A note on linear calibration curve for gel‐permeation chromatography developed from a single standard

Abstract

With the increased use of high-speed gel-permeation chromatographs (GPC) interfaced with mini-computers for quick communication of results, it is desirable to use a rapid reliable method of calibration. Consider a set of columns with an appropriate distribution of pores over the desired range such that the calibration curve may be described aswhere V is the elution count, C1 and C2 are constants, and M is the molecular weight. If we have a standard polymer with a broad distribution of molecular weights over the range of interest, and the weight-average and number-average molecular weights, aw and a,,, have been accurately determined by such methods as liiht scattering and osmometry, it is a simple matter to write a computer program to calculate the linear constants.From the definitions:where w is the weight fraction, it is trivial to show that:We calculate eq. (1) 36 times to find a unique C2 to the nearest 5 2 0 . The fact that the above expression is independent of C1 allows a simpler and faster calculation of C1 and C2 than the twovariable iteration method.' From an arbitrary C1 a final C1 is obtained by iterating the expression (usually twice): until This method can be extremely useful for polymer systems where narrow fraction standards are not available.

Molecular weight distribution of a branched epoxy polymer: 1,4-butanediol diglycidyl ether with cis-1,2-cyclohexanedicarboxylic anhydride

“…From SEC measurements, we can obtain the elution curve C(V) versus A typical unnormalized intensity-intensity photoelectron count autocorrelation function. Epoxy polymer sample 13 (1.11 X 10"4 g/mL; Afw = 4.97 X 106) in MEK measured at = 30°and 25 ®C using a delay time increment = 15 #is. The insert is relative deviation of the measured and the computed time correlation function using the MSVD method.…”

“…After obtaining (V), (V2), (log (D0°)>, and (log2 (D00)), we can combine them with eq 13 and 14 to solve for A and B. We also know that Mw can be calculated from SEC data by using f "MC(V) dV Mw = ^4- (15) f C(V) dV Jo if we know A and B in eq 10. By using D0°= fej>M_aD, A, and B, we can change eq 15 to jfeDl/«c r"io(A-V)/(aDB)C(y) dy Mw =--- (16) f°C(V) dV…”

“…We also know that Mw can be calculated from SEC data by using f "MC(V) dV Mw = ^4- (15) f C(V) dV Jo if we know A and B in eq 10. By using D0°= fej>M_aD, A, and B, we can change eq 15 to jfeDl/«c r"io(A-V)/(aDB)C(y) dy Mw =--- (16) f°C(V) dV…”

Calibration of size exclusion chromatography columns for determination of polymer molecular weight distribution

“…Many attempts have been undertaken to overcome the problem of the lack of suitable standards for each polymer type (5)(6)(7)(8)(9). These attempts employ a known set of molecular weight averages of broad molecular weight distribution polymers concerned.…”

A simple and efficient SEC/GPC linear calibration technique using broad‐range standards

“…For two independent determinations (subscripts i and j ) , it can easily be shown that However, for most applications, Dz,i = D2,,; for small changes in D2,, such that D2,, 9 AD2,,, it follows, therefore, that the functional form In ( P/Pi ) = Const. (D2 -Dzi (11) results. This is consistent with the results from our empirical observations.…”