A rapid dynamic method for osmotic pressure determinations

JOURNAL OF POLYMER SCIENCE YOL. 5.5, PAGES 381-391 (1961)

A Rapid Dynamic Method for Osmotic Pressure Determinations

D. R. BRUSS and F. H. STROSS, Shell Dcuelopmcnt Co., Emeryuiile, California

Osmotic pressure determinations of number-average molecular weight may be carried out by either static or dynamic methods. Of these two techniques, the static approach is by far most generally used, owing to the simplicity of the equipment and the smaller amount of operator manipulation required. Dynamic methods usually involve more elaborate equipment and considerably more attention. However, dynamic methods offer two advantages not found in the static-equilibrium technique. These are ( I ) rapidity of the measurement and (2 ) retention and measurement of solute which may permeate through the membrane in the course of a static determination.

The recent literature affords several examples of remarkably retentive membranes used for static determinations. The most notable are the ultrafine filter membranes described by Vaughaii14 and reported to have permeation limits of the order of 1500-2000 molecular weight. With such membranes, equilibration times may become excessive, depending on the pore size distribution of the membrane and the molecular weight distribution of the sample. Indeed, with “tight” gel-cellophane membranes, equilibration times of days and weeks have been encountered in these laboratories for samples that contain appreciable solute of size near the pore size of the membrane. One is then faced with the problem of waiting until a static head is attained and losing a portion of his sample, or of attempting some sort of extrapolation proredure. Extrapolation to zero time, to correct for solute permeation, has been shon n by Stavermaii11-12 to be theoretically unsound.

Dynamic methods may be used to obtaiii the osmotic pressure more rapidly. The half-sum method of Fuoss and the dynamic-eyuilih- rium method of Hepp,6 and the method of I’hilipplO are among the best known. The half-sum method involves adjusting the initial head of the osmometer to a value as close to the equilibrium position as possible and measuring the decrease in hydrostatic head as a function of time. The asymptote to this curve is estimated and the procedure repeated, starting with the initial head equidistant but below the estimated asymptote. One-half the sums of the ordinates of these curves for various values of elapsed time are plotted. The resultant curve is then extrapolated to zero

381

382 D. B. BRUSS AND F. I€. STROSS

time. A number of points are required close to the equilibrium position, which is often difficult to estimate. The speed of the determination de- pends upon the characteristics of the membrane; this makes the analysis quite tedious with slow membranes.

The dynamic equilibrium method of Hepp6 involves applying a negative or positive external gaseous pressure to one of the osmometer half-cells until a sensitive flow meter in series with the osmometer shows no net flow of solvent. The pressure a t this point, corresponding to the osmotic pressure, is then read from the manostat Alternatively, various pressures may be applied and the flow rates corresponding to these pressures can be interpolated to zero flow. For determinations in nonaqueous solvents, a modified Hepp osmometer8 has not proved suitable. It is felt that the membrane area exposed to solvent and solution was not sufficient for sensitive flow rate measurements with fairly retentive membranes.

Philipp’s methodlo is based on the assumption of an exponential decay in the hydrostatic head H . Three readings are taken a t equal time intervals and the osmotic pressure is determined by substitution in the equa- tion :

7r = (HI223 - HZ*)/(H, + H ; - 2H2)

The chief difficulty in this method is that the approach to equilibrium is not always exponential, particularly with permeable solute present in the solution.

Jn the dynamic-equilibrium method that is the subject of this paper, a high-speed small-volume osmometer3 (licensed for manufacture to J. Tr . Stabin Co., Brooklyn, New York), equipped with capillaries of small diameter, is used in measuring solvent transport rates across the membrane a t various hydrostatic heads. Solvent, transport rates are measured by timing with a stop watch and cathetometer the passage of the meniscus in the measuring capillary over a distance of 1 mm. The hydrostatic head is set a t various positions above and below the equilibrium position by manipulation of the osmometer push rod. Extrapolation of the plot of hydrostatic head versus solvent flow rate to zero flow gives the osmotic pressure. The method is very rapid, about ten minutes being required for the measurement of a single concentration. Since the measurement is made within a short time, a great deal of solute that might otherwise permeate through the membrane is counted by this method. Another advantage of this technique is that the instrumentation and maiiipulatioii are quite simple.

APPARATUS AND REAGENTS

Osmometer. A small-volume high-speed osmometer described pre- v-iously3 was modified by being equipped with capillaries of 0.36 mm. diameter. The diameter was measured by filling the capillary with mercury and weighing. Constancy of the diameter was checked by measuring a bead of mercury a t different positions with a cathetometer.

RAPID OSMOTIC PRESSURE DETERMINATIONS 383

Membranes. GC-300 membranes were sets of gel-cellophane membranes of grade No. 300 obtained from American Viscose Corporation, Fredericksburg, Virginia. These membranes were stored in 3oy0 alcohol and conditioned by 4-hr. immersion in 1 0 0 ~ o alcohol and in .!joy0 alcohol and 50% benzene or toluene before storing in pure solvent.

GC-450 membranes were sets of gel-cellophane membranes of grade No. 450 obtained from J. V. Stabin Company, Brooklyn, New York. The membranes were water-washed for several hours and conditioned in the manner described above.

GC-600 membranes were grade KO. 600 obtained from the same source and conditioned in the same manner.

UFF/AF were ultrafine filters of the type “allerfeinst” (superdense), obtained from Membranfiltergesellschaft, Gottingen, Germany. They were conditioned in the same manner as were the GC-300 membrane?.

The bath was constructed from a 39- gal. capacity aquarium jar (Aloe Scientific Co.). Two 1/16-hp. motors (Bodine Electric Co., Chicago, Ill.) were mounted above the bath and were fitted with shafts and jet stir impellers (Hallikainen Instrument Co., Berkeley, California) in such a manner that the impellers were located a t one-half the depth of the bath, equidistant from the sides of the bath, and each was one quarter of the distance in from the end of the bath. Control heat was supplied with a 300-w. low lag heater mounted in the back of the bath. A Thermotrol Temperature Regulator (Hallikainen Instrument Co., Berkeley, California) mas used as the controlling element. The bath was operated at 30°C. At this temperature, it was necessary to supply a small amount of cooling to the bath by running tap water through a short length of copper tubing.

With capillaries of small diameter, rather stringent temperature control is needed to prevent fluctuations in the meniscus of the measuring capillary during the measurement. By assuming a maximally allowable fluctuation (0.01 em.), the required temperature control can be calculated from the volume of the osmometer, the diameter of the capillary, and the coefficient of cubical expansion of the benzene. For the capillary used (d = 0.360 mm.) and an osmometer volume of 2 ml., the temperature control needed is 0.005”C. For osmometers of larger volume, such as the 10-ml. Stabin osmometer (J. V. Stabin Co., Brooklyn, Sew Tork), the temperature control would have to he correspondingly better.

Thermo-Graf measurements (Hallikainen Instrument Co., Berkeley, California) a t the osmometer position in the bath have shown that the temperature fluctuations (short range) are of the order of 0.002”C. and that the temperature drift over a 2 hr. period amounts to 0.003”C. The metal body of the osmometer and the solvent enclosed in the solvent jar will tend to damp out the short-range fluctuations. Since the period of measurement is 10-20 min., this temperature control is more than adequate. Visual observation of the measuring meniscus over short intervals of time showed no noticeable variations.

Constant-Temperature Bath.

384 D. B. BRUSS AND F. 11. S‘l’ttOSS

Other Accessories. A Gaertner cathetometer (Gaertner Scientific Co., Chicago, Illinois), reading to 0.005 cm. over a 100-em. scale, was employed. The stop watch had a timing interval of 30 min. and could be read to the nearest 0.2 sec. Reagent-grade benzene and toluene (Baker :md Adamson) were used without further purification.

TECHNIQUE

The osmometer was rinsed several times with solution hefore being filled for measurement. After filling of the osmometer and sealing of the well a t the top of the filling capillary with a pool of mercury, the time was noted. Five minutes was allowed for thermal equilibration and then the measurement was begun. The meniscus of the measuring capillary was adjusted to a position near or below thi: meniscus of the reference capillary :tnd the cathetometer mas adjusted so that the hairline was just above the meniscus of the measuring capillary. As the meniscus crossed the hairline, the stop watch was started. ‘The cathetometer was then raised exactly 1 mm. (timing distance) by meails of the vernier screw and scale, and the stop watch was stopped as the meniscus reached the hairline for the second time. After the time mas noted and the cathetometer read, the meniscus was raised to a new positioil by adjusting the osmometer push rod; the process was repeated. Two to three readings were taken with the meniscus rising, and the same number with the meniscus falling. Since the readings were taken over a dii.taiice of 1 mm., the pressures below the equilibrium value were corrected or “averaged” by subtracting 0.5 mm. and those above the equilibrium position mere corrected by adding 0.5 mm. to the filial reading recorded for eavh timing distance.

Flow rates were calculated for each position on the meniscus by applying the formula:

flow rate, ml./min. = 80rr2h/t

where r = radius of capillary in cm., 11 = timing distance, usually 0.1 cm., and t = time in seconds.

The osmotic pressure was obtained by plotting the flow rate versus the applied pressure and extrapolating to zero flow.

DISCUSSION

The requirements for rapid dyiiamic-equilibrium measurements of osmotic pressure are (1) large membrane area, rigidly supported, to insure rapid solvent transfer, (2 ) a capillary having as small a diameter as prac- tical for sensitive solvent transport measurements across the membrane, (3) small cell volume to minimize the “thermometer effect” of the osmometer, and (4) adequate temperature control SO that fluctuations of the measuring meniscus do not affect the flow rate measurement.

For a given osmometer, polymer solution, and hydrostatic head, the rate of solvent transport will depend upon the permeability of the mem-

RAPID OSMOTIC PHESSURI.: DE'I'ERMINATIONS 385

brane. Membranes of high solvent perment)ility (short half times) give more rapid flow rate measurements.

Since this type of dynamic. measurement is a fuiictioii of time, it is important that the measurement be started as quickly as possible after the cell has been filled and has come to thermal equilibrium. It is also important that the measurement be started a t the same time interval after filling, in order to obtain reproducible results. These considerations are important only when there is low molecular weight material present that is capable of membrane permeation. For all of the data discussed in this paper, the measurements were started approximately 5 min. after filling except where otherwise noted.

Osmotic pressure reflects the original solute concentration only to the extent that the solute is retained in the solution compartment of the osmometer at the time of the measurement. An osmotic pressure measurement counts the number of molecules; i t is most sensitive to low molecular weight substances since these give more molecules per unit mass of sample. In the case of samples containing substantial quantities of low molecular weight components, diffusion through the membrane of only a small per- centage of the total sample (by weight) will mean loss of a large number of molecules and will greatly affect the result. It is necessary, therefore, to characterize the membrane aiid have some knowledge of the range over which i t can be expected to perform satisfactorily. The permeability of the membrane, therefore, is the criterion for the degree of error to be expected from this source. Clearly, this error will be greater, for samples containing membrane-permeating solute, when static equilibration is attained, than a t any time before. The error will be correspondingly reduced if the time of measurement is so short that only small amounts of solute are allowed to pass through the membrane. Dynamic measurements, which are complete within 10 min., will yield more nearly true number-average molecular weights than measurements a t equilibrium, after from 4 to over 100 hours have elapsed.

It has been pointed out, however, that small molecules would not act in accordance with expectations. From consideration of the processes of irreversible thermodynamics, Staverman11r12 has concluded that molecules of such a size relative to the pore size of the membrane that they are capable of permeation will not contribute to the full extent possible to the osmotic pressure even when they have not yet permeated the membrane.

Staverman derived the relation:

T e x p = U T t h

where rpXp is the experimentally measured osmotic pressure, T t h is the theoretical thermodynamic osmotic pressure, and u is the reflection coefi- cient of the membrane. This reflection coefficient ranges from zero, for completely permeable membranes, to unity for completely retentive membranes. For a particular membrane, u will vary with the molecular weight.

386 D. B. BRUSS AND F. IT. STROSS

As a consequence of Staverman’s theory, extrapolation to zero time or zero flow, for a leaking membrane, will not yield the thermodynamic osmotic pressure. Only by knowing the variation of u with molecular weight for a given membrane can the true osmotic pressure be calculated.

Staverman further concludes that a solute may have a high permeability and still require a long time to reach a, uniform distribution in the osmometer and that the time required for the diffusion of a permeable component may be many times longer than that required for the decay in osmotic pressure, when the reflection coefficient of the component is near zero.

Recently Allen and Place’ and Alvang and Samuelson2 have shown that the actual diffusion of solute could not account for the observed decrease in osmotic pressure, thereby lending credence to St,averman’s theory.

Gardon and Mason,6 however, by extending the theory of Staverman and that of LaidlerTg conclude that the true osmotic pressure can be derived from the variation of pressure with time for the case in which the membrane is partially permeable to solute. The procedure set forth im- poses certain limitations on the osmometer and requires a knowledge of the partition coefficient of solute between membrane and solvent, rate constant of solute diffusion, and molar volume of the permeating fraction.

From kinetic considerations, Tung13 has shown that extrapolation to zero time is valid under favorable conditions providing the osmometer is “fast)’ and solute diffusion is not excessive.

While the theory of Staverman points out that a true number-average molecular weight for a leaking membrane cannot be sbtained even by rapid measurement, it is nevertheless true that such a measurement will a t least count a portion of the molecules that would be totally lost when the static equilibrium method is used.

EXPERIMENTAL RESULTS Characterization of membranes in these laboratories is done by osmotic

pressure measurements on a polydisperse polystyrene sample of low molecular weight that will present a spectrum of molecular weights to the membrane for possible membrane permeation. A weight distribution was obtained by using precipitation chromatography? By assuming values of permeation limits, one can caIculate corresponding number-average molecular weights from the weight distribution curve. From such data, a curve of permeation limit versus measured osmotic pressure may be drawn, and the permeation limit of a variety of membranes may be measured. The main difficulty with this method lies in the uncertainty that exists in the critical low molecular weight region of the curve. A comparison of the results obtained from various membranes with other number-averaging methods is given in Table I along with the calculated permeation limits of the membranes.

While this method is useful for obtaining a numerically defined measurement of the permeation limit of a particular membrane, i t cannot be as-

RAPID OSMOTIC PIIESSURE DETERMINATIONS 387

TABLE I Sumber-Average Molecular Weights Determined for Standard Polystyrene Fraction

Method Membrane permeation limita

Dynamic osmometry (GC-300) Ebullioscopic Weight distribution curve (calr.) Static osmometry (UFF/AF) Static osmometry (GC-600) Ultracentrifuge (calc.) Static osmometry (GC-450) Static osniometry (GC-300)

31,000 35,000 40,000 50,000 6,000 50,000 (i,OOO 50,300 55,000 9,000 80,000 >20,000

a Calrulated from weight distribution data.

sumed that all membranes of a given grade will have a similar permeation limit. Indeed, the permeation limits have been found to vary widely from membrane to membrane within a given batch and they are also markedly dependent on the conditioning procedure and on the length of time the

I I I I I I I

i . ' ~ s ~ u'r i . : , m i i m i n x l o 4 0.5 1.0 1.5 2.0 2.5 3.0 3 5 4.0

Fig. 1. Flow rate-pressure extrapolation for a poly-a-methylstyrene: ill, = 10,000.

3 88 D. R. RRIJSS AND F. 11. S’I’ROSS

1 0

9

8

7

6

6 5

4

3

2

1

0

v v v

I I I I I I I 0.1 0 . L 0 3 0.4 0 . 5 0.6 0.7 0 8

CONCENTRATLON, g/lOO rnl

Fig. 2. Extrapolation to infinite dilution for the polymer samples of Table 11.

membrane is in use. The ultracentrifuge calculation is subject to the errors that are inherent in the calcu1:itioii of number-average molecular weight from the weight distribution curve. Sothing is known about the repeatability of the ebullioscopic method a t this molecular weight level. Reference to the table shows that the dynamic results with GC-300 membranes are some two and one-half times lower than the static results with the same membranes.

Figure 1 is a typical graph of flow rate versus applied pressure for a low molecular weight poly-a-methylstyrene (an = 10,000). The flow rates correspond to timing intervals of from 20 to 200 see. In general, t,imes longer than about 200 see. are not used, since the length of time of the measurement becomes prohibitive. The hydrostatic head varied in a regular manner, starting with the meniscus below the equilibrium position and progressing to positions above the equilibrium position. In all of the dynamic results reported in this paper, the time required for a given hydrostatic head to fall to one half of its value with pure solvent on both sides of the membrane was between 7 and 20 min. Asymmetry pressure correc-


tions are measured by the dynamic method and afford a check on thermal equilibration and instrument behavior. The dynamic asymmetry measurement should agree with the static measurement if the solvent comes to thermal equilibrium within the 5 min. period allowed for equilibration and if the instrument and membrane support are performing satisfactorily. Some difficulty was experienced with a batch of membranes cut to a diameter slightly larger than the membrane well of the osmometer. Clamp- ing these membranes in the osmometer resulted in erratic flow measurements and an inability to determine an asymmetry pressure.

Table I1 gives the data for the comparison of the dynamic-equilibrium technique, the static-equilibrium method, and the ebullioscopic method, for a variety of samples over a wide molecular weight range. Both the dynamic and static osmotic pressure determinations were made with GC-600 membranes. Extrapolation to infinite dilution, for the dynamic determination of several of the polymers, is shown in Figure 2.

TABLE I1 Comparison of Dynamic Method with Static Method and Ihillioscopic: Results

Sample - MUJ Static Dyn. Ebull.

(1) Poly-a-methylstyrene A (2) Polystyrene fraction (3) Poly-a-methylstyrene B (4) Polymethacrylate (5) Polystyrene A (6) Polystyrene B (7) Polyester A (8) Poly-a-methylstyrene C (9) Polyester B

(10) Poly-a-methylstyrene D (11) Sucrose octaacetate

285,000 240,000 240,000 -

216,000 208,000 206,000 -

73,000 66,000 53,000 - 32,000 15,000 10,500 - 18,000 - 12,200 11,200 16,000 - '7,200 6,400

- >300,000 7,800 5,900 4,000 m 8,200 3,800

- m 6,700 2,500 2,100 m 7,100 2,200

679 (theory) m 14,500 679 (theory)

It is evident from the data of Table I1 that the dynamic method counts a great deal of solute in the low molecular weight region that is totally lost with the static method. By using the ebullioscopic results as the theoretical number-average, the fraction of the theoretical value obtained by the dynamic method may be plotted against the actual molecular weight, to illustrate how effectively the dynamic method is counting the solute molecules a t various molecular weight levels (Fig. 3 ) . This figure shows, for example, that a t molecular weight 2000, 30% of the molecules contribute to the dynamic osmotic pressure; in contrast to this, none are counted in the static measurement.

The curve of Figure 3 is membrane-dependent. Membranes with more favorable pore size distributions will count more of the molecules a t a given molecular weight level than will the membrane of Figure 3. For example, a determination of the molecular weight of sample 9 (Table 11) gave a result of 4900 with another set of GC-600 membranes, indicating

390 D. B. BRUSS AND F. H. STROSS

that this membrane was counting of the molecules a t a molecular weight level of 2500.

A comparison of the dynamic osmotic pressure results with static results, weight-average molecular weights, and iiitriiisic viscosities of a series of polystyrene fractions is given in Table 111. Dynamic results are shown for both the GC-BOO and GC-300 membranes. The dynamic results

(GC-600) exhibit both a linear correlation, on a logarithmic plot, with intrinsic viscosity, and a satisfactory agreement with the results obtained from the GC-300 membranes.

Table IV shows another instance in which the dynamic method indicated a low molecular weight solute that was not counted by a static determination. The original polymer was prepared by a process of anionic polymerization. Static osmotic pressure measurements, when compared with the light scattering measurement, gave a a,/ MNratio of 1.16, which indicated a polymer of rather narrow distribution. However, a dynamic


determination of the same material gave a much lower number-average molecular weight, showing the presence of a low molecular weight tail in the distribution curve. A simple one-stage precipitation was used to remove this low molecular weight fraction, with the result that the static

POLYESTER n C = 0.13951

0 I I I I I I I I I 0 20 40 60 80 100 120 1.10 160 180 Z O O

TIRIE, R l I N U T E S

Fig. 4. Mcasurement of dynamic osmotic pressure a t various times after filling osmometer.

aiid dynamic methods agreed, a t a higher number-average value. weight-average molecular weight also increased significantly. meiits were made with GC-600 membranes.

The Measure-

TABLE 111 Comparison of Molecular Weights Obtained on R Series of Polystyrene Fractions

an x 10-3 Per cent atu Dynamic Static

Fraction of total I.V. X GC-600 GC-300 GC-600

1 10.2 0.18 31 21 19 25 2 12.2 0.24 49 25 26 26 3 14.3 0.31 61 33 29 40 4 21 .o 0.39 97 46 40 42 5 32.8 0.56 143 68 72 87 6 9.5 0.98 311 125 - -

392 D. B. BRUSS AND F. 1%. STROSS

Figure 4 demonstrates the rate of decrease of separately measured dynamic pressures a t various times for the same solution of Polyester B (Table 11) with three different gel-cellophane membranes (Grade 600). The number-average molecular weight of 2500 measured by the ebullioscopic method is far below the permeation limit of the membrane. It is evident from the figure that extrapolation to zero time would give a n/c value well below the theoretical value of 16.7 calculated from the ebullioscopic measurement. Furthermore, from the rate of decrease of the measured osmotic pressure time, one has to assume almost instantaneous permeation of 70% of the molecules followed by an abrupt change in permeation rate, or that some other effect, such as that proposed by Staverman, is operating and that even though the molecules are retained a t the time of measurement they do not, contribute to their full capability to the pressure. This effect is even more pronounced for similar measurements with sucrose octaacetate. To account for the shape of the pressure-time curve, one would have to assume almost instantaneous diffusion of 96% of the molecules followed by an abrupt change in permeation rate. The differences in the curve of Figure 4 represent differences in the pore size distribution of the various membranes.

TABLE TV Comparison of Dynamic and Static Results on a Poly-a-methylstyrene

hefore and after Fractionation -

Sample M, I%',, (static) I%'% (dyn.)

Polymer, whole 220,000 190,000 128,000 285,000 240,000 240.000 Polymer, after removal of low m.w. portion

Certain anomalous behavior has been encountered in the extrapolation to zero flow rate, with samples of molecular weight below the permeation limit of the membrane or with samples containing appreciable material below the permeation limit. The pressure obtained by extrapolation of points taken successively further from equilibrium is larger than that obtained by taking readings approaching equilibrium. The slopes of the extrapolations differ also and, in addition, depend on whether the extrapolation is made from above or below the equilibrium position. This behavior appears to be a function of the direction of solvent transport across the membrane and the time required to obtain the point nearest the equilibrium value, i.e., whether this reading is taken first or last. These phenomena require further investigation.

In general, the repeatability of the dynamic measurement is approximately .5y0 with the same membrane and compares favorably with the static method. When membrane-permeable solute is present in the sample, both methods will be membrane-dependent, but this effect is much smaller

RAPID OSMOTIC YltESSC~l~E DBTEItMlNAI'IONS 393

with the dynamic method. 111 every case, the dynamic method will yield a result which more nearly approximates the true number-average than a static determination with the same and eveii with more retentive membranes.

The authors are indebted to Dr. D. E. Burge of these laboratories for the light scattering molecular weight determinations arid to Mr. G. A. Bordokoff for making many of the osmotic pressure measurements.

References 1. Allen, P. W., and M. A. Place, J . Polymer Sci., 26,386 (1957). 2. Alvang, F., and 0. Samuelson, J . Polymer Sci., 24,353 ( 1957). 3. Bruss, D. B., and F. H. Stross, Anal. Chem., 32,1456 (1960). 4. Fuoss, R. M., and L). J. Mead, J . Phys. Cheni., 47,59 (1943). 5. Gardon, J. L., and S. G. Mason, J . Polymer Sci., 26,255 (1957). 6. Hepp, O., Z. Ges. exptl . Med. , 99,709 (1936). 7. Jungnirkel, J. L., and F. T. Weiss, J . Polymer Sci., 49, 437 (1961). 8. Kammerer, H., W. Kern, and G. Heuser, J . Polymer Sci., 28,331 (1958). 9. Laidler, K. F., and K. E. Schuler, J . Chem. Phys., 17,851 (1949).

10. Philipp, H. J., J . Polymer Sci., 6,371 (1951). 11. Staverman, A. J., Kec. trav. china., 70, 344(1951); 12. Staverman, A. J., D. T. F. Pals, and Ch. A. Krussink, J. Polymer Sci., 23, 57

(1957). 13. Tung, L. H., J . PoEymer Sci., 32, 477 (1958). 14 Vaughan, M. F., J . Polynaer Sci., 33, 417 (1958).

ibid., 71, 623 (1952).

Synopsis A rapid dynamic osmotic pressure technique is described, which uses a high-speed

small-volume osmometer equipped with capillaries of small diameter to measure solvent transport rates across the membrane. Measurement of the osmotic pressure of a solution can be made in 10 to 15 min. Comparison of the dynamic results for molecular weight with those obtained by the static-equilibrium method indicates that the dynamic method affords a much closer approximation to the true number-average molecular weight than does the static method when membrane-permeable components are present in the sample.

R6sum6

On dkcrit une technique rapide de mesure dynamique de la pression osmotique. Cn osmomhtre de petit volume et de grande vitesse est equip4 de capillaires de petit dia- metre pour la rnesure des vitesses de transport du solvant b travers la membrane. La mesure de la presaion osmotique d'une solution peut &re faite en 10 b 15 minutes. La comparaison des r6sultats de la mbthode dynamique pour le poids mol6rulaire aver ceux obtenus par la mhthode statiqiie d'bquilibre indique que la mhthode dgnamique fournit line approximation plus voisine du poids mol6culaire moyen en nombre que la methode statique lorsque 1es composants dr la membrane permable sont prksents (inns l'echantil- lon.

Zusammenfassung Ein rasches dynaniisches Verfahren zur Messung des osmotischen Druckes wird

beschrieben. Ein Osmometer mit hoher Einstellgeschwindigkeit und kleinem Volumen

394 D. B. BRUSS AND F. 1%. STROSS

wird zur Messung des Losungsmitteltransportes durch die Membrane mit Kapillaren von kleinem Durchmesser versehen. Die hlessung des osmotischen Druckes einer Losung kann in 10 bis 15 Minuten ausgefiihrt werden. Ein Vergleich der Molekularge- wichtsergebnisse nach dem dynamischen Verfahren mit den nach der statischen Gleichge- wichtsmethode erhaltenen zeigt, dass die dynainische Mcthode im Falle der Anwesenheit permeationsfahiger Komponenten in der Probe eine vie1 bessere Anriaherung an den wirklichen Zahlmmittelwert des Molekulargewichts licfert als die statische Methode.

Received March 16, 1961

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A rapid dynamic method for osmotic pressure determinations