Methodology

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Chemical instrumentation

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Edited by GALEN W. EWING, Seton Hall University, So. Orange, N. J. 07079

These articles are intended to serve the readers O ~ T HJOURNAL I ~ by calliny allenlion lo new developmenls in t h Ihemy, & e n , or availability of chemical laboratory instrumenlalion, or by presenting useful insighls and ezplanations of topics that are of practical imporlance to those who use, or kach the use of, modern instrumenlation and instrumental lechniques. The editor invites correspondence jrom prospective contributors.

via a Rosenbrock search technique such that the difference between known and computed molecular weight averages for the polymer of interest is minimized. Two approaches are suggested for situations where a linear calibration does not adequately describe the true column response: (a) Modify the program t o compute polynomial expressionssuch as: GPC ret. vol. = C,

-

LII. Current Trends in Gel Permeation Chromatography. Part Two: Methodology

- Cnllog,~(mol. wt.)]

Cs[log,~(mol. wt.)]'

...

-C,[log,~ (mol. wt.)Jn-1 and have the computer search for n constants, given n pieces of data for n / 2 to n broad MWD polymer standards. ( b ) Search for linear segments that can he put together t o yield a non-linear calibration curve (see Fig. 2).

JACK CAZES, Mobil Reseorch and Development Corp., Paulsboro, N. J. 08066 VI. Calibration A variety of more or less "well charaoterized" polymers is now available for calibrating GPC columns for the estimation of molecular weight distributions of polymeric substances. Table 4 is a list of these commercially available substances. Some &re ~ l a t i v e l ymonodisperse (measured M J M , approaches 1.O) while others have somewhat broader distributions. The molecular weight averages given in the table were supplied by the respective manufacturers and were determined by a variety of techniques, including lightscattering, membrane osmometry, ultrsr centrifugation, vapor pressure lowering, etc. Additionally, the Polytechnic Institute of Brooklyn, Polymer Sample Bank has made available a wide variety of polymer samples together with "selected properties which will clea~lydifferentiate those compounds of similar type." These data while sparse, often, at least, can serve as a starting point for the construction of a reliable calibration curve. Distillation Products Industries, Div. of Eastman Kodak Co., Rochester, N. Y. 14603, serves as depository and distributor for this project and should he contacted for further details. Direct calibration of GPC columns in terms of molecular weight of a given polymer type remains the method of choice; this is achieved by recording the GPC response for a series of narrow MWD standards of the polymer of interest whose peak molecular weights have been determined independently and then platting their GPC retention volumes versus res~ective~ e a kmolecular weiehts. For suffirienlly itamow 3IWD polym~rsit i.r often H . I P U ~ I ~ Qthat ~ the p ~ a kmoleeular weight i c equivalent t o an average value such as M.

Alternatively, the widely used "Qfactor" calibration technique described earlier (1) can be used t o determine molecular weight averages for many polymeric systems with a cdibration curve constructed with narrow MWD polystyrene standards. The method works well only if the GPC column response for the polymer of interest is related t o the polystyrene response by a Constant factor. Several techniques have been suggested for constructing a calibration curve for a polymer of interest for which there are only available well characterized broad MWD samples. One such method that has been used with great success in the present miter's laboratory, even where the "Q-factor" method is inamlieable. is that which has berln d~.wriheclby Purdon nrirfly, vhromntop:tms a n a t 1 for b r o d hnIKI) amplrs of the polymer of interest whose molecular weight averages are known ere used in conjunction with a calibration curve constructed with narrow MWD polystyrene standards t o yield a plot of retention volume versus log (molecular weight) for the polymer of interest. Some slight manual adjustment of the rUNC thw ohtnined is grncrnlly rK?CQ3%3ry, but the result io n mlilmtiort r m w thnt vields relinl,le molcrulnr weight svernges. - Another potentially useful approach utilizing two or more known molecular weight averages for one or mare samples of a polymer of interest involves the use of a digital. computer program developed at McMaster University (18). (The program is available from Dr. A. E. Hamielec, McMaster Univ., Hamilton, Ontario, Canada.) A linear calibration is assumed:

..

GPC ret. vol.

=

C,

- Cnlog,, (mol. wt.)

where C, and CSare constants t o he found

Figure 2. Calibration curve condructed from lineor regrnenb

The most basically sound and universally applicable approach should have as its foundation that parameter on which GPC separatiansare based, namely, effective molecular volume in solution. It has been shown, for s m d , non-polymeric molecules (19) that molar volumes correlate well with GPC retention volumes. Similarly, GPC retention volumes of a variety of polymers have been correlated with their hydrodynamic volumes as measured viscametrically ($0); that the hydrodynamic volume is, indeed, a universal parameter regardless of chemical type or molecular shape was admirably shown with such suhstanees as linear. starshaped, and comb-shaped polystyrenes, polymethylmetbacrylate, polyvinylchloride, graft copolymers, polysilotanes, and more. Thus, a plot of the logarithm of the hydrodynamic volume (mol. wt. X intrinsic viscosity) versus GPC retention volume yields a single line regardless of polymer type with only minor deviations. This universal calibration apparently "corrects for" such solution phenomena as polymer-solvent interactions, hetero-contact interactions of copolymers, etc., since the measured hydrodynamic volumes of polymers in solution include the effects of such interactions.

VII. Estimation of Molecular Weight Distribution Conversion of raw GPC data (typically, (Continued on page A606)

Volume 47, Number 8, August 1970

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A505

Chrnkal Instrumentcrtlon the height of the GPC curve at several points dong the molecular size, or weight, axis) t o meaningful molecular weight averages sometimes first requires correction of the dat,a for that part of the axial dispeYsion of the sample that occurs in the column that is not due t o the GPC molecular size fractionation process. Many attempts have heen made t o mathematically correct for such axial dispersion and imperfect resolution in GPC columns. None have been universallv auulicable or yielded consistently satisfac&y results. There are a t least three methods that have been used by various workers t o salve the Table 4.

a"

a=

integral equation that describes the effect of instrumental spreading: solution by minimization solution by Fourier transform solution by polynomial represent* tion of the chromatogram.

herip.: of equation, 11191 nrr u d u l for m t l v r r l i n ~I:!'(: dnts to the variou. nwrnaurt of tlw r d t c u l n r wrinhr di~triburiontry the

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