INDUSTRIAL AND ENGINEERING CHEMISTRY
February. 1932
Such generalities must be restricted in their interpretations. For this discussion, they have been limited to the correlation of different grades of wood rosin produced from material of quite uniform chemical composition by the same carefully controlled process. The comparison is by no means complete nor final but is to be considered as a preliminary attempt of qualitative correlation. Comparisons on a similar basis are probably not justified with the gum samples obtained from different eources and varying methods of manufacture where considerable fluctuations may exist in the oxidation products, degree of isomeri-
177
zation, residual turpentine, and other factors which may materially affect the viscosity of the particular sample. LITERATURE CITED (1) Bingham, E. ,C,, “Fluidity and Plasticity,” 1st ed., p. 295, McGraw-Hdl, 1922. (2) Bingham, E. C., a n d Jackson, R. F., Bur. Standards, Sci. Papers 298, 64 (1917). (3) Nash, H. E., IXD. ENG.CHEM.,24, 177 (1932). (4) Peterson, J. M., Ibid., 24, 168 (1932). RECEIVED April 9 , 1931. Presented before the Division of Paint and Varnish Chemiatry a t the Slat Meeting of the hmerioan Chemical Society, Indianapolis, Ind., March 30 t o April 3, 1931.
Viscosity-Temperature Characteristics of Rosins Relations t o the Melting Points H. E. NASH,Experiment Station, Hercules Powder Co., Wilmington, Del. UMEROUS e q u a t i o n s have been suggested to fit the data relating the viscosity of various liquids to the temperature. Some of these have been based upon theoretic a l considerations, b u t m o r e often they have been offered as a means of correlating the existing data. With the latter object in view, s e v e r a l of t,hese equations were examined, and attempts made to fit them to the data on rosins as determined by Peterson and Pragoff (6). Madge (6) gives the equation: 7 =
where
F
A q =
b exP (DT)
THE E Q l J A T I O N j i x e d upon to represent the viscosity-temperature curves of rosin is given by log q = log A f b / ( T - e), where A and 0 are constants approximately the same for all the common American rosins and derivatives studied, and b is a constant determining the ciscosity of the rosin. The viscosity data are correlated with the so-called melting points as determined by the drop method. The work indicates that the viscosity of many rosins can be estimated, for any desired elevated temperature, f r o m the melting point through use of the formula 6.05 t , - 54 - 3.50, where 1, (” C.) log q = t - 20 is the “melting point,” t (” C.) is the temperature at which the viscosity is desired, and log q is the common logarithm of the viscosity.
viscosity
T = absolute temperature A , b, and p =constants e z p ( p T ) = e raised to the exponent, gT
This notation is used throughout the following discussion. However, in calculations and constants evaluated, in order to facilitate computation, the exponential function has been taken to be 10 raised to the power in parentheses. Black ( I ) proposes a hyperbolic function. Hatchek (3) reviews the empirical formulas suggested by various investigators. Of interest is a demonstration by Porter (7:l whereby the available data show that the equation should be of the
Andrade (2) points out that the equation, = A exp b T-e
(-)
where 0 = additional constant, holds well for associated liquids.
EXPERIMENTAL DATA EQUATION TO FIT VISCOSITY DATA.T h e first e q u a t i o n studied was (1) above. Taki n g l o g a r i t h m s , i t becomes log
7
- n log
T
=
log A
+ -bT
so that plotting the left hand 1 side against should give a s t r a i g h t l i n e with b as slope. This was d o n e for a n u m b e r of rosins, where n was first assumed to be zero. The resulting curves approximated straight lines, but no more so than the plot of log 7 against 2’. Therefore the equation, in this case, has no merit from an empirical point of view. Changes in the value of n were found not to affect the shape of the curves over the temperature range covered by the data. Equation 2 was then tried out. Constants were determined for a few of the typical rosins, data for which appear in Table 11, by the solution of three simultaneous equations. The constants obtained appear in Table I.
form:
TABLE I. CONSTANT FOR TYPICAL ROSINS
This, however, does not appear to be a limiting condition. Many investigators (6,4) have suggested the equation:
where b and A = constants and n is assigned values 0,
or 1
ROSIN
-log A
b A.
e
Wood I Treated B Gum N Treated Greek gum K
3.34 3.75 3.42
393 672 417 825 505
297 273 297 276 299
4.21 4.10
A.
The data for other rosins were tested graphically, and the following conclusions drawn. The constant, A , is nearly
IR’DUSTRIAL AND ENGINEERING CHEMISTRY
178
Lcs 15
-Io
&O
4 5
d.0
Vol. 24, No. 2
d,
L
lo
io
FIGURE1. VIECOSITY-TEMPERATURE CURVESOF VARIOUS ROSINS
FIGURE 2. VISCOSITY-TEMPERATURE CURVESOF V~RIOUS ROSINS
the same for all rosins, excepting treated rosin, abietic acid, Greek gum K, and possibly several other foreign gums. For these rosins it is generally high. For most rosins, A decreases slightly as b increases. The constant, 8, varies from 273 to 300, being somewhat higher for rosins having a low value of b. The only exception is French WW, which gives erratic values of 8, depending on what sets of data are chosen. The term ‘‘0” was therefore fixed at 293, and the data plotted as shown in Figures 1 and 2. The original data, obtained by Peterson and Pragoff (6), appear in Table 11.
The melting points here. used were determined by the thermometer drop method. Between 0.50 and 0.55 gram of rosin was molded about a thermometer bulb inch in diameter and 6,’s inch long. The thermometer was then suspended in a test tube I / , inch in diameter, and this in turn in a bath maintained a t 90” C. If the melting point of the rosin was above 80” C., the bath was maintained at a temperature about 10’ above the melting point. The temperature a t which the first drop left the end of the bulb was recorded as the melting point. Duplicates usually gave readings agreeing within 1’ C. These melting points, when located on the graph, were found to lie in more or less of a straight line, as shown by the dotted line in Figure 4. Assuming that the extrapolation is trustworthy, the curves show that the melting point is a temperature a t which the rosin attains a given viscosity somewhat higher the lower the melting point. According to the graph, the viscosity at the melting point of wood I is about 5000 poises, and about 2000 poises for 235” F. I
sol’
I -1.0
/
j
LOG , ’1
-35 ao
a5
4 ! 1.0
~5
j
j
eo
FIGURE 3. VISCOSITY-TEMPERATURE CURVESOF FF AND I WOODROSINS
Excepting French WW gum, where a distinct curvature is seen, all points fall fairly closely on straight lines. This is especially true of the ordinary American wood and gum rosins. It then became of interest to discover how far the lines might be extrapolated. A point was therefore determined for I wood rosin at. a temperature of 99.1” C. by means of a falling-ball viscometer. The data are given in the last line of Table 11, and by the point marked “F. B.” of Figure 3. MELTINGPOINTS.The results of the above work indicated that the lines might be extrapolated to a lower temperature. The curves for a number of typical rosins were then redrawn to a smaller scale, as shown in Figure 4, and extrapolated in the direction of lower temperature or increas1 ing values for The point was then located a t which each line crossed the line corresponding to the so-called melting point or softening point, as given in Table 11.
i
-io -lo
LOG
-!o
00
’7 60
d,
I
’
jo
!o
10
CURVESOF ROSINS, FIGURE4. VISCOSITY-TEMPERATURE THE MELTING POINTS INCLUDING
limed rosin. However, using the constants of Table I, the viscosity for treated B a t the melting point is calculated to be of the order of 500 poises, whereas the graph gives a value of 2200 poises, and similar figures for many other rosins. Therefore, the data can only fix the order of magnitude of the viscosity a t the melting point, though
I N D U S T R I A L A N D E N G I N E E R I N G C H EM I S T R Y
February, 1932
i t plainly indicates that the viscosity a t the melting point is lees for a rosin having a higher melting point. TABLE
11. D ~ T FOR A TYPICAL ROSINS
HOflS
Wood I (m. p Wood I (m. p
=
7
79.6' C.)
7:
C.)
-
Wood 1-20 (m p, 840' C
Wood B
(m. p
-
r'
98.6' C ,
rrested wood B (m. p. = 105.5' C.)
Limed, l95O F. (90.6O C \ (m. p. = 93.5' C . ) Limed, 235' F. (112.8' C . ) (m. D = 114O 0 ) .Abietic aoid (capillary in. p .
-
-
1.53' C .
Greek gum K (m. p. 89.5' C . )
-
French guin W W (m. p. 85.0' C.1
FF (m. p
Gum D (m. p
=
-
78.0' C.:
860'
Treated (m p
=
Gum N (m. p
= 79
C.)
1005O C
1
C.)
Oxidized wood I (m p = 74.0' C . ) fieat-trcateri n o o d I
Heat-treated wood F F
wood I
Poises 0.960 0.317 0.138 0.0728 2.83 0.501 0.158 0.0680 7.10 2.17 0.650 0.256 0.126 11.0 2.57 0.807 0.338 22.08 4.60 1.14 0.476 6.14 1.57 0.551 0.225 63.0 11.0 2.5 0.875 0.549 0.249 0.133 10.07 2.42 0.596 0.211 3.55 1.33 0.384 0.150 38.09 6.10 2.56 1.75 0.965 0.630 0.559 0.392 9.31 1.10 0.268 0.101 29.90 4.45 1.22 4.96 0.789 0.223 0.096 13.83 5.29 0.980 0.261 3.08 0.521 0.170 0.0737 4.23 0.724 0.207 0.088 63
LOQ 7
L
c. 140 160 180 200 125 150 175 200 125 140 160 180
200 140 160 150 200 140 160 180 200 140 160 180 200 140 160 180 200 160 175 195 125 140 160 180 125 140 160 180 105 120.5 130 134.8 143.2 151.0 153.2 160.1 12b 150 175 200 140 160 180 125 150 175 200 140 160 180 200 125 150 175 200 125 160 176 200 99.1
-T--1293
'Os
1
of course, contrary to observation and serves to prove that the equation breaks down somewhere between the melting point and room temperature. ESTIMATION OF VISCOSITYFROM MELTINGPOINTS.If the melting point of a rosin is located on the dotted line of Figure 4, and a line is drawn through this point and the point
0 7 .
-0.017 -0.499 -0.860 -1.138 0.452 -0.300 -0.801 -1.168 0.851 0.336 -0.186 -0.591 -0.900 1.04 0.410 -0.093 -0.471 1.358 0.653 0,056
-0.322 0.788 0.196 -0.255 -0.647 1.799 1.041 0.398 -0.057 -0.260 -0.604 -0.877 1.000 0.384 -0.225 -0.675 0.550 0.124 -0.416 -0.824 1.59 0.785 0.408 0.243 -0.015 -0.200 -0.252 -0.406 0.969 0.041 -0.571 -0.995 1.476 0.648 0.086 0.695 -0.104 -0.652 -1.043 1.141 0.723 -0.009 -0.585 0.486 -0.283 -0.769 -1.133 0.626 -0.142 -0.684 -1.055 1.799
9.52 7.69 6.46 6.66
8.33 7.14 6.25 5.55 8.33 7.14 6.25 5.55 5.33 7.14 6.25 5.55 8.33 7.14 6.25 5.55 8.33 6.45 5.88 9.52 8.33 7.14 6.25 9.52 8.33 7.14 6.26 11.97 9.95 9.09 8.70 8.11 7.63 7.50 7.14 9.62 7.69 6.45 6.66 8.33 7.14 6.25 9.62 7.69 6.45 6.56 8.33 7.69 6.45 5.66 9.52 7.69 6.45 5.56 9.52 7.69 6.45 6.56 11.26
The extrapolation to higher temperatures shows that the lines for each rosin, excepting abietic acid, treated rosin, Greek gum K, and oxidized wood I, pass through a point near to which T is injinity, confirming the conclusion arrived a t from the data in Table I that A is about constant. The constant, log A , varies from -3.4 to -3.6, or A varies from 0.00025 to 0.0004 poise. Extrapolation to temperatures lower than the melting points cannot be safely made. Examination shows that Equation 2 demands that, as the temperature T approaches 293, the viscosity shall approach an infinite value, This is,
179
3-T 1
0, log 7 = -3.5
=
any point on the line thus drawn determines the viscosity of the rosin for the corresponding temperature. The assumptions involved in this procedure are obvious. Assuming that all rosins have the same constant, A , and that all points representing the viscosity a t the melting point lie on the dotted line, a simple formula for the viscosity of 1 N, rosin can be derived. Let y stand for the variable, , j j 3 where t is in C., and z for log r]. ur t - 20' can then be represented by O
5 =
2.55
The dotted line
+ 67 y
(3)
and the viscosity line for any particular rosin by x
=
+ by
-3.8
(4)
The melting point, r m ,urn, is common to both lines. Putting these in Equations 3 and 4, and eliminating xm between them, an equation is obtained involving the four 1 constants and ym. Solving for b and substituting n o for y,
1
for ym, and log
r]
for
5,
the following equation is
obtained: log q =
- 54 - 20 -3.5
6.05 t, t
From the equation, given the melting point, L,au approximate viscosity may be calculated for any temperature t (in O C,). This has been done for a number of typical rosins. The values are given in Table 111, together with the observed viscosities. TABLE111. MELTINGPOINTSA N D ROSINS ROBIN Wood I
Limed, 235O F. (112.8" C . )
t
c. 99.1 125 150 200 140 160 180
200 Treated wood B
140 160 180
200 Heat-treated FE'
Gum N Gum D
Treated
125 150 175 200 125 150 175 200 125 150 175 200 140 160 180
\-ISCOSITIES
Obsvd. Poises 63 3.83 0.501 0.0680 63 11 2.5 0.875 22.8 4.60 1.14 0.476 4.23 0.724 0.207 0.0880 4.96 0.787 0.223 0.0906 9.31 1.10 0.268 0.127 29.90 4.45 1.22
OF
TYPICAL
Calod. Poisea 55 2.8 0.49 0.063 61 11 2.9 1.0 22.9 4.68 1.40 0.55 3.7 0.76 0.20 0.076 3.7 0.76 0.20 0.076 9.5 1.3 0.34 0.125 37 7.0 2 .o
The data on the last three rosins illustrate clearly the adaptability and limitations of the formula. The melting
INDUSTRIAL AND ENGINEERING CHEMISTRY
180
points of gum N and gum D do not lie on the dotted line of Figure 4; nevertheless the agreement between the calculated and observed values of viscosity is fairly good. On the other hand, treated rosin, although a straight line, does not fit with the formula. Several foreign gums also deviate widely from the calculated values. CONCLUSIONS The equation =
A exp
The constant b of Equation 2 determines the viscosity of the ordinary American gum or wood rosins. From this, an expression may 'be derived which gives the approximate viscosity of a rosin a t any desired temperature. It is: log7 =
where
t,
= 1 = log 7 =
(-) b
Vol. 24, No. 2
- 54 - 3.50 - 20
6.05 f,
melting pointb C., as determined by drop method temperature, C., at which viscosity is desired common logarithm of viscosity in poises. LITERATURE CITED
T - 0
fits all rosins investigated (eighteen altogether) with good agreement over the temperature range 100" to 200" C. The constant 8, excepting for French WW, is about the same for all rosins studied, and varies from 273 to 300. The constant log A is approximately the same for most rosins, varying from -3.4 to -3.6 when 0 = 293. Extrapolation of the lines obtained in this way can be extended to the so-called melting point of the rosin, to estimate the viscosity a t this temperature. It appears to be of the order of 5000 poises.
D. H., Nature, 125, 581 (1930). (2) Frenkel, J., Ibid.,-125, 583 (1930). (3) Hatchek, E., "Viscosity of Liquids," pp. 63-78, Van Nostrand, 1928. (4) Iyer, M. P. V . ,Indian J . Phys., 5,371 (1930). (5) Madge, E. W., J. Phys. Chem., 34, 1599-1606 (1930). (6) Peterson, J. M., and Pragoff, E. P., IND.ENG.CHEM.,24, 173 (1932). (7) Porter, A. W., Phil. Mag., 23, 458 (1912). (1) Black,
RECEIVED April 9,1931. Presented before the Division of Paint and Varnieh Chemistry a t the 81st Meeting of the American Chemical Society, Indianapolia, Ind., March 30 to -4pril 3, 1931.
Parallel Scale Charts R. C . STRATTON, J. B. FICKLEN, AND W. A. HOUGH, Chemical Laboratory, The Travelers Insurance Company and The Travelers Indemnity Company, Hartford, Conn.
R
ECEKTLY the authors were called upon to make a large number of calculations of boiler feed-water treatments, employing soda ash and lime as water-softening agents. The calculation of the necessary amounts of soda ash and lime in each case was made by using modifications of equations originally developed by Stabler (1-4). I n the original Stabler formulas the amounts of the various positive and negative radicals, such as calcium, magnesium, carbonate, and bicarbonate found by anaIysis of the water, were expressed in parts per million. The number of parts per million of each positive or negative radical was then multiplied by its own so-called reaction factor, and the algebraic sum of these products was in turn multiplied by a conversion factor to give the amount of soda ash, or soda ash and lime, necessary for softening the water. The result was expressed in ounces per thousand gallons. In the waters analyzed here, iron, aluminum, carbonate, and hydrogen ions were present in such negligible amounts that these radicals were omitted from the calculation, and the formulas were modified as follows: (To be used for a water conSODAASH TREATMENT. taining a large amount of calcium but only a small amount of magnesium). Ounces soda ash per 1000 gallons water
= 7.44 ( G a )
(1)
(To be used for a water LIMEAND SODAASHTREATMENT. containing a moderate or large amount of magnesium in addition to calcium.) Ounces soda ash per 1000 gallons water = 7.44 h C a r * M-g - nHC03) (21 Ounces lime per 1000 gallons water =
+
where Ca
Mg
HCOa
= p. p. = p. p. = p. p.
+
4.16 (mMg T3HC03j rI = 0.0499 r2 = 0.0822 TJ = 0.0164
rn. of calcium m. of magnesium m. of bicarbonate
(3)
By substituting the numerical vaIues of rl, rz, and r3 in the above equations and multiplying through by the coefficient in front of the parentheses, the following are obtained: Ounces soda ash = 0.371 (p. p. m. Ca) (soda ash treatment) (1) Ounces of soda ash = 0.371 (p. p. m. Ca) + 0.612 (p. p. m. Mg) - 0.122 (p. p. m. (2) (soda ash and HCOa) lime treatment) Ounces of Iime = 0.342 (p. p. m. Mg) 0.068 (p. p. m. HCO) (3)
+
I
Considering Equation 1, it is obvious that the amount of soda ash is a direct function of the number of parts per million of calcium to be removed, and that a pair of parallel scales can be laid out in which each part per million of calcium will correspond to 0.371 ounce of soda ash. Thus by knowing the amount of calcium in parts per million, one reads directly across to the correct amount of soda ash. Equation 2 is applied visually by using the two scales described above, and in addition a scale for the amount of magnesium and one for the amount of bicarbonate. Each part per million of magnesium is made to correspond to 0.612 of a division of the soda ash scale. On the bicarbonate scale each part per million of bicarbonate corresponds to 0.122 of a division of the soda ash scale. By means of these four scales placed side by side, Equation 2 can now be evaluated as follows: A straight edge is placed upon the amount of calcium and the corresponding amount of magnesium noted. To this amount is added the number of parts per million of magnesium actually found by analysis. The straight edge is then moved upward to the point representing the sum. The amount of bicarbonate corresponding to this sum is noted and from this amount is subtracted the number of parts per million of bicarbonate found by analysis. The straight edge is then moved downward to the point
