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CHROMATOGRAPHY, SIZE
EXCLUSION

Introduction

A polymeric product contains chains of varying lengths because of the statistical
nature of polymerization processes. All synthetic polymers, and many natural
polymers, have a molecular weight distribution (MWD), which may be represented
by the differential weight distribution w(M) as a function of molecular weight M
(1). From the normalized distribution w(M), the number-, viscosity-, and weight-
average molecular weights, M

n

, M

v

, and M

w

respectively, are calculated from the

relations

M

n

= 1/

1

/M



w (M) dM

(1)

M

a

v

= M

a

w (M) dM

(2)

M

w

= Mw (M) dM

(3)

Here, a is the exponent in the Mark–Houwink dilute solution viscosity equation

[

η] = KM

a

v

(4)

where [

η] is the intrinsic viscosity (dL/g) and K is a constant. Higher moments of

the distribution curve may also be used to derive the z and z

+ 1 average molecular

weights (1) (Molecular weight determination (GPC, osmometry)).

Various methods are available for the determination of average molecu-

lar weight (2), but the three averages in equations 1–3 cannot define a distribution

Encyclopedia of Polymer Science and Technology. Copyright John Wiley & Sons, Inc. All rights reserved.

614

CHROMATOGRAPHY, SIZE EXCLUSION

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within a polymer having many components. The polydispersity defined as M

w

/M

n

can provide an indication of the width of the MWD, but does not disclose distribu-
tion shape. Two polymers may have the same average molecular weight but quite
different MWD. However, measurement of a specific average molecular weight is
quite useful for correlation with polymerization kinetics and with a range of solu-
tion and bulk properties. Inevitably, attention was therefore directed to polymer
fractionation as a means of determining MWD (see F

RACTIONATION

). The classical

experiment is preparative fractionation from which a cumulative weight distribu-
tion I(M), and hence w(M), is calculated from the weights and average molecular
weights of the isolated fractions. By the mid-1960s, a range of fractionation meth-
ods was available (3,4), but the limitations of most of these were well recognized.
In particular, for polymer fractionations relying on the molecular weight depen-
dence of polymer solubility, the experimental methods were inefficient, tedious,
and time consuming.

Size exclusion chromatography (SEC) is now established as the most pop-

ular and convenient method for analytical polymer fractionation. Reliable and
reproducible chromatograms are obtained in relatively short time (elution

< 1 h),

permitting routine characterization and effective application to quality control. In
retrospect, it is perhaps surprising that SEC as a characterization method was not
established earlier. The characteristic separation of short chains having elution
times higher than those of long chains had been reported by a number of workers in
the published literature between 1935 and 1958 (5). The major advance by Porath
and Flodin (6) provided effective demonstration that polymers may be separated
by the size dependence of the degree of solute penetration into a porous pack-
ing. Their technique was named gel filtration (GF) involving cross-linked dextran
gels, which are soft and highly swollen networks for separations of water-soluble
polymers. The description of analytical gel permeation chromatography (GPC)
by Moore (7), and the subsequent availability of commercial instrumentation (8),
attracted widespread interest. Moore made two important contributions. First,
he prepared versatile porous cross-linked polystyrene/divinylbenzene (PS/DVB)
gel particles covering a wide range of pore diameters for separations of syn-
thetic polymers in organic media. These rigid gels (particle diameter d

p

exceeding

50

µm) had good mechanical stability and were packed in columns (length

120 cm) which could be operated at high pressures and fast flow rates. The sec-
ond contribution was the direct coupling of an on-line refractometer to the GPC
column (or columns) in order to measure continuously the concentration of the
polymer in the eluent. A chromatogram as recorded by a differential refractive
index (DRI) detector is thus a record of molecular size distribution as a function of
elution (or retention) time (or volume), and so the recovery and characterization
of fractions were avoided.

Initial work in GPC focused on the conversion of a chromatogram to an accu-

rate MWD. Column calibration methodologies were developed, and concentration
detectors based on infrared (IR) and ultraviolet (UV) spectrophotometers and on
evaporative light scattering were introduced. It was not until 1979 that a suitable
reference book became available (9), by which time the term SEC had become
widely accepted. The main advance during this decade was to identify conditions
for high performance separations. The advantages of microparticulate rigid gels
(particle diameter

∼ 10 µm) were demonstrated, resulting in the use of short

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CHROMATOGRAPHY, SIZE EXCLUSION

615

columns (30 cm) so that elution times were much reduced. In the next 10 years
up to 1990, instrumentation for multiangle laser-light scattering and differen-
tial viscometry appeared. These molecular size detectors, which generate on-line
molecular weight data as a function of elution time, may be coupled to the SEC col-
umn system, and in conjunction with an on-line concentration detector permit the
computation of MWD and average molecular weights. Examples of these advances
are detailed in several books (10–12). The principles, practice, and applications of
SEC are emphasized here, and further details on these and other aspects can be
found in two recent books (13,14).

Principles of SEC

The resolution of solute molecules in a complex mixture by a chromatographic
method depends on two types of processes. The separation process in the station-
ary phase controls the differential migration of the molecules, and in the SEC case
includes all the mechanisms that may determine the permeation of molecules in
the column packing. The dispersion process, which generally consists of at least
two mechanisms, determines the band broadening of one type of molecule, and this
broadening is influenced by molecular diffusion and column packing. In the deter-
mination of MWD and average molecular weights by SEC, an important part of
data interpretation is the establishment of a correct calibration relation between
the molecular weight M of a polymer and retention volume V

R

. An understanding

of the separation process is necessary because of the prevalent use of universal
calibration methods, which assume that SEC separations are controlled solely
by an exclusion mechanism. An understanding of the dispersion process is also
required because the experimental chromatogram will always correspond to a dis-
tribution of molecular weights, which is too broad because of band broadening of
all components in a polymer. Experimental conditions have to be chosen to mini-
mize chromatogram broadening in order to optimize accuracy of molecular weight
data and to obtain high resolution separations of low polymers, prepolymers, and
small molecules.

Separation Mechanism.

The basic separation mechanism in SEC as-

sumes that the column packing is “inert,” and interactive mechanisms that might
contribute to retention behavior are neglected. The size exclusion mechanism is
dependent on solute access to pore volume within gel particles determined by pore
size distribution and solute size. Consequently, all solute molecules are eluted
within one column solvent volume, corresponding to the sum of the interstitial (or
void) volume V

0

of solvent between porous gel particles, defined as the volume of

the mobile phase, and the volume V

i

of solvent within the porous gel particles,

defined as the volume of the stationary phase. Retention is given by the equation

V

R

= V

0

+ K

SEC

V

i

(5)

where the distribution coefficient K

SEC

represents the fraction of stationary phase

solvent that is accessible to the solute. For very large molecules, the value of K

SEC

will be zero at the exclusion limit because the sizes of these molecules prohibit
solute diffusion into the gel pores. Very small molecules, on the other hand, have

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CHROMATOGRAPHY, SIZE EXCLUSION

Vol. 1

Fig. 1.

Simple representation of the separation mechanism in SEC, showing larger

molecules eluting faster than smaller molecules.

total access to both stationary and mobile phases, ie, K

SEC

is unity at the per-

meation limit. As the chromatographic column is washed with solvent, the large
molecules are eluted first, followed by solutes of decreasing size, which penetrate
an increasing fraction of the solvent within gel particles. These observations are
illustrated in Figures 1 and 2.

Practical separations with a porous column packing in SEC are performed

close to equilibrium conditions. Elutions are performed at flow rates around
1 mL/min when V

R

is independent of flow rate. Although many theoretical models

have been proposed for polymer separations in SEC, thermodynamic treatments
provide a sound representation of separation behavior. For a separation operating
at equilibrium conditions, the standard free-energy change

G

0

for the transfer

of solute molecules from the mobile phase to the stationary phase at constant
temperature T is related to K

SEC

by

G

0

= H

0

− TS

0

= − RT ln K

SEC

(6)

where R is the gas constant and

H

0

and

S

0

are the standard enthalpy and en-

tropy differences between the phases, respectively. Thermodynamic theories for
SEC (15–18) calculate the pore volume accessible to a solute of given size in solu-
tion in terms of pore size for various models of pore shape. Such a treatment may
be regarded as an excluded volume problem in which small solutes are permitted
close approach to a pore surface whereas larger solutes have a larger exclusion

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CHROMATOGRAPHY, SIZE EXCLUSION

617

Partial
exclusion/permeation

Permeation

limit

Retention volume

log(solute size)

Exclusion

limit

K

SEC

1

0

V

0

V

0

+ V

i

Fig. 2.

Calibration curve for a size exclusion mechanism, presuming an inert column

packing.

zone. Presuming that the pore surface is indeed inert, then

H

0

will be zero and

the distribution coefficient is defined by

K

SEC

= exp(S

0

/R)

(7)

Therefore, K

SEC

is considered to be the fraction of accessible solute arrangements

within the porous packing to those within the mobile phase, and represents loss
in conformational entropy on solute transfer to a pore. Thermodynamic theories
demonstrate for various solute types, namely sphere, rod, and random coil, and
various pore geometries, such as lamellar and cylindrical shapes, that K

SEC

for

polymer separations may be generalized in terms of the relation

K

SEC

= exp( − sL

p

/2)

(8)

where L

p

is the mean external length or molecular projection, eg, L

p

is equal to

the diameter D of a sphere, and s is the surface area per unit pore volume. These
treatments of size exclusion therefore suggest that for a column containing a given
packing a characteristic molecular parameter L

p

will represent the behavior of all

solutes.

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CHROMATOGRAPHY, SIZE EXCLUSION

Vol. 1

Equilibrium theories therefore predict that the behavior of all polymers can

be represented by a universal size parameter. Benoit and co-workers (19) showed
that solute size should be the hydrodynamic volume V

h

of a polymer molecule in

solution defined by Einstein’s equation

V

h

= 40[η]M/N

0

(9)

where N

0

is Avogadro’s number (see Fig. 2). It follows that a plot of log [

η]M vs V

R

should be a universal calibration plot for all polymers, and many experimental
studies of a wide range of polymer-solvent-packing combinations have been per-
formed, confirming the validity of this approach (20). Consequently, a molecular
weight calibration curve for one polymer may be calculated from a calibration
curve established with polymer standards. The calibrations are related by the
expression

log M

p

− log M

ps

= log [η]

ps

/[η]

p

(10)

where p refers to the polymer and ps to an experimental study with well-
characterized standards having narrow MWD.

Separations of polymers in organic media with cross-linked PS/DVB gels are

generally performed with an eluent which is a good solvent for polystyrene. As long
as this eluent is also a good solvent for a polymer, then interactive mechanisms
are relatively unimportant compared with size exclusion, and it is reasonable
to presume that

H

0

is about zero for separations with cross-linked PS/DVB

gels. However, there are combinations of polymer and eluent, dependent on the
polarities of these components and good/poor solvency of the eluent, for which plots
of log [

η]M vs V

R

are displaced to high V

R

, indicating the presence of a secondary

mechanism such as adsorption (21). Thus, it is possible to conceive of columns of
cross-linked PS/DVB gels operating by two limiting mechanisms dominated by
size exclusion on the one hand (entropic effect) and by adsorption on the other
(enthalpic effect). These two limiting behaviors could be controlled by adjusting
the mobile phase, and could be represented by the retention equation

V

R

= V

0

+ K

SEC

V

i

+ K

ads

s

ads

(11)

where K

ads

is the distribution coefficient for the adsorption mechanism and s

ads

is

an equivalent volume related to the available surface area for the eluting polymer.
Therefore, a column will function solely in the adsorption mode for K

SEC

= 0 and

K

SEC

= 1, although the appropriate value of s

ads

for the stationary phase for each

limiting case will need to be defined in equation 11.

When there is a mixed mechanism consisting of a primary mechanism, which

is size exclusion, ie 0

< K

SEC

< 1, and a secondary interaction mechanism, then

retention can be defined by (22,23)

V

R

= V

0

+ K

SEC

K

p

V

i

(12)

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CHROMATOGRAPHY, SIZE EXCLUSION

619

where K

p

is the distribution coefficient for polymer–gel interactions. Therefore,

equations 5 and 12 are identical for K

p

= 1.0. Consequently, it can be suggested

that values of K

p

are given by

K

p

= exp



− H

0

/RT



(13)

Equation 12 has been shown to be a reasonable representation of a mixed mech-
anism for polymers in organic media separating on cross-linked PS/DVB gels
(21,22).

Water-based polymers have aqueous solubility based on hydrophilic func-

tionalities and/or ionic groups, and are likely to contain hydrophobic segments.
Because aqueous separations require the column packing to have a polar sur-
face, with or without ionic groups, a range of polymer–substrate interactions may
occur, giving rise to various secondary retention mechanisms. For example, sep-
arations may involve ion exchange, ion exclusion, ion inclusion, intramolecular
interaction, and adsorption (to include hydrogen bonding and hydrophobic in-
teractions) (12,14). To establish the validity of universal calibration for water-
based polymers, the choice of aqueous SEC system requires considerable care.
For anionic polyelectrolytes separating on inorganic packings, conditions involv-
ing addition of electrolyte to the mobile phase have been established in order to
minimize intrachain interactions and interactions between ionic groups on the
polyelectrolyte and charges on the surface of the column packing. However, this
methodology fails for cationic polyelectrolytes requiring modified inorganic pack-
ings with bonded phases. Alternatively, polymer-based packings may be preferred
because by analogy with GF matrices rigid macroporous polymeric gels may be
much less susceptible to secondary interaction effects. The absence of charged
sites may result in a tendency toward hydrophobic interactions, in which case it
may be necessary to introduce an organic modifier such as methanol or glycerol
to the mobile phase. In practice, the choice of composition of an aqueous mobile
phase for a specific polymer with a column packing may not be straightforward,
and a balance between the need to increase ionic strength to reduce ionic inter-
actions and to lower electrolyte concentration to limit hydrophobic interactions
may have to be determined. Guidelines for minimizing secondary interactions for
water-based polymers for a polymer-based packing are provided in Table 1.

Dispersion Mechanisms.

A measure of the efficiency of a chromato-

graphic column is the plate number N. Various procedures exist for calculating N
from an experimental chromatogram (9), and equation 14 is commonly utilized

N

= 5.54(V

R

/W

0

.5

)

2

(14)

where V

R

is computed from the point of application of the solution of polymer into

the column to the appearance of the peak height maximum of the chromatogram
and W

0

.5

is the width of the chromatogram at half height. This procedure assumes

that the chromatogram is symmetrical corresponding to a normal error (or Gaus-
sian) function. The plate number is a popular way of measuring column efficiency,
and a typical microparticulate packing with d

p

∼ 10 µm will generate a value

N

> 30,000 plates/m for a solute eluting at V

R

= V

0

+ V

i

.

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CHROMATOGRAPHY, SIZE EXCLUSION

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Table 1. Secondary Interactions in Aqueous SEC

Type

Symptom

Action

Ionic
exclusion

Peaks elute early, maybe before

SEC exclusion limit

Modify eluent, addition of salt,

and/or pH adjustment

Ionic
adsorption

Peaks elute late, maybe after SEC

permeation limit, peak tailing
or no peaks detected

Modify eluent, addition of salt,

and/or pH adjustment

Ionic
inclusion

Peak at total permeation due to

salt even though samples
prepared in eluent

Recognize salt peak, do not

include in sample integration

Hydrophobic
adsorption

Peaks elute late, maybe after SEC

permeation limit, peak tailing
or no peaks detected

Modify eluent, addition of

organic modifier (check column
compatibility)

If a polymer sample contains several species of very different sizes, then

peaks for each monodisperse species will be obtained when W

0

.5

is minimized.

However, because of the SEC elution volume range defined by 0

< K

SEC

< 1.0,

high efficiency columns are required for high resolution separations. It can be
estimated that an SEC column operating at 40,000 plates/m has a maximum
resolution of 40 peaks (24). For the case of two monodisperse solutes 1 and 2
having different sizes, column resolution R

s

is given by

R

s

= 2 (V

R2

− V

R1

)

/ (W

1

+ W

2

)

(15)

where V

R2

and V

R1

are retention volumes and W

1

and W

2

are peak widths at the

base of a chromatogram. The numerator in equation 15 will depend on separation
power, which is inversely proportional to the slope D

2

of the plot of log M vs V

R

defined by

log M

= D

1

− D

2

V

R

(16)

The values of D

1

and D

2

will depend on the pore size distribution of the packing,

gel capacity, ie pore volume, and on column length L, and these parameters need
to be optimized to increase separation power, and therefore peak resolution. Vari-
ables influencing the denominator in equation 15 are discussed in connection with
equation 19.

The definition of R

s

can be extended by considering molecular weight differ-

ences, in terms of the slope D

2

as defined by equation 16. It follows that a general

measure of SEC resolution may be developed (9), and the specific resolution R

sp

was proposed

R

sp

= 0.576/ (D

2

σ )

(17)

where

σ is the standard deviation of a Gaussian peak with 4σ = W

1

= W

2

and will vary with M. In practice, important parameters are D

2

, L, d

p

, and

σ, chosen so that R

sp

exceeds unity. Examples of column performance data are

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CHROMATOGRAPHY, SIZE EXCLUSION

621

Table 2. Column Performance Parameters

Exclusion limit

Efficiency,

a

Column type

(PS equivalent)

plates/m

σ,

b

mL

D

2

c

R

sp

d

PLgel 20

µm MIXED-A

40,000,000

15,100

0.204

1.155

1.061

PLgel 10

µm MIXED-B

10,000,000

34,200

0.166

1.138

1.703

PLgel 5

µm MIXED-C

2,000,000

47,600

0.115

0.915

2.376

PLgel 5

µm MIXED-D

400,000

50,100

0.115

0.737

2.949

PLgel 3

µm MIXED-E

30,000

96,000

0.106

0.605

3.898

a

Determined using toluene as test probe.

b

Determined using narrow PS standard, M

peak

= 9200.

c

Determined using narrow PS standards.

d

Determined using 0.25/(D

2

σ).

presented in Table 2 for a range of column types operating at an eluent flow rate of
1 mL/min.

Theoretical interpretations of column efficiency consider dispersion mecha-

nisms of solutes in the mobile and stationary phases. These mechanisms influence
the dependence of the height equivalent to a theoretical plate, or just plate height
H, on the linear flow velocity u of the eluent. The value of H may be determined
from an experimental separation from the equation

H

= L/N

(18)

The basic concepts for general chromatographic separations (25) can be applied
to SEC (9). For separations of polymers, it was proposed that only two column
dispersion terms influence H (26,27), namely eddy diffusion in the mobile phase
and mass transfer in the stationary phase. The expression for H for a permeating
monodisperse high polymer is

H

= 2λd

p

+



r

1

− r



ud

2

p



30D

s



(19)

where

λ is a constant (close to unity) characteristic of the packing, r is the reten-

tion ratio defined by V

0

/V

R

, and D

s

is the diffusion coefficient of the solute in the

stationary phase. Column dispersion by eddy diffusion, represented by the first
term in equation 19, arises because solute molecules reside in different stream-
lines with reference to their proximity to particles of the column packing. Column
dispersion by mass transfer, represented by the second term in equation 19, arises
because at any instant a fraction of the molecules will be within the porous column
packing and are left behind by the remaining fraction in the mobile phase.

Equation 19 identifies the experimental variables that have to be considered

in optimizing separations for reduced chromatogram broadening for high polymers
and for improved resolution of peaks for low polymers and small molecules. The
two column dispersion terms clearly demonstrate how lowering d

p

will maximize

column efficiency. For low polymers the mass transfer term will not be too signifi-
cant because D

s

is high, so that fast separations may be performed with little loss

in efficiency. Larger polymers that have lower values of D

s

will have higher mass

transfer dispersion. Therefore, a much more significant rise in H as u increases

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CHROMATOGRAPHY, SIZE EXCLUSION

Vol. 1

will be observed as molecular weight increases, and so high speed separations for
high polymers will operate with considerable broadening of a chromatogram.

These predictions can be compared with experimental studies of polystyrene

standards (26,27). However, all synthetic polymers will have an MWD, and it is
necessary to include a polydispersity contribution to the experimental value of
H. This is achieved by extending equation 19 to include a third term, presuming
that the permeating polymer has a logarithmic normal distribution for the MWD.
With this addition it is observed that equation 19 provides a good representation
of experimental results for plots of H vs u.

In practice, a polydisperse polymer having a range of solute sizes gener-

ates an SEC chromatogram which may be considered as a collection of a large
number of overlapping Gaussian peaks. Because of dispersion mechanisms, the
tails of the chromatogram result from broadening alone and so the computed w(M)
distribution is broader than the true MWD. Various correction methods have been
proposed to transform the experimental chromatogram into an MWD (4). How-
ever, it is not necessarily easy to achieve reliable corrected chromatograms before
calculating a w(M) distribution. The alternative approach is to reduce the level
of column dispersion in order to minimize broadening of a chromatogram for a
polydisperse polymer, according to the parameters in equation 19. If the optimum
separations can be achieved, then calculations of broadening corrections can be
omitted.

SEC Column Technology

SEC column packing materials, based on porous particles of a variety of sub-
strates, are commercially available from a large number of suppliers (13). In
the field of organic-soluble, mainly synthetic, polymers, column technology was
initially developed using both porous silica and porous PS/DVB particles as the
stationary phase. Although in the early days, columns of porous silica emerged
as popular candidates, mainly because silica was well established in liquid chro-
matography (LC), the production of very highly cross-linked PS/DVB particles
with well-controlled pore size and particle size distribution, and excellent tem-
perature and mechanical stability, led to their dominance in the field, which con-
tinues today (28). The continued refinement of PS/DVB particle technology has
produced smaller particle size packings (typically 5–10

µm), resulting in more

efficient columns and subsequent reductions in analysis times to typically 20–40
min. Recent years have heralded the emergence of 3

µm columns exhibiting ex-

tremely high efficiency (

>80,000 plates/m), which have particular application in

the very low molecular weight SEC separation range, competing with other types
of LC for the resolution of small molecules (29).

Columns for aqueous SEC have also been developed based on porous silica

and porous polymeric stationary phases. Columns of silica have excelled in the
field of monodisperse biopolymer separations (eg proteins and peptides) offering
very specific pore size distributions and small particle size for high resolution.
High performance packings, consisting of rigid hydrophilic polymeric particles,
were introduced in the early 1980s and offered considerable improvements in
both column efficiency and chemical and mechanical stability compared to the

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CHROMATOGRAPHY, SIZE EXCLUSION

623

early GF columns of soft polymeric networks. The continued development of high
performance, hydrophilic stationary phases has expanded the use of SEC for the
characterization of synthetic water-soluble polymers as they exhibit a much larger
separation range and better linearity of calibration curves, and much lower ad-
sorption effects compared to silica packings. In light of environmental issues, the
requirement to produce water-soluble polymers has in recent years significantly
increased the level of interest in aqueous SEC.

SEC column packing materials are generally represented by a characteris-

tic calibration curve produced using a series of polymer standards. Typical cal-
ibration curves for individual pore size columns, as illustrated in Figures 3a
and 4 for SEC columns with organic and aqueous eluents respectively, exhibit a

Fig. 3.

Calibration curves for columns of PLgel for organic SEC at ambient temperature:

(a) a range of individual pore size columns designated 50 ˚A to 10E6 ˚A, (b) a range of mixed
gel columns designated A to E. Eluent: THF, flow rate: 1 mL/min, calibrants: polystyrene
standards.

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CHROMATOGRAPHY, SIZE EXCLUSION

Vol. 1

Fig. 4.

Calibration curves for columns of PLaquagel-OH, designated 30 (

), 40 (
), 50

( ), 60 ( ), and Mixed ( ), for aqueous SEC at ambient temperature. Eluent: water, flow
rate: 1 mL/min, calibrants: poly(ethylene oxide/glycol) standards.

reasonably linear region spanning 1–2 decades in molecular weight, which defines
the optimum resolving range of that type of packing material. Most commercial
polymers exhibit a broad MWD demanding a very wide resolving range. Tradi-
tionally, this was achieved using combinations of several different individual pore
size columns, but nowadays the use of mixed gel columns (where a homogeneous
blend of individual pore size media is packed into the columns) is widespread
(30). This approach provides a linear calibration curve (as illustrated in Fig. 3b
and 4) over a specified molecular weight range, simplifies column selection, and
minimizes replacement stock.

Typical column dimensions for SEC are length of 25–30 cm and internal

diameter of 7–8 mm. SEC is normally a multicolumn technique and sets of two to
five columns are used routinely. It is a requirement that the column technology
should provide widespread solvent compatibility and good mechanical strength
for durability across a wide range of applications.

Eluent Selection

The primary consideration in eluent selection is that the polymer must be fully
dissolved for SEC analysis. A diverse range of organic solvents can be used for
SEC, covering a wide range of polarity from hydrocarbons through to alcohols.

Vol. 1

CHROMATOGRAPHY, SIZE EXCLUSION

625

Fig. 5.

Aqueous SEC analysis of three samples of chitosan at ambient temperature.

Columns: 2

× PLaquagel-OH MIXED 8 µm 300 × 7.5 mm, eluent: 0.5 M NaNO

3

/0.01 M

NaH

2

PO

4

/pH 2, flow rate: 1 mL/min, detector: DRI.

The physical characteristics of the organic solvent selected must be taken into
consideration with respect to detection, for instance, the refractive index of the
solvent if DRI is to be used, or the UV or IR spectrum of the solvent if spec-
trophotometric detection at a given wavelength is to be employed. Furthermore,
the viscosity of the eluent is important; if it is relatively high, then the SEC sepa-
ration may need to be carried out at elevated temperature in order to reduce the
eluent viscosity, thus decreasing column operating pressure and improving mass
transfer. In aqueous SEC, many water-soluble polymers contain charged species
or relatively hydrophobic groups which are likely to give rise to sample-column
packing interactions in the SEC separation. Such nonsize exclusion behavior as
shown in Table 1 must be suppressed if SEC is to be used for determination of
MWD, and this can be achieved by modification of the eluent. Water containing
salts and buffers successfully inhibit ionic interactions and the addition of a minor
volume of organic solvent (eg methanol) is used to suppress hydrophobic interac-
tions between the polymer and the column packing material. A typical aqueous
SEC separation is illustrated in Figure 5.

Instrumentation

An SEC system consists of a solvent reservoir, an isocratic pump to deliver the elu-
ent, an injection system to introduce the sample without interrupting the eluent
flow, SEC columns to perform the fractionation, a detector which, in its simplest
form, detects the concentration of the solute, and a form of data logging to record
detector response as a function of elution time (11).

Pumping/Injection Systems.

Because of the dependence of the tech-

nique on the precise measurement of elution volume, the pumping system must

626

CHROMATOGRAPHY, SIZE EXCLUSION

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be capable of delivering eluent at a constant volumetric flow rate, independent of
back pressure or temperature. The accuracy of the flow rate at which the solvent
is delivered is less important than the consistency, since very small variations in
flow rate can cause large errors if SEC is to be used for characterization of MWD.
Beyond the limits of acceptable pump performance, it is common practice to inject
an internal standard or marker such that corrections for flow rate variation can
be made to improve repeatability of results. When viscosity and light scattering
detectors are employed in the SEC experiment, it is also preferable for the pump-
ing system to exhibit minimal pulsations in pressure through the system so as to
improve detector baseline stability.

A two position injection valve, either manually or automatically actuated,

is usually employed for SEC, as for other forms of LC. The injection loop volume
should be minimized in order to avoid chromatogram broadening as a result of
dispersion in the injector. This is particularly the case when using SEC columns
packed with very small particles, where the column efficiency is very high. How-
ever, in the case of solutions of medium to high molecular weight polymer, at-
tempts to increase detector response by increasing sample concentration should
be avoided as the increase in solution viscosity may result in a change in elu-
tion volume and additional dispersion as a result of viscous streaming. In these
cases, it is necessary to increase the injector loop volume rather than increase
the solute concentration if additional detector response is required. As a rule of
thumb, an injection volume of 50

µL per column length of 30 cm in SEC is deemed

to be a good compromise between minimal dispersion and maximum detector
response.

Concentration Detectors.

In the simplest SEC system, the concentra-

tion of the sample eluting from the columns must be measured via some appro-
priate form of detector. The most commonly used type of concentration detector is
the DRI detector in which the difference in refractive index between pure solvent
and the eluent flowing from the separating columns is measured. The response
from the DRI detector is proportional to concentration, assuming that the specific
refractive index increment (dn/dc) for the eluting polymer is constant. Because
short chain polymers might have a molecular weight dependent dn/dc, a correc-
tion for the measured DRI response might have to be considered. In the case of
heterogeneous samples (eg block copolymers and formulated materials), where
the dn/dc for different components may vary as a function of elution volume, DRI
may not be the most appropriate choice of concentration detector. DRI detectors
are very sensitive to fluctuations in temperature and pressure, and baseline sta-
bility can be problematic if the system is not well conditioned. However, this type
of detector does have broad general application and is relatively low in cost.

Detectors operating on the principle of absorption of incident UV or IR radi-

ation are also used in SEC. These detectors rely on the polymer containing func-
tional groups that give rise to specific absorption at the wavelength of the incident
radiation and therefore are limited to certain applications where the polymer con-
tains a UV chromophore or has a characteristic IR absorption band. Furthermore,
the extensive use of a diverse range of organic solvents for SEC can restrict the use
of UV or IR detectors as the background absorption from the solvent itself can be
significant enough to mask out any contribution from the sample itself. Both UV

Vol. 1

CHROMATOGRAPHY, SIZE EXCLUSION

627

Fig. 6.

Comparison of detector responses for DRI and ELSD in the analysis of PS (top),

PDMS (middle), and PS/PDMS blend (bottom) at ambient temperature. Columns: 2

× PLgel

5

µm MIXED-C 300 × 7.5 mm, eluent: THF, flow rate: 1 mL/min.

and IR detectors can be useful for the characterization of copolymers using dual
detection, as the wavelength of the detector can be tuned to respond specifically
to one moiety.

The evaporative light scattering detector (ELSD) has found increasing ap-

plication in SEC over the last decade or so. In this device, the eluent stream is
mixed with an inert nebulizer gas to form a continuous stream of droplets that
pass through an evaporation chamber where the volatile solvent is driven off leav-
ing a plume of solute particles. The concentration of solute is determined by the
amount of light obscured by the particles as they pass through the optical cham-
ber of the device. This detector is often referred to as more “universal” than the
others mentioned above, since it does not rely on the characteristics of the so-
lute and is less affected by the choice of eluent. This is graphically illustrated in
Figure 6, which compares detector outputs from DRI and ELSD for the analysis of
a blend of polystyrene (PS) and polydimethylsiloxane (PDMS) using tetrahydro-
furan (THF) as eluent. In this case, there is a reasonable difference in refractive
index between the THF and PS, giving a positive peak response. However, PDMS
is isorefractive with THF and no peak is detected by DRI; hence the PS/PDMS
blend results in a chromatogram that reflects only the PS portion of the sample.
However, in the case of the ELSD, where eluent is evaporated, all solutes result
in a positive response and the chromatograms of PS, PDMS, and the blend are
suitable for quantification purposes.

Molecular Weight Sensitive Detectors.

Light scattering and viscome-

try are two classical techniques routinely applied to the characterization of poly-
mers in solution (2). When operated in a flow through mode, so-called molecular
weight sensitive detectors can be combined with the SEC separation to provide
direct measurement of molecular weight (light scattering) or a property related

628

CHROMATOGRAPHY, SIZE EXCLUSION

Vol. 1

Fig. 7.

Comparison of detector sensitivity for DRI (bottom), viscosity (middle), and light

scattering (top) for two narrow PS standards (M

peak

186,000 and 1260). Columns: 2

× PLgel

5

µm MIXED-C 300 × 7.5 mm, eluent: THF, flow rate: 1 mL/min, temperature: 40

◦

C.

to molecular weight (intrinsic viscosity), providing more accurate determination
of molecular weight as well as facilitating the study of polymer architecture. The
molecular weight sensitivity of such detectors compared to a conventional DRI
concentration detector is illustrated in Figure 7.

In light scattering measurements, the intensity of scattered light from the

polymer is expressed in terms of the excess Rayleigh factor R

θ

, which is defined

as the scattering intensity of the polymer solution to the scattering intensity of
the solvent at a given angle

θ. In practice for an SEC detector, R

θ

is the measured

response above the baseline, that is the detector output when there is no sample
in the eluent exiting from the column. The general light scattering equation

R

θ

= cM

w

(dn

/dc)

2

K

(20)

is applicable to on-line SEC measurements, where c is the polymer concentration
and K is an optical constant.

SEC detectors are available with single, dual, and multiple angles at which

the light scattering measurements are made and in each case the data treatment
will vary slightly to accommodate the number of angles. In all cases the light
scattering detector is used to determine the M

w

of each fraction of the polymer

as it elutes from the column, and by making a direct measurement of molecu-
lar weight, precludes the necessity to perform a column calibration. In order to
calculate MWD, the concentration of each fraction must also be determined, and
thus it is necessary to employ a concentration detector (usually DRI) as well as
the light scattering detector in the SEC system. The sensitivity of light scattering
detectors generally falls rapidly below around M

w

= 10,000. However, below this

limit the choice of solvent may be manipulated in order to increase dn/dc for a
given polymer type and also the solute concentration for low molecular weight

Vol. 1

CHROMATOGRAPHY, SIZE EXCLUSION

629

polymers can generally be increased with no deterioration in chromatographic
performance.

Viscometric detectors generally consist of one or more precision manufac-

tured stainless steel capillaries through which the eluent from the SEC column
flows and across which a pressure differential can be measured. Therefore, ac-
cording to Poiseuille’s law

P

=

8L

ηF

Pr

4

(21)

where L and r are the length and radius of the capillary, F is the flow rate, and P
is the pressure drop measured across the capillary. The specific viscosity (

η

sp

) of

a polymer solution passing through the detector can be determined as a function
of elution volume or time. Once again, an additional concentration detector is
required in order to precisely determine the concentration of each eluting fraction
such that a value of [

η] can be determined according to

[

η] = η

sp

/c

when c approaches zero



(22)

The measurement of [

η], also abbreviated IV, permits the determination of molec-

ular weight of the polymer under investigation according to the principle of uni-
versal calibration, using hydrodynamic volume as defined in equation 9 as long
as this polymer type is eluting by a size exclusion mechanism.

Conventional SEC calibration curves derived using different polymer types

will yield polymer specific calibration plots of log M versus retention time as
illustrated in Figure 8a. However, if an on-line viscometer is employed to measure
[

η] directly, then the universal calibration plot of log [η]M versus retention time

will hold for any polymer type so long as the separation mechanism is based on size
exclusion only, as illustrated in Figure 8b. Thus, having constructed a universal
calibration using well-characterized polymer standards, any type of polymer can
be analyzed, and by measuring [

η] on-line after the separation, the molecular

weight of each eluting fraction can be obtained from the universal calibration
plot.

In addition to the measurement of molecular weight, both light scattering

and viscosity detectors permit the study of polymer architecture, eg branching.
Figure 9 shows a series of typical Mark–Houwink plots for polyethylene sam-
ples derived from triple detector data (ie DRI, light scattering, and viscosity). A
linear unbranched polyethylene results in a straight line plot where the slope
and intercept equal the Mark–Houwink constants a and log K respectively. If
the polyethylene is branched, the branched polymer will have relatively higher
segment density compared to a linear polymer of equivalent molecular weight, re-
sulting in a decrease in intrinsic viscosity. The ratio of the intrinsic viscosity of the
branched polymer compared to a linear analogue will be dependent on the degree
of polymer branching. Previous reference to concentration detectors for samples
having compositional heterogeneity indicates that careful selection of a single

630

CHROMATOGRAPHY, SIZE EXCLUSION

Vol. 1

Fig. 8.

Comparison of (a) conventional SEC calibration and (b) universal calibration, gen-

erated for polystyrene and polyethylene standards. Columns: 3

× PLgel 10 µm MIXED-B

300

× 7.5 mm, eluent: TCB, flow rate: 1 mL/min, temperature: 160

◦

C.

Polystyrene;

polyethylene.

detector or dual detectors, together with light scattering or viscometric detectors,
will be necessary for characterizing specific copolymers and blends.

Data Treatment

A primary application of SEC is for the determination of MWD (31). In this ap-
proach the raw data chromatogram obtained as output from the concentration de-
tector is divided into a number of time slices of equal width, as shown in Figure 10.

Vol. 1

CHROMATOGRAPHY, SIZE EXCLUSION

631

Fig. 9.

Mark–Houwink plot from SEC with triple detection indicating linear polyethylene

and polyethylenes with increasing degree of branching.

Mi, Ni

Fig. 10.

Chromatogram from SEC indicating time slices for data manipulation.

For polydisperse samples the number of time slices must be selected in order that
the computed average molecular weights will be unaffected by the number of time
slices used. Since the introduction of high capacity computers with modern SEC
software, this is nowadays not a limitation for samples with narrow and broad
distributions. An average molecular weight is assigned to each time slice and it
is assumed for computational purposes that each time slice is monodisperse in
molecular weight. A table is constructed with one row assigned to each time slice
i and containing values for retention volume, area A

i

, cumulative area, molecular

weight M

i

, A

i

/M

i

, and A

i

× M

i

. The area of each slice is assumed to represent the

632

CHROMATOGRAPHY, SIZE EXCLUSION

Vol. 1

mole fraction N

i

(or number fraction) of each mondisperse species in Figure 10.

The moments of the distribution, and hence the average molecular weights, can
then be calculated:

Number average M

n

=



A

i



A

i

/M

i

(23)

Weight average M

w

=



A

i

M

i



A

i

(24)

z average M

z

=



A

i

M

2

i



A

i

M

i

(25)

When light scattering detection is employed, M

i

can be measured instantaneously

for each slice in the chromatogram.

Calibration Methods.

In the absence of a light scattering detector, the

calculation of MWD and average molecular weights from an experimental chro-
matogram necessitates the determination of the relationship

log M

= f (V

R

)

(26)

or, for a constant flow rate through the system

log M

= f (t

R

)

(27)

where t

R

is retention time. Thus, a value of molecular weight can be assigned

to each eluting slice based on its retention time or volume, and the MWD can
be calculated. To achieve this, the column set used for the analysis must be cali-
brated, most commonly using a series of narrow polydispersity, well-defined poly-
mer standards to establish the relationship. Narrow polydispersity standards,
where M

w

/M

n

is typically less than 1.1, are available in a reasonably wide range

of polymer types for both organic and aqueous SEC, for example, polystyrene,
poly(methyl methacrylate), poly(ethylene oxide), and polysaccharide. Such stan-
dards must be characterized using a combination of techniques including SEC,
since it is the peak molecular weight of the standard (M

peak

) that should be plot-

ted against peak retention time. Because of the relatively high efficiency of modern
SEC columns and the narrow polydispersity of the calibrants, several standards
are usually chromatographed together to save time, as illustrated in the upper
part of Figure 11. This gives a conventional SEC calibration curve relating molec-
ular weight to retention time for that specific polymeric calibrant type, as shown
in the lower part of Figure 11, and in the application of this curve any molecular
weight values calculated for unknown polymer samples must be quoted as relative
values.

If narrow polydispersity polymer standards are not available for the poly-

mer type under investigation, a calibration can still be established by applying
the principle of universal calibration. For a chromatographic system containing a

Vol. 1

CHROMATOGRAPHY, SIZE EXCLUSION

633

Fig. 11.

Separation of narrow polymer standards of low polydispersity, and subsequent

SEC calibration plot.

viscosity detector, an on-line measurement of intrinsic viscosity can be determined
for any polymer type, and hence be converted to a calibration of log M

p

against

V

R

according to equation 10. Alternatively, this approach can be modified by in-

corporating constants from the Mark–Houwink relation represented by equation
4, and by rearranging equation 10 it can be shown that

log M

p

=



1

+ a

ps



/

1

+ a

p

 

log M

ps

+



1

/

1

+ a

p

 

log

K

ps

/K

p



(28)

Values for the Mark–Houwink parameters K and a have been tabulated (14), and
should be utilized where the solvent and temperature are appropriate. If only a
value for M

n

for a sample is required, then the method proposed by Goldwasser

(32) can be applicable. This method requires the establishment of a universal
calibration curve in conjunction with a viscometric detector without the need for
a concentration detector or Mark–Houwink constants.

Software packages include calibration methods based on well-characterized

reference materials with an MWD that may be somewhat broader than a narrow
standard or with polydispersities exceeding 1.5. For calibrants with M

w

/M

n

<1.5,

634

CHROMATOGRAPHY, SIZE EXCLUSION

Vol. 1

M

peak

is close to M

w

or M

v

, which can be used in plotting the calibration curve,

whereas for M

w

/M

n

>1.5 search methods are required to generate a calibration

curve over the range of M for the reference material (20).

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J

OHN

V. D

AWKINS

Loughborough University
E

LIZABETH

M

EEHAN

Polymer Laboratories Limited