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JOURNAL OF POLYMER SCIENCE VOL. VI, NO. 3, PAGES 371-380

New Dynamic Method for Osmotic Pressure Measurements

HOWARD J. PHILIPP, Central Research Laboratories, Celanese Corpora- tion of America, Summit, New Jersey

INTRODUCTION

In recent years, the osmotic method has gained an important place in the determination of absolute molecular weights of high polymeric ma- terials. Development of the method has been greatly advanced by the very practical osmometer design and the dynamic method of measurement described by Fuoss and Mead. This method and apparatus is particularly well suited to the use of fast membranes, such as denitrated collodion. When slow7 membranes are employed difficulties arise from troublesome thermometer effects and from the long times required for each measurement.

The need for better temperature control to avoid the thermometer effect has previously been recognized.2 In this paper a simple means of accom- plishing this with only minor modification of the original Fuoss-Mead os- mometer is described. The main purpose of this paper is to report on a new dynamic method of measuring osmotic pressures which has been employed successfully at this laboratory for several years. The method requires con- siderably less time than any of the methods employed heretofore, is equally applicable with fast and slow membranes, and thus serves to increase the practical usefulness of osmometry.

PRINCIPLE OF NEW DYNAMIC METHOD

The rate of flow of solvent through an osmotic membrane is proportional to the driving head, h, which is given by:

h = H - r (1) where His the height of solution above the solvent or the hydrostatic pres- sure on the membrane, and T is the equilibrium osmotic pressure. When H > T, h is positive and solvent flows from the solution to the solvent side. This condition is here referred to as positive approach to equilibrium. When H < T, a negative head results, the direction of flow is reversed, and one can speak of a negative approach. In either case the driving head is an exponential function of time. Hence, the ratio of driving heads ob- served a t fked time intervals is constant. Denoting three consecutive driving heads measured in equal time intervals by the subscripts 1, 2, and 3, one may write:

371

373 HOWARD J. PHILIPP

h / h i = h3/h2 (2) Substituting the driving heads in equation (2) by expression (1) and re- arranging, one obtains :

= (HlH3 - -@)/(Hl + H3 - 2H2) (3) This equation forms the basis of a simple determination of osmotic pressure, involving the measurement of only three differences in liquid levels at equal time intervals.

A consideration of the errors to be expected in practical application of equation (3) shows that certain precautions must be observed if results of satisfactory precision are to be obtained. It is apparent that an error in Hz will have a much greater influence on the result than errors in Hl or H3 alone, since the former appears in the equation as the square. Hence, if but one of the three height measurements is in error, only the effect of an error in Hz need be considered in the calculation of the maximum error, en, of an osmotic pressure measurement by the new dynamic method. Des- ignating the maximum error in the measurement of H as eE, it follows from (3) that:

Substituting equation (1) in (4), and rearranging, one obtains:

Setting the driving head ratios in equation (2) equal to r , so that:

hz = rhl and h3 = rhi = rzh, and substituting this in equation ( 5 ) , it follows that:

If the initial driving head, hl, is sfliciently large, the second term in both the numerator and denominator becomes negligible and the equation re- duces to :

e, = 2eHr/(l - r )z (7) Assuming that a reading error was made in only one of the three read-

ings, and that the initial driving head is sufficiently large, it is seen from equation (7) that the precision of the dynamic measurement is independent of the equilibrium osmotic pressure, but dependent on err, the error of measuring differences in liquid levels, and on r , the driving head ratio.

The error ea is largely determined by the cathetometer used. Since most cathetometers may be read to either 0.005 or 0.01 cm., eE, the maxi- mum error of the difference between two readings, is fixed at either 0.01

OSMOTIC PRESSURE MEASUREMENTS 373

or 0.02 cm. Consequently, the prevision of the dynamic measurement is determined primarily by the driving head ratio, which for a given membrane is a function of the time interval chosen. For example, according to equa- tion (7), a precision of + 0.02 cm. may be obtained with a maximum reading error, eH, of * 0.01 cm., if a driving head ratio of 0.4 or less is employed.

Two assumptions were made in the derivation of equation (7) : (a) That a reading error may occur in only one of the three readings. Actually, er- rors may occur in all three of the measured height differences, and certain error combinations may lead to appreciably larger errors than calculated from equation (7). Since such special error combinations are rare, their effect on the precision of the dynamic method must be small. (b ) It was assumed that a large initial driving head is employed. In general, this requirement is fulfilled when the initial driving head is more than 0.5 cm., as may be seen by evaluation of equation (6), using various values of hl, eR, and r.

EXPERIMENTAL

Osmometer

A Fuoss-Mead type of osmometer' was used after slight modification. The glass stand pipes were replaced by stainless steel to avoid frequent breakage. Both stand pipes, instead of only one, were provided with long stem valves to allow both half-cells to be closed off from their stand pipes. The glass-to-metal seals for the two capillaries were made by means of Wood's metal. Finally, a short sleeve was soldered onto each valve block, as shown in Figure 1, to permit thermostating of the osmometer as de- scribed below. In all other respects, the osmometer was similar to that of Fuoss and Mead.

Constant Temperature Bath

It soon became apparent that very close temperature control was imper- ative for precise measurements, especially with slow membranes, in order to avoid the temperature effect which is due to the osmometer acting like a highly sensitive thermometer. A temperature control within * 0.001 "C. was indicated from preliminary experiments. To accomplish this the entire osmometer, including valve blocks and standpipes, was immersed in a con- stant temperature water bath, with only the glass capillaries and upper portions of the stand pipes extending into the air. Special provisions were made to allow simple assembly and disassembly in case of a membrane change and to permit all adjustments to be made from outside the bath. Details of the arrangement which has proved very convenient in several years' use are shown in Figure 1.

The bath was maintained at 26 f O.O0loC. by means of a low-lag heater, operated a t only about one-third its rated voltage, a slow flow of cooling water controlled with a constant-head device, a special, highly sensitive,

374 HOWARD J. PHILIPP

mercury thermoregulator (supplied by American Instrument Company, Silver Springs, Maryland) and an efficient circulating pump. Operated in an air-conditioned room, temperature variations in the bath were usually too small to be registered by a Beckman thermometer. It should be noted that such close temperature control is necessary not only in dynamic os- mometryz but also for static osmotic measurements where slow membranes are employed.

T O S T A N D P I P E

lt HANDLI

I N C H E S

Fig. 1. Detail of osmometer thermostat.

Membranes

The new dynamic method has been employed with equal success on fast membranes, such as denitrated collodion,l and on slow membranes, such as caustic treated cellophane3 or gel-~ellophane.~ The specific examples presented here were obtained with a gel-cellophane membrane, prepared from #600, nonwaterproofed, undried, wrinkle-free cellophane (supplied through the courtesy of Sylvania Division, American Viscose Corporation Fredericksburg, Virginia) treated by the method of Wagner.4

Procedure

The osmometer was flled in the usual manner. Solution and solvent were brought to bath temperature prior to filling, so that the measurement

OSMOTIC PRESSURE MEASUREMENTS 375

could be begun as soon as air bubbles were removed. Dynamic measure- ments on slow membranes (gel-cellophane, caustic treated cellophane) are performed with both half-cells closed in order to minimize the thermometer effect and to double the speed. With fast membranes (denitrated collo- dion) the solution side is open to the atmosphere through the stand-pipe so that its liquid height remains practically unchanged during a determina- tion. Liquid heights were measured by means of a cathetometer which could be read to the nearest 0.005 cm. The maximum error of a difference between two readings, en, was 0.01 cm., therefore. The readings were timed with an ordinary watch, provided with a second hand.

According to theory only three readings need be taken of the moving menisci, at equal time intervals. In practice it was found advantageous to make three overlapping dynamic determinations for every solution, by taking seven readings equally spaced in time by an interval one-half as long as required for the desired precision. The osmotic pressure is then computed by equation (3) for the three available sets of three readings each, separated by full time intervals. The advantage of this procedure is that any trends or irregularities, due, for example, to inadequate tempera- ture control or Musible impurities or unusually large reading errors, are immediately recognized by lack of agreement between the three results. When this occurs it is often simpler to allow the determination to continue as a static one than to repeat the dynamic measurement. In order to in- sure a sufficient initial driving head for the last set of three readings, the menisci are adjusted in the beginning, to a difference a t least 1.25 cm. above or below the expected equilibrium. With a little experience this point is easily recognized by the rate of movement of the menisci.

The time interval corresponding to the desired driving head ratio is best determined with solvent on both sides, by making a plot of pressure versus time. This is done only once for any given type of membrane and solvent. For very viscous solutions a somewhat longer time interval is employed than is obtained with solvent on both sides.

RESULTS

In order to test the reproducibility of osmotic pressure measurements by the new dynamic method, repeated dynamic zero correction determina- tions were made with a gel-cellophane membrane, using pure acetone on both sides. The zero correction is the small apparent osmotic pressure ex- hibited by most membranes when both half-cells are filled with pure sol- vent. It may be the result of membrane asymmetry, or of minute osmom- eter leaks, and must be subtracted from the measured osmotic pressures to obtain true readings. By the static method the particular membrane used had been found to have a zero correction of - 0.025 cm., the negative sign indicating a lower capillary height on the side normally used for solu- tion than on the side normally used for solvent. The permeability of the membrane for acetone was such that a given driving head fell to about four-

376 HOWARD J. PHILIPP

tenths its value in 5 minutes. Taking 7 readings in 2.5-minute intervals during each run thus gave 3 dynamic results per run, with a driving head ratio of 0.4. The data obtained in a typical run are shown in Table I; the results of 9 separate runs, yielding a total of 27 values, are presented in Table IIa. The grand mean of all 27 determinations with its standard error is seen to be -0.026 * 0.002 cm.

TABLE I TYPICAL DYNAMIC DETERMINATION OF ZERO CORRECTION. MEMBRANE, GFL-C-OPHANE. PURE ACETONE IN BOTH HALF-CELLS. POSITIVE

APPROACH Time. mia Hydrostatic preasuree. cm.

0.0 2 . 5 5.0 7.5

10.0 12.5 15.0 - Cdc. equilibrium.. ........

2.300

0.910

0.355

1.445

0.570

0.215

-0.014 -0.027

0.910

0.355

0.130 -0.023

Mean.. ................... -0.021 cm.

TABLE I1 EQUILIBR~CTM PRESSURES (ZERO CORRECTIONS), IN CENTIMETERS, OB- TAINED FROM A SERIES OF DYNAMIC MEASUREMENTS USING A GEL-CELLO-

PHANE MEMBRANE AND PURE ACETONE IN BOTH HALF-CELLS (a) Positive approach (b) Negative approach

-0.014 -0.022 -0.016 -0.026 -0.055 -0.021 - .027 - .024 - .017 - .048 - .032 - .015

- .045 - .039 - .024 - .023 - .019 - .031 Av. - .021 - .022 - .021 - .040 - ,042 - .020

- .022 - .024 - .023 - .055 - .028 - .052 - .022 - .025 - ,035 - .055 - ,029 - .031

- .029 - .050 - ,012 - ,050 - ,021 - .010 Av. - .031 - .023 - .023 - ,046 - ,036 - ,032

--- _ _ _ - -

- - - - ~ -

- .045 - .041 - .019 - .044 - .010 - .026 - .029 - .O% - .012

Av, - .039 - .032 - .019 ~ - -

Grand Mean -0.026 * 0.002 cm. -0.036 * 0.003 cm.

The above data were obtained by a positive approach to equilibrium (H > s), i.e., the liquid levels were adjusted, a t the beginning of each run so that the meniscus on the side normally used for solution moved in a downward direction. In another series of experiments, the dynamic zero correction was determined in exactly the same manner except that a nega-

OSMOTIC PRESSURE MEASUREMENTS 377

tive approach to equilibrium was employed ( H < T), i.e., the solution meniscus was adjusted to move in an upward direction in these tests. Six separate runs gave 18 values for the zero correction, which are listed in Table IIb. The grand-mean of these 18 determinations is -0.03, =t 0.003 cm.

It is seen that a different zero correction is obtained depending on the direction from which equilibrium is approached. The difference is statis- tically significant (by the t-test) and has been observed with all membranes and all solvents tested and for osmotic pressures as well as zero corrections. In every case, the value obtained by positive approach has been greater than that found by negative approach, the difference being smaller the more rigid the membrane, These observations seem to indicate a slight move- ment of the membrane, caused by the change in hydrostatic pressure dur- ing measurement. Therefore, equilibrium must be approached from the same direction in the zero correction determination as in the measurement of osmotic pressures of solutions. Also, determinations should be avoided where H passes through zero and changes its sign during the dynamic run, a situation which is possible only with a negative approach to low osmotic pressures. The static zero correction usually lies between the two dynamic values although, as in the present case, it is sometimes very close to one of the latter.

With regard to the precision of the dynamic measurement it is seen from the 45 measurements recorded in Table I1 that the maximum deviation from the grand mean is 0.024 cm., which is in good agreement with the maximum error of *0.022 cm. calculated from equation (7) for a driving head ratio of 0.4.

As a further example of the method, a complete dynamic osmotic molecu- lar weight determination is presented for a sample of commercial cellulose acetate in acetone, and the results compared with data obtained by the static method. Due to slight diffusion of low molecular weight cellulose acetate the ordinary static method was modified in that the hydrostatic pressure was plotted against time and the static osmotic pressure obtained by extrapolation of the linear portion of the plot to zero time. Measure- ments by both methods were made on the same 4 solutions of different concentrations. The reduced osmotic pressures, T / C , were plotted against

TABLE I11 COMPARISON OF DYNAMIC AND STATIC METHOD OF MEASURING OSMOTIC MOLECULAR WEIGHT OF A COMMERCIAL CELLULOSE ACETATE IN ACETONE

Concsn- Osmotic prassunt T, tretion cm. 7/c Molecular weisht

C. B.A. Dyn. stat. Dyn. Stat. Dyn. stat.

- - 7.181 5.2% 5.280 0.730 0.735 5.386 3.83s 3.850 0.712 0.715 - - 3.590 2.46s 2.460 0.686 0.685 - - 1.795 1.21, 1.210 0.675 0.674 - -

0 - - 0.651 0.652 49,600 49.500

378 HOWAFtD J. PHILIPP

concentration, c in the usual manner, the linear plot extrapolated to zero concentration by the method of least squares to obtain (T/c),, and the molecular weight calculated from this value by van't Hoffs equation. All the data are presented in Table 111.

Agreement between the dynamic and static method is seen to be very good for the individual osmotic pressures as well as for the molecular weights. A slight tendency may be noted for the dynamic osmotic pres- sures to be a trifle below the static values a t high concentrations. This is due to the fact that the static values are corrected for diffusion by the extra- polation procedure employed, while the dynamic measurements are taken about 5 to 10 minutes after filling. For so short a period of time the dif- fusion effect is too small to have a significant effect on the estimated molecu- lar weight.

DISCUSSION

It may be seen from the results presented in Tables I1 and I11 that the new dynamic method which is based on equation (3) is capable of yielding precise and accurate osmotic pressure measurements. The maximum error can be predicted by means of equation (7) and the desired precision attained by proper choice of the time interval between readings. The validity of equation (7) has been demonstrated by the good agreement between cal- culated and observed errors for the data of Table 11. When 3 overlapping determinations are made, by taking 7 readings instead of 3, the error of the mean is, of course, reduced t o l/G = 0.58 times the maximum error com- puted from equation (7). Molecular weights determined by the method are seen from Table I11 to be in good agreement with those obtained by the static technique.

In order to obtain consistently good results with this method and the Fuoss-Mead osmometer certain precautions must be observed. The most important is close temperature control. Variations must be kept within 0.00l"C. or less, which is readily accomplished with the apparatus de- scribed. To avoid erratic results immediately after filling the osmometer, solution and solvent should be at bath temperature prior to filling and the solvent should come from exactly the same supply as that used for making up the solutions. This is particularly important with acetone, where small differences in moisture content may cause erratic initial readings. While this may also be overcome by allowing a short time for equilibration before starting the measurements, such a procedure is undesirable for materials showing some diffusion through the membrane. Finally, osmotic equilib- rium must be approached from the same direction as in the zero correction determination, and a sufficient initial driving head (at least 1.25 cm. if 7 readings are taken) must be employed.

The method offers several advantages over other methods, particularly in relative simplicity and speed. Only a few readings-3 are sufficient, 7 are preferred-need be taken at equal time intervals, the number of read-

OSMOTIC PRESSURE MEASUREMENTS 379

ings being no larger than in the longer static method and very considerably less than in the dynamic method of Fuoss and Mead,' for which 30 to 40 readings are required. A further advantage is that the equilibrium value can be calculated from a single series of measurements along one direction of approach, whereas in the old dynamic method equilibrium must be ap- proached from above as well as from below. In the latter method the equilibrium osmotic pressure must be known within 1 or 2 millimeters. In the new method not even an approximate prior knowledge of the equilib- rium value is needed because it is merely necessary to adjust to an initial driving head above a certain value which is easily done after a little experi- ence by observing the rate of travel of the menisci. Also, computation of the osmotic pressure by means of equation (3) is shorter than the graphic solution employed by Fuoss and Mead.

Fig. 2. Relative lengths of time required for an osmotic pressure measure- ment by: (A) the static method, (B) the dynamic method of Fuoss and Mead, and (C) the new dynamic method. The time shown for the Fuoss- Mead method is only one-half the actual time, as the descending branch is not shown.

The main advantage is, of course, the new method's speed. A graphic comparison of the relative times needed for an osmotic pressure measure- ment by three different experimental methods, keeping other variables such as membrane, solution viscosity, etc., constant, is given in Figure 2. It may be seen that by the new dynamic method osmotic pressures may be obtained in about one-fifth the time required for the static method. This increased speed is desirable not only in itself, but also because it permits measurements on solutions which show some diffusion through the osmotic membrane. Measurements can be completed before any appreciable dif- fusion has taken place. This is illustrated by the data in Table 111. The modified static data are corrected for diffusion by extrapolation to zero time. The dynamic results, obtained as soon after filling as possible, are either the same or insignificantly lower than the extrapolated static values. Similar results have been obtained with other samples, membranes, and solvents than those described here.

The assistance of C. F. Bjork who collected the experimental data is gratefully ac- knowledged.

380 HOWARD J. PHILIPP

References

1. R. M. Fuoss and D. J. Mead, J. Phys. Chem., 47,59 (1943). 2. K. B. Goldblum, J. Phys. 4 Colloid Chem., 51,474 (1947). 3. R. E. Robertson, R. McIntosh, and W. E. Grummit, Can. J. Research, B24, 150

4. R. H. Wagner, Znd. Eng. Chem., 16,520 (1944).

English Synopsis, see Summaries, page S32, Vol. V, 1950.

(1946) -

R6sum6

Une nouvelle mBthode dynamique de mesure des pressions osmotiques des solutions de hauts polym&res est dkrite, grlce B laquelle les temps de mesures sont considBrable- ment raccourcis. L'exactitude et la prhision de cette mBthode sont semblables Q celles des autres techniques osmotiques. Un controle Btroit de la temp6rature est essentiel pour obtenir des rhultats concordants, surtout avec des membranes lentes. Un ap- pareil de controle de temperature dans les limites de 0.001 "C. est dkrit. Des exemples sont donnb pour la dhtermination de la correction du z&o des membranes, lorsque le solvant est rBparti de part et autre de cellesci; des exemples de dBterminations com- plhtes des poids molkulaires sont kalement donnb pour un acBtate de cellulose com- mercial, dissous dans I'acBtone.

Zusammenfassung

Es wird eine neue Methode zur Messung osmotischer Drucke von Hochpolymer- Lasungen beschrieben, die die Dauer jeder Messung stark reduziert. Die Genauigkeit und Pr'a'zision dieser Methode ist der anderer osmotischer Methoden anlich. Eine genaue Temperaturkontrolle ist wichtig, u m zuverl'issige Resultate zu erhalten, beson- ders fir langsame Membranen. Ein zweckmlssiger Apparat zur Temperaturkontrolle innerhalb 0.001 "C. wird beschrieben. Beispiele zur Bestimmung der "Null-Korrektur" einer Membran mit Liisungsmittel an beiden Seiten, und f i i eine vollsthdige Molekd- argewichtsbestimmung eines Handels-Celldoseacetates in Aceton werden gegeben.

Received May 15,1950

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