 4.58 4.58 4.65 A v . 963 solution for all ring intervals and 1.61 4.61 4.62 Cotton 293, 0-5 29.36 0.394 913 3.40 4.94 2.71 methods of treating the data. R = 0.0715 em.
5-10 10-15 15-20
24.21 19.02 13.78
0.294 0.195 0.121
Av.
Cotton 295, R = 0.0710 cni.
a
b C
0-5 5-10 10-15 15-20
29.25 24.01 18.77 13,53
0.368 0.273 0.181 0.105
682 453 282 566 873 649
430 250 Ar. 550
Length of ca illaries in all cases 2.50 cni. Strictly “mo‘%lity” although called “fluidity” for comparison. Interpolated t o velocity gradient of 500 sec.-l
3.06 2.57
2,19
2.80 3.28
2.95 2.49 2.00
2.68
4.91 4.91 6.38 5.28
2.74 2.75 2.72 2.73
4.74 4.70 4.72 5.66 4 96
2.65 2.67 2.64 2.68 2.66
Elimination of “Instrument” Errors I n the case of anomalous solutions the disturbances may be divided, for convenience of discussion, into two categories. One has to do with the instrument effect-i. e., the difference in fluidity or viscosity of an anomalous
August 15,
1941
A NA
L Y,T I C A L E D I T I O N
529
cellulose from ran- cotton, it seemed desirable to try the application of Kroepelin's technique. The results of such a test are shown in Figure 4, where the fluidity values from Table I are plotted on double logarithmic coordinates. The fluidities of the glycerol solution and mineral oil are seen to be independent of the velocity gradient, as would be expected for Seivtonian liquids. On the other hand, the two cotton cellulose solutions show fluidities falling on a linear curve inclined upward with increasing velocity gradients. By interpolation of the individual fluidities for the different liquids or solutions in Figure 4 parallel to the line representing their logarithmic regression on velocity gradient, to a velocity gradient of 500 cm. per second per centimeter, or see.-', the fluidities in the right-hand column of Table I were obtained. I n order to extend the results over a wider OF FLUIDITY OF 0.5 PERCENTCUPRAMMOXIUM FIGURE5 . RELATIOW range of velocity gradients, portions of two difSOLUTIONS OF COTTON CELLULOSE TO VELOCITY GRADIENT ferent samples of cotton cellulose were dissolved 0 . Cotton cellulose 1112 0. Cotton cellulose 300 to give approximately 0.5 per cent solutions. The hydrostatic head was then decreased and augmented externally, as previously described, to change the solution, when measured in different types of instruments, or in rates of flow and in turn the mean velocity gradients. The rethe case of capillary viscometers, with capillaries of different sults, covering a range of mean velocity gradients in one case radii. The other has to do with differences in results obfrom 15.3to 1295 and in the other from 27 to 1244 see.-', are tained in the identical instrument, but depending on the plotted in Figure 5. particular conditions of measurement-i. e., concentration of The observations are scattered somewhat, which is believed solution, total pressure, etc. Both influences trace their origin to be due, principally, to slight inaccuracies in reading short to a common source, the velocity gradient in the capillary time intervals with the stop watch, to slight variations in conduring flow.. I n the case of Sewtonian solutions the measured centration due to the hygroscopic nature of cellulose, and to fluidity is independent of the velocity gradient. However, the relatively very large influence of very slight variations of this is not the case with anomalous solutions. concentration. However, the results seem to indicate rather I n capillary viscometers the solution flows through a given unmistakably that the observations, when plotted in this way, capillary a t different velocities, most rapidly a t the center and are practically linear over the range of velocity gradients emslowest near the capillary wall. The solution in contact with ployed. [According to Philippoff (17, 18) the curves will, a t the wall is essentially a t rest. Therefore, there is always a a sufficiently low velocity gradient, eventually become parallel gradient of velocity-i. e., a change in velocity per unit of diswith the velocity gradient axis.] This conclusion has been tance, taken radially in the capillary. I n 1929 Kroepelin confirmed also on a large number of individual curves on (14) derived the follox-ing equation for mean velocity gramany samples of cotton cellulose, measured in the same range dient G, in capillaries : of mean velocity gradients. These results indicate, therefore, that serious instrument errors may occur in anomalous solutions if results are obtained a t different velocity gradients. where 1' is the volume of solution, flowing in time t through a However, they may be eliminated by expressing the apparent It is readily seen that Gt becomes a concaDillarv fluidities or viscosities in terms of some common mean velocity " of radius r. stant for a given instrument from which may be easily computed from observed values of t . [As Philippoff (18) has shown, G is not strictly TABLE 11. FLUIDITIES .kSD MEAN DEVIATIOSSO F REPLICATES the true mean velocity gradient in anomalous (Determined with and without adjustment t o a common velocity gradient, on different samples with viscometers of different capillary radii) solutions, but a close approximation.] Results S o t AdResults Adjustcd to Kroepelin showed that when the relative visMean justed f o r , Velocity Velocity Gradient Observed cosities of solutions of caoutchouc in benzene, Gradient of 500 Sec. -1 Sample Viscometer Capillary velocity Mean Mean nieabured in capillaries of widely different radii, SO. No. Radius Gradient Fluidity deviation Fluidity deviation xere plotted in linear coordinates against the cm. Set.-' Rhes Rhe Rhes Rhe mean velocity gradient they all fell on a smooth 67 0.0717 2.58 2.53 1270 0 055 0,000 68 2.47 2.53 0.0713 curve which rose rapidly a5 the gradient ap2.12 51 0.0719 2.25 1282 0 065 0.015 52 1.99 0.0702 2.22 proached zero. Before plotting in this way, 2 . 1 2 0.0719 51 2 .26 1300 0,070 120 0 widely different results were obtained, depending 52 0 0702 2.11 1.88 69 0.0722 2.84 2.83 1307 0 100 0,055 on the capillary radii. This method of plotting, 70 0.0710 2.64 2.72 64 0.0713 2.15 2.33 therefore, eliminated the instrument effect by 1321 025 0.010 0 2.20 65 0.0722 2.31 permitting the results to be read off a t some 51 0.0719 2.34 2.38 1325 0 080 0.010 52 2.22 2.36 0.0702 common velocity gradient. He showed, further, 1.8.5 64 2.17 0.0713 1320 0 160 0.055 65 2.17 0.0722 2.28 that when the data were plotted on double 52 2.54 2.5*5 0.0702 1350 0 055 0.030 logarithmic coordinates the points fell on an ap53 2.61 2.65 0.0710 70 2.38 0.0710 2.57 1362 parently straight line over a 100-fold range of 0,020 0 os5 71 2.55 0.0737 2.53 52 2.03 1.82 0.0702 velocity gradient. 1369 0.130 0.050 66 0.0715 2.13 2.08 I n view of the difficulties being experienced Mean 0.086 0.032 with the anomalous behavior of solutions of
INDUSTRIAL AND ENGINEERING CHEMISTRY
530
gradient. The extent of such improvement, where capillaries of slight variations of radius are used, can be seen by reference to Table 11, where replicate results are adjusted to a velocity gradient of 500 sec.-l.
Relation of Anomalous Behavior to Molecular Size
Vol. 13, No. 8
50 40
30
8 M 5
8L a
+
20
IO
9
z s
However, the problem is more complicated 0 than that involving merely instrument errors, I 5 20 30 40 50 70 100 200 300 500 700 IO00 2000 3000 WOO Eo00 especially if i t is desired that the fluidity or VELOCITY GRADIENT, S E C - ’ viscosity values shall be indicative of the FIGURE6 . RELATION OF INTRINSIC VISCOSITY TO MELU VELOCITY GRADIENT molecular magnitude of the solute. I n order 0 0 0 0 3 per cent nitrocellulose in butyl acetate, average d p 2650 (Staudinger and to clarify this point, i t will be necessary to conSorkin) 0 0 006 per cent nitrocellulose in butyl acetate, average d p 2680 (Staudinger) sider briefly the explanation of anomalous be8 0 009 per cent nitrocellulose in butyl acetate, average d p 1285 (Staudinger) havior as given by several investigators. e 0 03 per cent nitrocellulose In butyl acetate, average d p 955 (Staudinger) Q 0 5 per cent cotton cellulose 300 in cuprammonium solution, d p average about 2730 Signer (23) was the first to throw light on the 0 0 5 per cent cotton cellulose 1112 in cuprammonium solution, d p average about 2470 0 1 per cent nitrocellulose in butyl acetate (Philippoff) nature of anomalous behavior, through studies of flowing anisotropy of solutions of various longchain molecules. Signer’s results indicated that the degree of optical anisotropy is a measure of the orientation ment. Thus far it has not yielded an adequate expression of the extended filamentous molecules in the solution and that the which will permit extrapolation to zero velocity gradient from failure of such solutions to obey the Poiseuille law is due to the a region of partial orientation. energy required to orient these molecules. Several empircal procedures have been suggested, with the Staudinger (24) accepts Signer’s explanation and claims furthermore that anomalous flow is shown only by linear, but not aid of which the authors claim to be able to extrapolate visspherical, colloids and in linear cplloids only when the length of cosity to or near zero velocity gradient. the molecule exceeds about 3000 A. In the case of cellulose, this corresponds to a degree of polymerization of about 585 or a moOne of the most ingenious and interesting of these is that suglecular weight of, roughly, 100,000. In solutions of linear molegested by Williamson (29) in connection with the characteristics of cules of shorter length the influence of Brownian motion is suffipaints. Williamson derives the equation: cient to counteract and prevent appreciable orientation. Robinson (21) presents a dynamic picture of the extended molecules flowing through a capillary tube as being turned end-overm = f, f V m end by the gradient, rotating relatively rapidly when their long axes are in positions across the line of flow and relatively very slowly when in positions more nearly parallel to the line of flow. in whichfis the yield value corresponding to infinite rate of shear, The result at any given moment is a statistical distribution of the s is the curvature of the rate of shear-stress curve at f, and TJ is axes in which the proportion of molecules aligned with or near the the viscosity at infinite rate of shear. Williamson concluded that line of flow is larger the greater the gradient. the values off and q could be determined directly from a rate of shear-stress curve in which f is the intercept on the stress axis According to this picture, then, the apparent fluidity or of the asymptote of the curve and q is the reciprocal of the slope viscosity depends on the degree of orientation of the extended of the asymptote. The value of s must be determined by a number of observations at different points below the critical value of molecules. Beginning with zero gradient and advancing to stress where the curve turns toward zero rate of shear. higher gradients, the apparent fluidity is almost constant for slight changes, because of the predominance of the Brownian I n the results shown in Figure 5, there is no evidence that influence, after which it increases rapidly because of the overthe fluidity is approaching a constant maximum value a t the taking and predominance of the orienting influence. Finally, highest velocity gradient used, even though t h e stress rea t very high gradients in which the long molecules are statisquired to give this velocity gradient was far above t h a t a t tically essentially aligned in the direction of flow, the fluidity which the rate of shear-stress curve is noticeably curvalinear. levels off again and remains practically constant with further This means that even though the asymptote appears to be increase in velocity gradient. The S-shaped curve of visderivable from actual observations, actually in the case of the cosity thus traced has been formulated by Philippoff (17) accellulose solutions it is not. cording to the equation: Staudinger (25) considers that if dilute enough solutions are employed the anomalous effect can be greatly reduced. Thus, in eucolloids-e. g., cellulose having a degree of polymerization above 500-the anomalous behavior is much in which a’ is the apparent viscosity a t any intermediate exgreater in gel solutions than in sol solutions. He states furisting velocity gradient, 7 is a minimum limiting viscosity at ther that not only must low concentrations be employed but high velocity gradients, 70 is a maximum limiting viscosity a t low velocity gradients (near 100 set.-') must be used in order small gradients, approaching zero, P is the pressure, and y is that no, or only slight, orientation of the molecules can result. a material constant comparable to a modulus of elasticity. However, a critical examination of data furnished by It is obvious from the above discussion that in anomalous Staudinger (24, p. 508) and Staudinger and Sorkin (27) in solutions 70 is the viscosity value comparable to the viscosity comparison with data obtained in the present investigation and of Newtonian solutions-i. e., the condition of random dissome published by Philippoff (19) does not seem to indicate tribution of molecular axes. that in the case of very highly polymerized substances very dilute solutions behave very differently from the more concentrated solutions with respect to velocity gradient. This Methods for Approximating ao can be seen by reference to Figure 6 in which the data, recomAlthough a number of investigators have given special atputed to intrinsic viscosities tention to the viscosity of long-chain polymers of varying axial ratios a t minimum as well as a t maximum orientation (15, p. 271 et sep.), the theory is still in the processof develop-
-
August 15, 1941
ANALYTICAL EDITION
where qepis the specific viscosity and c is the concentration in grams per 100 ml., are plotted in logarithmic coordinates against velocity gradient. The intrinsic viscosities for the data of Staudinger and of Staudinger and Sorkin were computed directly as the quotient of the natural logarithm divided by the concentration, the remainder with the aid of Philippoff’s (16) eighth power modification of Baker’s (3) equation described below. As can be seen, the slope of the 0.003 and 0.006 per cent solutions is almost identical with that for the 1 per cent solution computed from Philippoff’s data and even greater than that for the 0.5 per cent cuprammonium solutions of cotton cellulose. This conclusion is in line with that of Fikentscher (9) who states, “Da er (pressure dependence) durch keine Aenderung des Losungmittels oder der Messtemperatur oder der Messapparatur auch nicht bei niedrigen Konzentrationen vermeiden werden kann, ist es auch hier notig, fur die Bestimmung der Eigenviskositat dieser Produkte eine bestimmte Schergeschwindigkeit bzw. einen bestimmten Ueberdruck festzulegen.” If the theory given above of the influence of velocity gradient on the viscosity of anomalous solutions is correct there would seem to he no a priori reason why dilution should overcome it. 4 second method suggested for approximating
is based on Philippoff’s (16) eighth power formula. Here again 70 is expressed in the form of the quotient with the concentration, as the intrinsic viscosity, [VI=,
8
70
(q&- 1)
in which c is expressed preferably in weight per cent-i. e., grams of solute per 100 grams of solvent-and vv is the relative viscosity. The intrinsic viscosity, [?I, is, exce t for the unit in which concentration is expressed, equivalent to Etaudinger’s expression: lim.
( T ~ ~+O ~ c ) ~
and since this expression is used by Staudinger for determination of molecular weight there is real advantage in obtaining the result in this form.
Hess and Philippoff (12) obtained very good agreements of the value of [7] of technical collodion in butyl acetate sohtions, in the wide range of concentrations from 0.05 to 15.00 weight per cent, except that the values for concentrations of 1 per cent and less were about 4 per cent higher than those for higher concentrations. More recently Philippoff and Kruger (20) found this equation to give good reproducibility of [ q ]in
TABLE111.
Product
REL.4TION OF IXTRINsIC VISCOSITY, COXPUTED BY FORMULA. TO VELOCITY GR.4DIENT
dokent
Cotton 30U
Cuprammonium
Cotton 1112
Cuprammonium
Nitrocellulose (Philippoff)
Butyl acetate”
Conoentration of Solution
Diameter Capillary
5;
Cm,
0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0,5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1,O 1.0 1.0 1.0 1.0 1.0
0.0717 0.0717 0.0717 0.0717 0.0722 0.0722 0.0722 0.0722 0.0714 0,0714 0,0714 0.0714 0.0702 0,0702 0.0702 0.0702 0.030 0.030 0.030 0.300
of
0.300
0.300 0.300
Length of Capillary Cni. 2.5 2.5 2.5 2.5 2.5 2.: 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 12.0 12.0 12.0 12.0 12.0 12.0 12.0
Velocity Gradient Sees. -1 1296 1048 873 637 3 53 212 82.2 10.7 1156 1015 SO6 608 368 224 108 27 1300 224 7s 17.06 01 . 18 8 26 1 0.0238
Absolute viscosity of butyl acetate a t 20’ C. was taken as 0.00727 poise.
531
viscose solutions, varying in concentration from 0.02 to 11.99 per cent, except that here again the values of [ q ] for concentrations of 1 per cent or less averaged higher, and in this case about 17 per cent. Both sets of solutions were highly anomalous, so that the success of this procedure is remarkable. Application of Philippoff’s equation to the results from undeteriorated cellulose shows a different result; however, it does not by any means overcome the anomalous effect. Table I11 gives data for 0.5 per cent cuprammonium solutions of two cottons, and for comparison, because of the much lower velocity gradients included, data by Philippoff (19) on 1 per cent nitrocellulose in butyl acetate. The latter have been recomputed to the same units, the absolute viscosity of butyl acetate in c. g. s. units a t 20’ C. being taken as 0.00727 poise. The very pronounced influence of velocity gradient is clearly shown. Even a t the lowest velocity gradient attained by Philippoff, 0.0238 set.-', the intrinsic viscosity has not yet become constant. It is scarcely possible to exceed this lower limit of velocity gradient with even the most specialized capillary viscometers. It is therefore evident that 70cannot be evaluated by this technique. Still a third method for the attainment of 7 0 has been suggested by Staudinger and Sorkin (a‘?), based on the extrapolation of the reciprocal of Staudinger’s value lim. (cltlep),o against velocity gradient, using linear coordinates. In dealing with a series of four nitrocelluloses, varying in degree of polymerization from 310 to 2650, they obtained, between the velocity gradients 500 and 16,000 sec.-l almost linear, slightly inclined curves, which were practically parallel and displaced from one another in the order of the degree of polymerization.
In view of the relationshir, indicated in Figure 6 it mieht be anticipated that this device could not be usedvfor extrapoiation to zero velocity gradient. Figure 7 shows that this is indeed Of the intrinsic viscosity are the case* The nearly linear with decreasing velocity gradient to approximately 500 sec.-l, whereupon they turn down sharply and extrapolation by this procedure to zero velocity gradient becomes impossible. Thus it is evident that none of the methods discussed above is adequate for evaluating 70. A means for interpolating viscosity from intermediate to zero velocity gradients will no doubt be worked out eventually. Meanwhile the best procedure for treating fluidity or viscosity data, measured a t various velocity gradients, seems to be to interpolate or extrapolate to some convenient PHILIPPOFF’S EIGHTH POWER gradient. Since the loearithmic curve relating fluidity and visAbsolute Relative Intrinsic Viscosity Viscosity Visooaity cosity, We’’ intrinsic visPoises cosity and Staudinger’s value 0.386 31.8 8.67 to velocity gradient 0.427 35.1 seems to be practically if not 0.449 36.9 0.530 43.6 9.65 actually linear (Figure 6) well 0.660 54.2 over the range for any ordinary 0.795 65.4 1.300 107.0 measurement, it does not seem 3.677 302.3 0.321 27.2 8 , 19 urgent that the viscosity meas0.334 27.5 8.22 urements be made a t the lowest 0.369 30.3 8.53 8.90 possible velocity gradients0.417 34.3 0.483 39.7 i. e., a t 100sec.-Lss suggested 0.585 48.1 0.781 64.2 10.93 by Staudinger and Sorkin (27). 1.374 113.0 12.90 0.95 130.7 6.70 It is desirable, however, that 4.23 582 9.74 the results of measurements 10.5 1,445 11.86 37.9 5,215 15.3s upon anomalous solutions be 755 206 reported in terms of some 1290 177,500 2s 24 convenient standard gradient. Since a large part of the data recorded in the literature has
-
!:;: i: ii ig:!
z:i;
lg:;$g:
E;:;
(7,ypb)c-,~,
v
INDUSTRIAL AND ENGINEERING CHEMISTRY
532
Vol. 13, No. 8
been obtained probably a t velocity gradients between 100 and 1000 set.-', a convenient value might be intermediate, say a t 500 set.-'. This would come within the range recommended by Schulz (22).
Calculation of Molecular Weight of Cellulose -4s is well known, Staudinger (24) computes molecular weights with the aid of the formula
[As has been beautifully shown by Fordyce and Hibbert (IO) as well as by others, this equation requires modification, especially for comparatively short-chained molecules. However, in the range of chain length discussed in the present paper the modification has an insignificant effect.] The value qsp/c is the limiting value as the concentration approaches zero and K,, is a constant which has been evaluated from substances of relatively low molecular weight. The value of K , found with Newtonian or near-Newtonian solutions will not apply, of course, to highly anomalous solutions, as is readily evident from Figure 6. A requirement for the use of Staudinger’s formula for highly anomalous solutions would seem to be the determination of the molecular weight by an independent method, such as the ultracentrifuge, as was done by Kraemer (Is),or less preferably by osmotic measurements such as those carried out by Staudinger and Schulz (26). The intrinsic viscosity of the same product determined then interpolatively a t a standardized velocity gradient would provide a value of K , suitable for molecular weight determinations a t this velocity gradient. Khether K , would prove to be strictly constant for different members of a homologous series under these conditions is a matter requiring further study. .4ssuining for the moment that the above relationships have been determined, that a velocity gradient of 500 sec.-l has been decided upon, and that a t this velocity gradient Kraemer’s (IS) value of DP/[ q ] = 260 can be accepted for cellulose in cuprammonium solution, the molecular weight of a cotton cellulose can be computed from the fluidity of 0.5 per cent solutions in the following manner: First, Philippoff’s equation may be partially evaluated:
16 (1.735
q1/F, - 1)
=
(12)
260 [?I
(13) 162 (260 [TI = 42,120 [ 7 ] (1 4) Thus, a cellulose in 0.5 per cent cuprammonium solution giving a fluidity of 0.80 rhe at a velocity gradient of 500 set.-' would have an intrinsic viscosity of 12.6, a degree of polymerization of 3280, and a molecular wight of 531,000.
Jf
c
02
I
I
1
01
I
0
I
8..
I
,
I
I
;
,
1
’
I
I
!
’
/
]
1
1
1 per cent nitrocellulose in butyl a c e t a t e (Philippoff, 19) 0.5 per cent cotton cellulose 1112 in cuprammonium hydroxide
0 . 0.5 per cent cotton cellulose 300 In cuprammonium hydroxide
The most promising procedure for anomalous solutions consists in obtaining fluidity or viscosity readings a t several velocity gradients and then interpolating the results logarithmically to some common mean velocity gradient. Methods for varying the mean velocity gradient are suggested. A mean velocity gradient of 500 sec.-l is recommended as convenient of attainment in ordinary capillary viscometers and probably representative of gradients for which results of anomalous solutions are recorded in the lit’erature. The adoption of a common mean velocity gradient for expression of the results of anomalous solutions will not only eliminate instrument errors but will provide a unique value for any given substance. Methods are suggested for relating this to the molecular n-eight.
Acknowledgment The writer is indebted to James H. Kettecing for much assistance with the fluidity measurements used in this paper.
where F. is the fluidity of the solution and F , that of the solvent (equals 82.25 rhes). The intrinsic viscosity having been computed the degree of polymerization, D P , and molecular weight, M, become, respectively DP
”
=
Summary and Conclusions In a study of methods of expressing the results of moderately to highly anomalous solutions, such as 0.5 per cent cuprammonium solutions of undeteriorated cotton cellulose, the velocity gradient a t which the measurement is macle was found to be an important factor, The results of the present study as well as a critical esamination of the literature do not suggest any practical means for overcoming or avoiding the anomalous effect, or of obtaining results equivalent to those for Sewtonian liquids.
Literature Cited (1) Am. C h e m . Soc., C o m m i t t e e on Viscosity of Cellulose, IND. ENG.CHEM.,Anal. E d . , 1, 49-51 (1929). (2) Am. Society T e s t i n g Materials, C o m m i t t e e D-13 o n Textile Materials, “ S t a n d a r d s o n Textile Materials”, Philadelphia, American Society for T e s t i n g Materials, 1939. (3) B a k e r , F., J . Chem. SOC.( L o n d o n ) , 103, 1653 (1913). (4) B i n g h a m , E. C., “ F l u i d i t y a n d Plasticity”, N e w Y o r k , McGrawHill Book Co., 1922. ( 5 ) Clibbens, D. A, a n d G e a k e , A., Shirley Inst. Memoirs, 6 , 117-32 (1927). (6) C o n r a d , C . M.,Testile Research, 7, 165-74 (1937). ( 7 ) F a b r i c s Research C o m m i t t e e , D e p t . Scientific a n d Industrial Research, “Viscosity of Cellulose Solutions”, L o n d o n , H . 11, S t a t i o n e r y Office, 1932. (8) F a r r o w , F. D., a n d Keale, S. >I., S h i r l e y Inst. Memoirs. 3, 6i-S2 (1924). (9) Fikentscher, H., Cellulosechem., 13, 58-64, 71-4 (1932). (10) F o r d y c e , Reid, a n d H i b b e r t , H a r o l d , J . Am. Chem, SOC., 61, 1912-15 (1939). (11) Herschel, W.H . , a n d Bulkley R . , ISD. EXG.CHEM.. 19, 134-9 (1927). Ber., 70, 639-65 (1937). (12) Hess, K . , a n d Philippoff, X., (13) K r a e m e r , E. O., IND. ESG.C H E Y . ,30, 1200-3 (1938). (14) Kroepelin, H . , Kolloid Z., 47, 294-303 (1929). (15) *Mark, H . , “ H i g h Polymers. S’ol. 11, P h y s i c a l C h e m i s t r y of High Polymeric S y s t e m s ” , Xew York, Interscience Publishers. 1940. (16) Philippoff, IT., Cellirlosechern., 17, 57-77 (1936).
August 15, 1941
ANALYTICAL EDITION
Philippoff, W., KoEEoid Z., 71, 1-16 (1935). Ibid., 75, 142-54 (1936). Ibid., 75, 155-61 (1936). Philippoff, W., and Kruger, H. E., Ibid., 88, 215-23 (1939). Robinson, J. R., Proc. Roy. Soc. (London) A170, 519-49 (1939). Schulz, G . V., 2.Elektrochem., 43, 479-85 (1937). Signer, R., 2.physik. Chem., 150, 267-84 (1930). Btaudinger, H., “Die hochmolekularen organischen verbindungen Kautschuk und Cellulose”, Berlin, Julius Springer, 1932. (25) Staudinger, H . , Papier Fabr., 36, 373-9. 381-8, 473-80, 481-5 (1938). (26) Staudinger, H., and Schulz, G. Y.,Ber.. 68, 2320-35 (1936). (17) (18) (19) (20) (21) (22) (23) (24)
533
(27) Staudinger, H., and Sorkin, M.,Ibid., 70, 1993-2017, 2518 (1937). (28) Technical dssoc. of Pulp and Paper Industry, “Testing Methods, Recommended Practices, Specifications”, Tentative Revision T206M (Apr. 15, 1935). (29) Williamson, R. V., IND. EXG.CHEM.,21, 1108-11 (1929). PRESENTED before the Division of Cellulose Chemistry a t the 99th Meeting of the American Chemical Society, Cincinnati, Ohio. The studies reported relate t o t h e program of work of the Cotton Quality and Standardization Research Section, Agricultural Marketing Service, under direction of Robert W.Webb.
Colorimetric Determination of Copper with Ammonia A Spectrophotometric Study J . P. JIEHLIG, Oregon State College, Conallis, Ore.
T
HE determination of copper, which depends upon the production of the intense blue color of the cupric amrnonia complex when ammonia is added to a solution of a cupric salt, is one of the oldest colorimetric methods. Among the first workers to use it was Heine (11) in 1830, followed by Dehms (6) and Bischof (5’). More recently it has been applied to t’he determination of copper in peas ( 4 ) ; in blast slags and tailings (1); in preserves (19); in marine organisms ( 1 7 ) ; in the human body (2); in iron, steel, and slag (20); in vegetables (9); and in rubberized fabrics (18). Snell (21) has claimed that the method is most sensitive when 0.01274 mg. of copper per milliliter is present and that a t this concentration the addition of 0.000016 mg. of copper can be detected. I t is doubtful, however, if the method is as sensitive as these figures would imply, for t-oe and Crumpler (27), using a roulette comparator, found that a solution containing 8 p. p. m. of copper could be distinguished only with difficulty from one containing 7 or 9 p. p. ni. nnd with certainty from one containing 6 or 10 p. p. m. The purpose of the work described in this paper was to make a critical study of this method by means of the photoelectric recording spectrophotometer (14,with particular attention to the effect of diverse ions upon the color system. Similar studies of other colorimetric methods have recently been m d e (5,7’,8’12, 13,22, $4).
Apparatus and Solutions All spectrophotometric measurements in the present work were made at Purdue University with the instrument used by the writer in two previous investigations (13). A standard stock solution of cupric sulfate pentahydrate, each milliliter of which contained 4 mg. of copper, was made by dissolving 15.7160 grams of the thrice recrystallized salt in redistilled water, adding 1 nil. of concentrated sulfuric acid, and accurately diluting to 1 liter. Ammonium hydroxide solutions of various concentrations, such as 1, 2, 3, 4, and 6 M, were made by suitable dilution of the concentrated solution of specific gravity 0.90. Standard solutions of the diverse ions were prepared from the chloride, nitrate, or sulfate salts of the cations and from the sodium, potassium, or ammonium salts of the anions. Redistilled water was used in all case^. Each milliliter contained 10 mg. of the ion in question. To produce the color system 5 ml. of the standard copper solution in a 100-ml. volumetric flask were just neutralized with 15 M ammonium hydroxide, diluted to the mark with 3 -If ammonium hydroxide (35),and thoroughly shaken. The spectral transmission curves were determined for a solution thickness of 1.961 cni. and a spectral band n-idth of 10 mp. Compmsation for the absorption of the glass cell and solvent was
obtained by placing in the rear beam of light a similar cc I filled with 3 M ammonium hydroxide. T h a t the color reaction may be reproduced to a high degree of precision is shown by the fact that eleven solutions of the cupric ammonia complex, each containing 200 p. p. m . of copper and prepared by the above procedure, gave transmittancies at 620p (the peak of the absorption band), the average deviation of which from the mean was only 0.1 per cent.
Conformity to Beer’s Law T h a t Beer’s law is followed by the color system is shown by the fact that a straight line resulted when the logarithms of the observed transmittancies a t 620 m p for six solutions, containing from 40 to 600 p. p. m. of copper, were plotted against the respective concentrations. This is in agreement with the work of other investigators (16’66, $7).
Effect of Ammonium Hydroxide Different workers have used various concentrations of ammonium hydroxide to produce the cupric ammonia complex. Yoe (26) used 3 M , Heath (10) 2.1 M , and Snell ($1) 1.5 -11. Yoe and Crumpler (27) have pointed out that ammonia solutions show an appreciable absorption of light in the visible region. I n a study of the effect upon the color of the concentration of ammonium hydroxide, the transmission curves produced by a series of solutions, each containing 200 p. p. m. of copper, but made by use of 1 M, 2 M, 3 M, 4 M, 6 M , and Snell’s approximately 1.5 M ammonium hydroxide, were compared. I n each case the corresponding concentration of ammonium hydroxide was used in the rear cell. The curves show that the hue gradually changes as the concentration of ammonium hydroxide varies. Both the maximum absorption and the wave length of maximum absorption increase as the concentration increases. This is in accordance with the findings of Keigert ($3) and of Yoe and Barton ($6)who used only two concentrations of ammonium hydroxide. Therefore, i t is necessary that the concentration chosen for the determination be used throughout in making all the unknown as well as standard solutions n-hich are to be used for comparison. In the present work the 3 Msolution ($5) was selected. Because of the high concentration of ammonia, no attempt was made to determine pH values.
