Direct observation of intermediates in a thermodynamically controlled solid-state dynamic covalent reaction

Article abstract of DOI:10.1021/ja500707z

We present the first polymorph interconversion study that uses solid-state dynamic covalent chemistry (DCC). This system exhibits unexpected and rich behavior, including the observation that under appropriate conditions the polymorph interconversion of a heterodimer proceeds through reversible covalent chemistry intermediates, and this route is facilitated by one of the two disulfide homodimers involved in the reaction. Furthermore, we demonstrate experimentally that in all cases a dynamic equilibrium is reached, meaning that changing the milling conditions affects the free energy difference between the two polymorphs and thus their relative stability. We suggest that this effect is due to the surface solvation energy combined with the high surface to volume ratio of the nanocrystalline powder.

Full text of DOI:10.1021/ja500707z

Article
pubs.acs.org/JACS
Direct Observation of Intermediates in a Thermodynamically
Controlled Solid-State Dynamic Covalent Reaction
Ana M. Belenguer,*,†,§ Giulio I. Lampronti,‡,§ David J. Wales,† and Jeremy K. M. Sanders*,†
†Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.
‡Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K.
S
* Supporting Information
ABSTRACT: We present the first polymorph interconversion
study that uses solid-state dynamic covalent chemistry (DCC).
This system exhibits unexpected and rich behavior, including
the observation that under appropriate conditions the
polymorph interconversion of a heterodimer proceeds through
reversible covalent chemistry intermediates, and this route is
facilitated by one of the two disulfide homodimers involved in
the reaction. Furthermore, we demonstrate experimentally that
in all cases a dynamic equilibrium is reached, meaning that
changing the milling conditions affects the free energy
difference between the two polymorphs and thus their relative
stability. We suggest that this effect is due to the surface
solvation energy combined with the high surface to volume
ratio of the nanocrystalline powder.
is dictated by its relative free energy; therefore, any phenomenon
that can affect the stability of one or more DCL members will
affect the concentration of all the library members inthe DCLand
therefore the overall DCL composition. For example, the
addition of a template which selectively binds noncovalently to
a specific library member amplifies the amount of this particular
member at the expense of other less successful molecules.3c The
dynamic equilibrium in DCL is easily demonstrated by the
establishment of a new equilibrium in response to any perturbing
stimulus. Many reversible reactions have been explored to date in
DCC,3f,6 including the base-catalyzed disulfide exchange used in
this work; adding acid quenches the exchange and freezes the
composition for analysis.2
In this report, we extend the study of DCC from the traditional
dilute solution to the solid state. Not only does this abolish the
need for substantial quantities of solvents but also crystal
stability2 can act as a new driving force for establishing the
position of the equilibrium.
1.2. Mechanochemistry Induced by Ball Mill Grinding.
Mechanochemistry7 is the field of chemical reactions induced by
mechanical energy; this can involve reagents in any aggregate
state (solid, liquid, or even gas), though typically it refers to fully
solid state processes.8 The term mechanochemistry embraces a
broad range of areas, the mechanical energy required to activate
the chemical reaction being provided by ultrasound,9 an atomic
force microscope (AFM),10 manual and mechanical grinding,11
vortex grinding,12 or even simple mechanical forces, such as
1. INTRODUCTION
Using both ball mill neat grinding and ball mill liquid assisted
grinding (LAG), we demonstrate here the rich and unexpected
behavior of a simple dynamic covalent chemistry (DCC) system,
focusing on three remarkable observations: (i) the system
exhibits reversible interconversion of polymorphs of a disulfide
heterodimer under thermodynamic control; (ii) in the presence
of catalyst, polymorph interconversion involves sequential
covalent reactions with observable covalent intermediates; (iii)
one of the intermediates facilitates the covalent chemistry.
We conclude that the outcome of these ball mill grinding
reactions is driven by thermodynamics associated with nano-
particulate surface solvation. More importantly, we believe this
interpretation to be applicable to many other ball mill grinding
reactions, not necessarily involving covalent chemistry. The
system under study is illustrated in Figure 1.
Since this work is effectively the first detailed study of DCC in
mechanochemical grinding (other than our preliminary report),2
we first provide some background on these two previously
separate fields.
1.1. Dynamic Covalent Chemistry (DCC). DCC provides
an approach to the discovery of complex architectures and
receptors that may be inaccessible or unimaginable by rational
design.3 It also has potential applications in a wide range of
chemical and biological problems that involve binding equilibria
in chemistry4 and biology.3f,5 The members of a dynamic
combinatorial library (DCL) are molecules that form in a
combinatorial way by linking building blocks together through
reversible covalent bonds that are dynamic, being continuously
broken and re-formed. The concentration of each library member
Received: January 29, 2014
© XXXX American Chemical Society
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Figure 1. Solid-state DCC reaction through ball mill grinding: (a) under neat conditions; (b) under LAG conditions. From the solid-state DCC reaction
of the homodimers (CCDC1 codes ODNPDS02 and DCPHDS for 1-1 and 2-2, respectively) only the relevant stable polymorph of the heterodimer
crystallizes. When seeds of the metastable polymorph of the heterodimer are introduced in the grinding system, two simultaneous and competitive
pathways are possible: a direct polymorph interconversion (route to the right) or a sequential transformation from (1-2)A to homodimers to (1-2)B
(route to the left) under ball mill neat grinding conditions or vice versa under ball mill LAG conditions. The details of (1-2)A (CCDC code FUQLIM01)
and (1-2)B (CCDC code FUQLIM) have been previously reported.2
gripping with tweezers or puncture by a needle.9b While the
mechanochemistry of inorganic solids13 and metal complexes14 is
a well-established field, developments have been taking place
more recently in organic and organometallic15 chemistry.
Organic reactions explored in manual or mechanical ball mill
grinding16 include the formation of disulfides from thiols,17
disulfide exchange,2 imine formation,8b,16c,18 boronic ester
formation,16c,18a hydrazone formation,8b,16c and a range of
C−C bond forming reactions such as carbonyl condensa-
tions8b,16c,19 and pericyclic reactions.8b,16a,c,20 This has opened
the field for the mechanochemical synthesis of complex chemical
architectures,15b such as metal-coordinated cages,21 fully organic
cages,18a rotaxanes,22 and capsules.19e
Much of the mechanochemistry literature has been generated
using manual grinding with a pestle and mortar, where the
reaction system is open: i.e., the solvent can escape from the
system and the supplied mechanical energy is neither constant
nor measurable. Here we perform ball mill grinding using a
mechanical mixer mill (also called vibratory mill), which allows
for reproducible and controlled milling frequencies and times.11a
The milling jars are closed systems that allow the achievement of
thermodynamic equilibrium, as has already been proposed in the
field of metal alloys.23 Some authors consider milling to be a
nonequilibrium environment and refer to “pseudo-equilibria” or
“equilibrium states of milling”.11a
Mechanical ball mill grinding can be performed neat (without
added solvent) or solvent assisted (LAG): in the latter, very small
amounts of added liquid can dramatically accelerate and even
enable mechanochemical reactions between solids.11b,24 As yet,
little is known about the mechanisms and the driving forces
involved in the chemical syntheses and supramolecular reactions
induced by ball mill grinding. In two recent publications, the
formation of organic and metal−organic supramolecular
compounds by ball mill grinding under LAG and neat conditions
was monitored in situ and in real time by X-ray diffractometry
(XRD) at a synchrotron facility.25 The resulting kinetic reaction
curves clearly show a terminal plateau that may be indicative of a
thermodynamic equilibrium: the authors did not comment on
the possible driving force of the reactions studied.
Crystallization from solution may be thermodynamically or
kinetically driven or be a combination of both: the initial
formation of nuclei promotes the exponential growth of a specific
polymorph, as indicated by a sigmoidal kinetic curve.26 In general,
the kinetic curves for ball mill grinding reactions are observed to
exhibit a sigmoidal shape, this being consistent with the initial
formation of nuclei promoting the exponential growth of the
product.25,27
Ball mill grinding is preceded or accompanied by a crystal size
reduction of the starting materials, often down to an amorphous
intermediate phase.24,25,28 Whether this possible amorphous, and
therefore nondiffracting, material includes more than one state or
any crystal nuclei is not known.29
Whether the ball mill grinding process as a whole can be
regarded as a purely solid state process is uncertain, even in the
neat case, because of the difficulty in controlling or measuring the
exact reaction conditions such as average and local pressure and
temperature.13b Some authors propose that the heat generated in
the course of a mechanochemical process can induce local
melting of crystals,8a melting at the interface between crystals,30
or formation of liquid eutectic intermediate phases,11b,13b,28b,31
so that in such cases the reaction takes place in the liquid phase
even though a solid product is ultimately produced. We
previously investigated and excluded an eutectic-based mecha-
nism for the current system,2 but a discussion of these
mechanistic aspects is beyond the scope of this paper. We will
focus here on the relative energy minima of the ball mill grinding
process as an approach to interpret our experimental results as a
thermodynamic outcome. Indeed, we show below that, after the
reaction reaches completion, equilibrium is achieved, with a
stable phase composition.25,32
Unlike crystallization in solution or a slurry experiment, the
ball mill grinding process leads to extremely small crystals whose
size is hard to predict or even to estimate. One report of in situ
and in real time monitoring by XRD of a ball mill grinding
reaction describes the crystal size ina ball mill grinding reaction to
B
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approach the order of tens of nanometers, giving a very different
surface to volume ratio (S/V) from microcrystals.25a Thus, while
thermodynamics conventionally assumes surface effects to be
negligible (i.e., infinite bulk structures as in the case of slurry
experiments), this is not the case in continuously mechanically
ground systems.8a These thermodynamic aspects are general and
must apply to any milling system, independent of the
mechanisms involved in the chemical reaction.
morphic form of the quantitative product at equilibrium was
determined by powder X-ray diffraction (PXRD). Brief
investigations using solid-state NMR and solid-state FTIR did
not reveal any useful quantitative information; therefore, we have
not included them.
We also reported in our previous work that solid-state DCC
can lead to different polymorphs of the heterodimer depending
on whether the experiments correspond to ball mill neat grinding
conditions, forming a polymorph of 1-2 referred to here as
(1‑2)A, or ball mill LAG conditions, forming a different
polymorph of 1-2 referred to here as (1-2)B.2 It was implied
that both polymorphs (1-2)A and (1-2)B represent the final
equilibrium product of the reaction under ball mill neat and ball
mill LAG conditions, respectively, but no proof was provided.
Indeed, the very idea that adding one drop of solvent to a milling
jar could switch the thermodynamic equilibrium from one
polymorph to the other is challenging. Thus, the thermodynamic
aspects of these milling systems required the further inves-
tigations reported below.
In the present work we have added the solid-state composition
obtained by Rietveld refinement of PXRD data collected
throughout the grinding process, giving us the opportunity of
identifying and quantifying which, and how much, of each
polymorph is formed during the ball mill grinding reaction. All
samples were also analyzed by HPLC. Performing kinetic studies
of seeding experiments provides us with a powerful tool to
elucidate the reaction pathway of solid-state DCC reactions by
monitoring the solid-state composition as grinding proceeds.
Equipped with these tools, we now explore whether the
heterodimer polymorph crystallization is determined by kinetics
or thermodynamics, what are the intermediate products, if any,
and how mechanochemical crystallization by ball mill grinding
proceeds.
We show here that the experimental milling conditions of the
DCC reaction, i.e. the presence or absence of a small quantity of
solvent, which allows for solvated surfaces of the nanosized
crystals, determine the polymorph selection at equilibrium (see
section 3.1): under ball mill neat grinding conditions the DCC
reaction exclusively yields polymorph (1-2)A, which is thus the
stable polymorph under these conditions (Figure 1a); when the
reaction is carried out under ball mill LAG conditions, (1-2)B is
formed, which is the stable polymorph under ball mill LAG
conditions (Figure 1b). If polymorph (1-2)B is added to the
equimolar mixture of the two homodimers under ball mill neat
grinding conditions (Figure 1a), then it is fully transformed to
(1‑2)A; (1-2)B is therefore the metastable polymorph under ball
mill neat grinding conditions. Similarly, polymorph (1-2)A is
metastable under ball mill LAG conditions and rapidly transforms
to (1-2)B (Figure 1b). Polymorph transformations are crucial in
the pharmaceutical industry and generally in any field where the
final product is used and commercialized as a solid phase.37
Small crystallites have higher enthalpies and free energies than
large crystals because of a positive surface energy.33 Reactions
occur not in the whole bulk of the sample but at the interfaces
between the phases.8a The role of mechanical action is usually to
provide mixing, decreasing the particle size, and generating fresh
surface for the contact.8a In contact with a solvent, as it happens in
crystallization experiments in solution or in ball mill grinding
under LAG conditions, the particle surfaces are solvated. Solvated
surfaces are not simply a sharp boundary but have a finite depth
that can extend up to 1 nm.34 Thus, at high S/V ratio as in the case
of nanocrystals obtained by ball mill grinding, the contribution of
the solvated surface to the free energy minimum of a given
polymorph is significant. In the case of ZnS nanocrystals (3 nm in
diameter) absorption and desorption of methanol were found to
reversibly change the atomic arrangement of the bulk structure.35
Hence, the free energy minima of different polymorphs at the
nanoscale will depend on the energetics of the bulk structures, the
S/V ratio of the crystallites, and the extent of solvation of the
surface of the crystallites. Therefore, the relative free energy of
one polymorph versus another will depend on the solvent used in
the case of ball mill LAG or in the lack of solvent in the case of ball
mill neat grinding.36
1.3. Solid-State DCC. The solid-state DCC reaction shown
in Figure 1 has been selected to utilize one of the simplest DCC
systems available: the metathesis of two linear symmetric
disulfide homodimers which can result only in the formation of
a linear asymmetric disulfide heterodimer. What we learn from
this simple solid-state DCC reaction should then be relevant to
more complex oligomeric DCC systems, including other
reversible chemistries. In solution, the system leads to a statistical
mixture of the two homodimers (25% each) and the heterodimer
(50%). Using ball mill grinding, the thermodynamic outcome is
dramatically biased toward the heterodimer (97% yield) rather
than homodimers (1.5% each).2 We also demonstrated in earlier
work that solid-state DCC can lead to two different polymorphs
of the same product, depending on whether the ball mill grinding
reaction is performed under neat or under LAG conditions.2 This
is a new aspect of DCC only possible in the solid state.
1.4. Background to the Present Study. In our previous
paper we demonstrated that the solid-state DCC reaction in
Figure 1 was under thermodynamic control. The two
homodimers 2-nitrophenyl disulfide [(2-NO2PhS)2] and 4-
chlorophenyl disulfide [(4-ClPhS)2] are here referred to as 1-1
and 2-2, respectively, the corresponding heterodimer is referred
to as 1-2, and the base catalyst is 1,8-diazabicyclo[5.4.0]undec-7-
ene (dbu).
2. EXPERIMENTAL DETAILS
We present here 14 kinetic studies, which were designed to explore the
different kinetic and thermodynamic features of our solid-state DCC
reaction, both under ball mill neat grinding conditions (i.e., in the
absence of solvent) in studies A1−A7 and under the corresponding ball
mill LAG conditions (i.e., with 50 μL of acetonitrile added to 200 mg of
powder in the grinding jar) in studies B1−B7.
The kinetic curves presented here were prepared from PXRD or
HPLC data obtained from individual experiments, each experiment
corresponding to a single grinding time. This approach avoids disrupting
the delicate equilibrium achieved during grinding among the vapor, the
Two separate tests proved that the constant composition of the
product observed on reaching the plateau was thermodynami-
cally determined: (a) the same final composition was obtained
regardless of the composition of the starting state, provided that
the equimolar stoichiometry of the added homodimers 1-1 and
2‑2 was respected; (b) we proved that the plateau was not a
kinetic sink, by demonstrating its dynamic nature.2 The chemical
composition of the reaction mixture was monitored using high-
performance liquid chromatography (HPLC), and the poly-
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Figure 2. Solid-state DCC studies reacting 1-1 and 2-2 in an equimolar ratio (no added seeds of 1-2) in the presence of catalyst (dbu): (a, b) reaction
scheme; (c, d) kinetic curves prepared as obtained from the Rietveld quantitative phase analysis; (e, f) free energy diagrams. The parts framed in blue on
the left represent ball mill neat grinding conditions. The parts framed in red on the right represent ball mill LAG conditions using 50 μL of MeCN.
liquid, and the solid components in the enclosed chamber of the snap-
closed grinding jar.
by HPLC analysis. While the PXRD analysis is not as sensitive or
accurate (estimated accuracy 3% M absolute and estimated sensitivity,
limit of detection (LOD) as 3% M) as HPLC (estimated sensitivity 0.1%
M relative to the main component), it supplies the phase composition.
Therefore, all further discussion regarding kinetic profiles will be based
on the Rietveld refinements of the PXRD data. The agreement between
PXRD and HPLC analysis was found to be excellent (see the Supporting
Information). More details about the analytical methods can be found in
the Supporting Information.
Samples of the components of the homodimers 1-1 and 2-2 and the
added seeds of the polymorph of 1-2, as required, were accurately
weighed, resulting in a typical loading of 200 mg. The solid powders were
individually placed in a 14.5 mL stainless steel grinding jar together with
two 7 mm i.d. stainless steel ball bearings. After the addition of 2 μL (2%
M) of catalyst (dbu) into the jar, nothing else was added for ball mill neat
grinding, while 50 μL of acetonitrile was added for ball mill LAG
experiments. The jars were snap-closed, and grinding was performed at
30 Hz on a MM400 Retsch automated grinder (see Figures SI 39 and SI
40 in the Supporting Information) for the specified period of time. After
completion of the grinding period, the jar was immediately opened and
the contents were analyzed; the results obtained as % M concentration
versus grinding time were used to construct the corresponding kinetic
profiles.
The number of grinding experiments and grinding times for a given
study depended on how many points were required to represent, with
good definition, the sigmoidal segment of the kinetic curve and ascertain
that the system had finally reached a plateau. Indeed, the rigorous
experimental procedures detailed in the Supporting Information were
found to be crucial for reproducibility. The solid-state composition of the
samples, reported here as % M, was determined by Rietveld refinements
from PXRD data. The chemical composition of the sample was obtained
3. RESULTS AND DISCUSSION
To help the reader, kinetic curves for ball mill neat grinding
studies are shown framed in blue, while ball mill LAG
experiments are shown framed in red for Figures 2−7. No fitting
was performed, and the kinetic curves are only a guide to the eye.
Each time point in these kinetic plots corresponds to a single
grinding experiment. The findings of these studies are
summarized at the top of Figures 2−7 in the form of reaction
schemes for each kinetic study. To appreciate the thermodynamic
aspects and to recognize the relative predominance of the
competing kinetic pathways, we summarize these relative free
energy minimum (FEM) states for the starting state, intermediate
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Figure 3. Solid-state DCC studies reacting 1-1 and 2-2 in an equimolar ratio seeded with 3% M of the stable polymorph of 1-2 in the presence of catalyst
(dbu): (a, b) reaction scheme; (c, d) kinetic curves prepared as obtained from the Rietveld quantitative phase analysis; (e, f) free energy diagrams. The
parts framed in blue on the left represent ball mill neat grinding conditions. The parts framed in red on the right represent ball mill LAG conditions using
50 μL of MeCN.
state, and reaction product at the bottom of each figure in the
form of a free energy level diagram. These levels and the
corresponding energy barriers between the starting state and
intermediate state and reaction product have been inferred from
our kinetic studies. Analysis of these kinetic data has allowed us to
distinguish alternative reaction pathways, preferred as well as
unlikely pathways, for each grinding study.
3.1. Unseeded Solid-State DCC Experiments. We will
start this discussion with unseeded grinding studies. These solid-
state DCC experiments were performed by grinding equimolar
amounts of the homodimers, 1-1 and 2-2, in the presence of
catalyst (2% M dbu). Figure 2 shows the findings of the ball mill
neat grinding experiments (study 1A) on the left and ball mill
LAG experiments with 50 μL of MeCN (study 1B) on the right.
The solid-state DCC reaction reached equilibrium, always
resulting inquantitative formation of the stable polymorph of 1-2,
its composition being maintained for extended grinding periods
(i.e., 24 h). The metastable polymorph of 1-2 was never observed
at any time point of the grinding process. These unseeded
reactions exhibited a long delay before a significant concentration
(7% M) of the stable polymorph of 1-2 was observed: 25 min for
ball mill neat grinding studies (Figure 2c) and 10 min for ball mill
LAG studies (Figure 2d), showing that the ball mill LAG process
is faster than the ball mill neat process. It is known that very small
amounts of added liquid can dramatically accelerate mechano-
chemical reactions between solids. In other words, given a
mechanochemical reaction, ball mill LAG is generally faster than
ball mill neat grinding.11b However, in our case ball mill LAG and
ball mill neat grinding lead to two different polymorphs, (1-2)B
and (1-2)A, respectively; therefore, their reaction rates cannot be
directly compared.11b,38
Both ball mill neat grinding and ball mill LAG reactions
exhibited a nucleation phase (around 5 min) and a sharp
transition before reaching a constant plateau.
Any change in the phase composition affects the position of the
free energy minima (FEM) levels and their corresponding energy
barriers. For brevity, we designate AFEM as the FEM containing
(1-2)A and BFEM as the FEM containing (1-2)B. The
composition of the FEM level of the starting state for studies
1A and 1B was equimolar amounts of 1-1 and 2-2.
Under ball mill neat grinding conditions (Figure 2e) the
equilibrium is represented by the AFEM containing (1-2)A,
E
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Figure 4. Solid-state DCC studies reacting 1-1 and 2-2 in an equimolar ratio seeded with 23% M of the metastable polymorph of 1-2, in the absence of
catalyst (dbu): (a, b) reaction scheme; (c, d) kinetic curves prepared as obtained from the Rietveld quantitative phase analysis; (e, f) free energy diagrams.
The parts framed in blue on the left represent ball mill neat grinding conditions. The parts framed in red on the right represent ball mill LAG conditions
using 50 μL of MeCN.
which is the stable polymorph and the only polymorph of 1-2
observed in the ball mill neat grinding reaction. Under ball mill
LAG conditions (Figure 2f) the equilibrium corresponds to
BFEM containing (1-2)B, which is the stable polymorph and the
only polymorph of 1-2 observed in the ball mill LAG reaction. As
the kinetic curves for ball mill neat grinding (Figure 2c) are slower
than those for ball mill LAG (Figure 2d), the energy barrier
between the starting state and the reaction product (AFEM) for
ball mill neat grinding (Figure 2e) must be higher than that
between the starting state and the reaction product (BFEM) for
ball mill LAG (Figure 2f).
shown inFigure 3c for ball mill neatgrinding studies and inFigure
3d for ball mill LAG studies.
The Rietveld refinement of PXRD data showed that only the
stable polymorph was formed under these experimental
conditions, but the reaction rate was greater than that in the
corresponding unseeded studies. The interpretation of these data
in the form of free energy level diagrams is shown in Figure 3e for
ball mill neat grinding studies and Figure 3f for ball mill LAG
studies: the increase in the reaction rate must be predominantly a
consequence of a significant reduction of the energy barriers
between the starting state and the reaction product.
3.2. Solid-State DCC Reaction Seeded with the Stable
Polymorph of the Heterodimer. Figure 3 displays the results
from grinding experiments seeded with 3% M of the stable
polymorph of 1-2 to an equimolar amount of 1-1 and 2-2 in the
presence of catalyst (2% M dbu). The ball mill neat grinding
experiments (study 2A) and the ball mill LAG experiments with
50 μL of MeCN (study 2B) are on the left and right sides of the
figure, respectively. These studies showed a decrease in the lag
time by 10−12 min in comparison to the times for the unseeded
studies, maintaining the shape of the sigmoidal segment, as
3.3. Direct Polymorph Interconversion in the Absence
of Catalyst. Direct polymorph interconversion from the
metastable to the stable polymorph requires only a supra-
molecular rearrangement of the crystal lattices of (1-2)B →
(1‑2)A for ball mill neat grinding studies and (1-2)A → (1-2)B
for ball mill LAG studies. Such direct transformation in milling
experiments has been reported before in other systems.39 We
explored these direct polymorph interconversions in study 3-A
under ball mill neat grinding conditions and in study 3-B under
ball mill LAG conditions; their outcomes are shown on the left
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Figure 5. Solid-state DCC studies reacting 1-1 and 2-2 in an equimolar ratio seeded with the metastable polymorph of 1-2 in the presence of catalyst
(dbu): (a, b) reaction scheme; (c−f) kinetic curves prepared as obtained from the Rietveld quantitative phase analysis; (g, h) free energy diagrams. The
partsframed in blue onthe left represent ball mill neatgrinding conditions (3% Mof seeds shown in (c)); 23%M of seeds shown in(e)). The partsframed
in red on the right represent ball mill LAG conditions using 50 μL of MeCN (3% M of seeds shown in (d); 23% M of seeds shown in (f)).
and right sides of Figure 4, respectively. In these experiments 23%
M of the metastable polymorph of 1-2 was added to 77% M of
equimolar amounts of 1-1 and 2-2 homodimers in the absence of
dbu to prevent any DCC reaction from taking place.
As expected, the 77% M concentration of equimolar amounts
of 1-1 and 2-2 remained unreacted. Under ball mill neat grinding
conditions, the 23% M concentration of the metastable
polymorph (1-2)B was fully transformed into the stable
polymorph (1-2)A in around 10 min, the kinetic curve presenting
a shallow sigmoidal kinetic segment and the conversion starting
soon after grinding was initiated (Figure 4c). Similar kinetic
curves were observed under ball mill LAG conditions, where
(1‑2)A transformed into (1-2)B in around 10 min as well (Figure
4d). In summary, direct polymorph interconversion rapidly
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Figure 6. Solvent-free DCC studies reacting 77% 1-1 with 23% M of the metastable polymorph of 1-2, in the presence of catalyst (dbu): (a, b) reaction
scheme; (c, d) kinetic curves prepared as obtained from the Rietveld quantitative phase analysis; (e, f) free energy diagrams. The parts framed in blue on
the left represent ball mill neat grinding conditions. The parts framed in red on the right represent ball mill LAG conditions using 50 μL of MeCN.
transformed the metastable to the stable polymorph in very little
time.
sponding increase in the concentration of 1-1 and 2-2. After the
first 1minand for the next 9min, the concentration of 1-1and 2-2
stayed constant at 48% M while the concentration of (1-2)A was
around 3−5% M. The freshly formed 1-1 and 2-2 were therefore
the covalent intermediates in the first step of the reaction ((1-2)A
→ 1-1 + 2-2) of a sequential pathway, where (1-2)A is
transformed to (1-2)B. This process involves bond breaking and
bond forming of the reversible disulfide bond. This is the first
time we are aware of that a purely covalent reaction has been
reported to be involved in a polymorph interconversion.40
The interpretation of this sequential mechanism in the form of
free energy level diagrams is shown in Figure 5h. Since we
observed an accumulation of the covalent intermediates for over
10 min, the second step of the sequential mechanism (1-1 + 2-2
→(1-2)B) must be the rate-determining step (RDS).
The kinetics in study 5B were found to be significantly faster
(3−4 min) in comparison to those for the corresponding
unseeded experiments (study 1B). This result seems counter-
intuitive. If the two-step sequential transformation were to be the
only operative pathway in study 5B, it should have resulted in a
delay of the kinetics. This slight increase in the reaction rate with
respect tothat of study 1Bcould indicate thatan alternative minor
3.4. Solid-State DCC Reaction Seeded with the
Metastable Polymorph of the Heterodimer. Unexpected
phenomena were observed in studies 4 and 5, where seeds of the
metastable polymorph of 1-2 were added to equimolar amounts
of 1-1 and 2-2 in the presence of dbu catalyst (2% M). These
experiments were initially performed at 3% M concentration of
the added seeds (Figure 5c,d, study 4), the composition of which
could only be analyzed by HPLC, 3% M being the limit of
detection of the PXRD method. A higher concentration of seeds
(23% M, Figure 5e,f, study 5) was required to monitor the solid-
state composition by PXRD.
3.4.1. Ball Mill LAG. The kinetic curves for the ball mill LAG
case in study 5B illustrated in Figure 5f present an unexpected
observation.
The rapid disappearance of (1-2)A from the initial
concentration of 23% M down to 3−5% M within the first 1
min of ball mill grinding was accompanied by a simultaneous
increase of the concentration of 1-1 and 2-2 from the initial
concentration of 37.5% M up to 47−48% M. In other words, the
reduced concentration of (1-2)A exactly matched the corre-
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Figure 7. Solvent-free DCC studies reacting 77% M 2-2 with 23% M of the metastable polymorph of 1-2, in the presence of catalyst (dbu): (a, b) reaction
scheme; (c, d) kinetic curves prepared as obtained from the Rietveld quantitative phase analysis; (e, f) free energy diagrams. The parts framed in blue on
the left represent ball mill neat grinding conditions. The parts framed in red on the right represent ball mill LAG conditions using 50 μL of MeCN.
but faster pathway (the direct polymorph interconversion) is
acting competitively and simultaneously in study 5B to the
sequential transformation as depicted in Figure 5h. We suggest
that the residual fraction of (1-2)A not immediately consumed by
the sequential pathway was transformed into (1-2)B within a few
minutes by the direct interconversion pathway, these freshly
created seeds of (1-2)B acting as a template and thus increasing
the DCC reaction rate.
3.4.2. Ball Mill Neat Grinding. Unlike the case under ball mill
LAG conditions in study 5B (Figure 5f), the kinetic curves of
study 5A under ball mill neat grinding conditions (Figure 5e)
showed no signs of accumulation of covalent intermediates.
Despite this observation, we propose that the transformation of
the metastable (1-2)B to the stable polymorph (1-2)A under ball
mill neat grinding conditions also proceeds through two
competitive and simultaneous pathways, the sequential mecha-
nism being the predominant path (Figure 5g).
corresponding studies seeded with the stable polymorph (Figure
3c, study 2A). Had the direct polymorph interconversion been
the predominant or exclusive pathway, we should have seen a
sharp nucleation phase as in studies 1A and 2A.
The delay in the polymorph interconversion and the shallow
kinetic curve can be explained by the transformation happening
competitively and simultaneously through a direct polymorph
interconversion and a sequential mechanism, the latter being the
predominant one. Since there is no accumulation of the covalent
intermediate, the first step of the sequential process ((1-2)B →
1‑1 + 2-2) must be the RDS: as soon as the covalent
intermediates 1-1 and 2-2 are formed in the RDS step 1, they
are immediately consumed in the lower energy barrier step 2 to
form (1-2)A.
3.5. Effect of the Nature of the Homodimers on the
Competition between the Sequential and the Direct
Polymorph Transformation. We were interested in under-
standing if the presence of the two homodimers, 1-1 and 2-2, had
any effect on the polymorph interconversion reaction. We
therefore designed kinetic studies so that 23% M seeds of the
metastable polymorph of 1-2 were added to either 77% M of 1-1
In the ball mill neat grinding case the sequential path has to be
inferred from the reaction rate and the kinetic curve in Figure 5e,
which shows a shallow sigmoidal shape. This shallow curve is
different from the sharp sigmoidal segments for the correspond-
ing unseeded experiments (Figure 2c, study 1A) or the
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only (Figure 6, study 6) or to 77% M of 2-2 only (Figure 7, study
7) in the presence of catalyst.
metastable polymorph. Therefore, we have experimentally
demonstrated that the identity of the stable and metastable
polymorphs is reversed under ball mill neat grinding and ball mill
LAG conditions. Predictably, the rate of reaction was increased
when the material was seeded with the stable polymorph. The
addition of seeds of the metastable polymorph leads to a rich and
unexpected reaction path affecting the kinetics without changing
the final phase composition at equilibrium: the metastable
polymorph is always converted into the more stable form. In the
absence of catalyst the seeds of the metastable polymorph were
transformed into the more stable polymorph exclusively by direct
polymorph interconversion, as no DCC chemical reaction can
take place. In the presence of catalyst, this polymorph
interconversion occurred by two simultaneous and competitive
routes: a direct transformation and a sequential route, which is
predominant. In the latter route, the first step is the conversion of
the metastable polymorph of the heterodimer into its
corresponding homodimers, which thus are the covalent
intermediates in this reversible reaction. This is the first time
that a purely covalent bond breaking and re-forming has been
reported in the literature to be involved in a polymorph
interconversion. Under ball mill LAG conditions the RDS is
the second step, while under ball mill neat grinding conditions the
RDS is the first step of the sequential route. Furthermore, we have
proved that the presence of 2-2 homodimer promotes direct
polymorph interconversion of the heterodimer, while the
presence of 1-1 homodimer promotes the two-step sequential
polymorph transformation, which exploits the reversible covalent
disulfide bond. This work may be seen as an important step
toward an understanding of the mechanisms and potential of
solid-state DCC.
Adding metastable polymorph seeds just to 1-1 resulted in very
similar kinetic curves for ball mill neat grinding (Figure 6c, study
6A) and ball mill LAG studies (Figure 6d, study 6B). Both graphs
have the tell-tale signs of the sequential covalent route:
immediate reduction of the metastable polymorph of 1-2 with
simultaneous accumulation of 1-1 and 2-2 (Figure 6a,b). The
accumulation time before conversion to the stable polymorph of
1-2 product molecule was now much longer in comparison to
that of study 5B. This result indicates that the direct polymorph
interconversion does not occur to any significant extent in study
6A-B, and the two-step reaction thus takes longer than an
unseeded experiment. The free energy level interpretation of
study 6 is consistent with a significant stabilization of energy level
of this intermediate state with respect to the starting state, both
under ball mill neat grinding (Figure 6e) and under ball mill LAG
(Figure 6f); this resulted in a lowering of the energy barriers for
the sequential mechanism, while the energy barrier for the direct
conversion was increased. Under these experimental conditions,
the sequential mechanism was predominant or exclusive, the
second step of the sequential mechanism being the RDS, with
relative accumulation of 1-1 and 2-2.
In contrast, when the same seeds of the metastable polymorph
of 1-2 were added to 77% M of pure 2-2 (Figure 7), the direct
transformation pathway was predominant or exclusive for both
ball mill neat grinding (Figure 7c, study 7A) and ball mill LAG
(Figure 7d, study 7B) and showed the same kinetic profile as
those in study 3A (Figure 4c) and study 3B (Figure 4d)
performed in the absence of dbu, where only the direct
polymorph transformation could take place. The free energy
level interpretation of study 7 is consistent with a significant
destabilization of energy level of this intermediate state with
respect to the starting state, both under ball mill neat grinding
(Figure 7e) and under ball mill LAG conditions (Figure 7f); this
resulted in an increase of the energy barriers for the sequential
mechanism, while the energy barrier for the direct conversion was
decreased. Under these experimental conditions, the direct
mechanism was predominant or exclusive.
The milling process reduces the crystallite size: we believe that
the nanosized dimensions of the crystallites and/or the surface
solvation free energy are key to understanding why the
polymorph stability order is different in the presence or absence
of the acetonitrile solvent. More importantly, this interpretation
of the system may be general and may apply to many other
grinding processes.
ASSOCIATED CONTENT
* Supporting Information
Text, tables, and figures giving detailed procedures for the solid-
state DCC reaction, HPLC data, PXRD patterns, data, and their
corresponding Rieltveld refinement for each of the 14 studies,
and a discussion of the methodology used for the Rieltveld
refinement. This material is available free of charge via the
Internet at http://pubs.acs.org.
“Seeding assisted” polymorphic transformation was recently
reported for the covalent synthesis of imines by manual grinding,
where the addition of seeds of a specific polymorph directed the
selection of the polymorph formed.41 In contrast, for the solid-
state DCC system studied here, we have demonstrated that while
seeding with the stable polymorph leads to an acceleration of the
reaction (Figure 3), “seeding assisted” polymorphic trans-
formation did not take place: i.e., seeding with the metastable
polymorph resulted in its complete transformation to the stable
polymorph (Figures 4−7).
■
S
AUTHOR INFORMATION
Corresponding Authors
*E-mail for A.M.B.: amb84@cam.ac.uk.
*E-mail for J.K.M.S.: jkms@cam.ac.uk.
■
4. CONCLUSIONS
We have provided extensive experimental evidence that only the
more stable of the two polymorphs of the heterodimer is
exclusively formed in almost quantitative yield in our solid-state
dynamic covalent chemistry model reactions. No further change
in the equilibrium composition was observed after up to 24 h of
continuous grinding. The experimental conditions, especially the
absence of solvent for ball mill neat grinding or the presence of a
few drops of acetonitrile for ball mill LAG, determines which
polymorph of the product is formed on grinding. Under ball mill
neat grinding conditions (1-2)A is the stable polymorph and
(1‑2)B is the metastable polymorph. Under ball mill LAG
conditions (1-2)B is the stable polymorph and (1-2)A is the
Author Contributions
§These authors contributed equally.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
We are grateful to the EPSRC (A.M.B., J.K.M.S., and D.J.W.) and
the ERC (D.J.W.) for financial support. We thank T. Frisc
valuable discussions on the theory of ball mill grinding. We thank
G. Day, P. Bygrave, and V. Ruhle for discussions on the energy of
■
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Journal of the American Chemical Society
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