Adlard E.R. (ed.) Chromatography in the Petroleum Industry
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Chapter
3
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This Page Intentionally Left Blank
E.R.
Adlard
(Ed.),
Chromatography
in
the
Petroleum
Industry
Journal
of
Chromatography
Library
Series, Vol.
56
0
1995 Elsevier Science B.V. All rights reserved
95
CHAPTER
4
Hydrodynamic chromatography
of
polymers
Jaap
Bos
and
Robert
Tijssen
Koninklijke/Shell-Luboratorium,
Amsterdam
(Shell
Research B.
V.),
Badhuisweg
3,
I031
CM
Amsterdam,
The
Netherlands
4.1
INTRODUCTION
Hydrodynamic chromatography
(HDC)
is nowadays a well-known technique,
which is mainly used for the separation of colloidal particles of different sizes.
Basically, particle size separation takes place when the finite dimensions of the
particles are large enough to interfere with the flow profile in a packed bed or
open tubular flow system. For geometric reasons, particles are excluded from the
slower moving wall regions in the flow channel and will therefore travel at a
velocity greater than the average velocity of the solvent. Hence, larger particles
elute first from the flow system, followed by the smaller ones, as is also the case
in the well-known polymer separation technique
of
gel permeation chromatogra-
phy (GPC), also called size exclusion chromatography
(SEC).
The technique was pioneered by Small
[
1-31,
who also coined the name HDC.
In his work, he demonstrated the practicability
of
HDC for the separation of
mixtures of polymer latexes and colloidal suspensions, using packed beds of im-
permeable particles as the separation column. Pedersen
[4],
Mori
et
al.
[5],
Prud’homme
et
al.
[6]
and Hoagland
et
al.
[7]
showed that packed-column
HDC
was
a
suitable technique not only for particle separations but in principle also for
the separation
of
large molecules such as proteins, polystyrenes, and water-
soluble polymers
of
high molecular mass (such as xanthanes and polyacryla-
mides). More recently,
Kraak
et
al.
[8]
and Stegeman
et
al.
[9]
greatly improved
the separating power of HDC by using columns packed with extremely small
(1.2
pm) non-porous silica particles.
References
pp.
125-126
96
Chapter
4
Mullins and Orr [lo], Noel
et
al.
[ll],
Brough
et
al.
[12] and Shuster
et
al.
[
131 demonstrated experimentally that HDC separations of differently sized par-
ticles can also be effected in a single open capillary tube with a diameter of the
order
of
several tenths of
a
millimetre. Elie and Renaud
[
141
succeeded in sepa-
rating fibrous particles in paper fibre suspensions using even wider open tubes of
15
mm internal diameter.
Although microcapillaries (defined here
as
having internal diameters less than
10pm) had already been used by Silebi and DosRamos
[
151 and DosRamos and
Silebi [16] for the separation
of
particles, Tijssen
et
al.
[17,18] and
Bos
et
al.
[
191 specifically used these capillaries for the separation of polystyrenes and for
studying the dissociation behaviour
of
micelles of two-block polymers.
Only for microcapillary HDC has the theory been sufficiently developed to
calculate the size of an eluting species solely fiom its residence time relative to
that of a small molecule, without recourse to calibration standards. In capillaries
of a larger diameter, and in most packed-bed columns, the situation is more dif-
ficult, since exclusion fiom the wall is then not the only separating mechanism,
because other, only partly understood phenomena, such as “tubular pinch” and
molecular elongation, also strongly influence the transport mechanism through
the column. Moreover, in the separation of particles that are charged or can ob-
tain a surface charge, such as polystyrene latexes in water, there is a pronounced
influence of the electric double layer at the column wall on the migration
mechanism. In this case, ionic strength and velocity
of
the mobile phase are of
importance. Since
in
the context of “Chromatography in the Petroleum Indus-
try”, HDC separations of polymeric species are the more important ones, they
will be treated in detail. For a review
of
particle separations by HDC, the reader
is
referred to articles by Dodds [20] and McHugh [21].
4.2
MICROCAPILLARY HYDRODYNAMtC
CHROMATOGRAPHY
4.2.1
Theory
Throughout this chapter, a microcapillary
is
(rather arbitrarily) defined as a
column of circular cross-section with an internal diameter of less than 1Opm.
This size is sufficiently small to ensure that in normal HDC operation with the
flow of dilute solutions
of
macromolecules, “extra” effects such as tubular pinch
are absent. It can safely be assumed that the flow profile is laminar, i.e. a para-
bolic Poiseuille profile exists (see Fig.
4.1),
where the local velocity
u(r)
for a
radial position
r
in a tube of radius
R
(0
2
r
I
R)
is given by
U(r)=2u[l-(r/R)*]
(4.1)
Hydrodynamic chromatography
of
polymers
97
I
/
Fig.
4.1.
Schematic representation
of
the laminar
flow
transport
of
a spherical solute particle
(diameter
2a)
in Poiseuille
flow
through a cylindrical capillary (diameter
2R).
here the average velocity
ii
is
R
U
=
(2
/
R2)l
u(r)r
dr
(4.2)
for point molecules that rapidly exchange between all available streamlines.
These molecules (e.g. the solvent molecules) emerge from
a
column of length
L
after time
L
t
=-
m-
24
(4.3)
Now, as is schematically depicted in Fig.
4.1,
the centre of gravity of a parti-
cle or macromolecule of size
2a
in the flow field cannot sample the low-velocity
regions near the wall. The average particle velocity
lip
is now
again provided that the diffusion process with coefficient
Dm
of the particles is
sufficiently fast to sample all the available streamlines in the time
t
of the trans-
port process, i.e. the dimensionless Fourier number
Fo
=
DJR2
%
1.
Combining
References pp.
125-126
98
Chapter
4
Eqs.
(4.1)
and
(4.4),
and introducing the aspect ratio
A
=
a/R,
we find
zp
=i7(1+213.-2) (4.5)
The average residence time for the particle is thus found from tp
=
L/iip,
and the
dimensionless residence time
z
(compared to a small molecule) is now
t=t, It,
=(1+2A-A2)-1
(4.6)
Equation
(4.6)
is still rather idealized, because the polymer molecules have
been regarded as rigid, non-rotating particles. Actually, since the part of a mac-
romolecule that
is
closest to the capillary wall is in a region of a lower velocity
line than the opposite side of the molecule, the resultant couple of forces will
make the particle rotate, which influences the translational velocity. This hydro-
dynamic problem has been investigated theoretically by DiMarzio and Guttman
[22-241
and Brenner and Gaydos
[25].
Tijssen et
al. [18]
showed that their re-
sults could be described by a modified quadratic term in Eq.
(4.6):
t
=
(1
+
22
-a?)-'
(4.7)
where
C
has a value of
2.698
for permeable macromolecular coils, while for im-
permeable hard spheres its value is
4.89.
The importance of Eq.
(4.7)
is that
it
shows that microcapillary
HDC
can be
used to calculate the size of an eluting species without recourse to calibration
standards. From the measured relative residence time,
z,
the aspect ratio,
A,
can
be calculated, and from this and the known diameter of the capillary, the size of
the particle can be obtained. Even if the conformation
of
the macromolecule is
unknown, and
so
the exact value of constant
C
in Eq.
(4.7)
is in doubt, the size
can be estimated with only a small error. By assuming that for random coil mac-
romolecules,
C
will have a value between the two extremes mentioned above
(C
=
2.698
for macromolecules in a good solvent, and
C
=
4.89
for the limiting
case of an impermeable hard sphere),
Bos
et
al.
[
191
showed in a practical ex-
ample for a separation with
z
=
0.95
that the sizes calculated with these
two
val-
ues differed by less than
4%.
A
plot of
13.
versus
t,
the calibration curve of microcapillary
HDC,
is shown in
Fig.
4.2
(Eq.
(4.7)
with
C=
2.698
and
4.89).
The curve is very steep close to
z
=
1,
where the exact value of
C
is not too important, but where a small error
in
the determination oft will lead
to
a large error in
A,
and hence a large error in
the calculated size of an eluting species. This is not the case at lower
t
values,
where the slope of the calibration curve is less, but in this region exact knowl-
edge of the conformation of the macromolecule or particle is needed to use the
Hydrodynamic chromatography ofpolymers
99
Aspect
Ratio,
A
I00
Dimensionless
residence
time
Fig.
4.2.
Calibration curves for microcapillary HDC
(Eq.
(4.7),
't
=
(1+U
-
C,E2)-')
with
C
=
2.698
(random
coils)
and
C
=
4.89
(hard
spheres).
correct value of
C,
and
so
to obtain meaningful values for the calculated sizes.
We do not think that the upper part of the calibration curves where the quadratic
term in Eq.
(4.7)
is the leading term, and where ever larger particles will elute at
ever longer residence times, has any physical meaning. Here, the aspect ratio
il
is
so
large
(>0.2)
that the concept of a particle eluting in an undisturbed Poiseuille
profile that is used in the derivation of Eq.
(4.7)
is
probably invalid. Mavrovoun-
iotis and Brenner
[26]
proposed a complicated theory to describe this case
of
closely fitting particles.
4.2.2
Expressing the size
of
macromolecules
For macromolecules, there exist a number of different measures for their
mean size, e.g. the radius of gyration
(rg),
the hydrodynamic radius
(rh),
the end-
to-end distance, etc.
In
hydrodynamic chromatography, the size that we deter-
mine is yet another one, the effective radius
(T),
related but not equal to the ra-
dius
of
gyration. To appreciate the difference, let us look more closely
at
the
time scale on which these
two
measures are determined. The radius of gyration
is
usually determined by dynamic light scattering, by the interaction of a photon
with a macromolecule. This is a very fast process and during this interaction, the
conformation of
a
given macromolecular coil
is
not changed. Averaging over the
conformation of a number of molecules will give the radius of gyration.
References pp.
125-126
100
Chapter
4
By contrast, the interaction
of
a macromolecule with a wall is a slow process
compared with the time scale on which a given coil will change its conformation.
So
now we average over a number
of
macromolecules that all have assumed
every possible spatial configuration. The resulting concept of the “mean maxi-
mal cross-section”,
2F,
as introduced by Volkenstein
[27]
and further discussed
by van Kreveld and van den Hoed
[28],
determines the distance,
r,
by which a
random-coil macromolecule is excluded from the wall. Now
T
is related to the
radius of gyration by the following equation:
F
=
(&
/
2)rg
=
0.886rg
(4.8)
The factor of
0.886
in this equation
is,
however, only valid for random coil
macromolecules in good solvents where internal rotation of the segments is pos-
sible, since the macromolecular
coil
is expanded
by
the interaction with the sol-
vent molecules. However,
in
a theta solvent, where, by definition, the expansion
of the
coil
by solventlsegment interaction
is
exactly compensated by intra-
molecular segmentlsegment attraction, the polymer chain is rather contracted
and behaves more as a rigid sphere with hindered internal rotation. In this case,
the coefficient
in
Eq.
(4.8)
will more probably approach a value
of
1
[18].
For
a
more detailed discussion on the size
of
polymer molecules, the reader is referred
to
[29].
4.2.3
Instrumentation
4.2.3.1
General aspects
The demands for the instrumentation that
is
needed to work with microcapil-
laries follow from the characteristic values of the chromatographic parameters
that are presented in Table
4.1
for a typical microcapillary
HDC
column that has
been used in
[
181:
TABLE
4.1
TYPICAL
VALUES
FOR
A
MICROCAPILLARY HDC COLUMN
Length (cm)
330
Internal diameter (um)
2.68
Votume (nl)
16
Volumetric
flow
rate (nl/min)
0.7
-4
Volume
of
detected zones (pl)
-230
Head pressure
(bar)
200
Length
of
detected zones (cm)
Hydrodynamic chromatography
of
polymers
101
From the values, we see that a standard liquid chromatograph is not suitable
for this type of analysis. High-pressure pumps that can deliver volumetric flows
of the order of several nl/min do not exist and a standard detector (with a flow
cell of say
1
,u
1)
cannot accommodate peak volumes in the picoliter range. Also,
operation
of such a column would require an injection size in the picoliter range,
another specification not met by standard liquid chromatographic injectors. All
this leads to a home-made instrumental set-up schematically represented
in
Fig.
4.3.
A
standard
HPLC
pump is used to deliver the mobile phase through
a
T-
piece at a volumetric flow rate of 2-3 ml/min. The major part of the solvent
flows through a restriction capillary dimensioned such that the required head
pressure on the microcapillary
HDC
column is attained. The length
L
and the
radius
R
(in cm) of the restriction capillary can be calculated from the Poiseuille
equation
where
F
is the volumetric flow rate (cm3/s), q is the dynamic viscosity (Poise),
and
AP
the required head pressure
(bar).
The sample is introduced into the mi-
crocapillary by means
of
an injector, the loop of which is only partly emptied by
actuating the valve for say
1-4
s.
This ensures that the injected sample reaches
resistance capillary
Mobile phase vessel-
I
D,,...*
-
Injector
-
UV
Defector
Fig.
4.3.
Schematic representation
of
the apparatus
for
microcapillary
HDC.
References
pp.
125-126