Molecular Tensile Machines: Anti-Arrhenius Cleavage of DisulfideBondsYuanchao Li,† Alper Nese,‡,§ Krzysztof Matyjaszewski,‡ and Sergei S. Sheiko*,†

†Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3290, United States‡Department of Chemistry, Carnegie Mellon University, 4400 Fifth Avenue, Pittsburgh, Pennsylvania 15213, United States

*S Supporting Information

ABSTRACT: Molecular tensile machines are bottlebrushmolecules where tension along the backbone is self-generateddue to steric repulsion between the densely grafted side chains.Upon adsorption onto a substrate, this intrinsic tension isamplified to the nanonewton range depending on the sidechain length, grafting density, and interaction with thesubstrate. In this paper, bottlebrushes with a disulfide linkerin the middle of the backbone were designed to study theeffect of force and temperature on the scission of an individualdisulfide bond. The scission process was monitored onmolecular length scales by atomic force microscopy. Thescission rate constant has been shown to increase exponentiallywith bond tension but decrease with temperature. This anti-Arrhenius behavior is ascribed to the decrease of substrate surfaceenergy upon heating, which overpowers the corresponding effects of thermal energy and temperature dependent pre-exponentialfactor. Quantitative analysis using the force-modified Arrhenius and transition state theory (TST) equations, respectively, wasconducted to determine the dissociation energy, maximum rupture force, and activation barrier of a disulfide bond under tension.

■ INTRODUCTION

Mechanochemistry has been thriving during the past decadedue to the development of micromechanical tools and strainedmacromolecules that allow management of bond tension onmolecular length scales.1−4 It has been shown that mechanicalforce can break specific bonds,5,6 steer reaction pathways,7

control spin states in transition-metal complexes,8 trap diradicaltransition states,9 and enable many other interestingapplications.10−14 Our contribution to this field was thecreation of macromolecular architectures that are able togenerate and control bond tensions without applying anexternal force.6,15−20

Connectivity of atoms into molecules and molecularassemblies results in a decrease of entropy causing net tensileforce in chemical bonds on the order of 100 pN.21 Additionalenhancement of the bond tension to the nanonewton level canbe achieved through modification of molecular architecture,e.g., by dense branching and grafting. Steric repulsion betweenthe branches is transmitted to the covalent skeleton of abranched macromolecule and causes additional tension in itscovalent bonds.6,15−20 Unlike other micromechanical devicesthat typically control strain or loading rate, the moleculartensile machines enable accurate tension control. The tensiondepends on the branching (or grafting) density, length of thebranches, and interaction with the surrounding environment(e.g., solvent molecules and substrate). In addition to tensionamplification, the concept of strained macromolecules allowsdesign of molecular architectures with a well-defined

distribution of tension over their chemical bonds. This providesa unique opportunity to prepare strained macromolecules, suchas bottlebrushes,22 pom-poms,23 and tethered stars,24 that notonly generate mechanical tension but also enable focusingtension to specific chemical bonds.18

Here, we applied this concept to study mechanical activationof disulfide bonds that play a vital role in many life systems,especially in protein folding and unfolding.25−27 A singledisulfide bond was incorporated into the center of a bottlebrushbackbone as described elsewhere.6 The role of the bottlebrusharchitecture is to generate a well-defined constant tension andtransfer it to the disulfide bond in the middle of the backbone.While analysis of the effect of tension is a well-establishedprocedure,28−31 the effect of temperature on a mechanochem-ical process is a more complex task.20,32 Temperature exhibitsmultiple effects, including (i) change of the thermal energy(kBT), (ii) change of the pre-exponential factor,33,34 and also(iii) change of bond tension.20 Complementary to the previouspaper, where we introduced the anti-Arrhenius behavior ofstrained macromolecules through random scission of multiplebonds,20 here we studied scission of individual disulfide bonds.We have analyzed specific contributions of the above-mentioned temperature effects to the disulfide scission rateand showed that the temperature effect on bond tension plays a

Received: June 7, 2013Revised: August 9, 2013

Article

pubs.acs.org/Macromolecules

© XXXX American Chemical Society A dx.doi.org/10.1021/ma401178w | Macromolecules XXXX, XXX, XXX−XXX

dominant role compared to the thermal energy and the pre-exponential factor.

■ EXPERIMENTAL SECTIONMaterials. The bottlebrush macromolecules with a disulfide bond

in the middle of the backbone were synthesized by ATRP.6,35−39 Thepolymer brush consists of a poly(2-hydroxyethyl methacrylate)backbone and poly(n-butyl acrylate) (PBA) side chains (Figure 1).A combination of molecular characterization techniques (GPC, LS,gravimetric analysis, and AFM) was employed to measure the number-average degree of polymerization (DP) of the brush backbone and sidechains as 2N = 1300 and n = 130, respectively.6

Langmuir−Blodgett Monolayers. The bottlebrush macromole-cules were deposited from a dilute solution in chloroform onto asurface of water/2-propanol mixtures (0.4−0.8 wt % of propanol) in aLangmuir−Blodgett trough (KSV-5000 instrument equipped with aWilhelmy plate balance). Mixing water (Milli-Q double-distilled, ρ =18.2 MΩ) and 2-propanol (Aldrich, 99%) allowed accurate (±0.1mN/m) control of the spreading parameter of the macromoleculeswithin a range of 14−18 mN/m. The measurements were performedunder controlled vapor pressure of 2-propanol to minimize the effectof solvent evaporation on the spreading parameter. Insignificantevaporation of 2-propanol and corresponding variations of bondtension were monitored and neglected within duration of ourexperiments (<2 h).19 The temperature was controlled throughcirculation of a thermostated liquid around the trough andindependently monitored by a set of thermocouples placed at thewater/2-propanol surface. The accuracy of the temperature measure-ments was ±0.5 K. After different exposure times (time spent on air/water−propanol interface), the monolayer films were transferred fromthe air/water interface to freshly cleaved mica substrates at a constantpressure of 0.5 mN/m for AFM studies.Atomic Force Microscopy. Topographic images of individual

molecules were collected using a multimode atomic force microscope(Bruker) with a NanoScope V controller in PeakForce QNM mode.40

We used silicon cantilevers with a resonance frequency of 50−90 kHz

and a spring constant of about 0.4 N/m. Digital images of individualmolecules were analyzed using a custom software program developedin-house. The length distributions were obtained from two 3 μm × 3μm micrographs, including more than 600 molecules to ensure arelative standard deviation of the mean below 4%.

Selectivity of Scission Reactions. In uniformly strainedbottlebrush backbones, scissions of C−C, C−S, and S−S bondsoccur simultaneously but on significantly different time scales. On thebasis of the previous studies of the scission of S−S, C−S, and C−Cbonds,6 we have estimated that within about 2 h more than 95% of thescission reactions is attributed to S−S bonds (Figure S1 in SupportingInformation). As such, we have conducted our experiments at lowerbond tensions (<1.9 nN) to further suppress C−C and C−S scissionand thus increase the contribution of S−S scission. The bond tensionwas controlled in a range from 1.2 to 1.6 nN by adding 2-propanol tothe water subphase as described above in the Langmuir−BlodgettMonolayers section.

■ RESULTS AND DISCUSSION

The results are presented in two sections. In section 1, wereport experimental data on the individual effects of temper-ature and tension on the rate constant of disulfide scission. Insection 2, we analyze the measured data and evaluate theactivation parameters of the disulfide linker in bottlebrushmacromolecules.

1. Effects of Temperature and Bond Tension. Everyscission of disulfide bond yields two molecular bottlebrushes ofhalf-length, resulting in a characteristic bimodal lengthdistribution. The characteristic bimodality is favorable for thisstudy as it provides a clear reference for the midchain scission.As shown in Figure 2, two bands at L ≃ 320 nm and L/2 ≃ 160nm correspond respectively to (i) the full length ofbottlebrushes with the intact disulfide linker and (ii) half-length monosulfide bottlebrushes due to midchain scission of

Figure 1. Chemical structure of the bottlebrush macromolecule with N = 650 and n = 130 (left); Langmuir−Blodgett experiment setup (right).

Figure 2. Length distributions along with AFM height images of the bottlebrush macromolecules captured after exposure of 15 min to 0.4% 2-propanol (21 °C), 0.7% 2-propanol (21 °C), and 0.7% 2-propanol (5 °C) substrates (from left to right).

Macromolecules Article

dx.doi.org/10.1021/ma401178w | Macromolecules XXXX, XXX, XXX−XXXB

the disulfide linker.6 When the concentration of 2-propanol ortemperature was decreased, the molecular fraction at L ≃ 320nm decreased, while the fraction of shorter molecules at L/2 ≃160 nm correspondingly increased.Molecular imaging allows monitoring the scission process for

a large ensemble of individual macromolecules subjected toidentical mechanical and thermal conditions providing amplestatistical information on bond-scission kinetics.40−42 It alsooffers two complementary methods for quantitative analysis ofthe kinetics of bond scission. The first method is based oncounting the number of molecules per unit area, whichcorresponds to the number of ruptured bonds. The secondmethod used in this paper is based on the analysis of lengthdistribution. Assuming that the observed bond scission is a first-order unimolecular reaction, the time dependence of theaverage molecular length can be written as19

=− +∞

−∞

LL L L

1(1/ 1/ )e 1/kt

0 (1)

where L0 is the initial average length at t = 0 and L∞ = 161 ± 2nm is the average length of the midchain cleaved macro-molecules. For each data set, the initial time (t = 0) wasassigned to the first collected data point.Figure 3 shows how the number-average contour length

depends on temperature (Figure 3a) and bond tension (Figure3b), which was controlled by tuning the chemical compositionsof the liquid substrate. As shown previously,15,20,22 thebackbone tension in molecular bottlebrushes adsorbed to aflat substrate increases linearly with the spreading parameter Sas

≃f Sd (2)

where d is the width of a bottlebrush macromolecule adsorbedto the substrate. In our experiments, the substrate correspondsto the water/2-propanol subphase, the liquid is a melt of PBAside chains, and the gas is air. Addition of propanol undercontrolled vapor pressure allows accurate tuning of thespreading parameter and thus the backbone tension.16 Thespreading parameter S = γsg − (γsl + γlg), that is, the differencebetween the interfacial energies for the substrate/gas (sg),substrate/liquid (sl), and liquid/gas (lg) interfaces, wasindependently measured as a function of the propanolconcentration and temperature (Figures S2 and S3). Thewidth d was measured as an average distance between worm-like macromolecules in AFM micrographs of Langmuir−Blodgett monolayers prepared at a transfer ratio of 98%. Forexample, on 0.7% 2-propanol solution substrate at T0 = 21°C,we measured d ≃ 90 nm and S ≃ 14.9 mN/m, which gives abackbone tension of f ≃ 1.34 nN.Equation 1 has been applied to fit the data points in Figures

3a and 3b using the rate constant k as a single fitting parameter.Thus, obtained rate constants are plotted as a function ofreciprocal temperature (1/T) (Figure 3c) and force (Figure3d), respectively. The semilog plot of ln k(1/T) clearlydemonstrates the anti-Arrhenius behavior as the rate constantdecreases with temperature, while the ln k( f) plot confirms theexponential dependence of force reported previously.28,43−45

The anti-Arrhenius effect is ascribed to a decrease of spreadingparameter with temperature (Figure S3), leading to thecorresponding decrease of backbone tension (Figure 4),which overpowers the corresponding increase of the thermal

Figure 3. Kinetics of the disulfide-bond scission was studied by monitoring the decrease of the number-average contour length of molecularbottlebrushes at different temperatures (a, c) and bond tensions (b, d). (a) The effect of temperature was studied on the same substrate (0.7 wt % 2-propanol) by varying the temperature in a range from 5 to 26 °C as indicated. (b) The effect of bond tension was studied by varying the 2-propanolconcentration: 0.4% (■); 0.5% (●); 0.6% (▲); 0.7% (▼); 0.8% (◆) at the same temperature T0 = 21 °C. The solid lines in (a, b) are obtained byfitting the data points with eq 1 using the rate constant k as a single fitting parameter. (c) The Arrhenius plot of the rate constant ln k as a function ofthe reciprocal temperature 1/T measured on the same substrate (0.7 wt % of 2-propanol). (d) The rate constant ln k as a function of backbonetension f at a constant temperature T0 = 21 °C. The solid lines in (c, d) correspond to linear fits ln k = (4.02 ± 0.31 K) × 103/T − (22.1 ± 1.0) andln k = (8.44 ± 1.65 nN−1)f − (20.0 ± 2.4), respectively.

Macromolecules Article

dx.doi.org/10.1021/ma401178w | Macromolecules XXXX, XXX, XXX−XXXC

energy.20 Within the studied temperature range from 278 to299 K, the backbone tension can be approximated as

= −f a bT (3)

where a = 4.99 ± 0.14 nN and b = 0.0124 ± 0.0005 nN/K.2. Data Analysis. The kinetics of disulfide scission under

the concurrent effect of temperature and tension was analyzedby two different models: (i) Arrhenius equation, adapted byEyring, Zhurkov, Bell, and their co-workers for variousmechanochemical processes,28,29,43,44 and (ii) force-modifiedTST equation with the Morse potential of a covalent bond.46

The rationale for using the TST equation was to take intoaccount the effect of temperature on the pre-exponentialfactor.33 The Morse potential was introduced explicitly todemonstrate the effect of tension on the activation barrier ofdisulfide scission.Force-Modified Arrhenius Equation. The force-dependent

rate constant of the scission reaction can be described by thephenomenological Arrhenius equation

= − − Δk Ae E f x k T( )/a B (4)

where A is temperature (T) independent pre-exponentialfactor, Ea is activation energy, f is applied force, Δx is activationlength (the distance from equilibrium state to transition statealong the reaction coordinate), and kB = 1.38 × 1023 J/K is theBoltzmann constant. Note that both the activation energy andactivation length are independent of force. This approximationis acceptable for low forces ( f ≪ Ea/x0 ≃ 1 nN); however, itcannot be used for higher forces.From the slopes in Figures 3c and 3d, we determine Δx =

0.34 ± 0.07 Å and Ea = 69 ± 24 kJ/mol. The Δx value

determined here agrees with theoretical calculations.47

However, the Ea value is substantially lower than typicaldisulfide bond dissociation energies reported for smallmolecules (190−310 kJ/mol).48−51 Possible causes of thisunderestimation will be discussed later. By extrapolating thedata points in Figure 3d to zero force, we can estimate a pre-exponential factor of the order of 104 s−1. This number is wellbelow the nominal frequency of attempts v = kBT/h ≃ 1012 s−1,where h = 6.63 × 10−34 J s is the Planck constant. Such a largediscrepancy could be due to (i) the very inaccurate zero-forceextrapolation performed for a small force range and (ii)significant conformational constrains of the backbone withinbottlebrush macromolecules that may affect the entropychange.20

TST Equation with Morse Potential. Considering a disulfidebond under a constant uniaxial force f, the effective potentialcan be written as a function of reaction coordinate x:

= − −β−V V fx(1 e )x0

2(5)

where the first term Vb = V0(1 − e−βx)2 is a cumulative Morsepotential of a unperturbed bond, which includes both bondelongation and opening of the bond angle.20 The parametersβ−1 and V0 determine the width and depth of the potential well,respectively. The second term corresponds to the mechanicalwork of the force applied. By taking the derivative of eq 5 withrespect to x, we find two local extrema (Figure 6) that give thefollowing relations for the height ΔVTS and width ΔxTS of theactivation energy barrier as a function of force:

Δ = − − ΔV V f f f x1 /TS 0 m TS (6)

=+ −

− −x

Vf

f f

f f2ln

1 1 /

1 1 /TS0

m

m

m (7)

where fm = (∂Vb/∂x)max = βV0/2 is the maximum bond tension.The temperature effect on the pre-exponential factor was

analyzed using the Eyring equation that is the rate constantexpression from TST33

κ= Δ −Δkk T

he eS k V k T

TSTB / /TS B TS B

(8)

where the energy barrier ΔVTS = V(xTS) −V(x0) is the energydifference between transition state (x = xTS) and equilibriumstate (x = x0), ΔSTS = S(xTS) − S(x0) is the correspondingentropy change, κ is the transmission coefficient (κ < 1), andκ(kBT/h)e

ΔSTS/kB = A is the pre-exponential factor.

Figure 4. Backbone tension (eq 2) in adsorbed bottlebrushes on 0.7wt % 2-propanol aqueous substrate decreases with temperature. Thesolid line is a linear fit with eq 3.

Figure 5. (a) Linear fit of ln(k/T) as as a function of 1/T with the fitting equation ln(k/T) = (4.31 ± 0.31 K) × 103/T − (28.8 ± 1.0). (b) Linear fitof ln(k/T0) as a function of force at T0 = 21 °C with the fitting equation ln(k/T0) = (8.44 ± 1.65 nN−1)f − (25.6 ± 2.4).

Macromolecules Article

dx.doi.org/10.1021/ma401178w | Macromolecules XXXX, XXX, XXX−XXXD

To analyze the rate constant data, we rewrote eq 8 in thelogarithmic form as follows

κ= + Δ − Δ⎛⎝⎜

⎞⎠⎟k T

kh

S k V k Tln( / ) ln / /TSTB

TS B TS B(9)

and replotted Figure 3c,d as ln(k/T) versus 1/T and f,respectively (Figure 5). From the slopes in Figure 5, we candetermine the barrier parameters for both unperturbedpotential (V0 and fm) and strained potential (ΔVTS andΔxTS) as described previously,20 which were then used toconstruct an effective potential of the disulfide linker in thebottlebrush backbone (Figure 6).

The results of the fitting analysis are summarized in Table 1.The determined maximum force fm = 4.8 ± 1.3 nN agrees withthe rupture forces of disulfide bonds from theoreticalcalculations in the range of 3.4−4.8 nN depending on themethod used.52 The bond dissociation energy V0 = 80 ± 27 kJ/mol is slightly larger than Ea = 69 ± 24 kJ/mol obtained byusing the force-modified Arrhenius equation (eq 4). The goodagreement is due to relatively low force values f/fm ≃ 0.3studied in this paper. For larger forces ( f ≃ fm), the force-modified Arrhenius equation is not applicable. Yet, the obtainedV0 is substantially lower than typical disulfide bond dissociationenergies (190−310 kJ/mol) reported for small disulfidemolecules.48−51 Also the pre-exponential factor (A = κ(kBT/h)eΔSTS/kB) determined as ∼106 s−1 is significantly smaller thanthat for pyrolysis of dimethyl disulfide in gaseous state (1013

s−1)53 and the nominal attempt frequency (kBT/h ≃ 1012 s−1.These discrepancies can have different causes including the so-called enthalpy−entropy compensation effect,54 complex stressdistribution in branched macromolecules adsorbed to aninterface, and potentially reactive aqueous environment.Currently, it is assumed that the entropy of activation doesnot depend on force. This assumption might not be valid forcomplex molecules adsorbed to an aqueous interface, whereforce-dependent conformational and orientational entropiesmay contribute to the free energy and cause partialcompensation of the interaction potential. By applying

enthalpy−entropy compensation to the bond-scission reactionas TΔS( f) = αΔH( f) + β, where α and β are constants, we canestimate new values for the dissociation energy barrier and pre-exponential factor as 80/(1 − α) kJ/mol and 10(6+8α)/(1−α) s−1

(Supporting Information). For example, α = 0.4 would result ina dissociation energy of ∼133 kJ/mol and a pre-exponentialfactor of ∼1015 s−1 which are closer to the literature data.Inherent stress in polymer molecules has also been discussed inthe literature as one of the causes of lowering the dissociationenergy,55,56 but this stress is significantly smaller than theinternal stress in the backbone generated by the side chains inbottlebrush polymers, and we may exclude it from ourconsideration. However, the tension in the disulfide bondmay still differ from backbone tension due to complex tensiondistribution in bottlebrush molecules, leading to under-estimation of the dissociation energy and pre-exponentialfactor. Involvement of water into reaction is another likelycause of the underestimated energy barrier and pre-exponentialfactor as it may change the mechanism of reaction. Kumar et al.have found second-order kinetics for cis−trans thermalisomerization of azobenzene dimers at an air/water interfacesimilar to the Lindemann−Hinshelwood mechanism for theunimolecular reactions at low concentration of reactants.57

■ CONCLUSIONS

We have employed bottlebrush molecules as molecular tensilemachines to probe the strength of a disulfide linker in themiddle of the backbone and to study the kinetics of disulfide-bond scission under controlled force and temperature. Thescission rate showed exponential increase with force and anti-Arrhenius temperature effect. This unusual temperature effect isascribed to the decrease of backbone tension with temperature,which overpowers the effects of thermal energy and temper-ature dependent pre-exponential factor. From the kineticanalysis, we have determined the activation barrier parametersof the disulfide linker. At moderate forces studied here ( f/fm ≃0.3), the force-modified Arrhenius equation provides a goodestimate for both the dissociation energy V0 = 69 ± 24 kJ/moland activation length Δx = 0.34 ± 0.07 Å of the disulfide bond.These estimates are in good agreement with the correspondingparameters V0 = 80 ± 27 kJ/mol and Δx = 0.34 ± 0.07 Åobtained from TST equation using the force dependent Morsepotential. In addition, we have obtained the height and thewidth of the activation barrier at bond tensions around f = 1.4nN. The dissociation energy calculated from the force-modifiedArrhenius equation (Ea) deviates from that obtained from TSTequation with Morse potential (V0) approximately by a factorof (1 − f/fm)

1/2. In small force range ( f ≪ fm), the deviation isnegligible since (1 − f/fm)

1/2 ≃ 1; if the applied force f iscomparable to the maximum force fm, the model that takes theforce dependent potential into consideration should be moreappropriate and accurate. The obtained disulfide bonddissociation energy and pre-exponential factor are under-estimated compared to literature data, which could resultfrom several factors: (i) enthalpy−entropy compensation effect,(ii) complex stress distribution in branched macromolecules

Figure 6. Morse potential of the disulfide linker: (---) potential ofunperturbed bond with dissociation energy V0 = 80 kJ/mol; ()effective potential of stretched bond under the force of 1.43 nN withΔVTS = 38 kJ/mol and ΔxTS = 0.34 Å.

Table 1. Bond Potential and Activation Parameters Obtained from Different Models

model V0, kJ/mol fm, nN ΔVTS, kJ/mol Δx, Å A, s−1

force-modified Arrhenius equation 69 ± 24 NA NA 0.34 ± 0.07 ∼104

TST with Morse potential 80 ± 27 4.8 ± 1.3 38 ± 15 ( f = 1.43 nN) 0.34 ± 0.07 ( f = 1.43 nN) ∼106

Macromolecules Article

dx.doi.org/10.1021/ma401178w | Macromolecules XXXX, XXX, XXX−XXXE

adsorbed to an interface, and (iii) potentially reactiveenvironment at the water−air interface.

■ ASSOCIATED CONTENT*S Supporting InformationContribution of S−S bond scission and spreading parameter asa function of 2-propanol concentration and temperature;evaluation of the enthalpy−entropy compensation effect. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: sergei@email.unc.edu.Present Address§A.N.: Department of Chemistry and Biochemistry, Universityof South Carolina, Columbia, SC 29208.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe gratefully acknowledge funding from the National ScienceFoundation (DMR 0906985, DMR 0969301) and Departmentof the Army (59646-CH).

■ REFERENCES(1) Beyer, M. K.; Clausen-Schaumann, H. Chem. Rev. 2005, 105,2921−2948.(2) Caruso, M. M.; Davis, D. A.; Shen, Q.; Odom, S. A.; Sottos, N.R.; White, S. R.; Moore, J. S. Chem. Rev. 2009, 109, 5755−5798.(3) Liang, J.; Fernandez, J. M. ACS Nano 2009, 3, 1628−1645.(4) Huang, Z.; Boulatov, R. Chem. Soc. Rev. 2011, 40, 2359−2384.(5) Yang, Q.-Z.; Huang, Z.; Kucharski, T. J.; Khvostichenko, D.;Chen, J.; Boulatov, R. Nat. Nanotechnol. 2009, 4, 302−306.(6) Park, I.; Sheiko, S. S.; Nese, A.; Matyjaszewski, K. Macromolecules2009, 42, 1805−1807.(7) Hickenboth, C. R.; Moore, J. S.; White, S. R.; Sottos, N. R.;Baudry, J.; Wilson, S. R. Nature 2007, 446, 423−427.(8) Parks, J. J.; Champagne, A. R.; Costi, T. A.; Shum, W. W.;Pasupathy, A. N.; Neuscamman, E.; Flores-Torres, S.; Cornaglia, P. S.;Aligia, A. A.; Balseiro, C. A.; Chan, G. K.-L.; Abruna, H. D.; Ralph, D.C. Science 2010, 328, 1370−1373.(9) Lenhardt, J. M.; Ong, M. T.; Choe, R.; Evenhuis, C. R.; Martinez,T. J.; Craig, S. L. Science 2010, 329, 1057−1060.(10) Davis, D. A.; Hamilton, A.; Yang, J.; Cremar, L. D.; Van Gough,D.; Potisek, S. L.; Ong, M. T.; Braun, P. V.; Martinez, T. J.; White, S.R.; Moore, J. S.; Sottos, N. R. Nature 2009, 459, 68−72.(11) Lenhardt, J. M.; Black, A. L.; Craig, S. L. J. Am. Chem. Soc. 2009,131, 10818−10819.(12) Piermattei, A.; Karthikeyan, S.; Sijbesma, R. P. Nat. Chem. 2009,1, 133−137.(13) Tennyson, A. G.; Wiggins, K. M.; Bielawski, C. W. J. Am. Chem.Soc. 2010, 132, 16631−16636.(14) Wiggins, K. M.; Hudnall, T. W.; Shen, Q.; Kryger, M. J.; Moore,J. S.; Bielawski, C. W. J. Am. Chem. Soc. 2010, 132, 3256−3257.(15) Sheiko, S. S.; Sun, F. C.; Randall, A.; Shirvanyants, D.;Rubinstein, M.; Lee, H.-i.; Matyjaszewski, K. Nature 2006, 440, 191−194.(16) Lebedeva, N. V.; Sun, F. C.; Lee, H.-i.; Matyjaszewski, K.;Sheiko, S. S. J. Am. Chem. Soc. 2008, 130, 4228−4229.(17) Park, I.; Shirvanyants, D.; Nese, A.; Matyjaszewski, K.;Rubinstein, M.; Sheiko, S. S. J. Am. Chem. Soc. 2010, 132, 12487−12491.(18) Park, I.; Nese, A.; Pietrasik, J.; Matyjaszewski, K.; Sheiko, S. S. J.Mater. Chem. 2011, 21, 8448−8453.

(19) Li, Y.; Nese, A.; Lebedeva, N. V.; Davis, T.; Matyjaszewski, K.;Sheiko, S. S. J. Am. Chem. Soc. 2011, 133, 17479−17484.(20) Lebedeva, N. V.; Nese, A.; Sun, F. C.; Matyjaszewski, K.; Sheiko,S. S. Proc. Natl. Acad. Sci. U. S. A. 2012, 109, 9276−9280.(21) Brock, J.; Panyukov, S.; Liao, Q.; Rubinstein, M. Manuscript inpreparation.(22) Panyukov, S.; Zhulina, E. B.; Sheiko, S. S.; Randall, G. C.; Brock,J.; Rubinstein, M. J. Phys. Chem. B 2009, 113, 3750−3768.(23) Panyukov, S. V.; Sheiko, S. S.; Rubinstein, M. Phys. Rev. Lett.2009, 102, 148301.(24) Sheiko, S. S.; Panyukov, S.; Rubinstein, M.Macromolecules 2011,44, 4520−4529.(25) Freedman, R. B.; Hirst, T. R.; Tuite, M. F. Trends Biochem. Sci.1994, 19, 331−336.(26) Wedemeyer, W. J.; Welker, E.; Narayan, M.; Scheraga, H. A.Biochemistry 2000, 39, 4207−4216.(27) Myers, J. K.; Nick Pace, C.; Martin Scholtz, J. Protein Sci. 1995,4, 2138−2148.(28) Bell, G. Science 1978, 200, 618−627.(29) Evans, E.; Ritchie, K. Biophys. J. 1997, 72, 1541−1555.(30) Beyer, M. K. J. Chem. Phys. 2000, 112, 7307−7312.(31) Dudko, O. K.; Hummer, G.; Szabo, A. Phys. Rev. Lett. 2006, 96,108101.(32) Liang, J.; Fernandez, J. M. J. Am. Chem. Soc. 2011, 133, 3528−3534.(33) Wynne-Jones, W. F. K.; Eyring, H. J. Chem. Phys. 1935, 3, 492−502.(34) Kramers, H. A. Physica 1940, 7, 284−304.(35) Matyjaszewski, K.; Xia, J. Chem. Rev. 2001, 101, 2921−2990.(36) Pakula, T.; Zhang, Y.; Matyjaszewski, K.; Lee, H.-i.; Boerner, H.;Qin, S.; Berry, G. C. Polymer 2006, 47, 7198−7206.(37) Sheiko, S. S.; Sumerlin, B. S.; Matyjaszewski, K. Prog. Polym. Sci.2008, 33, 759−785.(38) Lee, H.-i.; Pietrasik, J.; Sheiko, S. S.; Matyjaszewski, K. Prog.Polym. Sci. 2010, 35, 24−44.(39) Matyjaszewski, K. Macromolecules 2012, 45, 4015−4039.(40) Sheiko, S. S.; Moller, M. Chem. Rev. 2001, 101, 4099−4124.(41) Sheiko, S. S.; Prokhorova, S. A.; Beers, K. L.; Matyjaszewski, K.;Potemkin, I. I.; Khokhlov, A. R.; Moller, M. Macromolecules 2001, 34,8354−8360.(42) Sheiko, S. S.; Moller, M. In Macromolecular Engineering: PreciseSynthesis, Materials Properties, Applications; Matyjaszewski, K., Gnanou,Y., Leibler, L., Eds.; Wiley: New York, 2007; Vol. 3, pp 1515−1574.(43) Kauzmann, W.; Eyring, H. J. Am. Chem. Soc. 1940, 62, 3113−3125.(44) Zhurkov, S. N. Int. J. Fract. Mech 1965, 1, 311−322.(45) Wiita, A. P.; Ainavarapu, S. R. K.; Huang, H. H.; Fernandez, J.M. Proc. Natl. Acad. Sci. U. S. A. 2006, 103, 7222−7227.(46) Morse, P. M. Phys. Rev. 1929, 34, 57−64.(47) Iozzi, M. F.; Helgaker, T.; Uggerud, E. J. Phys. Chem. A 2011,115, 2308−2315.(48) Koval, I. V. Russ. Chem. Rev. 1994, 63, 735−750.(49) Benson, S. W. Chem. Rev. 1978, 78, 23−35.(50) Antonello, S.; Daasbjerg, K.; Jensen, H.; Taddei, F.; Maran, F. J.Am. Chem. Soc. 2003, 125, 14905−14916.(51) Xiao-Hong, L.; Xiao-Yang, G.; Xian-Zhou, Z. J. Sulfur Chem.2011, 32, 419−426.(52) Iozzi, M. F.; Helgaker, T.; Uggerud, E. Mol. Phys. 2009, 107,2537−2546.(53) Coope, J. A. R.; Bryce, W. A. Can. J. Chem. 1954, 32, 768−779.(54) Liu, L.; Guo, Q.-X. Chem. Rev. 2001, 101, 673−696.(55) Stoliarov, S. I.; Lyon, R. E.; Nyden, M. R. Polymer 2004, 45,8613−8621.(56) Smith, K. D.; Bruns, M.; Stoliarov, S. I.; Nyden, M. R.; Ezekoye,O. A.; Westmoreland, P. R. Polymer 2011, 52, 3104−3111.(57) Kumar, B.; Suresh, K. A. Phys. Rev. E 2009, 80, 021601.

Macromolecules Article

dx.doi.org/10.1021/ma401178w | Macromolecules XXXX, XXX, XXX−XXXF