Molecular Weight Determination
Matrix-Assisted Laser Desorption Ionization – Time of Flight Spectroscopy
Polymer Characterization Lab
Course Co-ordinator: Prof. Shaw Ling Hsu
Date: 10/30/2003 Submitted By: Rajeev Kumar
Gel Permeation Chromatography
Virtually all synthetic polymers have a molecular weight distribution (MWD) and the
experimental determination of MWD became possible after 1960 with the development
of suitable porous packing for size exclusion chromatography (SEC) which is based on
the fundamental that polymers can be separated by the size dependence of degree of
solute penetration into a porous packing. First experiment was carried out by employing
dextran gels. The term Gel Permeation Chromatography (GPC) was developed sometime
later by Moore, who developed rigid cross-linked polystyrene gels, covering a wide range
of pore sizes, which are suitable for separations of synthetic polymers in organic media.
These gels, which are extensively cross-linked, undergo limited or no swelling with the
solvent and so have good mechanical stability for separations at high pressures and fast
Theory: Separation Mechanism
The dominant separation mechanism in GPC is assumed to be size exclusion, which
requires minimum interactions between solute and gel. In a typical gel chromatogram
eluted polymer as a function of time or retention volume, Vr. The volume of eluent Vr
required to elute a particular component from a column is measured from the injection
point to the peak height maximum of chromatogram. The retention time tr is related to Vr
where fv is the volumetric flow rate.
Basic separation mechanism in GPC assumes that the column packing is inert i.e. that
interactive mechanisms such as partition and adsorption do not contribute to retention
behaviour. The separation is determined by a size exclusion mechanism in which the pore
volume in the gel particles accessible to a given molecule is determined by pore size
distribution and solute size.
The separation of a solute of given size in solution is determined by a distribution
coefficient Ksec which governs the fraction of volume of solvent within the porous gel
particles, known as volume of stationary phase Vi. The retention volume Vr for this solute
is given by
where Vo is interstitial (or void) volume of solvent between porous gel particles, known
as volume of mobile phase.
So very large molecules having a zero value of Ksec will elute at Vo because the sizes of
these macromolecules prohibit solute diffusion into the gel pores. On the other hand, very
small molecules have free access to both stationary and mobile phases i.e. Ksec is unity.
As the chromatographic column is washed with solvent, the large molecules are eluted
first, followed by solutes of decreasing size, which penetrate an increasing fraction of
solvent within the gel particles.
In practice, sample and reference columns are normally run side-by-side with pure
solvent streaming through both of them. A dilute solution of the polymer sample is
injected into the solvent stream of the sample column. Both streams are then passed
through a differential refractive index detector and output of which is recorded. At first
the signal is zero as the refractive index of the two streams is identical. When the
polymer molecule appear in stream from the sample column there is a difference in
refractive index and a signal is registered. In fact, its possible to measure the
concentration of polymer in solvent from the knowledge of the relationship between the
refractive index and concentration but this information is often not required.
GPC is not an absolute method of polymer characterization and requires calibration with
samples of known molar masses. It is often found for a given polymer-solvent system
that the molar mass of the polymer can be related to the retention volume through an
equation of the form
logM= a + b Vr
where a and b are constants. For a flexible random-coil like polymer, from Flory-Fox
theory of solution viscosity, the dimensions of polymer coil can be related to [η]M by
Mark-Houwink relation given below:
log([η]M) = logK + (1+a)logM
where [η] is limiting viscosity number; M is molar mass of a monodisperse polymer; K
and a are known as Mark-Houwink constants which are characteristics of a polymer-
solvent system. Typically value of ‘a’ lies in between 0.5 and 1. In fact it’s found to be
about 0.5 for a solution in Theta condition and is higher for better solvents.
Using Mark-Houwink relation and Universal Callibration curve molecular weight of an
unknown sample can be calculated.
Matrix Assisted Laser Desorption Ionization – Time of Flight
It is perhaps the most important mass spectrometry technique currently being used to
analyze polymer systems. MALDI is used in applications ranging from sequencing
peptides to measuring the average molecular weights of complex synthetic polymer
materials. In MALDI, a dilute solution of the polymer is mixed with a more concentrated
matrix solution. Typical MALDI matrices are aromatic organic acids. A small aliquot of
the mixture is applied to the MALDI target and it crystallizes as the solvent evaporates.
After the target is placed in the source of the mass spectrometer, a laser irradiates the
target, vaporizing the matrix, and desorbing polymer oligomers into the gas phase.
Neutral gas-phase oligomers are cationized by protons or metal cations. The ions are
extracted into the mass spectrometer, mass analyzed, and detected. These ions are
accelerated by an electric field. The potential applied at the end provides kinetic energy
to the ions according to the relation given below:
ZV = ½ (mv2) => v = √(2zV/m)
As Time of flight=tf = L/v => tf ~ √ (m/z)
where V is the potential applied, v is velocity of the ion, L is the distance between
accelerating potential source and the detector. Thus ions with different m/z reach the
detector at varying times. In this way the number of polymer chains with different
molecular weights can be determined which helps in determining the average molecular
weight of polymers.
The MALDI experiment is dominated by sample preparation issues. The sample
preparation method is vital to the success of polymer MALDI experiments.
The sample preparation for polymer MALDI must accomplish five different roles, one
for the solvent and four for the matrix. The roles are as follows.
(1) Separation of the individual oligomers-the solvent must effectively separate the
molecules of the sample. The interactions between the analyte molecules need to
be minimized and generate individual molecules for the MALDI experiment to
(2) Isolation of the oligomers-the matrix must maintain the separation of the
oligomers accomplished by dissolving the sample in a good solvent. Most of the
matrices used in polymer MALDI are small aromatic organic acids that readily
form crystals as the solvent evaporates.
(3) Absorbtion of energy- the matrix must absorb the energy delivered to the sample,
usually by a 337 nm laser.
(4) Desorbtion of the analyte- the matrix must convert the energy delivered by the
laser to eject the analyte molecules into the gas phase.
(5) Ionization of the analyte- the matrix must provide an ionization path to the analyte
Several different strategies for sample preparation have been demonstrated for MALDI.
The simplest is the dried droplet method. In the dried droplet method, a dilute solution of
analyte is prepared in a good solvent. This analyte solution is then mixed with a more
concentrated matrix solution in the same solvent. The solvent must be selected carefully
to be a good solvent for both the analyte and the matrix. Almost any relatively volatile
solvent can be used. The mix ratio of the two solutions should result in a matrix-to-
analyte ratio of between 100 and 10 000 depending on the chemistry and molecular
weight of the polymer. For low molecular weight polymers, typically 5 mg/mL polymer
solutions are used and they are mixed in ratio of 1:7 with 0.25 M matrix solutions. About
1 μL of the resulting solution is then simply spotted on the target substrate and allowed to
dry. For many of the simpler polymer MALDI experiments, this method is adequate to
produce good data.
Another method is the layer method. In the layer method, the matrix solution is applied to
the target surface first and allowed to dry. The sample solution is then applied to the dry
matrix crystals. In some cases, the sample preparation can be aided by the addition of a
The choice of solvent is critical to the success of a polymer MALDI experiment. If the
polymer sample is not fully soluble in the solvent, only the dissolved portion of the
sample will be observed by MALDI.
A very important role of the matrix is to provide a suitable ionization pathway for the
polymer oligomers. Polymer samples observed in MALDI are cationized: e.g. amine
functions tend to protonate, oxygen functions tend to alkali cationize, and unsaturated
hydrocarbons tend to copper or silver cationize. Since most of the matrices are organic
acids they can readily supply a proton. If metal cationization is required, then a source of
the appropriate metal must be included in the sample preparation method. While the
mechanisms of ionization in MALDI are not yet well understood, a combination of
preformed ions and gas-phase cationization reactions probably explains most of the
MALDI molecular weight measurements have been very successful for narrow
polydispersity samples. MALDI average molecular weight measurements are typically
accurate for samples with a PD less than about 1.2. For samples with PD between 1.2 and
1.6, there are few well-characterized standards. For samples with PD above about 1.6,
MALDI has problems in accurately measuring the average molecular weight
distributions. Issues that effect the measurement of accurate molecular weights for broad
polydisperse polymers include sample preparation, fragmentation, multiple charging, and
MALDI can be used for end-group analysis, copolymer composition determination, the
number average molecular weight and polydispersity of polymers.
The set up of GPC instrument is shown below:
Still Pump Injector (200ml) Inline Filter Columns (3 in number)
Recycling of polymer Detectors (UV and Refractive Index)
This experiment was carried out using THF as eluent at a temperature of 36οC. Injection
volume used for this experiment was 200 ml. Two mixes of polystyrene were used for
calibration purposes. Following table shows different molecular weights present in each
Mix1-Molecular Weights Mix2-Molecular Weights
With the help of these standard samples calibration curve was obtained based on the data
Retention Time Molecular weight Log (MW)
14.6833 390,000 5.591065
15.4000 200,000 5.30103
16.9667 52,000 4.716003
17.8667 24,000 4.380211
17.9833 22,000 4.342423
19.7333 5,000 3.69897
20.8667 2,700 3.431364
21.9167 1,300 3.113943
The Calibration curve obtained using this data was used to determine the molecular
weight of an unknown polystyrene sample, which gives a peak at retention time of
16.4333. The calibration curve obtained from above data is shown on next page:
Polystyrene Standard Callibration Curve
y = 18.559e-0.0812x
0 5 10 15 20 25
Universal Callibration Curve
y = 2E+16e-1.3663x
0 5 10 15 20 25
With the help of polystyrene standard calibration curve, molecular weight of the
unknown PS sample was determined to be 77083.64 g/mol. Next sample run on GPC was
Polyethylene Glycol (PEG). In order to determine molecular weight of PEG, Universal
Calibration curve was obtained using eight standard polystyrene samples and Mark-
Houwink equation (shown on last page).
The values of the Mark-Houwink parameters ‘K’ and ‘a’ used for Polystyrene-THF
system were 11.0 x 10-3 ml/g and 0.725 respectively. The Universal calibration curve
obtained was used to calculate the molecular weight of PEG with the help of its retention
time (19.7833) and Mark-Houwink equation. K and a values used for PEG-THF system
were 0.02 ml/g and 0.73 respectively. The molecular weight of PEG was estimated to be
This sample of PEG was run using both detectors i.e. refractive index and UV detector.
No peak was seen in chromatogram obtained using UV detector while there is a peak in
chromatogram obtained using refractive index detector. This can be attributed to the
absence of UV absorbing group in PEG.
The next sample was block copolymer of PS and PMMA. Two peaks were obtained in
chromatogram while there is only one peak in a standard sample of diblock PS-PMMA.
The presence of an extra peak in chromatogram can be because of the presence of some
unreacted PS left in reaction mixture during synthesis of di-block copolymer. Thus, GPC
helps in characterizing some of the impurities in the sample.
This experiment was carried out for PEG and hydroxyl terminated polystyrene (PS)
samples. Both experiments were carried out using tetrahydrofuran (THF) as a solvent.
Samples were prepared using polymer: matrix: salt ratio of 1:5:1. Spectrum were
obtained using linear as well as reflected detector on machine. The spectrum obtained
using linear detector were very poor in resolution while spectrum obtained using reflected
detector were so good that effect of isotopes can also be seen in spectrum.
In case of PEG spectrum, adjacent peaks differ from each other by mass difference of 44,
which indicates that that each of these peaks represents chains whose mass differ by one
ethylene oxide group (-CH2-CH2-O-) which is the repeat unit in PEG.
Degree of polymerization of different polymer species in sample was calculated by
subtracting the weight of cation present in polymer chains and adding weight of end
groups and dividing by the weight of repeat unit. For example, in case of PEG polymer
chains (ionized using sodium chloride as a salt and gentisic acid as a matrix) the peak
labelled 3382 was estimated to be made up of 76 repeat units of ethylene oxide (after
subtracting 23 as weight of sodium cation) and hence has a DP of 76.
In order to calculate molecular weight of sample and PDI, y-axis in spectrum was taken
as proportional to number of polymer chains of different masses and; as charge on each
chain is one so x-axis was taken as the weight of different kinds of polymer chains.
Number average molecular weight was calculated using the formula:
Mn = (∑NiMi) / (∑ Ni)
As is clear from above formula that in the calculation of number average molecular
weight contributions from polymer chains, which are higher in number, is more as
compared to massive chains, which are less in number. Hence, number average molecular
weight is always biased toward that part of spectrum, which has higher number of chains.
For PEG sample number average was calculated to be 3205.016 gm/mol.
Weight average molecular weight for same sample was also calculated using the formula:
Mw = (∑NiMi2) / (∑NiMi)
In contrast to number average molecular weight, weight average molecular weight is
affected by chains with higher masses. Weight average molecular weight for PEG was
calculated to be 3339.364-gm/mol. From the values of number average and weight
average molecular weight, polydispersity index (PDI) of sample was calculated using
PDI= Mw/ Mn
and PDI for PEG sample was calculated to be 1.0419.
Another spectrum was obtained for polystyrene sample with hydroxy terminated chains.
This experiment was carried out using silver triacetate as a salt and dithranol as a matrix.
Same analysis was carried out for this sample. Adjacent peaks in spectrum differ from
each other by a mass difference of 104, which is weight of repeat unit in polystyrene. So
in order to calculate degree of polymerization of different polymer chains, weight of
silver cation is needed to be subtracted. Number average, weight average molecular
weight and PDI was calculated using above formulae and found to be 2894.261, 2958.48
and 1.0221 respectively.
If there was some comtamination of this sample by polystyrene with hydrogen as its end
group then there should be peaks at a mass difference of 16 (weight of oxygen) from the
dominant peaks corresponding to polystyrene with hydroxyl end groups. A peak was
found around peak labeled 3116 in the spectrum at a mass difference of 16 and this peak
can be attributed to polystyrene with hydrogen as its end group.
Also by having a closer look at peak around 2805, the presence of different isotopes in
the sample can be identified (due to different carbon and hydrogen isotopes).
The results of this experiment can be tabulated as below:
Sample Mn (g/mol) Mw (g/mol) PDI
PEG 3205.016 3339.364 1.0419
PS 2894.261 2958.48 1.0221
GPC and MALDI
GPC and MALDI are two techniques of mass spectrometry, which complement each
other. GPC is dependent on hydrodynamic volume of polymer sample and that depends
on the solvent-polymer interaction. Also in GPC molecular weights are measured using
calibration curves obtained using polystyrene standard samples. So in GPC, molecular
weight measurement is relative to polystyrene standard samples and the molecular weight
obtained is weight average molecular weight. In contrast to GPC, MALDI gives absolute
molecular weight (number average and weight average both). MALDI is very sensitive
technique. In fact it can sense each and every polymer chain with the help of charge and
mass of chain (which is the characteristic of that particular chain distinguishing it from
other chains). MALDI is so sensitive that it can detect the presence of isotopes in
polymer samples. But there are some problems with MALDI for samples with higher PDI
such as sample preparation, fragmentation, multiple charging, and detector saturation.
On the other hand GPC has an advantage over MALDI that GPC can be used as a
purification technique also.
Molecular weight of PEG sample obtained from GPC (3498.03 gm/mol) and MALDI
(3339.364 gm/mol) differ from each other and the difference can be attributed to solvent-
polymer interaction in case of GPC and discrepancy in value of K and a used in
calculation of molecular weight using Mark-Houwink equation.
1.Hanton S.D., Mass Spectrometry of Polymers and Polymer Surfaces, Chem. Rev., 2001,