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Measurement of the molecular weight of a polyester and evaluation of its molecular volume
MEASUREMENT OF THE MOLECULAR WEIGHT OF A POLYESTER AND EVALUATION OF ITS MOLECULAR VOLUME Henri L. Rosano Department of Chemistry, Columbia University, New York, New York Received May 5, 1955 ABSTRACT The micro- and macromanometer technique for the determination of molecular weight has been applied to a polyester (m.w. = 4000). The polymer was studied in several solvents; the values obtained for the molecular weight are practically the same. However, the surface area occupied by one molecule is a function of the solvent. This result leads to the hypothesis that a molecule deposited on the surface is more or lessspread out depending on the degree of solvation. 2. INTRODUCTION Surface monolayers at great dilutions can be considered as surface gases. These gases obey the Mariotte L a w (in two dimensions) P S = R T either for a fairly extended region (tricapryline) or as a limiting law at great dilutions (myristic acid) (i). Putting nonvolatile substances in the gaseous state (as in osmometry) permits the determination of molecular weights.
The first attempt at such determination was made on protein films in 1939 (2). Since then, this technique has hardly been used for reasons essentially practical. The problem to be solved is the measurement of the extremely small pressures. Recently, G. C. Benson and R. L. Macintosh (3) deduced from their experiments in spreading polymers of polyvinyl acetate on water the impossibility of extrapolating surface pressure vs. surface area curves for calculating molecular weights. In 1946, J. Guastalla tried to determine the molecular weight of several samples of polyvinyl chloride with the help of this technique; the study was discontinued because of poor results. Nevertheless, we have kept an important hypothesis, namely, that a molecule will probably keep the same shape in the gaseous monolayer state that it has in solution. M. Abribat and J. Pouradier (4) have confirmed this idea in the case of cellulose acetate. Except for the above-mentioned references, no workers seem to be interested in this technique for studying polymers; we felt that by using 362
MOLECULAR WEIGHT OF A POLYESTER
363
it we could get more information for determining molecular dimensions as well as molecular weights than by other methods. To verify our method, we reproduced the molecular weight of myristic acid; before each experiment we repeated this measurement as a check on the technique. We measured the molecular weight of a sample of polyester in solutions of different solvents (benzene, acetone, methylethylketonel chloroform, and also mixtures of benzene and methanol) and determined the compression isotherm in each case with the aid of another apparatus. The results obtained with our method checked with the molecular weight of the polyester which has been previously determined. This study of the behavior of the polymer with different solvents showed us that the molecular weight obtained was constant and that only the cosurface, defined below, was a function of the solvent. II. APPARATUS The apparatus could be used with either of two measuring devices developed by J. Guastalla (1).
1. Pendulum Surface Manometer (Fig. 1) The pendulum surface manometer consists of a metallic piece P hung from the roof of the apparatus by two wires of equal length, each of which forms a V. The branches of the V are parallel and constrain the piece P to move only by translation. All the points of the piece describe arcs of
FIG. 1. P e n d u l u m surface manometer. P: metallic piece hung from roof of apparatus by two wires of equal length, each of which forms a V. B: movable mica barrier coated with paraffin. F1, F~.: vaselinated silk thread.
364
HENRI L, ROSANO
identical circles when one displaces the pendulum from its equilibrium position, and the force necessary to maintain it in any position has the same value no matter where the point of application is. This force is the force directed toward the point of equilibrium and is equivalent to a pendulum of the same mass as the piece concentrated at a point attached to a weightless suspension of the same length. The piece P has two vertical needles which penetrate a movable paraffined mica barrier B through two holes. The mica is a rectangle with one of its longer sides missing and separates the surface, which is confined in a floating frame, into two compartments. The separation is assured by two vaselinated silk threads F~ and F~, each attached to one of the sides of the barrier and the frame, which become U-shaped under the action of surface pressure. The liquid surface is cleaned in the two compartments by dropping calcinated talcum powder on it to detect impurities, which can then be removed by blowing the film into one corner of the mica frame with compressed air and removing them by suction. A film is spread in one compartment where a movable barrier can compress it. The pressure exerted by the film on the barrier is determined by the displacement of the pendulum piece multiplied ten times by an optical system and projected onto a vertical scale. The sensitivity of this apparatus is 0.1 dyne/cm.
2. Surface Micromanometer Using a Stretched Thread (Fig. 2) In the stretched thread micromanometer, a floating rectangular frame of paraffined mica is separated into two compartments by a long thread of vaselinated silk. A horizontal rod B suspended freely from a vertical
/
E
I.
/
s
FIG. 2. Surface m i c r o m a n o m e t e r . B: h o r i z o n t a l rod h u n g f r o m t h e t o r s i o n wire. L: lens which p r o j e c t s image of t h e s t r e t c h e d t h r e a d on t h e scale. E: g r a d u a t e d scale. S: light source.
MOLECULAR WEIGHT
OF A P O L Y E S T E R
365
torsion wire has a vertical needle at one end; the needle passes through a hole in the center of a small piece of paraffined mica floating on the surface. The mica is joined to the frame by two silk threads; t h a t on one side is a short thread used only to contain the film, that on the other is a long thread whose displacement determines the pressure of the film. When a film is spread on one side of the surface, the longer silk thread becomes curved because of the pressure of the film. The displacement of the center of this thread is measured by an optical system; a glass trough allows the transmission of light to project an image of the thread on a scale. One millimeter deflection on the scale is equivalent to 1/1000 dynes/cm, of surface pressure. The spreading of a polymer on the water surface, starting with a known weight of polymer in solution in several solvents, is done with the aid of a very fine pipet previously calibrated. One deposits a certain number of drops. III. FILM OF THE POLYMER The curve of compression of a polymer film represented in the coordinate surface pressure vs. area is composed of three distinct parts analogous to those obtained with films of proteins. 1. AB, which does not have any change in direction from extremely dilute concentration, represents very low surface pressure, and corresponds to the gaseous state of the film.
D
J/ CONCENTRATION
FIG. 3. Schematic curve of compression isotherm of a macromolecule.
366
HENRI
L.
ROSA,N O
0.072 0064
0.056
/
0O48 2E
o
0.040----
z
:,-. 0 0 3 2
o
0.024
0
----
016
//
0 008
0
/
/
/
/
/
/
J C0UCENTRArl0N
FI~. 4. Surface isotherm of the polyester dissolved in benzene in the gaseous region. 2. B C represents the transition between the gaseous state and the highpressure curve. 3. CD corresponds to the curve at high pressure. Study of the compression isotherm of the polymer shows a variation in the thickness of the molecular layer depending on the nature of the solvent; this fact proves that the polymer molecule is more or less spread according to the solvent used. Figure 3 represents the compression isotherm of the polyester; a similar curve is obtained with the proteins. IV. S T U D Y OF T H E G A S E O U S FILM
As a first approximation, the law of the gaseous film in the limit of dilution is P S = R T for 1 mole. The pressure vs. concentration curve in the gaseous region of the polyester studied, which would be a straight line if the gas were perfect, is concave at higher concentrations. Figure 4 represents an isotherm in the gaseous region of a polyester in dissolved benzene. In the same way that the introduction of covolume changes the equation of perfect gases to an equation better adapted to real gases, we have introduced the concept of cosurface (b) which appears to represent the facts better. P (Smolo - P (S or
bmole)
=
b) = R T / M
RT
for 1 mole, for 1 g., M being the molecular weight,
MOLECULAR WEIGHT OF A POLYESTER
P (1/C
-
b) = R T / M ,
367
C being the surface concentration in g . / c m ? ,
from which one deduces P (1 - bC) = ( R T / M ) C
1 - bC = ( R T / M ) C / P . Thus, using the idea of a cosurface, the ratio C/P vs. C is a straight line. T h e d a t a bear out this assumption. Figure 5 is a curve C/P vs. C deduced from the isotherm of Fig. 4. Extrapolating the line to the x-axis gives the value of C/P at infinite dilution, from which the molecular weight, which is equal to R T (limit C/P), can be calculated.
eli 0
i
'
2
'
i
1
i
i
I
I
i
CONCENT RATION
FIG. 5. Curve C/P vs. C deduced from the isotherm of Fig. 4. If the line is extrapolated to the x-axis at the intersection C/P -- O, bC = 1, and C = 1/b. The concentration obtained is therefore the inverse of the cosurface. F r o m the found value of the cosurface, the space occupied b y a molecule at zero surface pressure can be easily deduced. V. EXPERIMENTAL RESULTS
The polymer chosen was t h a t obtained from the condensation of sebacic acid and dioxyethylene glycol which has a formula HO-- (CH.~h--O-- (CH2).~--[--OOC-- (CHe) s--COO-- (CH_~).~--O--(CH2)2--]n--OH The molecular weight, determined b y the n u m b e r of free hydroxyl groups, was close to 4000; the density was determined as 1.1. The polymer was insoluble in water, and distilled water was used as the subphase. According to the molecular weight of the polymer, n had a value of about 15. The chain length of the polymer was about 250 A. With the aid of the pendulum surface manometer, the compression isotherm of the polyester described above was determined using different
368
HENRI
L.
ROSANO
16
14
12
Io
~
s
a.t 6
4
2
o
5o
70
Ito
90
s -
t30
i50
I?o
tgo
210
cm~
FIa. 6. Compression surface isotherm obtained with benzene as the spreading solvent,. spreading solvents. Figure 6 is the compression surface isotherm obtained with benzene as the spreading solvent. With the aid of the surface micromanometer, a value of the molecular weight was determined, and the molecular area occupied at zero pressure (~) was deduced. T h e results are given for different solvents in Table I. The first column represents the molecular weight, the second the molecular area ~, the third the calculated molecular area at the point corresponding to the end of the gaseous state (point B), the fourth the area at high pressure (point C), and the fifth the film thickness at point C (5). The thickness of the films from different solvents appears to v a r y inversely with the molecular area. F r o m the values of the area obtained at different points, the diameters of circles of equal area were calculated. In each of these cases (Table I I ) , from the values given together with the length of the molecule (which is TABLE I Results Obtained for Different Solvents Solvents
Cell6 CeH~ -4- 10% CH3OH C6H~ -{- 22% CH3OH C6H~ + 36% CH3OH CH3--CO--C2H~ CHC13 CH3--CO--CH~
M
~ (A. 2)
4370 4370 4130 4370 3900 4130 3900
4619 4691 5112 5269 3862 2863 2316
B(A.2)
Areain
C(A.2)
Areain
Thickness in C (A.)
3815 2670 2712 2884 2300 2000 1615
2501 2202 2280 2402 1683 1482 964
3.19 2.97 2.7 2.6 4.18 4.95 7.37
MOLECULAR WEIGHT OF A POLYESTER
369
TABLE II
Calculated Diameters of Circles of Equal Area Solvents C6H6 CsH8 q- 10% CHaOH C6H6 -t- 22% CH~OH C~H6 q- 36% CH~OH CH3--CO--C2H5 CHC13 CH ~ - - C O - - C H ~
Diameter deduced from ~ (A.) 76.4 77.4 81.4 81.6 71 62 54.4
Diameterin B (A.) 72 58.4 58.8 63.4 54.1 52 45.4
Diameterin C (A.) 56.4 52.8 53.9 55.4 46.3 43.3 36.6
about 250 A.), one can deduce that the spread molecule is always curled up even in the best solvent. It can be deduced from these tables that the molecular weight is constant and is practically independent of the solvent used; the molecular area is a function of the solvent and depends directly on the extent of solvation. Tests made using benzene as solvent with successive additions of from 10 % to 36 % methanol seem to show that mixtures of methanol and benzene are better solvents for the polymer than pure benzene. Tests were also made with higher percentages of methanol, but the instability of the films led us to believe that the polymer becomes slightly soluble in water. T h a t the addition of methyl alcohol (in which the polymer is insoluble) to benzene makes it a better solvent can be seen from the solubility of propylene glycol in benzene only in the presence of sodium stearate (6). We imagine that hydrocarbon chains are easily solvated by the benzene and that the terminal hydroxyl groups of the polymer are associated with the methanol. This technique has been used to determine the molecular weight of several substances. In the case of slightly soluble substances, it was possible to determine the surface pressure as if the substance were insoluble. Saraga (7) has shown that in the case of laurie acid films (slightly soluble in water) the surface pressure is a linear function of the square root of time a short time after spreading. I t is therefore possible to obtain the surface pressure of the substance by extrapolating surface pressure vs. square root of time to zero time. REFERENCES
GUASTALLA,J., Thesis Montpellier, pp. 44-48 (1948). GUASTALLA, J., J. chim. phys. 13, 71 (1945). BENSON, G. C., AND MACINTOSH, R. L., J. Colloid Sci. 3,323-331 (1948). ABRIBAT, M., AND POURADIER, J., Compt. rend. 233, 1006-1008 (1951); J. chim. phys. 49, No. 5, 248-249 (1952). 5. ROSANO, H. L., AND VA]LLET, G., Peintures, pigments, vernis 29, No. 9, 719-724 1. 2. 3. 4.
(1953). 6. PETIT, S. R., AND McBA~N, J. W., Ind. Eng. Chem. 38, 741 (1946). 7. SARAGA, L., M~m. services, chim. ~tat (Paris) 37, 28-43 (1952).
The first attempt at such determination was made on protein films in 1939 (2). Since then, this technique has hardly been used for reasons essentially practical. The problem to be solved is the measurement of the extremely small pressures. Recently, G. C. Benson and R. L. Macintosh (3) deduced from their experiments in spreading polymers of polyvinyl acetate on water the impossibility of extrapolating surface pressure vs. surface area curves for calculating molecular weights. In 1946, J. Guastalla tried to determine the molecular weight of several samples of polyvinyl chloride with the help of this technique; the study was discontinued because of poor results. Nevertheless, we have kept an important hypothesis, namely, that a molecule will probably keep the same shape in the gaseous monolayer state that it has in solution. M. Abribat and J. Pouradier (4) have confirmed this idea in the case of cellulose acetate. Except for the above-mentioned references, no workers seem to be interested in this technique for studying polymers; we felt that by using 362
MOLECULAR WEIGHT OF A POLYESTER
363
it we could get more information for determining molecular dimensions as well as molecular weights than by other methods. To verify our method, we reproduced the molecular weight of myristic acid; before each experiment we repeated this measurement as a check on the technique. We measured the molecular weight of a sample of polyester in solutions of different solvents (benzene, acetone, methylethylketonel chloroform, and also mixtures of benzene and methanol) and determined the compression isotherm in each case with the aid of another apparatus. The results obtained with our method checked with the molecular weight of the polyester which has been previously determined. This study of the behavior of the polymer with different solvents showed us that the molecular weight obtained was constant and that only the cosurface, defined below, was a function of the solvent. II. APPARATUS The apparatus could be used with either of two measuring devices developed by J. Guastalla (1).
1. Pendulum Surface Manometer (Fig. 1) The pendulum surface manometer consists of a metallic piece P hung from the roof of the apparatus by two wires of equal length, each of which forms a V. The branches of the V are parallel and constrain the piece P to move only by translation. All the points of the piece describe arcs of
FIG. 1. P e n d u l u m surface manometer. P: metallic piece hung from roof of apparatus by two wires of equal length, each of which forms a V. B: movable mica barrier coated with paraffin. F1, F~.: vaselinated silk thread.
364
HENRI L, ROSANO
identical circles when one displaces the pendulum from its equilibrium position, and the force necessary to maintain it in any position has the same value no matter where the point of application is. This force is the force directed toward the point of equilibrium and is equivalent to a pendulum of the same mass as the piece concentrated at a point attached to a weightless suspension of the same length. The piece P has two vertical needles which penetrate a movable paraffined mica barrier B through two holes. The mica is a rectangle with one of its longer sides missing and separates the surface, which is confined in a floating frame, into two compartments. The separation is assured by two vaselinated silk threads F~ and F~, each attached to one of the sides of the barrier and the frame, which become U-shaped under the action of surface pressure. The liquid surface is cleaned in the two compartments by dropping calcinated talcum powder on it to detect impurities, which can then be removed by blowing the film into one corner of the mica frame with compressed air and removing them by suction. A film is spread in one compartment where a movable barrier can compress it. The pressure exerted by the film on the barrier is determined by the displacement of the pendulum piece multiplied ten times by an optical system and projected onto a vertical scale. The sensitivity of this apparatus is 0.1 dyne/cm.
2. Surface Micromanometer Using a Stretched Thread (Fig. 2) In the stretched thread micromanometer, a floating rectangular frame of paraffined mica is separated into two compartments by a long thread of vaselinated silk. A horizontal rod B suspended freely from a vertical
/
E
I.
/
s
FIG. 2. Surface m i c r o m a n o m e t e r . B: h o r i z o n t a l rod h u n g f r o m t h e t o r s i o n wire. L: lens which p r o j e c t s image of t h e s t r e t c h e d t h r e a d on t h e scale. E: g r a d u a t e d scale. S: light source.
MOLECULAR WEIGHT
OF A P O L Y E S T E R
365
torsion wire has a vertical needle at one end; the needle passes through a hole in the center of a small piece of paraffined mica floating on the surface. The mica is joined to the frame by two silk threads; t h a t on one side is a short thread used only to contain the film, that on the other is a long thread whose displacement determines the pressure of the film. When a film is spread on one side of the surface, the longer silk thread becomes curved because of the pressure of the film. The displacement of the center of this thread is measured by an optical system; a glass trough allows the transmission of light to project an image of the thread on a scale. One millimeter deflection on the scale is equivalent to 1/1000 dynes/cm, of surface pressure. The spreading of a polymer on the water surface, starting with a known weight of polymer in solution in several solvents, is done with the aid of a very fine pipet previously calibrated. One deposits a certain number of drops. III. FILM OF THE POLYMER The curve of compression of a polymer film represented in the coordinate surface pressure vs. area is composed of three distinct parts analogous to those obtained with films of proteins. 1. AB, which does not have any change in direction from extremely dilute concentration, represents very low surface pressure, and corresponds to the gaseous state of the film.
D
J/ CONCENTRATION
FIG. 3. Schematic curve of compression isotherm of a macromolecule.
366
HENRI
L.
ROSA,N O
0.072 0064
0.056
/
0O48 2E
o
0.040----
z
:,-. 0 0 3 2
o
0.024
0
----
016
//
0 008
0
/
/
/
/
/
/
J C0UCENTRArl0N
FI~. 4. Surface isotherm of the polyester dissolved in benzene in the gaseous region. 2. B C represents the transition between the gaseous state and the highpressure curve. 3. CD corresponds to the curve at high pressure. Study of the compression isotherm of the polymer shows a variation in the thickness of the molecular layer depending on the nature of the solvent; this fact proves that the polymer molecule is more or less spread according to the solvent used. Figure 3 represents the compression isotherm of the polyester; a similar curve is obtained with the proteins. IV. S T U D Y OF T H E G A S E O U S FILM
As a first approximation, the law of the gaseous film in the limit of dilution is P S = R T for 1 mole. The pressure vs. concentration curve in the gaseous region of the polyester studied, which would be a straight line if the gas were perfect, is concave at higher concentrations. Figure 4 represents an isotherm in the gaseous region of a polyester in dissolved benzene. In the same way that the introduction of covolume changes the equation of perfect gases to an equation better adapted to real gases, we have introduced the concept of cosurface (b) which appears to represent the facts better. P (Smolo - P (S or
bmole)
=
b) = R T / M
RT
for 1 mole, for 1 g., M being the molecular weight,
MOLECULAR WEIGHT OF A POLYESTER
P (1/C
-
b) = R T / M ,
367
C being the surface concentration in g . / c m ? ,
from which one deduces P (1 - bC) = ( R T / M ) C
1 - bC = ( R T / M ) C / P . Thus, using the idea of a cosurface, the ratio C/P vs. C is a straight line. T h e d a t a bear out this assumption. Figure 5 is a curve C/P vs. C deduced from the isotherm of Fig. 4. Extrapolating the line to the x-axis gives the value of C/P at infinite dilution, from which the molecular weight, which is equal to R T (limit C/P), can be calculated.
eli 0
i
'
2
'
i
1
i
i
I
I
i
CONCENT RATION
FIG. 5. Curve C/P vs. C deduced from the isotherm of Fig. 4. If the line is extrapolated to the x-axis at the intersection C/P -- O, bC = 1, and C = 1/b. The concentration obtained is therefore the inverse of the cosurface. F r o m the found value of the cosurface, the space occupied b y a molecule at zero surface pressure can be easily deduced. V. EXPERIMENTAL RESULTS
The polymer chosen was t h a t obtained from the condensation of sebacic acid and dioxyethylene glycol which has a formula HO-- (CH.~h--O-- (CH2).~--[--OOC-- (CHe) s--COO-- (CH_~).~--O--(CH2)2--]n--OH The molecular weight, determined b y the n u m b e r of free hydroxyl groups, was close to 4000; the density was determined as 1.1. The polymer was insoluble in water, and distilled water was used as the subphase. According to the molecular weight of the polymer, n had a value of about 15. The chain length of the polymer was about 250 A. With the aid of the pendulum surface manometer, the compression isotherm of the polyester described above was determined using different
368
HENRI
L.
ROSANO
16
14
12
Io
~
s
a.t 6
4
2
o
5o
70
Ito
90
s -
t30
i50
I?o
tgo
210
cm~
FIa. 6. Compression surface isotherm obtained with benzene as the spreading solvent,. spreading solvents. Figure 6 is the compression surface isotherm obtained with benzene as the spreading solvent. With the aid of the surface micromanometer, a value of the molecular weight was determined, and the molecular area occupied at zero pressure (~) was deduced. T h e results are given for different solvents in Table I. The first column represents the molecular weight, the second the molecular area ~, the third the calculated molecular area at the point corresponding to the end of the gaseous state (point B), the fourth the area at high pressure (point C), and the fifth the film thickness at point C (5). The thickness of the films from different solvents appears to v a r y inversely with the molecular area. F r o m the values of the area obtained at different points, the diameters of circles of equal area were calculated. In each of these cases (Table I I ) , from the values given together with the length of the molecule (which is TABLE I Results Obtained for Different Solvents Solvents
Cell6 CeH~ -4- 10% CH3OH C6H~ -{- 22% CH3OH C6H~ + 36% CH3OH CH3--CO--C2H~ CHC13 CH3--CO--CH~
M
~ (A. 2)
4370 4370 4130 4370 3900 4130 3900
4619 4691 5112 5269 3862 2863 2316
B(A.2)
Areain
C(A.2)
Areain
Thickness in C (A.)
3815 2670 2712 2884 2300 2000 1615
2501 2202 2280 2402 1683 1482 964
3.19 2.97 2.7 2.6 4.18 4.95 7.37
MOLECULAR WEIGHT OF A POLYESTER
369
TABLE II
Calculated Diameters of Circles of Equal Area Solvents C6H6 CsH8 q- 10% CHaOH C6H6 -t- 22% CH~OH C~H6 q- 36% CH~OH CH3--CO--C2H5 CHC13 CH ~ - - C O - - C H ~
Diameter deduced from ~ (A.) 76.4 77.4 81.4 81.6 71 62 54.4
Diameterin B (A.) 72 58.4 58.8 63.4 54.1 52 45.4
Diameterin C (A.) 56.4 52.8 53.9 55.4 46.3 43.3 36.6
about 250 A.), one can deduce that the spread molecule is always curled up even in the best solvent. It can be deduced from these tables that the molecular weight is constant and is practically independent of the solvent used; the molecular area is a function of the solvent and depends directly on the extent of solvation. Tests made using benzene as solvent with successive additions of from 10 % to 36 % methanol seem to show that mixtures of methanol and benzene are better solvents for the polymer than pure benzene. Tests were also made with higher percentages of methanol, but the instability of the films led us to believe that the polymer becomes slightly soluble in water. T h a t the addition of methyl alcohol (in which the polymer is insoluble) to benzene makes it a better solvent can be seen from the solubility of propylene glycol in benzene only in the presence of sodium stearate (6). We imagine that hydrocarbon chains are easily solvated by the benzene and that the terminal hydroxyl groups of the polymer are associated with the methanol. This technique has been used to determine the molecular weight of several substances. In the case of slightly soluble substances, it was possible to determine the surface pressure as if the substance were insoluble. Saraga (7) has shown that in the case of laurie acid films (slightly soluble in water) the surface pressure is a linear function of the square root of time a short time after spreading. I t is therefore possible to obtain the surface pressure of the substance by extrapolating surface pressure vs. square root of time to zero time. REFERENCES
GUASTALLA,J., Thesis Montpellier, pp. 44-48 (1948). GUASTALLA, J., J. chim. phys. 13, 71 (1945). BENSON, G. C., AND MACINTOSH, R. L., J. Colloid Sci. 3,323-331 (1948). ABRIBAT, M., AND POURADIER, J., Compt. rend. 233, 1006-1008 (1951); J. chim. phys. 49, No. 5, 248-249 (1952). 5. ROSANO, H. L., AND VA]LLET, G., Peintures, pigments, vernis 29, No. 9, 719-724 1. 2. 3. 4.
(1953). 6. PETIT, S. R., AND McBA~N, J. W., Ind. Eng. Chem. 38, 741 (1946). 7. SARAGA, L., M~m. services, chim. ~tat (Paris) 37, 28-43 (1952).