Standard Methods of Molecular Weight Measurement: Part II
3.1 Sedimentation Equilibrium and Sedimentation Velocity
Both sedimentation methods referenced in the heading can be performed in the same
standard analytical ultracentrifuge, so the two will treated together, although the physics
of M measurement are distinct.
As sketched below, an analytical ultracentrifuge rotates a measuring cell at extremely
high angular velocities. The rotor makes ~60,000-70,000 revolutions per minute, and
with the cell located off-axis by ~5 cm, the sample in the cell experiences a centrifugal
force of the order 200,000-400,000 g, where g is the acceleration of gravity. The
surrounding enclosure maintains constant temperature and acts as a barrier should
anything fly loose! The limit to the g-force is set by the strength of the rotor material,
which is usually titanium or an esoteric metal alloy.
1=motor and gear; 2=rotor; 3=measuring cell(s); 4=quartz window; 5=optics;
6=light source; 7=optical detector; 8=thermostated enclosure
[E. Schröder, G. Müller, and K.-F. Arndt, Polymer Characterization, Hanser, 1989, p 80]
The distribution of polymer along the axis of the measuring cell can be determined in a
number of ways, but most commonly, UV absorbance or Schlieren optics are chosen.
The optical path for either detection method follows the sketch, with a light beam
traversing through windows that form the top and bottom of the measuring cell. UV
absorbance is potentially the more sensitive of the two approaches, but many polymers
don’t absorb UV or visible light significantly relative to solvent, in which case, this
detection can’t be selected. Schlieren optics won’t be described here in any detail, but for
this approach, the light detector measures a signal proportional to the gradient of
refractive index (dn/dx, where x is measured outward from the center of rotation), and
thus indirectly, of mass concentration c.
3.1.1 Theory.
The centrifugal force Fb exerted on a dissolved polymer molecule arises from the
polymer’s buoyancy, i.e., the difference in density between polymer and solvent,
1
M
1  1v2  2 x
NA
Fb = meff  2 x =
where meff is the effective mass of one molecule in the solvent,  is the angular velocity
of the rotor, NA is Avogadro’s number, 1 is the solvent density, and v2 is the partial
specific volume of polymer, effectively the reciprocal of the polymer density when
dissolved in the solvent. For simplicity, a polymer denser than solvent is assumed in the
subsequent analysis, directing Fb outward, in the direction of increasing x. The opposite
case is almost as common.
A balance of Fb with the polymer’s hydrodynamic resistance Fh to translational motion
through stationary solvent sets the sedimentation velocity dx/dt,
dx
Fh = f
dt
where f is the chain’s friction coefficient. The sedimentation coefficient s relates dx/dt to
the centrifugal acceleration 2x,
dx
s = dt2
 x
s is commonly expressed in Svedberg units, where 1 Svedberg equals 10-13 s. Equating
Fh to Fb, an expression for M is obtained
fsNA
M =
(1 1v2 )
By adopting the Einstein equation for solute friction, f = kT/D, where k is the Boltzmann
constant, T is temperature, and D is the polymer’s tracer diffusion coefficient in the
solvent (evaluated at dilute conditions), the so-called Svedberg equation is obtained,
RTs
M =
(1 1v2 )D
which connects sedimentation to tracer diffusion while offering a route to M if s is
measured, and D and v2 are known (or measured separately).
Solving for x in the equation that defines s, one finds that a narrow band of homogeneous
polymer migrates such that band position changes exponentially in time t.
Diffusion about the mean band position during centrifugal migration has been ignored so
far. Adding diffusion to the force balance leads to a sedimentation-diffusion governing
equation (Lamm’s equation) in the form of a differential equation,
c
1  
c 
=
sc 2 x 2  Dx 

t
x x 
x 
When D is set to zero, this equation describes migration of a solute concentration pulse at
a velocity s2x, reproducing the result of the simpler analysis given above.
2
When equilibrium across the cell is achieved at large t, i.e, when dc/dt=0 at all x, outward
sedimentation balances inward diffusion down a steady c gradient. One can solve the
same differential equation for c and then eliminate D and s through the Svedberg
equation, finding for the steady c profile,


M
c = cb exp 
1 1v2  2 x 2  x b2 


2RT

where at x=xb, the position of the outer end of the measuring cell, the no polymer flux
condition allows the polymer to accumulates to c=cb, a parameter dependent on the
original mass of polymer added to the cell. With v2 known by a separate density
measurement, M can be calculated at equilibrium by measuring c at any two positions x,
c
2RT ln 2
c1
M =
2
1  1v2  x 22  x12


where “1” and “2” designate c and x at the two positions.
For a polydisperse system at equilibrium, each component of molecular weight Mi and
concentration ci obeys a concentration profile analogous to that given above, and adding
these profiles together to obtain c,
 2 x 1  1v2  ci Mi
dc
=
dx
RT
This equation can be manipulated to find various molecular weight averages; the
formulae will not be given here.
The first equation given for M, derived in absence of diffusion, suggests that for large M
(a condition which restricts diffusion of away from the mean band position because D is
small) s should correlate with M similarly to f, i.e., with a power law,
s  KM a
Coefficients K and a, derived from a set of nearly monodisperse samples, are tabulated
for many polymer/solvent combinations. When the two parameters are available in this
manner, the velocity sedimentation method provides the full M distribution if the
distribution of s is measured.
3.1.2 Practice
Measuring cells are from 0.2 to 3 cm in length and have a segment shape such that cell
width increases toward the bottom (sector angle ~ 2-4º). The initial distribution of
polymer within the cell is uniform, i.e., c is not a function of x.
To measure sedimentation velocity, the rotor speed is set so high that diffusion of
polymer is negligible. Then, at some intermediate time t, well before equilibrium across
3
the cell is achieved, one can envisage transient c profiles much as drawn below for the
case of two discrete M fractions in the sample.
The top curve corresponds to complete neglect of diffusion. Each “step” corresponds to a
sharp interface between two regions, one in which the concentration of a specified
polymer fraction is uniform (for x greater than the step position) and one where this
polymer fraction is absent (for x less than the step position). Adding diffusion, these
interfaces are smeared, as shown in the middle sketch; the new profile parallels an the
absorbance measurement of c. With Schlieren optics, which detects the gradient of c,
measurement yields the bottom sketch.
Considering a single component polymer solution, as the c step approaches the bottom of
the cell at larger t, its character changes, reflecting approach to the equilibrium c profile.
This time evolution is sketched below:
Whereas initial concentration co was uniform, at intermediate t, a c step migrates to the
right. Simultaneous to migration, at the bottom of the cell, c rises above co as polymer
arrives in this region and is trapped by the closed cell end. Eventually, the migrating step
4
merges with the perturbed bottom region and a continuously increasing c profile is
obtained. Eventually, at equilibrium, the profile becomes time-invariant.
Only at intermediate t will a c step migrate as described in the theory derived without
diffusion. Measurements in this t domain made with Schlieren optics for the theta system
of polystyrene migrating in cyclohexane are shown below. As the simplified theory
predicts, polymers move such that their x-positions move exponentially in t. The
linearity of the semilog plot for specified integrated mass fractions I (M) are shown
further down; slope differences among the I(M) lines reveal there is a distribution of M,
the different fractions migrating at different s.
For this model system,
s  1.55x10 2 M 0.5
where M is in g/mol and s is in units of Svedbergs. The M distribution calculated using
this s-M correlation is given in cumulative form at the top of the next page.
As described above: t is time in minutes
As described above: I is integrated mass fraction
5
Integral weight fraction distribution of M. The five points correspond to the 5 slopes of
the preceding plot.
[all plots from: E. Schröder, G. Müller, and K.-F. Arndt, Polymer Characterization, Hanser, 1989, pp 88-89]
Issues:
 An analytical ultracentrifuge is very expensive, ~$300-400,000.
 The volume of sample is small (<1 ml of dilute solution).
 One must have a pycnometer to measure v2 .
 The velocity method is fast (hours) but the equilibrium method is slow (days); for
this reason, the equilibrium method is rarely performed.
 There is really no upper M limit, especially for the velocity method.
 The low M limit is established by the magnitude of g-force available.
 The larger is v2 and the larger is dn/dc (or absorbance), the better is accuracy.
Accuracies of 5-10% are typical for model systems.
 Unless s is known as a function M by correlation with M standards, the velocity
method requires input of D. Ideally, one can get D for a narrow distribution
sample by the width of the step of c. For a polydisperse sample, the Mdependence of D convolutes onto the M-dependence of s, making the velocity
measurement hard to interpret.
 Some investigators have connected a light scattering detector to the measuring
cell such that unmixed sample fractions are streamed to the light scattering
detector for absolute M measurements. The combination gives the absolute M
distribution without further assumptions, but operation is tricky.
 Equilibrium sedimentation in a solvent with a density gradient has often been
used to study biopolymers. Use of this approach for synthetic polymers has been
extremely rare. A density gradient can be created by adding a cosolute such as
sucrose, which rapidly sediments to its own equilibrium concentration profile.
 Data analysis is more straightforward for a system containing a few discrete
molecular species than for a system containing a distribution of species. This
makes the method more popular for biopolymers than for synthetic polymers.
 Although seemingly suitable for studying composition distributions in
copolymers, especially graft and block copolymers, over the past ten-fifteen
years, I’ve only seen sedimentation used to study branched polymers. In the latter
case, measuring M was not the objective.
6
3.2 Solution Viscometry
Dilute solution viscometry, the first relative M method to be described, is based on
measuring the increase in viscosity  as a polymer is added at varying dilute
concentrations c to a solvent. The normalized relative change in viscosity is referred to
as the “specific” viscosity sp,
  o
sp =
= rel  1
o
where o is the pure solvent viscosity, and rel (=/o) is termed the “relative”
viscosity. Dividing sp by c, one obtains the “reduced” viscosity red, which varies
linearly with c when c is low. The linear increase is captured in the empirical Huggins
equation,
red =  + k H 2 c + ..
where [] is the “intrinsic” viscosity and kH is the Huggins coefficient. The latter has a
value of ~0.3-0.4 in a good solvent and ~0.5 in a theta solvent.
The value of [] captures the degree to which a small increment in c raises . Adding
larger polymers at the same c increment causes a greater increase in , as derived in the
next subsection.
3.2.1 Theory of Dilute Solution Viscosity
To understand the viscosity method, we begin with a relationship derived by Einstein for
the viscosity at volume fraction  of a dilute suspension of uniformly sized spheres. He
found by difficult theory [difficult enough that Einstein made an math error that he had to
correct in a 2nd publication] a rather simple result:
 = o[1 + 2.5 + …]
To connect to polymer solution measurements, we must relate the actual experimental
variable c to , which doesn’t have a clear definition for flexible polymer molecules.
Assuming that the molecules behave hydrodynamically as rigid spheres, we can assign to
each chain in dilute solution a “hydrodynamic radius” Rh. This radius can be interpreted
as the size of the sphere that would give a contribution to  equal to that from a single
7
polymer. We do not know precisely how Rh relates to the size and structure of the
dissolved polymer, but we can be confident that Rh is proportional to any choice of
average coil size. Letting C be an undetermined coefficient, we can write, for example,
Rh = CRg
The effective “hydrodynamic volume” Vh of one chain is then,
Vh = (4/3)Rh3 = (4/3)C3 Rg3
Adopting this volume, we next transform c [mass/volume] into , effectively making this
step a units conversion,
c[mass / vol]Vh [vol / molecule] N A[molecules / mole]
 =
M[mass / mole]
Eliminating  and Vh,
[] = 2.5 (4/3)C3NA[Rg 3/M]
The multiplicative factors outside of the […] on the right-hand-side define a universal
constant of unknown value. For long enough linear polymers, Rg depends on M raised to
a power,
Rg  M
Combining the two previous formulae and gathering the incompletely specified constants
into empirical parameters, K and a,
[] = KMa
where a=3-1. Many values of the constants K and a, called “Mark-Houwink
coefficients”, are tabulated in reference books.
If K and a are known a priori for a particular polymer chemistry and solvent, and [] is
measured for a sample of the same chemistry in the same solvent, we deduce the
sample’s M by direct substitution into the preceding formula.
The value of M obtained in this manner is an average over the sample’s M distribution.
To be specific, we subscript the value of M determined in this fashion with a “v”, terming
Mv the “viscosity-average” molecular weight, calculated from the M distribution as

Mv =  w i Mi a

1/ a
Experimental determination of v also reveals whether a solvent is a good, marginal, or
theta solvent for the tested polymer.
The preceding analysis of polymer dilute solution viscosity assumed that a coiled
polymer behaves hydrodynamically as a rigid sphere, an assumption known as the
“nonfree-draining” hypothesis since it implies that a nearly time-invariant spherical
solvent domain is dragged along with the polymer during flow. One might guess that this
8
hypothesis is awful, as the segment density inside a coil can be quite small. An opposing
hypothesis regards polymer chains as “free-draining”, with solvent readily able to
penetrate and flow within the coil. To judge between the nonfree-draining and freedraining hypotheses, solvent flow must be analyzed within a polymer coil, a theoretically
difficult problem. Those who do this sort of analysis report that the free-draining
approach fails for dissolved high molecular weight polymers. Although many texts
debate the two draining hypotheses at length, we need only to recognize that the nonfreedraining hypothesis is correct. Perhaps a physical analogy can best explain the result,
that a tenuous porous solute effectively immobilizes all solvent in its interior: Although
the branches and leaves of a bush might be sparse (comparable to the sparseness of
segments within the envelop of a polymer coil), the branches and leaves effectively
screen a strong wind so that air at the bush’s center is nearly stagnant.
For linear homopolymers, the Mark-Houwink relationship is only valid asymptotically,
i.e., at large M, where the exponent a must have one of three values, 0.33, 0.5, or 0.6,
corresponding to poor, theta, and good solvent conditions. Although other values of a are
reported, any value other than these three implies that measurements were not made in
the asymptotic high M regime. If so, the power law relationship is only approximate,
extending over a limited range of M. The values of K and a are typically determined by
examining a series of M standard polymers. Molecular weights of the standards could be
determined by any method but typically these values are determined by light scattering.
3.2.2 Practice of Dilute Solution Viscometry
To assure that the tested polymer solution is dilute, viscosity measurements are
performed over the range 1.0<rel<2.0 (the coil overlap concentration c* is commonly
defined by this upper limit). The solution thus has a viscosity within a factor of 2 of the
solvent, and since viscosities of most simple solvents are in the range of centipoises,
capillary viscometers are preferred for intrinsic viscosity measurements. Other types of
commercially available viscometers don’t have the accuracy for such low viscosity fluids.
For very high M polymers, however, as discussed below, one might be able to use a
rotational viscometer with cylindrical Couette fixtures. Viable viscometers of this type
were once commercial, but few remain in use today.
Two capillary viscometers are popular, Ubbelhode and Ostwald, shown left and right,
respectively on the following sketch:
In both types, one measures the time t needed for a solution or solvent to drain through
the test section of a glass capillary under the action of gravity. The Ubbelhode type is
9
superior, since the drainage height doesn’t vary over the duration of the experiment.
Texts often describe various hydrodynamic corrections for entrance/exist effects, but in
modern capillary viscometers, assuming laminar flow,  is almost perfectly proportional
to t, so these corrections aren’t needed.
However, appropriate values of t ARE necessary. If t for solvent is 60 s, the lowest
solution t will be about 66 sec (i.e., rel=1.1). If the measurement uncertainty is 0.2 s
(the human reaction time during use of a stop watch), an error in sp of the order 0.4/6=
will be incurred, about 5-10%. Upon extrapolation to zero c, this level of error can
generate larger uncertainty in [], perhaps of the level 50%. The consequential error in
M is even larger. If a stopwatch is to be used, I recommend selection of a viscometer
such that t is greater than 150 s. The timing problem is much reduced if t is measured
automatically, as done in some commercial instrument packages. Drainage time is
typically controlled through the length and diameter of the capillary, so different
capillaries are often stocked in a lab that does these measurements routinely.
Many instruments allow dilution inside the viscometer; this feature requires a larger
bottom bulb. One simple adds an aliquot of solvent after the preceding measurement is
complete.
Issues:
 Temperature control can be crucial, since viscosities of simple fluids vary
exponentially with temperature. For example, the viscosity of water drops by
more than 10% as temperature rises from 20ºC to 25ºC. Temperature control is
typically achieved by immersing the viscometer in a transparent fluid bath with
temperature controlled to better than 0.1ºC. Measurements in open air are only
qualitative, and quantitative measurements in a bath at high temperature are
extremely difficult.
 Dust has a large effect, increasing artificially raising t. The problem is
exacerbated by the small diameter of the capillary. Solutions/solvents should be
filtered directly into the viscometer.
 Since the solution moves up and down, polymer can readily be adsorbed or
deposited on the capillary walls as the solution dries between runs. There is no
easy way to clean the walls other than to add an aggressive solvent.
 Co-solutes can be a killer. I tried to measure the molecular weight of a polymer
that was dissolved in a surfactant solution, but I could never eliminate the bubbles
generated by siphoning the solution up the capillary. The presence of even a
minute bubble substantially raised t.
 Polymers larger than about 0.5-1x106 g/mol generate shear-thinning solutions,
and the appropriate viscosity for M determination is that at zero shear rate. Many
capillaries generate shear rates of several hundred s-1. To avoid shear thinning,
one commercial Ubbelhode design has four test sections in sequence, each with a
different capillary diameter and thus producing a different shear rate. The four
measured drainage times can be extrapolated to the drainage time corresponding
to zero shear rate. Often, however, a large extrapolation is necessary, making the
10




final measured quite uncertain. I would never attempt the solution viscosity
method with standard capillaries for M greater than 107 g/mol even if supporting
literature exists. Values above M~106 g/mol are open to question. Several tactics
have been suggested to extend solution viscosity measurements to higher M,
including accordion-like capillaries that drain on the tens-of-minute timescale.
To avoid the problems of the last two bullets, I have used a rotational viscosmeter
made by Contraves, and I have also built a so-called Zimm-Crothers viscometer.
Both viscometers have extremely high torque sensitivity and can monitor
viscosities of the appropriate magnitude at shear rates of 1 s-1. (Indeed, I could
measure the viscosity of simple solvents to an accuracy of better than 1% in the
latter instrument. Unfortunately, it was extremely difficult to operate and clean.)
No appropriate rotational viscometer for intrinsic viscosity measurement is
currently commercial available.
In absence of calibration standards, what can one do? Not much. Unlike some
other relative methods, one cannot make use of calibration standards of a different
chemical type – the value of K varies too widely. Many industries characterize
the size of their polymer products through specific viscosity at some standard
polymer concentration.
One should never extrapolate to find M outside the range in which the MarkHouwink coefficients were obtained.
Although solution viscosity dominated M measurements from the period 19401990, usage has dropped rapidly with the advent of simpler/cheaper light
scattering instruments and GPCs. Most uses today relate to the probing of
polymer architecture, not the measurement of M.
11
3.3 Gel Permeation Chromatography
Gel Permeation Chromatography (GPC), also called Size Exclusion Chromatography
(SEC), has become the most practiced method of M measurement for synthetic polymers.
Since modern column packing particles are rigid solids, able to withstand large pressures,
the allusion to gel packing particles in the older name is a little inappropriate, but still this
name is the most widely employed for the method. GPC does not really offer a method
for M measurement but rather a method for the separation by M of mixed polymer
fractions. Only when the separation is calibrated, i.e. the position of an eluted fraction
can be related to the fraction’s M, is the method capable of measuring M.
The operation of a GPC instrument is as for any chromatographic method except that the
interactions of the solute with the packing are principally steric (entropic); in other forms
of chromatography, reversible adsorption (enthalpy) is the dominant interaction. The
degree of separation by GPC is generally much smaller than in other forms of
chromatography, with peaks for all M values spread over about a two-fold range of
elution volume, so maintenance of a constant chromatographic flow rate is crucial. Most
practitioners add a low M marker to each polymer sample so as to track flow rates
relative to flow rates maintained during calibration runs; variation of flow rate should be
less than ~0.3%. If the flow rate shifts by 1%, depending on the calibration curve, errors
in M of order 25% can be incurred.
The basic elements of a GPC instrument are sketched below.
KSEC
12
The partition coefficient KSEC is the ratio, at equilibrium, of polymer concentration
inside the packing pores to the concentration outside these pores, and the separation relies
on the M dependence of this coefficient. The range of KSEC is 0<KSEC <1, spanning
from complete exclusion for the former to full permeation for the latter. Since the
morphologies of the particle pore structures are quite complex and heterogeneous, KSEC
can be defined only in average terms across a collection of parking particles.
As a polymer bands sweeps by a packing particle, one might question whether the
polymer enjoys a long enough residence time to equilibrate between the inside and
outside of the packing particle. However, chromatographic theory shows that
equilibration at this local level is not needed. Instead, equilibration is achieved over a
column length called the Height Equivalent of a Theoretical Plate (HETP), which
typically corresponds to a column length of several packing particle diameters.
Efficiency of a GPC column is assessed by the number of theoretical plates present for a
low molecular weight species with KSEC =1,and the number of HETPs is usually in the
tens of thousands for a good column.
Since equilibration at some level is established between intra- and inter-particle pore
volumes, the separation (positions of peaks) across a full column should be independent
of flow rate, a fact confirmed by many experiments. However, HETP does depend on
flow rate, and the minimum HETP for most columns is at a lower flow rate than chosen
for experiments (conventional value: 1 ml/min). Operating at the minimum HETP
maximizes peak resolution, since peak widths are minimized at this condition.
Twenty years ago, the typical GPC set-up had five columns in series, each of different
pore size so as to separate different M ranges. Such a set-up could create good resolution
across the range 1,000 g/mol<M<4,000,000 g/mol for a model system such as
polystyrene in toluene or THF. Today, with more efficient columns of mixed pore size,
two columns do the same job faster.
The role of KSEC is highlighted in the next figure:
Vr = Vo + KSECVp
Vr = retention volume
Vo = interstitial packing volume
Vp = pore volume
KSEC = partition coefficient
KSEC = e Sc / k
Sc = confinement entropy
Chains lose configurational entropy upon entering
13
The value of KSEC depends on the polymer-polymer confinement geometry and size
ratio, as sketched below.
Model Configurational
Entropy Loss
Measure in Experiment
1.0
1.0
Log KSEC
Log KSEC
Solute size
Solute size
The typical size ratio of polymer-to-pore is about 0.1 to 0.001, allowing equilibration to
be achieved rapidly and thus to minimize HETP. However, a larger ratio would create
larger degrees of polymer separation, since KSEC is more sensitive to solute size when
the polymer-to-pore size ratio is about unity.
Calibration is the major issue in GPC. The conventional calibration is by M standards of
the same polymer chemistry as the test sample. This procedure is illustrated in the figure
on the top of the next page and was mentioned in the first handout. Good separation is
only achieved across the “operating range”, where logM is approximately linear in Vr.
The operating range depends on the pore sizes and pore size distributions of the packing
beads, and in a mixed bead column – packed with beads of various pore sizes - this range
can extend over several orders of magnitude in M, bounded by total exclusion (upper M
limit) and total permeation (lower M limit). Linearity of this plot is not really required,
just that a solid correlation between M and Vr. When Vr is highly sensitive to M, the
logM vs. Vr plot has a low slope in the operating range; however, this feature means that
the column’s M range is sharply limited, perhaps to as little as one order-of-magnitude.
Note that Vr fundamentally distinguishes M fractions. Most instruments monitor
fractions by their elution time t rather than their elution volume Vr. If so, to connect t to
14
V
Vp
Operating
Range
Log M
Total
exclusion
Total permeation
Vr
Chromatogram
Vr
Vr, the flow rate must be kept rigorously constant, as noted before. To monitor Vr during
the experiment, needed for precise work, a GPC must have a capability to measure flow
rate or collect fractions of constant volume; I am unaware of a commercial instrument
that does either.
To avoid calibration by standards, which usually are unavailable for a new polymer or
even many older ones, universal calibration was devised, a concept exploiting that GPC
separation is governed by polymer “size”. As indicated in the top sketch on page 13, the
degree of separation (i.e., KSEC and thus Vr) correlates with a molecular size sometimes
called the “mean projection length”, the average closest separation of polymer to pore
wall computed from the full ensemble of free polymer configurations. Universal
calibration recognizes that for a linear flexible homopolymer, all measures of chain size
are proportional to each other. Thus, as shown in the discussion of dilution solution
viscometry, the product []M, capturing the hydrodynamic size raised to the third power,
can be taken as a variable correlating GPC separation. The quality of this correlation is
illustrated in the sketch on the top of the next page. Universal calibration eliminates large
errors (typically 10-50%) incurred by calibration with M standards of different
backbone chemistry, usually polystyrene (organic solvents) or PEO (aqueous solvents).
15
Issues:
 GPC can be coupled to a M-sensitive detector to reduce errors associated with
calibration by standards. With a static light scattering detector, this addition
makes the method absolute, while with a viscosity detector, the method remains
relative. However, for the latter, assuming universal calibration is valid, results
are expressed directly in terms of M. I believe viscosity detection is only
warranted when a branched or architecturally complicated polymer is studied;
stick with light scattering – it is more rigorous.
 One only obtains the correct M distribution if all of the sample elutes past the
detector(s). If adsorption is a possible complication, one should check that all of
the sample has passed the detector by constructing a by-pass from the injection
value to the detector.
 Several issues can complicate the study of high M polymers – (i) Really large
open pores structurally weaken the packing particles, and thus, large polymers
cannot be studied at the same polymer-to-pore sizes as with smaller polymers.
This constraint reduces column efficiency and makes equilibration difficult. (ii)
The strain rates in and around the particles may generate hydrodynamic forces
large enough to break chains. If this effect is a concern, an eluted fraction should
be reinjected to assure that it elutes in its original position (iii) Other exclusion
mechanisms may dominate, especially hydrodynamic chromatography, the
exclusion of the polymer from the particle surface and not from inside pores.
 Most aqueous GPC systems require solvent additives to preclude adsorption on
the packing.
16