Feedback Kinetics in Mechanochemistry: The Importance of Cohesive States

Article abstract of DOI:10.1002/anie.201706723

Although mechanochemical synthesis is becoming more widely applied and even commercialised, greater basic understanding is needed if the field is to progress on less of a trial-and-error basis. We report that a mechanochemical reaction in a ball mill exhibits unusual sigmoidal feedback kinetics that differ dramatically from the simple first-order kinetics for the same reaction in solution. An induction period is followed by a rapid increase in reaction rate before the rate decreases again as the reaction goes to completion. The origin of these unusual kinetics is found to be a feedback cycle involving both chemical and mechanical factors. During the reaction the physical form of the reaction mixture changes from a powder to a cohesive rubber-like state, and this results in the observed reaction rate increase. The study reveals that non-obvious and dynamic rheological changes in the reaction mixture must be appreciated to understand how mechanochemical reactions progress.

Full text of DOI:10.1002/anie.201706723

A Journal of the Gesellschaft Deutscher Chemiker
Angewandte
International Edition Chemie
www.angewandte.org
Accepted Article
Title: Feedback kinetics in mechanochemistry; the importance of
cohesive states
Authors: Stuart Lloyd James, Ben Hutchings, Peijun Hu, Lei Gao, and
Deborah Elizabeth Crawford
This manuscript has been accepted after peer review and appears as an
Accepted Article online prior to editing, proofing, and formal publication
of the final Version of Record (VoR). This work is currently citable by
using the Digital Object Identifier (DOI) given below. The VoR will be
published online in Early View as soon as possible and may be different
to this Accepted Article as a result of editing. Readers should obtain
the VoR from the journal website shown below when it is published
to ensure accuracy of information. The authors are responsible for the
content of this Accepted Article.
To be cited as: Angew. Chem. Int. Ed. 10.1002/anie.201706723
Angew. Chem. 10.1002/ange.201706723
Link to VoR: http://dx.doi.org/10.1002/anie.201706723
http://dx.doi.org/10.1002/ange.201706723

Angewandte Chemie International Edition
10.1002/anie.201706723
COMMUNICATION
Feedback kinetics in mechanochemistry; the importance of
cohesive states
Benjamin P. Hutchings, Deborah E. Crawford, Lei Gao, Peijun Hu, and Stuart L. James*
Abstract: Although mechanochemical synthesis is becoming more
widely applied and even commercialised, greater basic understanding
is needed if the field is to progress on less of a trial-and-error basis.
We report that a mechanochemical reaction in a ball mill exhibits
unusual sigmoidal feedback kinetics that differ dramatically from the
simple first-order kinetics for the same reaction in solution. An
induction period is followed by a rapid increase in reaction rate before
the rate decreases again as the reaction goes to completion. The
origin of these unusual kinetics is found to be a feedback cycle
involving both chemical and mechanical factors. During the reaction
the physical form of the reaction mixture changes from a powder to a
cohesive rubber-like state, and this results in the observed reaction
rate increase. The study reveals that non-obvious and dynamic
rheological changes in the reaction mixture must be appreciated to
understand how mechanochemical reactions progress.
For the milling experiments, the reaction was conducted at 0.5g scale
using a Retsch MM400 shaker-type ball mill. Addition of water (10%
wt) was required to enable full conversion within a practical timescale
(40 minutes). Periodic sampling of a given reaction run would require
stopping the mill and opening the jar, during which the reaction vessel
would cool which could skew the results. Therefore, each data point
was obtained from an individual reaction run which was then
discarded. For each time point, several repeat runs were performed
for each time point and data were averaged. A composite of the
averaged raw conversion data is shown in Figure 1 (red data points).
Strikingly, the kinetics of the milling reaction are sigmoidal, starkly
contrasting the solution phase kinetics. In particular, there is an
induction period during which the reaction is slow (reaching ~25%
conversion after 25 minutes) followed by a dramatic increase in
reaction rate (to give ~95% conversion within a further 10 minutes).
Though related sigmoidal kinetics have been noted under
[
7]
mechanochemical conditions previously, the origin of this deviation
from simple kinetic models, to our knowledge, has not been
investigated or indeed commented upon. Self-sustaining
mechanochemical reactions in the context of inorganic materials are
M
echanochemical synthesis, in which solid starting materials are
induced to react by grinding, attracts ever-increasing attention
because it can provide low-waste, solvent-free chemical
[
1]
manufacturing as well as unique products. This approach to
chemical synthesis is now being successfully scaled in continuous
processes and even commercialised. However, many basic aspects
of mechanochemical reactions remain poorly understood. For
example, even the kinetics of such reactions have yet to be broadly
investigated and interpreted, and as a result general reaction models
are lacking. As such the field advances largely through trial and
error. Recent work has revealed in some cases quite simple first- or
second-order kinetics for ball milling reactions which support a
[
8]
known which have superficially similar kinetics, i.e. an induction
period followed by an explosive increase in reaction rate, but those
reactions are highly exothermic and, unlike the reaction studied here,
[
2]
proceed
by
combustion.
[
3,4]
[
3]
‘pseudo-fluid’ reaction model. However, mechanochemical reactions
are highly diverse, and reaction mixtures can undergo changes in their
[
4,5]
rheological properties during reactions,
account in the above reaction models.
which are not taken into
Scheme 1) The mechanochemical Knoevenagel condensation of
vanillin and barbituric acid (MM = mixer mill).
Here, we report that the kinetics of an apparently ‘simple’ ball milling
reaction are in fact quite complex and differ dramatically from the
kinetics of the same reaction in the solution phase. Specifically, we
observe sigmoidal kinetics, (superficially similar to those of auto-
catalysed reactions), which indicate that a feedback mechanism is
operating. A series of experiments has revealed the nature of this
mechanism, the key factors in which are both chemical and
mechanical.
Since the kinetics of covalent organic reactions have not been studied
in detail under milling conditions, we chose as a model reaction the
archetypal Knoevenagel condensation of vanillin and barbituric acid,
(
Scheme 1) first reported under mechanochemical conditions by
[
6
]
[
7
]
Kaupp, and investigated in planetary mills by Stolle et al. This
reaction is also appropriate for study since all the organic components
should remain predominantly solid throughout the reaction (the
o
reactants and product have m.p.s of 83, 245 and 263 C respectively).
For comparison, the kinetics of the reaction were first measured in
6
1
solution (d -DMSO, from H NMR spectra) and were found to be
relatively straightforward (Figure 1, blue data points), being
satisfactorily modelled as first-order (see Supplementary Information).
B. P. Hutchings, Dr. D.E. Crawford, L. Goa, Prof. P. Hu, Prof. S. L.
James
School of Chemistry and Chemical Engineering
Queen’s University Belfast
David Keir Building
Figure 1 Comparison of conversion versus time for the Knoevenagel
reaction in solution (d -DMSO) and under mechanochemical
6
conditions (Mixer Mill, 25 Hz with added water 10 % wt). Error bars
were calculated from three standard deviations from the mean of each
dataset for each time point.
Stranmillis Road, Belfast, BT9 5AG
E-mail: s.james@qub.ac.uk
Supporting information for this article is given via a link at the end of
This article is protected by copyright. All rights reserved.

Angewandte Chemie International Edition
10.1002/anie.201706723
COMMUNICATION
The effects of alternative milling frequencies (15Hz, 30Hz) and scales
counterintuitive, similar rate-decreasing effects of premilling have
been reported in some inorganic reactions under mechanochemical
conditions.
(
0.25g, 1.00g) on the reaction kinetics were also investigated. As
[3]
[11]
might be expected, the rate of reaction increased with increasing
frequency (see Figure S6) and decreased with increasing scale (see
Figure S7). Generally, the greater the scale of the reaction, the longer
was the induction time. Notably, in all cases where the reaction
reached 25% conversion before the end of the run, similar sigmoidal
kinetics were observed.
Regarding a reaction exotherm, once the reaction is initiated, the rise
in temperature due to an exotherm could in principle cause a run-
away increase in the reaction rate. Indeed, over the temperature
o
o
range 40 C to 70 C, an un-milled solid mixture of starting materials
and water (10% wt, as in the milling experiments) when simply heated
in a glass vial did exhibit increasing reaction rate with increasing
temperature (Figure 3a). Also, during the milling reactions, the
temperatures of the outside of the jar, the inside of the jar and of the
ball itself were all found to increase during the sigmoidal increase in
reaction rate and to decrease after it (Figure 3b). To evaluate if this
temperature increase could be due to the reaction exotherm, the
Gibbs free energy change of the reaction was calculated with the
Gaussian Software Package 09, performed by restricted exchange-
correlation method B3LYP and basis set 6-311 G++ (d,p) at 348.15
K. This method gave the Gibbs free energy to be only 13.2 kJ/mol
(see Supplementary Information). Taking into account the heat
capacity of the steel jar and ball, this energy could only give rise to an
The sigmoidal kinetics observed here indicate that a positive feedback
mechanism is operating, a phenomenon most familiar in the context
[
9]
of autocatalysed reactions. We initially considered three factors
which could potentially give rise to such kinetics: i. formation of water
as a by-product, which could act as an auto-generated solvent, or
acid- or base-catalyst, ii. milling-induced reduction in particle size to a
critical point at which the reaction suddenly accelerates, iii. internal
heating due to a reaction exotherm and consequent rate acceleration.
However, each of these possibilities was discounted in turn as follows.
a 100
o
average temperature increase of ca. 0.2 C over the jar and its
80
60
40
20
0
contents (see Supplementary Information). Since a temperature rise
of 12 C was observed even at the outside of the jar and much greater
o
increases were observed on the inside and at the ball, the reaction
exotherm alone cannot account for the temperature increases seen.
We also probed the effect of external cooling on the reaction on the
reaction kinetics, by using a Retsch Cryomill, which employs liquid
o
nitrogen to cool the outside of the mill jar to -195 C.
a 100
0
20 Time / min 40
60
80
60
40
20
b 100
8
6
4
2
0
0
0
0
0
0
0
20
40
60
Time / min
55 ꢀC
4
0 ꢀC
70 ꢀC
b
80
60
40
20
0
20
40
60
Time / min
Figure 2a) Reaction kinetics observed upon increasing the added
water to 30 wt %. b) Reaction kinetics observed after premilling of the
reactants to reduce their particle size,
Regarding the water by-product, this reaction is known to be catalysed
in solution by both acid and base,
[
10]
and inhibited in aprotic media
(such as chloroform), both as a bulk solvent and as an additive under
0
milling conditions. However, when we increased the amount of water
added at the start of the milling (to 20 wt % or 30 wt %) or decreased
it (to 5 wt %) the reactions still exhibited similar sigmoidal kinetics
0
KTC
20
40
60
Time / min
Outside
Top
Ball
Side
c1
00
(Figure 2a). This indicates that the generation of one equivalent of
water as a by-product (7 wt %) is not directly responsible for the
feedback kinetics.
8
6
4
2
0
Regarding the reduction in particle size, milling of solids normally
reduces their particle size, in turn increasing the surface area
available for reaction, and this could potentially result in a sudden
increase in reaction rate as the particle size reaches a critical value.
To test this possibility, the reagents were pre-milled individually to
reduce their particle sizes before being combined and milled in the
reaction vessel. If the reduction in particle size was the cause of the
observed increase in reaction rate, then premilling should cause the
reaction to accelerate earlier. However, this was not observed (Figure
0
0
0
0
0
20
40
60
Time / min
2b). In fact, premilling was found to slightly retard the reaction, which
did not reach complete conversion until 50 min. Though
This article is protected by copyright. All rights reserved.

Angewandte Chemie International Edition
10.1002/anie.201706723
COMMUNICATION
Figure 3a) Conversion graph of the induced by heating an umilled
mixture of reactants and 10 % wt water, b) Temperature monitoring of
the milling reaction revealing the increase in temperature during the
inbcrease in reaction rate; the increase in temperature is greatest at
the ball, c) Conversion graph of the reaction in a cryogenic mixer mill,
at 25 Hz with water 10 % w/w, at -195 °C.
Figure 4a) Photograph of the reaction vessel and grinding ball
showing the conversion of the free-flowing powder to a plastic-like
phase which coats the ball, and which occurs during the increase in
reaction rate. b) Temperature graph using a PVA glue coated ball
bearing, c) Temperature graph using cellulose.
Remarkably, even at this low temperature, although the reaction was
slower than without cooling, it did still progress, reaching ca. 23 %
conversion after 60 minutes (Figure 3c). However, the sigmoidal
acceleration of the reaction was not observed, possibly because the
reaction had not progressed far enough. Collectively, these results
indicate that, although an increase in temperature of the system may
be at least partially associated with the feedback mechanism, the
exotherm of the reaction alone is not large enough to cause the
observed temperature change.
The reasons for the formation of these cohesive states are likely to be
complex and may result from a combination of several factors such
as changes in the chemical composition, particle size and
temperature of the reaction mixture as well as the compaction effects
of milling.
We noted that on removal of the coated ball from the reaction vessel
the cohesive state became brittle and began to revert to a powder
after approximately one minute which may be due to evaporation of
water and/or cooling and/or further progression of the reaction. As a
result, it was not possible to characterise the rheological properties of
the cohesive state in detail. However, clearly it can be expected that
the characteristics of mass transfer including molecular diffusion
during this state are likely to be dramatically different to those during
the powder state. Therefore, the observed increase in reaction rate
can be correlated to the formation of the cohesive state. In addition, it
is well-documented that plastic or elastic deformation of related
A fourth explanation for the sigmoidal kinetics was suggested by the
observation of dramatic changes in the physical form of the reaction
mixture as the reaction progressed. Specifically, the reaction mixture
changed from a dry, free-flowing powder during the induction period
to a cohesive rubber-like state that formed a robust coating around
the ball during the sigmoidal increase in reaction rate (Figure 4a, see
also ESI Figure S11), after which it returned again to a free-flowing
powder. During this cohesive state the sound of the mixer mill also
changed notably. This type of change in the physical form of the
reaction mixture has also recently been reported in the context of a
[
13]
cohesive phases generates heat. To test whether this might be the
origin of the observed increase in temperature during the reaction, we
conducted control experiments using chemically inert materials with
different rheological properties. Firstly, a milling ball was coated with
a layer (0.6 mm) of a chemically inert material (PVA glue), whose
rubbery consistency mimicked the cohesive state transiently adopted
by the reaction mixture. With this PVA-coated ball (in the absence of
any other material such as reactants), milling did indeed result in a
ball milling co-crystal synthesis (described as
a ‘snowball’),
suggesting that it may be a general phenomenon in mechanochemical
synthesis, although not often observed since the jars used normally
[
5]
are opaque. In fact, we have also observed this state to form
transiently during the synthesis of the metal organic framework
[
12]
o
[
2
Zn (fumarate)
2
(4,4’-bipyridine)].
substantial rise in temperature (to 111 C). The temperature increase
was also greatest at the ball itself, as in the reaction system itself
(Figure 4b). Second, we milled cellulose as a chemically inert powder
to mimic the powder state of the reaction mixture. In this case an
o
increase in temperature to only 47 C occurred. Therefore, it is
possible that deformation heating during the cohesive state may
contribute to the observed increase in temperature during the reaction
under study.
Overall, the above observations can be depicted as a feedback cycle
as illustrated in Figure 5. As the reaction progresses, changes in the
reaction mixture, potentially combined with compaction from the
milling process, cause it to change transiently from a powder to a
cohesive rubber-like consistency. This in turn changes (accelerates in
this case) the reaction kinetics. This shows clearly that the
progression of this mechanochamical reaction results from an
interplay of interplay of chemical and mechanical factors.
This article is protected by copyright. All rights reserved.

Angewandte Chemie International Edition
10.1002/anie.201706723
COMMUNICATION
Figure 5 Feedback cycle for the mechanochemical Knoevenagle
reaction which accounts for the feedback kinetics and observed
rheological changes.
Puskaric, C. Mottillo, P. Julien, V. Strukil, V. Honkimaki, R.E. Dinnebier
Faraday Discuss. 2014, 170, 203.
[
4]
A.A.L. Michalchuk, I.A. Tumanov. S. Konar, S.A.J. Kimber, C.R. Pulham.
E.V. Boldyreva Adv. Sci. 2017, 1700132; H. Kulla, M. Wilke, F. Fischer,
M. Rollig, C. Maierhofer and F. Emmerling Chem. Commun. 2017, 53,
In conclusion, therefore, we note the following key points: 1)
Sigmoidal feedback kinetics have been observed in a ball milling
reaction, 2) these kinetics starkly contrast with those of the same
reaction in solution, 3) the nature of the feedback loop has been
investigated and involves an interplay of both chemistry and
mechanics.. Overall, this study highlights that the kinetics of
mechanochemical reactions can be rather complex and mechanical
factors need to be considered. Also, it must be borne in mind that
these properties change over time. The dynamic nature of these
properties must be appreciated in order to understand the progress,
or otherwise, of mechanochemical reactions.
1664; K. Uzarevic, V. Strukil, C. Mottillo, P.A. Julien, A. Puskaric, T.
Friscic and I. Halasz Cryst. Gr. Des. 2016, 16, 2342;
E. Boldyreva, Curr. Pharm. Des. 2016, 22, 4981-5000.
G. Kaupp, M. R. Naimi-Jamal and J. Schmeyers, Tetrahedron, 2003, 59,
3753- 3760.
[
5]
6]
[
[7]
A. Stolle, R. Schmidt, K. Jacob, Faraday Dicuss. 2014, 170, 267-286; C.
F. Burmeister, A. Stolle, R. Schmidt, K. Jacob, S. Breitung-Faes, A.
Kwade Chem. Eng. Technol. 2014, 37, 857-864.
[
8]
9]
L. Takacs, Prog. Mater. Sci. 2002, 47, 355–414.
[
S. P. Fletcher, A. J. Bissette, Angew. Chem. Int. Ed. 2013, 52, 12800-
12826; Angew. Chem. 2013, 125, 13034-13061.
[
10] M. L. Deb, P. J. Bhuyan, Tetrahedron Lett. 2005, 46, 6453–6456
11] V. Nachbaur, G. Tauvel, T. Verdier, M. Jean, J. Juraszek, D. Houvet,
J.Alloy Compd. 2009, 473, 303-307.
Experimental Section
[
All materials were purchased from Sigma Aldrich UK with >98% purity
and were used as received, unless indicated. Ball mill experiments
were carried out using a Retsch MM400 mixer mill or a Retsch
Cryomill. Temperature measurements were carried out using a Fluke
[
12] K. Fujii, A. Lazuen Garay, J. Hill, E. Sbircea, Z. Pan, M. Xu, D.C.
Apperley, K.D.M. Harris and S.L. James Chem. Commun. 2010, 46,
7572.
[
13] W. S. Farren, G. I. Taylor, Proc. R. Soc. Lond. A. 1925, 107, 422-451; S.
5
(
61 IR thermometer and the corresponding k-type thermocouple
KTC). The temperature measurements were taken at the outside of
the ball via both the IR thermometer and the k-type thermocouple
outside, KTC), the top of the inside of lid if the mill jar (top), The side
of the inside of the mill jar (side) and the grinding ball (ball). NMR
C. Chou, K. D. Robertson, J. H. Rainey, Exp. Mech, 1973, 13, 422-432
(
6
analysis was carried out with a Brüker Advance DPX 300 with d -
DMSO as solvent.
Mixer mill experiments: vanillin (0.29 g, 1.9 mmol), barbituric acid
0.24 g, 1.9 mmol), the require amount of water and grinding ball (13.6
(
3
g) were added to a 25 cm stainless steel jar which was shaken at 25
Hz for the required amount of to time produce a powder, yellow if the
reaction was incomplete, orange if complete.
Solution experiments: vanillin (0.29 g, 1.9 mmol), barbituric acid (0.24
g, 1.9 mmol), water (0.05 ml) and grinding ball (13.6 g) were added to
3
a 25 cm stainless steel jar which was shaken at 25 Hz for 1 min to
produce a yellow powder. A sample of this homogenised mixture
(
0.07g) was dissolved in d -DMSO (0.6 ml), and sealed in an NMR
6
1
tube. The sample was monitored daily by H NMR.
Keywords: Feedback cycle • Kinetics • Mechanochemistry •
Solid-state reactions • Milling
[
1]
S. L. James, C. J. Adams, C. Bolm, D. Braga, P. Collier, T. Friščić, F.
Grepioni, K. D. M. Harris, G. Hyett, W. Jones, A. Krebs, J. Mack, L. Maini,
A. G. Orpen, I. P. Parkin, W. C. Shearouse, J. W. Steed and D. C.
Waddell, Chem. Soc. Rev. 2012, 41, 413-447; G. A. Bowmaker, Chem.
Commun. 2013, 49, 334-48; G. W. Wang, Chem. Soc. Rev. 2013, 42,
7668-7700; A. Stolle, T. Szuppa, S. E. S. Leonhardt and B. Ondruschka,
Chem. Soc. Rev. 2011, 40, 2317-2329; T. Friščić, J. Mater. Chem. 2010,
20, 7599-7605; A. Bruckmann, A. Krebs and C. Bolm, Green Chem.
2008, 10, 1131-1141.
[
2]
R. Dhumal, A. Kelly, P. Coates, P. York, A. Paradkar, Pharm. Res. 2010,
7, 2725; C. Medina, D. Daurio, K. Nagapudiand F. Alvarez-Nunez, J. Pharm.
2
Sci., 2010, 99, 1693; D. Daurio, K. Nagapudi, L. Li, P. Quan and F.-A.
Nunez, Faraday Discuss., 2014, 170, 235; D. Crawford, J. Casaban, R.
Haydon, N. Giri, T. McNally and S.L. James Chem. Sci. 2015, 6, 1645;
D.E. Crawford, L.A. Wright, S.L. James and A.P. Abbott Chem. Commun,
2
016, 45, 4215; D. E. Crawford, C. K. G. Miskimmin, A. B. Albadarin, G.
Walker,S. L. James, Green. Chem. 2017, 19, 1507;
www.moftechnologies.com accessed 27th May 2017.
X. Ma, W. Yuan, S. E. J. Bell and S. L. James, Chem. Commun. 2014,
0, 1585-1587; I. Halasz, T. Friscic, S.A.J. Kimber, K. Uzarevic, A.
[
3]
5
This article is protected by copyright. All rights reserved.

Angewandte Chemie International Edition
10.1002/anie.201706723
COMMUNICATION
Entry for the Table of Contents (Please choose one layout)
COMMUNICATION
Author(s), Corresponding Author(s)*
Page No. – Page No.
Title
Text for Table of Contents
Unusual sigmoidal kinetics in mechanochemical reactions can be
explained by a feedback loop involving chemical and mechanical
factors.
This article is protected by copyright. All rights reserved.