OSMOTIC PRESSURES OF POLYVINYL CHLORIDE SOLUTIONS
59
(5) PAULING, L.: T h e Nature of the Chemical Bond, 2nd edition. Cornel1 University Press, Ithaca, New York (1940). (6) SEITZ,F.: T h e Modern Theory of Solids. McGraw-Hill Book Company, Inc., New York (1940). (7) SUODEN, S.: T h e Parachor and Valency. George Routledge and Sons, Ltd., London (1930). (8) SUGDEN, S., AND WILKINS,H . : J. Chem. SOC.132,1291-8 (1929). (9) SUN, K. H., TAYLOR, N. W., AND $AFFORD, H. W.: “The Properties of Soda-Silica Glasses a t High Temperatures,” paper presented a t the 44th Annual Meeting of the American Ceramic Society, Cincinnati, Ohio, April 19-25, 1942. (10) WYCKOFF,R. W. G.: T h e Structure of Crystals, American Chemical Society Monograph Series, No. 19. The Chemical Catalog Company, Inc., New York (1931).
OSMOTIC PRESSURES OF POLYVINYL CHLORIDE SOLUTIOSS BY A DYNAMIC METHOD RAYMOND M . FUOSS
AND
DARWIN J. MEAD
Research Laboratory, General Electrw C o m p a n y , Schenectady, N e w York Received August $1, lQ@ I. INTRODUCTION
In the limit of low concentrations, osmotic pressure furnishes a means of determining the (number average) molecular weight ( 5 ) of a high polymer which is independent of structural details such as branching. Aside from the ultracentrifuge, it is the only absolute method at present available. Determination of molecular weights of polymers by viscosities requires an absolute calibration and, even so, gives correct relative values only when the polymers investigated have the same structure as the calibrating sample, because molecules of the same molecular weight but different shapes (9) can give widely different specificviscosity increments. The original purpose of this investigation was a systematic study of viscosities and osmotic pressures of polymers prepared in different ways, in order to obtain information on the dependence of degree of branching on the conditions of polymerization. Pressure of emergency work has made it necessary to discontinue the research; we have, however, developed an osmometer and a technique which give reproducible results in fairly short times, and, in view of the interest in high polymers, it seems worthwhile to present the experimental methods, together with our preliminary results. By the osmometer, we obtain a molecular weight of 100,000 for a fractionated polymer of vinyl chloride which gave 102,000 by the ultracentrifuge diffusion method. Two other fractions from the same original polymer (and therefore presumably of the same structure) gave osmotic pressures proportional to their equivalent viscosities, which substantiates our value ( 7 ) of 7 x for the Staudinyer constant for vinyl chloride polymers similar in branching to our material. The agreement also shows that our method of fractionation was satisfactory.
60
RAYMOND >I FUOSS . AND DARWIN J. MEAD
11. EXPERIMENTAL
Osmometers The cell consisted of two stainless-steel plates, clamped together over the membrane by means of machine screws a t the edge. The face of each disk had
A
3
/ . . . I
I
I
I
I
I
3 4 5 6 INCHES FIG.1 a FIQ.1 a , b. Osmometer with vertical capillaries
0
I
2
a $-in. flat ring, 5 in. outside diameter (figure 1); inside this ring was a set of concentric cuts 2 mm. wide and 2 mm. deep, connected by a vertical cut which ran from inlet to outlet of each half-cell. The faces of the half-cells were ground flat. The membrane was simultaneously the gasket; since the membranes we
OSMOTIC PRESSURES OF POLYVINYL CHLORIDE SOLUTIONB
61
used were fairly soft, only moderate pressure (a little more than finger-tight) was needed to preventleakage a t the edges of the 5-in. ring. The plates carried guide pins to permit accurate matching of the circles in the two half-cells. A thermometer was inserted in a boring in one of the plates. After assembly, the osmometer was packed into a bass-wood box, using cotton waste as heat insulator. Slow temperature drifts were occasionally noted as the room temperature (average, 27°C.) changed, but the error produced was negligibly small. A more serious source of error due to temperature changes lies in the change of surface tension with temperature; it affects the results with osmometer designs
U
FIG.1 b having a horiaontal capillary, but does not influence the results with vertical capillaries. To the plates were attached filling tubes and measuring apparatus, which projected outside the insulating jacket. Of a number of designs which we tried, three will be described. All gave satisfactory results; we prefer the third. In the first two, the solution half-cell was filled through a vertical )-in. glass tube, which was connected through a fernico bushing to a &-in. copper tube. The latter was soldered to a brass nipple which was fastened to the cell by a lock nut and lead gasket. The top opening of the half-cell was closed by a needle valve after filling. Tho solution half-cell was thus open to atmospheric pressure through the vertical stand pipe, and the zero of pressure reference was the
62
RAYMOSD RI. FUOSS AND DARWIK J. MEAD
level of the meniscus in this tube. The solvent half-cell was also closed a t the top by a needle valve after filling. To the bottom opening was attached a valve block carrying a filling tube which could be closed off by a needle valve, and a drainage tube which could also be closed by a needle valve. The location of the meniscus in the capillary was controlled by means of these last two valves. I n the first design, the lower valve block carried a 25-mil. capillary mounted over a steel scale. A spirit level attached to the scale showed when the capillary was horizontal. Then the rates of meniscus flow (in millimeters per minute) were determined for different levels of liquid in the stand pipe in the other halfcell. The diameter of the latter is so large compared to that of the capillary that no visible change in level occurred for sufficient travel of the meniscus to determine the rate. The zero point on the pressure scale was determined by running solvent in both half-cells; the zero is below the center of the capill&ryby the capillary rise in the latt,er. The zero point thus changes with temperature. A bit of simple geometry shows that errors in osmotic pressure can occur if the capillary is not exactly horizontal and if the pressure scale for the stand pipe is not vertical to the horizontal plane through the capillary. I n a second design, the capillary and the pressure scale were mounted on a steel block, which was floated in mercury. A seven-turn thin-glass spiral served as a flexible coupling between the capillary and the lower valve block. on the solvent. half-cell. This device automatically kept the geometry of the apparatus correct but was very fragile. A4typical run with the horizontal capillary apparatus is shown in figure 2, where rate of flow in the capillary (in millimeters per minute) is plotted against readings of the pressure column. (Zero on the scale is obviously not the pressure zero.) It will be seen that the rate of flow is linear in the hydrostatic pressure. The line at the left is for solvent in both half-cells, and its intersection with the horizontal axis determines the zero of the pressure scale. The line at the right is for a solution of polyvinyl chloride in the solution half-cell against solvent in the other half-cell: the differently designated points refer to different fillings of the cell. (The cell was refilled with solution and drained repeatedly in order to rinse out solvent completely.) The difference between the intersections of the two lines on the horizontal axis gives the osmotic pressure of the solution. The slope of the lines depends on temperature through viscosity, of course, while the intersection is independent of the slope. We then decided to use a dynamic osmometer with vertical capillary, in order to eliminate the errors due to possible changes or uncertainty in the zero point. The details of the apparatus' are shown schematically in figure 1; since it' is designed for organic solrents, it is constructed entirely of glass and metal, and steel needle valves seated in brass replace stopcocks. On long standing, a little corrosion of the brass and copper occurred; if the apparatus is rebuilt, stainlesssteel or nickel should replace the brass and copper parts. The method of use is fairly obvious from the diagram. After placing a membrane between the two 1
A limited number of full-scale blueprints of the shop drawing are available.
OSMOTIC PRESSURES OF POLYVINYL CHLORIDE SOLUTIONS
63
half-cells and tightening the peripheral screws, the two capillaries and the two valve blocks with the filling tubes are locked into place. Lead washers make these joints liquid-tight. The glass-to-metal seal is a t a fernico bushing, which is soft-soldered to the brass valve block. With valves 1 and 2 closed and valve stem 3 removed, solution is poured into the left-hand tube, while solvent is simultaneously poured into the right one, so that the liquid level rises a t about the same rate on both sides of the membrane. Filling from the bottom of the half-cells in this way eliminates air bubbles. Then with both sides filled nearly to the top, valves 1 and 2 are opened wide for a few seconds to sweep any en-
FIG.2 FIG.3 FIG. 2. Rate curves for osmometer with horizontal capillary FIG. 3. Rate curves for osmometer with vertical capillaries
trapped air out of the valve blocks. (The borings in the valve blocks and connector tubes are & in. in diameter.) Valve stem 3 is inserted, and valve 3 closed. Since both cell and solutions have been standing at room temperature, and since the heat capacity of the cell contents (about 14 cc.) is very small compared to that of the steel plates, temperature equilibrium is very quickly established. Valve 1 is then opened to drop the meniscus in the solution stand pipe to its desired position. The height pf the meniscus in the left capillary against a vertical steel scale mounted behind both capillaries is read through a telescope, furnished with cross hairs and level. Then the rate of motion of the meniscus in the right capillary is follom-ed, as mill be described later. The telescope is
G4
RAYMOND M. FUOSS AKD D.%RWIN J. MEAD
mounted on a post, where a rack and pinion provide vertical motion. To raise the meniscus in the right capillary, valve 3 is opened; to drop it, valve 2 is opened. In the left capillary, t'he meniscus is lowered by opening valve 1 and raised simply by pouring solution into the open tube. The essential feature of this design is that the meniscus in the left capillary remains (within the reading error of 0.02 cm.) stationary, while the motion of the right meniscus is being followed. With a horizontal capillary, the meniscus travel is, as shown in figure 2, proportional to the driving head; with vertical capillaries, on the other hand, the rate of travel is a function of elapsed time, because the pressure head is constantly changing. A simple calculation shows that the difference in height is an exponential function of time, when one side is held a t fixed pressure, as we maintain it with the open-end stand pipe of diameter large compared to that of the capillary. The exponential curve is still inconvenient for analysis, but the following device gives a practical solution of t,he exponential rate curve in a very short time, as is shown in figure 3. Suppose A h is the expected difference in pressure. We set the meniscus in the moving side a t a height somavhat greater than (Ah z), where z is of the order of 1 or 2 cm. and corresponds to a whole millimeter mark on the pressure scale. As the meniscus drops through this mark, a stop watch is started, establishing a zero in time. Readings of the moving meniscus are m d e a t 30-sec. intervals for 6 to 8 min., by which time the meniscus is moving quite slowly. Then a second run is made, starting the meniscus below (Ah - z) and starting the timing a t a convenient cross mark near (Ah - 2). A plot of meniscus height against time is now a concave-down exponential. We then plot the half-sum of the rising and falling curves against time; since the curves mere started approximately t'he same distance from equilibrium, but from opposite sides, the half-sum differs from their mut,ual asymptote only by small second-order terms. In practice, the half-sum is constant within several minutes, and determines the desired asymptote directly. This is t o be contrasted with the static method, using vertical capillaries, where one waits until no further visible motion of the capillary can be seen and hopes that the difference is the osmotic pressure. If this indefinite waiting time is too long, adsorption of polymer on the cell walls or on the membrane, diffusion of polymer through the membrane, volume changes due to temperature fluctuations, or possible chemical changes, such as hydrolysis or depolymerizat'ion in the cases of some solutes, may have introduced errors of uncertain magnitude. With the method described above, an unambiguous answer is obtained in less than 20 min. after filling the cell. The rapidity of convergency of the half-sum depends, of course, on the foreknowledge of A h ; one preliminary run based on merely the order of magnitude of the molecular weight will give a value of sufficient accuracy to use in subsequent runs. On check runs, the approximation is naturally better each time. If the starting points are correct within 2 or'3 mm., the half-sum becomes constant after about 3 min.
+
OSMOTIC PRESSURES OF POLYVINYL CHLORIDE SOLUTIONS
65
Membranes A variety of membranes was tried, and a number of interesting leads for further work were found. It is our opinion, although we do not have sufficient experimental evidence to prove the point, that it is necessary that a membrane swell in the solvent in order to be satisfactory as an osmometer diaphragm. Mere mechanical permeability to the solvent is not sufficient, but rather, some means for establishing dynamic equilibrium of solvent through the membrane must be present. If the solvent swells the membrane material, then the chemical potential of the solvent inside the membrane has a definite value (1)and furnishes a phase which can exchange solvent molecules with either half-cell. Soft vulcanized rubber, for example, is suitable as a membrane for methyl amyl ketone solutions, while cellophane is impermeable. Most of our work was done using partially denitrated nitrocellulose films as osmometer membranes. They were prepared by slow evaporation on mercury, following Montonna’s (8) recommendations. A 0.25-in. chromium-plated steel ring, 5.75 in. inside diameter, was floated on mercury in a spun-steel cup, and 20 g. of Merck’s C.P. collodion diluted with 10 cc. of alcohol-ether (50-60) was carefully poured inside the ring. Any bubbles which formed were pulled to the edges by a glass rod. Then the assembly, which stood on a perforated brass plate, was covered with a bell jar, and a slow air stream was directed against the roof of the jar. After 60 to 70 min. of evaporation, the ring carrying the partially dried collodion waa lifted by means of two pins set vertically in the ring, and was immersed in water for several hours. At this stage the membrane still retains considerable solvent, but has enough mechanical strength to permit cautious handling. Usually the membrane pulls away from the ring after standing in water a short time; if it does not, it is carefully loosened, and the raised edge is trimmed off. We have found that membranes prepared by partial precipitation of the nitrocellulose ‘are much faster than those in which most of the solvent is allowed to evaporate before the water immersion (10). After soaking in water, the membranes were denitrated in a mixture (9) of 125 cc. of concentrated ammonium hydroxide, 325 cc. of water, and 50 cc. of alcohol, into which a vigorous stream of hydrogen sulfide had been bubbled for 10 min. Two hours were allowed for the denitration, and the membranes were turned every 15 min. or so. After denitration, the membranes were soaked in several changes of water, remaining in the last one overnight. They were then ready for conditioning to the organic solvent, which is accompliihed by pickling them for a t least 2 hr. in the following sequence of liquids: (1) 50-50 water-alcohol; (8) alcohol; (3)50-50 alcohol-ketone; and (4) methyl amyl ketone. The membranes were prepared in lots of six, and stored under methyl amyl ketone. They must never be allowed to dry out. Membranes prepared in this way contain partially denitrated nitrocellulose in the center, as proven by simple combustion tests. Probably the surface consists of a thin film of almost completely regenerated cellulose, which acts as an envelope for the central phase.
66
RAYMOND &FUOSS I. A h 3 DARWIN J. MEAD
Time was not available for a detailed study of the permeability of the membrane in its dependence on the conditions of preparation. Most of the membranes prepared by the above method were satisfactory; occasionally, however, an unsymmetrical membrane appeared. When placed in the osmometer, with pure solvent in both half-cells, the meniscus rose in the half-cell to which the mercury side of the membrane faced. The difference in lcrels was of the order of 1 mm., although several as high as several millimeters mere obtained. Sometimes the difference could be eliminated by long soaking, but usually a difference of about' 0.5 mm. persisted even after repeated washings; the difference %vas applied as a correction to the osmotic pressures. -4possible explanation is that some ends of long nitrocellulose molecules projected into t,he solution on the mercury side (the water-precipitated face) and kinetically, at least, simulated a thin layer of solution at the membrane. On the air side, ivhere the nitrocellulose was laid doivn by evaporation, partial disentangling of membrane molecules either did not happen a t all, or else always was less than on the mercury side. When an initial pressure difference decreased on further washing, presumably some of the molecules held on the surface were only slightly entangled with the bulk of the membrane, and Brownian motion vas sufficient to free them. None of the membranes was completely impermeable to solute molecules such as polyvinyl chloride of molecular weight of the order of 100,000. The diffusion coefficient for the polymer was, however, very much lower than for the solvent. I n a typical experiment made to test this point, a solution containing 5.78 g. of polyvinyl chloride per kilogram of solution gave an osmotic pressure of 1.44 em. as the short-time equilibrium value (molecular weight = 102,000). On standing overnight, the pressure dropped to 0.89 em. If the decrease of 0.55 cm. were due to diffusion of polymer, half the decrease would be due to depletion of the solution side, and half due to back pressure of the solute which had reached the solvent half-cell. Then the osmotic pressure of the solution remaining on the s o l u h n side vould be 0.89 plus 0.55/2 or 1.1G em. The solvent half-cell was drained, rinsed, and refilled with fresh solvent,, and a determinat'ion of osmotic pressure mas made again by the short-time dynamic method. Thevalue found was 1.10cm. The small difference of 0.0Gcm. may hare been experimental error, or may have been caused by further depletion of the solution by adsorption. Insufficient data were obtained to determine quantitatively how the diffusion of polymer t'hrough the membrane depended on molecular weight; we did, however, find that the drop in pressure on standing overnight was considerably greater for our lorn-molecular-weight fraction than for the high, as might have been expected. Highly branched polymers, or stiff chain polymers such as polymethyl methacrylate or cellulose derivatives, probably would have still smaller diffusion coefficients through the membrane than the fairly flexible polyvinyl chloride. It would also be interesting to study the diffusion of polystyrene, and other (- CHtCHX), polymers, n-here the size of the substituent group X could be varied systematically. I n making osmotic-pressure determinat,ions, it was found that eight or ten fillings with solution were sufficient to rinse a membrane. Apparently some
OSMOTIC PRESSURES O F POLYVINYL CHLORIDE SOLUTIONS
67
adsorption of polymer on the membrane occurred, because high values of osmotic pressure were obtained if a dilute solution followed a more concentrated one in contact with the same membrane; in any case, many more rinsings with a dilute solution following a more concentrated one were necessary before successive determinations checked, than when a given solution followed pure solvent on a given membrane. Also, many rinsings or long soaking were required before solvent equilibrium a t zero pressure difference could be obtained, after a membrane had been used with solution. We therefore either used a fresh membrane with each solution (putting used membranes aside for a long-time soak in solvent) or else used a sequence of increasing concentrations with a given membrane. We also found that we could condition a membrane to a given solution by using a solution of the same concentration of %less sharply fractionated polymer of about the same average molecular weight. In other words, the preliminary rinsings could be made with a solution approximating the final one, and thereby we could conserve on our best fractionated material. To fill the solution half-cell and the stand pipe required about 20 cc. of solution. Working in the low concentration range has one advantage from the point of view of membrane behavior. Our maximum pressure differences were only of the order of several centimeters, which did not appreciably distort the membranes. In some preliminary experiments, working with pressure differences of the order of 10 to 20 cm., elastic lags in the membranes were found to be very annoying. A change of pressure produced a fairly rapid initial distortion of the membrane, which was followed by a slow creep which, especially for rubber membranes, took a very long time to become unnoticeable in the rate measurements. The difficulty was eliminated by casting the membranes on a rollednickel screen, but after we decided to work only in the low-pressure range, this complication proved unnecessary.
Materials Methyl amyl ketone was used as the solvent. I t was fractionally distilled, after standing over activated aluminum oxide for several days. Four samples of polyvinyl chloride were used. The first, designated as A5, was the L38 polymer (2) used in much of our previous work, from which the low-molecular-weight material had been removed by acetone extraction. Most of the exploratory work was done with A5 polymer, because it was easily prepared. Sample 7.1, also used in earlier work, and for which we have diffusion and ultracentrifuge data (7), is the refractionated middle fraction of L38. Sample A4.3 was obtained from the acetone extract of polyvinyl chloride L38 as the material unprecipitated a t 15 per cent methyl alcohol but precipitated a t 20 per cent, and sample A4.5 was that fraction of the acetone extract which was not precipitated a t 25 per cent methyl alcohol but was precipitated at 35 per cent alcohol. Polymer A5 is represented by an unsymmetrical distribution curve, in which the low-molecular-weight fractions are miming, while the other three can probably be represented by fairly sharp symmetrical distribution curves (6). Solutions were prepared in the same way as for the viscometer (7).
68
RAYMOND 11. FUOSS AND DARWIN J. MEAD 111. RESULTS AND DISCUSSION
The experimental data for polymer 7.1 are summarized in figure 4, where osmotic pressure ).( in centimeters of solution is plotted against weight concentration w (in grams of solute per kilogram of solution). If these units are used, the densityof the solution drops out of the equations. The open circles are points obtained using the horizontal capillary, and the solid circles are those
FIG.4 . Osmotic pressure of polyvinyl chloride solutions
FIG.5. Extrapolation function for determining molecular weights
obtained with the vertical capillary. The curve is fiomewhat concave upwards, showing that, even a t these lower concentrations, the higher terms in the osmotic equation are still perceptible. Empirically, we find, as is shown in figure 5 , that
+
W /. = (1033RT/M) AW where R is 0.0821 lit. atm. per l o , T i s the absolute temperature, M is the molecular weight, and A is a constant. The radii of the circles are drawn to correspond
69
OSMOTIC PRESSURES OF POLYVINYL CHLORIDE SOLUTIONS
to an error of 0.05 cm. in a, and naturally increase with dilution. At still higher concentrations, higher powers of concentration would also appear, of course. The numerical results are summarized in table 1, where the first column gives the polymer designation; the second XO, the limiting equivalent viscosity (7) in cyclohexanone a t 25°C.; the third, the molecular weight, M*, calculated for the Staudinger constant; and from XO, using our previous value of '7 X the fourth, the molecular weight M calculated from the limiting value of a/w at zero concentration, obtained by the extrapolation of figure 5. The data of table 1 permit a cross-check of several methods of determining molecular weight. The value of 102,000 for polymer 7.1 is based on ultracentrifuge and diffusion determinations made on this polymer a t the Rockefeller Institute, and the other values in the M* column are based on this value as a calibration figure and on the limiting viscosities of the second column. The values in the last column are entirely independent figures and, as will be noted, check the third column well within the experimental errors of both methods. Sample A5, although only partially fractionated, gives a weight average M* which is in close agreement with the number average M . This result might be
TABLE
1
Molecular weights of vinyl chloride polymers POLYMER NO,
A5, ............................ 7.1.. ........................... A4.3. ........................... A4.5. ...........................
A0
IO-: M'
10-1 M
6.85 7.19 3.61 1.95
97 102 51 28
93 100 48 32
70
TERRELL L.. HILL
REFEREXCES (1) BR@KSTED, 3. N.: Compt. rend. tmv. lab. Carlsberg, SBr. chim. 22, 99 (1937). (2) Fuoss, R . &I.:J. Am. Chem. Soc. 63, 2401 (1941). (3) Fuoss, R . hI.: J. Am, Chem. Sac. 63, 2404 (1941). (4) LANSING, W. D., AKD RRAEUER, E. 0.: J. Am. Chem. Soc. 67, 1369 (1935). ( 5 ) MARK,H.: Physical Chemistry of H i g h Polymeric Systems, p. 228 ff. Interscience
Publishers, New York (1940). (6) Reference 5 , page 252, ( 7 ) ~ I E A D ,I). +I.,AND Faoss, R. M.: J. Am. Chem. Soc. 64, 277 (1942). (8) ~ I O N T O N N RA . ,E.: lOlst Meeting of the Ameriran Chemicnl Society, St. Louis, Missouri, April, 19-11, The nuthois nre grateful t o Professor Montonna for several private communicntions in regard to nitrorelliilose membranes. (9) SIMHA, R.: J. Applied I’hys. 13, 147 (1942). (10) SFURIJN,H . 31.: Private communication.
THEORY OF THE ISOELECTRIC POINT. IV
APPLICATIOSS TO W ~ a ACIDS s AXI) RASESANI) TO THEIR IXTERMEDIATE SALTS: THERELATIVE
ISOELECTRIC P O I N T
TERRELI, I,. HILT, ilforley Chemical Lahoialoiy, Western R e s e m liniucrslty, Cleveland, Ohio
Received November 6 , 1046
In the first three papers (1, 2 , 3 ) of this series the iboelectric point and some of its properties were investigated. Naturally, amphoteric electrolytes received most if not all of the attention. It will be the purpose of the present paper to show how the concept applies to non-amphoteric weak electrolytes (that is, to weak acids and weak bases). In particular, in the third section, it will be shown that intermediate salts of polybasic weak acids and of polyacidic weak bases have an entirely analogous hydrogen-ion concentration (the relative isoelectric point) at which the characteristic minima (e.g., solubility) occur. Minimum solubility for such compounds should be of importance,-for example, in quantitative analysis. The generalization employed in defining the relative isoelectric point reduces the status of the earlier discussion of the isoelectric point to that of a special case. In the first section the applicability of results obt,ained previously to solutions containing non-amphoteric electrolytes will be pointed out explicitly; that is, weak acids and weak bases are considered as merely special cases of ampholytes. In thc second section it will be shown that the isoelectric concept applies to many systems other than the two (saturated solutions of ampholytes; unsaturated solutions of ampholytes) which have been discussed up to this point in the series, I n particular, systems containing solid salts of weak acids and bases are of interest.
