From: Prof.Dr. M.D. Lechner <lechner@rz.Uni-Osnabrueck.DE>
  To  : RASMB@bbri.harvard.edu
  Date: Tue, 5 Mar 1996 11:09:06 +0100

Message of Tom Laue

Dear Tom,
thank you very much for your email message with respect to the determination
of Mz.
May I take the freedom to give a few more remarks. I agree fully that a
pointwise computation of the z-average molar mass is possible according to

Mz,r = (1/L){dln[(dC/dr)/r]/d(r^2)}                (1)

with L = (1 - v2 rho1)omega^2/(2 R T). This Mz,r (more precise Mz,r,app) is
a special Mz and depends both on distance of rotation r and rotational speed
N = 2 pi omega. If you want Mz (more precise Mz,app) for the entire sample
you have to use the equations

Mz = (Mw,b Cb - Mw,m Cm)/(Cb - Cm)                 (2)

Mw,r = (1/L)[dlnC/d(r^2)] = (1/L)(dC/dr)/(2 r C)   (3)

with Cb, Cm, Mw,b and Mw,m the concentrations and molar mass averages at the
bottom and at the meniscus of the cell.Mw,b and Mw,m may be calculated
according to equation (3) with r = b and r = m.

The extrapolation of the concentration curve to the meniscus and to the
bottom of the cell is comparatively easy with the old Beckman model E
machine with interference, Schlieren and absorption optics because the
signal is not so noisy that that of  the new Beckman XLA machine with
absorption and interference optics.

Please excuse me very much, but I have evaluated a lot of measurements with
the old and the new Beckman machines: the signal to noise ratio of the new
machine is especial in the vicinity of the meniscus and of the bottom to
large to perform a proper extrapolation. Would it be possible to improve the
noise of the Beckman XLA with absorption and interference optics? Then it
would be possible to determine absolutely Mn, Mw, Mz and the whole molar
mass distribution with sufficient accuracy.
Best wishes M. Dieter Lechner