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Appendix C NanoPlus Operator’s Manual
C-2 Mar 2014
Determining Alpha and Beta
Photon correlation spectroscopy (PCS) is an indirect means of determining the molecular weight
of polymeric samples, such as proteins, polymers, and colloidal particles. The principle of using
PCS to determine the molecular weight of a sample in solution or in suspension is based on the
empirical relationship between the molecular weight (M
w
) and the translation diffusion coefficient
(D
T
) of the sample:

(1)

The two constants in this empirical equation represent the structural effect (parameter

) and the
solvent effect (parameter

), respectively, on the translational motion of the molecules (or
particles). For polydisperse samples, the obtained molecular weight is an ill-defined mean value
that may not be the same as the mean values obtained by other means.
The values of

and

can be obtained from literature or experimentally. There are listings of

and

values in this appendix and in the Polymer Handbook and CRC Physical Chemistry Handbook .
The values are only valid for the specific molecules (or particles) in the specific solvent (or
dispersing medium) and temperature, although the temperature variation may be minimal in the
normal temperature range. If the literature values are not available,

and

can be obtained
experimentally with the NanoPlus using the following procedure, provided that two (or more)
samples of known molecular weight are available.
Sample Solvent Temp.
( C)
Alpha
(

)
Beta
(

)
Poly(methyl methacrylate) Ethyl acetate 20 1.61×10-4 0.48
Poly(m-phenylene isophthalamide) Dimethylacetamide 26 1.13×10-4 0.56
Poly(m-phenylene isophthalamide) Dimethylacetamide/

3% LiCI
25 0.55×10-4 0.56
Poly(n-butyliminocarbonyl) Tetrahydrofuran 20 1.69×10-4 0.85
Poly(N-isopropyl methacrylate) Water 20 2.02×10-4 0.57
Poly(oxydiphenylsilylene) Benzene 21 6.16×10-4 0.63
Poly(p-carbethoxyphenylmethacrylamide) Ethyl acetate 21 2.8×10-4 0.69
Poly(p-ethoxycarbonyl phenylmethacrylate) Ethyl acetate 2.8×10-4 0.69
Poly(styrene) Methyl ethyl ketone 25 3.1×10-4 0.53
Poly(styrene) Toluene 20 unknown 0.53
Poly(styrene) NBS 419 Cyclohexane 35 1.21×10-4 0.5
Poly(styrene) NBS 705 Methyl ethyl ketone 25 1.96×10-4 0.49
M
w

D
T
-------
 
 
1

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=