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David- please make sure “track changes” is on- I will be using it to leave you
comments about the concepts you address in the document.
Polymer MW, Viscosity, and Branching Measurements by Mass Spectrometry
David J. Strumfels
CHEM755 (Mass Spectrometry)
Drexel University Chemistry Dept., Philadelphia PA 19102
Summary:
Measurements of synthetic polymer molecular weights, MWs, intrinsic viscosities ([]), branching
parameters such as Mark-Houwink constants and branching densities, and the distributions of these
properties over an entire polymer MW distribution, have been largely the domain of Size Exclusion
Chromatography (SEC or GPC), Low/Multi-Angle Laser Light Scattering (LALLS / MALLS), and/or
viscosity measurement techniques.1,2 Often these techniques are combined into a single system, e.g., a
GPC 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 are, or can be, determined by mass spectrometry
(MS) alone, with or without GPC to fractionate polydispersed polymers. Although the measurement of
molecular weight of polymers by MS is already an established science, albeit one with limitations4, there
has been little or no determination of branching via this technique. In addition, by making use of the
theory to calculate branching from viscosity and MW, if MS can measure branching directly, it should
also be able to “back” predict[]of a polymer (distribution) as well as other properties related to
viscosity and MW, such as hydrodynamic size of polymers in solution.
Background:
Polymers are often compared to very long strands of spaghetti, strands that are often randomly spread in
and around each other, inter-entangled, coiled (as in many elastomers), or sometimes rigidly/semirigidly aligned (in crystalline 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’
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forces and hydrogen bonding). For example, the viscosity of a polymer melt or solution is largely a
function of the length of the “spaghetti” 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 actually, 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
phenomenom 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 – actually geometric -- analysis. A linear polymer, being long and thin, has a
relatively high surface area / MW, and therefore possesses a large hydrodynamic volume (HV – the
volume it effectively has in solution) 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), and so leads to a smaller HV in solution. Although this is not a universal
feature of macromolecules (proteins – and some other water-soluble polymers – are linear, but have a
small HV / MW because of intramolecular hydrogen and other bonding which causes 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 GPC 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,
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.
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With this in mind, how to proceed is clear. Measure the MW of a polymer – either through light
scattering, GPC, 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)
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 Mark-
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Houwink plot, it is of course necessary to fractionate the polymer first, generally by GPC. 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 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. The main obstacles standing in the way of this analysis were
the difficulties in getting such large molecules to survive the volitilization and ionization steps necessary
for MS: older techniques, such as electron ionization at high eV impact energies, and even relatively
soft, chemical ionization techniques available, invariably resulted in polymer fragmentation and
degradation to the extent that measurement of the parent ions was exceedingly difficult if not
impossible. In addition, the MS designs available did a poor job of achieving the mass range and
resolution, and that only with difficulty. Finally, the techniques to directly couple MS with
chromatographic instruments, e.g., MW fractionation by GPC, were not well developed; such techniques
were required if a full analysis of polydispersed 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 volitilization and ionization of
even very high high MW polymers has been made possible by the development of Matrix Assisted Laser
Desorption Ionization7, or MALDI, while other, “soft” ionization techniques such as Fast Atom
Bombardment (FAB), and Electro-Spray Ionization (ESI) have been improved to the point of handling
*
fairly large macromolecules when handled properly10 . On the technique and instrument interface end,
particularly regarding HPLC and GPC, 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.
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*except where otherwise indicated, reviewed material comes from references 5., and 7. through 11., and personal
communications, discussions, and classroom instruction (12.).
For the high polymers (105 – 106 and more daltons) which are the focus of this report, 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. For these molecules, other existing techniques still lead to unnacceptable degrees of
fragmentation and degradation. Unfortunately, MALDI as a sample preparation / introduction method
cannot be easily interfaced with GPC, although TOF as an analytical instrument can be (and usually is
the instrument of choice if LC-MS methods); thus, for most high polymers, particularly non-aqeous
ones, the only practical way of obtaining MW and other MS information on polydispersed systems is by
the extremely tedious method of physcially isolating fractions with (semi) preparative GPC and then
individually analyzing the fractions and combining the data for all fractions. This of course would still
not achieve the MW resolution (on the GPC end) a direct interface would*.
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 mechanism of
MALDI is simple, albeit not well understood. The polymer of interest is first dissolved, dispersed, or
otherwise intermixed13,14 in a suitable matrix material. The solution / dispersion 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. Exactly how the matrix assists in the process is unknown, but it permits these steps to be
performed so softly that the polymer molecules remain intact with very little fragmentation, allowing the
parent ion molecular weight to be directly measured.
Electrospray techniques of sample introduction turn a polymer solution (e.g., from an HPLC / GPC) into
a spray of very fine droplets, which are then given an electrical charge via an electron or chemical
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pathway, such as a chemical ionization technique or low energy electrons. The tiny droplets are injected
into the MS chamber, where the solvent evaporates to leave behind ions of various multiple charges.
*The fraction isolation would not need to be done with preparative-scale GPC columns. Analytical columns
running multiple repetitions / collections on a sample can easily provide the quantities needed for MS. This
process can be readily automated, including the data combining. The resolution available in such fractions would
still be less than that of a direct interface, however, and the procedure still analyst time / energy intensive.
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 wieghts 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 monodispersed (single MW) polymers, whether prepared
synthetically or by the GPC semi-preparative fractionation described above; the difficulty with
polydispersed polymer systems is that the data become severely complicated and messy when the
polymer molecules span a range of weights. Also, again, for high MW polymers it is not as effective as,
say, 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 volitilized 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 the gradient boosts all the
ions to the same kinetic energy ½mv2, thus necessitating differing velocities for molecules of different
masses (morely 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 and being
recorded by the detector. As the actual impact energies or velocities of the different polymer ions
cannot be easily measured, the most straightforward way of determining their molecular weights is
literally by the time they spend in the drift region; ergo, the technique’s name.
Described this simply, TOF is, and was, a instrument of poor resolution, particularly when applied to
increasingly higher MW materials, relegating it as a niche technique until sufficient improvements were
devised. The poor precision was 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, form in the same region of space, and be accelerated all at
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both the same times and with the same energies. In practise, of course, no operating MS instrument can
perform all these tasks perfectly, but the basic TOF design is a notoriously poor performer here precisely
because, for example 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.
In contemporary TOF instruments, these design flaws are 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 instrument / technique with very high resolution, 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 preparation / introduction method.
The combination of MALDI-TOF therefor allows quick, efficient, high-resolution analyses of polymer
MWs up into the millions of daltons. 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
(almost) directly; although calibration of the TOF instrument is usually necessary, only a single
calibration is needed for all polymers despite chemical differences. (Contrast this with straight GPC,
where each polymer must be calibrated with known standards of the same chemical species, e.g.,
polystyrene for polystyrene, pMMA for pMMA, etc., 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 LALLS / MALLS 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 easily interfaced to a gel permeation chromatograph. This lack is far
from fatal, as the MS technique, TOF or otherwise, separates the different MW species anyway. If it
were possible to perform a GPC separation of a polydispersed polymer sample prior to introduction into
the MS however, then even better resolution of the different MW species (and simpler spectra!), as well
as more information on them, would be obtainable. Fortunately, TOF-MS has established itself as an
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excellent detector for GPC, an achievement that can be built on. What is needed is a sample
introduction / ionization technique as “soft” as MALDI, but which can be used in the chromatograph (or
at least the interface between the two); the softest existing ionization techniques, electrospray, chemical
ionization (CI), and FAB can only rarely handle polymers much above ~50,000 daltons, and these
generally aqeous systems such as biopolymers. The routine measurement of organic-soluble synthetic
polymers in the 100K – 1000K+ dalton range by GPC-MS awaits additional development.
Indirect Measurement of Polymer Branching and Viscosity by Mass Spectrometry
Branching measurements in polymer systems by MS is an area of polymer research not yet well
explored. Indeed the question of whether it can be done, in a practical and efficient manner that is, is
currently unanswered. One of the purposes of this report is to explore, theoretically, how such
measurements might be made, and to suggest potential techniques for doing so.
As a first approach to this problem, basic to fragmentation patterns in mass spectrometry is the fact that
branching points in molecules are generally more susceptible to cleavage, a result of a combination of
electronic and steric effects. For example, in molecules such as branched (non-linear) alkanes, cleavage
is more prevalent at secondary and tertiary carbons than at primary carbons in the backbone, due to the
relative stability of secondary and tertially carbanions compared to primaries and the larger number of
possible rearrangements (e.g., H-shifts and further fragmentations) these carbons provides (Equations 4
and 5). This complicates the analysis of these molecules by MS by intering with the much more
straightforward and simple fragmentation pattern of linear alkanes, although it also helps in elucidating
their structure.
(Eq. 5)
(RRHCsec–CH2CH2CH3)·-
(Eq. 6)
(RHCsp3–CH2CH2CH3)-


(RHCsp3–CH2CH2CH3)- + R·
(CRsp3=CHCH2CH3)- + H2, etc.
If polymers can be analogously regarded as very long chain alkanes – a literal fact in the case of
polyethylene, and essentially true for addition polymers if one only considers the carbon backbone of the
molecule – then the possibility of using the same approach to measure polymer branching would appear
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promising. However, the extreme complexity of a branched polymer’s fragmentation pattern would
seem to make this approach daunting if not impossible. Fortunately, here we can perhaps use another
analogy, this time between MS fragmentation patterns and GPC “molecular weight” (actually
hydrodynamic volume) distribution patterns to make the analysis tractable. To see how this might be
done, consider the MW distribution patterns of a two polymers, both with the same chemical
compositions, MWs, and polydispersities but one being linear while the other highly branched. When
these are analyzed by standard GPC, the distribution of the branched polymer appears to show lower
MW and broader dispersity than the linear analogue. This is easily explained by the basic GPC
separation mechanism. Bearing in mind that GPC actually separates by hydrodynamic volume, not
molecular weight, and that branched polymers have a smaller volume than their linear counterparts, it is
to be expected that a branched chain will elute later in a GPC chromatogram than a linear, and that
variations in degrees of branching will make the final distribution appear broader as well.
A similar line reasoning, though due to different causes, ought to apply to the mass spectrum as well.
As in GPC, the distribution of polymer MWs leads to a roughly gaussian distribution in the data (in
GPC, for polydispersed polymers made by free radical chain polymerization, the distribution should
actually be poisson, a shape that can be modeled by modifying a gaussian curved with a exponential),
and the placement and shape of the distribution should be affected in a similar manner for branched
species. That is, branch points in a polymer chain ought to yield greater fragmentation, leading to
successively smaller MW ions being detected, and thus a seemingly lower overall molecular weight,
while variations in the degree of branching / fragmentation ought to broaded the distribution.
Repeating equations 2, 3 and 4 for GPC
(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, straight or universally calibrated GPC, etc.) and
assuming model  for the polymer system being measured, and HVB, MW and HVL, MW having been
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obtained by GPC (via universal calibration or viscometry), using GPC it is therefor possible to calculate
gMW and hence branching type and / or degree of the system.
Given that there is, or should be, an
analogue of (HVB, MW / HVL, MW)1/ for MS in the form
(Eq. 7)
gMW
= ([FMW]B, MW / [FMW]L, MW)1/MS
where [MWF] is the molecular weight of the ion fragment, the branching measurements should follow
from the MS as well. Whether there is a universal correlation, or calibration, between branched and
linear polymer patterns, or one for each polymer by chemical type as in GPC, would need to be
evaluated. Either way, it would only be necessary to possess this correlation / calibration, and the
distribution of the linear polymer, to perform the branching determinations. In addition, having the
[]L, MW for the linear polymer, []B, MW can also be computed; or conversely, the Mark-Houwink
constants can be generated.
(Semi) Direct Measurement of Polymer Branching and Viscosity by Mass Spectrometry
The problem with the above method is that, like the GPC techniques discussed before them, they are
indirect, reliant on calibrations / correlations, assumptions of the branching model, and sensitive to both
the data and the inputted parameters. Given the expense of MS instruments compared to light scattering
and viscosity detectors, it therefore would probably not pose a practical alternative to branching
calculations. What is desirable is a direct, or nearly direct, method of measuring branching in polymers;
one that requires few or no assumptions, calibrations, or other algorithms, or where such data
manipulations are firmly based in theory and practice, or a combination of both.
It is, in fact, unlikely that mass spectrometry can be used to measure polymer branching directly. This is
because all it detects and analyzes are ions and ion fragments and, as noted, although there should be a
correspondence between branching and fragmentation, the resulting data sets are probably too
complicated to tease branching measurements from. We are still stuck with at least some indirection in
our approach.
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An approach to measuring branching at least more directly by MS is to look at polymer end groups.
Polymers made by free-radical addition (and non-living polymers by ionic processes) are usually capped
at the ends of their chains by species that serve to either terminate the addition process or prevent it from
restarting (in living polymer systems, missing end groups allow additional growth of the molecules even
after the initial polymerization process has completed). The result is that for each chain there is at least
one group, depending on whether it is a branch or the main backbone chain. For the main backbone
chain there is necessarily two groups, one for each end. This allows for a very straightforward equation:
(Eq. 8) #BPs = #GROUPS – 2
where #BPs is the number of branch points, and #GROUPS is the number of end groups. We subtract 2
because of the two groups belonging to the backbone. Thus, if there are 7 end groups on a polymer
molecular, there should be 7 – 2 = 5 branch points.
Mass spectrometry is currently used as a method of end group analysis. Over the last several years it has
become possible to both identify end group composition and quantitate the number of groups in a
polymer system. If a polymer distribution can be resolved into individual mers, then it is possible to
evaluate the structure of ions of the type:
[G1-AAAAAAA…AAAAAAA-G2]C+
where the As are the mer units of the polymer backbone, G1 and G2 are the end groups (preferably the
same), and C+ is a cation which often results in ionization by ESI and other chemical ionization
techniques. The average number of end groups can be determined by performing a linear least-squares
fit on the mer peaks after subtracting values for C+ and the mer units to yield a poly-ended (di-ended for
linear polymers, di + # branches, for branched) group mass. This method works to give quantitative
mass yields if one assumes this residual mass does not correspond to groups with one or multiples of
mer units; that is, if the MW of the end groups equals that of the mer units. This may or may not be a
valid assumptioon.
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This type of quantitation should works, if it does, only for relatively narrow polymer distributions,
where differing mers are resolved and measured with high accuracy. In a broad, polydispersed system
of high average MW, that kind of resolution and accuracy will not be possible: thus, it is not possible as
of this date to perform the quantitation as a function of the individual polymer MWs. in a polydispersed
system, unless the distribution is separated into narrow, preferably monodispersed, fractions. However,
if the distribution is separated by a technique such as GPC, then information can be obtained across the
breadth of the chain.
This suggests that polymer branching determinations are, or should be, fairly straightforward by this end
group analysis by MS. If so, then by rearranging the equations for the calculation of branching type /
number from gMW factors, and the equations relating these factors to intrinsic viscosities []MW, and / or
hydrodynamic volumes HVMW, it should also be possible, again assuming the correct branching model
for a given polymer system, to obtain the viscometric and chromatographic measure directly by GPC
and viscometry. Added to the molecular weight and composition information already provided by MS,
the technique (when coupled with GPC) can give a wide gamut of data on a polymer with one
instrument instead of two or three.
Thus we see how the different macroscopic, physical properties of polymers – extremely important in
the consideration of its overall behavior and practical applications – relate to its microscopic properties
(MW, branching, HV, etc.), and the microscopic properaties interrelate, in such a way that obtaining one
or two allows determination of the others. This fact is what allows structure determination to be made
from MW + viscosity measurements, and viscosities to be inferred from structural measurements. Both
the older methods, GPC with light scattering and / or viscometry, and the mass spectrometry methods
described in this paper simply come at these issues from opposite ends. The main barrier as of this
report is the lack of a suitable sample preparation / introduction instrument and / or technique to
properly introduce large polymer molecules into a mass spectrometer without unacceptable levels of
fragmentation; as we have seen, while MALDI is effective in the preparation aspect, it cannot be
interfaced with HPLC / GPC systems easily. Future developments in ESI or other interfaces with the
required ionization softness are needed.
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Conclusions
Determination of polymer molecular weights, viscosities, and branching have traditionally been
performed by a combination of GPC, light scattering, and viscometric measurements. The
determination of molecular weight by mass spectrometry is already an established science, and some
work into branching measurements have been done. The full elucidation of polymer structure by MS
awaits future work. 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 semi-direct 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 GPC 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 hudreds of thousands daltons.
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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.