Crossover experiments applied to network formation reactions: Improved strategies for counting elastically inactive molecular defects in PEG gels and hyperbranched polymers

Article abstract of DOI:10.1021/ja5042385

Molecular defects critically impact the properties of materials. Here we introduce a paradigm called isotopic labeling disassembly spectrometry (ILDaS) that facilitates unprecedented precise experimental correlations between elastically inactive network defects (dangling chains and primary loops) and network formation kinetics and precursor structure. ILDaS is inspired by classical crossover experiments, which are often used to interrogate whether a reaction mechanism proceeds via an inter- or intramolecular pathway. We show that if networks are designed from labeled bifunctional monomers that transfer their labels to multifunctional junctions upon network formation, then the extent of junction labeling correlates directly with the number of dangling chains and cyclic imperfections within the network. We demonstrate two complementary ILDaS approaches that enable defect measurements with short analysis times, low cost, and synthetic versatility applicable to a broad range of network materials including polydisperse polymer precursors. The results will spur new experimental and theoretical investigations into the interplay between polymer network structure and properties.

Full text of DOI:10.1021/ja5042385

Article
pubs.acs.org/JACS
Crossover Experiments Applied to Network Formation Reactions:
Improved Strategies for Counting Elastically Inactive Molecular
Defects in PEG Gels and Hyperbranched Polymers
Huaxing Zhou,† Eva-Maria Schon,†,‡ Muzhou Wang,§ Matthew J. Glassman,§ Jenny Liu,†
̈
Mingjiang Zhong,†,§ David Díaz Díaz,‡,∥ Bradley D. Olsen,§ and Jeremiah A. Johnson*,†
§
†Department of Chemistry and Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts
Avenue, Cambridge, Massachusetts 02139, United States
‡Institut fur Organische Chemie, Fakul tat fur Chemie und Pharmazie, Universitat Regensburg, Universitatsstr. 31, 93053,
̈
̈
̈
̈
̈
Regensburg, Germany
∥IQAC-CSIC, Jordi Girona 18-26, 08034 Barcelona, Spain
S
* Supporting Information
ABSTRACT: Molecular defects critically impact the proper-
ties of materials. Here we introduce a paradigm called “isotopic
labeling disassembly spectrometry” (ILDaS) that facilitates
unprecedented precise experimental correlations between
elastically inactive network defects (dangling chains and
primary loops) and network formation kinetics and precursor
structure. ILDaS is inspired by classical crossover experiments,
which are often used to interrogate whether a reaction
mechanism proceeds via an inter- or intramolecular pathway.
We show that if networks are designed from labeled
bifunctional monomers that transfer their labels to multifunc-
tional junctions upon network formation, then the extent of junction labeling correlates directly with the number of dangling
chains and cyclic imperfections within the network. We demonstrate two complementary ILDaS approaches that enable defect
measurements with short analysis times, low cost, and synthetic versatility applicable to a broad range of network materials
including polydisperse polymer precursors. The results will spur new experimental and theoretical investigations into the
interplay between polymer network structure and properties.
chains bridging two B3 junctions (Figure 1d). Higher-order
loops and chain entanglements (not shown) are further
examples of elastic defects.
The properties of polymer networks are defined by their
composition and connectivity. Synthetic advances and creative
hierarchical molecular engineering strategies continue to
produce novel polymer networks for a range of next-generation
applications.1−12 All networks, especially those composed of
flexible molecular precursors that are covalently linked under
irreversible conditions, e.g., polymer networks, will possess
chemical and topological defects across various lengths
scales.13,14 For example, consider a network with trifunctional
branch points, which can be prepared via coupling bifunctional
(A2) and trifunctional (B3) monomers (Figure 1a). Such a
network can possess several distinct junction connectivities. In
the “ideal junction” case (Figure 1b), a B3 molecule is
connected to three unique A2 molecules that are themselves
connected to unique B3 molecules. The “elastically inactive
defects” (Figure 1c) are those where the B3 junction or the A2
chain end possess one or more unreacted functional groups
(dangling chains) or where a single A2 chain has reacted twice
with the same B3 junction (primary loop). Finally, there are
many possible “elastic defects” that can impact network
properties. Examples are catenanes, which are two interlocked
primary loops and “secondary loops” that result from two A2
The experimental methods available for analysis of defects in
real materials (as opposed to simulated ones)15−17 are severely
limited. Spectroscopic techniques can reveal dangling chains if
they have a unique spectroscopic signature and if they are
present in sufficient number.18,19 Rheology can provide
qualitative insights into defect content, though such analysis
is convoluted by the counteracting effects of different defects
on the modulus; this approach requires acceptance of
assumptions related to polymer network structure that have
not been rigorously verified experimentally.20,21
Multiple-quantum NMR (MQ-NMR) techniques16,19,22−24
can provide semi-quantitative information related to secondary
loops and other high-order16 loop defects, but they cannot
discriminate between the elastically inactive dangling chain and
primary loop defects. We recently reported “network
disassembly spectrometry” (NDS), which is the first direct
Received: April 28, 2014
Published: May 29, 2014
© 2014 American Chemical Society
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Figure 1. Schematic of trifunctional end-linked network formation. (a) General reaction between a bifunctional A2 monomer and a trifunctional B3
monomer to form a network. (b) Triply reacted “ideal” junctions. (c) Elastically inactive molecular defects. (d) Two possible elastic defects.
assumption-free method for quantitative analysis of the primary
loop and dangling chain elastically inactive defects in polymeric
networks.25 Though NDS was informative, it suffered from the
need to use monodisperse network precursors, HPLC
separation of network degradation products, and special UV
chromophores for analysis. New developments in network
analysis, and in particular, new synthetic strategies for the
programmed introduction and precise quantification of specific
defects in materials will reveal structure−property relationships
between network topology and network formation conditions,
and will allow for validation of theories14,17,26−38 of network
formation and properties.14,20−33
Herein, we describe a new strategy for network design called
“isotopic labeling network disassembly spectrometry” (ILDaS).
ILDaS is inspired by classical crossover experiments in physical
organic chemistry, which are routinely used to differentiate
between inter- and intramolecular reaction mechanisms.39 In
this case, the extent of isotope crossover from macromer to
junction is directly related to the fraction of elastically inactive
defects within the polymer network. We use ILDaS to provide
direct, unprecedented correlations between elastically inactive
defects and (a) network precursor concentration using
polydisperse precursors, (b) chain length, and (c) reaction
time (kinetics) for a series of end-linked poly(ethylene glycol)
(PEG) hydrogels. ILDaS concepts enable elastically inactive
defect analysis in networks composed of polymer precursors
with any chain length and mass dispersity in a low-cost, high
throughput manner.
AILDaS macromer could be synthesized via polymerization
from a labeled initiator followed by chain end modification or
via desymmetrization of a telechelic molecule. We use the latter
strategy for demonstration of AILDaS (vide infra).
THE SILDAS BUILDING BLOCK
■
Symmetrically Labeled Macromer. SILDaS uses a
mixture of two distinct A2 monomers wherein both are
telechelic and possess cleavable sites near the chain ends; one
possesses labels on both chain ends and the other is nonlabeled
(Figure 2a). These macromers could be prepared via chain end
modification of telechelic polymers with either labeled or
nonlabeled end groups. Again, any label, even two macromers
of different composition, could be used as long as the relative
reactivity of the labeled versus nonlabeled macromers is known.
Given the complementary synthetic approaches to AILDaS and
SILDaS macromers, one of these two strategies is applicable to
a wide range of network materials.
THE KEY TO ILDAS
■
Relating Junction Labeling to Loop Fraction. The
reaction of either macromer type with a trifunctional monomer
yields nine possible junction labeling patterns (Figure 2b). We
refer to these products by their extent of reaction and their
labeling pattern as follows: singly reacted junctions can be
nonlabeled (n00) or labeled (i00); doubly reacted junctions can
be entirely nonlabeled (nn0), singly labeled (ni0), or doubly
labeled (ii0); triply reacted junctions can have any number of
labels between zero and three (nnn, nni, nii, or iii). The first five
of these products, i.e., those that correspond to singly and
doubly reacted junctions, arise from dangling chain defects or
primary cyclic molecules. The latter four products arise from all
possible triply reacted junctions including ideal junctions,
primary loops on triply reacted junctions, and higher order
defects.
Implementations of ILDaS could take many forms. In this
report we describe and demonstrate two distinct, comple-
mentary approaches to network synthesis and analysis that fall
within the ILDaS paradigm. These approaches are referred to as
“asymmetric ILDaS” (AILDaS) and “symmetric ILDaS”
(SILDaS). AILDaS and SILDaS differ by the location of
isotopic labels placed within network precursors (Figure 2a).
Synthetic considerations will define which approach is more
useful for a given material class.
Under the assumption of equal reactivity,32 the probability of
forming each of the above junctions can be easily calculated
(values are listed in Figure 2b). For an AILDaS network with
no primary loops we expect a 1:1 ratio of n00 and i00 at singly
reacted junctions, a 1:2:1 ratio of nn0, ni0, and ii0 at doubly
reacted junctions, and a 1:3:3:1 ratio of nnn, nni, nii, and iii at
triply reacted junctions. For SILDaS, the probabilities depend
on the fraction of nonlabeled A2 macromer (x) as listed in
Figure 2b.
THE AILDAS BUILDING BLOCK
■
Asymmetrically Labeled Macromer. AILDaS uses a
telechelic (A2, Figure 2a) monomer with one isotopically
labeled chain end (i), one nonlabeled chain end (n), and two
cleavable groups located near the chain ends. One must not
necessarily use isotopic labels as long as the chain ends can be
distinguished and their reactivity is equivalent or known. The
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Importantly, for both AILDaS and SILDaS, the probabilities
for forming junctions that do not have primary loops
(“pnon‑loop”) are different than for those that do have primary
loops (“ploop”). Defects that do not possess primary loops have
no effect on the junction probabilities. For example, the
junction labeling distribution for a second order loop (Figure
1d) is identical to an ideal junction (Figure 1b); they are
indistinguishable from ideal junctions in this analysis. In
contrast, catenanes (Figure 1d) will be labeled as if they were
two primary loops. This critical distinction enables the precise
quantification of the number of primary loops directly without
assumptions or deconvolution of complex data sets that depend
on mechanical properties and/or chain mobility.
Based on the discussion above, if an AILDaS network has no
primary loops then it will have a 1:3:3:1 ratio of the
trifunctional junctions shown in Figure 2b regardless of the
number of dangling chains; the latter yield their own sets of
junction products, which can be used to quantify the number of
dangling chains. The same holds for SILDaS when x = 0.5. In
contrast, if the network is 100% cyclic, i.e., it is not a network
but two primary loops connected together in a dumbbell-like
architecture, then the ratio of trifunctional junctions for
AILDaS and SILDaS will be 0:1:1:0 and 1:1:1:1, respectively.
The relationship between the junction ratios and fraction of
trifunctional junctions that contain a primary loop, nλ3, can be
readily derived for any value between these extremes. For
AILDaS, the relationship is identical to that for our previously
reported NDS method. For SILDaS, the junction concen-
trations vary quite differently and they depend on x according
to the following equations (see Supporting Information for
derivations):
[nnn] = x3 + x2(1 − x)nλ
[nni] = 3x2(1 − x) − (3x3 − 4x2 + x)nλ
[nii] = 3x(1 − x)2 − (3x3 − 5x2 + 2x)nλ
[iii] = (1 − x)3 + x(1 − x)2nλ
Given these equations all that is necessary to quantify nλ3 and
the dangling chain content (including the fraction of doubly
reacted junctions that possess a primary loop, nλ2, vide infra) is
knowledge of the relative junction concentrations. We obtain
these values by selective network disassembly and mass
spectrometry of the disassembly products (vide infra). Note
that these relationships were all derived for trifunctional
networks, though the same concepts apply to networks of
any branch functionality f. General equations that relates the
fraction of loops at a given branch functionality, nλf, to the
junction ratios for both AILDaS and SILDaS are provided in
eqs S1 and S3, respectively.
Experimental Validation of AILDaS. PEG-based macro-
mers for AILDaS were prepared from monodisperse PEG diols
with degree of polymerization (m) 12 (PEG12) and 28
(PEG28) (Figure 3a). Both macromers were synthesized via a
desymmetrization sequence that began with carbodiimide
coupling of a norbornene-phenylalanine (Phe) carboxylic acid
to one chain of the PEG oligomer, followed by purification to
yield the monoester, and a second carbodiimide mediated
coupling to the remaining PEG hydroxyl using a norbornene-
Phe-d5 derivative.
Figure 2. AILDaS and SILDaS vary based on the location of mass
labels in bifunctional network precursors. End-linking with a
trifunctional monomer leads to network formation. Dangling chains
give rise to mono- (n00 or i00) and di- (nn0, ni0, ii0) functional
junction products. Fully reacted junctions generate four possible
labeling patterns: nnn, nni, nii, and iii. The probability for forming each
junction depends on whether or not a primary loop exists at that
junction; it is not affected by secondary loop or higher-order loop
formation. General equations that relate the junction formation
probability with branch functionalities (f) and fraction of nonlabeled
macromer (x) values can be found in equations S1−S5.
Polymer networks were constructed using an inverse electron
demand Diels−Alder reaction between the norbornene-
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Figure 3. (a) Chemical structures of the macromers (A2) and the tris-tetrazine (B3) monomer used for demonstration of AILDaS. Network
formation, followed by hydrolysis yields a mixture of disassembly products (structures shown) with known masses. (b) Rheological analysis of
network formation reactions between the PEG28 macromer and T. (c) Mass spectra for doubly charged disassembly products of PEG28-based
networks prepared at three different initial macromer concentrations. (d) Measured and calculated loop fractions as a function of initial macromer
concentration, [PEGm]0, for PEG12 and PEG28 macromers. (e) Evaluation of loop formation kinetics during network formation.
terminated macromers and tris-tetrazine T with 1:1 norborne-
ne:tetrazine stoichiometry (Figure 3a).12,25,40−42 Reactions
were performed both well above and well below the overlap
concentrations (c*) for the network precursors. Soluble,
hyperbranched polymers were obtained for reactions run at
<50 mM and 30 mM for PEG12 and PEG28, respectively.
Above these concentrations, chemical gels were obtained as
confirmed by rheology (Figure 3b). The observation of a G′
and G″ crossover point at time tc, as determined by the time
when tan δ = 1, identifies the gel point for end-reactive polymer
networks with balanced stoichiometry.43 Due to the slow
evolution of N2 gas during the cross-linking reaction,
macroscopic void formation within the parallel plates of the
rheometer was unavoidable; quantitative measurement of the
true bulk moduli was not possible in our experiments. Visual
inspection of samples during and after gelation shows that they
remain translucent, with gas sequestered into large (>1 mm)
voids that span the entire height of the sample. Therefore, the
primary effect of the voids is to reduce the effective volume of
the sample in the testing geometry, with only a minor impact
on tan δ. After complete tetrazine conversion, the materials
were treated with excess 2,3-dichloro-5,6-dicyano-p-benzoqui-
none (DDQ) for 60 min and then 2 M aqueous LiOH solution
for 60 min. Under these conditions, both the ester and imide
linkages from the macromers are hydrolyzed to give the
differentially labeled junction disassembly products (Figure 3a
for trifunctional junctions, Figure S1 for complete list of all
possible junctions).
precise 1:1 functional group stoichiometry, we observe no mass
distributions pertaining to singly or doubly reacted junctions.
Thus, these dangling chain defects are present in very low
abundance; we focus here on analysis of nλ3. Representative MS
spectra of the trifunctional junction products from three gel
samples prepared at varied PEG28 concentration are shown in
Figure 3c. Due to natural isotopic distributions, multiple peaks
are observed for each junction structure; only the three most
prominent are shown. From left to right, the distributions
correspond to nnn, nni, nii, and iii. The spectra are normalized
by the height of the symmetric nni and nii peaks. Under the
assumption that deuterium labeling has no effect on ionization
propensity, the relative concentration of each junction can be
read directly from the MS peak heights.
Trifunctional primary loop fractions (nλ3) for several gels and
sols prepared from PEG12 and PEG28 macromers at various
initial macromer concentrations, [PEGm]0, are plotted along
with calculated loop fractions obtained from Stepto’s rate
theory and Monte Carlo simulation methods (Figure 3d, Table
S1).26,29 As we would expect, the number of primary loops
increases with dilution. The loop fraction curve decreases more
dramatically for the longer PEG28 macromer; loop formation is
less likely for the longer precursor. This trend continues for
longer, polydisperse PEG chains as demonstrated below using
SILDaS. Though these results may seem intuitive/obvious/
expected, a direct assumption-free analysis of the interplay
between loop formation in a polymer network and network
precursor chain length has never before been reported.
The degradation product mixtures were subjected to LC/MS
analysis. In this system, which was allowed to react to
completion (as monitored by tetrazine conversion) with a
Kinetics of Primary Loop Formation During Network
Synthesis. We next applied AILDaS to the temporal analysis
of defects during network formation. In this case, we consider
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several different loop fractions. As before, nλ3 is the fraction of
triply reacted junctions that contain a primary loop (empty
black circles, Figure 3e), which is obtained from the mass
spectra of the triply reacted junctions at different time points.
In analogous fashion, nλ2 is the fraction of doubly reacted
junctions that contain a primary loop (empty red circles, Figure
3e); these values are obtained from the mass spectra of the
doubly reacted (nn0, ni0, and ii0) junctions collected at
different time points (Figure S3). Both nλ3 and nλ2 are by
definition undefined at time zero, since no reactions have
occurred and no trifunctional or bifunctional junctions have
formed. We find that nλ3 is approximately constant throughout
the gelation process, which suggests that loops form at triply
reacted junctions with equal likelihood both before and after
the gel point (labeled tc, Figure 3e). In contrast, nλ2 gradually
decreases until bifunctional junctions cannot be detected (less
than 1% abundance after ∼380 min). In other words, nonloop-
containing doubly reacted junctions, i.e., dangling chains,
persist longer than doubly reacted cyclic molecules. Differences
in mobility of the network bound (nonloop) versus molecular
(cyclic molecule) junctions could explain this trend. Rate
theory analysis (Figure S4) provides qualitative agreement with
these results, though significant quantitative difference suggests
new avenues for theoretical development.
PEG12 and PEG28, and polydisperse PEG105 and PEG136,
symmetrically labeled macromers were prepared. In this case,
the macromers were generated via a one-step carbodiimide-
mediated coupling of labeled and nonlabeled norbornene-Phe
derivatives to the ends of PEG diols to give the labeled and
nonlabeled macromers, respectively (Figure S6). Network
formation reactions were carried out identically to the AILDaS
experiments with one key difference: reactions were performed
with varied fractions of nonlabeled macromer, x.
Figure 4a shows mass spectra for three different x values and
three different initial PEG28 concentrations, [PEG28]0, values
per x value. When x = 0.56, the distributions are relatively
The parameters nλ3 and nλ2 represent fractions specific to a
given junction. It is useful to consider the fraction of all
network junctions that possess loops at a given time. Under the
principle of equal reactivity, the relative concentration of
junction types, e.g., bifunctional and trifunctional, can be
calculated (Figure S5) based on the starting concentration of
trifunctional monomer T ([junctions] = [T]0 = 26.7 mM) and
the measured second order rate constant for the Diels−Alder
coupling reaction (0.00658 M−1 s−1).25 Multiplying nλ3 by
[trifunctional junctions]/[T]0 provides nT3 (filled black circles,
Figure 3e), which is the fraction of all network junctions that
possess a triply reacted primary loop. Similarly, multiplying nλ2
by [bifunctional junctions]/[T]0 provides nT2 (filled red circles,
Figure 3e), which is the fraction of all network junctions that
are cyclic molecules (i.e., doubly reacted primary loops). The
sum of these values, nT3 + nT2, is the total fraction of all primary
loops (both at doubly and triply reacted junctions) at all
junctions (filled blue circles, Figure 3e). The values of nT3 and
nT2 must be zero at time zero, since no junctions have reacted
and no loops have formed. At early time points, the total
fraction of primary loops (nT3 + nT2) increases rapidly. At later
times this value continues to increase, though more slowly. The
same trend is observed for nT3. In contrast, nT2 reaches a
maximum at ∼100 min and then decreases to near zero as the
doubly reacted junctions are converted to triply reacted
junctions. These results conclusively demonstrate that primary
loop formation continues to steadily increase through the gel
point (marked as tc, Figure 3e) even as dangling chains (i.e.,
doubly reacted junctions) are driven to zero.44 To the best of
our knowledge, these data are the first direct experimental
measurements of elastically inactive defect formation kinetics
throughout the entire course of a network formation reaction.
They could not be directly obtained via any known
experimental method; AILDaS makes the task trivial. These
results are of fundamental importance to understanding the
mechanism of network formation. They highlight the pervasive
nature of primary loop defects.
Figure 4. (a) Mass spectra for doubly charged disassembly products of
PEG28-based networks prepared at different initial macromer
concentrations and with different ratios of nonlabeled to labeled
macromer (i.e., x values). (b) nλ3 values as a function of initial
macromer concentration, [PEGm]0, for SILDaS networks prepared
from various x values.
Experimental Validation of SILDaS. To demonstrate
SILDaS in an analogous context to AILDaS, monodisperse
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symmetric; the mass spectrum resembles that of the AILDaS
case. However, note that for SILDaS, the height of iii and nnn
increases with the number of primary loops, which is opposite
to AILDaS. Therefore, the nnn and iii peaks are tallest for the
most dilute sample (30 mM); they gradually decrease in height
as the concentration increases (number of loops decreases).
When x is increased to 0.75, i.e., 3:1 nonlabeled to labeled
macromer, the likelihood of forming labeled junctions
decreases; the junction ratios no longer resemble the symmetric
a:b:b:a pattern observed when x ∼ 0.5. When the mass spectra
are normalized to the height of the nnn peak, a clear change in
the height of the nni peak is observed as a function of
[PEG28]0. Again, this difference reflects the decreasing number
of loops with increased concentration. Interestingly, the
junction concentration equations listed above predict that the
ratio of nnn:nii should be exactly three when x = 0.75 regardless
of the value of nλ3 (see Figure S7 for discussion). The data in
Figure 4a agree with this prediction. The height of nii (marked
with a red dashed line) is ∼33.3% for the three concentrations
tested; the value of nnn:nii for all concentrations is three. This
observation suggests that our assumption of equal ionization
propensity for junction isotopologues is valid, and that the
principle of equal reactivity applies for these network formation
reactions, as the statistics used to derive the equations listed
above depend on equal reactivity.
(SILDaS). Experimental demonstrations of both AILDaS and
SILDaS provided the first direct measurements of cyclic defect
formation in polymer networks as a function of chain length
and reaction kinetics. ILDaS methods provide greatly improved
accuracy and convenience compared to our previous network
disassembly spectrometry (NDS) method and other classical
techniques. Given their synthetic complementarity, AILDaS or
SILDaS can be applied to most types of degradable, covalent
molecular networks. The ease of preparing telechelic polymers
combined with the demonstrated ability to reduce the amount
of isotopic label without sacrificing experimental accuracy
makes SILDaS a particularly convenient, low-cost approach for
these analyses. Our results point to a number of possible areas
where both experiment and theory should be updated. For
example, we find that when nλ3 values are plotted against the
PEG12, PEG28, PEG105, and PEG136 polymer mass fractions
(Figure S8), the data collapse to a single curve. We are
currently exploring the origin for this unexpected scaling (see
Figure S2 caption for discussion). Furthermore, we have found
interesting variations between theory and experiment in studies
of loop formation kinetics (Figure S4). These studies as well as
application of the ILDaS concepts to supramolecular (physical)
networks11,45 and dynamic covalent networks12,46,47 are
underway in our laboratories.
A key advantage of SILDaS is that it offers the opportunity to
measure defects in bulk materials using a small fraction of
labeled material, which, in the case of isotopologues, lowers the
cost of the experiment. We prepared gels using 93% nonlabeled
and 7% labeled macromer (x = 0.93). In this case, nnn and nni
are the dominant peaks in the mass spectrum (Figure 4a). The
height of the nni peak varies with [PEG28]0; the nλ3 values
agree with those obtained using other x values (vide infra).
Values of nλ3 from SILDaS networks prepared from PEG12,
PEG28, PEG105, and PEG136 across several x values and
concentrations are plotted in Figure 4b (Tables S3−S5). The
PEG12 and PEG28 data are overlaid with analogous measure-
ments obtained via AILDaS. There is excellent agreement
between both AILDaS and SILDaS for all x values tested.
Though the standard deviation is slightly higher when x = 0.93
(∼1−4%, Table S4), the measured nλ values fall within
experimental error of AILDaS and SILDaS with smaller x
values. These data demonstrate that SILDaS can be used for
defect measurements with only a small fraction of labeled
macromer. Though these materials were designed for
mechanistic analysis, where added costs are often justifiable,
and we would not likely advocate using any of these isotopically
labeled macromers in large scale commercial applications, we
note here that the cost of labeled macromer varies from ∼4.5¢
(for SILDaS with PEG28 when x = 0.93) to ∼52.3¢ (for
AILDaS with PEG12) per data point shown in Figure 4b. Thus,
SILDaS offers a low cost strategy for the measurement of
elastically inactive defects in networks with polydisperse
precursors.
ASSOCIATED CONTENT
■
S
* Supporting Information
1
Synthetic procedures; H and 13C NMR spectra of isotope
labeled macromers; methods of polymer network formation
and degradation; supplemental figures and schemes cited in the
main text. This material is available free of charge via the
Internet at http://pubs.acs.org.
AUTHOR INFORMATION
■
Corresponding Author
jaj2109@mit.edu
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
J.A.J. and B.D.O. acknowledge support from the National
Science Foundation (CHE-1334703). B.D.O. acknowledges
support from the Institute for Soldier Nanotechnologies (U.S.
Army Research Office contract W911NF-07-D-0004). M.W.
acknowledges funding through a NDSEG Fellowship. D.D.D.
thanks Universitat Regensburg (Anschubfinanzierung von
̈
Wissenschaftlichen Projekten-2011) for funding and DFG for
the Heisenberg Professorship Award. We are grateful for
computational resources on a local cluster administered by the
T. A. Hatton group.
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■
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CONCLUSIONS
■
A new paradigm for the design and analysis of molecular
networks, called “isotopic labeling disassembly spectrometry”
(ILDaS), is introduced. ILDaS offers strategies to experimen-
tally quantify the elastically inactive dangling chain and primary
cyclic defect contents in end-linked networks. The fundamental
and practical aspects of ILDaS were derived and validated for
two cases: asymmetric-ILDaS (AILDaS) and symmetric-ILDaS
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