Cellulose Ester Viscosities by the Ball-Drop Method CARL J. MALM, LEO B. GENUNG, A N D GEORGE B. LAPHAM Eastman Kodak Company, Rochester, N. Y . determination of conversion factors are presented. The Faxen equation is particularly useful for the latter purpose. If viscosity data are to have practical significance,it is necessary to use solvents, concentration, and temperature closely duplicating use conditions. Pronounced viscosity effects may be caused by variations in concentration; temperature; solubility; density, viscosity, and purity of solvent; and presence of certain ions. It is not possible to predict viscosities of concentrated solutions accurately from data obtained on dilute solutions.
The ball-drop method is useful for measuring viscosities of concentrated solutions of cellulose esters. Several ball-drop viscometers are described, which are readily constructed from simple apparatus, are useful over a considerable range of viscosity, and are easily calibrated. Viscosity results expressed in seconds are acceptable for control purposes, but they should be converted to absolute or kinematic units for engineering purposes and for a more thorough understanding of the properties of the solutions. Procedures for the measurement of viscosities and
V
d . The sphere is rigid. e. The motion is steady and free from accelerations. j . There is no slip between fluid and sphere-i.e., the fluid film in contact with the sphere moves with the same velocity and direction.
ISCOSITIES of solutions of cellulose esters are measured under many different conditions. The viscoeities of dilute solutions, including intrinsic and inherent viscosities (4), are of considerable value as a measure of an average molecular weight or degree of polymerization. They show the extent of degradation, which influences the general level of physical properties. Viscosity determinations in dilute solutions are, however, of only secondary usefulness as a measure of the viscosity which a given cellulose ester will have in the more highly concentrated solutions encountered in commercial practice. Other factors including temperature, solubility of the ester in the solvent, and the presence of certain metallic ions may produce increases in viscosity to the point of gel formation. The measurement of viscosities of solutions of cellulose esters under practicsl conditions is, therefore, necessary and of considerable importance for production control. The ball-drop method for the measurement of viscosity is widely used because of the simplicity of apparatus required and the versatility attainable. By varying the ball-drop distance and the diameter and density of the ball, viscosities may be measured conveniently over the range 10 to 10,000 poises. Older ball-drop viscometers tended to use comparatively large balls in tall, narrow tubes and long distances of fall. In some of the newer apparatus small balls are used in large containers to decrease the wall effect and minimize errors due to improper centering of the ball. An exception is the Hoeppler rolling-ball viscometer, a very precise reference instrument in which comparatively large balls roll through a tube of uniform dimensions mounted a t an angle from vertical. Viscosity results may be expressed in absolute units (poises or centipoises), in kinematic units (stokes or centistokes), or more commonly in commercial practice, in seconds. The latter unit is practical for production control purposes because it does not involve a calculation. The other units are preferable, in general, because they do not require a complete description of the a p paratus in order to define a viscosity, and viscosities determined with various apparatus are directly comparable. The conversion of ball-drop seconds to absolute or kinematic units is simple and convenient because equations, particularly that of Faxen (6),can be used to calculate conversion factors. The use of this equation was thoroughly investigated by Bacon (S), whose conclusions as to its general usefulness have been confirmed in this laboratory. The Faxen equation is actually the expression of Stokes (9) applied to the falling-ball viscosity method with a correction for wall effect. The Stokes equation and viscometry based on it involve the following assumptions (3): a.
b. e.
The Faxen equation provides a correction for assumption b. The other requirements are more often fulfilled, as discussed by Bacon (3).
Stokes Equation.
-
2gr*(b s)t 9L
tl=
where 7 = Q =
r = b = s = t =
L =
(1)
absolute viscosity, poises acceleration due to gravity, cm. per sq. sec. radius of ball, cm. density of ball, grams per cc. density of fluid, grams per cc. time of fall, seconds ball-drop distance, cm.
Faxen Equation. 2gr*(b - s)t tl =
9L
11
- 2.104(d/D)
+ 2.09 (d/D)' - 0.95 (d/D)'] (2)
fhere d = diameter of ball, cm. D = diameter of tube, cm. Equation 2 simplifies to the form customarily used for the calculation of ball-drop viscosities: t)
=
K(b
- s)t
(3)
where K , the apparatus constant, may be determined experimentally with fluids of known viscosity and density, such as oils from the National Bureau of Standards. This constant may also be calculated, for from Equations 2 and 3 it can be seen that
K
=
-2 [l 9L
- 2.104 ( d / D ) + 2.09 ( d / D ) 3 - 0.95 ( d / D ) ' ]
(4)
Equation 4 was used for the calculation of apparatus constants reported in some of the following sections. The calculated values usually agree closely with values obtained by calibration. Kinematic viscosities in stokes, Y , can be calculated from absolute viscosities in poises and the solution density by the following relationship: " = -tl 8
APPARATUS
The motion of the sphere relative to the fluid is slow. The fluid is infinite in extent. The fluid is homogeneous.
Many different ball-drop viscometers of varying dimensions are now in common use. Some of the confusion thus created can be 656
657
V O L U M E 22, NO. 5, M A Y 1 9 5 0 by
the viscosities in seconds t,, poises
" L . , "
dimnetor of ball = 0.3125 * 0.0005 inch or 0.794 0.001 em. Weight of ball = 2.035 * 0.010 g r a m d
=
+
h = ball density =
2.035 = 7.76 gram.? per cc. 1.333 X 3.111G X 0.397'
* 0.02 inches or 2.54 cm. bull-drop distance = 10.0 * 0.10 inohes or 25.4 em. g = acceleration of gravity = 080.4 at Rochester, Substituting the ahove data into Ec-"-- 1 A,--.
D
= diameter of cylinder = 1.0
L
=
K
5
* 0.05 * 0.25 N. 1..
0.545
Viscosities measured in this apparatus may be calculated as follo*.s: n = 0.col present; the acid solution is heated on a steani bath for 30 minutes and cooled to 30" C., and then a freshly prepared solution of 1-naphthol in sulfuric acid is added. The intensity of the
T
HE vapors of triethylene glycol and of propylene glycol have been found to possess marked bactericidal activity when dispersed in small quantities in the air (9, 6, 7). The formar compound, having much the lower vapor pressure (0.0013 mm. of mercury a t 25" C., 4 ) , is the more efficient, and is currently receiving widespread application as an aerial disinfectant for occupied premises. The bactericidal effectiveness of triethylene glycol vapor depends upon the extent to which the atmosphere is saturated with this vapor. The saturation concentration of triethylene glycol vapor in the air in the absence of water vapor has been reported by Wise and Puck (11) to be of the order of 11 micrograms of glycol per liter of air at 25' C., and the variation of this saturation concentration with relative humidity and temperature of the air has been determined (IO). Losses of unknown magnitude, caused by condensation and by ventilation of the room, make it desirable to have an analytical method of determining the concentration of triethylene glycol in the air. This method must be sufficiently sensitive to determine quantities of glycol in the saturation range, between 1 and 10 micrograms per liter of air, a t normal temperatures and relative humidities, Wise, Puck, and Stral (f8)bubbled the air through water and determined colorimetrically the extent to which an aliquot of the aqueous glycol solution reduced a standard dichromate-sulfuric acid mixture. Because of the small quantities of triethylene glycol which must be analyzed, large volumes of air (ea. 300 liters) and long sampling periods must be used. Another method of determining triethylene glycol (3, 6) depends upon the condensation of the vapor upon a cooled surface, and subsequent measurement of the amount of light scattering caused by this condensed film. Instruments embodying this principle (glycometers) have been built and successfully used in these laboratories for several years. They are, however, complicated and eupensive, and are not yet commercially available. This paper describes a simple, rapid, and reasonably precise
yellow color formed is measured spectrophotometrically, and is proportional to the quantity of triethylene glycol present. The presence of water affects the development of color; different calibration curves must therefore be used for different relative humidities. A formula relates the optical density of the treated sample to both the water and the glycol content, so triethylene glycol concentrations may be calculated directly from spectrophotometer readings. When conditions of analytical treatment are carefully controlled, the method gives deviations of about *5% of the glycol concentrations.
method for the analysis of triethylene glycol in air. Concentrated sblfuric acid is used as the collecting medium for the glycol, and the analysis is performed spectrophotometrically by determining the intensity of the color produced upon the addition of 1-naphthol t o the heated acid solution of glycol. APPARATUS AND MATERIALS
i\ c
c
c r
Figure Absorption Tube
Sampler. The sampler used is a glass a b s o r p tion tube (Figure 1). Air is drawn through the tube by means of a vacuum pump, which is protected from corrosion by a soda-lime tube placed in the line. The flow of air is controlled by a suitable critical flow orifice installed between the sampler and the pump. It is desirable to have as little absorbing fluid as possible left in the tube after draining, and to prevent the liquid from splashing over into the vacuum system during operation. The Vigreux-type indentations have been found helpful in the second regard. When 10 ml. of sulfuric acid are used in the tube illustrated, whose over-all height is 26 em., the acid level is about 3 cm. above the outlet. When air is being drawn through the acid a t a rate of 15 liters per minute, the acid level rises to about 6 cm. above the base. The arrangement of the ground-glass joint (24/40) at the cap is convenient for refilling the bubbler. The sulfuric acid acts as stopcock lubricant; both the regular and the siliconebase types of stopcock grease were found to interfere with the test. The rubber retaining washer must be removed from the stopcock. Other Equipment. A spectrophotometer (Coleman Universal, Model 14, was used in this laboratory), a steam bath, and a water bath capable of maintaining a temperature of 30" C. are required. A vacuum pump and appropriate flowmeters should be available for taking the samples. Reagents. Triethylene glycol (air sterilization grade, Carbide and Carbon Chemicals
