Nonstandard Methods of Molecular Weight Measurement
4.1 Gel Electrophoresis (and related methods)
4.1.1 Description
Electrophoresis refers to the electric-field directed translational motion of a charged
solute through a quiescent medium. If the medium containing the solute is an open
solvent containing only added low molecular weight electrolyte, electrophoresis is said to
occur in “free solution.” The translational motion of dilute charged polymers in free
solution is independent of M for M above the oligomer range. Therefore, electrophoretic
methods for the determination of M are performed in a porous matrix that hinders
polymers according to M.
These methods apply only to polyelectrolytes (i.e., highly charged polymers), and the
permissible solvents – those that support charge on the polyelectrolyte – are those with
high dielectric constant. Nearly always the solvent is pure water or water that contains
additives such as salts and buffers. There are a few exceptions: some neutral polymers,
such as PEO and polypeptides, dissolve in an aqueous solution that has a charged
surfactant that “coats” the polymer, creating a “pseudopolyelectrolyte”. It will be
assumed here that the polyelectrolyte’s charges are distributed uniformly along the chain
backbone from end to end. Such a distribution is not found on most polypeptides and
proteins, but this potential complication is eliminated in the presence of the anionic
surfactant sodium dodecyl sulfate (SDS), which binds densely to polypeptides and
proteins in a manner nearly independent of amino acid sequence.
Many different porous media have been used to create separation by M in an
electrophoresis experiment. The dominant media have been hydrogels, so I will refer to
all these electrophoretic methods by the term “gel electrophoresis”. However, many of
the methods do not employ a gel or even an obvious porous matrix. For example,
electrophoresis can be performed in a dilute or semi-dilute solution of neutral polymers,
where there are no “pores”. For such cases, some investigators use the term “obstacle
matrix” in place of “pore matrix”.
Since the solvent medium for electrophoresis is conductive, the resistive heat generated
during an experiment can cause density variations of the solvent. In a traditional
experiment, the gel thus has a second purpose, providing resistance to thermally driven
fluid motion (i.e., natural convection); unchecked, this motion would be a more
significant effect than electrophoretic motion. Electrophoresis in nonstandard media,
such as the neutral polymer solutions just mentioned, must be performed in small tubes or
channels, where the solid boundaries of the tube or channel effectively suppress thermal
motion. The latter class of methods falls under the label “capillary electrophoresis”; a
typical capillary has a diameter of about 50 m.
Gel electrophoresis has much in common with GPC: polymers are separated spatially by
M during migration through a porous medium. In both cases, since the medium has a
poorly characterized and hetererogeneous pore/obstacle structure, the actual transport
1
dynamics are impossible to model with rigor. Therefore, to get M information, one must
correlate the rate of migration to M. Most often, calibration is by narrowly distributed M
standards. Use in GPC of a second detector that is M-sensitive has not gotten much
attention in gel electrophoresis, but mass spectrometry is occasionally used for this
purpose.
Biopolymers form the largest class of polymers characterized by gel electrophoresis.
Two kinds of biopolymers dominate, proteins and DNA (both single-stranded and
double-stranded). Well-characterized M standards are readily available for both. This
fact explains the low usage of M-sensitive detectors. Other biopolymers such as
polysaccharides present more difficulty for the calibration-by-M-standards approach, and
so these polymers are motivating the slow development of M-sensitive detectors for gel
electrophoresis.
In analogy to GPC, where one can choose flow rate, in gel electrophoresis one can
choose the magnitude of the imposed electric field. Unlike GPC, where an optimal flow
minimizes HETP, in gel electrophoresis there may not be an optimal field magnitude for
smaller polymeric solutes; one simply uses the largest field possible in order to increase
the migration rate. There is a limit: the instrument must have good enough temperature
control to remove the heat generated resistively or the temperature will rise
uncontrollably over the course of the experiment.
For large flexible polymers, there is an optimal electric field; this is the field magnitude
that causes the fastest migration without deforming the equilibrium, coiled polymer
conformation. This field magnitude drops as M rises.
One might wonder if electrophoresis through an ordinary GPC column might produce a
useful separation by M. The answer: it would. Indeed, the electrophoretic separation
would ordinarily be better than the one by GPC. The reason for the difference would lie
not in the migration rate of bands, which would not change, but in band breadths, which
normally would be reduced in the electrophoresis experiment. Band-broadening in gel
electrophoresis is caused only by diffusion, while other mechanisms play a role in GPC.
In theory, resolution of bands by gel electrophoresis would nearly superimpose on that
achieved by GPC at the optimal flow rate (i.e., at minimal HETP). Usually, GPC is not
operated at this flow rate but at a flow rate many times higher.
Methods employing a chromatographic separation medium in conjunction with solute
migration driven by an electric field are known by the term “electrochromatography”.
Electrophoretic migration is not the only possibility. When an electric field is imposed
across a porous medium that has fixed charges (e.g., silanol groups on glass beads or
surfaces), the presence of counterions in the fluid drives “electroosmotic” flow. Such a
flow causes both charged and neutral solutes in the fluid to migrate at approximately
fluid’s velocity, a feature vastly expanding the possibility for M separation. For example,
I have seen reports of incredible separations of narrow M polystyrene fractions driven
through a GPC packing under an electric field [see Venema et al, Chromatograhia, 48
(1998) 347]. Unfortunately, commercial instruments and columns for this approach are
2
not yet available. The solvent must be polar enough to solvate counterions released from
packing, so this approach won’t work universally (the previous citation was for
polystyrene in DMF with surfactant).
The presence of electroosmosis can be disastrous to ordinary gel electrophoresis because
the flow is typically opposite to the direction of electrophoresis (opposing directions are
obtained whenever the solute has the same charge as the matrix). For this reason, in gel
electrophoresis, the porous matrix is almost neutral.
4.1.2 Examples
Although numerous methods have been described in the literature, two general
experimental approaches currently afford the best opportunity for M characterization.
These are (I). slab gel electrophoresis, and (II). capillary electrophoresis in gels and
neutral polymer solutions. A general description for both is provided here.
The traditional separation matrix for slab gel electrophoresis is either a covalently or
physically crosslinked gel in the form of a slab (nominal 20 cm x 20 cm x1 cm). Unlike
chromatography, relatively few matrix chemistries have been explored for gel
electrophoresis. To suppress undesired electroosmotic flow, gels/matrices must be nearly
neutral. Two common choices are poly(acrylamide) and agarose, which both contain a
nominal low density of bound acid units. Dilute polyelectrolyte samples, introduced in
wells cast at one end of the gel, migrate in the electric field for a fixed time interval
(nominal 1 to 10 hr). During this interval, the field transports solutes of higher mobility
more than solutes of lower mobility, separating sample bands from each other over
distances on the order of half to two-thirds of the largest gel dimension. A specific
staining or labeling of solutes is needed to determine the final band position, and this task
can be accomplished either before or after electrophoresis. Densitometry then quantifies
the location and distribution of stained or labeled bands. Staining, the most common
detection procedure, typically involves two steps; first, the displaced solute is exposed to
an absorbing or fluorescent dye by immersion of the gel in a dye bath, and second,
unattached dye is removed by immersion of the stained gel in a bath free of the dye.
Many staining procedures employ a dye of charge opposite to solute and rely on
electrostatic attraction to attach the dye to the solute irreversibly.
Gel electrophoresis has been the main method for biopolymer analysis for several
decades, and many strategies for synthetic polymers can be directly appropriated from
this experience.
At a minimum, one must choose a gel material (chemical type,
concentration, crosslink density), an electrolyte (electrolysis reactions at the electrodes
discourage use of nonbuffering electrolytes), an electric field strength, and a detection
procedure. Gel electrophoresis equipment is rather inexpensive, and many runs can be
performed in parallel, lowering cost further.
Chemically crosslinked poly(acrylamide) gels contain pores or passages with diameters
appropriate to the size analysis of all but the largest proteins. Moderately sized synthetic
polyelectrolytes (M<100,000 g/mol) can be examined in the same environment.
Adjusting the ratio of crosslinker to monomer (nominal molar ratio 1:25) and/or the
3
overall gel concentration (nominal 3 to 20 wt. %) allows one to optimize the
electrophoretic resolution within a defined window of M. However, adjustments are not
limitless, establishing bounds on separation (nominal low M limit ≈ 2,500 g/mol; nominal
high M limit ≈ 500,000 g/mol). After electrophoresis at substantial field strength
(nominal 100 V/cm), to minimize analysis time, the solutes are selectively stained in the
presence of gel (nominal detection threshold is about 0.1 g for protein; higher for
synthetic polyelectrolytes). Large field strengths necessitate good cooling, enhanced by
use of thin, vertically oriented gels.
Electrophoresis of ss-DNA in poly(acrylamide) gels permits routine, high throughput
sequencing (single base resolution) up to about 300-400 bp. The sizing of larger ss- and
ds-DNA chains cannot be achieved in poly(acrylamide) gels, and because of their larger
average pore size, thermoreversible agarose gels are used instead. Agarose is a marine
polysaccharide related to agar. For these long DNA chains, resolution by gel
electrophoresis does not extend to the level of a single repeat unit. Fortunately, most
large DNA chains are prepared by methods that yield a mixture of discrete,
monodispersed DNA fractions. A traditional agarose DNA gel electrophoresis
experiment separates these fragment mixtures in a horizontal slab gel under constant
electric field (nominal 1 to 10 V/cm), with samples introduced and run in much the same
manner as described for a poly(acrylamide) gel.. The agarose concentration (nominal 0.4
to 4 wt. %) determines the pore size and thus the range of M separation.
Vertical
Horizontal
Two variants of slab gel electrophoresis. The vertical method allows
for much greater field strengths and usually is employed with
polyacrylamide gels. The horizontal method is usually employed with
agarose gels.
4
Separation by gel electrophoresis. The top shows DNA
sequencing, the separation of ss-DNA molecules in a
vertical gel by differences of a single base length
(polyacrylamide gel). The middle shows the separation of
large ds-DNA molecules in a horizontal gel (agarose gel).
The bottom shows capillary electrophoresis in a set-up that
allows parallel separations in multiple capillaries. (from
Time Magazine, 2000)
5
The next figure shows the separation of poly(styrene sulfonate) M standards and
poly(styrene sulfonate) star polymers in a horizontal agarose gel. Note the high
resolution of bands corresponding to M= 880,000 g/mol and M=560,000 g/mol in a gel
tailored for optimal resolution in this M range
The higher resolution of gel electrophoresis compared to GPC leads an ability to
characterize more narrowly distributed M fractions. Applying the same calibration
procedures as for GPC (in fact, a program developed for GPC), one calculates the
polydispersity index for some of the M fractions shown above is less than 1.01.
The figure at the top of the next page shows analogous separations achieved in capillary
filled in a matrix of dilute pullulan, a neutral linear polysaccharide. The resolution is
comparable to above, but the run time is less – 10-20 minutes as opposed to 10 hr for the
slab gel analysis.
6
Highest M
Lowest M
5,6 ,7
3
Relative Amount
N=1,660,000
5
4
N=853,000
3
2
2
6
4
7
5
3
1
6 7
2
1
1
4
2
1
3
PSS Molecular Weight:
1=1.188 x 106 g/mol
2=8.01 x 105
3=5.05 x 105
4=2.62 x 105
5 = 1.04 x 105
6 = 5.7 x 104
7 = 3.1 x 104
N=380,000
6
4
5
7
N = Pullulan (Host)
Molecular Weight
N=186,000
3.0
3.5
4.0
4.5
 x10 (cm /Vs)
4
2
Hosts: c=c*/2
Issues:
 The polymer must be charged and soluble in a polar solvent, which are both
significant constraints.
 When the sample is not eluted to a detector (slab gel methods), some form of
staining (visible detection) is needed. Often, a simple staining of the polymer
leads to the same staining of the gel and hence to no contrast. Visible detection
is not nearly as sensitive as that achieved in a chromatography detector unless
the polymer has a high extinction coefficient chromophore or is fluorescent
 Detectors for capillary electrophoresis must perform analysis on a very small
amount of sample, << 1 l, and so they must be very sensitive. Unfortunately,
refractive index detectors cannot provide this resolution with such small
volumes. Most capillary detectors sense UV/Vis absorbance or fluorescence,
sharply limiting use with synthetic polymers unless labeling can be done
 As in GPC, separation is developed through configurational (steric) interactions.
Adsorption to the porous matrix must therefore be avoided. Unlike GPC,
switching of a new solvent to avoid adsorption is difficult or impossible
 There are many types of configurational interactions at play in gel
electrophoresis, resulting in many possible dependencies of migration rate on M.
In some instances, the migration rate–M relationship is not monotonic, a
disastrous situation.
 In my experience, when detection of polymer in gel or capillary is simple, gel
electrophoresis is must easier than GPC and offers M information of much higher
quality.
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3.2 Field Flow Fractionation
(Discussion here is based on 1. Giddings et al., Polymer Characterization: Spectroscopic,
Chromatographic, and Physical Instrumental Methods, Adv. In Chem. Ser. 203,
American Chemical Society, 1983, chapter 14; Giddings was the inventor of this method
and its chief advocate until his death; and Messaud et al., Prog. Polym. Sci. 34 (2009)
351.)
A generic schematic for Field Flow Fractionation (FFF) is shown below (figure from the
first reference). Polymer sample is injected as a pulse into a steadily flowing stream of
solvent, as for any chromatographic method, and then the pulse is separated by M as it is
driven by flow through a narrow channel (gap~1-3 mm, length~1m). A concentration
detector lies at the far end.
The velocity field of the flowing fluid in the narrow channel is parabolic (laminar, low Re
flow of a Newtonian fluid; “plane Poiseuille flow”), as sketched above. The key element
in FFF is a transverse field, which drives solutes toward the bottom channel wall. The
more strongly driven is a solute toward this wall, the slower is the solute’s average
migration in the parabolic velocity field, which is smaller near the wall than away from
the wall.
At equilibrium, a steady transverse c profile is established through balance of the drift in
the perpendicular forcing field to the counter-drift of random Brownian motion (i.e.,
diffusion); this situation is exactly the same as in equilibrium sedimentation. The balance
8
leads to an exponential decay of c with distance from the lower wall. The decay length
will be designated the “mean layer thickness” l.
The perpendicular field can be applied long enough to achieve equilibrium either with the
longitudinal flow turned on or just before this flow is turned on. The latter approach is
more straightforward but requires that the switching on of the flow field and subsequent
elution be rapid compared to the rate of solute diffusion across the channel. This
condition is typically met with high M polymers. The former approach requires an
extremely low flow rate to ensure that perpendicular equilibration is achieved before
elution.
To model migration down the channel, we first define the dimensionless layer thickness 
as l/w, where w is the channel width. In terms of diffusion coefficient D, the exponential
concentration profile establishes that l=D/U, where U is the steady transverse velocity of
the solute induced by the perpendicular field (i.e., calculated without walls present).
Using the Einstein formula for mobility, U=kT/F, where F is the force applied to a single
solute molecule by the field. Combining the definitions/expressions of this paragraph,
RT
 
Fw
Separation by M results in different polymer fractions reaching the detector at different
times. This separation is quantified through the “retention factor” rf, defined as the ratio
of the overall channel volume Vo to the solute fraction’s elution volume Vr.
In terms of the parameters and assumptions given above, simple theoretical analysis of
the standard convective-diffusion equation finds that
rf = 6 coth(1 / 2 ) - 2 
This is the general operating equation of FFF. Unlike GPC and gel electrophoresis, since
the separation geometry is so simple, the migration rate is rigorously determined in terms
of molecular parameters: no M calibration is needed.
The same convection-diffusion analysis provides a theoretical expression for bandbroadening, which in concert with the operating equation, defines the resolution. The
theoretically calculated resolution is extremely high in most polymer cases, much
superior to that of GPC and comparable to that of gel electrophoresis.
To illustrate actual operation, an appropriate transverse field must be identified.
Different fields are possible, such as a thermal field, an electrical field, a sedimentation
field, or a flow field, and this list of choices defines submethods respectively referred to
as thermal-FFF, electrical-FFF, sedimentation-FFF, and flow-FFF.
The quality of the separation depends on the nature of the field. Each type of field
introduces its own transport coefficient. For example, when an electric field is applied,
separation depends on the electrophoretic mobility , and  is specified
9
 =
D
Ew
As seen from the form of this equation, M discrimination in electrical-FFF depends
entirely on the ratio D/. For polyelectrolytes, the obvious targets for electrical-FFF,
since  in free solution is independent of M, fractionation depends solely on the Mdependence of D, a dependence that is weak. Thus, electrical-FFF doesn’t work well for
polyelectrolytes (or for any other polymer class).
Sedimentation-FFF is the most general, and commercial instruments have been
developed for sale. Sedimentation-FFF entails a specially constructed analytical
ultracentrifuge, so the method is quite expensive. The other FFF submethods are
cheaper.
Walls of the channel are another important issue for FFF, and these must be inert to the
polymer, flat, and capable of applying/withstanding/supporting the applied field. For
example, walls for thermal-FFF are typically made of polished copper plates, which have
high thermal conductivity. For flow-FFF, the walls must be porous, which makes this
submethod difficult.
Shown below is an example of thermal-FFF separation of polystyrene M standards
achieved in a channel with copper walls; the temperature difference varied from 19 to
41ºC over the run time to optimize separation across the full M range. In this case, the
separation depended, in part, on the thermal diffusion coefficient Dt, which governs how
a polymer drifts in a thermal gradient when a solution is otherwise homogeneous.
[from Messaud et al., Prog. Polym. Sci. 34 (2009) 351-368]
10
Issues:





FFF works best with large solutes that have low diffusion coefficients. In recent
years, most efforts seem to involved particle characterization rather than polymer
characterization
Despite many commercialization attempts, the method has not really caught on
due to many small practical difficulties such as adsorption of polymer to the
walls, cleaning of the channel, sealing, applying a uniform field, etc.
Despite claims otherwise, the practical performance does not meet the theoretical
performance in most cases. The resolution for the polystyrene case shown on the
previous page, for example, is far below that calculated assuming the M standards
are essentially monodisperse. Compare the FFF result here to the gel
electrophoresis result given earlier in the handout.
The transport coefficients needed in the different fields are rarely known for
specific polymers. Without these, the method is not absolute if the needed
transport coefficient depends on M. If it doesn’t, separation is really by D alone,
which doesn’t have a strong M-dependence, so M separation is not great.
FFF has rarely been used in polymers, but the method is widely known in the
polymer community due to energetic promotion by Calvin Giddings, its
discoverer, who had great prominence in the analytical community.
11
3.3 Diffusion Coefficient
The advent of dynamic light scattering (DLS) made the direct measurement of diffusion
coefficient D fairly straightforward for polymers in dilute polymer. As known to most
polymer scientists, at high enough M, D is related to M via a straightforward power law
relationship,
D ~ M-
Assuming calibration by M standards, measurement of D offers a technique for M
measurement akin to that of intrinsic viscosity. For a polydisperse sample, the
appropriate M average is of the z-average. Further, for polydisperse samples, one might
hope that deconvolution of the experimental correlation function by a theoretical method
such as CONTIN would provide information about the M-distribution.
The approach has numerous practical difficulties. First, D measurement by dynamic light
scattering isn’t precise (10-20%), making the obtained M values even more imprecise.
Intrinsic viscosity offers a much more precise physical measurement. Second, D is very
sensitive to experimental conditions, particularly, through solvent viscosity, to
temperature. Thus, to validate comparable conditions, one really has to determine the
calibration coefficients in the instrument of use.
Another major difficulty is the deconvolution of the correlation function for polydisperse
samples; since the deconvolution is an ill-posed mathematical problem, in the presence of
finite noise in the correlation function measurement, more than one distribution of M may
give indistinguishable correlation functions. Anyway, the devconvolution is imprecise;
one has difficulties getting well-separated peaks for bidisperse samples in which D varies
by a factor of 2 or 3 or less.
Nonetheless, the method has value on occasion. Assuming data of good quality are
collected (no dust, long enough sampling times, good baseline), using the cumulants
methods, one can directly measure a polydispersity index based on the ratio of Mz to Mw,
2
Mz / Mw  1
=
2
1
4
for polymers of low polydispersity (i.e., Mz /Mw<1.25). Here, 1 and 2 are the first and
second cumulants, respectively, parameters easily and unambiguously determined from
the correlation function. This formula should be used mainly as a quality indicator for
narrow distribution polymers when GPC data aren’t available, for example, when M is
very large (>106 g/mol) and GPC can’t be performed.
Sizing of particulates by DLS is widely accepted in the colloid community.
A dynamic light scattering GPC detector was recently commercialized, allowing
measurement of the distribution of molecular size for polydisperse polymers.
12
3.4 Liquid Chromatography
Liquid chromatography develops solute separation via the reversible adsorption of solute
from a “mobile phase” (i.e., solvent) to a “stationary phase” (i.e., separation medium)
under conditions of “local equilibrium”. The more strongly adsorbed components
thereby elute later than those that are weakly adsorbed. By this definition, liquid
chromatography is fundamentally based on a negative enthalpy of adsorption that creates
an attractive interaction between the solute and the packing (the entropy of adsorption is
always negative and thus not favorable to adsorption). Liquid chromatography thus
differs from GPC and gel electrophoresis at the most basic level.
Unfortunately, polymer adsorption and desorption do not occur at equilibrium; there is no
well-defined adsorption isotherm for polymers as there is for small molecules. Instead, at
high M (M>104 g/mol), adsorption is essentially irreversible – unless the solvent is
changed, adsorbed polymers do not detach from a surface even on extremely long
timescales or even when the overlying polymer solution concentration drops to zero.
Thus, liquid chromatography is not generally useful in the measurement of M except
when M is low. Even here, the thermodynamics of adsorption may not reflect M in a
clear manner.
Thus, outside of a few biopolymer examples, liquid chromatography does not offer a M
measurement for polymeric samples. Ion exchange chromatography of oligomeric DNA
is the one successful example I’ve seen (this application is apparently no longer
commercial). Liquid chromatography does provide many good opportunities for the
purification of high M polymers, especially when the polymer can be made to desorb
when a “displacer” is added to the mobile phase.
On reflection, for the reasons stated above, I probably should have deleted liquid
chromatography from the table M methods in my opening lecture.
The use of liquid chromatography to separate polymers of complex architectures has
interesting applications, most targeted at separation by composition, not by M. However,
the residual M dependence may be important, so a brief discussion is made here.
The most notable liquid chromatography technique for polymers, Liquid
Chromatography at the Critical Condition (LCCC), is relatively new and unexplored. It
occurs in a chromatographic medium in which the steric constraints responsible for GPC
create a polymer-packing interaction entropy S that exactly balances the polymerpacking interaction enthalpy H responsible for liquid chromatography:
G = H - TS = 0
where G is the free energy difference that determines whether depletion or adsorption
on/into/from the packing is observed.
Allowing H and S to have an unspecified M dependences, one can conceive of the
following elution behavior in a good solvent if equilibrium between polymer and packing
can be established (i.e., for oligomers, which DON’T irreversibly adsorb),
13
LCCC
Log M
LC
SEC
Retention Volume
Empirically it is seen for LCCC that elution is nearly M independent (a non-obvious
result).
Suppose that LCCC is established for component A of an AB diblock copolymer while
normal SEC is established for component B. Then, the overall elution behavior of the
diblock will effectively reflect SEC separation of the B block. This principal is shown in
the following sketch, which displays the distributions of M for the polystyrene block of
three polystyrene-poly(methyl methacrylate) diblocks. Superimposed are the GPCdetermined distributions for the polystyrene precursors. Agreement is very good.
This technique requires many preliminary experiments to find the LCCC condition (in
this case, at 49% THF in THF/acetonitrile mixtures at room temperature), and the method
only works in the oligomer-to small polymer range, where polymer adsorption remains
reversible at the critical condition. As indicated by the figure below, this range is raised
compared to usual liquid chromatography.
[adapted from Pasch and Trathnigg, HPCL OF Polymers, Springer, 1999]
14
3.5 Mass Spectrometry
[Good references are: Mass Spectrometry of Polymers, G. Montaudo and R. Lattiner,
eds., CRC Press, New York, 2002 (particularly M. Polce and C. Wesdemiotis, Chapter 1,
“Introduction to Mass Spectrometry of Polymers”; G. Montaudo and C. Puglisi, Chapter
4, “Electrospray Ionization (ESI-MS) and On-line Liquid Chromatography/Mass
Spectrometry (LC/MS)”; and Chapter 10, “Matrix-Assisted Laser Desorption/Ionization
Mass Spectrometry of Polymers (MALDI-MS)”. Also, H.J. Räder and W. Schrepp, Acta
Polymer., 48 (1998) 272]
The placement of mass spectrometry on my list of “nonstandard” polymer M methods
might be debated; proponents of mass spectrometry, the newest of the methods described
in these lectures (first reported for high M synthetic polymers in 1992), would likely feel
that technical advances merit a shift of the technique to any “standard” list. Most
polymer scientists, however, still are uncomfortable with the method, for reasons I’ll
explain later. When first introduced, polymer mass spectrometry gained much positive
attention, sometimes touted as replacement for all previous polymer M methods, but then
serious deficiencies emerged, and only now are many polymer scientists willing to give
the method a “second look”.
Mass spectrometry naively seems out of place in the polymer field. Traditional mass
spectrometry requires the formation of gaseous ions in a near vacuum, a feat
accomplished by the heating of test samples. High M polymers can never heated to
volatility because they decompose first. Mass spectrometry in the polymer context was
thereby reduced to analysis of polymer degradation products.
3.5.1 Instrument Layout and Physics
In mass spectrometry, the gaseous ions are first accelerated by an electric field, where
these ions are separated in space according to their mass to charge ratio m/z, and then the
separated ions are detected, facilitating the plotting of relative ion abundance against m/z.
Two new “soft” approaches to polymer ionization, Matrix-Assisted Laser
Desorption/Ionization (MALDI) and Electrospray Ionization (ESI) changed polymer
applications of mass spectrometry in the 1990’s.
In MALDI, the polymer (termed the “analyte”) is first mixed with the “matrix” in the
presence of a common solvent, the resulting mixture is then loaded as a liquid droplet
onto a target surface, and finally, the solvent is evaporated away, creating a solid solution
of polymer in a highly crystalline matrix. Before evaporation, the droplet volume is of
the order 1 l. The molar ratio of matrix to analyte is high, ranging from 100:1 to 10 6:1,
so analyte molecules are homogeneously distributed throughout the matrix as isolated
molecules. Higher ratios are appropriate to higher M polymers.
The matrix is central to the MALDI process. A high power laser pulse of UV (337 nm,
N2 laser) or IR (10.6 m, CO2 laser) light impinges on the matrix, which because of its
high absorption at the laser wavelength, is ionized and dissociated as a supercompressed
gas. As the “plume” of gaseous matrix expands, it explosively transports the dissolved
15
polymers from the target surface into the gas phase. The polymer molecules are not
energized by light but by charge transfer interactions with the matrix.
[from M. Polce and C. Wesdemiotis,
Spectrometry of Polymers, G. Montaudo
and R. Lattiner, eds., CRC Press, New York,
2002, chapter 1.]
Of course, to perform mass spectrometry, the polymers must gain charge. How they do
this in MALDI isn’t always clear. Most likely, ionization is achieved by light-induced
matrix-analyte interactions in the gas phase plume.
In many cases, ionization is achieved only when alkali metal ions (sodium, lithium,
potassium) are doped into the polymer/matrix/solvent droplet as salts. The alkali metal
cation inefficiently form “adducts” with the polymer, and the inefficiency turns out for
the best, as relatively few adducts (less than one per chain, are created). In this manner,
the problem of multiple charging is mostly avoided. MALDI can volatilize intact
polymers with M exceeding 106 g/mol, although for M larger than 50,000 g/mol, multiple
charging becomes a problem. With single charging z=1, and the measured m/z value is
readily converted to M.
Each polymer type is best paired with a particular matrix, and appropriate pairs have been
identified mostly by trial-and-error; tabulations of matrices suitable for important
polymer classes are available. Polymers vary greatly in their tendency to ionize by
protonation or cationization. Popular matrices for UV MALDI are 2,5-dihydroxybenzoic
acid (DHB), 2-(4-hydroxyphenylazobenzoic acid) (HABA), trans-3-indoleacrylic acid
(IAA), and 3,5-dimethoxy-4-hydroxy cinnamic acid (sinapinic acid); some of these also
work for IR MALDI.
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During MALDI, biopolymers (mainly proteins) with basic functional groups mainly gain
charge through H+ transfer (protonation) from the matrix, while synthetic polymers
acquire alkali metal ions (cationization) through nonspecific functional group
attachments, even when there is no obvious source for the cations. Polymer functional
groups such as -OH and -COOH make the ionization process more effective. Some
polymers, such as olefins and fluoropolymers, lacking polar functional groups, are
difficult to ionize, and for them, establishing mass spectrometry for high M samples has
been difficult.
Sample preparation for MALDI is crucial, as poor dispersal of analyte or incomplete
crystallization of matrix make experimental results irreproducible.
ESI, the second common means to volatilize polymers for mass spectrometry, relies on
the slow flow (1-10 l/min) of dissolved analyte through a narrow metal capillary into a
spray chamber. Thus ESI, unlike MALDI, can be performed continuously, making the
approach suitable in the context of chromatography. The capillary is held at a high
positive voltage (3-6 kV) relative to a transfer tube held several millimeters away. Fluid
emerging from the capillary is sprayed outward as highly charged droplets. Spraying is
performed at atmospheric pressure and room temperature, while a slow flow of N2
downstream aids solvent evaporation. As solvent is lost due to evaporation, charges
accumulate on the droplet surface, and through electrostatic destabilization, the droplets
split into small units, eventually releasing volatilized single polymers. Differently than in
MALDI, multiple charging of the polymer is typical.
[from M. Polce and C. Wesdemiotis, Spectrometry
of Polymers, G. Montaudo and R. Lattiner, eds.,
CRC Press, New York, 2002, chapter 1.]
After MALDI or ESI, the next instrument component is the mass analyzer. Mass analysis
is generally accomplished by the time-of-flight (TOF) approach, with an electric field
first linearly accelerating the ionized polymers, which then travel down a drift tube until
they encounter the detector. These motions occur in vacuum.
The ions accelerate such that the drop in their electrostatic energy across the electric field
is transformed into kinetic energy,
1 2
mv = zeV
2
where v is the ion velocity at the end of acceleration zone and through the drift tube. If
the length of the drift tube is d, then the time t to reach the detector is readily calculated,

17
t =
d
2eV
m
z
Thus, if all ions of the same z are released at the same time, the larger ions take longer to
reach the detector than smaller ones, providing discrimination by mass.

Actually, due to the disorganization of the ionization process, not all ions of the same
mass accelerate to the same kinetic energy, as idealized above. To correct for this
problem, the ions are typically passed through a “reflectron”, an element that changes the
direction of ion motion by applying a reversing electric field. Faster ions penetrate
further into this field and thus take more time to switch direction. All ions enter and exit
the reflectron at the same kinetic energy. With reflectron parameters appropriately
adjusted, after passing back through the drift tube in a direction opposite to their initial
pass, ions of identical m reach the detector at t unaffected by initial kinetic energy. Use of
a reflectron lowers the mass sensitivity.
[from M. Polce and C. Wesdemiotis, Spectrometry of Polymers, G. Montaudo and R.
Lattiner, eds., CRC Press, New York, 2002, chapter 1.]
A second t error arises from a short lag between the time of the laser pulse (t=0) and the
start of ion flight. Further, ions are produced over a finite window of t, not
instantaneously as supposed. To compensate for this finite breadth, “delayed extraction”
may be employed. With delayed extraction, the electric field applied during desorptionionization is weak, allowing gaseous ions to collect near the target for 50 to 1000 ns after
the laser pulse. Then, the collected ions are extracted by an abrupt rise to high electric
field, effectively separating the desorption/ionization step from the acceleration step.
Because of uncertainties in t, while MS-TOF is conceptually a tool for the absolute
determination of m/z, in reality, instrument calibration is needed. For calibration, the
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flight times for two mass standards are employed to calculate a and b from the
relationship,
m
= at 2  b
z
In either MALDI-TOF or ESI-TOF, ions are detected by an electron- or photomultiplier. The measured detector signal is an ion current proportional to the number of
ions arriving at any time 
t. Detection thereby produces a signal independent of M,
differently than for the detectors employed in chromatography.
Ionization of polymer is accompanied by ionization of matrix, and the matrix ions are
much more abundant than the polymer ions. Not too surprisingly, then, MALDI-TOF
spectra are accompanied by high matrix backgrounds at low M (m/z<1000). To reduce
this background, a lowering of laser power may be helpful. Otherwise, procedures for
deflecting low M ions from the detector may be necessary to prevent detector saturation.
3.5.2 Examples
Polymers of Narrow M Polydispersity The next figure shows the impact of the various
corrections discussed in the last subsection on the mass distribution of a narrow
distribution polymer standard determined by MALDI-TOF. One sees that mass
resolution improves with reflection and then even more with delayed extraction. For this
oligomer PEG sample, individual mass fractions differing by one degree of
polymerization can be resolved, and the mass difference between the discrete peaks gives
the repeat unit molecular weight. Further, from the absolute positions of the peaks, it is
possible to extract with substantial confidence the
identity of the end groups.
While many factors affect mass resolution, for
optimal systems studied under appropriate
experimental
conditions,
repeat
unit
mass
discrimination may extend up to M50,000g/mol.
After this threshold, the mass distribution begins to
appear more like that seen by GPC. This M threshold
is highlighted in the next figure, showing MALDITOF results of 9,400 g/mol and 49,000 g/mol PMMA
samples. M averages derived from the MALDI-TOF
m/z distributions are compared to the M averages for
the same samples derived by other methods, and the
agreement is quite good.
Mass spectrometry results are typically presented as
number fraction distributions plotted against M. As
noted before, SEC results are typically presented as
[from G. Montaudo and C. Puglisi, in Spectrometry
of Polymers,G. Montaudo and R. Lattiner, eds.,
CRC Press, New York, 2002, chapter 10.]
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[from G. Montaudo and C. Puglisi, in
Spectrometry of Polymers,G. Montaudo and
R. Lattiner, eds., CRC Press, New York,
2002, chapter 10.]
weight fraction distributions plotted again
logM.
Not surprisingly, the “raw”
distributions can appear quite different
even when the data sets are consistent.
In many MALDI-TOF distributions,
multiple peaks are seen, and often these
can be rationalized readily. For example,
the next figure shows the presence of
dimeric polymer ions as well as singly and
doubly charged single polymer ions.
Peaks identities here, however are easily
assigned by their positions and some
knowledge of the starting polymer’s M.
[from G. Montaudo and C. Puglisi, in Spectrometry of Polymers,G. Montaudo and R. Lattiner,
eds., CRC Press, New York, 2002, chapter 10.]
Under ideal experimental conditions, for some polymers MALDI can provide baseline
level discrimination of discrete M fractions according to absolute values of M up to M of
about 10,000-15,000 g/mol, as well illustrated for the following figure, showing the M
distribution of an anionically polymerized polystyrene of average M about 10,000 g/mol.
For this and similar polymers made by living polymerization, polymerization theory
predicts an ideal Poisson distribution of M, with a PDI of about 1.01, in close
conformance to experimental measurements.
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[from M. Polce and C. Wesdemiotis, Spectrometry of Polymers, G. Montaudo and R. Lattiner,
eds., CRC Press, New York, 2002, chapter 1.]
Polymers of Broad M Polydispersity
All the mass spectra so far displayed were obtained with M standards made by living
polymerization; their PDIs are less than 1.10, and sometimes, closer to 1.01. What about
the use of mass spectrometry to assay the MWD for “real” polymers, those encountered
in commercial materials? Let us define a polydisperse polymer as one with a PDI greater
than 1.2. Nearly all commercial polymers have PDIs far higher than this threshold.
In the first decade of polymer mass spectrometry, roughly 1992-2002, proponents
repeatedly reported M distributions that agreed well, for the same sample, with those
obtained by more traditional M methods, namely GPC. Encouraged, many in the
polymer community with less experience bought mass spectrometry instruments and tried
to replicate literature data. Sometimes they could, but more frequently, they couldn’t. A
large argument ensured. Typical findings:
[[from G. Montaudo and C. Puglisi, in Spectrometry of Polymers,G. Montaudo and R. Lattiner,
eds., CRC Press, New York, 2002, chapter 10.]
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All mass spectrometry values of Mw in these findings are far too low (by factors of 3 to
8), and values of Mw are low too (by factors of 2 to 4). While PDIs inferred from the
mass spectrometry values naively look more reasonable, actually, upon reflection, one
finds they are also far too low.
The mass spectrometry M approach, which looked so good for narrow polydispersity,
now appears useless!
To obtain quantitative mass spectrometry results, those in which the relative abundance at
each M has significance, there can be no “mass discrimination” inherent in the method.
This statement means that the relative abundance of species in the test sample must
correspond to the relative intensity of the mass peaks. Polymer fragmentation, ionization
yield, ion transmission to the detector, and detector response must all be independent of
M. Unfortunately, such is not the case.
Show below is a MALDI-TOF mass spectrum for an equimolar mixture of four PMMA
M standards. Absent mass discrimination, the spectrum should display four peaks of
equal area. Obviously, that is not what is seen.
[from G. Montaudo and C. Puglisi, in Spectrometry of Polymers,G. Montaudo and R.
Lattiner, eds., CRC Press, New York, 2002, chapter 10.]
Because of lower volatilization and less efficient detector response, lower M components
are “oversampled” by mass spectrometry.
Paraphrasing Chapter 10 of the first reference given for this subsection, the “conditions
necessary for determination of MWD are certainly not met by any mass spectrometry
technique of current use”. Another paper [R. Saf, C. Mirtl, K. Hummel, Acta Polymer.,
48, 1997, 513) says that determination of M distributions “is not yet a reliable method.”
While both opinions are about a decade old, the situation has not changed subsequently,
so the judgments still hold.
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An empirical answer to this problem is to collect ion yield as a function of M. The yield
curve from the last plot is shown below.
[from G. Montaudo and C. Puglisi, in Spectrometry of Polymers,G. Montaudo and R.
Lattiner, eds., CRC Press, New York, 2002, chapter 10.]
Holding experimental conditions rigorously constant, this curve can be employed to
correct for mass discrimination, empirically adjusting upward the measured mass
spectrum at larger M.
Another solution is to study broad distribution polymers only after their separation by M,
as achieved, for example, by GPC. This solution suggests GPC-ESI-TOF, a technique
which has not yet been much employed by the polymer community.
I hope you now see why mass spectrometry remains on my list of nonstandard methods.
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