FRACTIONATION OF POLYMERS 691
Vol. 3, N o . 5, September-October 1970
whose mean value is greater than zero. Let us suppose that the banks of length I are interleaved with mixing regions of length d. The distribution function for the time spent in each mixing region is \k(t)and that in each bank is w(t). The first three central moments of s(t) are assumed t o be M i , M?, and and that of w(t) are /n,, in?, and i v 3 . By virtue of the central limit theorem we know that the final distribution for time spent in the column, W(t),is Gaussian
each mixing region. The velocity c across a mixing region is a constant value determined by
Qr
=
Ac
Particles travelling in this fluid will elute out of the n consecutive mixing regions with a n average time
nM1
nd
= -
c
and a variance
Thus we have where (t),
=
nnil t inMI
pc
=
ntn.
+ nM2
(B2) (B3)
Now the validity of the above equations is independent of the order in which the n functions e(t)and the n functions w(z) are shown. We may, therefore, choose the w(t) functions first and then the \k(t) functions. In this way n/n! and nin? are seen t o be the first and second moments for elution from a column in which there is n o time spent in the mixing region
nnzl
= it)
034)
nin? = p 2
(B5)
where ( r ) and p! are given by eq 4.17 and 4.18. Similarly nM1 and nM? are the first and second moments of the distribution time for the emergence of a particle from a stack of n mixing regions. Consider the flow in
I n eq B10 V,, is the total volume of the mixing region. ( V J Cis the average elution volume from the column, and (( V , - ( V,)JZ),is the breadth of the elution volume peak. One should observe that the only effect of the added terms is t o rescale the value of a; the interstitial volume is now identified as the sum of the total volume in the large tubes plus the volume in the mixing regions. The above equations enable one to predict the elution characteristics of a stack of permeable membranes.
Fractionation of Polymers by Thin Layer Chromatography. 11. Molecular Weight Distributions by Direct Scanning Densitometry E. P. Otocka Bell Teleplione Luborutories, Inc., Murrcij, Hill, New Jersey Receiced July 22, 1970
07974.
ABSTRACT: The molecular weight distribution of a commercial polystyrene is determined from a gradient elution thin layer chromatogram using scanning densitometry. Results of the tlc determination are in good agreement with those from gel permeation chromatography. Further experiments are described which indicate that fractionation by tlc may occur through a combination of solubility and adsorption effects.
I
n a previous publication it was reported that sharp fractions of polystyrene could be separated by thin layer chromatography (tlc) using gradient elution techniques. 1 Additional experiments have been carried out t o investigate the feasibility of molecular weight determination by tlc. The crucial factor in determining molecular weight distribution is accurate analysis of polymer concentration as a function of distance along its elution path.
One method involves photographing the developed, visualized chromatogram followed by scanning densitometric analysis of the negative. This process has been recently used t o make a successful molecular weight determination from a thin layer chromatogram. * However, instruments have become available for direct densitometric scanning of the chromatogram itself. One such instrument is the Schoefel SD3000 scanning spectrodensitonieter (Schoeffel Instrument Co.)
( I ) E. P . Otocka and M. Y . Hellman, Mucromolecrrles, 3, 362 1970).
(2) H . Inagaki, personal commutiiciitioii; also F. Kamiyama, H . Matsuda, and H . Inayaki, P o / ~ . mJ . , in press.
Mncrotnolecules
692 OTOCKA
W
5 0.2
v)
cz
>
3
r-
> a
v)
z
a
n
t
W
J
9 0.1
a
l-
4
0
W
K
0,Am F L U O R E S C E N T INDICATOR 265 Mp O = H C L O , C H A R 400 Mp
C
I
4
I
I
,
0 12 16 POLYMER W E I G H T , p g
I
20
Figure I . Calibration curves for fluorescent indicator and perchloric acid visualization. Densitometer scanning wavelengths are noted. which has been successfully employed in several quantitative applications. a-6 T h e operation of the instrument will not be detailed here.
Experimental Section Two preliminary experiments were conducted to test the validity of tlc-densitometry molecular weight determination. The first involved the calibration of the densitometer. Varying amounts of polystyrene were spotted on a silica gel tlc plate containing zinc silicate fluorescent indicator. The scanning wavelength was 265 mp, observed to give the most intense fluorescence. The nominal excitation wavelength is given as 254 mp. The spots of polystyrene quench the fluorescence and appear dark on the bright green background. The integrated area indicated by the densitometer was proportional to the amount of the polystyrene up to cu. 18 wg. When spot dimensions were carefully controlled, peak height was also found proportional to polymer weight (see Figure 1). The second experiment involved elution of mixed fractions. For the molecular weight calibration curve to be valid, the
Figure 3 . Appearance of “unknown” polydisperse sample: acetonegradient, acetone-isopropyl alcohol (96:4) chloroform-isopropyl alcohol (66: 30 :4); traced from densitometer recording. --f
components of a polymer mixture must have the same Rr as when they are eluted alone. Several tests showed that this is indeed the case provided that the total amount of polymer deposited does not approach complete monolayer coverage. For polystyrene, this amounts to -7 X IOw4 mg/cm2 adsorbent surface. l i d When monolayer coverage is approached, the amount of a lower molecular weight fraction appearing at the proper R fis reduced, and the apparent amount of higher molecular weight material increases. Apparently. the shorter chains can become trapped by longer chains at high surface coverages, giving false results. In the course of these experiments, a full-scale range of 0.2 OD unit was often used, and a noise level of about 5z was noted during the scan of the plate. On the same scale, using 500 mp as the scanning wavelength, the noise level is only 1-2%. It was concluded that the noise arises from uneven distribution of the fluorescent indicator rather than thickness variation of the adsorbent itself. This noise level poses somewhat of a problem since signal strengths are often on the
c
\
Figure 2. Separation of PS-3 and PS-5in dioxane-methanol 0 solvent. Traced from densitometer recording. (3) P. I
