David R. Smith1 I Polymer Molecular Weight Distribution

M a n y undergraduate physical chemistry

and John W. Raymonda2 University of Arizona

Tucson, 85721

laboratory texts contain an experiment on the deter- mination of thc molecular weight of a high polymer either by osmotic pressure or intrinsic viscosity me* surements (1) . However, to these authors' knowledge, none of the presently available experiments makes clear the relationships between the average molecular weights determined by different methods. We have devei- oped an experiment in which the viscosity average (M,) and number average (M,) molecular weights arc determined for samples of a given polymer; the factor relating these may then be calculated and compared with theory. We feel that the student obtains a better feeling for molecular weight distributions in polymers by being required to consider explicitly thc influence of the distribution upon the magnitudes of the average molecular weights than is possible from a determination of just a single kind of average weight. I t would, of course, be even better if we could have the students determine the weight average (M,) molecular weight also, but the necessary light scattering measurements are beyond the scope of the usual undergraduate's abilities and require apparatus not generally available as well.

The theory of polymer molecular weight statistics has been treated by Flory (2) and need not be repeated here. We have found the presentation in reference ( I b ) excellent for our purposes. Supplementary refer- ence material for undergraduates can be found in THIS

JOURNAL (3,4). Materials, Apparatus, and Procedures

All measurements are done on polyvinyl alcohol (PVOH). This polymer has the advantage of being readily soluble in water; thus the need for handling large quantities of organic solvents such as toluene, used as solvent in work on polystyrene ( l a ) , is elimi- nated. I t has the disadvantage that concentrated solutions are prone to form, rendering quantitative transfers difficult. We have used Elvanolm 71-30,3 a completely hydrolyzed preparation with M , of about 60,000. The apparatus and procedures employed are those described in reference ( l b ) except for certain modifications which we now describe.

A stock solution of concentration no greater thad 16 g/l is made by the student. It is best to prepare this well in advance of the planned working days since the

Present address: Department of Chemistry, University of Oregon, Eugene, Ore. 97405.

To whom inquiries should be directed. Present address: Di- visionof Physics, Rm 1057, National ResearehCouncil of Canada, 100 Sussex Dr., Ottawa, Ontario KIA OR6, Canada.

We thank Dr. A. Beresniewiea of E. I. Du Pont de Nemours and Co. for providing generous samples of several PVOH samples, including tho Elvan& 71-30.

A n undergraduate physical

chemistry experiment

PVOH should be dissolved slowly with stirring and gentle heating. The PVOH is added to somewhat less than 1 1 of distilled water; the solution is transferred quantitatively to a volumetric flask and the volume is carefully brought up to 11.

For the viscosity determinations, we employ the dilution type viscometer divised by Ubbelohde (5 ) . We did not obtain these commercially; rather, we had standard Ostwald-Fenske type viscometers altered in the departmental glass shop. A scale drawing of a typical instrument is shown in Figure 1. This viscom- eter has the advantage that the pressure head driving the flow is independent of the total amount of solution being used, as long as the solution does not rest above the bottom of thc capillary at quiescence. To make a run, the operator closes tube A and sucks solution into B with an aspirator bulb until it has risen above the upper fiduciary mark F1. Then B is held closed and A is opened. Now the solution below the capillary can return to the ballast bulb E. The pressure head now is always measured from the bottom of the capillary.

Figure 1. Scale drawing of UbSelohde vireometer. All distances in cm. dr = 0.6, dB = 0.8, dc = 1 . 8 . d ~ = 5.0. F, and F2 are the flduciory marks. To operate, A is closed and solution is drawn by ruction into B until it is above F,, Then B is closed and A is opened. The solution below the bulb D drops bock into reservoir E. Told volume of solution must be such that level in tuba B it below D at the end of a run. E holds about 50 mi in this model.

Volume 49, Number 8, August 1972 / 577

The operator releases B and times the passage of the solution from F, to Fz as in the usual viscosity mea- surement.

Since flow times are independent of the volume of solutions, measurements a t a series of concentrations can be made by successive dilutions right in the vis- cometer. This has the advantages of speed and of alleviating problems connected with cleaning the vis- cometer when different solutions are introduced. As a result, our students have been able to do measurements of up to six concentrations in the time formerly required for three. Concentrations approaching zero are espe- cially easy to investigate simply by adding successive pipets full of solvent. The student can collect enough data that extrapolation of rl,,/c (lb) to its limit. at c = 0 can be made with confidence. Some sample data collected by students is shown in Figure 2.

0 1 2 3 * . I 7 B 9 CONC. IN gml / lWml. -

Figure 2. . Some typical vixosity results found by students for unclewed Elvonol@ 71-30. The upper line is q.& versus c and the low'er, Rot line is l /c In &. The liner ore determined by least squoros usingonly the data of the authors ID. R. Smith). The liner extrapolate to In1 = 0.834 ( M a = 60,000) and [v] = 0.848 (Ml = 60,0001.

Viscometers having capillary sizes4 designated as 50 and 100 were tried. The flow times vary from about 300 sec for water to 500 sec for polymer stock in the size 50. This is well in excess of the recommended 100 sec (6) and is, in fact, so long as to be inconvenient. Flow times for the size 100 were in the 60-100-see range, shorter than recommended. However, results obtained \*ith both sizes agreed to within experimental error.

The osmometry was carried out using a Zimm-lllyer- son type osmometer similar to that shown in reference (lb). It was found satisfactory to use retaining plates, bolts, and nuts all of brass instead of the recommended stainless steel, even though aqueous solutions were being studied. Different metals cannot be used in the same assembly because corrosion quickly occurs due to electrolysis effects.

Cellulose membranes were employed. Fresh mem- branes were conditioned by boiling in distilled water for 1 hr; membranes once conditioned were never allowed to dry out.

Procedures followed reference (1 b) exactly. Students were given the choice of using the static method or the half-sum method. Comparable results were obtained by both methods.

Data and Calculations

The PVOH normally polymerizes in the so-called ''head-to-tail" fashion: -CH2-CHOH-CH2-

These sizes are those specified by Van Waters and Rogers for their Cannon-Fenske viscometers. This vendor also can supply an Uhhelohde-type viscometer in similar sizes.

CHOH-. However, a certain percentage of "head- to-head" linkages are also present: -CH,-CHOH- CHOH-CH2-. Following the procedures of refer- ence (lb), these were cleaved with KI04, and M , and M , were determined for both uncleaved and cleaved polymer. The relationship between M , and M , for PVOH having "the most probable distribution" of molecular weights is (7)

M , / M , = 1.89 (1)

Values around 1.9 are typically found by the students for the uncleaved polymer, in striking agreement with the literature. However, for the cleaved polymer, much smaller values are found, sometimes even less than 1. We attribute this to permeation of the membrane by the lower molecular weight species. This problem is nearly always present, even for heavy polymers, un- less an extremely small-pore membrane is used. It seems reasonable that the problem would be much more severe for the degraded polymer. The expected result is that osmotic pressures which are too low are observed, leading one to calculate an M , which is too high. We are searching for a suitable membrane for use with low molecular weight polymers in the hope that the student can measure M J M , accurately for both uncleaved and cleaved polymer. If the occurrence of "head-to-head" linkages is random in the original polymer, the values of M,/M, should be equal for cleaved and uncleaved samples. Suggested Research Project for Interested Students

Two partnerships have undertaken to fractionate the uncleaved Elvanole 71-30 in order: (1) to verify the stated molecular weight distribution supplied with the sample and (2) to observe the decrease of M,/M, to- wards 1 that should occur as the molecular weight dis- tribution is narrowed by measurement of both M , and M , for all the fractions. Fractionation was achieved by adding isopropanol (iPOH) to an aqueous PVOH solution causing precipitation of successively lower molecular weight polymer as the iPOH content of the solvent was increased. Fractions vere separated by decantation and washing. M , and M , were measured for each fraction as described above; the weight con- centrations of the solutions were determined by aeigh- ing the polymer which remained after evaporating aliquots to dryness.

The authors will be happy to provide further pro- cedural details and sample data to interested persons. Acknowledgment

The authors acknowledge fruitful conversations with Professors James E. Mulvaney and Carl S. Marvel, as well as the assistance of Professor Marvel in obtain- ing PVOH samples from Du Pont. We thank undergraduates Fern Wood, Julie Ramsey, Joseph Tadano, and William Roberts for permission to repro- duce their data. Literature Cited (1) For examplesee (a) DANIEGB. F . WILLIAMS, J. W., BENDER, P.. ALBERTI,

R. A,. CORNWELL, C. D.. AND HARRIMAN. J. E.. "Ex~eriments.1 Physi- cal Chemistry" (7th Ed.) MoGraw-Hill Book Co.. Ine.. New York, 1970, gp. 329. 335; ( b ) Saosmas~. D.. m o G ~ n ~ m o , C. . "Expen- mentain Physichl Chemistry" (2nd Ed.) MeGraw-Hill Book Co.. Inc.. New York, 1967, pp. 272, 278.

(2) F~onr. PAUL J.. "Principles of Polymer Chemistrg;' Cornell University Press, Ithaca. New Yark, 1953, Chap. VII.

(3) RODIN, A,, J. CHEM. EDUC., 46, 595 (1969). (4) P u d r . S. R.. J. C R ~ M . Eouc.. 24, 199 (1947). (5) See BIL~MerEB. F. W.. "Textbook of Polymer Soienoe," John Wilev 61

Sona. Ino, New York. 1962. D. 80. (6) Br~bueren, o p . cil., p. 81. (7) FLOE?, P. S., m n LEUTNEB, F. S., J . PoLymeiSci., 3,880 (1948); 5, 267

(1950).

578 / Journal o f Chemical Education