Page 30 - Engineering Plastics Handbook

4 Introduction

42.08 g/mol. For these low-molecular-weight molecules MW = W/N, where
W = total sample weight and N = number of moles in the sample.
Macromolecule MW and molecular weight distribution (MWD) are
affected by polymerization conditions. Macromolecules are polydispersed;
i.e., macromolecules have different chain lengths and different molecu-
lar weights, even from the same polymerization reactor. Macromolecule
molecular weight is determined from the number average (MW ) and
n
weight average (MW ). Professor Hermann Staudinger awakened the
w
world in the 1920s to macromolecules—molecules with 10,000 or more
atoms. Prior to his discovery, molecular weights were thought to be no
more than a few thousand, and materials such as cellulose and natural
rubber were considered to be the combination of a lot of small molecules.
Macromolecule molecular weight is calculated by various parameters,
primarily as number average MW and weight average MW , using the
w
n
following equations [1, 2, 4, 9]:
Number average molecular weight MW = ∑ i nM i
i
n
∑ i n i
i
Weight average molecular weight MW = ∑ i nM i 2
w
∑ i nM i
i
where n = number of moles of specie i
i
M = molecular weight of specie i
i
Number average molecular weight is determined by osmometry; and
weight average molecular weight is determined by light scattering, small-
angle neutron scattering (SANS), and sedimentation velocity [9].
A third way to determine MW is via the viscosity average molecular
weight, determined by dilute solution viscometry, the intrinsic viscos-
ity of a polymer solution [4].
1+
a
Viscosity average molecular weight MW =  ∑ i nM i  1/ a
i
v
 ∑ i nM i 
i
Here a is a Mark-Houwink constant for a given polymer. The exponent
a is a function of polymer geometry with a range of 0.5 to 2.0, typically
about 0.75 [5]. It is experimentally determined by measuring the intrin-
sic viscosity of several samples of a given polymer. Prior to measuring
the intrinsic viscosity, the MW of the given polymer is determined by a
method such as light scattering or osmometry (osmotic pressure). On a
log graph, plot the log of intrinsic viscosity, 0.1 to 10 dl/g (y axis), versus
4 6
log of MW, 10 to 10 g/mol (x axis) [5]. Fit a straight line to the exper-
imental data. The slope of the line is a.
Intrinsic viscosity is frequently used for linear macromolecular char-
acterization, and intrinsic viscosity number values can be used to deter-
mine the molecular weight [15]. The intrinsic viscosity number is the