January 1949
INDUSTRIAL AND ENGINEERING CHEMISTRY CONCLUSIONS
With pertinent experimental data, the equations concerned with mass transfer by diffusion are well suited for establishing the
extent of fuel vaporization in the intake system of an aircraft engine and in the precombustion zone of a jet propulsion burner. The equations related to batch differential distillation, if applied a t 1 atmosphere, represent a means of calculating the experimental A.S.T.M. distillation vapor and liquid compositions. The equilibrium flash distillation calculations can be used t o determine the liquid and vapor compositions related to a corresponding equilibrium air distillation. ACKNO W LEUGWI JShT
’
The writers wish to express their appreciation to L. F. Stutzrnan, E. F. Obert, and G. M. Brown, all of Northwestern University, for their helpful suggestions, and also to the Pure Oil Company, Chicago, Ill., for rxperimental data arid financial aid reccived in the course of this study. LITERATURE CITED
American Society for Testing Materials, A . S .T.M. Standards Part I I I , 1945 Supplement. Berliner, J. F. T., and May, 0. E., J . Am. Chem. SOC.,49, 1007 (1927).
Bridgeman, 0. C., J . Research Natl. Bur. Standards, 13, 53 (1934).
Brown, G. G., Univ. Michigan, Dept. Engineering Research, Bull. 7 (May 1927). Ibid.,14 (May 1930). Brown, G. G., Souders, M., Jr., and Sinit,h, K. L., IND.ENG. CHEM.,24, 513 (1932). Buckler, E. J., and Norrish, It. G.W., J . Chem. SOC.,1936,1567. Calingaert, G.,Beatty, H. A., and Neal, €I. R.. J. Am. Chem. SOC.,61,2755 (1939). Coats, H. B., arid Brown, G. G., Univ. Michigan, Dcpt. Engineering Research, Circ. Ser. 2 (December 1928). DeJuhasz, K. J., Zahn, 0. F., Jr., and Schweitzer, P. €I.,
I89
Pennsylvania State College, Engineering Expt. Station, Bull. 40 (Aug. 22, 1932). Geddes, R. L., IND. ENG.CHE,M., 33, 795 (1941). Gilbert, M., Howard, J. N., and Hicks, B. L., National Advisory Committee for Aeronautics T.N . 1078 (May 1946). Gilliland, E. R., IND. ENG.CHEM.,26, 681 (1934). Gilliland, E. R., and Sherwood, T. K., Ibid., 26,516 (1934). Henle, II. R., and Blair, C . M., J. Am. Chem. SOC.,53, 3077 (1931). IOid., 55, 680 (1933).
Hershey, R. L., Eberhardt, J. E., and Hottel, H. C., S.A.E. Journal, 39, 409 (October 1936). Holooinb, D. E., and Brown, G. G., IND.ENG.CHEX.,34, 590 (1942).
Hull, W. L.,and Parker, N. A., S.A.B. Quarterly Trans.,1, No. 2, 185 (April 1947). Jones, Vir. J., Evans, D. P., G u l ~ ~ e lT., l . and Griffiths, D. C., 6.Chem. SOC.,1935, 39. Kats, D. L.. and B ~ O W IG. I , G., IND. EKG. CHEM.,25, 1373 (1933).
Lange, N. A , , “Bandbook of Chemistry,” 3rd ed., Sanduaky, Ohio, Handbook Publishers, 1936. Maxwell, J. C., Phil. Mag., 35, 185 (1868). Newtou, A., J . Am. Chem. Soc., 65,320 (1943). O’Brien, L. J., thesis in chemical engineering, Northwestern Tecliriological Iristitute, 1947. Perry, J. H., “Chemical Engineers’ Handbook,” 2nd ed., Is’ew York, McGraw-Hill Book Co., 1941. Pratt and Whitney Co., “Installation Handbook.” Pratt and Whitney Co., “Manual of Engine Operation.” Rayleigh, 0. M., Phil. Mag., 4, 521 (1902). Rossini, F. D., et al., J . Research Natl. Bur. Standards, 35, 219 (1945).
Sniitli, R. L., and Watson, K. M., IND.L ~ N G . CHEM.,29, 1408 (1937).
Stefan, Sitz. Alcad. Wiss. Wien, Abt,. 11, 62, 385 (1870). Thomson, G. W.. Chem. Rev., 38, No. 1, 1 (February 1946). Watson, K. M., IND. ENG.Camx, 23,360 (1931). Ibid., 35, 398 (1943). Watson, K. M., et al., Ibid., 27, 1460 (1935). R E C ~ I V EMarch D 13, 1948. Presented before the Division of Petroleiiin Chemistry at the 113th Meeting of t h e AUERICAI CHEMICAL S o c r m u Chicago, Ill.
Physical Pro erties of Solutions of a Sodium Phosphate Glass JOHN R. VAN WAZER Rumford Chemical Works, Rumford, R . I .
The
viscosity of aqueous solutions of a sodium phosphate glass containing 62.59” phosphorus pentoxide was meamred in the temperature range of 0 ” to 75” C. and in the concentration range from 0 to 70% glass. The viscosand lo4 poises and ity of these solutions lay between did n o t vary with rate of shear. An analysis of the data according to Eyring’s absolute rate theory led to the conclusinn that below a Concentration of about 20% glass, the Bow units are water; above this concentration the
flow units are segments
LTHOUGH the sodium phosphate glasses are of great commercial importance, little information (9,IS) has been published on the physical properties of their aqueous solutions. Such information is useful in the various engineering problems connected with industrial application of the phosphate glasses. For example, the flow data reported in this paper have been used in the design of equipment for handling stock solutions of the phosphate. The vapor pressure data find application in the formulation of alkaline detergent mixtures and water softeners since a knowledge of the vapor pressure is necessary to predetermine if the resulting product will cake.
This study was confined to a glass containing 62.5% phoephorus pentoxide. This glass is typical of the commercial products as all sodium phosphate glasses in the range between and tripoly composition (57.9% P 2 0 6 ) the meta (69.6% Pz06) exhibit similar properties in pure aqueous solution. Qualitative studies have shown that the magnitude of the properties reported here is only moderately affected as the composition of the glass is varied throughout this range. The samples of the glass used in the experiments were taken from a regular production run of Quadrafos (a registered trade-mark of Rumford Chemical Works). This commercial sodium phosphate glass has been found t o be
of hydrated phosphate molecule ions. The partial pressure of water vapor over aqueous solutions containing 0 to 90% glass (62.5% phosphorus pentoxide) was measured by a direct manometric procedure and also with an electric hydrometer. The experimental data can be fitted to Raoult’s law, assuming that the only particles present in solution are water molecules, sodium ions, and polyphosphate molecule ions. Density of the phosphate solutions also was measured.
190
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 41, No. 1
VlSCOSiTY
(Poises)
i
I 1
I-
I
t
TABLE I. VISCOSITY ~ ~ E A ~ U R E M E NOTF S SOLUTIO\\ 01 dour[ M PHOSPHATE GLMS C O \ T ' I I U I h G 62.5yG P205 Concentration of Glass, Viscometer Stormer Rotational
%
Wt.
70.0 65.0
I
100.
60.0
Capillary tube No. 1
Viscosity, Poises
17 24 5 9 15.5 26 28 41 60 74.5 96
4 . 1 X 108 1 . 9 x 10; 5 . 8 X 10 3 . 1 X 10' 8.0 X 109 130. 110. 22.5 6.1 3.4 1.2 97. 16.0
14
27 35 60 15 26.5 35 50 70 0 25 50 70 0
50.0
10.
40.0
i
tiire, C. rempera-
30.0
I _
t
/
n ,054
70
o.0178
1 0.01
/ io
20
30
40
50
60
70
WEIGHT PERCENTAGE OF PHOSPHATE GLASS
Figure 1. Viscosity Coefficient at 25" C. of Aqueous Solutions of Sodium Phosphate Glass (62.5y~PzOa) as Function of Concentration
Capillary tube No. 2 (smaller capillary than S o . 1)
0 (pure water) 30.0
20.0
0.058 0.0319 0,0236 n. 0144
0 14 24 50
0,0305 0.0177 0.0141 0,0091 0.0068 0.0233 0 0142 0.0107 0.0074 0.0054 0.0105 0 0112)a 0,0083 0089) a
70
8.5
0,075
0.0269
0 18 25 50
70
10.8
0.86
0,192 0.072 0.040 n. 161
;: 50
20.0
6.9 1.53 2.45 1.04 0.61 0.282 n. 128
0 15 26 60 70 16 25 25.0 48.6 69.2 0.6 25.0
n. oioo
48.8 69.2 0.2 25.0 48.6 69.3 3.0 .4 25.0 50.2 69.5 n 0.2 25.0 50.2 69.0 Accepted values. Because of uncertainty i n the kinetic energy correc. tion, values obtained with capillary tube viscometer No. 1 for viscosities below about 0.015 poise ?re apparently too small. As evidenced by the d a t a for water, low viscosities were determined correctly with capillary viscometer No. 2.
10.0
a
consistently uniform and completely free of crystalline material. [This statement, which is contrary to an opinion recently published by Quimby (Q),is based on numerous microscopic examinations and some x-ray studies of samples produced over a period of several years. It would seem that the crystalline material observed by Quimby was formed by surface hydrolysis of an aged sample that had been exposed to a moist atmosphere.] Since a glass is a supercooled liquid of high viscosity-, a mixture of a sodium phosphate glass T? ith water can exist as a one- or twophase liquid system (IO)similar to an alcohol-water mixture or a phenol-water mixture. On the basis of the polyphosphate molecular structure, the one-phase system seems most probable. All of the experiments that have been performed in this laboratory indicate that a single phase is present throughout the concentration range from 0 to 100%. This conclusion is borne out by the experiments reported here, since no discontinuities were observed in the viscosity, density, or vapor pressure of the solution as the relative proportion of phosphate glass to mater was varied. I n the author's opinion the solubilities reported ( 4 )for metaphosphate glass are practical limits beyond which the rate of 2 0 1 ~ tion of the glass becomes extremely slow because of the high viscosity of the solution. I n the studies reported here fresh solutions of the phosphate were made up every day, and the experiments were completed within 5 hours of the time the solutions had been prepared. I n this manner the effects of hydrolysis were avoided. I n solutions containing more than 60% of the phosphate by weight, hydrolysis nrould have had an appreciable effect on the viscosity at lower temperatures, The solutions in most cases were prepared by adding the finely powdered glass t o Ivater T\ hich was
mechanically stirred and kept in a thermostat to avoid ovwheating with resulting hydrolysis during dissolution. It should be emphasized that the data given in this paper are not the result of precision measurements. These studies were undertaken only to provide information that would be adequate for engineering calculations and gross generalizations concerning the nature of the solutions. Further refinements in experimental procedures vould have necessitated an unwarranted expenditure of time. VISCOSITY
EXPERIIIEXTAL STUDIES.The viscosity measurement> on solutions having a concentration less than 50% phosphate glass were made in modified Ostmdd-Fenske capillary tube viscometers (6). At higher concentrations the viscosity was measured in either a Stormer or RlacMichael viscometer (8). All of the viscometers were calibrated with standard viscosity oils (furnished by the National Bureau of Standards, Washington, D. C.) using the usual equations of viscometry ( 3 ) . Standard vir-
January 1949
191
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
cometric corrections for kinetic energy, end effects, etc , also were made ( 3 ) . The viscometers were used with manually adjustcd thermostats so that the effect of temperature on the viscosity could be ascertained. Measurements at the lower temperatures mere made first and a new sample was used for each determination a t the higher temperatures to avoid effects of hydrolysis. In using the capillary tube viscometers, samples were found to reach temperature equilibrium, as shown by the flow time, after several passes through the capillary. Then the flow time was measured three or more times giving a mean deviation between measurements of about 0.1%. Thus it appears that hydrolysis had no appreciable effect on these measurements. To convert from kinematic to absolute viscosities the density data given in a following section of this paper were used. Since densities were measured only at 25" C., the densities a t other temperatures had to be computed by using a value of the coefficient of expansion estimated from the knoivn coefficients of other salt solutions. As the greatest temperature correction to the density a as only 2% of the density a t 25 O C., this procedure can not be an important source of error. m'hen viscid solutions with a concentration greater than 48% glass wcrr allowed to hydrolyze for an extended period of time, a white precipitate would settle out; and, if the concentration were greater than 58% glass, this precipitate would fill up the entire volume of the solution. The viscosity of aging samples a t elevated temperatures was found to be relatively unaffected (several per cent increase) by hydrolysis until this precipitate began to form, whereupon the inorease of the over-all viscosity was greatly accelerated. Therefore, measurements on the concentrated solutions in which there was a trace of precipitate were discarded. The precipitate would form rather rapidly a t high concentrations and temperatures-for example, a 65% solution became milky within 10 minutes a t 70" C. Fortunately the temperature of the solutions could be rapidly adjusted in the rotational viscometers and an entire measurement was completed in several minutes. The temperature was obtained to about 0.5" C. by immersing a thermometer directly into the viscous material between the inner and outer cylinders. I n the MacMichael viscometer, surface skin formation from evaporation at elevated temperatures was a major source of error; hence most of the work was done in the Stormer instrument as its operation is relatively unaffected by skin formation. It is estimated that the error in viscosity measurement due to hydrolysis and evaporation TWS always less than 15% for the highly viscous samples. In general, non-Newtonian behavior of anomalous solutions increases with increasing concentration of the solute-for example ( I d ) . Therefore, if solutions of the sodium phosphate glass exhibit viscositv anomalies, this behavior should be most apparent at high phosphate concentrations. However, the viscositv coefficient of solutions containing from 50 to 70% of the glass did not vary when the rate of shear was changed tenfold. Therefore, it was assumed that these solutions are true Newtonian liquids. The experimental d a b are presented in Table I. I n Figure 1 the viscosity of an aqueous solution of a sodium phosphate glass containing 62.5% phosphorus pentoxide is reported as a function of concentration a t 25" C. It is apparent from this figure that the viscosity increases greatly when the concentration is raised above approximately 60% by weight. Since a tarlike solid can in practice be defined as a substance with a viscositv higher than IO5 poises and a glassy substance as one with a viscosity greater than 10'0 poises, it is seen that the solution is glassy when the water content is less than about 5% and is tarlike in the range from 5 to 20% water. Of course, there is no discontinuity in internal friction in going from solid to solution such as is found in the case of a crystalline material. In Figure 2 the viscosity is given as a function of temperature. I n general, viscous liquids have a greater temperature coefficient of viscosity
VISCOSITY
I
(Poises)
Ccoc. cf glass
-
Irl;/ 100.
10.
L€
0.1
r
/
/
/
/
30.0%
0 01
90
80
70
60
50
40
30
20
IO
0
TEMPERATURE ("C)
F i g u r e 2. T e m D e r a t u r e V a r i a t i o n of V i s c o s i t y for V G i o u s A q u e o u s S o l u t i o n s of S o d i u m Phosphate-Glass
(62.5% P2Od Plot of log viscosity against reoiprooal absolute temperature
than do those that are more fluid (8). This effect has been found for the solutions studied. Bince the curves of Figure 2 are not straight lines, it must be assumed that the solutions are appreciably associated ( 6 ) . .4ccording to the absolute theory THEORETICAL DISCUSSION. of reaction rates (e), viscosity can be trrated as a regular kinetic process to obtain the following equation:
where 7 is the coefficient of viscosity, h is Planck's constants N is Avogadro's number, V is the molar volume, AS$ is the difference in entropy between the activated and initial states per mole of flow units, AH$ is the difference in enthalpy or heat content between the activated and initial states per mole of flow units, and. R is the gas constant. Since the molar volume and entropy of a liquid do not vary appreciablywith temperature, Equation 1 takes the form:
,
= B~AH$/RT
(2)
When the activation energy of viscous flow-the limiting slopes a t high temperature (50 O to 70 O C.) of the curves in Figure 2 were used for the calculation-is plotted as a function of phosphate concentration (Figure 3), it is seen that AH$ does not change with concentration from 0 to about 15%, and then increases in linear manner. The point corresponding to 100% sodium phosphate
192
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
Val. 41, No. 1
d i e s of a number of the solutions wcre measured a t 25” (‘. For the sake of completeness, these measurements were extended throughout the complete conrentration range. At the 1 o . i ~ ~ ~ concrritrations the densitie. mere measured with a Westphal balance, and a t higher coneentiations with pycnometers. The density data arc shown in Figure 5 where they are compared with the theolntical curve calculated for no volume change on mixing. As might be expected for a binary system exhibiting strong molecular interaction, the total volume of a mixturr is less than the sum of the volumes of the t t 5 o components. VAPOR I’IRESST R E E x P m I m m r A L STUDY.Sirice most accepted method. tri measuring the vapor presyixre of solutions are time-consuming, 01 J they cannot be applied to the determination of the partial prrs0 20 40 60 80 100 sure of water vapor over an aqueous solution of a sodium phosphate gla-s because the yhoiphate may hydrolyze appreciai)l\ WT. % of GLASS during a peiiod of many days. Therefore, it was felt advisable Figure 3 . Activation Energy for Visto use a fast procedure even a t the expense of precision. ThP w u s Flow of Aqueous Solutions of S ~ ~ d i u i n studies were made by two independent methods. Phosphate Glass (62 5 % fpOs) nt 60” C. The direct manometric measurement of vapor preqsurr w t i b chosen as one method, since in this procedure the driving Eo, cc for the attainment of equilibiium is not only the equalization of glass was taken from the u ork ot Aindt 011 niolteri aodiurn motapartial pressure at constant total pressure but is a total preiaure phosphate ( I , 2 ) . hrndt’s data follow Equation 2 vrith precision, gradient as well. In t,he experiment a freshly prepared phosphatv although this equation (7) was not pioposed until 4 years after solution was placed in a 50-cc. thermostated bulb connected by a the data were obtained. hlolteii sodium metaphosphate (69.G% ground-glass joint to ariothcr bulb of the same size which W Z PzO,) and the sodium phosphate melt containirig 62.5% phosattached to a high vacuum apparatus. The prrszure was phorus pentoxide must be +imilar with respect to Ihcir flow bcmeasured by mcans of a manometer read with a cathetometer havior, as they probably contain a great number of the same calibrated to 0.01 mm. Beforc each run the apparatus was types of associated molecules. It is t o be expected that they tested for leaks and a pressure of less than 0.001 mm. of mercury will have practically the same temperature coefficients of viswas achieved. Between earh measurement the zero poiiit, of the cosity. aathetometer was rhecked. The shape of the curve in Figuie 3 l e d ? to the conclusion 1 hat The samples corresponding to points 1, 2, and 3 in Figure 6 up to a concentration of appr,>ximately 18% glnsi the flow units were made up qualitatively by weight. Pressure equilibrium are water molecules, and above this concentration the flow can be was essentially obtained in I hour, and two readings were taken attributed to the motion of segments of the hydrated polyphosfor each point; the system was pumped out before each reading phate molecule ions. I n other words, at a temperature of 60“ C. -4s a 70% solution is extremely viscous, it seemed worth while and a concentration of 1870 the water is completely bound in to stir the solution in the caqe of point No. 3. A small magiict the hydration shells of the polyphosphate molecules, and flow therefore mas put irito the flask, and stirring was effected b j from this point on consists in disturbing these units. This conmoving a large magnet around the flask by hand. ‘!hvo tletercentration corresponds to a mole ratio of water to phosphorus minations were made on this sample with stirring for 5 minutes equal to 30. This interpretAion is consistent with the entropy preceding each determination. The sample corresponding to calculated froln the viscosity data at BO ’C. This entropy differpoint No. 4 was made up by dehydrating a 50% solution in vacuo ence between the activated state in f l o ~and the original state several times. During each evacuation bubbles in the solutioii changes with concentration in swelled up so that the material was in the form of thin films the manner shown in Figure 4. which were kneaded together after each dehydration. This As’ The partial molal volume of method of preparation assured homogeneity. The concentration eu water was used in the hryt part of this sample was found to be 80 * 3y0as judged from its visof the calculation, and the cosity. Sample KO.5 nas prepared by exposing a finely powIO volume of the amount of ioludered sample of the sodium phosphate glass to moist air arid tion containing 1atomic weight passing it through a 40-mesh screen several times during the of the phosphorus-that is the process. This meant that each paiticle of glass con 5 partial molal volume of PO1” dry nucleus surrounded by a partially hydrated shell. The groups-in thc second part. particles then were put into the vacuum apparatus and evacuated for several minutcs. After an hour had been allowed for pressure As might be expected, the 0 entropy of the molten sodium equilibrium, a measuiement oi prrssure wa3 made. This cycle metaphosphate does not corwas repeated seveixl times until the pressure did not change much respond to an extrapolation of from one reading to a i i o t h ~ . Then the apparatus was allowed t o -51 the above values. set overnight to obtain the pressure reading that wai finally Figure 4. Entropy of Activation for Viscous reported. I t i s believed that this is the equilibrium partial Flow of Aqueous S O ~ U - pressure, as the t1estinc.111of the inaterial was designcd to esDENSITY tions of Sodium Phospedite the rate of attainment of homogeneity. The concentrrtphate Glass (62.5% PzO6) Since it is necessary t o tion of this \ample was obtained by melting it in a platiiiuin Curve ABC was computed asknow the density in order crucible at 800” C until bubbling became slight (about 1. hr.), suming that a molecule of water was the flow .unit and to compute the viscosity of The loss of weight of the crucible on heating was assumed to the curve DEF waa wmputed on the assumption that the a liquid measured in a capilequal approximatclb the amount of water containcd in the flow unit contained one atom lary tube viscometer, the denixmple. of phosphorue
~
Ianuary 1949
193
INDUSTRIAL AND ENGINEERING CHEMISTRY
monoxide. This water determination was based on titration of a solution of the glass to the weak acid neutralization endpoint as suggested by Quimby (9) and also loss of weight on extensive dehydration at 500 C. From this data and titration curves the number-average chain length of the polyphosphate ions was found to be 4.9 phosphorus atoms per chain. Therefore, if complete dissociation is assumed, 70 grams of the sodium phosphate glass contains 0.84 mole of sodium ion and 0.16 mole of polyphosphate molecule ions or one mole of particles in all. The number average chain length, %, can be calculated from the analytical data assuming that small amounts of water can replace NanOin the glass. Thus, from the formula ( N a , H ) n + z P n O ~ n + ~ ,
2 -%PZOb 142.04 = %bT\TazO
61.99 WEIGHT PERCENTAGE OF PHOSPHATE GLASS
Figure 5. Density of A u e o u s Solutions of Sodium Phosphate Glassy62.5% P z O ~a) t 25" C.
TABLE11. RELATIVL I~UMIIXTY AT 2 5 " C. OVER SOLUTIONS OF SODIUM PHOSPHATE GLASSCONTAINING 62.5% PzOj By Direct Pressure Measurements Relative Concentration, humidity. wt. 7% glass 04 91.4 30.0 zo.0 81.9 70 * 1 56.8 80 * 3% 48 91 rt 2 24 * I
By Electric Hygrometer Relative Concentration, humidity, wt. 'Z glass % 9.8 24.6 40.8 50.0 60.0 68
98.5 95.5 85.7 83.5 71 53
V~P~O~ 142.04
where % ' PzOs,% NazO, and % HzOequals the weight percentage of the respective constituents. The chain length can be computed from titration data according to the following formula: n=2
The second series of measurements was made using an Aminco electric hydrometer. The Aminco-Dunmore electric hygrometer is manufactured by American Instrument Company, Silver Spring, Md. The operation of this instrument depends on $he variation of the electrical resistance of a thin hygroscopic film with its water content, I n these studies the phosphate qolutions were made up in the manner described in the section qn viscosity and placed in two thermostated, sintered-glass, gas dispersing bottles, Air then was passe& through a flow meter into the thermostated bottles. Behind the second bottle was a therinostated glass chamber barely large enough to contain the sensing element of the hygrometer. An experiment consisted of two parts. First, the air was passed through a drying bottle before entering the system, and the reading of the hygrometer was measured as a function of time. Secondly, the air was passed through a wash bottle containing water before going into the system, and the hygrometer was read again a t various times. Thus, attainment of equilibrium was assured, since it was approached from both the dry and wet sides. I n all of the data reported by this method, the relative humidity readings as approached from above and below agreed to 1% relative humidity. THEORETICAL DISCL-SSIO~. Since vapor pressure is a colliga5ive property, it depends primarily on the number of particles present in solution. ,4t the present time a large weight of evidence supports the conclusion that dilute solutions of sodium phosphate glasses having a mole ratio of sodium to phosphorus greater than or equal to 1, dihsociate into only sodium ions and polyphosphate molecule ions, the average chain length of which can be obtained from titration curves (11). By analysis, the phosphate. glass used in these experiments was shown to contain 92 5 phosphorus pentoxide and 0.3% water; the balance is sodium
H~O +-%18.02
Equivalents of strong acid Equivalent3 of weak acid
Raoult's law can be given by the following equation : 5 =
p/p" =
yo relative humidity
(3)
100
where p is the vapor pressure of the solute, p O is the vapor pressure of the pure solvent, and 2 equals the mole fraction of the solvent. I n Figure 6, theoretical curves computed from Raoult's law, assuming that a certain weight of the phosphate glass contains 1 mole of dissociated particles, are given. It is seen that the experimental points lie near the theoretical curve for 1 mole of particles in 70 grams of glass. I n the more dilute solutions the experimental points are somewhat above this curve, an effect which might be ascribed to the formation of phosphato-sodium complexes. It is surprising that the data can even be fitted approximately throughout the entire concentration range from
0
20
40
60
80
100
WEIGHT PERCENTAGE OF PHOSPHATE GLASS
F i g u r e 6.
P a r t i a l Pressure of W a t e r Vapor
at 25" C. over Aqueous Solutions of Sodium P h o s p h a t e Glass (62.5% Pz06) Numbered points (open ellipses) were determined by direct pressure measurements and aolid points by an electric hygrometer; eurves were computed from Raoult's law. Starting with the loweat curve 6 0 , 7 0 , and 80 grams of original glass were assumed to contain 1 mole of particles.
194
INDUSTRIAL AND ENGINEERING CHEMISTRY
0 to 100% glaas to a theoretical curve based on the bimple assumption of complete ionization and ideal behavior. Doubtlessly, the true state of affairs is much more complicated then i s indicated by a pseudo-ideal solution containing only water molecules, sodium ions, and polyphobphate molecule ions. These data emphasize the fact that the measurement of colligative properties in systems as complicated as those found in solutions of the sodium phosphate glasses will not lead to any clear-cut measurement of molecular weight (13) since the number of particles in and hence the colligative properties of an ideal solution is primarily dependent on the degree of ionization of the sodium i n thiq case. 4CKNOWLEDGIIPEhT
The author wishes t o thank Arthur Razee for suggesting this problem and R. L. Copson for his permission to undertake it. A large number of the experimental determinations of viscosity and density were performed by Linn Howiclr. Doris Campanella made the vapor pressure mrasurementq with the i m i n r o hvgrom-
eter.
Vol. 41, Na. I
LITERATURL CITED
(1907) (2) Arndt, K., and Gessler, A, Ibid., 14, 665 (1908) (3) Barr, G., “Monograph of Viscometry,” London, Oxford UnixwGty Pres?, 1931 (4) Bionnikov, A. K., J . A p p l i e d @hem. (C.S.S.R.), 12, 1287 (1939) (5) Fenske, M. R., and Cannon, M .R., IWD. ENGCEEZ, ANAL.En 10,297 (1938). (6) Glasstone, S., Laidler, K., arid Eynng, H., “Theory of Rara Processes,” pp 484, 504, Ken, Yo1 la, McGraw-Hi11 Book 1941. (7) Guzman, J. de., Anales SOC. e s p a f i . f i s . y g u h . , 11, 353 (19131. (8) Lewis, W, K , SquireJ, L., and Broughton, G., “Industrial Cbem istry of Colloidal and Amorphous Materials,” pp. 22. 29 Kew York, Maemillan Co., 1942. (9) Quimby, 0 . T., Chem Rea., 40, 141 (1947), Bbz’d, 40, hyo L Eirata (1947). ( I O ) Smith, G . W., Am. DqestufReptr., 23,KO.12, 313 (1934) (11) Yan Wazer, J. R., J.Am. Chem. Soc.. in Dress. (12) Van Wazer, J. R., and Goldberg, H., f,A p p l i e d Phys., 18,’207 (1947) (13) Y o s t , D. A I . , and Russell, H., “Systematic Inorganic Cherrrr+ t r y , ” pp. 209-33 New Yorlc, Prentice-Hall, 1946. (1) Arndt, K., 2. Elehtrochem., 13, 578
e
a
a
RECEIVEDJ u l y 2 i , 1947
in
or ymerizati J
G. vi’. SCOTT AND Pi. W. WALKER E.
r. du Pont de Nernours h Company, Wilmington, Del.
The
viscusitj and yield point of a po1Jmerizing chloroprene emulsion, as measured with a Mooney-Ewart rotating cylinder viscometer, rise during the first stages of the process and drop to a fixed value as the polymerization is completed. The magnitude of the viscosity and yield point change and the conversion at which the maxima in these properties occur depend upon such factors as the concentration of the starting emulsion, rate of polynierization, polymerization temperature, concentration, and nature of the soap. The viscosity changes appear to result from interparticle dimensional changes as predicted b! the mechanism of the micellar hypothesis of emulsion polymerization. The dimensional changes are influenced by gel content and swelling index of polymer particles.
HEN chloroprene is polymerized in an aqueous emulsion the viscosity of the emulsioii progressively increases to a maximum and then decreases as the polymerization is completed. The increase in viscosity during the first stages of a polymerization is an important factor in controlling the reaction, as it reduces the heat transfer coefficient i n a poly~nerizingvessel and limits the rate at vihich a polyrrierization can be conducted Certain polymerizations a,re difficult, if not impossible, to carry out owing to the excessive thickening that, develops. Therefore, methods of reducing the viscosity rise are of practical and thooretical interest. To fiiid out how some of the polynierizat,ion variables affect the viscosity and to gain a better understanding of its causcs, a study has been made of certain of the factors in the polymerization of chloroprene in a rosin soap emulsion.
Newt’oriian in H o ~ vcharacteristics--that is, the ratio bctmen t h shear stress and rate of shear is variable at low stresses, but becomes constant above some minimum shear stress. This const’ant ratio determines the limiting viscosity which is couvenient for characterizing a non-Newtonian liquid. The limiting viscosity, in centipoises, is defined as the reciprocal of the slope of the Iinear portion of the shear stress-rate of shear curve multiplied by an instrument const,ant, or Limiting viscosity =
K
(shear stress)/(shear rate)
Figure 1 shows the relation between the shear stress, in grain,+ applied, and the rate of shear, in revolutions per second of t,he cylinder, for a glycerol-water mixture which is a Newloniwc liquid, and neoprene latices containing 50 and 63% solids tvhicl:, like the polymerizing emulsions, are non-Newtonian. The 63y0latex was made by concentrating the .5OoJ, latex by distill&
cn.7
4, 46
J
t
I
58% NEOPRENE LATEX
8 5 w4
E
3 3 x “2
I APPARATUS
The Mooney-Ewart rotating cylinder viscometer (6) was used for measuring the limiting viscosity and yield point (2?) of the polymerizing chloroprenr emulsions. Such liquids are non-
I 400 500 100 200 300 SHEARING STRESS, GRAMS APPLIED LOAD
Figure 1.
Relation between Shear Stress an11 Rate of Shear
