ARTICLE
pubs.acs.org/jchemeduc
Polymer Molecular Weight Analysis by 1H NMR Spectroscopy
Josephat U. Izunobi and Clement L. Higginbotham*
Polymer Engineering Department, Athlone Institute of Technology, Dublin Road, Athlone, Ireland
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bS Supporting Information
ABSTRACT: The measurement and analysis of molecular weight and molecular weight
distribution remain matters of fundamental importance for the characterization and
physical properties of polymers. Gel permeation chromatography (GPC) is the most
routinely used method for the molecular weight determination of polymers whereas matrixassisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS)
is a fast-emerging absolute, and therefore accurate, technique. Although NMR spectroscopy
is one of the most powerful tools available for polymer microstructure characterization,
among others, its utility in the molecular weight analysis of polymers is somewhat
underappreciated. It is a reliable and more readily available teaching tool in comparison
to other known techniques, such as GPC and MALDI-TOF MS, for the molecular weight
determination of polymers. Demonstrated herein are the simplicity, reproducibility, and
convenience of 1H NMR spectroscopy in the analysis of polymer number-average
molecular weight (Mn), using R-methoxy-ω-aminopolyethylene glycol (MPEG-NH2)
and R-methoxy-polyethylene glycol-block-poly-ε-(benzyloxycarbonyl)-L-lysine (MPEG-b-PLL(Z)) as model homopolymer and block
copolymer, respectively. The molecular weight data from 1H NMR analysis are compared to those from GPC and MALDI-TOF MS.
KEYWORDS: Graduate Education/Research, Upper-Division Undergraduate, Polymer Chemistry, Inquiry-Based/Discovery Learning, Problem Solving/Decision Making, Chromatography, Mass Spectrometry, NMR Spectroscopy
P
olymers are large molecules (macromolecules) that are built
up of smaller repeating structural units called monomers.1
They possess an extraordinary range of properties, which aid
their essential and ubiquitous roles in virtually all facets of human
endeavor. Synthetic polymers are rapidly and successfully replacing many natural polymers because the latter are limited and in
short supply, as well as for the former’s often-superior physical,
chemical, and mechanical properties. Polymers are employed in
one form or the other in a wide array of applications such as in
food, textiles, electronics, photography, computing, medicine,
pharmaceuticals, tissue engineering, and in a variety of biomedical appliances, ranging from implantable devices to controlled
drug delivery systems.2
Copolymers are frequently formed by the chemical combination of polymers. They benefit from the synergistic characteristics of their constituent (homo)polymers (or monomers)
thereby overcoming many deficiencies inherent to their component polymers. Homopolymers are synthesized from single
monomers whereas copolymers are prepared from two different
monomers (or polymers). Block copolymers, on the other hand,
consist of two or more covalently bonded polymer blocks with
diverse physicochemical properties. They form phase-separated
microdomains in selective solvents and in the bulk.3 Polyethylene
glycol (PEG) is a highly investigated synthetic polymer for the
covalent modification of biomacromolecules and surfaces for
many pharmaceutical and biotechnical applications,4 whereas the
block copolymers of polyethylene glycol and poly-L-lysine (PEGb-PLL) have been explored for biomedical applications5 and are
considered nontoxic, biocompatible, and biodegradable.6
Copyright r 2011 American Chemical Society and
Division of Chemical Education, Inc.
The molecular weight of a polymer represents an average of the
distribution of its various constituent molecules with different chain
lengths. It is an extremely important variable as it relates directly to
the physical properties of the polymer.7 The determination of
molecular weight and molecular weight distribution is therefore
of central interest in polymer analysis. Commonly used techniques
for the molecular weight determination of polymers include size
exclusion chromatography, solution viscosity, osmometry, endgroup analysis, ebulliometry, cryoscopy, light scattering, and
ultracentrifugation.8 Comparatively, mass spectrometry has found
little use in the polymer field beyond the characterization of degradation products because of its requirement of volatilizable
samples.9 Most polymers thermally degrade before attaining vaporization. Even so, recent years have witnessed the development of
new soft ionization systems, such as electrospray ionization (ESI)
and matrix-assisted laser desorption/ionization (MALDI) mass
spectrometry.10
Of the aforesaid, the methods that measure a polymer’s colligative
properties give the number-average molecular weight (Mn) as the
methods count the number of molecules of each weight, whereas
the methods that determine molecular weight based on the weight
of the constituting molecules give the weight-average molecular
weight (Mw). Expressed mathematically,
M ¼
∑Ni Mi a þ 1
∑N i M i a
ð1Þ
Published: May 31, 2011
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where M is the average molecular weight; Ni is the number of
molecules of species i; and Mi is the molecular weight of species i.
From eq 1, a = 0 for Mn and a = 1 for Mw;11 that is,
∑ N i Mi
Mn ¼
∑ Ni
∑Ni Mi 2
Mw ¼
∑ N i Mi
ð2Þ
ð3Þ
In other words, Mn is a summation of the product of the mole
fraction of each species and its molecular weight, whereas Mw is a
summation of the product of the weight fraction of each species
and its molecular weight. Thus,
Mn ¼
∑Ni Mi ¼ ∑Xi Mi
∑N i
∑Ni Mi 2 ¼ ∑wi Mi ¼ ∑Wi Mi
∑Ni Mi ∑wi
Ai µ Ni Mi
ð5Þ
where wi is the weight of species i and Wi is the weight fraction of
species i.12
Nuclear magnetic resonance (NMR) spectroscopy is a wellestablished method for the characterization of polymers. It has
been applied in the determination of monomer sequence and
reactivity ratios and polymer microstructure including stereoregularity, relaxation phenomena, and end-group composition.13
The role of NMR in polymer composition and microstructure
characterization is unrivalled, with its utility in continuous
expansion. Conversely, its potential in molecular weight determination is oftentimes underappreciated. Nonetheless, NMR has
been applied in the determination of the molecular weight of
some polymers.14
Gel permeation chromatography (GPC), on the other hand, is
the most commonly used technique for the determination of
polymer molecular weight.15 Yet, the underlying principle of
separation on the basis of polymer hydrodynamic volume and
not molecular weight remains a vital disadvantage in GPC;
commensurate monodisperse standards (for calibration) are
not always readily available, making the method susceptible to
significant errors. Moreover, there are inherent drawbacks with
respect to solvent, column, and analysis time; coupled with the
fact that it is a relative method, that is, the raw data has to be
converted into a molecular weight scale using a calibration
procedure obtained under similar conditions to that of the
polymer being analyzed. In comparison, 1H NMR is a primary
quantitative method, requiring no calibration,16 and it is routinely run in most laboratories. NMR is therefore a relatively
simple, fast, and fairly accurate method of analysis. Also, MALDI
mass spectrometry is increasingly becoming a highly accurate and
absolute method for macromolecular weight determination but it
is fraught with problems, such as mass discrimination, poor
reproducibility, and matrix selection.17
A particularly useful feature of 1H NMR in molecular weight
determination is that the areas under the resonance peaks in the
spectra are proportional to the molar concentration of the species
in the sample being analyzed.16 That the area or intensity of the
proton signal of a given species is proportional to the amount of
that species present in a given sample implies that the area of ith
peak is proportional to Ni, the number of molecules of species i
ð6Þ
where Ai, Ni, and Mi are the area or intensity of the 1H NMR
peak, number of molecules, and molecular weight of species i,
respectively. Equation 6 can be rewritten as,
Ai ¼ KNi Mi
ð7Þ
where K is a constant of proportionality. Assuming that K = 1,
then Ai = NiMi and substituting eqs 2 and 3 become
Mn ¼
∑
Ai
ðAi =Mi Þ
∑
∑A i M i
Mw ¼
∑A i
ð4Þ
where Xi is the mole fraction of species i, and
Mw ¼
with molecular weight Mi, that is,
ð8Þ
ð9Þ
The measurement of a polymer’s Mw is dependent on the total
weight and total number of polymer particles present in its dilute
solution, whereas Mn is dependent on the total number of
polymer particles in its dilute solution regardless of polymer size
(weight). The determination of Mn is therefore equivalent to
dividing the total weight of a given sample of the polymer by the
total number of its constituent molecules. So that, mathematically,
Mn ¼
∑w i
∑N i
ð10Þ
Comparing eqs 5 and 9, wi = Ni Mi = Ai; and substituting for wi,
eq 10 becomes
Mn ¼
∑A i
∑N i
ð11Þ
where Mn is the number-average molecular weight, Ai is the area
or intensity of the 1H NMR peak of species i, and Ni is the
number of molecules of species i. Equation 11 establishes the
relationship between the number-average molecular weight and
the 1H NMR resonance peaks of the detectable hydrogen atoms
of a polymer.
It is noteworthy that the determination of Mn by NMR
spectroscopy for polymers of molecular weights >25 kDa can
be intractable because resolution is diminished the higher the
molecular weight. This limitation in measurable Mn is inherent to
most colligative methods, and it is due to the loss of sensitivity, at
high molecular weights, in the techniques as much as the inability
to purify samples and reagents.18 The development of highfrequency NMR instruments and improved methods of derivatization are, nevertheless, making the measurement of higher Mn
possible.19 Furthermore, the dependence of Mw on a polymer’s
total mass and number of molecules preclude its measurement by
NMR, presently. However, there are auspicious advances in this
area.20
13
C NMR spectra are proton-decoupled and usually better
resolved than 1H NMR spectra. They have a large chemical shift
(δ) range of 200 ppm but a relatively poor signal-to-noise ratio.21
Mn can be calculated from 13C NMR spectra providing the NMR
experiments are run under quantitative conditions.16 This can
prove cumbersome and requires a little more than a working
knowledge of NMR as well as higher sample concentration. In
addition, some polymers (e.g., telechelic polymers) cannot be
analyzed because many functional group signals (e.g., NH, OH)
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Table 1. Salient 1H NMR Data for Molecular Weight Determination of Homopolymer MPEG-NH2 and Block Copolymer MPEGb-PLL(Z)
MPEG-NH2
Feature
End-groups
a
Moiety
δ (ppm)
Multiplicity
MPEG-b-PLL(Z)
Peak area
δ (ppm)
Multiplicity
Peak area
CH3O
3.25
singlet
0.9
3.26
singlet
0.18
NH2
2.71
broad triplet (J = 5.6 Hz)
NDa
7.90
singlet
ND
Repeating units
(OCH2CH2)n
C6H5CH2
3.52
broad singlet
133.1
3.53
5.01
broad singlet
singlet
26.71
2.00
ε-CH2
2.992.97
multiplet
2.05
Copolymer linkage
CONH
7.58
singlet
ND
ND is not determined.
are not detectable in 13C NMR. It is also pertinent to point out
that the incidence of poor peak resolution due to the overlap of
signals in the 1H NMR spectra do not constitute a significant
hindrance to molecular weight determination because of the
additive nature of the resonance peaks. However, the accurate
integration and assignment of requisite peaks are imperative.
This article highlights the simplicity and convenience of utility
of 1H NMR in Mn determination, using R-methoxy-ω-aminopolyethylene glycol (MPEG-NH2) and R-methoxy-polyethylene
(MPEG-bglycol-block-poly-ε-(benzyloxycarbonyl)-L-lysine
PLL(Z)) as model homopolymer and block copolymer, respectively. Requisite working equations are also derived, and the
molecular weights of the polymers were determined by size
exclusion chromatography (GPC) and mass spectrometry
(MALDI-TOF) for comparison. Students can perform the 1H
NMR analysis of the two model polymers and the molecular
weight calculations in a 3-h laboratory. A student handout is
available in the Supporting Information.
’ COLLECTION AND ANALYSIS OF 1H NMR SPECTRA
A total of 15% (w/v) of the polymer, dissolved in deuterated
dimethyl sulfoxide (DMSO-d6), was loaded on a Varian Inova
500 spectrometer (499.8 MHz)a at 60 °C to obtain the requisite
1
H NMR and (1H1H) COSYb spectra.
The requisite peak areas were obtained by the numerical
integration of the 1H NMR spectra, after completing a full assignment of each spectrum and identifying well-resolved peaks.c To
obtain a reliable baseline for the numerical integration, an isolated
resonance signal was chosen as a reference peak, to which a
theoretical value was assigned based on the number of protons
resonating at that chemical shift (δ). For example, for the block
copolymer, MPEG-b-PLL(Z), the integration value for the singlet at
5.01 ppm (C6H5CH2; cf. Figure S3 in the Supporting Information) was set to 2.0. The computer-generated peak areas for
the protons of the methoxy (CH3O) end-group and oxyethylene
((OCH2CH2)n) repeating units of the homopolymer, MPEGNH2, were 0.9 and 133.1, respectively. In each case, the values of the
integrated peak areas were extracted from the spectrum and divided
by their respective numbers of responding protons to afford the
relative peak areas. The composition and Mn of the polymers were
calculated by substituting the values obtained into the appropriate
equations (vide infra).
’ HAZARDS
Dimethyl sulfoxide is harmful if swallowed, inhaled, or
absorbed through skin. It causes irritation to skin, eyes, and
respiratory tract. DMSO-d6 is also hygroscopic and combustible.
MPEG-NH2 and MPEG-b-PLL(Z) may cause irritation to skin,
eyes, and respiratory tract and may be harmful if swallowed or
inhaled.
’ RESULTS FROM 1H NMR SPECTROSCOPY
The degree of polymerization (DP) or number of repeating
units of a polymer is determined from its 1H NMR spectrum by
comparing the relative proton peak intensity of a known moiety
(typically an end-group(s) with a known number of protons) to
that of the repeating chain unit of interest. Herein, an equation is
derived to calculate the DP as follows: rewriting eq 7,
ai ¼ kni mi
and making k the subject of the formula,
ai
¼k
ni mi
ð12Þ
ð13Þ
where ai is the area or intensity of the 1H NMR peak of species i;
ni is the number of repeating units of species i; mi is the number of
protons of species i; and k is the constant.
Considering the 1H NMR signals of two moieties x and y, from
eq 13:
ax
¼ kx
nx mx
ð14Þ
ay
¼ ky
ny my
ð15Þ
where kx = ky in a given polymer,
ay
ax
¼
nx mx
ny my
ð16Þ
where ax is the area or intensity of the 1H NMR peak of moiety x;
nx is the number of repeating units of moiety x; mx is the number
of protons of moiety x; ay is the area or intensity of the 1H NMR
peak of moiety y; ny is the number of repeating units of moiety y;
and my is the number of protons of moiety y. Rearranging eq 16
for nx,
nx ¼
ax my ny
ay mx
ð17Þ
where nx can be used to assess the polymer’s DP or number of
repeating units.
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Consequently, Mn can be calculated by substituting for n in
eq 18,
Mn ¼ nM0 þ Me
ð18Þ
where n is the number of repeating units or DP; M0 is the
molecular weight of one repeating unit, and Me is the combined
molecular weight of the end-groups.
Some of the data extracted from the 1H NMR spectra of the
model polymers for molecular weight determination are collected in Table 1.
1
H NMR Spectrum of Homopolymer
The spectrum of MPEG-NH2 (Figure S2 in the Supporting
Information) was well resolved, thereby making its assignment
straightforward. The protons of the methoxy (CH3O) and
amino (NH2) end-groups resonated as a singlet and broad
triplet, respectively, at 3.25 and 2.71 ppm (J = 5.6 Hz), whereas
the prominent peak of the oxyethylene protons
((OCH2CH2)n) was centered at 3.52 ppm.
Determination of the Number of Repeating Units
To calculate the number of repeating units (n) in the MPEGNH2 chain, the peak areas of CH3O (OMe, δ 3.25) and
(OCH2CH2)n (OEt, δ 3.52) were obtained from the 1H
NMR spectrum (cf. Table 1) and appropriately substituted into
eq 17:
aOEt 3 mOMe 3 nOMe
nMPEG ¼
aOMe 3 mOEt
133:1 3 1
¼
0:9 4
¼ 110:92 111
Molecular Weight Determination
Having obtained n, the Mn of MPEG-NH2 was estimated by
the summation of the atomic masses of the constituent
atoms thus:
(m) of the PLL(Z) block was obtained. It suffices to compare a
well-resolved 1H NMR peak of one of the moieties in the MPEG
block ((OCH2CH2)n or CH3O) to another in the PLL(Z)
block (C6H5CH2 or ε-CH2). Equation 17 afforded the ratio
of the proton intensities of CH3O (OMe, δ 3.26) and (OCH2CH2)n (OEt, δ 3.53):
aOEt 3 mOMe 3 nOMe
nMPEG ¼
aOMe 3 mOEt
26:71 3 1
¼
0:18 4
¼ 111:29 111
The DP of the PLL(Z) block (m) was then similarly calculated
by comparing the 1H NMR integrals of C6H5CH2 (Bn, δ 5.01)
and (OCH2CH2)n (OEt, δ 3.53), using the value of nMPEG
calculated above:
aBn 3 mOEt 3 nOEt
mPPLðZÞ ¼
aOEt 3 mBn
2:00 4 111:29
¼
26:71 2
¼ 16:67 17
Alternatively, comparing ε-CH2 (εCH2, δ 2.992.97) to
CH3O (OMe, δ 3.26):
aεCH2 3 mOMe 3 nOMe
mPPLðZÞ ¼
aOMe 3 mεCH2
2:05 3 1
¼
0:18 2
¼ 17:08 17
Determination of Copolymer Composition
The monomer ratio of L-Lys(Z) in the MPEG-b-PLL(Z)
block copolymer was also estimated from 1H NMR,7 by comparing ε-CH2 (from the PLL(Z) block) to (OCH2CH2)n (from
the MPEG block), using eq 19,
ax
mx
%LysðZÞ ¼ ax ay 100%
ð19Þ
þ
mx my
where ax is the area of the 1H NMR peak of ε-CH2; mx is the
number of protons of ε-CH2; ay is the area of the 1H NMR peak
of (OCH2CH2)n; and my is the number of protons of
(OCH2CH2)n. Substituting into eq 19,
1
%LysðZÞ
H NMR Spectrum of Block Copolymer
Distinct signals were observed in the copolymer’s spectrum
for the protons resonating at 7.58 ppm (CONH), 7.337.32
ppm (C6H5), 6.97 ppm (ε-NH), 5.01 ppm (C6H5CH2), 3.53
ppm ((OCH2CH2)n), and 3.26 ppm (CH3O). The relatively small and partially overlapped singlet for the end-group
methoxy protons (CH3O) is enlarged (Figure S3 in the
Supporting Information).
Determination of the Degree of Polymerization
The determination of the block copolymer’s DP was done in
two parts: the number of repeating units (n) in the MPEG block
was calculated as above, whereupon the degree of polymerization
1:03
100%
1:03 þ 6:68
¼ 13:36%
¼
Comparing C6H5CH2 to (OCH2CH2)n similarly, using
eq 19, gave a result of 13.02%.
Neither of the peak area values obtained for the end-groups
can be substituted into eq 19 to calculate copolymer composition
because they are not representative of the polymer. It is equally
important to note that eq 19 only holds on the assumption that
the relative contributions of the end-groups are negligible. To
illustrate, the percentage composition of one of the end-groups
(CH3O) was estimated to be <1% from its 1H NMR peak by
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Table 2. Comparative Molecular Weight Distribution of Homopolymer MPEG-NH2 and Block Copolymer MPEG-b-PLL(Z)
1
H NMR
GPC
Polystyreneb
DMSO-d6a
Theoretical
Polymer
MALDI-TOF MS
Polyethylene glycolb
Dithranolc
R-CHCAc
Mp/Da
Mp/Da
PDI
DP Mn/Da Mn/Da Mw/Da (Mw/Mn) Mp/Da Mn/Da Mw/Da PDI (Mw/Mn) Mp/Da
Molecular Weight
5006
4996
5505
1.102
6158
5030
5122
1.018
5193
4904
4825
MPEG-b-PLL(Z) 9470 (n = 113, m = 17) 17
9482
9279
9555
1.030
9822
9686
10220
1.055
11222
9987
MPEG-NH2
5010 (n = 113)
(4843)d
(15070)e
a
b
c
d
þ e
Solvent. Calibrant. Matrix. [Mn] .
[MnMm]32þ.
appropriately substituting into eq 19:
%OMe
0:06
100%
0:06 þ 6:68
¼ 0:89%
¼
To check the accuracy of the previous DP calculation (from
eq 17), eq 20 was used,
m
z
¼
ð20Þ
n
100% z
where m is the degree of polymerization of the PLL(Z) block; n is
the number of repeating units of the MPEG block; and z is the
percentage monomer ratio of the PLL(Z) block.
m
111:29 13:36%
86:64%
¼ 17:16 17
¼
MPEG-b-PLL(Z). The apparently better compatibility exhibited by
the PS standards toward MPEG-b-PLL(Z) may be attributable to
the aryl moiety, which is common to both calibrant and analyte
copolymer.
The Mn values obtained from the PS-calibrated curve were
lower than the theoretical molecular weights for MPEG-NH2
and MPEG-b-PLL(Z), whereas the opposite scenario was
evident with the PEG standards (cf. Table 2). Comparing
the experimental and calculated values for Mw, the PS calibrant
gave a higher deviation for MPEG-NH2 but a much lower
deviation for MPEG-b-PLL(Z). The PEG curve also overestimated the block copolymer’s Mw. It is instructive to note
that because the constituent blocks in a copolymer usually
have different refractive indices, the GPC elution curve is only
truly representative of its molecular weight distribution if the
chemical composition of the block copolymer is invariant with
the elution volume.22
MALDI-TOF Mass Spectrometry
Molecular Weight Determination
With the respective values of n and m of the MPEG and
PLL(Z) blocks known, the Mn of the block copolymer, MPEG-bPLL(Z), was assessed:
The molecular weights of MPEG-NH2 and MPEG-b-PLL(Z) were also measured by MALDI-TOF MS, using two
different matrix systems: 1,8-dihydroxyanthrone (dithranol)
and R-cyano-4-hydroxycinnamic acid (R-CHCA). Significant
successes have been recorded in the application of the dithranol
matrix in the MALDI MS of synthetic polymers in the past
decade10 while R-CHCA has found wide utility in the analysis of
peptides and proteins.23
MALDI-TOF Mass Spectra of Homopolymer
’ MOLECULAR WEIGHT DETERMINATION BY ALTERNATIVE METHODS
Gel Permeation Chromatography
The GPC experiments to determine the molecular weights
of MPEG-NH2 and MPEG-b-PLL(Z) were carried out with
BHT-stabilized THF as mobile phase (cf. Figure S4 in the
Supporting Information). Twelve polystyrene (PS) and five
PEG narrow polydispersity standards were used as calibrants
to obtain the universal calibration curves. The PEG calibration
curve gave a better polydispersity index (PDI) than the
PS curve for MPEG-NH2. The converse was the case for
The MS of MPEG-NH2, obtained with sodium cationization
and dithranol, gave an envelope of partially mass-resolved signals
centered at 4900 Da (Figure S5 in the Supporting Information).
Two clusters of signals (labeled i and ii) were observed. Similar
peak clusters were separated by a nominal value of 44 Da, which
is consistent with the (OCH2CH2)n repeating unit of
MPEG-NH2. Furthermore, the i and ii peaks were separated
by 16 Da; implying the presence of nonsodiated (i) and sodiated
(ii) polymer chains. The nonsodiated peaks were probably due
to adventitious lithium adducts of the polymer.24 The onset and
end of the high signal intensity were observed around 4 and
6 kDa, respectively.
The combined molecular weight of the homopolymer’s endgroups was estimated from its mass spectrum,10,25 as exemplified
below, using the peak at 4903.8027 (Mp). To calculate the
combined molecular weight of the end-groups (Me) from the
selected m/z signal, the atomic mass of sodium was first
subtracted from the mass of the peak, and the result was then
divided by the molecular weight of the repeating unit to afford
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the number of repeating units (n) of the polymer chain:
4903:80 22:99 ¼ 4880:81
4880:81
¼ 110:776
44:06
0:776 44:06 ¼ 34:19
Check : Me ¼ MCH3 þ MNH2 ¼ 15:04 þ 16:03 ¼ 31:07 Da
The product of the residual value of n (i.e., 0.776) and the
molecular weight of the repeating unit gave the combined mass of
both end-groups as 34.19 Da, which is close to the total mass of
the methyl and amino end-groups. The difference (ca. 3 Da)
between the experimental and calculated values is isotoperelated.
The MS of MPEG-NH2 in the R-CHCA matrix was also
examined (Figure S6 in the Supporting Information). It proved
to be better resolved than the dithranol-based spectrum, showing
the polymer chains present as mass-resolved signals. The expanded portion of the spectrum revealed three major series of
peaks (i, ii, and iii), which were each 44 Da apart. Within each set
of peaks having the same number of repeating units, i and ii were
lower than iii by 33 and 20 Da, respectively. The peaks were
assigned, based on the n and Me calculations (vide supra), after an
extensive series of permutations of the adventitious cations (such
as, Liþ, Naþ, and Kþ)17 with the expected Hþ ions. An underlying factor in the calculations and subsequent assignment of
peaks was the proximity of the calculated values to the theoretical
Me (31.07 Da).
Considering the six consecutive peaks in the m/z 4800 region
(Table S1 in the Supporting Information), for example, the
signals at m/z 4825 and 4869 were assigned to the MPEG-NH2
polymer chain with 108 and 109 oxyethylene repeating units,
respectively, with proton, lithium and sodium adducts (Mþ þ
5Hþ þ Liþ þ Naþ).26 The peaks at m/z 4836 and 4880 had two
proton adducts (Mþ þ 2Hþ); so that n = 109 and 110,
respectively. The m/z 4849 and 4893 signals, respectively,
corresponded to 109 and 110 oxyethylene repeating units, as
well, but were cationized with two adducts of lithium and a
proton (Mþ þ Hþ þ 2Liþ). Consequently, the MS signals
at m/z 4836, 4849, and 4869 can be attributed to the MPEGNH2 chain with 109 repeating units of oxyethylene (i.e.,
(OCH2CH2)109). The agreement of the experimental and
theoretical data lends credence to the validity of this approach.
Nevertheless, requisite software is being developed27 as the
foregoing approach is laborious.
MALDI-TOF Mass Spectrum of Block Copolymer
The MALDI-TOF MS of MPEG-b-PLL(Z) with the dithranol
matrix, and CF3COONa as cationization agent, neither gave
signals in the linear nor reflectron modes. The reason for this has
yet to be elucidated, as peptides have been previously analyzed
using dithranol.28 A partially resolved spectrum (Figure S7 in the
Supporting Information) was, however, obtained with the RCHCA matrix. The MS showed three major envelopes of signals
centered on 5, 10, and 15 kDa. In the first envelope in the m/z
46 kDa region, two series of signals, each bearing a repeating
unit of 44 Da, were discernible. The other envelopes of intense
signals in the higher mass region were not mass-resolved.
On the basis of the observation of peaks separated by 44 Da,
which is consistent with the oxyethylene repeating unit, in the
MALDI-TOF MS of MPEG-b-PLL(Z), it appears that a main
fragmentation process involving the cleavage of the block
ARTICLE
copolymer’s ethylamide linkage (OCH2CH2NHCO) to
the two constituent blocks (i.e., MPEG and PLL(Z)) may have
occurred. Przybilla et al.29 reported a similar observation for
poly(ethylene oxide)-b-poly(p-phenylene ethynylene). Notably,
the lowering of the baseline observed at high m/z in the MS is
more of a reflection of the low molecular weight component of
samples than a saturation of the detector.17
In Table 2, the nominal molecular weight values of the
homopolymer, MPEG-NH2, and block copolymer, MPEG-bPLL(Z), obtained from 1H NMR, GPC, and MALDI-TOF MS
analyses are compared.
’ CONCLUSION
The utility of 1H NMR in Mn determination of polymers has
been discussed. Some known equations have been modified and
requisite new equations have been developed. The average
molecular weights of the model polymers were also determined
by GPC and MALDI-TOF MS, and the concomitant data were
compared with good agreement. The Mn determinations of
MPEG-NH2 and MPEG-b-PLL(Z) highlight the application of
1
H NMR in this area. 1H NMR is rapidly becoming routine and
remains unrivalled in the elucidation of polymer microstructure.
The current state-of-the-art also bodes well for the surmounting,
presently, of one of its foremost drawbacks—the inability to
measure Mw. 1H NMR spectroscopy is a fast, reproducible, and
relatively simple technique.
Although GPC is the most widely used method for the
determination of molecular weight distribution of polymers,
the strong dependence of its data on the calibrant, as exemplified
by the model polymers herein, remains an encumbrance. Additionally, GPC is a relative method, requiring a molecular weight
detector, and can be used only in conjunction with other absolute
methods. It is equally noteworthy that in block copolymers, for
example, where detailed information about segment composition
and block length are pertinent,30 GPC is incapable of measuring
the molecular weight of the constituting blocks. The molecular
weight analysis of polymers by MALDI-TOF MS, on the other
hand, is a relatively new and auspicious (absolute) method but it
is plagued by a number of shortcomings, albeit mostly nascent.
The difficulties and uncertainties associated with matrix choice,
sample preparation, and the interpretation of the mass spectra,
for instance, detract from its potential benefits.
It is incontrovertible that each of the methods discussed above
has pros as well as cons with respect to the molecular weight
determination of polymers, and ideally complement one another.
In a hypothetical scenario of mutual exclusivity, however, 1H
NMR has the advantage of not only being simple and routine, but
fundamentally multifarious, yielding reliable information regarding polymer microstructure and molecular weight, among others.
1
H NMR is a more readily available teaching and learning tool in
comparison to GPC and MALDI-TOF MS.
’ ASSOCIATED CONTENT
bS Supporting Information
This includes a student laboratory handout and details of the
analytical parameters, calculations, mechanism of polymerization, and spectra (1H NMR, GPC, MALDI-TOF MS) for the
model polymers. This material is available via the Internet at
http://pubs.acs.org.
1103
dx.doi.org/10.1021/ed100461v |J. Chem. Educ. 2011, 88, 1098–1104
Journal of Chemical Education
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: chigginbotham@ait.ie.
’ ACKNOWLEDGMENT
We gratefully acknowledge the financial support of the Irish
Government’s National Development Plan (NDP) Technological Sector Research program (Strand III). We also thank Stefan
Oscarson (CSCB, University College Dublin) for the use of,
and Florence Sallas (UCD) for help with, the MALDI-TOF mass
spectrometer.
’ ADDITIONAL NOTE
a
A low-frequency 1H NMR spectrometer can be used for the
molecular weight analysis of polymers (Mn e 25,000) providing
the salient proton resonance peaks are properly resolved for their
accurate assignment and subsequent comparison.
b
Two-dimensional NMR experiments, such as the protonproton correlation spectroscopy (COSY), facilitate accurate peak
assignments.
c
The molecular weight determination of more complex polymer
systems (e.g., random copolymers) by 1H NMR can be quite
challenging because of the polymers’ often-complicated spectra. In
cases as these, knowledge of the polymer’s mechanism of polymerization is a prerequisite (see the Supporting Information).
’ REFERENCES
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1104
dx.doi.org/10.1021/ed100461v |J. Chem. Educ. 2011, 88, 1098–1104
Polymer Molecular Weight Analysis by 1H NMR Spectroscopy
Josephat U. Izunobi and Clement L. Higginbotham*
Polymer Engineering Department, Athlone Institute of Technology, Dublin Road, Athlone, Ireland
*e-mail: chigginbotham@ait.ie
Table of Contents
Instrumentation
Proton NMR Spectroscopy
Gel Permeation Chromatography
MALDI-TOF Mass Spectrometry
S2
S2
S2
Calculations
Theoretical Molecular Weight of MPEG-NH2 2
Theoretical Molecular Weight of MPEG-b-PLL(Z) 4
S3
S3
MALDI-TOF MS Peak Assignment (Table S1)
S4
Mechanism of Polymerization
S5
References
S6
1
H NMR Spectra
Homopolymer MPEG-NH2 2
Block Copolymer MPEG-b-PLL(Z) 4
S7
S7
GPC Plots
S8
MALDI-TOF MS Spectra
Homopolymer MPEG-NH2 2 (Dithranol/CF3COONa)
Homopolymer MPEG-NH2 2 (α-CHCA/TFA)
Block Copolymer MPEG-b-PLL(Z) 4
S9
S10
S11
Student Laboratory Handout
S13
Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
Instrumentation
Proton NMR Spectroscopy
1
H NMR was carried out in DMSO-d6 at 60 oC on a Varian Inova 500 spectrometer at 499.8
MHz, using tetramethylsilane (TMS) as internal standard. About 1–5% w/v sample solutions were used
in the 1H NMR measurements. Two-dimensional NMR (COSY) experiments were run on a Varian
Inova 500 spectrometer.
Gel Permeation Chromatography
GPC was conducted at a flow rate of 1.0 mL min–1 in tetrahydrofuran (THF; stabilized with 250
ppm BHT) at 40 oC, using a Polymer Laboratories PLgel 5 μm MIXED-D column (300 x 7.5 mm) in a
PL-GPC 120 integrated system instrument, equipped with a PL-AS RT GPC Autosampler and PL
DataStream monitor, for data acquisition, running on CirrusTM GPC software. The system was
calibrated with narrow polydispersity polystyrene (PS) and polyethylene glycol (PEG) standards
(Polymer Laboratories, UK), and the signals were refractive-index detected.
MALDI-TOF Mass Spectrometry
MALDI-TOF MS measurements were done on a Scientific Analysis Instruments LaserToF LT3
mass spectrometer equipped with a pulsed UV 337 nm nitrogen laser. Spectra were acquired in
positive ion and linear modes with an acceleration voltage of 20 kV. The data was summed over 512
laser shots; slowly moving the probe to avoid poor signals as well as the complete ablation of the thin
analyte at a single spot. The laser power was tuned to yield sufficient signals. Analyte solutions were
prepared by mixing 1.0 μL each of 100 mg mL–1 of dithranol, 1.0 mg mL–1 of CF3COONa and 2.0 mg
mL–1 of the polymer in anhydrous THF. 1.0 μL of the resulting mixture was spotted, in duplicate, on a
MALDI sample plate and air-dried at ambient temperature. With α-CHCA, 1.0 μL of saturated matrix
solution (in 1:1 acetonitrile–water and 0.1% TFA solution) and 1.0 μL of the polymer solution (2.0 mg
mL–1 in anhydrous THF) were mixed to prepare the analyte solutions. 1.0 μL of the resulting mixture
was spotted, in duplicate, on a MALDI sample plate and dried in air.
S2
Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
Calculations
Theoretical Molecular Weight of MPEG-NH2 2
C = 12.01, H = 1.01, O = 16.00, N = 14.01.
Structural Formula:
H3C
O
NH2
113
Molecular Formula:
Empirical Formula:
CH3[OCH2CH2]113NH2
C227H457O113N
= 227(12.01) + 457(1.01) + 113(16.00) + 14.01
= 2726.27 + 461.57 + 1808 + 14.01
Molecular Weight
= 5009.85 g mol–1
Theoretical Molecular Weight of MPEG-b-PLL(Z) 4
C = 12.01, H = 1.01, O = 16.00, N = 14.01.
O
Structural Formula:
H3C
O
N
H
N
113 H
H
17
(CH2)4
HN
O
Molecular Formula:
Empirical Formula:
O
CH3[OCH2CH2]113NH[COCH((CH2)4NHCO2CH2C6H5)NH]17H
C465H763O164N35
= 465(12.01) + 763(1.01) + 164(16.00) + 35(14.01)
= 5584.65 + 770.63 + 2624 + 490.35
Molecular Weight
= 9469.63 g mol–1
S3
Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
MALDI-TOF MS Peak Assignment
The calculated values for six consecutive peaks in the m/z 4800 region of the MALDITOF mass spectrum of MPEG-NH2 2 are shown in Table S1 below for illustrative purposes.
Table S1. MALDI-TOF MS signals of homopolymer MPEG-NH2 2 in the m/z 4800 region, showing
peak assignments based on the number of repeating units, mass of end-groups and adduct cations.
MALDI-TOF MS signals (m/z)
4836
4849
4869
Cations
4825
+
H
Li+
Na+
K+
2H+
H+ + Li+
H+ + Na+
H+ + K+
2H+ + Li+
2H+ + 2Li+
H+ + 2Li+
H+ + Li+ + Na+
2H+ + Li+ + Na+
4H+ + Li+ + Na+
5H+ + Li+ + Na+
H+ + 2Li+ + Na+
𝑛
109
109
108
108
109
109
108
108
109
109
109
108
108
108
108
108
𝑀𝑒
21.46
15.52
43.53
27.42
20.44
14.51
42.52
26.41
13.50
6.56
7.57
35.58
34.57
32.55
31.54
28.64
𝑛
109
109
109
108
109
109
109
108
109
109
109
109
109
108
108
108
𝑀𝑒
32.46
26.52
10.47
38.42
31.44
25.51
9.46
37.41
24.50
17.56
18.57
2.52
1.51
43.55
42.54
39.64
* Calculation:
5H+ + Li+ + Na+ = 5(1.01) + 6.94 + 22.99 = 34.98
m/z 4825 − 34.98 =
4790.02
44.06
= 108.7158
0.7158 x 44.06 = 31.54
𝑛
110
109
109
109
110
109
109
109
109
109
109
109
109
109
109
109
𝑀𝑒
1.4
39.52
23.47
7.36
0.38
38.51
22.46
6.35
37.50
30.56
31.57
15.52
14.51
12.49
11.48
8.58
𝑛
110
110
109
109
110
110
109
109
110
110
110
109
109
109
109
109
𝑀𝑒
21.40
15.46
43.47
27.36
20.38
14.45
42.46
26.35
13.44
6.50
7.51
35.52
34.51
32.49
31.48
28.58
4880
𝑛
110
110
110
109
110
110
110
109
110
110
110
110
110
109
109
109
𝑀𝑒
32.4
26.46
10.41
38.36
31.38
25.45
9.40
37.35
24.44
17.50
18.51
2.46
1.45
43.49
42.48
39.58
4893
𝑛
111
110
110
110
111
110
110
110
110
110
110
110
110
110
110
110
𝑀𝑒
1.34
39.46
23.41
7.30
0.32
38.45
22.40
6.29
37.44
30.50
31.51
15.46
14.45
12.43
11.42
8.52
* 𝑛 = no. of repeating units, 𝑀𝑒 = total mass of end-groups.
* Agreeable 𝑀𝑒 values in bold.
* Theoretical total mass of end groups: 𝑀𝐶𝐻3 + 𝑀𝑁𝐻2 = 31.07
S4
Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
Mechanism of Polymerization
It is crucial to know the mechanism of polymerization when determining the number-average
molecular weight (𝑀n ) of polymers by 1H NMR spectroscopy, especially when analyzing complex
polymer systems. The proposed mechanism for the block copolymer is delineated in Figure S1.
The mechanism of reaction for the formation of the block copolymer, MPEG-b-PLL(Z) 4 from
ε-(benzyloxycarbonyl)-L-lysine N-carboxyanhydride, L-Lys(Z)-NCA 1, using MPEG-NH2 2 as macroinitiator was anionic ring-opening polymerization (ROP). The anionic ROP proceeds via the “normal
amine” mechanism (1,2), outlined below.
O
(a)
O
HN
+
..
H2N
O
OCH3
n
O
(CH2)4
CbzHN
1
2
_ CO
2
O
(b)
O
HN
+
O
(CH2)4
O
..
H2N
N
H
(CH2)4
CbzHN
O
OCH3
n
NHCbz
1
3
_ (m-1) CO
2
(c)
H
H
N
O
m
N
H
O
OCH3
n
(CH2)4
NHCbz
4
Figure S1: Proposed “normal amine” mechanism for the formation of MPEG-b-PLL(Z) 4.
To initiate the ring-opening reaction of L-Lys(Z)-NCA 1, the lone-pair electrons of the terminal
primary amino group of MPEG-NH2 2 exclusively attacks the carbonyl carbon (C-5) of the Ncarboxyanhydride ring (of L-Lys(Z)-NCA, 1), with concomitant decarboxylation (cf. Figure S1(a)).
S5
Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
Chain growth (propagation) subsequently proceeds similarly via a nucleophilic attack on the C-5 of
another NCA molecule (Figure S1(b)).
The initiation step (a) is faster than the propagation step (b) because the primary aliphatic
amino functionality of the macroinitiator (MPEG-NH2, 2) is more nucleophilic than the growing active
chain end (1). Consequently, all the molecules of MPEG-NH2 should be incorporated into the growing
L-Lys(Z)
peptide chain to afford the block copolymer, MPEG-b-PLL(Z) 4. The polymerization
reaction is self-terminating (c) – ceasing when L-Lys(Z)-NCA 1 is exhausted.
References
1. Kricheldorf, H. R. α-Aminoacid-N-Carboxyanhydrides and Related Heterocycles; SpringerVerlag: Berlin, 1987; pp 1–213.
2. Goodman, M.; Peggion, E. Pure Appl. Chem. 1981, 53, 699–714.
S6
Supplemental Information
1
2011
Izunobi, J. U.; Higginbotham, C. L.
H NMR Spectra
Figure S2: 1H NMR spectrum (DMSO-d6; 60 oC) of the homopolymer, MPEG-NH2 2, with peak
assignments. (Inset: 3.72–2.68 ppm, enlarged.)
Figure S3: 1H NMR spectrum (DMSO-d6; 60 oC) of the block copolymer, MPEG-b-PLL(Z) 4, with
peak assignments. (Inset: 3.42–3.04 ppm, enlarged.)
S7
Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
GPC Plots
Figure S4: Molecular weight distribution plots (GPC) of the homopolymer, MPEG-NH2 2, and the
block copolymer, MPEG-b-PLL(Z) 4, using narrow polydispersity standards (a) polystyrene (PS) and
(b) polyethylene glycol (PEG).
S8
Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
MALDI-TOF MS Spectra
Figure S5: MALDI-TOF MS spectrum of MPEG-NH2 2 in dithranol/CF3COONa. (Inset: m/z 4000–6000 and m/z 4920–5180, enlarged.)
S9
Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
Figure S6: MALDI-TOF MS spectrum of MPEG-NH2 2 in α-CHCA/TFA. (Inset: m/z 4000–6000 and m/z 4860–5160, enlarged.)
S10
Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
Figure S7: MALDI-TOF MS spectrum (α-CHCA/TFA) of block copolymer, MPEG-b-PLL(Z) 4.
S11
Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
Student Laboratory Handout
Aim: To determine polymer number-average molecular weight (𝑀n ) using 1H NMR spectroscopy.
Overview
The molecular weight measurement and analysis of polymers is of fundamental importance,
especially because of the intrinsic relationship of polymer molecular weight to its physical properties.
Typically, the area of a 1H NMR peak is proportional to the molar concentration of the species
resonating at the given chemical shift value, i.e., the area or intensity of the proton signal of a given
species is proportional to the amount of that species present in a given sample. Since the numberaverage molecular weight of a polymer (𝑀n ) is a summation of the product of the mole fraction of each
species and its molecular weight, and is dependent on the total number of polymer particles in its dilute
solution regardless of polymer size (weight), 1H NMR spectroscopy can be used to determine 𝑀n .
Procedure
1.
Collection of Spectra
In the collection of the requisite 1H NMR spectra, good sample preparation is paramount as the quality
of the resulting spectrum has a profound effect on 𝑀n determination.
• Dissolve 1–5% w/v of the polymer in a suitable deuterated solvent.
The quantity of dissolved polymer is vital. If the concentration is too low, the peaks of the polymer’s
end-groups, for example, may become lost in the baseline. Also, the peaks from common contaminants
(e.g., water) tend to dominate the spectra. Highly concentrated solutions result in a broadening of
signals. Filter off any solid particles and avoid very viscous solutions.
• Load, set up, and acquire spectrum.
• Process the acquired spectrum.
This usually involves performing a number of data processing tasks, such as a Fourier Transform,
phasing, resolution and/or sensitivity enhancement, peak-picking and integration, in order to plot the
required spectrum.
S12
Supplemental Information
2.
2011
Izunobi, J. U.; Higginbotham, C. L.
Analysis of Spectra
The accurate measurement of 𝑀n hinges on the proper integration and full assignment of the requisite
peaks in the 1H NMR spectrum.
• Carry out a complete peak assignment.
2D-NMR spectroscopy, such as COSY, usually facilitates the accurate assignment of 1H NMR peaks.
• Mark out a reference peak (for numerical integration).
To obtain a reliable baseline for numerical integration, identify an isolated resonance signal and assign
a theoretical value based on the number of protons resonating at that chemical shift (δ). (For example,
the integration value for the singlet at 5.01 ppm (C6H5CH2–; MPEG-b-PLL(Z)) in Figure S3 was set to
2.0.) As much as possible, the chosen reference peak should be distinct and prominent, and should not
be used in the 𝑀n calculations.
• Identify well-resolved and salient peaks for 𝑀n determination.
In cases where the resonance signals required for the determination of Mn overlap with other peaks, the
normalized peak area is obtained indirectly by subtraction.
• Extract the values of the salient peak areas from the 1H NMR spectrum and tabulate.
Note: Use area of peak; not height of peak.
Model Table (Table S2):
Moiety
Chemical Shift (δ)
(ppm)
Peak Area
No. of Protons
No. of Repeating Units
CH3O–
–(OCH2CH2)n–
ε-CH2
C6H5CH2–
3.26
3.53
2.99–2.97
5.01
0.18
26.71
2.05
2.00
3
4
2
2
1
n
m
N/A (reference peak)
3.
Calculations
The values collected in the table (Table S2) are appropriately substituted into the requisite equations.
*(see this Journal for equations.)
(a)
To determine the number of repeating units (n)
•
Choose the moiety (x) with the unknown number of repeating units and an end-group (y) from
S13
Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
the Moiety column of the table (cf. Table S2).
•
Substitute into eqn. (17).
𝑎𝑥 𝑚𝑦 𝑛𝑦
𝑛𝑥 =
𝑎𝑦 𝑚𝑥
(17)
where 𝑎𝑥 = peak area of moiety x, 𝑛𝑥 = no. of repeating units of moiety x, 𝑚𝑥 = no. of protons
of moiety x, 𝑎𝑦 = peak area of moiety y, 𝑛𝑦 = no. of repeating units of moiety y, and 𝑚𝑦 = no.
of protons of moiety y.
(b)
•
To determine polymer molecular weight (𝑴𝐧 )
Calculate the formula molecular weight (molar mass) of the repeating unit (𝑀0 ). (For example,
for –(OCH2CH2)n–, 𝑀0 = 44.06.)
•
Calculate the combined formula molecular weight of the end-groups (𝑀𝑒 ). (e.g., CH3 + NH2 =
31.07.)
•
Substitute into eqn. (18).
(18)
𝑀n = 𝑛𝑀0 + 𝑀𝑒
where 𝑛 = no. of repeating units, 𝑀0 = molecular weight of one repeating unit, and 𝑀𝑒 =
combined molecular weight of the end-groups.
(c)
To determine copolymer composition
•
Choose moieties (x and y) from the constituent polymers (polymers A and B, respectively) of
the copolymer. For example, ε-CH2 from PLL(Z) (polymer A) and –(OCH2CH2)n– from MPEG
(polymer B). Note: end-groups cannot be used.
•
Substitute into eqn. (19).
𝑎𝑥
𝑚𝑥
% (polymer 𝐴) = 𝑎
𝑎𝑦 x 100%
𝑥
+
𝑚𝑥 𝑚𝑦
(19)
where 𝑎𝑥 = peak area of moiety x and 𝑚𝑥 = no. of protons of moiety x for constituent polymer A,
and 𝑎𝑦 = peak area of moiety y and 𝑚𝑦 = no. of protons of moiety y for constituent polymer B.
(d)
To determine copolymer degree of polymerization
The degree of polymerization of a copolymer may be determined in two ways:
(i) by first determining the number of repeating units (n) of one of the constituent polymers, using
eqn. (17), and subsequently substituting the previously obtained n (of the first constituent polymer)
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Supplemental Information
2011
Izunobi, J. U.; Higginbotham, C. L.
into eqn. (17) of the other constituent polymer. *(see this Journal for an example.)
(ii) by determining the number of repeating units (n) of one of the constituent polymers, using eqn.
(17) and then substituting for n in eqn. (20).
𝑚
𝑧
=
𝑛
100% − 𝑧
(20)
where 𝑚 = degree of polymerization of the second constituent polymer, 𝑛 = no. of repeating
units of the first constituent polymer, and 𝑧 = percentage monomer ratio of the second
constituent polymer.
Note: percentage monomer ratio (𝑧) = copolymer composition (calculated above in (c)).
To determine copolymer molecular weight (𝑴𝐧 )
(e)
The 𝑀n of a copolymer can be estimated via one of two ways viz: (i) by the summation of the atomic
weights of its constituent atoms and (ii) by appropriately substituting into eqn. (21).
(i)
Atomic weight summation:
•
Using eqn. (17), find n and m.
•
Calculate the formula molecular weight.
Example:
C = 12.01, H = 1.01, O = 16.00, N = 14.01.
MPEG-b-PLL(Z)
NHCbz
(CH2)4
O
H3CO
H
N
O
O
n
Formula Mol. wt.:
𝑀n
(ii)
•
=
=
75.1
44.06n
43.08
N
H
262.34m
H
m
1.01
75.1 + 44.06 x 111.29 + 43.08 + 262.34 x 17 + 1.01
9482.41 g mol–1
Substituting into eqn. (21):
Calculate the formula molecular weight of one repeating unit of constituent polymer A (𝑀𝐴 )
and the formula molecular weight of one repeating unit of constituent polymer B (𝑀𝐵 ).
Example: for –(OCH2CH2)n–, i.e., the repeating unit of MPEG (polymer A), 𝑀𝐴 = 44.06; and
for PLL(Z) (polymer B), 𝑀𝐵 = 262.34 for –[COCH((CH2)4NHCO2CH2C6H5)NH]m–.
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•
2011
Izunobi, J. U.; Higginbotham, C. L.
Calculate the formula molecular weight of the copolymer linkage (𝑀𝑗 ) and the combined
formula molecular weight of the end-groups (𝑀𝑒 ).
Example: for the block copolymer, MPEG-b-PLL(Z), 𝑀𝑗 = 43.08 (CH2CH2NH) and 𝑀𝑒 = 32.05
(CH3O + H).
•
Substitute into eqn. (21).
𝑀𝑛 = 𝑛𝑀𝐴 + 𝑀𝑗 + 𝑚𝑀𝐵 + 𝑀𝑒
(21)
where 𝑛 = no. of repeating units of polymer A, 𝑀𝐴 = molecular weight of one repeating unit of
polymer A, 𝑀𝑗 = molecular weight of the copolymer linkage, 𝑚 = no. of repeating units of
polymer B, 𝑀𝐵 = molecular weight of one repeating unit of polymer B, and 𝑀𝑒 = combined
molecular weight of the end-groups.
Example:
Copolymer: MPEG-b-PLL(Z)
For n = 112, m = 17, 𝑀𝐴 = 44.06, 𝑀𝐵 = 262.34, 𝑀𝑗 = 43.08, and 𝑀𝑒 = 32.05,
Substituting into eqn. (21):
𝑀𝑛 = 𝑛𝑀𝐴 + 𝑀𝑗 + 𝑚𝑀𝐵 + 𝑀𝑒
𝑀𝑛 = 112 x 44.06 + 43.08 + 17 x 262.34 + 32.05
𝑀𝑛 = 9469.63 g mol−1
(21)
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