.
Topics in..
Chemical lnstrumentlrtion Edited by 5. Z. LEWIN. New York University, New York 3, N. Y.
These art&, most of whkh are to be cdribvted by puesl aulhors, are intended to serve the readem of lhia JOI~RNAL by calling auenlim, to new developments in the theory, design, or availability of chemical lnbwotmy instrumentation, m by presenting useful i n s i g h and explanations of tothd are of practical impwtance to those who w e , or teach the use of, modem i ~ t r u m l a t i c mand instrumental techniques.
XXVI. lnstrumentation for Osmometry Peter F. LOW a n d Frank Millich, Department of Chemistry, University of Missouri at Kansas City, Kansas City, Missouri 641 10
A variety of "osmomelers" are now available from a small number of inntrumen1 manufacturers. The appellation "osmometer" is used rather loosely to apply generally to s. more inclusive clzss of instruments which are designed to measure eolligative properties of solutions and include, for instance, instruments designed for cryoscometry and ebulliometry. On the other hand, instruments which fnnction on the basis of the phenomenon of osmosis are generally referred to as "membrane osmometers." The distinction is important because the two sub-classes generally are not applied to the same subjects of study. This article treats the subclasses separately, and includes coverage of theory and applications of the methods and a SUNey of commercially available instruments.
of higher conrentration (Fig. I). I f the flow of solvent is opposed, the diKusion tendency is appreciated as a pressure imbalance. knawrr as osmotic oresslrre.
The number-average moleculsr weight,
,
z N , Mi &",is:
7
="
,
x
.
This average is dis-
Ni
, = m
tinct from other averages which e m be cdcnlated or determined from the same polydispersity of Ni number of species of molecular weight Mi. For example, the weighbaverage molecular weight, M,, is rn
Z N , MiZ
given by
i= n
Bu= ,
feofure
to counteract the flow. Pure osmometry would thus consist of measurements of osmotic pressure and woold be performed with membrane type osmometers. Membrane osmometry is usually applied to soluble substances of molecular weights in the range 20,000 to 200,000 and further, with lessening accuracy, to 1,fl00,000, beyand which the osmotic effect becomes too small to measure. If the sample is of a polydispersity of molecular weights, then osmometry yields a colligative average value, a number-average molecular weight.' Thestudy of mechanisms of polymerizations-inclusive of biopolymers and synthetic molecules-requires an understanding of polydispersity. An index of this can be gained by comparing numberaverage molecular weight with other molecular weight averages (e.g., weightaverage molecular weight obtained fram light scatterng). There are few convenient, general physical or chemical methods that are alternative to membrane osmometry for number-average molecular weights in the range of 20,000 to 1,000,000. Therefore, osmometry is presently a vital tool to polymer chemistry.
Dr. Peter F. Lon obtoined his Ph.D. degree in phydcoi chemistry from the University o f Connecticut in 1956. He received his B.S. 119491 and MS. 119501 fram St. Lawrence University. Dr. Lott has worked os a research chemist for DuPont and the Pure Carbon Company. He previously taught a t the University of Mirsouri in Roiio, and a t St. John's Univerrity in Jamaico. New York. Dr. Lot1 is in charge of the analytical program a t the University o f Missouri a t Konror City, and is teaching both undergraduate and groduate onaiyticol chemirtry. His research interests lie in onaiyticol and phyricoi chemirtry. He hos published about 20 articles pertoining to the development of new methods o f onoiyrir and hor previovrly contributed orticier to "Topics in Chemical in.trumentotion."
Membrane Osmometers When two solutions of different cnncentrations are placed in contact with eaoh other, the spontaneous tendency is far equalization of the concentrations by mutual interdiffnsion. Should these two solutions be separated by a "porous" divider of such permeability that thesolute cannot pass through the barrier the solvent will diffuse from the compartment of lower solnte concentmlion to the compartment
I
Dr. Fronk Miiiich is an orrociote professor in the Polymer Chemistry division o f the Chemistry Department o f University of Mirrovri a t Kanrar City. in the doctoral curriculum in polymer chemistry, which he he presides over the founded ot U.M.K.C., graduate lecture and ioborotory courser devoted to instrumenfoi chorocterirotian o f polymer roiutionr. Dr. Miiiich received his education at City College o f New York 1B.S.. 19491, and Polytechnic institute o f Brooklyn 1M.S.. 1956; Ph.D., 19591. He held American Cancer Society post-doclord research feiiowrhips a t Combridge Univenily, Engimd, 11958-591, vnder Sir A. R. Todd, and ot the University of California, Berkeley (1959-601, vnder Dr. M. Calvin. He has conrvited for industry, ond hor Rve yeors o f industrial experience in research.
2 NiM; Volume 43, Number 3, March 1966
/
A1 91
Chemical instrumentation The freeenergy lowering per mnle of solvent, AF, caused by the presence of non-volatile solute is give11 in terms of the lowering of t h e equilibrium vapor p r e s a m from ps for the pure solvent to the value of p far the solution; bhus, AF = RT In p/pa
(1)
w.here R is the gas constant and T i i the absolute temperature. The free energy increase per mole of solvent, when i t is subjerted to an excess pressure, r, is AF = ?rV
(2)
where V is the volume of a. mole of solvent,.
assumption for liquids. At eqnilibrium, balance between these opposed phenomena is arhieved, and
?rV = -RT In p l p ,
(3)
A relation must be known between the vapor pressure and composit,ion of the solution in order to derive an expression in terms of molecular weight. Such a relation is provided by Raoult's Law which is valid only with cases of ideal mixing (i.e., in the absence of strong changes in solvent-solute interactions). I n many actual cases and especially in polymer solutions, Kaoult's Law behavior is approximated only in the limit of infinite dilution. With these limiting conditions:
plpo = N . . I ~ .=~ l-N.,s,t. ~
(4)
and
TV
=
-RT ln(1-N.,I.*)
E
R
T
N
(5)
where N . , I , ~is the mole fraction of solute and (in terms of n numher of moles) is The apequal to n..~udna.~nt. n.,l,.d proximittion of in(1 -A') EN,also iu valid in the limit oi infinite dilution, where the solute mole fraction is very much less than unity. As a consequence of these assumptions i t is required that, in general, osmotic pressure measurements are made far s series of finite concentrations and graphically extrapolated to zero concentration. With the reasonable approximat,ion in infinite dilution that V..I,,~ may be replaced by V.,l.ti,. the desired expression for osmotir pressure, extrapolated to infinite dihtion, is obtained:
+
RTm = RTc/Al ( 6 ) where m is molarity of solute in the wlution, c is concentration in grams of solute per liter of sulution, and .If is the sahlte molecular weight in grams per male. Illustrated in Figure 1 is a simple type of static usmometer (Welch Scientific Ca.). Here the solvent is retained in the beaker and thesolution is maintained in the chamber over the membrane. Flow of solvent from the beaker through the membrane (Continued on page A194)
A 192 / Journal of Chernicol Education
Chemical instrumentation
Figure 1 .
Welch
Scientific
Co.,
Osmomefer,
No. 0540A.
increases the volume of the solution which is reflected by s. rise of liquid in the narrow capillary tnbe until a su~ffieienthydrostatic head is produced to balance the osmotir pressure. Since the pores of the divider are nearly of molecular size and mixing of sulvent and solut,ion generally occurs by diffosion, t h e static method is inherently slow and t h e rate of approach to eqnilihrium is asymptotic. Complete eqnilibration may require over 24 hours per determination. A modified static osmometer useful for certain routine measurements is t,he Hellfritz osmometer, Figme 2. This instrument, supplied by Ced Sehleicher and Schoell Co., is mitable for certaill routine osmotic pressure measurements, particularly for molecular weights from about 20011 to 50,000. The instrument is supplied either ss a. single or double chambered osmomet,er, requires a sample volume of 211.5 ml, and has a comparison capillary for ease in reading of the osmotic pressnre. I t is suitable for investigation of membrane characteristics and may be operated from, -10 to ZOOT. M w h of the re..earrh in polymer chemistry requires measurements of the osmotir pressure of a large numher of solutions, as for exam& in the evaluation of cnncen-
time-saving factors are an important cansideration. An alternative to the static methods are the dynamic membrane osmometers, instrument8 in which the pressure differential existing between the solotion and solvent side of the membrane is sensed immediately and a corresponding counter pressore is applied to the solution side of the osmometer. Thus, with a minimum or negligible amount of solvent transport, a fim.1 pressure measurement
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Journal of Chemical Education
Figure 2.
Hellfritz Rapid Osmometer.
may be made as soon as the divider comes
to equilibrium with its environment and thermal eauilibrium is achieved for the system. depending
on
the
chemical
nature and mass of the divider, and the heat capacities of the thermostating system components, measurements on presently available instruments can he made in ametter of minutes. A beneficial by-product of the shorter operating-time feature in the dynamic method is the achievement of measuring truer (higher) osmotic pressures (thus, lower molecular weight valucq) than are apparently evident in static determinabions, with low molecular weight samples i e 15,000-60,000). Two causes contribute to smaller resultant pressures in the static method. The statio method permits some solvent trrtnsport and a volume increase of the solution which dilutes the original concentration. More important, the pore size of the memhrsnes, which partially determine the lower limit. of measureable molecular weight, is not uniformly single-valued. For this reason and others, a finite amount of low molecular weight material seeps across the membrane wall into the pure solvent. This causes a reduction in the vapor pressure in the pure solvent compartment, and an increase in the origins1 vapor pressure of thesolution compartment due to alessened concentration; it also produces a truncated polymer distribution of molecular weights in the solution of 8, polydispeme sample; that is, it produces an enrichment of the solution in the higher molecular weight constituents. Short periods of operating time reduce the amount of such sol,,te ~~~~~i~ osmometers based the (Conlinued on page 8196)
Chemical Instrumentation
Figure 3. Hollma.nen m o d e Ormometer.
,361 outomrtic
work a t Shell Development Ca. (1) are offered by both Hallikilinen Instrumentq as their Model 1361 osmometer (Fig. 3 ) and by Dohrmann Instruments Ca. as their Model M-100 osmometer (Fig. 4).
Figure 4.
Dohrmonn model M-100. Automatic
Olmometer.
A block diagram of the instruments is shown in Figure 5. I n this osmometer system the cell compartment consists of two cavities sepsrated by a. semi-perme* ble membrsne. The bottom of the sample half-cell is framed by a thin metal diaphragm which responds to changes in volume. Displacement of this berylliumcapper diaphragm due to solvent flow across the membrane is sensed as a change in electrical capacitance in a n oscillator circuit in which the diaphragm is one-half of s, capacitor in a tuned R.F. circuit. This change in the frequency of the oscillator circuit is amplified and fed into a servo mechanism. The servo motor, through appropriate gearing, drives a plummet in a, manometer tube, so as to adjust the solvent head to zero osmotic flow and return the pressure sensing diaphragm as well as the oscillator circuit t,o (Codlnucd on page A200)
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Journol of Chemical Education
Figure 5. View
of Hollikainen O m o m e t e r
cell
and oscillator. Recorder
its initial null balance state. The 0.0015 inch thick oressure sensine dia~hraemis spaval II.UIl'2 inch fronl thr statlonary elwt r d r by n,rsr,suf syrrthrtw mbiw. Thtls, under c.perating conditions, rhr diaphragm k displaced only s. fraction of one micro inch. To prevent erratic volume changes
.. . ..
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Journol of Chemical Education
Figure 6. Block diogram of Dohrmann/Shell Osmometer. during osmotic pressure messurementa, the temperature of the osmameter cell is regulated to keep the temperature change to less than 0.00l0C per minute. The over-all sensitivity of the servo system is such that i t operates on a 10-0 cm de-
flection a t the center of the diaphragm which corresponds to a cell volume change of about 10-8 microliter, and results in a change of only 0.01 em of head in the solvent manometer. Since the beryllium (Continuedon page AfO.9)
copper diaphragm is in contact with the sample i t can became corroded under eertuiu conditions, such as with acid solntioos. The semi-permeable membrane of the osmometer is quite rigidly supported between t,he concentric ridges of the two half cells, Figure 6. The instrument is capable of operating a t any temperahm from about 3.5 to 135°C and the adjustment of lemperature is continnous within this range. The instrnment requires a sample volwne of about 5-10 ml, and the osmotic pressure is read after a period of about T-10 minutes. The pressme is read directly to onrhu~tdredthof a rer~timeter over s I0 em range on a mechsniexl counter. The halancing servo mechanism ronaurrent,ly drives the pen on a built-in recorder which permils the operator to ohserve (.hebalmring pnwess and to aseerlain bhal equilibrium has heen reached. A series of dyrmmir osmometers are onered also by Meehmlah, Inr., Figure 7. In these osmometers an air bnbhle is trapped in a, capillary in the solvent side oi the osmometer membmne compartment. In operation, n light. source is focused on the upper meniscw of the air bubble, and a. phalacell is placed a t a right angle to the light beam. Fluid flow across the membraue acts to displace the airsolvent menisms. This displacement of the meniscus changes the refractive index in the path of the monitor beem and, irr turn, the intensity of [.he light reaching the photocell Figore 8. The deteelor cell analyses this chmge and sends a signal
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Journal o f Chemical Education
Figure 7.
Mechrolab Inc. membrane Ormometer, model 501.
which is amplified and trmsmitted to a servo system which adjusts the height of a hydrostatic solvent reservoir on s. 0-20 cm turn screw stack to restore the capillary air brtbble meniscus to its init,ial nlrll
balance position. The pressure is read directly to +0.01 cm on a mechanical digital counter on the face of the instnlmerit. A recorder out'put is also provided (Continued on p a p AAB04)
to chart the dynamics of the osmotic pressure measurements. With salutes that partially permeate through the membrane, the chert record permits extrapolation to pressure a t "zero time" and also indicates when the equilibrium pressure has been attained. The instruments are designed to operate in the range from 5 t o 135'C. A minimum of approximately 0.5-1 ml of sample is required for a. single determinntion. --SERVO
DRIVEN ELEVATOR h a OSMOTIC PRESSURE
SOLUTION
MEMBRANE
SOLVENT OPTICAL DETECTOR
Figure 8. Block diagram of optical detector system of Mechrolob, Inc. membrane Osmometer.
I n membrane osmorneters, organocolloid membranes are used which permlt the determination of molecular weights from below 20,000 up to 1 million. Membranes for osmotic oressure measurements in lheseinstrumentd may also be purchased from ArRo Lab, Inc., and Carl Schleicher and Srhnell. Inc. I n these instrument,^.
is important since i t governs the species which permeate through the membrane. The osmotic dividers, generally, may be constituted of either metal, ceramic, or, more commonly, of synthetic or animal tissue membranes. Since the latter are constructed t o give appropriate mechanical support and restraint to the membrane position so that the pressure differences between the fluids do not deform the membranes sufficiently to alter the usually small volume capacities of the fluid chamber. Membrane permeability toward nonelectrolytes is not solely a process of mechanical filtration based only on the sizes of the pores, i t can be appreciated that ad~arption phenomena also take place among the membrane, the solvent, and the solute. The flexible membranes are swollen by the liquid media, thus chemical affinities can be expected to play a role in the onse of transport of solute into or through the membranes. Accordingly, different solvents will swell flexible membranes t o various degrees. I n practice, i t is often necessary to slowly condition the membranes to a change of solvent, to degas the membrane in warm solvent and just prior to measurement, to contact memlrranes wilh rinse portions of the sample. A conditioning schedule whirh permits loo sudden s change in the membrane ("shocking" the membrane) will cause distortion and hnrkling of the membrane whirh completely destroys its (Conlin~~ed on page d206)
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Journal o f Chemical Education
utility. This is easily noticeable with anisotropic membranes (as often occurs in membrane sheet which was calendered in its manufacturing process), ass membrane of airnder emss section can be seen to b e a m e oval in shape. With an isotropic membrane, boo rapid a ronditioning srhednle to solvent narrows or collapses the eRwtive pore sise which may imlnde the pl.evious solvent and thereby alter the trsrrsoort ahnmrberisLies and uniformitv uf the membrane. Acrordirrgly, the selerbion and treatment of the rnemhrane is an important concern i u the experimentd measurements and effectively determines l.he lower limil of meas~trable moleeulrr weights. It is also a cornll:~rythat present instrumentation is capable of extension tr, lower molecular weight xnmples simply Ihrough improvemeut ill the permeability chararleristirs of memhrane msterisls.
Other Applications of Membrane Osmomelry Typical ertrapolatio~~suf membrane mmnmetry data f n m dilution series 01 two samples of R. non-electrolyte polymer is shown i u Fig. 9. The intercepts yield t,he number-average molecular weights for the two samples; the positive slopes of bath curves reveal the concentration dependence af osmotic pressure. The latter r h l s contains vnlnable informalion. A steep m d upward-concave curve is obtained for sulr~tiorrsin which the solvent, is especially effective in dissolving the polymer, and expanding the intra-twined, m a a ~ l i k eeonfarmatior of a flexible maerarnolewle to or:eupy a large regim of the medirtm. Conversely, a linear u v v e with sew slope may be ohtsirred for snlutions
A206 / Journal o f Chemicol Education
of the same polymer in w-hich the ROIVCII~. polymer solute interactions are nil. (By n jidicious choice of sulvent one may exploit the lslter fart tu minimize error or passihly avoid extrapolation.)? Theoretical interpretations exist converning the signifirnure of the concerltr;ttion dependet>ries. Thwe attribute the maguitude of the xlapes to entropy factors; specifically, to the dissimilarity it, sise and ~ : d o r m a t i o n a lpnsiihilities between the solvent and polymerir aulnte m o l e c i h : and to enthalpy efferts of molenllar intcvwtiotm. Serial dilution dnln are valnable i l l nndher way. Aggregatioll or dissrwiatir,~, ~,heuomenaovciwring over the rourenlr:tt i r r u range being s t i l d i ~ dmay he detected :md roufirmed. This may he revealed wheu lhe molertrlur weights whivh are ralcdnted from extrapolation of d:tln taken a t high co~~centlation nrefntlnd to l,e greater (sometimes by whole nnmher rnulliples) than the molenllar weights olrlnined by erlrapalatiun of data taken :,I. low nxrcentration where R high polymer has dissoriitted into polymeric suh- ini its. .4n example
