Field Flow Fractionation in Analysis of Polymers and Rubbers
S. Kim Ratanathanawongs Williams and Maria-Anna Benincasa
in
Encyclopedia of Analytical Chemistry
R.A. Meyers (Ed.)
pp. 7582–7608
 John Wiley & Sons Ltd, Chichester, 2000
FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
Field Flow Fractionation in
Analysis of Polymers and
Rubbers
S. Kim Ratanathanawongs Williams
Colorado School of Mines, Golden,
USA
Maria-Anna Benincasa
Universitá di Roma, Rome, Italy
1 Introduction
2 Theory
2.1 Basic Theory of Retention
2.2 Molecular Weight Dependence on
Physicochemical Parameters
2.3 Conversion of a Fractogram to
Molecular Weight Distribution
2.4 Calibration Methods
2.5 Zone Broadening
2.6 General Theory of Asymmetric
Flow Field-flow Fractionation
2.7 Retention in Hollow-fiber Channels
1
2
3
5
6
6
7
8
9
3 Instrumentation
3.1 Flow Field-flow Fractionation
3.2 Thermal Field-flow Fractionation
3.3 Detectors
4 Experimental Procedures
4.1 Sample Preparation and Handling
4.2 Sample Injection and Relaxation
4.3 Operation with Constant or Programmed Field
5 Applications
5.1 Organic-soluble Polymers
5.2 Water-soluble Polymers
6 Method Development
6.1 Determining Experimental
Conditions
6.2 Effect of Sample Size
6.3 Membranes in Flow Field-flow
Fractionation
Acknowledgments
List of Symbols
9
9
10
10
11
11
12
Abbreviations and Acronyms
21
Related Article
References
21
21
13
13
13
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17
17
18
19
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Encyclopedia of Analytical Chemistry
R.A. Meyers (Ed.) Copyright  John Wiley & Sons Ltd
1
Field-flow fractionation (FFF) was conceived by J. Calvin
Giddings in 1966 as a separation and characterization
method for macromolecules, colloids, and particulates.
Like chromatography, sample migration is caused by
differential interaction with a field acting along an axis
orthogonal to that of the transport liquid. Unlike chromatography, where separation is achieved by solutes
partitioning between mobile and stationary phases, separation in FFF arises from the distribution of sample
components in fluid laminae flowing at different velocities
in a single phase. The different flow velocities, described by
a parabolic profile, arise from the high aspect ratio of the
FFF channel. Different types of fields can be used in FFF as
long as they interact with some physicochemical property
of the sample. The FFF channel design makes it highly
suited for analyses of fragile aggregates, high-molecularweight polymers, and gels. In comparison with packed
columns, shear rates in the channel and the probability
of plugging the channel are low. The ability of thermal
FFF to differentiate polymers and latexes of different bulk
and surface composition is unique among currently used
separation techniques. The FFF family of techniques can
provide a great deal of information about the sample but
an initial time investment is often required for methods
development.
In this article, the fundamental mechanism of FFF is
shown at play in the separation and characterization of
polymers and rubbers by the two techniques par excellence
in this field: flow FFF and thermal FFF.
1 INTRODUCTION
FFF is a separation method conceived by J. Calvin
Giddings in 1966..1/ It is particularly suitable for macromolecular, colloidal and diverse particulate materials
extending from a few hundred.2,3/ to 1018 Da..4/ It is
an elution technique and is often referred to as a
chromatography-like technique. In chromatography, the
solute’s rate of migration is determined by its partitioning
between a mobile phase and a stationary phase in a column. In FFF, an externally applied field induces selective
distribution of solutes in fluid laminae flowing at different
velocities in a single phase inside a channel. The difference
in the type of forces used in chromatography and in FFF
defines the range of applicability of the techniques. While
forces in chromatography are localized at interfaces and
very selective, those used in FFF and electrophoresis
are more diffuse and weaker. Consequently, the mass
transport phenomena occurring in a chromatographic
technique, such as high-performance liquid chromatography (HPLC), tend to be slower as the solute molecular
weight increases. When the molecule’s energy of interaction with the interface is significantly greater than the
2
thermal energy kT, adsorption becomes irreversible..5/
However, even before irreversible adsorption appears,
structural disruption and denaturation of the macromolecular component may occur because of the strong
shear forces present in the irregular flow in the tightly
packed chromatography column..6/ By contrast, the FFF
separation is carried out in the absence of a stationary
phase within an open channel. This channel is obtained by
removing a geometrical portion from a Teflon, Mylar, or
polyimide spacer and then clamping the spacer between
two flat parallel plates. As shown in Figure 1, the removed
section of the channel is a parallelepiped with tapered
ends that facilitate the flow of liquid and sample in and
out of the channel. The most commonly used channel
dimensions are 27 – 87 cm in length L, 1 – 2 cm in breadth
b and 0.0075 – 0.05 cm in thickness w. Because of the very
high aspect ratio of the FFF channel and the frictional
drag at the walls, the velocity of a liquid carrier moving
in the longitudinal direction has a parabolic profile with
a maximum in the center and minima, virtually zero, at
the walls. In the normal mode of operation, the field
applied perpendicular to the flow direction drives sample
components toward one wall, referred to as accumulation
wall,.7/ with a velocity determined by the particle – field
interaction. This field-induced displacement, optimized in
the absence of longitudinal flow, is always counteracted
by the diffusive flux that originates from the concentration gradient across the channel. The combination of
these opposing effects results in a nonuniform distribution of components across the channel, those with a
higher rate of back-diffusion being driven further away
from the accumulation wall than those with a lower diffusion rate. Because of the parabolic flow velocity profile in
the channel, the faster-diffusing component C shown in
Figure 1 will be displaced along the channel more rapidly
than component B, which has a lower diffusivity. The
output signal, collected by a detector sensitive to some
solute property, will thus register the elution profile of
distinct peaks.
The normal mode of operation described above is the
one mostly used for polymer separations because of the
molecular size/weight range of these particular materials.
Another retention mechanism, steric FFF,.8,9/ comes into
play when the component size is significant relatively
to the channel thickness. This is generally the case for
particle dimensions higher than 1 µm. The solute elution
velocity is determined, in this case, by the extension
of component particles into the flow. Larger particles
extend into regions of faster streamlines because of steric
exclusion from the accumulation wall and elute earlier
than smaller particles. The retention order in this mode
is reverse of that in the normal mode of operation.
Given the precise channel geometry and the flow
profile that may be described mathematically, retention
POLYMERS AND RUBBERS
Inflow
x
Field
y
Separated
bands
Outflow
z
FFF A
channel
BC
D
Field
w
b
w
Parabolic
flow profile
B
C
Figure 1 Schematic diagram of a typical FFF channel and
the normal mode FFF separation mechanism. (Reproduced
from L.F. Kesner, J.C. Giddings, High Performance Liquid
Chromatography, eds. P.R. Brown, R.A. Hartwick, Chapter 15,
1989. Copyright  1989, John Wiley & Sons, Inc. Reprinted by
permission of John Wiley & Sons, Inc.)
in FFF may be accurately calculated in theory and related
to various solute physicochemical properties..10,11/ The
particular sample property controlling retention depends
on the type of the applied field. The use of different
fields has generated a number of FFF techniques, such as
sedimentation field-flow fractionation (SdFFF).12/ when
a centrifugal force is used to induce retention, flow fieldflow fractionation (FlFFF).13/ when the field is established
by a transverse or crossflow of liquid, thermal field-flow
fractionation (ThFFF).14/ when a thermal gradient is used,
and electrical field-flow fractionation (ElFFF).15/ when
a potential gradient is applied to electrically charged
solutes.
FFF is particularly suitable for the separation of macromolecular samples and suspended colloidal particles of
various origins because of the minimal surface area of the
channel compared with the total surface area of a packed
chromatographic column (107 cm2 )..16/ For this reason,
adsorption phenomena are greatly reduced in FFF. The
driving force may be accurately adjusted to yield the
desired levels of retention without the need to change the
column as in chromatography and sample distribution
between zones is very fast because no phase boundaries
must be crossed. A rich literature is available for a great
number of applications from colloids of environmental
origin.17/ to bacteria and viruses..18/
2 THEORY
The theory of retention discussed in this section is
developed for point particles at infinite dilution, that
3
FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
is, for species with negligible size with respect to the
channel dimensions, particularly its thickness. When this
assumption is not satisfied corrections must be made
to account for the particle size. One such correction is
considered in the retention model for steric FFF.
2.1 Basic Theory of Retention
Let us consider the space between two parallel plates
and a field applied orthogonal to them in the xdirection (measured across the channel thickness from
the accumulation wall). Under the effect of the field alone,
component particles are displaced with a velocity U. The
particles’ motions give rise to a field-induced flux Uc
defined as the number of particles per unit cross-sectional
area per unit time directed toward the accumulation
wall, that is in the negative x-direction. The field-induced
displacement is, however, counteracted by a diffusive flux
proportional to the concentration gradient dc/dx through
the component’s diffusion coefficient D and directed in
the positive x-axis direction. The mass transport across the
channel determines a net flux Jx given by Equation (1):
Jx D Uc
D
dc
dx
.1/
The concentration profile across the channel thickness
reaches a steady state when the field-induced and diffusive
fluxes are at equilibrium. At this point the net flux is equal
to zero. Equation (1) is integrated and solved, assuming
constant U and D, to give an equation that describes the
steady state concentration profile (Equation 2):
c.x/
jUj
x
.2/
D exp
c0
D
where c0 is the concentration at the accumulation wall,
x is the distance from the wall, and jUj is negative for
consistency with the coordinate system. Concentration
decreases exponentially from the accumulation wall.
Since it may be shown that an exponential distribution
behaves as a much thinner layer positioned at a
characteristic height `, Equation (2) may be rewritten
as Equation (3):
x
c.x/
.3/
D exp
c0
`
where (Equation 4)
`D
D
jUj
.4/
The mean layer thickness ` is a measure of the average
distance of a sample component from the accumulation
wall. It is apparent from Equation (4) that ` depends on
the opposing effects of the field that acts to compress the
solute layer and the diffusion process that broadens it. The
quantity ` is frequently expressed in the dimensionless
form shown in Equation (5):
lD
`
D
D
w
jUjw
.5/
where w is the channel thickness and l is the retention
parameter basic to FFF equations. Since l may be
shown to be dependent on the field strength and on a
sample – field interaction constant, each component will
have a characteristic l value.
After the formation of the steady-state zone, a stream
of liquid is allowed to flow along the longitudinal axis
of the channel. Component particles are then carried
downstream with an average velocity that depends on the
region where they are found. The sample distribution
at this point assumes a Gaussian distribution in the
longitudinal direction because of the free diffusive motion
of component molecules between regions of different
velocities across the channel. The elution time will then
be different for different components and may be used
to measure the sample elution velocity once the channel
void volume is known. Elution time, however, is not
the most universal parameter defining the behavior of a
species migrating along a chromatographic column or an
FFF channel since it always depends on the average fluid
velocity. The dimensionless retention ratio R, defined as
the ratio of component migration velocity vp to the mean
fluid velocity hvi (Equation 6),
RD
vp
hvi
.6/
is a more useful parameter. R is widely used in separation
techniques as a measure of the retardation of the solute
relative to the liquid carrier flow velocity. It is a more
universal measure of retention than elution time and
only depends on the field strength and on the particle
property responding to the field, regardless of the flow
velocity. It then frees the mathematical architecture from
a variable. In the expression of R, the solute mean
migration velocity is the average of the particle velocities
expressed as vp D hcvi/hci..19/ Inserting this expression
into Equation (6), substituting the concentration term
with Equation (3) and the parabolic function to calculate
v, and using Equation (5), one obtains an expression for
R whose solution is given by Equation (7):
1
2l
.7/
R D 6l cot h
2l
Equation (7) is the basic retention equation in FFF. It
shows that retention is solely dependent on l, which is
characteristic of each eluting species. Approximate forms
of Equation (7) may be used for low l values or high levels
of retention. In particular, the approximation R D 6l has
4
POLYMERS AND RUBBERS
an error of 20% at R D 0.25. The empirical relationship
R D 6.l 2l2 / has the greater range of applicability
with less than 10% error up to R D 0.7. The retention
ratio may also be written as R D t0 /tr since V D L/tr and
hvi D L/t0 , where t0 is the residence time of the eluent or
of a nonretained component and tr the average sample
residence time or retention time.
In theory, any external field to which sample components are responsive may be used to induce selective
retention and fractionation by FFF. The applied field
determines the type of interaction and hence the sample
property that will be measured. Besides FlFFF, ThFFF,
SdFFF and ElFFF, the theoretical foundation has also
been laid down for many less developed FFF techniques.
One such technique uses a concentration gradient in a
solvent mixture to establish a chemical potential gradient
capable of driving solutes towards regions of lowest potential [concentration field-flow fractionation (CFFF)]..20/ A
nonuniform electric field that induces charge polarization
may exert selective dielectrophoretic forces on component particles and generate fractionation..21/ Interesting
applications are reported using a magnetic field..22/ Photophoretic FFF.23/ is based on the transfer of momentum
from a photon to a particle. An acoustic wave field.24/ may
induce retention selective to particle diameter in addition
to other parameters.
The present discussion focuses on the FFF techniques
that have been applied to polymer separations: FlFFF
and ThFFF. These techniques have been extensively used
for a great number of different samples. They are the
FFF techniques par excellence for polymer fractionation.
ElFFF has shown its potential only with a new channel
design.25/ and may prove to be very useful for the
characterization of charged polymers.
In his investigations on the theory of Brownian motion,
Einstein.26/ showed that in a system of point particles at
infinite dilution, i.e. in the absence of flow perturbations
due to the motion of one particle affecting another,
the diffusion coefficient is inversely proportional to the
friction coefficient (Equation 8):
DD
kT
f
.8/
If D is replaced with the Einstein equation and the
relationship for the field-induced velocity specific for
FlFFF (U D VP c /Lb) is used in Equation (5) one obtains
lD
kT V 0
f VP c w2
.9/
In Equation (9), the relationship V 0 D Lbw is also used to
replace Lb with V 0 /w. It is worth noting that Equation (9)
depends on the friction coefficient f as well as on the
instrumental parameters V 0 and w. This is not the case
with SdFFF where both D and U depend inversely
on f , which then cancels out in the ratio D/jUj. The
dependence of the retention parameters l and R on the
friction coefficient in FlFFF is the key to obtaining solute
physicochemical parameters from FFF measurements.
More than a century before Einstein’s work in this area,
Stokes.27,28/ found a quantitative relationship between
the shape and the dimensions of a moving particle and
its friction coefficient. For a spherical body of radius R0
moving in a fluid of viscosity h he showed that the friction
coefficient could be expressed by Equation (10):
f0 D 6phR0
.10/
Stokes’ equation may be used to relate diffusion coefficient to particle dimensions. Correction factors that
extend Stokes’ relation to nonspherical particles were
first introduced by Perrin.29/ and Herzog et al..30/ for
solids of revolution such as prolate (cigar-shaped) and
oblate (disk-shaped) ellipsoids. They chose to express the
departure of the actual friction coefficient f , for an ellipsoid with axes of symmetry of different length from the
friction coefficient of a sphere of same volume f0 . They
found a quantitative relation between f /f0 and the ratio
a/b of the semimajor axis a to the semiminor axis b. By
combining Equations (8) and (10), Equation (11):
D0 D
kT
6phR0
.11/
is obtained. The Stokes – Einstein relation in Equation (11) is derived considering equivalent particle orientation which applies rigorously only to spherical bodies.
The substitution of Equation (10) into Equation (9) gives
the expression for l in FlFFF (Equation 12):
lD
V0
kT
6phR0 VP c w2
.12/
which shows explicitly the effective size-based separation
in normal-mode FlFFF where samples are retained
proportionally to their hydrodynamic dimensions.
The expression for l in ThFFF is derived using
a conceptual procedure similar to that followed for
FlFFF. The derivation of this expression is complicated,
however, by the distortion of the parabolic flow profile
due to changes of viscosity with temperature across the
channel..31,32/ In 1856, Fick (and later Soret in 1859)
showed that if a salt solution of uniform concentration
in a tall container is heated at the top and cooled at the
bottom, a flux of matter originates that increases the salt
concentration at the cold end of the column. This effect,
named after Soret, is known as thermal diffusion since it
is clearly a diffusive effect occurring only in the presence
of a thermal gradient. The equation of flux (Equation 1)
5
FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
set for molar thermal and diffusive fluxes gives
dT
dT
dc
C cg
DT c
Jx D D
dx
dx
dx
to Equation (16):
.13/
where DT is the thermal diffusion coefficient and g is the
coefficient of thermal expansion. The solution for zero
net flux at the steady state yields the retention parameter
for ThFFF (Equation 14):
dT a
Cg
lD w
T
dx
1
.14/
where a is the thermal diffusion factor equal to DT T/D..33/
Both a and dT/dx depend on the local position x and thus
on the temperature. The ordinary diffusion coefficient
is strongly dependent on the temperature through the
T/h term in Equation (11) where 1/h also increases
with T. In the case of flexible-chain macromolecules,
it must be borne in mind that, on polymer chemistry
theoretical grounds, the molecular coil is expected to
expand on increasing temperature as a consequence of
the increased excluded volume. This property is treated
in terms of the second virial coefficient..34/ The tendency
of polymer hydrodynamic dimensions to increase with
temperature is reported in light-scattering studies..35/ The
local temperature gradient is not independent of T .31,32/
but the dependence is relatively small. DT is shown to
depend on temperature.36/ but to a smaller extent than
the ordinary diffusion coefficient. In the standard theory
of FFF, however, l is generally used in an approximate
form that is valid at high retention where the sample
cloud is very close to the accumulation wall. The local
values of dT/dx and a may therefore be assumed to be
the same as those at the cold wall..37/ The term g becomes
negligible.31/ and l may be rewritten as in Equation (15):
l³
D
T
c D
dT
dT
aw
DT w
dx c
dx c
.15/
where .dT/dx/c is the temperature gradient at the cold
wall.
2.2 Molecular Weight Dependence on Physicochemical
Parameters
Synthetic polymers are often flexible-chain molecules
whose dimensions cannot be defined precisely and must
be considered as average values of all the configurations
that the molecules assume. In such a situation it is
convenient to introduce a new parameter called the radius
of gyration, Rg . It is found from polymer theory that
molecular weight may be related to polymer molecular
dimensions through this statistical parameter according
R2g /
M
M0
.16/
where M is the molecular weight and M0 is the
molecular weight of the repeat unit (constant for synthetic
homopolymers). The equivalent radius Re , defined as the
radius of an equivalent sphere having the same value of
the friction and diffusion coefficients as the polymer, is
a convenient parameter that is often used. Since it may
be demonstrated that Rg / Re ,.34,38/ equations dependent
on Rg may be written in terms of the equivalent radius.
For approximately spherical molecules, the volume of the
molecule is linearly related to molecular weight. This may
be expressed as Equation (17):
R0 / M1/3
.17/
where R0 is the radius of a spherical particle. Globular
proteins are an example of a real system that satisfies
the model of a rigid spherical body. Even in such a
simple case however, correction factors must be applied
to Equation (17) to account for the hydration volume and
deviation from the perfectly spherical symmetry. When
the polymer molecule is a statistical chain that is allowed
to meander randomly in a Brownian-like way with no
forbidden physical volume, polymer theory shows that
hR2g i is proportional to the number of repeat units in
the macromolecule chain given by N D M/M0 . It follows
that the equivalent radius (or Stokes radius) is given by
Equation (18):
Re / M1/2
.18/
If the polymer chain is not allowed to self-cross, there
is some space occupied by other polymer segments from
which each segment is excluded. Polymer conformations
are significantly affected by the excluded volume and the
equivalent radius for a three-dimensional polymer chain
model becomes (Equation 19):
Re / .M6/5 /1/2
.19/
Based on the model of the equivalent sphere (Stokes –
Einstein relationship), Equation (11) may be applied to
polymers in solution, and the diffusion coefficient, at a
given temperature, may be related to molecular weight
through the polymer equivalent dimensions Re and the
friction coefficient..38,39/ Substituting Equation (18) or
(19) into Equation (11) and grouping together all the
constants, we obtain Equation (20):
D D AM
b
.20/
where A is constant for a given polymer type and b is an
exponent that depends on the polymer conformation in
6
POLYMERS AND RUBBERS
solution. The value of the exponent in Equation (18)
is obtained on theoretical grounds, considering zero
attractive or repulsive interactions between different
polymer segments as well as between polymer molecules
and the surrounding medium. It also assumes infinitely
dilute systems of neutral, nonfree draining molecules
with average spherical symmetry. A system under these
conditions is defined as a -system (theta-system) at temperature. -conditions are set by the type of solvent
(which determines the energy of interaction with the
polymer molecules) and by the temperature. Generally,
only one solvent behaves as a -solvent for a given
polymer type. Therefore, the theoretical value of the b
exponent is always related to a specific polymer – solvent
system at -temperature. The excluded volume has a
considerable swelling effect on flexible-chain molecules
and on the dependence of particle size on molecular
weight. The excluded volume effect is similar to and
may also be thought of as that due to a good solvent
or to a temperature higher than the -temperature. By
relating the diffusion coefficient and molecular weight at
a given temperature, Equation (20) allows FFF-measured
parameters to be correlated with the polymer molecular
weight. Combining Equations (12) and (20), it appears
that l in FlFFF is inversely dependent on molecular
weight, that is, the zone mean migration layer decreases
as the polymer molecular weight increases (Equation 21):
l D AM
b
V0
VP c w2
.21/
A similar expression for ThFFF is complicated by the DT
term in Equation (15). In the classical theoretical treatment of FFF, DT is considered independent of molecular
weight,.37/ as predicted and experimentally observed by
some authors.40/ (see section 5.1). Other authors,.41,42/
however, report a molecular weight dependence of the
thermal diffusion coefficient. Assuming that, at a given
temperature, we have (Equation 22):
DT D BMb
.22/
and considering Equation (20) for the dependence of the
ordinary diffusion coefficient on molecular weight, the
overall contribution of molecular weight to l in ThFFF is
given by the D/DT term as Equation (23):
A
D
D M
DT
B
.bCb/
D M
n
.23/
where  D A/B and n D b C b. The parameter  must
be temperature dependent because of the dependence
of D on temperature. Equation (23) substituted into
Equation (15) yields a negative exponential correlation
between l and the molecular weight (Equation 24):
l D M
n
w
1
dT
dx c
.24/
2.3 Conversion of a Fractogram to Molecular Weight
Distribution
To obtain a meaningful molecular weight distribution
of a polymer sample, it is necessary that elution occurs
in the same mode (normal, steric, etc.) over the entire
retention time interval with a monotonic function of some
sample property. Transformation of a fractogram from
a time-based function to a molecular weight function
is readily accomplished but requires a correction to
the amplitude to account for the nonlinear relationship
between M and tr . The mass abundance in a time
P r , must equal the
interval dtr , corresponding to c.tr /Vdt
mass comprised in the corresponding molecular weight
interval dM. Integrating the mass distribution m(M) over
that interval yields Equation (25):
P r
m.M/ dM D c.tr /Vdt
.25/
where c(tr ) is the detected sample concentration at time
tr and VP is the volumetric channel flow rate. For dtr ! 0,
Equation (25) becomes Equation (26):
dtr
m.M/ D c.tr /VP
dM
.26/
The scale correction function dtr /dM allows the conversion of the retention timescale to the molecular
weight scale. For a normal-mode elution, the molecular weight distribution may be obtained in theory from
first principles..43/
2.4 Calibration Methods
It may be shown that the scale correction function
depends on the constants A and b for FlFFF and 
and n for ThFFF, through the dependence of l on
molecular weight. These constants may be found from
theory and are available in literature for a wide number
of polymer – solvent systems. However, it is common
laboratory practice to obtain them through a calibration
procedure with a set of well-characterized, narrowly
distributed polymer standards whose molecular weights
have been measured by some absolute technique such as
light scattering, viscometry or osmometry. To obtain A
and b values that can be transferred to an unknown
polymer sample, calibration must be performed with
standards of the same or similar composition as the
unknown, in the same carrier liquid and at the same
temperature. Constants A and b for the FlFFF analysis of
7
FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
polymers are obtained from the intercept and slope of a
plot of the measured log D versus log M (Equation 27):
log D D log A
b log M
.27/
derived from Equation (20). The plot of log l versus log
M would also give these constants. A similar log lT
versus log M plot provides the constants  and n for the
calibration in ThFFF. Gao and Chen.44/ and Giddings.45/
have shown the system transferability of the ThFFF
calibration constants. A more detailed treatment of the
‘‘universal calibration’’ in ThFFF.46/ also accounts for
the change of the cold wall temperature on polymer
retention and on the calibration constants. FFF constants
allow a more universal calibration than size-exclusion
chromatography (SEC) since they are derived from
fundamental physical properties of the carrier liquid and
of the polymer under investigation and do not depend
on any system parameter. In contrast, calibration in SEC
has no rigorous theoretical grounds; it is not valid for
some pore structures.47/ and it is therefore not system
transferable. Moreover, it is still under evaluation for
some types of polymers.48 – 50/ and does not always apply
to different polymer samples.51,52/ even when run in the
same column under the same conditions..16/ Calibration
in FFF may also be performed using a set of polydisperse
standards.53,54/ or with a single broadly disperse sample
when the relative molar mass is measured at two or more
retention times by an absolute technique such as light
scattering.55/ or mass spectrometry..56/ It should be noted
that absolute molecular weight (M) measurements made
by FlFFF combined with mass spectrometry show an
excellent data fit for log l (and thus D) versus log M at
molecular weight values far lower than those predicted
from polymer theory.
2.5 Zone Broadening
The previous discussion on calibration in FFF assumed
that broadening of the peak was due solely to molecular
mass differences. In contrast, a number of concomitant
effects contribute to the increase in peak width. A
measure of zone spreading, and hence of resolution,
is given by the plate height. As with other separative
techniques, the overall plate height in FFF is given by the
sum of contributing uncorrelated terms (Equation 28):
X
H D Hl C Hn C Hr C Hp C
Hi
.28/
In Equation (28), the zone spreading due to longitudinal
diffusion Hl arises from concentration gradients along
the sample plug and increases with the residence time.
It is linearly related to the diffusion coefficient as
Hl D 2D/Rhvi and therefore becomes negligible for very
slowly diffusing components such as macromolecules. In
contrast, the nonequilibrium term Hn arising from the
random displacement of component molecules across the
channel is one of the dominant contributions to peak
broadening in FFF. The band spreading associated with
the time needed for the zone to reach the equilibrium
position in the presence of the longitudinal flow, Hr ,
may be minimized by adopting aPstop-flow procedure
(see later). Other contributions,
Hi , associated with
system nonidealities such as dead volumes or injection
volumes, may be disregarded in a well-designed channel.
The spreading due to differences in a characteristic
property such as molecular weight Hp is only an apparent
broadening. It arises from the fact that individual
molecules of a macromolecular or a particulate sample
may differ somewhat from one another in their relative
mass or size and are retained to a slightly different
extent. If the difference in M is not large enough to
produce distinct peaks, the sample zone will appear
as a broadened peak with different mass elements
continuously distributed in a molecular weight interval.
It may be shown that (Equation 29):.57/
Hp D LS2M .µ
1/
.29/
where µ D MW /MN is the sample polydispersity index
which gives a measure of the departure of the weightaverage molecular weight MW from the number-average
molecular weight MN . For monodisperse samples, the two
averages coincide. It appears from Equation (29) that the
plate height, and hence resolution, strongly depend on the
system selectivity SM , which is defined as the retention
volume difference of components of different M relative
to the molecular weight difference (Equation 30):.58/
d ln Vr d ln R D
.30/
SM D d ln M d ln M The subscript M denotes a molar mass-based selectivity
whose value is a measure of the system ability to
discriminate samples by their mass. Under conditions
of high retention, the approximation R D 6l may be used
and SM becomes in the limiting form (Equation 31):
d ln l .31/
SM D d ln M Application of Equation (31) to Equations (21) and
(24) shows that selectivity values for FlFFF and ThFFF
coincide with the exponent of molecular weight, i.e. b
in FlFFF and n in ThFFF. Assuming that the thermal
diffusion is independent of molecular weight, b and
n may be associated with the polymer molecule conformation in a given solvent and temperature system.
From polymer theory, values of exponent b are predicted to be 0.33 for solid spheres, 0.5 for random-coil
macromolecules.39/ in -conditions and about 0.7 for
8
flexible-chain polyelectrolytes..59/ The theoretical selectivity for FFF is considerably higher (0.5 – 0.7).60/ than
that for SEC, where typical values range between 0.05
and 0.1..58,61/ Differences in selectivity when polymers
are analyzed in organic solvents or aqueous solutions
are expected considering that water generally behaves
as a good solvent for hydrophilic polymers whereas
-systems are mostly reported for neutral polymers in
organic solvents. The theoretical value of 0.588.38,62/ for
polystyrene (PS) in tetrahydrofuran is obtained in ThFFF
at a specific cold wall temperature..46/ The same polymer, run in ethylbenzene by FlFFF,.63/ gives a selectivity
ranging between 0.51 and 0.56. Synthetic water-soluble
polymers are generally fractionated with a selectivity
above 0.6..64 – 69/ Polyvinylpyridine is an interesting example of a polymer that behaves as a neutral statistical
chain in tetrahydrofuran and as a charged coil in water
where it is soluble only as a polyelectrolyte. This polymer, bearing a six-term aromatic ring in the repeat unit,
is fractionated with a selectivity of 0.51 in tetrahydrofuran by ThFFF and of 0.62 in an aqueous medium at
low pH..65/ Systematic studies of polyelectrolytes in aqueous solution by FlFFF indicate a strong effect of the
solution ionic strength on the selectivity, which generally decreases with increasing concentration of the
added simple electrolyte..68/ Further investigations on
the change in selectivity with the ionic strength of aqueous solutions and with the type of added electrolyte
have been used to show specific interactions between the
polymer and some metal ions..69/ Retention and selectivity in ThFFF of neutral polymers in organic solvents
appear to increase with rising solubility parameters of
the polymer – solvent system..70/ This effect was first registered in early investigations on ThFFF of polymers..37/
Comparative studies on the separation of copolymers
by ThFFF and gel permeation chromatography (GPC)
show that only the former yields a good separation of
a diblock copolymer of poly(styrene-co-isoprene) from
a triblock poly(styrene-co-isoprene-co-styrene)..71/ This
ThFFF separation is attributed to the difference in thermal diffusion coefficient of the two polymers.
2.6 General Theory of Asymmetric Flow Field-flow
Fractionation
The general concepts of FFF were first developed for
uniform field strengths and constant flow velocities along
the channel. The symmetric FlFFF channel, shown in
Figure 2(a), was designed to achieve these characteristics.
In 1987, Wahlund and Giddings.72/ introduced a new
design of a FlFFF channel with only one permeable wall
and no independent transverse flow. In this variant of
FlFFF named ‘‘asymmetric FlFFF’’, shown in Figure 2(b),
the permeable upper wall is replaced by a solid glass
POLYMERS AND RUBBERS
Symmetric flow FFF
Crossflow in
Permeable
frit
Membrane
Permeable
frit
(a)
Crossflow out
Asymmetric flow FFF
Glass
wall
Membrane
Permeable
frit
(b)
Crossflow out
Hollow-fiber flow FFF
Crossflow out
Hollow-fiber
membrane
walls
(c)
Crossflow out
Figure 2 Different configurations of FlFFF channels. The
symmetrical (a) and asymmetric (b) channels are commercially
available and thus more commonly used than the hollow-fiber
configuration shown in (c).
plate that conveniently allows visual inspection of the
interior of the channel. Both the channel and crossflow
originate at the channel inlet but exit the channel
as two separate streams at the channel and crossflow
outlets. Using this asymmetric channel configuration,
a crossflow velocity gradient is established across the
channel thickness. The sample concentration in the
transverse coordinate in this design may no longer
be described by Equation (3), but it approaches the
exponential distribution of the standard FFF model for
highly retained samples. Expressions for R and l are
found following the same mathematical procedure as
in the symmetric configuration but taking into account
that the flow velocity profile is linearly decreasing along
the channel at a rate determined by the crossflow
velocity. For high retention levels (x/w ³ 0.1), l may
again be approximated by Equation (9). Rectangular
and trapezoidal.73/ shaped channels have been used
in asymmetric FlFFF. In the latter case, the breadth
decreases as a function of channel length. An exponential
9
FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
decrement in channel breadth.74/ is shown to give a
constant average channel flow velocity.
2.7 Retention in Hollow-fiber Channels
An interesting but commercially unavailable configuration of FlFFF utilizes a hollow cylindrical fiber with
porous walls in place of the rectangular channel..75/ In
this arrangement, illustrated in Figure 2(c), the axial flow
is provided by an external pump connected with the inlet
of the hollow-fiber membrane while the transverse flow
is obtained by removing liquid radially from the channel
with a second pump. The two flow velocity profiles in
this configuration are different from any of the previously described FlFFF systems, both being variable with
the distance Z from the inlet because of the pressure
drop along the channel. From studies of fluid dynamics
in hollow fibers,.76/ it is found that the axial and radial
flow velocities decrease exponentially as a function of Z
and the permeability of the fiber and the fluid viscosity.
Retention time in this type of channel is a function of
channel length and Péclet number.
3 INSTRUMENTATION
An FFF system is generally assembled in a manner similar
to that of a chromatographic apparatus. It uses most of the
ancillary equipment employed in chromatography such
as injector valves, pumps for the carrier liquid delivery,
detectors, and some data acquisition devices such as chart
recorders or more conveniently computers. A generalized
FFF system is shown in Figure 3.
3.1 Flow Field-flow Fractionation
FlFFF is the most universally applicable FFF technique
because any solute particle is subject to transport in a
liquid stream. As shown in Figure 4, the spacer containing the channel form is clamped between two parallel
blocks of some material such as Plexiglas, polyethylene,
anodized aluminum, or stainless steel that accommodate
two porous frit panels with 2 – 5-µm pores. Ceramic
frits are more commonly used while polyethylene,.64,77/
polypropylene,.18,78/ and stainless steel.63,64,79/ are generally employed with clamping blocks of the same material.
An important component of the FlFFF channel is a permeable, generally polymeric, membrane placed over the
accumulation wall to impede sample loss through the frit.
Given the importance of the membrane in the successful application of FlFFF, a specific section (section 6.3)
is dedicated to this topic. The design of the asymmetric
FlFFF channel is somewhat different from that of the
symmetric channel, as shown in Figure 2(b), but besides
the dissimilarity of the channel geometry and the absence
of the top porous wall it bears few differences from the
symmetric FlFFF system. Some operational procedures,
such as sample injection and relaxation, however, differ
from those routinely used in the symmetric channel. A
hollow-fiber channel has to be placed in a mantle, possibly
of cylindrical symmetry, such as an empty stainlesssteel chromatographic column, and the two coaxial tubes
sealed to each other at the ends. The mantle must have a
port connected to a crossflow pump that draws fluid out
through the wall of the fiber. The channel flow is supplied
by another pump connected to one of the hollow-fiber
extremities. Sample injection and relaxation also in this
case are particular to the set-up and will be dealt with in
section 4.2.
Standard FFF theory assumes constant and uniform
field strength and average flow velocity in the length and
breadth dimension (edge effects not considered). Therefore, accurate control and continuous measurements of
both these parameters are necessary when operating an
FFF system. In FlFFF, the pump flow rates for both
the longitudinal and transverse streams must be kept
constant and continuously checked because, after mixing inside the channel, both flows may exit the channel
through the outlet with the lower pressure. It is therefore of primary importance to equalize the pressures at
the channel and crossflow outlets. This is achieved by
placing back-pressure regulators at one or both outlets
Control
Computer
Injection
valve
Data acquisition
Pump
Detector
Field
Flow rate
measurement
Fraction
collector
Carrier
reservoir
Channel
Figure 3 FFF system assembled with the ancillary equipment.
Waste
10
POLYMERS AND RUBBERS
Channel flow in
(sample injection)
Crossflow in
Channel flow out
(to detector)
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
FFF
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
chan
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
nel
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Clamping
block
Porous frit
Spacer
Membrane
Porous frit
Clamping
block
Crossflow out
Figure 4 Diagram of the constituent elements of a FlFFF channel. (Reprinted from M.H. Moon, J.C. Giddings, J. Pharm. Biomed.
Anal., 11, 911 – 920 (1993). Copyright 1993, with permission from Elsevier Science.)
and checking the pressure with in-line pressure gauges.
An easy, cheap, but time-consuming method to check the
flow rates is to measure the liquid volumes displaced over
unit time with a buret and a stopwatch. Alternatively, a
balance can be used to measure the weight of the carrier liquid exiting from each outlet as a function of time.
The balance may be connected to a computer.80/ to store
data on time-dependent flow rates that may be used for
accurate calculations of the retention parameters. This is
particularly useful in programmed runs (see later) where
the field strength, and hence the crossflow rate, is varied
with some function of time.
3.2 Thermal Field-flow Fractionation
ThFFF channels (Figure 5) are formed by clamping a
polyimide spacer (with the FFF channel volume removed)
between two copper blocks with highly polished nickel
or chromium surfaces. The field in this system is a
thermal gradient that is provided by electrically heated
metal elements inserted into one block and a stream
of cold water flowing through the second block. Holes
are drilled into the copper blocks to allow the insertion
of temperature-measuring probes at different positions
along the channel.
3.3 Detectors
Virtually any of the detectors used in chromatography is
compatible with FFF apparatus. The HPLC separation
Channel inlet
Channel outlet
Hot copper bar
yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Cartridge heater
Spacer
Cold copper bar
Coolant circulation
Figure 5 ThFFF channel. (Reprinted with permission from
J.C. Giddings, V. Kumar, P.S. Williams, M.N. Myers, Adv.
Chem. Ser., 227, 3 – 21 (1990). Copyright 1990, American Chemical Society.)
mechanism generally induces a concentration of the
initial sample plug so that samples of continuously
decreasing concentration may be detected. In FFF,
the solute plug undergoes considerable concentration
during the relaxation process.81/ and considerable dilution
during separation and elution. While reduction of the
injected sample mass is always sought, particularly
for high-molecular-weight polymer samples, the final
concentration must be considered and the injected load
adjusted to give a good signal-to-noise ratio. Nonspecific
detection methods, such as refractive index.61,71,82,83/ or
viscosity,.84/ may be generally used while others may
be employed only when the solute is susceptible to
specific response. This is the case for spectrophotometric
detection, one of the most widely used methods in
chromatography and FFF. Spectrophotometric detection
FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
M
106
105
0.7
0.8
0.9
1.0
1.1
1.2
Ve (mL)
(a)
1.0
dW/dM
0.8
0.6
0.4
0.2
0.0
105
106
MW
(b)
Rg (nm)
100.0
mass distribution..85/ The Mie theory.86/ used in these
corrections takes into account the dependence of the
scattered intensity on the particle size, the refractive
index, and the scattering angles. Fluorescence detection
is most often used with derivatized samples..87/ A recent
development in polymer characterization is the coupling
of FFF with a multiangle light scattering (MALS)
detector..88 – 91/ This hyphenated system combines the
high resolution capabilities of FFF with the absolute
and independent molecular weight determination of light
scattering, thus eliminating the need to calibrate the
FFF system. The absolute determination of molar masses
by MALS also allows for small nonidealities in the
operating conditions such as fluctuations in temperature
and flow rate. The best results are obviously obtained
when optimum separation conditions are used and in the
absence of nonidealities. The high fractionating capability
of FFF is registered as an increase in the relative molar
mass along the eluted peak as shown in Figure 6(a – c). The
integrated FFF MALS apparatus has also allowed an indepth study of the effect of experimental conditions such
as injected sample mass or crossflow rate on the elution
and fractionation of polymer samples..92/ A detailed
discussion on these topics may be found in sections 6.1 and
6.2. The generally low sensitivity of laser light scattering
detection is a problem, particularly for low-molecularweight components and polyelectrolytes whose molar
mass determinations are meaningful only at high ionic
strength..93/ This problem has been overcome by coupling
an electrospray mass spectrometer to a FlFFF channel.56/
as mentioned in section 2.4.
4 EXPERIMENTAL PROCEDURES
10.0
4.1 Sample Preparation and Handling
1.0
105
(c)
11
106
M
Figure 6 ThFFF/MALS of PS microgel. (a) Increase in molecular weight with increasing elution volume Ve ; (b) molecular
weight distribution determined from MALS (dashes) and calculated by calibration (open circles); (c) radius of gyration
Rg versus molecular weight. (Reproduced by permission of
Wiley-VCH from Antonietti et al..90/ )
depends on the absorption of radiant energy of specific
wavelengths by the chromophores. However, when the
solute particle size becomes comparable to the detector
wavelength, the output signal is considerably affected
by light scattering. Consequently, the measured signal
must be corrected in order to obtain an accurate
No special treatment is generally required for the preparation of samples to be analyzed by FFF. Specific
procedures, such as extraction, purification, and concentration, may be necessary for polymers of natural
origin since synthetic polymers undergo sample purification as part of the production process. As mentioned
previously, the narrow sample pulse injected in an FFF
channel undergoes considerable changes in concentration as it is relaxed and fractionated.81/ (see later). The
concentration of the injected polymer sample solution is
therefore a parameter that must be carefully controlled.
Injection of large sample masses affect the plate height.94/
even before the effect of overloading is registered by
other retention parameters. The sample concentration
during relaxation depends on the mass injected and can
be one or more orders of magnitude higher than that
of the initial sample solution depending on the retention ratio (concentration at the wall is approximately
12
equal to the sample concentration divided by l which
is expected to be 0.1). The effect of molecular dimensions on the concentration of polymer solutions is known
from theory. Four model polymer solutions are generally
identified: the dilute solution corresponding to a concentration of molecules separated by large volumes of
solvent, the intermediate regime with a much reduced
distance between polymer chains that may touch each
other but still do not overlap, the semidilute, and the
concentrated regime. In the last two cases, the polymer
concentration is so high that chain entanglement dominates and the system may not be regarded as that of
individual molecules suspended in a liquid medium. The
solution properties are not governed by the properties
of individual molecules and such systems will therefore
have a behavior very different from that of any concentrated solution of small molecules. For this reason, the
concentration cŁ corresponding to that of the intermediate regime has been the subject of several theoretical
and experimental investigations. In a number of studies,
the dependence of cŁ on molecular weight was found
to follow a power law of the type cŁ / M a , where a
is ¾0.7..95 – 97/ From considerations of the polymer coil
density and volume fraction , it may be shown that
the threshold value Ł for the transition between the
dilute regime and the semidilute is related to the number
of repeat units N in the macromolecular chain and the
square of a characteristic parameter d/l (the ratio between
the coil thickness d and its length l). An estimate of the
volume fraction Ł shows that the onset of the semidilute regime occurs at much lower concentration for more
elongated macromolecular chains. Theoretical findings
are corroborated by experiments when the behavior of
flexible chain polymers, for which the d/l value is between
1/2 and 1/3, is compared with that of DNA, which has a
value of ¾1/50. The critical concentration for this macromolecule hence decreases 2500-fold. The experimentally
determined critical concentration reported for DNA is
2.2 – 2.6 µg per 100 µL..98,99/ An injection concentration
100 times lower than the critical value is recommended in
FFF experiments. For synthetic polymers, concentrations
of 0.05 – 0.50 g L 1 and injection volumes of 1 – 10 µL give
easily detectable peaks under conditions of total sample
recovery..68/
4.2 Sample Injection and Relaxation
Sample solutions may be introduced into an FFF channel through an injection valve with a constant-volume
loop such as those commonly used in chromatography or
through an on-line tee-union fitted with a septum. The
latter does not limit the injected volume but the polymer septum should be isolated from the channel with an
on-line zero-dead-volume filter. When sample particles
POLYMERS AND RUBBERS
are first introduced into the channel, they are dispersed
over the entire cross-section and experience the same
field strength but different longitudinal migration velocities depending on their distance from the accumulation
wall. While under the effect of the field alone the sample
plug would concentrate in a narrow layer of exponential
concentration. However, with displacement by the longitudinal flow, the plug undergoes a considerable dispersion
along the channel length. This happens because molecules
starting their migration far from the accumulation wall
will take longer to reach the equilibrium position and
will be swept ahead of species closer to the accumulation
wall. A simple way to circumvent this problem and greatly
reduce the relaxation contribution to the plate height is
to halt the longitudinal flow as soon as the sample enters
the channel. This stop-flow procedure allows the field
to complete the sample relaxation process without the
undesirable effects of differential migration velocities..1/
The stop-flow time, tsf , depends on the channel thickness,
the field strength, and the final transverse position of the
zone’s center-of-gravity. It has limits for low and high l of
w2 /2D and w2 /12D, respectively. In practice, the relaxation process is started when all sample molecules have
entered the channel. The delay time between the injection
and the beginning of the relaxation is given by the ratio of
the volume of the tubing between the injection port and
the channel inlet and the volumetric flow rate. Although
the stop-flow procedure has proven successful in yielding
well-shaped peaks at the expected retention times, it is
associated with a number of nonideal phenomena such
as sample loss due to adsorption on the accumulation
wall, baseline disturbance and increased analysis time.
Different channel designs have been adopted to achieve
sample relaxation without stopping the axial flow. A wellrelaxed sample zone can rapidly form by applying a strong
field in a small area localized at the channel inlet or by
reducing the channel thickness in the same region. Hydrodynamic relaxation, currently applicable only to flow
systems, may be achieved by isolating the inlet portion
of the depletion wall and applying a higher field strength
only in that area..100/ Sample components entering the
channel are rapidly transported to the accumulation wall
and relaxed. This system has been mostly used for biological macromolecules..101/ The pinched-inlet channel,
applicable in principle to any FFF system,.102/ has been
tested experimentally on latex particles in an FFF channel
under gravitational force..103/ Hydrodynamic relaxation
obtained with a thin channel splitter.104/ has been examined in SdFFF with latex particle samples..105/ Hybrid
split and frit-inlet FlFFF systems have been designed and
tested..106/
The relaxation procedure in asymmetric FlFFF is
somewhat different from that in a symmetrical system. It
may be achieved virtually at any point along the channel
FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
13
length by injecting sample material at a chosen distance
from the channel inlet when two inflows of carrier liquid
are introduced at both the channel inlet and outlet..72/
This procedure is termed ‘‘opposing flows relaxation’’.
The two flows entering the channel through the inlet
and the outlet meet at a focusing point that depends
on the ratio between the inlet flow rate and the sum of
the inlet and outlet flow rates. The focusing point in an
asymmetric channel may thus be adjusted by selecting
the flow rates. Alternatively, the flow entering through
the inlet end may be eliminated so that only the reverse
flow is maintained. This procedure defined ‘‘reverse flow
relaxation’’ allows the sample to migrate to the very
beginning of the channel and relax at the inlet point. When
the opposing flows relaxation is used sample material may
be loaded through either the inlet or the outlet or even an
independent port at a given point along the channel. In
this case, an additional pump must be used. The opposing
flows approach has given rise to the opposed flow sample
concentration procedure which allows very large volumes
of dilute sample to be loaded on to a FlFFF channel..107/
As much as 105 -fold concentration has been reported (1-L
sample volume introduction). This sample concentration
technique can be applied to symmetrical, asymmetric, and
hollow-fiber FlFFF. In the hollow-fiber FlFFF technique,
sample relaxation is obtained much as in the asymmetric
set-up by pumping opposing flows in from the inlet and
outlet while maintaining a constant radial flow.
undergo adequate retention and separation before starting the programmed decrease of the field or increase of
the fluid velocity. It has been shown that the fractionating
power is a convenient universal parameter for comparing
the effectiveness of different forms of programming. The
diameter-based fractionating power, Fd , or the molecularweight-based FM , is defined as the resolution Rs of two
sequentially eluting species divided by the relative difference in their size or molecular weight..109/ Linear and
parabolic decay programs,.64,110/ the first functions to
be investigated for polymer separations, resulted in a
considerable improvement over a constant field strength
separation. However, closer examination showed an initial rise in Fd followed by a rapid decrease as the field
strength went to zero..111/ The exponential field decay
program introduced by Kirkland et al..112,113/ for particle
size analysis by SdFFF has been applied to polymer separations by FlFFF.114/ and ThFFF..110,115 – 117/ This type of
program also resulted in an initial increase of the fractionating power followed by a strong decrease..109/ Only
a power-law dependence of the field decay proposed by
Williams and Giddings.118/ yielded a constant molecularbased fractionating power for a wide range of molecular
weights..119/
4.3 Operation with Constant or Programmed Field
5.1 Organic-soluble Polymers
When complex mixtures have to be analyzed, differences
in the property of interest of the species under investigation may be so large that no constant experimental
condition may yield a satisfactory result for all species
in a single run. This situation, well known in the chromatography of complex natural mixtures, is circumvented
in HPLC with the so-called gradient elution, where the
eluent composition is changed with time. The basic concept of gradually decreasing the retention power in order
to let the most retained sample elute in a shorter time,
thus gaining in detectability, has been applied to FFF..108/
Programmed field strength and/or flow rate are particularly useful for polydisperse samples whose elution would
be spread over a wide time interval because of the high
system selectivity. In FFF, there is an almost unlimited
number of programming choices considering that both the
field and the channel velocity may be varied as needed.
In principle, the eluent composition may also be programmed but this option has only been applied to the
carrier fluid density in SdFFF..108/ Both the fluid velocity and field strength may follow a step, linear, quadratic,
parabolic, or exponential time-dependent function. In any
of these forms of programming a period at constant conditions is usually applied to allow early-eluting particles to
The high versatility of FFF has proven suitable to so many
applications in different fields that a complete survey
would be impossible. We therefore choose to report here
only selected examples of the most innovative and recent
applications. Many others may be found in the literature.
ThFFF with field-strength programming has been used
to separate PS standards with molecular weights spanning
4000 – 7 100 000 Da. In Figure 7(a), the T follows a
parabolic function that decreases from 70 to 0 ° C..110/
Since this early ThFFF work, the analysis time has been
dramatically reduced to 20 min without significant loss
of resolution by the advent of new instrumentation and
the introduction of the power program function..119/ An
application of this form of programmed elution is shown
in Figure 7(b).
Although FFF was conceived as a separative technique,
its rigorous theoretical background has demonstrated that
measurements of fundamental physicochemical properties may be very accurate and in some cases unachievable
by other techniques. This is the case for investigations
of the thermal diffusion of polymers and copolymers and
their correlation with the polymer and solvent chemical
composition. Studies in this field showed a linear relationship between the thermal diffusion coefficient DT and the
5 APPLICATIONS
14
POLYMERS AND RUBBERS
1h
6h
p(SI)2 + p(SIS)l
70°C
97k
20 k
4k 51k
411k
860 k
1800k 7100 k
∆T
(a)
GPC
Response
200k
Inject
Void peak
Void peak
p(SI)2
p(SIS)l
80°C
t 0 35 k
ThFFF
∆T
90 k
200 k
13°C
400 k
10
20
30
40
Time (min)
Response
900 k
Figure 8 Co-elution of a sample of diblock copolymer of
poly(styrene-co-isoprene)
and
triblock
poly(styreneco-isoprene-co-styrene) from a GPC column and separation
of the same mixture by ThFFF based on the difference in
thermal diffusion coefficient. (Reprinted from Cho et al.,.71/ by
courtesy of Marcel Dekker Inc.)
3800 k
0
(b)
0
5
10
15
20
Time (min)
Figure 7 Separation of two mixtures of PS standards in a
similar molecular weight range with field strength decay.
(k D kDa) (a) Parabolic programming. (Reprinted with permission from J.C. Giddings, L.K. Smith, M.N. Myers, Anal. Chem.,
48, 1587 – 1592 (1976). Copyright 1990, American Chemical
Society.) (b) Power programming. (Reprinted with permission
from M. Myers, P. Chen, J.C. Giddings, ACS Symp. Ser., 521,
47 – 62 (1993). Copyright 1993, American Chemical Society.)
temperature at the center of the sample zone for PS in
ethylbenzene.36/ and a similar correlation between DT
and the mole fraction of one of the monomers in random
copolymers..120/ This finding has a number of implications,
one of which is that ThFFF has an additional separating
dimension that allows samples to be resolved according
to chemical composition as well as hydrodynamic size.
This is shown in Figure 8, where the diblock copolymer
poly(styrene-co-isoprene) is separated from the triblock
of same size poly(styrene-co-isoprene-co-styrene) only by
ThFFF. Hydrodynamic chromatography (HDC), another
analytical technique for polymer separations, has a higher
efficiency than FFF but, like GPC, discriminates samples
only by size. Consequently, fractions of PS, polyisoprene and polybutadiene (PB) with similar hydrodynamic
dimensions are only partially separated by HDC whereas
they are completely resolved by ThFFF.121/ because of
their different thermal diffusion coefficients. Although
retention in ThFFF is dependent on DT , the evaluation of
absolute values of this parameter is not straightforward
since the measurable retention parameter l yields values
of D/DT . DT alone may therefore be determined only if
the diffusion coefficient is measured by an independent
technique. One approach is to couple SEC to ThFFF
and determine D using light scattering. This multidimensional approach allows the fractionation of polymer
samples according to size by SEC and to thermal diffusion by ThFFF..122,123/ The usefulness of the combined
SEC/ThFFF technique is demonstrated in the analysis of
polydisperse samples of copolymers whose relative composition, which may vary with molecular weight, gives
rise to materials with different properties. The preliminary fractionation of a polydisperse sample of PS by
SEC may occur with a selectivity of 0.15 in the molecular
weight range 150 000 – 1 000 000 Da and drops to 0.04 for
lower M fractions..122/ This selectivity, well below that
commonly found in FFF, is obtained after a system calibration with well-characterized PS fractions and the lightscattering determination of diffusion coefficients. The
thermal diffusion coefficient, calculated from retention
measurements once both molecular weight and ordinary
diffusion coefficients are known, is generally independent
of molecular weight..124/ Fractionation according to
15
FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
SEC
1
(a) 8
2
4
3
10
12
B
A
B
2
14
B
B
5
18
22
20
A
A
C
B
C
A
6
B
7
A
B
8
B
9
0
(b)
16
A
A
B
4
9
ThFFF
B
3
8
7
6
5
2
A
4
6
8
10
12
14
Time (min)
Figure 9 (a) Size exclusion chromatogram of a blend of PS,
is different and that it increases with M in the second
case..122/ Increasing DT with increasing weight fractions
of vinyl acetate is reported for poly(ethylene-co-vinyl
acetate) copolymers..83/ Multidimensional analysis may
also be obtained by coupling a ThFFF system with
HDC..126/ Samples with the same D/DT eluting from the
ThFFF system are subsequently fractionated according
to size by HDC.
ThFFF appears to be the only separation technique
suitable for the analysis of gels and rubbers.82,90,127/
because irreversible adsorption evident in other methods
is minimized..90,127/ In addition, the need to filter
samples prior to their injection into a GPC column
results in the removal of high-molecular-weight polymer
components as well as of the gel. This causes the average
molecular weight and molecular weight distributions to
be consistently lower in GPC than in ThFFF..127/ The
open FFF channel design eliminates the problem of
plugging that is encountered in GPC when gel containing
samples are not filtered before the analysis. Hence
polymer and gels may be completely separated within
a single run by ThFFF,.128/ as shown in Figure 10.
PB and PTHF and (b) ThFFF of individual fractions taken
after the SEC elution. Numbers along the y-axis of the ThFFF
fractogram correspond to the labeled SEC fractions in (a).
(Reprinted from A.C. van Asten, R.J. van Dam, W.Th. Kok,
R. Tijssen, H. Poppe, J. Chromatogr. A, 703, 245 – 263 (1995).
Copyright 1995, with permission from Elsevier Science.)
Void + soluble polymer
Response
differences in thermal diffusion coefficient alone gives
information on the copolymers’ chemical composition.
Figure 9(a) and (b) show the partial fractionation (a)
by SEC of a blend of PS, PB, and polytetrahydrofuran
(PTHF) and then (b) by ThFFF of some SEC fractions
collected at different retention times. The ThFFF fractogram indicates the presence of different polymer species
(fractions 3 – 6) whose measured DT are in good agreement with values of the corresponding PB and PTHF
homopolymers determined by ThFFF and light scattering, e.g. 0.22 ð 10 7 and 0.47 ð 10 7 cm2 s 1 K 1 versus
0.23 ð 10 7 and 0.50 ð 10 7 cm2 s 1 K 1 ..125/
The measurement of the thermal diffusion coefficient
has become a key step in the determination of copolymer relative chemical composition. Two styrene – methyl
methacrylate copolymers with different styrene content
analyzed by SEC/ThFFF.122/ show different DT versus
retention time trends when analyzed by ThFFF, although
the SEC traces are almost identical. Using a calibration plot for the SEC column based on PS standards
(which is not a rigorous procedure), the fractions may be
assigned a molecular weight and DT may be related to this
parameter. The invariant trend of the thermal diffusion
coefficient of one sample and the clearly increasing values
of the second sample suggest that the styrene percentage
∆T = 90 K
∆T profile
Rubber particles
∆T = 5 K
0
20
40
60
80
Time (min)
Figure 10 Separation and characterization of the polymer and
gel components present in acrylonitrile – butadiene – styrene
plastics. (Reproduced from P.M. Shiundu, E.E. Remsen, J.C.
Giddings, J. Appl. Polym. Sci., 60, 1695 – 1707 (1996). Copyright
 1996, John Wiley & Sons, Inc. Reprinted by permission of
John Wiley & Sons, Inc.)
16
Molecular weight and particle size distributions are
calculated for both the polymer and the gel components.
Although other techniques have been used successfully
to analyze gels and rubbers, SEC has been considered
the separative methodology par excellence in spite of
its limitations..129,130/ It was shown that the different
DT values for different polymers have been exploited
in the ThFFF analysis of core-shell latex particles..131/
The retention time is sensitive to the composition of
the polymer shell. A calibration curve may be drawn
to relate retention time and percentage of methacrylic
acid in the shell. The sensitivity of DT to the particle
surface composition is further illustrated using similar
sized particles of different polymeric and inorganic
surfaces..132,133/
5.2 Water-soluble Polymers
Early studies in ThFFF.37/ showed that different organic
solvents had a very similar effect on the retention of
polymers. In contrast, when water is used as the carrier
liquid, the thermal diffusion factor a is very low and
retention is negligible unless a considerable amount of
some organic solvent (¾60%) is present. Except for a few
results confirming the poor retention in such a solvent,.117/
water-soluble synthetic polymers have been analyzed by
the most versatile technique of the FFF category, FlFFF.
This technique was recognized since its first appearance as
highly suited to polymer fractionation..134,135/ Although
resolution and analysis time were not optimized, the
early results allowed the determination of molecular
parameters, such as hydrodynamic size, on the basis of
theoretical concepts that have subsequently been extensively confirmed. Polyacrylamide (PAAm) is a widely
employed polymer in many fields that is difficult to characterize and fractionate. Commercially available fractions of PAAm generally have a broad distribution..136/
The FlFFF fractograms of the three PAAm samples
illustrated in Figure 11 consistently show the presence
of low-molecular-weight components in each polymer
sample..68/ A similar peak asymmetry is also observed for
broadly disperse samples in organic solvents..63/ As mentioned earlier (section 2.4), in the absence of an absolute
technique for the molar mass determination, the molecular weight distribution may be accurately determined
by calibration. The calibration procedure, however,
should be performed with narrowly distributed, wellcharacterized standards of closest possible chemical composition to the unknown. When standards with these characteristics are not available, absolute measurements of the
diffusion coefficient may be used to evaluate the polymer
hydrodynamic size using the Stokes – Einstein equation.
The absence of non-ideal sample – wall interactions on the
elution of PAAm is verified by comparing measurements
POLYMERS AND RUBBERS
Hydrodynamic size (nm)
Poly(ether sulfone) Cellulose
membrane
membrane
80 k
80 000
500 000
1 400 000
500 k
12
28
49
12
29
54
1400 k
0
50
t
0
100
150
Time (min)
Figure 11 FlFFF separation of three samples of PAAm
of different nominal molecular weight. The hydrodynamic
diameters were determined using two different membranes.
(Reproduced from M.-A. Benincasa, J.C. Giddings, J. Microcol.
Sep., 9, 479 – 495 (1997). Copyright 1997, John Wiley & Sons,
Inc. Reprinted with permission of John Wiley & Sons, Inc.)
made in solutions of identical ionic strength but with
membranes of different composition, namely poly(ether
sulfone) and cellulose..137/
As discussed in the theory section, the overall polymer molecular dimensions are anticipated to depend,
to a certain extent, on the properties of the surrounding medium. This effect is expected to be enhanced
for charged polymers. The effect of solvent and ionic
strength was identified in the first study in FlFFF of
water-soluble polymers..135/ Poly(ethylene oxide) (PEO),
a polymer widely used in biomedical and biotechnological
applications because of its non-toxicity, shows an almost
ideal correlation between the measured diffusion coefficient and molecular weight in aqueous sodium sulfate
solutions..69/ Similar to the observation reported by Hassellöv et al.,.56/ this correlation is found for polymers with
molecular weights well below the range for which the
general polymer scaling laws are expected to hold. The
correlation between diffusion coefficient and molecular
weight in potassium sulfate is very different to that in
sodium sulfate. The authors attribute this difference to
the capability of low-molecular-weight PEO fractions to
form complexes with some metal cations, as reported in
independent studies..138/ The elution profiles of PEO samples in a molecular weight range 250 000 – 1 000 000 Da
may be obtained by FlFFF with good resolution as
shown in Figure 12. Charged amphiphilic graft copolymers are a particular type of sample that may dramatically change their conformation in different solvents
because of the presence of hydrophilic and hydrophobic
17
FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
250 000
A
Absorbance
990 000
590 000
0
25
t0
50
0.002 AU
B
C
75
Time (min)
D
Figure 12 Separation of three PEO samples by FlFFF in
aqueous 0.025 M Na2 SO4 .
moieties derived from different homopolymers. In aqueous solutions, they form a hydrophobic core with the
hydrophilic moieties on the surface. At low pH and in the
presence of salts, aggregation may occur for the copolymer of styrene, methyl methacrylate and maleic anhydride
with grafts of poly(ethylene oxide) monomethyl ether
(MPEO)..139/ The polymer molecular conformation and
solubility in water depend on the pH, which affects dissociation of the carboxyl groups, and on the solvent
ionic strength. An extended conformation may exist at
high pH or aggregation may occur at low pH and high
ionic strength. The copolymer hydrodynamic diameter
increases with decreasing pH. This effect is attributed to
the formation of aggregates of less charged copolymers
at low pH, a phenomenon that seemed amplified when
long stop-flow times are used. When a ca. 0.002 M buffer
solution is used as the carrier liquid, the molecular dimensions are considerably higher (16 – 40 instead of 2 – 20 nm)
than those measured in unbuffered solutions. It is postulated that the buffer salts cause shielding of charged
sites which consequently promote aggregation through
hydrophobic interactions of the polymer backbone. Formation of aggregates is evidenced by the particle size
distributions shown in Figure 13..140/
SdFFF is a technique usually associated with particle rather than polymer analysis. The maximum field
strength or centrifuge speed of currently available commercial instruments is insufficient to induce transport of
the polymers to their equilibrium positions at the accumulation wall. Consequently, retention and separation
by SdFFF are poor. However, an instrument with highfield-strength capabilities can be used to characterize
high-molecular-weight polymers..141/
0
5
10
15
20
25
30
35
40
45
d H (nm)
Figure 13 FlFFF-derived particle size distributions of an
amphiphilic grafted copolymer poly(styrene-co-methyl methacrylate-co-maleic anhydride) and MPEO. Aggregation is
observed as the sodium sulfate concentration is increased. The
carrier liquids used were (A) pure water, (B) 1 µM Na2 SO4 ,
(C) 10 µM Na2 SO4 , and (D) 100 µM Na2 SO4 . (Reprinted
with permission from B. Wittgren, K.-G. Wahlund, H. Dérand,
B. Wesslén, Langmuir, 12, 5999 – 6005 (1996). Copyright 1996,
American Chemical Society.)
6 METHOD DEVELOPMENT
6.1 Determining Experimental Conditions
Before starting an analysis, specific requirements may
be set for a number of experimental parameters such
as analysis time, resolution, and selectivity. A thorough
discussion of this topic would require a long navigation
through FFF theory and is beyond the scope of this article.
Therefore, some practical recommendations are given
here with reference to theoretical fundamentals on which
they are based. Demonstration of these concepts may be
found in the specific literature and will not be dealt with
here. A generally desired characteristic is short analysis
times. The retention time in FFF is linearly related to the
applied field strength, ceteris paribus. This translates into
a dependence on the temperature gradient, crossflow rate,
solvent viscosity, channel thickness, and void volume.
18
Although in theory values of these parameters may
be accurately determined, common laboratory practice
has shown that void volume V 0 and channel thickness
determination in FlFFF is not a trivial procedure. A
peak breakthrough technique.142/ has been proposed that
allows the determination of the channel void time, and
related volume, from the time needed for an unretained
sample to emerge from the channel under high-flow-rate
conditions. Experiments must be carried out with great
care and in the total absence of a crossflow. A simple
way to ensure this is to block the crossflow inlet and
outlet. More accurate void volume determinations may
be obtained by sandwiching the spacer and the membrane
between two glass plates with holes drilled through one
of the plates to act as the channel inlet and outlet. The
determination of the actual void volume in FlFFF may not
be bypassed since it also yields a measure of the channel
thickness. This last parameter is the most critical in FlFFF
since the retention time varies with w2 . Molecular weight
measurements, obtained from retention parameters, are
strongly affected by the channel thickness. The crossflow
rate VP c and channel flow rate VP have opposing effects on
P An increase in
tr since they contribute as the ratio VP c /V.
the two flow rates which does not alter this ratio would
have no effect on tr . However, l and t0 would decrease.
This would translate into a decrease of the retention ratio
t0 /tr and a higher compression of the sample zone with a
greater probability of overloading and sample interaction
with the accumulation wall. Resolution, which depends
P 1/2 , would increase with the 3/2 power of the
on .VP c3 /V/
crossflow rate and decrease with the 1/2 power of the
channel flow rate. Studies on the effect of field strength
and injected sample load on polymer fractionation by
FlFFF have shown that the molar mass distribution seems
to broaden with increasing crossflow rates or decreasing
injected sample loads..92/ Unlike ThFFF, where the flow
profile is considerably affected by the field, perturbations
due to the crossflow in FlFFF are negligible..143/ In
general, axial flow rates of 0.2 – 2 mL min 1 are used for
polymer analysis. Low flow rates and velocities protect
samples from shear degradation and peak broadening due
to the nonequilibrium contribution to the plate height that
depends linearly on the flow velocity.
Unlike FlFFF, the retention time in ThFFF does not
depend directly on the channel thickness. It depends
on the void time t0 , which is related to w. The
retention time is a function of the thermal gradient
dT /dx, which can be increased by reducing w or
increasing the hot wall temperature. The first approach
is useful when the working temperature is above the
solvent boiling point and further pressurization of the
system to elevate the boiling point.3/ is not an option.
However, the reduction of w in ThFFF is limited by
heat transfer that may require substantial heat fluxes
POLYMERS AND RUBBERS
between the hot and cold walls. In addition to the
previous considerations, w affects resolution and sample
dilution in all the FFF techniques. Generally, 90 – 99% of
the FFF channel volume is occupied by pure solvent
during elution. The injected sample is hence very
diluted on elution from the FFF channel. This effect
may be reduced using stream splitters.104/ or frit outlet
systems..100/ All channel dimensions may in principle
be varied. An increase or reduction of either b or
L has some advantages and some disadvantages. An
extensive discussion on the theoretical and practical
aspects of changing these dimensions is reported in
the literature..144/ The dimensions of asymmetric FlFFF
channels are subject to more constraints..145/ Commonly
used channel flow rates in ThFFF are of the same order of
magnitude as those used in FlFFF. Data collected over a
15-year period using a number of different channels have
shown that retention in ThFFF is affected by the absolute
value of the cold wall temperature Tc ..146/ Higher Tc
values lead to lower retention with the same T. The use
of binary solvents in ThFFF has been shown to enhance
retention considerably in some cases. This result may be
used to extend the range of applicability of ThFFF toward
lower molecular weight limits..147/
6.2 Effect of Sample Size
Sample size effects on retention were described in
early FFF studies..135/ These effects, common to other
separation techniques, manifest themselves in FFF as
distortions of the elution profile and shifts in retention
time that cannot be related to any sample physicochemical
property but rather to the amount of sample injected.
It was also recognized in the early FFF work that the
ionic strength changes remarkably the effect of sample
load on retention time..135,148/ The effect of sample load
depends on the polymer – solvent system rather than
on the FFF technique employed. The general trend
of increasing retention time with increasing injection
amount is observed for FlFFF and ThFFF of PS in
ethylbenzene and tetrahydrofuran..81,149/ In this case
the role of molecular weight in enhancing the effect
of load even at very low T values was shown.
Longer retention times are also reported for higher
amounts of PTHF analyzed in toluene by ThFFF..150/
The opposite trend is found in aqueous separations
of particles by SdFFF.148/ and for synthetic.65,68,135/
and biological polymers..151/ The dependence of sample
overloading on the physicochemical properties of the
polymer – solvent system rather than on the analytical
technique is substantiated by the findings that aqueous
synthetic and biological polymer systems also show a
decrease in retention time with increase of load in
FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
hollow-fiber FlFFF..152,153/ The observed decrease in
retention time with increasing sample load for particles
and charged polymers has been explained on the basis of
excluded volume effects. For systems where the sample
volume fraction is not negligible, l values are expected
to be higher than those predicted from standard FFF
theory, which assumes infinitely small non-interacting
species..154/ Since both the interparticle electrostatic
repulsion and chain expansion due to intramolecular
repulsion contribute to an increase in the effective
volume occupied by the sample species, an enhanced
overloading effect is expected for charged particles.
In contrast, a depression of the phenomenon may be
predicted with a reduction of the electrostatic effects. It
follows that the ionic strength of the carrier liquid should
considerably affect the onset of sample overloading. High
ionic strength is expected to reduce both the overall
molecular dimensions of flexible-chain macromolecules
and the double-layer thickness. The reduction of these
parameters decreases the effective sample volume to
a greater extent than the lower solvating power of
a concentrated salt solution alone. Experiments on
synthetic water-soluble polymers show that the ionic
strength.65/ and the type of electrolyte added to the carrier
liquid may affect the relationship between sample size and
retention..69,139/
6.3 Membranes in Flow Field-flow Fractionation
A unique feature of the FlFFF system is the semipermeable membrane that is laid over the frit and serves as the
accumulation wall. The possibility of wrinkling or swelling
of the membrane and uncertainties in the performance
of the different polymer materials used in their fabrication have been the main deterrent in the development
of FlFFF. The membrane used in the FlFFF channel
must meet a number of specific requirements not necessarily fulfilled by commercially available membranes.
The pore size and the pore density, i.e. the number of
pores per unit area, have to be uniform. Inhomogeneous
pore density leads to regions of nonuniform permeability and crossflow rate. The nominal and effective pore
sizes are often given by the manufacturer. While the
first is an absolute measurement obtained by electron
microscopy, the second must be considered an indication of the membrane performance with respect to the
specific probe and to the conditions used for this determination and may not be directly transferred to samples
with different physicochemical properties. For example,
the Celgard isotactic polypropylene membrane is marketed with a nominal pore size of 50 nm and an effective
pore size of 20 nm, but samples of much smaller diameter are retained..65/ It is known that filtration through
19
a membrane is not a purely mechanical process and
that a number of parameters contribute to the sample
permeation or retention by a membrane. A higher percentage of latex particles of considerably smaller diameter
than that of PS samples in tetrahydrofuran are retained
by a polytetrafluoroethylene (PTFE) membrane with a
nominal 20-nm pore size..155/ A regenerated cellulose
membrane from Millipore with a 10 000 molecular weight
cut-off (MCO) retains PEO samples in the 4000 – 1 000 000
molecular weight range whereas a membrane of the same
material and from the same supplier with a lower cut-off
shows no elution of the PEO samples..156/ Considering the
lower MCO, it may be inferred that adsorption occurred
in this case. Specific tests to check sample permeation
through the membrane are always recommended, however. They may be carried out by connecting the crossflow
outlet to a detector and monitoring the eluted carrier liquid for the presence of sample. The general scarcity of
membranes capable of withstanding organic solvents has
been one of the main limitations in the application of
FlFFF to organosoluble polymers. Cellulose nitrate gave
a good performance in the first experiments of FlFFF
in ethylbenzene,.81/ but many more membrane materials
compatible with organic solvents such as fluoropolymers,
polyvinylidene, polyaramide and PTFE are now commercially available..155/
Ultrafiltration membranes such as those commonly
used in FlFFF may be classified as cellulosic and
noncellulosic. Cellulose and its derivatives were one
of the first materials employed as a semipermeable
membrane and successfully used in the FlFFF analysis
of aqueous systems of proteins, synthetic hydrophilic
polymers, and latex particles. Cellulosic ultrafiltration
membranes are available in a variety of MCOs and
are cast on a thicker, more permeable support material.
The presence of this support adds robustness and ease
of handling to the membrane. Thin-film (5 – 25 µm)
unsupported membranes, most often noncellulosic, are
more difficult to handle but their flexibility allows
easy positioning on the frit wall. Unlike cellulosic
ultrafiltration membranes, these mainly hydrophobic
membranes do not allow wicking of carrier liquid out
of the area of permeation (no leaking). An ample variety
of membranes used with various solvents and samples is
listed in Table 1. Besides preliminary considerations on
the physicochemical properties of both the membrane
material and the sample to be analyzed, an unambiguous
answer on the performance of a membrane is given by
a test of the absolute sample recovery..68,137,157/ This is
accomplished by comparing the peak area of the output
signal of a regular FFF run with the area acquired
upon injecting the same sample amount through an
open tube.
20
POLYMERS AND RUBBERS
Table 1 Summary of membrane materials and their applications in FlFFF
Membrane material
Acrylic copolymer
Cellulose
Cellulose acetate
Cellulose nitrate
Fluoropolymer
Polyamide
Polyaramide
Polycarbonate
Polyelectrolyte complex
Poly(ether sulfone)
Poly(ethylene terephthalate)
Poly(phenylene oxide)
Polypropylene, isotactic
Polysulfone
PTFE
Polyvinylidene
Regenerated cellulose
Regenerated cellulose,
modified
Sample
Carrier composition
Proteins, lipoproteins
PAAm, humics
Viruses, proteins
PS
PS
Polyethylene,
toner pigment
PS
Antibodies, proteins,
humic and fulvic acids
Proteins, viruses
PAAm,
PEO,
Poly(styrene sulfonate),
PS, carbon black,
Polyethylene
Proteins
PS
Poly(styrene sulfonate),
polyvinylpyridine, proteins
Minerals, cells, humic and
fulvic acids, poly(styrene
sulfonate), dextrans, latex
PS, PEO, latex, silica
PS
Algae, bacteria,
amphiphilic copolymers,
DNA, hemoglobin,
microspheres, lipoproteins,
liposomes, nucleic acids,
plasmids, pollens,
polysaccharides, PEO,
ribosomes, silicas,
Poly(methyl methacrylate)
PEO
Aqueous solution
Aqueous solution
Aqueous solution
Ethylbenzene
Tetrahydrofuran
Xylene
Toluene
Tetrahydrofuran
Aqueous solution
Aqueous solution
Aqueous solution
Xylene, cyclohexane
Xylene
Aqueous solution
Tetrahydrofuran
Aqueous solution
Aqueous solution
Tetrahydrofuran,
acetonitrile
Tetrahydrofuran
Aqueous solution
Tetrahydrofuran
Ammonium acetate in
methanol solution
Literature related to the applications reported here may be found elsewhere..137,155,157,158/
ACKNOWLEDGMENTS
c.tr /
K.R.W. acknowledges support from the Colorado School
of Mines by a start-up grant for this work.
d
D
D0
DT
f
f0
Fd
Fm
H
Hi
Hl
LIST OF SYMBOLS
a
A
b
b
b
B
c
c0
axis of prolate or oblate particles
constant defined by DMb
axis of prolate or oblate particles
field-flow fractionation channel breadth
exponent in diffusion coefficient expression
empirical constant in Equation (22)
particle or molecule concentration
particle or molecule concentration
at the wall
Hn
Hp
time-dependent sample mass
concentration at elution
width of polymer chain
diffusion coefficient
diffusion coefficient at infinite dilution
thermal diffusion coefficient
friction coefficient
friction coefficient of an isolated sphere
diameter-based fractionating power
molecular weight-based fractionating power
plate height
instrumental contribution to plate height
longitudinal diffusion contribution to plate
height
nonequilibrium contribution to plate height
polydispersity contribution to the plate
height
21
FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
Hr
Jx
k
`
l
L
m.M/
M
M0
dM
Mw
MN
n
N
R
Re
Rg
R0
Rs
SM
t0
tr
dtr
dtr /dM
tsf
T
Tc
T
U
VP
VP c
V0
Vr
hvi
vp
w
relaxation contribution to plate height
flux of particles
Boltzmann constant
sample mean layer thickness
length of polymer chain
channel length
mass distribution as a function of molecular
weight
molecular weight
molecular weight of repeat unit
difference in molecular weight interval
weight-average molecular weight
number-average molecular weight
exponent in Equation (24)
number of repeat units
retention ratio in Equation (6)
equivalent sphere radius
radius of gyration
spherical particle radius
resolution
molecular weight selectivity
void time
retention time
retention time difference
scale correction function
stop-flow time
absolute temperature
cold wall temperature
temperature difference across the
channel
field-induced velocity
volumetric flow rate
volumetric cross flow rate
void volume
retention volume
mean fluid velocity
zone migration velocity
channel thickness
Greek characters
a
thermal diffusion factor
b
exponent in thermal diffusion
Equation (22)
g
thermal expansion coefficient
h
fluid viscosity
l
retention parameter
µ
molecular weight polydispersity

coefficient in Equation (24) or polymer
volume fraction (section 4.1)
FFF
FlFFF
GPC
HDC
HPLC
MALS
MCO
MPEO
PAAm
PB
PEO
PS
PTFE
PTHF
SdFFF
SEC
ThFFF
RELATED ARTICLE
Biomolecules Analysis (Volume 1)
High-performance Liquid Chromatography of Biological
Macromolecules
REFERENCES
1.
2.
3.
4.
5.
6.
ABBREVIATIONS AND ACRONYMS
7.
CFFF
ElFFF
Concentration Field-flow Fractionation
Electrical Field-flow Fractionation
Field-flow Fractionation
Flow Field-flow Fractionation
Gel Permeation Chromatography
Hydrodynamic Chromatography
High-performance Liquid Chromatography
Multiangle Light Scattering
Molecular Weight Cut-off
Poly(ethylene oxide) Monomethyl Ether
Polyacrylamide
Polybutadiene
Poly(ethylene oxide)
Polystyrene
Polytetrafluoroethylene
Polytetrahydrofuran
Sedimentation Field-flow Fractionation
Size-exclusion Chromatography
Thermal Field-flow Fractionation
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24
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FIELD FLOW FRACTIONATION IN ANALYSIS OF POLYMERS AND RUBBERS
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S. Lee, M.N. Myers, J.C. Giddings, ‘Hydrodynamic
Relaxation Using Stopless Flow Injection in Split Inlet
Sedimentation Field-flow Fractionation’, Anal. Chem.,
61, 2439 – 2444 (1989).
M.-K. Liu, P.S. Williams, M.N. Myers, J.C. Giddings,
‘Hydrodynamic Relaxation Using Both Split and Frit
Inlets’, Anal. Chem., 63, 2115 – 2122 (1991).
H. Lee, S.K.R. Williams, J.C. Giddings, ‘Particle Size
Analysis of Dilute Environmental Colloids by Flow
Field-flow Fractionation Using an Opposed Flow Sample
Concentration Technique’, Anal. Chem., 70, 2495 – 2503
(1998).
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P.S. Williams, J.C. Giddings, R. Beckett, ‘Fractionating
Power in Sedimentation Thermal Field-flow Fractionation with Linear and Parabolic Field Decay Programming’, J. Liq. Chromatogr., 10, 1961 – 1998 (1987).
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J.J. Kirkland, S.W. Rementer, W.W. Yau, ‘Molecularweight Distribution of Polymers by Thermal Field-flow
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25
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M.E. Schimpf, J.C. Giddings, ‘Characterization of Thermal Diffusion of Copolymers in Solution by Thermal
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