Chromatographia

, Volume 20, Issue 1, pp 13–19 | Cite as

Averaged molecular weight of complex mixtures as determined by rapid measurements of diffusion

  • W. Steuer
  • K. Jost
  • I. Halász
Originals

Summary

The concept of a diffusion-averaged molecular weight, Md′ is presented, and Md is defined for polydisperse samples. It is shown via oligostyrene mixtures that Md can be determined in 20 minutes with common chromatographic equipment. If Md is measured and Mn or Mw is known, the polydispersity can be obtained.

Key Words

Column liquid chromatography Open tubes Diffusion coefficient Calibration curve for oligostyrenes Diffusion-averaged molecular weight Polydispersity 

List of Symbols

A

empirical constant in Eq. (6)

a

constant in Eq. (20)

B

longitudinal diffusion term in hvs. u-curve

b

empirical constant in Eq. (6)

C

C-term of hvs. u-curve for ideal tube

c(x)

cross-sectionally-averaged concentration of peak as function of x-coordinate

cmax

cross-sectionally-averaged concentration at peak maximum

D

diffusion coefficient of sample component in eluent

Deff

effective diffusion coefficient

Dres

diffusion coefficient of polydisperse sample obtained from C-term measurements

DresC

=Dres

DresB

diffusion coefficient of polydisperse sample obtained from B-Term measurements

F

peak area

Fres

peak area of polydisperse sample

G

constant in Eq. (16)

h

height equivalent to theoretical plate

hres

h-value of polydisperse sample

H

height of theoretical Gaussian peak

Hmax

height of measured peak

Hres

height of polydisperse peak

k

constant

L

length of ideal tube (capillary used)

M

general molecular weight

Mn

number-averaged molecular weight

Mw

weight-averaged molecular weight

Md

diffusion-averaged molecular weight (C-term)

MdC

=Md

MdB

diffusion-averaged molecular weight (B-term)

mi

mass of sample component i

Pd

polydispersity

r

radius of ideal tube

R2

correlation coefficient

t

time

u

linear flow velocity

x

general x-coordinate (length)

β

weight fraction

Δ

position of diffusion-averaged molecular weight relative to number- and weight-averaged molecular weights as defined in Eq. (13)

weight-based extinction coefficient

σ

standard deviation of theoretical Gaussian peak

σx

standard deviation along length axis of tube

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References

  1. [1]
    G. I. Taylor, Proc. Roy. Soc., A219 (53) 186.Google Scholar
  2. [2]
    R. Aris, Proc. Roy. Soc., A225 (54) 67.Google Scholar
  3. [3]
    W. Steuer, Ph. D. Thesis, Saarbrücken, FRG, 1983.Google Scholar
  4. [4]
    G. Görlitz, Ph. D. Thesis, Saarbrücken, FRG, 1981.Google Scholar
  5. [5]
    K. Jost, Master Thesis, Saarbrücken, FRG, 1981.Google Scholar
  6. [6]
    G. Ahr, Ph. D. Thesis, Saarbrücken, FRG, 1982.Google Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH 1985

Authors and Affiliations

  • W. Steuer
    • 1
  • K. Jost
    • 1
  • I. Halász
    • 1
  1. 1.Lehrstuhl für Angewandte Physikalische ChemieUniversität des SaarlandesSaarbrückenFRG

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