533559934
Page 1 of 14
Polymer MW, Viscosity, and Branching Measurements by Mass Spectrometry
David J. Strumfels
Drexel University Chemistry Dept., Philadelphia PA 19102
Summary:
Measurements of polymer molecular weights and MW distributions, intrinsic viscosities ([]), and
branching parameters such as Mark-Houwink constants, have been historically performed by a
combination of Size Exclusion Chromatography (SEC), Laser Light Scattering (LALLS / MALLS),
and/or viscosity techniques.1,2 Often these techniques are combined into a single system, e.g., a SEC
with refractive index (RI) mass detection, in-line LALLS, and viscosity detection, the outputs from the
three detectors used together to calculate all MW, viscosity, and branching results.3
This report will describe how branching properties might be determined by mass spectrometry (MS)
alone, with or without SEC to fractionate polydisperse polymers. Although the measurement of
molecular weight of polymers by MS is already an established science, thanks to developments in
sample preparation (e.g., ESI and MALDI) and detection techniques such as TOF, there has been little in
the way of attempting branching measurements in this field. Basic principles of MS suggest however
that such measurements should be possible. Given that MS instruments are already routinely employed
for polymer analyses, the ability to extract this additional information would be valuable if it can be
done practically; this is especially true in the case of chromatographic systems interfaced to MS
detectors, where the use of additional detectors such as light scattering and viscosity would then be
unnecessary. In addition, by making use of the theory used to calculate branching parameters from
viscosity and MW, if MS can measure branching directly, it should also be able to calculate[]of a
polymer distribution as well as other properties related to viscosity and MW, such as solution
hydrodynamic volume.
Background:
A typical approach to explaining the behavior of polymeric molecules is to compare them to very long
strands of (e.g.) spaghetti, strands that are often randomly spread in and around each other, interentangled, coiled (as in many elastomers), or sometimes rigidly/semi-rigidly aligned (in crystalline
533559934
Page 2 of 14
forms) or found in other arrangements. This is an apt analogy as far as it goes, which explains many of
the physical and even chemical properties of polymers (though of course the chemical properties also
require consideration of chemical properties too, such as van der Waals’ forces and hydrogen bonding).
For example, the viscosity of a polymer solution is largely a function of the length of the strand, or
chain; the longer the chain, the more entanglements between chains, and hence greater resistance to
flow. Crystallinity and its macroscopic effects – melting and glass transition temperatures, chemical
resistance and physical stiffness/ impermeability – are also explained in part as functions of chain
length.5
The analogy is inapt or at least incomplete in several respects, however. Unlike spaghetti, polymer
strands are literally chains, made of many repeating small chemical units, the MW of the polymer
depending only on the MW of the unit and the number of units per chain. This allows for the
phenomenon of branching in many polymers; side-chains which branch off the major chain. Branching
is, in fact, a common feature of many synthetic polymers prepared by free-radical polymerization.5
The effects of branching on macroscopic properties, like polymer length, again can be understood well
by a purely physical analysis. A linear polymer, being long and thin, has a relatively high surface area /
MW, and therefore also possesses a large hydrodynamic volume (HV – the volume it effectively has in
solution) / MW ratio because it can sweep out a large volume in its random tumblings and twistings in a
solvent. A highly branched polymer, however, has a lower surface area / MW (as it is more spherical in
shape), which leads in turn to a smaller solution HV / MW. Although this is not a universal feature of
macromolecules (proteins – and some other water-soluble polymers – are linear, but have a small
surface area / HV and thus HV / MW because intramolecular hydrogen bonding cause them to fold up
into specific shapes), for many non-aqueous soluble synthetic polymers it accurately describes their
solution behavior; so well in fact, that a plot of log (HV), or, in measurement terms, log (MW[])
versus retention time / volume can be used as a “universal” calibration in SEC for many polymers of this
kind – calibrations with standards of the specified polymer are unneeded.6
The observed consequence of high HV / MW versus low HV / MW is a higher solution viscosity of the
former compared to the latter. This is because the greater surface area, hence hydrodynamic volume, of
linear polymers, leads to both more intermolecular entanglements and solute + solvent interactions,
533559934
Page 3 of 14
resulting in retarded solution fluidity – the essential definition of viscosity. The relatively non-spherical
shape of linear polymers also yields a higher surface area to volume ratio, also increasing polymer
interactions and so viscosity.
With this in mind, how to proceed is clear. Measure the MW of a polymer – either through light
scattering, SEC, or other means – and the solution viscosity, and HV can be calculated directly: HV =
MW[] (thus, hydrodynamic volume turns out to be the parameter used in the universal calibration
technique described above). Having the HVs of both our 100% linear and branched polymers, we can
calculate the so-called “g” factors, defined as the ratio of a polymer molecule’s unperturbed mean
squared radius of gyration (roughly, the volume “swept out” in the solution by the freely moving
polymer chain) to that of a linear polymer with the same composition and molecular weight:3
(Eq. 1)
gMW
= <S2>0,B / <S2>0,L
Experimentally, this ratio is calculated and used to determine either the number of branch points in the
chain or their functionality:4
(Eq. 2)
gMW
= (HVB, MW / HVL, MW)1/ = ([]B, MW/[]L, MW) 1/
where[]B, MW is the intrinsic viscosity of the branched polymer, and[]L, MW of the linear species at
the same molecular weight, and  depends on the model of branching assumed plus various
experimental factors, and where [] can be used in lieu of HV at the same MW values.
Other quantities related to branching can also be determined from MW and []. Mark-Houwink
parameters, which are also useful in structural studies of polymers, can be calculated by plotting
log([]) versus log(MW) for the linear polymer; in the resulting equation2
(Eq. 3) log ([]) = log (K) +   log (MW)
533559934
Page 4 of 14
K and  are the Mark-Houwink constants for the given polymer, and comparisons of the plots of linear
versus branched versions of the polymer will show the differences qualitatively. To construct a MarkHouwink plot, it is of course necessary to fractionate the polymer first, generally by SEC. The
relationship between Mark-Houwink constants and g factors is, combining equations (1) and (2)
(Eq. 4)
gMW
= [[]B, MW /(K  MW)]1/
Measurement of Polymer Molecular Weights by Mass Spectrometry:
MW measurements of high molar mass (~ 50,000 and up) synthetic polymers by mass spectrometry has
been possible for well over a decade now, and a number of reviews7, 8, 9 and a book10 have been
published on the subject during the last several years. Historically, the main obstacle in the way of MS
analysis of polymers, prior to the 1980s, was the difficulty in enabling very large molecules (e.g., 10,000
Daltons and up) to survive the volatilization and ionization steps necessary for MS: the main techniques
available, such as electron ionization at high eV impact energies, and relatively soft, chemical ionization
techniques, usually result in severe polymer fragmentation and degradation to the extent that
measurement of parent ions is exceedingly difficult if not impossible using them. In addition, the MS
designs then available did an inadequate job of achieving the mass range and resolution, and that only
with difficulty. As for making measurements across polymer MW distributions, the techniques to
directly couple MS with chromatographic instruments, e.g., fractionation by SEC, were not yet well
developed; such techniques were required if a full analysis of polydisperse polymer systems was to be
accomplished.
Over the last twenty years however, advances in sample preparation, new and/or improved MS
techniques, and interfaces with other analytical instruments, have made it possible to measure polymer
MW and MW distributions of increasingly larger polymers, both synthetic and natural, organic and
aqueous soluble. On the sample preparation end, achieving the needed volatilization and ionization of
even very high MW polymers has been made possible by the development of Matrix Assisted Laser
Desorption Ionization (MALDI)7, while other soft ionization techniques, such as Fast Atom
Bombardment (FAB), and in particular Electro-Spray Ionization (ESI), have been improved to the point
533559934
Page 5 of 14
*
of handling fairly large macromolecules when handled properly10 , although FAB is not used heavily
anymore. On the technique and instrument interface end, particularly regarding HPLC and SEC, Mass
Spectrometry Time Of Flight, or TOF, combined with ESI, is now a standard method of performing MS
on the effluent of high pressure liquid chromatographic systems. This technique combination has
proven essential in work with large biomolecules, such as proteins and nucleic acids.
For polymers which are the focus of this research proposal, which range in MW from approximately 104
– 105 up to 106 Daltons, currently only MALDI (usually combined with TOF to give the acronym
MALDI-TOF) generally possesses the molecular weight range and resolution needed for the MW
measurements, particularly for non-aqueous soluble polymers (above this range TOF’s detection
efficiency still suffers due to an excess of multiply charged species). For these molecules, other existing
techniques still lead to unacceptable degrees of fragmentation and degradation. Although MALDI as a
sample introduction method cannot be directly connected to an SEC (although TOF can be and often is
the detection method of choice of LC-MS methods), a number of indirect techniques exist for
interfacing, such as (semi) preparative fractionation and manual or robotic sample preparation, do exist,
thus making it possible to obtain MW and other data on polydisperse systems. This of course still
cannot not achieve the MW resolution a direct interface would be capable of.
As MALDI combined with TOF mass spectrometry is the only existing technique developed well
enough for the polymer systems discussed here, it will be described first. The basic technique of
MALDI is straightforward. The polymer of interest is first dissolved, dispersed, or otherwise
intermixed13,14 in a suitable matrix material. The resulting mixture, usually a solution, is then deposited
on the sample introduction surface and briefly irradiated by a pulsed laser of intense but short duration.
The laser burst accomplishes the first two steps of any mass spectrometry technique: it vaporizes the
analyte (along with the matrix), thereby allowing it to be swept into the MS acceleration chamber, and
ionizes it, which is what allows the MS mechanism to separate the polymer molecules by their
molecular weight differences.
*except where otherwise indicated, reviewed material comes from references 5., and 7. through 11., and personal
communications and discussions.
533559934
Page 6 of 14
Electrospray techniques of sample introduction turn a polymer solution (e.g., from an HPLC / SEC) into
a spray of very fine droplets, which then obtain electric charge via an electron or chemical pathway,
such as a chemical ionization technique or low energy electrons. The droplets are then injected into the
MS chamber, where the solvent evaporates to leave behind ions of single and various multiple charges.
The multiply-charged species, ideally mostly parent ions, are separated by their mass to charge (m/z)
ratio as in other forms of MS separation; here, however, the main separation factor is the varying
number of charges on unfragmented parent ions, not the molecular weights of singly-charged ions,
parent and fragments. The positions of the species in ESI are used to determine the parent molecule
MW. This technique works well for narrow MW disperse polymers, whether prepared synthetically or
by the SEC semi-preparative fractionation described above; the difficulty with more broadly
polydisperse polymer systems is that the data are complicated when the molecules span a large range of
weights, leading to peaks both of different m/z and MW. Also, again, for high MW polymers, especially
synthetic systems, it is generally not as effective as MALDI in preventing fragmentation, adding still
further to the spectrum’s complexity. ESI is still, as noted, for technical reasons the main technique for
interfacing chromatographic systems with MS.
If TOF is the ion separation technique used, the volatilized and charged polymer ions, however
prepared, are swept into the acceleration region of the MS, where an electric field gradient is used to
boost the ions to their initial range of velocities. The velocities are MW dependent because this gradient
boosts all the ions to the same kinetic energy ½mv2, thus necessitating differing velocities for molecules
of different masses (more strictly, of different M /Z ratios). From the acceleration region, the ions move
into the “drift” region, where their velocity spread allows them to separate by MW before striking the
detector and being recorded. As all the polymer ions possess the same kinetic energy, higher MW
species pass through the drift region slower than low MW species, and thus their molecular weights can
be directly determined as a function of the time they spend in the region; ergo, the technique’s name.
Some history is needed here to explain how TOF became the instrument of choice for polymer analyses
in chromatographic system. The problem with the basic TOF design as described above is its poor
resolution, particularly when applied to increasingly higher MW materials. This problem is mostly due
to two interrelated flaws in the acceleration part of the basic design. Fundamental to high resolution
mass spectrometry is the need for all the ions generated from a sample to be created at the same time in
533559934
Page 7 of 14
the same region of space, and to be accelerated at both the same times and with the same energies. In
practice, of course, no operating MS instrument can perform all these tasks perfectly, but the
unmodified, original TOF design was a notoriously poor performer precisely because, for example
compared to magnetic sector designs, its separation method relies so directly on these parameters and
their effects of ion time of flights in the drift region. Even the resolution losses from the small
imperfections of all MS instruments are heavily exaggerated in TOF.
TOF is used so heavily now because these design flaws are now compensated for in a variety of
ingenious ways, notably the use of reflection plates and acceleration delay times to correct for ion
spreading in time and space (without, of course, reducing desired spread by differing m/z ratios). The
net result is that modern TOF-MS has evolved into an technique with very high resolution, even at very
high molecular weights. This is why it is commonly used as the instrument of choice in polymer
analyses, particularly, as noted, in combination with the MALDI sample introduction method.
The combination of MALDI-TOF therefore allows quick, efficient, high-resolution analyses of polymer
MWs up into the millions of Daltons (although MALDI still suffers from problems of detection
efficiency above 106). Mw, Mn, and polydispersity indexes (Mw / Mn) can be readily determined for
many synthetic polymers of even quite high MW, swiftly and with far less analyst time than many other
techniques. Another advantage of MALDI-TOF is that is measures these quantities much more directly
than other techniques; although calibration of the TOF instrument is usually necessary, only a single
calibration is needed for all polymers, regardless of chemical composition. (Contrast this with straight
SEC, where each polymer must be calibrated with known standards of the same chemical species, or
where at best one can use the universal calibration technique already mentioned – a technique built
around a number of variables, and not at all as universal as the name suggests.) Other MW
measurement techniques, such as light scattering and viscosity techniques, although often called
absolute, still require a variety of specific polymer inputs – such as solution refractive indexes and
Mark-Houwink parameters – to give accurate results.
As mentioned, MALDI cannot be directly interfaced to a size exclusion chromatographic system, only
indirectly by methods of collecting and prepping separate fractions (this can be highly automated). In
one sense, this is irrelevant, as the MS technique itself, TOF or otherwise, separates the different MW
533559934
Page 8 of 14
species anyway. It is nevertheless desirable to perform an SEC separation of a polydisperse polymer
sample prior to introduction into the MS, as even better resolution of the different MW species (leading
to simpler spectra), can be obtained, simplifying analyses and in general providing more information on
the system. Indeed, even the use of SEC alone may be inadequate here. The reason for this is a
consequence of the SEC separation method, which is by hydrodynamic volume, not MW: when
analyzing polymeric materials which vary by both MW and branching, even the narrowest fraction of
the column eluent will represent not a narrowly disperse MW slice but in fact a mixture of lower MW
linear and higher MW branched material. Thus, we are still looking at a fairly complex composition,
complicating the MS spectra. If better separation is needed, one approach here would be to perform an
additional chromatographic separation, this time via an absorption technique. Absorption-based
chromatography can separate linear and branched polymers of similar hydrodynamic volume due to the
fact that at a given HV branched molecules have lower surface area (because they are more spherical in
solution) than linear.
Measurement of Polymer Branching and Viscosity by Mass Spectrometry
Branching measurements in polymer systems by MS is an area of polymer research which has only
begun to be significantly explored over the last decade. The purpose of this report is to propose, from a
theoretical viewpoint, how such measurements might be made, and to suggest potential techniques for
doing so.
Fundamental to this approach is an examination of the fragmentation patterns produced by polymer
molecules analyzed by mass spectrometry. That is, instead of honing techniques designed to eliminate
fragmentation, we ask, from a statistical viewpoint, what the spread and shape of the patterns tell us. If
the molecules fragment too severely, for example all the way down to mer units, of course no useful
information can be obtained. On the other hand, if we can control fragmentation to the point where it
occurs only at the branch points of a polymer chain, the resulting spectra would provide a fingerprint of
the branching structure, one that could be read as straighforwardly as a crystal structure from an X-ray
diffractogram. In practise, we should expect the information to be neither so murky nor so clear, but
somewhere in between.
533559934
Page 9 of 14
Are the branch points of a polymer chain particularly succeptible to cleavage, in a way that would allow
us to distinguish structure in MS spectra? One way of answering this question is to look at simpler
molecules such as branched alkanes. Here we find cleavage more prevalent at secondary and tertiary
carbons than at primary carbons, due to the relative stability of secondary and tertiary carbanions
compared to primaries and the larger number of possible rearrangements (e.g., H-shifts and further
fragmentations) these carbons provide (Equations 5 and 6).
(Eq. 5)
(RRHCsec–CH2CH2CH3)·-
(Eq. 6)
(RHCsp3–CH2CH2CH3)-


(RHCsp3–CH2CH2CH3)- + R·
(CRsp3=CHCH2CH3)- + H2, etc.
Since many polymers can be approximated as very long chain alkanes – essentially true for addition
polymers if only the carbon backbone of the molecule is considered (condensation polymers such as
polyesters and polyamides contain heteroatoms in their backbones, complicating this picture) – this
argument alone suggests that fragmentation will occur preferentially at branch points, leading to
different patterns between linear and branched molecules. Another argument for preferential cleavage is
that branch points should be regions of high intra-molecular stress, weakening the bonds and making
them more vulnerable to rupture.
If the arguments presented here hold, then we can predict that there will be both qualitative and
quantitative differences in the mass spectra of a branched polymer versus a linear one of the same
chemical composition and molecular weight. An idealized version of these expected differences are
illustrated below, in Figures I and II (these “spectra” are actually generated Gaussian curves):
533559934
Page 10 of 14
Intensity
Figure I: Fragmentation Pattern of Linear Polymer
m/z
Intensity
Figure II: Fragmentation Pattern of Branched Poly mer
m/z
533559934
Page 11 of 14
We see that that the m/z distribution of the branched polymer is both broader and occurs at lower MW
than that of the linear. This is what we should expect if indeed branch points in a polymer chain lead to
more extensive fragmentation.
The question then is, what use can we make of these differences? Here I would like to propose an
analogy, one between these MS fragmentation patterns and standard, calibrated SEC MW (actually
hydrodynamic volume) distribution curves. Consider the MW distribution curves of two polymers, both
with the same chemical composition and MW dispersities but differing in their degree of branching.
When these are analyzed by standard SEC, the distribution of the branched polymer appears to show
lower MW and broader dispersity than the linear analogue. As explained previously, this is caused by
the SEC separation mechanism, in that branched polymers have a smaller HV than their linear
counterparts and so will elute later, with variations in degrees of branching making the final SEC
distribution curve broader as well.
To develop this concept more generally, consider a mixture of (monodisperse) linear and highly
branched polymers of the same molecular weight, one analyzed by an idealized MS system which
causes ion fragmentation purely at branch points. Using such a system, it would be easy to distinguish
linear and branched species of the same molecular weight, as the former will yield only a single peak
(ignoring multiply-charged ions), the parent molecular ion, while the branched will produce a broad
distribution, from small fragments up to and including the parent molecular ion (which would overlap
with the linear polymer ion). Not only could the differently branched species be readily identified, it
should be possible, given a quantitative theory of fragmentation combined with the branching model,
e.g., random versus star, to calculate branching parameters and even otherwise measured properties such
as solution viscosity from the distribution. In practice of course, neither the polymer systems analyzed
nor our MS instrumentation will be ideal, complicating the analysis; but a systematic survey of model
polymer mixtures should lead to promising results.
533559934
Page 12 of 14
Repeating equations 2, 3 and 4
(Eq. 2)
gMW
= (HVB, MW / HVL, MW)1/ = ([]B, MW/[]L, MW) 1/
(Eq. 3) log ([]) = log (K) +   log (MW)
(Eq. 4)
gMW
= [[]B, MW /(K  MW)]1/
we see that, having measured MW (by light scattering, standard or universally calibrated SEC, etc.)
along with HVB, MW and HVL, MW from SEC (via universal calibration or viscometry), and assuming the
branching model represented by  for the polymer system being measured in the given experimental
setup, it is then possible to calculate gMW and hence the degree of polymer branching. Given that there
is an equivalent to (HVB, MW / HVL, MW)1/ for MS in the form
(Eq. 7)
gMW
= ([Mw]B, MW / [Mw]L, MW)1/MS
where [Mw] is the weight-average molecular weight of the fragments comprising the MS spectrum and
MS an analogue of the same parameter in equation 2, branching measurements should be calculable
from MS as well, assuming that  can be either measured or determined theoretically. It is desirable of
course, though not strictly necessary, that MS be constant across the MW range of a polymer.
However MS is obtained, the procedure for measuring branching and related parameters of an unknown
polymer sample is straightforward. A set of [Mw]s for the corresponding fully linear polymer of the
same chemical composition will allow us to calculate the of the gMWs of the unknown. In combination
with the[]distribution of the corresponding linear polymer, obtained from viscometry measurements,
the[]distribution of the branched unknown can then be derived, and from this additional properties,
such as Mark-Houwink constants and hydrodynamic volumes.
533559934
Page 13 of 14
Naturally, for this method of branching determination to work, there must be fragmentation patterns in
the MS spectrum for the polymer system being measured, or at least there must be patterns for the
branched polymer. As the MALDI technique for generating ions is intended to minimize fragmentation
– this is its advantage in measuring polymer MWs – modifications to the technique may be needed to
insure that a suitable amount of fragmentation occurs in branched molecules while linear species are left
relatively intact. Also, the fragmentation patterns must be such that they can be effectively summarized
by Mw, or perhaps another suitable average will be needed. Finally, it should be emphasized that only
polymers of uniform chemical composition are being considered here, at least in the initial stages of the
research; the complications introduced by co-polymers in their various configuration (random, block,
alternating) may even be too severe for this type of analysis.
Conclusions
Determination of polymer molecular weights, viscosities, and branching have traditionally been
performed by a combination of SEC, light scattering, and viscometric measurements. The determination
of molecular weight by mass spectrometry is already an established science. The full elucidation of
polymer structure, including branching, by MS awaits future work however. This paper suggests two
possible approaches to the problem of branching, viscosity, and hydrodynamic volumes of polymer
molecules: an indirect method, which may be feasible but impractical on a routine basis; and a semidirect method, which is more promising theoretically but would require considerable time and effort to
work out the details. In either case, what is desired is a structure determination method requiring the
fewest assumptions / models / calibrations and/or other inputs which complicate the analysis and add to
its uncertainties. Mass spectrometry would appear promising in this regard as, unlike SEC and even
light scattering, it does measure molecular weights directly, even, with the proper application of
techniques / instruments such as MALDI, electrospray ionization, and time of flight, molecules with
MWs in the tens and hundreds of thousands Daltons.
533559934
Page 14 of 14
REFERENCES
1.
W. W. Yau, J. J. Kirkland, and D. D. Bly, Modern Size Exclusion Liquid
Chromatography, Wiley, New York, 1979.
2.
H. G. Barth and W. W. Yau, International GPC Symposium Proceedings,
Millipore Corporation, 1989, 26.
3.
T. G. Scholte, Developments in Polymer Characterization – 4, J. V. Dawkins,
ed., Applied Science, New York, 1983, 1.
4.
T. G. Fox and P. J. Flory, J. Am. Chem. Soc., 1951, 73, 1904.
5.
H. R. Allcock and F. W. Lampe, Contemporary Polymer Chemistry 2’nd Ed,
1990, 536.
6.
H. Benoit, Z. Grubisic, and R. Remmp, J. Polymer Science, 1967, B5, 753.
7.
C. N. McEwen, and P. M. Peacock, Analytical Chemistry, 2002, 74, 2743.
8.
S. D. Hanton, Chemical Reviews, 2001, 101, 527.
9.
J. H. Scrivens, and A. T. Jackson, Int. Journal Mass Spectrometry, 2000, 200, 261.
10.
G. Montaudo, and R. P. Lattimer, Eds., Mass Spectrometry of Polymers; CRC Press:
Boca Raton, FL, 2002.
11.
J. T. Watson, Introduction to Mass Spectrometry, 3’nd Ed.; Lippencott – Raven:
Philadelphia, PA, 1997.
12.
K. Owens, personal communications and classroom instruction.
13.
R. Skelton, F. Dubois, and R. Zenobi, Analytical Chemistry, 2000, 72, 1707.
14.
S. Trimpin, A. Rouhanipour, R. Az, H. J. Rader, and K. Mullen, Rapid Commun. Mass
Spectrometry, 2001, 15, 1364.