Topics in..
.
Chemical Instrumentation
I
feature
Edited by S. Z. LEWIN, New York University, New York 3, N.Y. Gel permeat,ion chmmaingrspl,y is ideally mited for the rapid deberminstirm of the moleeulm weight distribnl.ions and molen~larweigh1 averages of polymers. The ehmmatngraphie system rrumt first., however, he ealihrated wiLh rclai,ively
These articles, most of which are to be contributed by guest authors, are intended to serve Me readers of this Jormrrn~by calling attentima to new developments i n the theoy, design, or availability of chemical laboratory instrumentation, or by presenting useful insighls and explanations of topics that are of p~UCtkal importance to those who use, or teach Me use of, modern instrumentation and instrumental tech,nipas.
XXIX. Gel Permeation ChromatographyPart Two Jack Cares, Mobil Chemicol Company, Metuchen, N.I. Average Molecular Weights of Polymers Polymers, hot,h natural and synlbelic, contain molecules having a distribution of different m d e c u l a aim6 rst,her than one molecular size as is the cme for low molecular weight monomerio substances. Most of the physical methods generally used for the measurement of molecular weight such as light scat,tering, osmometry, viscometry, elyoscopy, ebulliometry, sedimentation, and cenlrifogstion yield average values. The Lwn molecnlw-r weight averages that are most, eommortly calculated and which can he determined by the gel permeation ehrnmatugmphia method are the number-average moleenlitr and the weight-average moweight lecular weight ( M , ) . Tho weight average is alwayseil,her greater than or equal to 1.lic number average; tho oqrmlity exists only idedly in the ease of monodisperse polymers, i.e., those in which all of the molecules are of a single molecular weighl. The numher-average molecular weighl is defined by the eqnathm:
(an)
Figure 8.
Figure 7. Relative locotionr of Mx and on a distribution curve.
M.,
molccr~lasweight disb~ihtllioncurve fur polydisporso polymer are shown in Irigtwr 7. Tho ratio %/A?", commrn~ly rallod t,he "heterogeneity f2~elor," is wed la describe bhe degree of polydispersity of a polymer, i.e., tho broadness or spread of it5 moleculxr weight dist,rib~t,ion~ curve. The larger t,he value of M A ilre hroader will he its molce,dsr weight distrihntion.
Table 1.
Typical colibrafion curve.
mrrnodisperse polymer^ whose average molemlar sizes (or moleat~larweighis) are known. The molecrdar weights 01. sizes of these "standards" are plol.t,ed xgtgai~isl, t,heir peak elrkion volmnes ohtained from their gel permeation ehn,mat*,grams. A typical calibration curve for polystyrene is given in Figure 8. While it is common pracliae to refer to "chain length" when desrrihing the size of a polymer moleet~le in s l i i t is probably more correct to w e t,hc rnrlilcs of gtralion of the miled pniymcr molecde since this is t,he elomst approximation lo the real effective size of s w h a. molecule i l l s non-ideal solution. The radins of gymtion, S, is defined a s the rontrmeatl-sqnaro distance of t,he elements of s. polymer chain from its oent,er of gravity and can be enlculated from the intrinsic visr:osity of the
Commercially Available Polystyrene Standards
while t,he weightaverage moleculat. weighl is defined by t.he e q ~ a i i o n : s-102 S-103 S-10s S-109 8-114 5-1159 NBS-705 PCC 860 I'CC 41 1 PCC 160
(3) where
W Wi
.
= l.otal woieht of oolvmer. "
weight fraction of a givcn species, i. Ni = number of molcs of each speeics, =
PCC
i
Mi
=
molecular weight of each specics, i.
The reliti.ive loeations nf
~ 7and % J?~ ou %:
o m
I'CC 0510 PCC 0198 I'CC 0103 "
11 = Uow Chemical Co., Midland, hliehigan. N = Nation$ Bureau of Standards, Washington, U. C. 1' = Pressttro Chcmicnl Cr,., Pil.tshorgh, Pa.
(('onlinuerl on pagc A6%6)
Volume 43, Number 8, August 1966
/
A625
polymer. Far linear polymeis the meansquare end-to-end distance, I?,is related to the radios of gyration: R2 = 6 9 . The polystyrene standards that were used in the constn~ct.ionuf the calibration curve are listed in Table 1 together with their molecular weight averages and calc~~lated molecular sizes. At present, it is common practice to use a polystyrene calibration m e for the determination of molecular weight averages of other polymers. This is due to the fact that polystyrene is the only polymer far which there are several mmmercially available standard samples. Experiment,ally determined correction fact,ors are used to convert from polystyrene to other polymers. Many attempts have also been mzdde to mathematiodly estimate such conversion factors. Approaches such as these are valid only if the calibre tion curve for the polymer being studied has the same ~ h a p eas the curve constructed with polystyrene standards and runs parallel to it throughout the range of interest. This is nsuallv not the ease!
same polymeric species as the polymers being examined. Since polystyrene is the only polymer for which standards are mmmercially wailable, other polymer standards must be prepared, as needed, either by one of the classical fractionat,ion m e t h o d ~ f r a c t i o n a lprecipitation or extraction, elution or precipitation ohmmatogrephy, or turbidimetric titrationor by gel permeation chromatographic fractionation itself. An automatic preparative-scale gel permeation chromate graph is commercially available for this purpoue, and is described later in this paper. After polymer fractions having narrow molecular weight distributions have been prepared, i t is necessary to oharacteriae them, i.e., determine their weighbaverage and number-rtverage moleculsr weights and heterogeneity factors. One can determine weigh6average molecul~r weights with light scattering or equilibrium ultracentrifugation while number-average molecular weight can bedetermined with cryosmpy, ebulliometry, or osmometry. I n many cases it is also possible to correlate molecular weight with such properties as sedimentation and diffusion rates, melt viscosity, or intrinsic viscosity. With a calibration c u y e in h a ~ ~ idt, is possible to determine Mu and M. for a polymer. The sample whose molecular weight averages are to be determined, is passed through the gel permeation column and its chromatogram recorded. The chromatographic curve is then divided into vertical segments of equal elution volume as shown in Figure 9. The height of each segment together with its carresponding averagemolenllar size, obtained from the calibration curve, are then used to calculate 2- and A, for the polymer. I t is convenient to arrange the data in t,zbular form as shown in Table 2 for ease in carrying out the summing and averaging processes. A factor Q, whioh represents the number oI molecular weight units equivalent to one angstrom of ef(Conlinued on page A8?28)
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Journal of Chemical Education
per cent (column 4, Table 2) is calcolated so that n normnlised integml disll.iln~(.iou
Figure
10.
Normalized
integral
distribution
curve.
Mi Table 2.
Sample Calculation of
M,.a n d M ,
-
.I ' -
= AiQ
(5)
I Z'M,N, - XCalumn 2 (Table 2) - Xolurnn 6 (Table 2 )
(6)
A'
=
1V
0 L.MiNi
= ZCol~lrnn7 (Table 2)
ZCohmrr 2 (Table 2)
Hi = height of s given segment, (arbh r y units). A c = nvorrtge angst,rom size of the SPRrneut. Mi = average mul. wt. uf the segment,. N , = mmher of partrticlesrepresented by the segment. 0 = molecular weight m t i t u per angstrom. (Approx. 41 for polystyrene) ( f ' o n l i n l ~ non l page Afi.90)
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Journal of Chemical Education
A,
A, 1%
=
number-average molemlilr size
= weight-average molec~darsize = weight average moleculxr weight
M,.= weight-average rnolecl~lar.weight, Solvents Solvents for gel permextion chromatograph) must meet certaiu requirements. Ideally, the eluting solvent and the gel should be similar in polarity lo prevent partitioning of the sample between two unlike phases. I n actual practice, it is often necessary to use 8, highly palm solvent in order to he able to dissulve the sample. This does not seem to present any Table 3.
problems in man," cases, especially where only s fract,ioustim of the sample is desired, without calcdation of molecular weights. Also, adsorptive effects of polar samples, small as they are when a polystyrene gel is used, are completely eliminated when the polarity uf t,he eluting solvent is high. The sdvent s h d d also have a. low viscosily and a relatively high boiling poinl and shodd not dissolve, react with, or degrade the cohmn parking. While compatibility of the solvent with the sample and the gel are important, compatibility of t,he solvent with the det,eetion system must also be considered. For example, if one uses s, refractrlmeter
Solvents Used for Gel Permeation Chromatography
Solvent
Refraetive indexa
Benzene 5. Perrhloroethylene 6. ma-Cresol i. 1)imethylsulfoxide 8 . N-methvl~vrrolidone 3 . o-Chloro~hknol 10. Chloroform 11. Nethvlene chloride 12. Carbon tetrachloride 13. I)imethylformsmide 14. Uimethylaeetamid~ 15. Tolnene 4.
Vis cosity,' cp
Be
SP." gr.
for detectiou and estimal.ion of (he sample
as i t emerges from the enlumn, then the solvent most have 3 refractive index that is different from that of the sample. If continuous monitoring of ultraviolet absorption is employed, theu the ellvent, should be one that is trauspsrent, a t the wavelength being used. The greater the difference between solvent and sample in the value of the physical property heing measured, the greater will be the sensitivit,y of thedetector. %me of the solvents thet have been found to be compatible wit,l~polystyrene gels are given in Table 3 a l m g with physical properties of interest in gel permeation work. This list is not intended to be exhaustive. Solvents that are generally incompatible include water, awtone, many alcohols, and mosl carbonylie acids. Some of the p d g m a s that have been st,udied with gel permeatior chromatagrap11.v are listed in Table 4. Soitshle solvents also n w given whrrever dxia :we available. Table 4. Polymers Studied b y Permeation Chromatography Polymer
atwe\ Copolyethwdiol Epoxy resms Ethylene o r o ~ v l e n e
Gel
Solvenl(~)"
1 1, 8 2. 3
Pol~butene Polyeaprolaciam Polyoarlr,nstei Polyet,hers Polyethylene Polyglyrnls ~oijrisoprene Polypropylene Pr,lysl.yrene
3 2, 3 1, 2, B, 4, ti, S, 11, 1:3, 1.7 1, 8, 1:; 1, 3, 13 13 13 2, 3, 8, 13, 1.5
Varnishes X'ariuus waxes Poly(s1yrene-mnleic anhvdride) Polyphthslsmide Polyethylene oxideetlrylenimine Polyepoxypropane Palv(ethvler,amaleic
8, 13, 15
I, 2, 3, 13, I 5 3, 8, 13
a Solvent nnmbers are the same a- those used in Table 3.
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Commercially Available Equipment Waters Associates (fil Fountain St., Frsmingham, Mass.) is, s t present, the only msrmfaeturer of mmplet,e gel permeation ehronralographs. They also offer a complete line of columns and accessories for use with their instmment and other liquid ehmmatographs. Many of the accessories can he readily adapted for conversion of other exi~tingliquid chromatographic eq~tipmentfor application to the
Figure 12.
Figure 1 I . Woters M o d e l 200 gel permeation chramotogroph q u i p p e d with automatic injector m d collection unit.
Woters model 200 g e l permeation ch romdogroph Row diagram.
gel permestion method. Following is a brief survey of the equipment that is available. The Waters analytical-scale gel permeation chromatograph (model 200, 116,000), shown in Pixwe 11, is designed to fractianat,e sampl& in the milligram range, accepting up to 2 ml of a '/s to I/,% solut,ion of the sample. I n cases where fractinnst,ion is being carried ont primwily fm the pnrposo of chs;racteriaat,ian of collected fractions by other teehniqaes, it. is pssihle to either operate the existing in. o.d. columns mnder overload conditions or to replace t h e e columns
with larger columns. The sample size is increased by a factor proportional to the ratio of the cmas-sectional areas uf the columns. Figme 12 is a flow diagram of the Wst,em unit. Solvent is pumped from a reservoir through a heater to degas the solvent, and then thrortgh a filter to a mixing chamber. The mixing chamber serves to damp out the pumping p~dsations and to prevent sudden changes in solvent properties due tu differences between batchcr. of solvent that are added to the reservoir. The solvent is then split into two streams, one serving as a sample stream and the other as a reference. A ~miqnecdumn switching dual gsug mnltipart valve is set to direct the sample Row t,hruugh the desired set of mh~mns. I n this way, two different sets of columns, having different maximum pore sizes, enable one to examine samples having widely different moleeulnr weight distributions. The sampling valve arrangement is similar to that which ii ilhistrated in Fignro 5. When the sample is ready to be placed on the colunnt, the srvmpling valve is ttlrned 90a, placing the 2 ml sample loop in t,he solvent stream. The sample is t,hen carried to the colomn where it is fractioneted. EtRoents from the coh~mns pass through the .ample and reference cells of a differential refraetometer which is capable of detecting a differencein refractive index of ooe part in ten million. The solvent that pwws thmnglr the reference cell is recycled. The sample stream pmses to x 5 rnl syphou and then to a fraction collector. When each 6 ml fraction empties fwm the syphon a light beam through the syphon tuhe is interrupted and a pulse is rerorded or, the recorder chart. In this manner, the ehtion vohme is aotamatirnlly recorded on $.he chart. Aceessuries for the chmmatogrzph include an automatic injectiou system (53500) which makes it posaihle to sna1y.e up to sir samples in atr autrrnatic, unattended fashion, a frarriun collector (Warner-Chilrott, modified for GPC, 81000) capable of collecting up to 150 f~.actionsautomatirally, and an aoxilliary pumping system (52300) rhich allows for
rapid solvent changeover. Columns are available having maximum porosities ranging approximately from 30 to 1,000,000 Oangstroms. Prices for columns vary from 8135 to $235 depending upon the resolutiou desired. Waters also oBers the column packing alone under the name "Styragel" far 30 cents per ml. The Waters "Ana-Prep" gel permeation chromatograph (825,000) is actually two chromatographs in one. With this &Nment it is possible to do both analytical and ~ r e ~ a r a t i vwork. e The analvticd part & e&entially the same as in the ~jladel 200 chromalograph. I t is coupled, trr gether with the preparative seotion, to the differential refractometer via a selector valve. Figure 13 is an operational diagram of t,he instnment. The preparative section employs 2.4 in. diameter columns eepa.ble of handling samples of up to 100 ml of 0.5% sample if the are operated in an overloaded condition. It has an automatic sampling syst,em that is fed from a 10 gal resemior. If only one eight foot preparsbive w h m n is used, the instrument will fractionahe up to thirty-six samples in a twenty-lorn hour period. There are many types of multipart valves that can be used for both sampling and column switching. The cost of such ~~
Figure 13.
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Journal of Chemical Educofion
-~
Waters Am-Prep operational diagram.
valves ranges from $100 ta $500 depending upon eomplcxity and mtlterirsls of construction. Stainless steel aud Teflon are recommended for w e with the organic solvents employed in gel permeation chromatography. Some of the avrtila,bl.ble valves ran be heated while others cannot. Naturally, the ability to be heated raises its price. A few of the manufacturers of multipart valves are given here. Instrument Co,,
8030 oeorgis .kve.
sher
mi 20810
~ e o k m a ninstrumenta, he.
~~~P,I~,";p";d~&&4
:Houston %,Bg::&27. & Tersa circle seal products
co. lnc.
2181 East Foothill ~ l v d . ' g1107
Consolidated Eleotrod~namiorC o w Analytical $ Control Uiviaion 360 sierra x a d r e villa Pas"de"a. Calif. G . Xi-. Ud,I Co.. Ino. ~&~,e~,S~02809
F & M Scientific Corp. D i m . of Hedett-Paekard Corp. Route 41 and Starr Rd. v""dale'
(Continued on page dfl36)
Loenoo. Ioe.
2092 N. Lincoln Ave.
Altadena. Cdif. 91002 lllatronie Instrument Co, 132 IGng Rd.
New Castle, Delaware
process variables an t,hese properties. While measurements of bulk properties may be related to the average molecular weight of s. polymer, they do not give any real indication of the tnie shape af the molecular reight distribution. For example, t,wo experimental polystyrene samples were h u n d to have the following average molecdar weights:
MlerO-Tek Instrument., 1na. P. 0.Ror 15409 Ihton Rouge, La. Perkin-Elmer C o w 870 Main Ace. Nonvalk, c o n n . Re~ublioMfa. Co. 35685 nrookphrk Rd. Cleveland 35. Ohio
These data would lead one to believe that the polystyrene samples have relatively narrow molecular weight dislrihutions and
Wilkena Instrument & Research. In"
2730 miteh hell Dr. l h x 313
Valnut Creek, Calif.
\!'oh1 nenius Institute, Inc. 4206 North Brohdrvsy Chicago 13, Illinois
Applications An area of research that has profited greatly through the use of gel permeation chromatography is that of polymer process development. Here, the usual aim is that of producing, in large quantities, 8. polymer having properties closely approximating those of either a commercially mailable polymer or one which has been prepared on a small scale in the lshoratory. The classical approach to this problem has been to measure as many physical properties as possible for a sample of the bulk polymer whose properties are to he matched and then to study the effects of
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Figure 14. Gel permeation polystyrenes1 and I1
chromatogromr
could he used to calibrate equipment ta be nsed for measurement of molecular weights of polymers. The gel permeation chromatograms of both of these polymers (Fig. 14) not only shows that each has a distribution that is broader than expected, hut also that each has two peaks in its distribution. This illustrates a uniqne advantage in the use of gel permeation chromatography. One e m actually see what the shape of the distribution is directly rather than having to guess s t it by examination of the data, obtained for the hulk polymer. The speed with which 8. gel permeation chromatogram can be obtained makes i t ideal for application to quality control of polymer processes. This method may lead not only to the early detection of poor, o&&,pecifieation prodnetion batches, but d s o may give some indication of wherein the trouble mieht lie. The
blending operations one would have a rapid method for ascertaining whether the product contains t,he proper proportions of the constituents and whether extensive degradation has occurred durrng the blending. A question that often arises from stndies of copolymerization of two or more monomers is that of whether one has produced a true copolymer or a mixtnre of homopolymers. It is possible that when homopolymers are formed from a mixture of monomers, that these homopolymers will have different average molecular weights. (Continued on page A 6 W
If such is the case, then gel permeation chromatography would detect their presence and, on a preptlrat,ive scale, could offer s. means of separating and isolating each of the components for further charsct.erisation by other physical and chemical mebhods. The analysis and fractionalion of organic coatings is an area which shows promise hut has been almost completely overlooked by gel permeation chromatographers. A brief deseript,ion h a . been given by C. A. Lmchesi (see Bibliography). The coatings chemist has always coveted his colleagues in other chemical areas for the separation techniques applicable in the ot,her areas. Certainly, gas chromatosra~hvoffers a means of exammning salve& in k i n g s while pyrolytic gas chromatography may reveal the identity of the nmnomerr that have been nsed in the mmufscture of some resins. However, since heating and vaporization of the sample are involved in the gas chromatographic techniques, the coating material very often undergoes unpredictable changes which produce results that are difficult to interpret; many components of organic coating materials are not SUEeiently volatile to pass through a gas ehromstogreph. Since gel permeation chromatography separat,e~solvent caat,ing systems solely on t,he hayis of effective molecular size, and without prior volatilization, it offers the coatings chemist a "handle" that he has never had available to him for the fractionation of unpigmented coating systems. Since molecular sizes of the various components of a coat-
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Journol of Chemical Education
ing are umally different (resins, solvents, antioxidants, plasticizers, etc.) there is no need to carry out a preliminary separation to remove undesired components. For example, if information is desired regarding the nature of the molecular weight distribution of the resin in a costing, present methods require that the solvent and other additives he removed first. Gel permeation ehromatogrrtphic examination of many coatings can he carried out on the entire unpigmentad coating. This approach, consequently, could yield more information about both the molecular weight and the composition of a coating than other techniques and in a much shorter time. Preparative-scale gel permealion chromatography provides R. means of preparing large quantities of polymer fractions havine.. verv. narrow molecular weieht d i ~ r v i l ~ ~ tai. o r'lYae~vfrw T N W :ma ~ u+itd for d i l m ~ i o ! t s I~I ~i V: ~ ~ t ~ i I w w d1wr11wi~yrl
enable the polymer chemist to study the effectsof polymer stmetitre and molecular weight on physical properties. Having almost monodisnerse nalvmer fractions. he
ment around available polymers whose campositions are not completely clear. Correlation of properties with composition could be put on a. more scientific and predictable basis than is the case today. The avaihhility of polystyrene gels
having low permeability limits now extend the advant.ages of gel permeation chromatography to non-polymeric substances. Same monomeric substances have already been examined. Included in t,he list of srtch srthstances are lubricants, fatty acids, glycols, and low molecular weight tars. Gel permeation chromatography could be applied as a. separation tool to non-polymeric substances wherever there is a molecdar size difference. I t would provide a great advantage where sample polarity complicates other chromatographic methods. Gel permeation may provide a means for studying fundamental properties of molemles in solution. For example, measnrement of moleoular size in more than one solvent, having different solvating properties, may yield an insight into the type of coiling that is present in a polymer chain. GPC data obtained in a "theta" solvent (a substance which is a poor solvent for a polymer, i.e., doesnot solvate the polymer) would he valoable here. Studies of this type might show the extent of hydrogen bonding ss reflected in the effective size of a molecule. While very little work of this type has been done, this is certainly s fertile area for future resemch. There is no doubt that the gel permeation chromatographic technique will continue to he extended to different kinds of substances in many different chemical disciplines. A bibliography b w been included a t the end of this paper which includes most of
(Continued m page A64O)
the applications of GPC that have been published. However, since most of the commercially manufactured instruments are in indust,rial laboratories, a great deal of literatore remains unpublished due to its proprietary nature. Pharmacia Fine Chemicals, Inc. (800 Centennial Ave., Piscataway, N. J. 08854) a manufacturer of dexbran gel filtration materials, periodically issues literature abstract cards. These references, however, are primarily in t.he biomedical field and deal mostly with aqueous systems and the non-rigid dextran gels. There are some references in this literature collection of a general nature that are of interest to those working with non-aqueous systems and utilizing rigid, eross-linked polystyrene gels.
Conclusion I t is evident that gel permeation chromatography has emerged from its artistic cradle to became a valnable fractionation and characterization technique. One can liken the present status of gel permeation chromatography to t,he status of gas chromatography just a short time ago. I t has been only a few years since the chemical industry was provided with an analytical technique (gas chromatography) which seemed t,o produoe "too much" data . . . more than one could cope with Eonyeniently. The chemist was suddenly awakened to the revelation that his "pure" chemical3 were, in fact, not so pure; his standards for purity had become obsolete. He had became a part of a new era in chemical analysis. I t is in such an atmosphere thal, one fin& gel permeation
A640 / Journal of Chemical Education
chromatography today, ready to he used hy and to be useful to anyone willing to take advantage of its unhav&ed cap%hilities in areas virgin to this technique. Future improvements in gel permeation chromatography will probably include: 1. New, more versatile gel materials having compatibility with a wider vmiety of solvents and polymers. These would make ppossihle the examination of polymers whose extreme insolubility presently prevent their fractionation by gel permeat,ion chromatography. Such polymers include the fluorocarbon polymers and crosslinked polymer gel. 2. Instrument,al refinement.? which would permit completely automatic onattended operation. Also included would be an electronic integration system coupled directly to s. digital computer and auboplotter possibly by punched or magnetic tape. 3. Scale-up of the gel permeation chromatograph would he the ultimate in development of the equipment. Frsetionation of materials on a. Imze (oossiblv
a homogeneous flow through large d i m eter columnr. Higher capacity gels would certainly be a step in the right direction. Gel permeation chromatography has opened up new areas of polymer research. Although the terhnique has already been put on s. mare or less practical basis, it is uhvious from the above disc~mionthat, much remaim to be done. No doubt, advances in this area. rill be fast in coming,
since the technique has afforded sohtions not only to problems that were previously difiicult to resolve, hut also ta some that, completely defied soliltion by classical methods.
Appendix Collection devices, the operalion of which has already been briefly described, are ilvaililahle from most suppliers of liquid chromatographic equipment. Someof the manufacturers of such devices are listed here for convenient reference. (Prices range from $5011 to $2000.) I3uolller 1nstr.menrs. 1827 Sixteenth Sl.
Ine.
Fort Lee, N. J.
Chromatopraphy C'orp, of Americr 00 East Mhi" S t . Carpentersrille. Ill. Gilson Medical Elpctronios C o w 3000 West Beltline Highway Middleton, \Vise. L K B Instruments, Ino. 4840 Rupby Are. \Vashinpton 14. D. C. National Instrument Lnborstorier 12300 Parklawn Drive Roekville. Md. Psekard lnstrrzmenr Co. 2200 \Varrenville Rd. nuw"e,s 0ior.e. Ill.
Vanguard Instrument CO. 1 4 1 lVhs11ington Are. Nortli Haven. Con".
Werner-Chiloott Laboratories ~ ~nirislon ~ 201 Tabor Rd. a h r i a Plains. iY..I.
t
~
~
MALEY,L. E., "Application of Gel Permeation Chromatography to High and AUAMS,H. I$., FARHXI,, K., A N D JOHNSON, Low Molecular Weight Polymevs." B. L., Fireslone Tire and Rubber ComPolymer Sei., Part. C , N o . 8, pp. 2%-268 i,m n~,~ i. pany, Akron, Ohio. "Gel Permeation MEYERHOPP, G., "(:el Permeation ChroChromat,ography of Polybutrtdiene!' matography it, Organic solvent,^," Rcr. ACS Rubber Chemistry Division, Philadelphia, I'eonsylvania, Oatober, 1965. Bunscnym. Physik., 69,866 (1965). K. 11.. "A Study of Asphalts and MILES, 23. If., "Applications of Gel PerALTGELT, Asphaltineii hy Gel Permeation Chromameation Chrometography to the Chartography." Petroleum Chemistry Discteriaation of Epoxy Resins." -4CS vision of ACS, Allantir Cit,y, New Organie Coatiugs Division, Chicago, Jersey, September, 196.5. Illinois, September, 1964. ALTGELT,K. H., "Fr&cbionation of ASMOORE,J . C., "Gel Permeation Chromsphitltenes by Gel Permeation Chromatography. I. A New Method far Molecular Weight ilistribution of High tography," J. Appl. Polymer Sci., 9 , 3389-93 (1965). Polymers." J. Polumer Sci., AZ, S35 F., "Textbook of Polymer (1064). BILLMEYER, Science," Interscience Publishers, New J. G., MOORE,J. C., AND ~IENDRICKSON, York, 1962. "Gel Permeation Chromatography. 11. R. S., and CANTOW, M. J. P., PORTER, The Xat,ure of the Separation." JourJOHNSON,J. F., "A Comparison of nal of Polymer Science, Part C, No. S, pp. Y33-241 (1965). Molecular Weieht Distributions for " Polviaohutenes as IMermined from Gel NAKAJIMA, N., "Fractionation of Polyethylene By Gel Permeation Chromatography." T o he published. (.4& stract in Polymer Pr&ws, Vol. 1, Issuc lecular Conference, Prague, Czechoslo7, 1965). vakia, 1965. DEVRIES, A. J., Pechiney-Saint Gobain, M. J. R., .4xu PICKEYI,,H. E., CANTOW, Research Centcr, Authony (Seine), JOHNSON, J . F., "A Computer Program France. 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