This journal is c The Royal Society of Chemistry 2012 Chem. Commun., 2012, 48, 10443–10445 10443

Cite this: Chem. Commun., 2012, 48, 10443–10445

Ring opening vs. direct bond scission of the chain in polymeric triazoles

under the influence of an external forcew

Hans S. Smalø and Einar Uggerud*

Received 12th April 2012, Accepted 29th August 2012

DOI: 10.1039/c2cc34056a

Density functional theory calculations show that both ring

opening and chain dissociation of polymeric triazoles are facili-

tated by mechanical stretching of the molecules—the latter more

than the former. Experimentally observed ring opening upon

sonication can therefore not be explained by a mechanical

stretching mechanism alone.

1,2,3-Triazoles undergo ring opening mediated by ultrasound.1

The reaction is illustrated in Scheme 1 where R1 and R2 are

long alkyl chains (molecular weight is 96 kDa). The polymer

molecules were prepared in an acetonitrile solution and sub-

jected to ultrasound for 2 hours. Infrared spectroscopy of the

post-sonicated polymer solution was used to identify the two

products. In addition, gel permeation chromatography

showed that the average molecular weights of the product

polymers were half that of the reactant. Furthermore, heating

the solution in the absence of ultrasound showed no indication

of reaction. Therefore, the authors hypothesized that mecha-

nical stress induced by the ultrasound is the driving mechanism

behind this reaction, which was considered to be due to a

simple 1,3-dipolar cycloreversion of the otherwise robust 1,2,3-

triazole moiety.

Mechanochemistry is a general concept covering all aspects

of how the application of an external mechanical force may

influence chemical properties and reactivity.2–4 For example, it

has been demonstrated that a polymer molecule may be

anchored between the tip and the base of an atomic force

microscope (AFM), and then mechanically manipulated by

the motion of the cantilever to which the tip is attached. In this

manner, the molecule can be stretched, which may activate the

bonds and promote chemical reaction.5–8 In the extreme limit,

covalent bonds may break under the influence of a sufficiently

strong force alone.2

The application of ultrasound to reaction mixtures is a well

established technique for enhancing reaction rates and altering

product compositions.9 During sonication it is observed that

small bubbles form, grow, and collapse. The current under-

standing is that strong forces apply to the molecules when the

bubbles become unstable and burst, which in turn affects

reactivity.2,10 In addition to this powerful mechanochemical

component, the formation of transient hot spots in the

solution may also be of significance.9,11

The purpose of this communication is to examine the

influence of an external force on ring opening of polymers

containing a 1,2,3-triazole unit using quantum chemical method-

ology by calculating the energy profile of the reaction as a

function of the force. In addition, we are interested in investi-

gating how the mechanical strength of the C–C bonds of the

polymer chain varies with the external force and comparing

the critical energy of polymer scission of the two processes. In

this manner, we intend to get better insight into the factors

that govern ultrasound induced polymer dissociation. For our

model calculations we have applied hybrid density functional

theory in the common B3LYP implementation.12 This method

is known to provide rather accurate estimates of elementary

bond breaking processes up to the bond-breaking point,13,14

but it is also known that this approach becomes less reliable

beyond this point, i.e. for extended bond elongations, mainly

due to the neglect of static electron correlation.

All calculations were performed using the Gaussian 09

software package15 using the built-in methods B3LYP12 and

G4.16 We considered two model systems, R1 = R2 = CH3 and

R1 = R2 = C2H5 (Scheme 1). The energy profiles of the

reactions were first obtained in the absence of any external

force, and the key data are reproduced in Table S1 (ESIw). Thepresence of a transition state was confirmed by identifying one

imaginary frequency (see Table S3, ESIw) and by performing

intrinsic reaction calculations starting from the found transi-

tion state. The computed high energy of reaction and critical

energy (barrier height), being 272 and 337 kJ mol�1, respec-

tively, are in good accord with the fact that 1,2,3-triazoles

possess strong intrinsic resistance towards ring opening, and

that they are conveniently formed in the laboratory by the

reverse reaction—addition of alkynes to azides.

Table S1 (ESIw) also confirms that B3LYP with the basis set

6-31++G(d,p) offers a good compromise between moderate

computational effort and high accuracy in describing the energy

Scheme 1 Ring opening of a 1,2,3-triazole.

Department of Chemistry, University of Oslo, P.O. Box 1033,N-0315 Oslo, Norway. E-mail: einar.uggerud@kjemi.uio.now Electronic supplementary information (ESI) available: Backgroundtheory and additional figures. See DOI: 10.1039/c2cc34056a

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10444 Chem. Commun., 2012, 48, 10443–10445 This journal is c The Royal Society of Chemistry 2012

profile of the reaction, since the values obtained using this method

are similar to those obtained with the composite G4 method. The

latter is known to provide relative energies and critical energies of

so-called chemical accuracy, which is �10 kJ mol�1.17

From Table S2 (ESIw) it is seen that the critical energies for

ring opening of dimethyl- and diethyl-1,2,3-triazoles are essen-

tially the same. If this trend can be extrapolated to molecules

with longer alkane chains, this finding indicates that the

barrier height for ring opening of the polymers investigated

by Brantley et al.1 is probably not very different from the

model molecules studied here, at least not in the purified

gaseous state. However, since the sonication experiments were

conducted on molecules in solution and not on isolated

molecules, it is important to evaluate the role of the medium.

Ignoring the detailed molecular interactions, it is possible to

estimate the average electrostatic interaction using a polariz-

able continuum model (PCM)18 using PCM-B3LYP with the

same basis set. By applying the value er = 35.7 for the

dielectric constant of acetonitrile we obtain a critical energy

which is 26 kJ mol�1 higher than the in vacuo value, Table S2

(ESIw). In other words, it appears that the solvent has no

stabilizing effect on the transition state.

To simulate the effects of an external force, constrained

geometry optimizations were then performed using the

COGEF (COnstrained Geometries simulate External Force)

approach.14 In a COGEF optimization two anchor nuclei are

identified, one at each end of the molecule, and the distance l

between the two is increased gradually in a step-by-step

fashion. For each step the energy is fully minimized by varying

all degrees of freedom except l. In consequence, the net force

on all nuclei along a COGEF path is zero except for the two

anchor nuclei. For the two cases investigated here—the

dimethyl substituted (Fig. S2, ESIw) and the diethyl substituted

(Fig. S3, ESIw) triazoles—the carbons labeled C3 and C4, and

C5 and C6, respectively, were chosen to be the anchor nuclei.

The procedure was repeated for both the transition state and

the initial state geometries. The resulting force modified

potential energy curves are reproduced in Fig. S4 and S5 (ESIw).The most important parameter in controlling the reaction rate

is the critical energy E which is defined as

Ez(F) = ETS(F) � EIS(F) (1)

where ETS is the force modified potential energy (see theory in

ESIw) of the transition state and EIS of the initial state. Using

the available data we obtain the force modified variation of the

critical energy Ez(F), Fig. 1. It is evident from this plot that the

critical energy decreases with increasing applied force for both

reactions, showing that the critical energy for the ring opening

is reduced by applying a stronger force. The plot also shows

rather minor differences between the two analogue molecules

in this respect.

It is well known that the C–C bonds of polymer chains are

vulnerable to mechanical stress and demonstrate characteristic

lowering of the critical energy for dissociation with increasing

force.13,14 In the present context it therefore became pertinent

to investigate this alternative to ring opening. This reaction

type was modelled using the same methodology and the same

model systems, Schemes 2 and 3. For R1 = R2 = CH3 it turns

out that the mechanically weakest bond is the bond between

the substituent and the ring, while for R1 = R2 = C2H5 it is

the C–C bond next to the ring (a-cleavage). It seems reason-

able to consider the generally favourable a-cleavage observed

for the diethyl analogue also to be typical for the situation in

longer polymer chains, and that this non-polar reaction is not

much affected by the solvent. In the absence of any external

force the critical energies computed for breaking the respective

C–C bonds are above 400 kJ mol�1, which are higher than

for ring opening. However, as evident from Fig. 2 the critical

Fig. 1 Critical energy for ring opening (Scheme 1) as a function of

the applied force for R1 = R2 = CH3 (�) and R1 = R2 = C2H5 (J).

Scheme 2 C–C bond cleavage in dimethyl-1,2,3-triazole.

Scheme 3 C–C bond cleavage in diethyl-1,2,3-triazole.

Fig. 2 Critical energy as a function of external applied force, for ring

opening (Scheme 1, J) and C–C bond scission (Scheme 3, }) for

R1 = R2 = C2H5.

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This journal is c The Royal Society of Chemistry 2012 Chem. Commun., 2012, 48, 10443–10445 10445

energy—calculated using eqn (1) with elongation beyond the

bond critical point treated as the transition state—falls off

more quickly with increasing force. It is important to note that

under a constrained geometry optimization it is l not F that is

allowed to vary, so we do not control the external force

directly during calculation. As a result, immediately after the

bond critical point for 1,4-diethyl-1,2,3-triazole is reached, the

geometry optimization converged to a situation where one

bond is broken and all other bonds relax. Thus, we do not

obtain data for the critical energy for reaction (3) beyond

2.1 nN.

As an alternative, a constrained geometry optimization was

also performed by pulling the atoms labelled N3 and C2 in

Fig. S2 (ESIw), resulting in the ring opening illustrated in

Scheme 1. However, the critical force needed to break the ring

is 13.5 nN, which is significantly higher than the force required

to break a general C–C bond in a polymer.

At this stage of the discussion it seems clear that for

F o 1.0 nN—below the crossing point of the two curves of

Fig. 2—ring opening is preferred, while for F > 1.0 nN, the

a-bond is more likely to break. This is a key point, since

Brantley et al. interpreted the observed ring opening to be due

to a directed mechanical force induced by the stress resulting

from cavitation. At the crossing point, the critical energy is

320 kJ mol�1, which is substantial.

The fact that ring opening is preferred therefore suggests

that a mechanical force alone cannot fully explain the effect of

ultrasound. On the other hand, the experimental results

provided by Brantley et al. clearly indicate that mechanical

force is essential. We cannot rule out nonadiabatic effects

including rapid heating during bubble collapse, the involve-

ment of excited electronic states, as well as relevant mecha-

nistic alternatives. The latter could include solvent molecule

assisted ring opening as well as radical initiated processes—

both processes that may be aided by mechanical force.

In conclusion it should also be mentioned that after sub-

mission of the present manuscript, Brantley et al. published a

paper discussing other aspects of the mechanism than those

discussed here.19

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