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Polymer 84 (2016) 178e184

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Polymer

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Sonication-induced scission of molecular bottlebrushes: Implicationsof the “hairy” architecture

Yuanchao Li a, Zhenbin Niu b, Joanna Burdy�nska c, Alper Nese c, Yang Zhou a,Zachary S. Kean b, Andrey V. Dobrynin d, Krzysztof Matyjaszewski c, Stephen L. Craig b,Sergei S. Sheiko a, *

a Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599, United Statesb Department of Chemistry, Duke University, Durham, NC 27708, United Statesc Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15213, United Statesd Department of Polymer Science, University of Akron, Akron, OH 44325, United States

a r t i c l e i n f o

Article history:Received 22 October 2015Received in revised form16 December 2015Accepted 22 December 2015Available online 29 December 2015

Keywords:Polymer brushesMechanochemistrySonication

* Corresponding author.E-mail address: sergei@email.unc.edu (S.S. Sheiko

http://dx.doi.org/10.1016/j.polymer.2015.12.0440032-3861/© 2016 Elsevier Ltd. All rights reserved.

a b s t r a c t

Polymer bottlebrushes may be viewed as hairy flexible cylinders with a long backbone and a thick coronaof densely grafted polymer chains. The corona not only controls the bottlebrush diameter, but alsoprovides an additional drag force. We report the study of backbone scission by external forces caused byultrasonication. A series of bottlebrushes with the same backbone and different side-chain lengths wasprepared by ATRP. Bond fracture was induced by pulsed ultrasound in a dilute chloroform solution andex-situ monitored through molecular imaging of reaction products by atomic force microscopy. Thescission rate was found to increase with side chain length, while the limiting length of fractured bot-tlebrushes displayed a decrease. The experiment showed a good agreement with the Rouse model ofpolymer dynamics, which suggests that solvent drains through the corona of bottlebrush side-chains.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Molecular bottlebrushes are a unique class of graft copolymersexhibiting extended comb-like conformation due to steric repul-sion of densely grafted side chains [1,2]. The special spatial di-mensions and tunable architecture of bottlebrush macromoleculeslead to potential applications including supersoft elastomers [3e6],nanomaterials fabrication [7,8] and molecular tensile machines[9e13]. We have been particularly interested in the use of bottle-brushes as molecular tensile machines where tension is self-generated along the backbone due to steric repulsion betweendensely grafted side chains [14,15]. The intrinsic tension can befinely tuned by adjusting molecular architecture (side chain lengthand grafting density) and environmental conditions (solventquality and temperature), enabling mechanical activation of intra-molecular chemical reactions in response to minute variations intemperature [11], surface energy [16], and concentration ofreducing agents [17]. In addition to the internal tension, the

).

bottlebrush architecture may effectively mediate the effect ofexternally applied forces, e.g. during shear flow upon sonication-induced solvent cavitation. Nowadays, sonication is widely usedin the dispersion of nano- and mesoscale particles and filaments. Inaddition, it can also break carbon nanotubes [18e21], cylindricalmicelles [22e24], and polymer fibers [25,26]. It is generallyaccepted that the destructive force is caused by ultrafast shear flowof the solvent created by cavitation, which involves the nucleation,growth, and collapse of microbubbles in solution. As such, soni-cation has become a popular technique to control the length ormeasure the mechanical strength of nanostructured materials,including carbon nanotubes, nanowires, cylindrical micelles andfibrils [19,27,28].

In this work, we study the ultrasound-induced scission of mo-lecular bottlebrushes in dilute chloroform solutions, which couldbe the result of contributions from both intrinsic and externalforces. Unlike solid cylindrically shaped objects, molecular bottle-brushes are “soft” and their hydrodynamic diameters depend onboth side-chain degree of polymerization (DP) and solvent quality.Here, we are particularly interested in the effects of the side chainDP on the sonication-induced backbone scission, including thescission rate and the limiting length of the fracture products. The

Y. Li et al. / Polymer 84 (2016) 178e184 179

side-chain effect depends on the sonication-induced flow rate,which may result in solvent draining through the bottlebrushcorona producing an additional drag force and leading to amplifi-cation of the scission process. As a result, the contribution ofpolymer architecture to sonication induced chain fracture is ex-pected to be much richer than has been observed, for example, inthree-arm star polymers [29]. Molecular bottlebrushes preparedfrom the same backbone with different side chain DPs were sub-jected to pulsed ultrasound to cause backbone scission. The scissionkinetics was followed by monitoring the average contour length ofthe bottlebrushes via molecular imaging with the use of atomicforce microscopy (AFM). We have analyzed the data and shown thedependence of the limiting contour length of the bottlebrushbackbone and the scission rate on the side chain DP.

2. Experimental section

2.1. Materials

n-Butyl acrylate (nBA, 99%, Acros) and (2-trimetylsiloxy)ethylmethacrylate (HEMA-TMS, Scientific Polymer Products) were pu-rified by passing the monomer through a column filled with basicalumina to remove the inhibitor, 2,20-azobis(2-methylpropionitrile)(AIBN, 98%, Aldrich) was recrystallized from methanol and driedunder vacuum prior use. Sulfuric acid (20% fuming) was purchasedfrom Alfa Aesar. All other reagents: 2-cyano-2-propyl 4-cyanobenzodithioate (98%), copper(I) bromide (CuIBr, 99.999%),copper(II) bromide (CuIIBr2, 99.999%), 4,40-dinonyl-2,20-dipyridyl(dNbpy, 97%), potassium fluoride (KF, 99%), tetrabutylammoniumfluoride (TBAF, 1.0 M in THF), a-bromoisobutyryl bromide (98%),2,5-di-tert-butylphenol (DTBP, 99%), triethylamine (TEA, �99%), 1-butanol (ACS reagent, �99.4%) and solvents were purchased fromAldrich and used as received without further purification.

2.2. Synthesis and characterization

The conversion of nBA was determined from 1H NMR spectrarecorded in CDCl3 as a solvent using Brüker 300 MHz spectrometer.Molecular weight distributions of the polymers were characterizedby gel permeation chromatography (GPC) using Polymer StandardsServices (PSS) columns (guard, 105, 103, and 102 Å), with THF eluentat 35 �C, flow rate 1.00mL/min, and differential refractive index (RI)detector (Waters, 2410). The apparent number-average molecularweights (Mn) and molecular weight dispersities (Mw/Mn) weredetermined with a calibration based on linear poly(methyl meth-acrylate) (PMMA) standards and diphenyl ether as an internalstandard, using WinGPC 6.0 software from PSS. In addition to theconventional GPC technique, we used a combination of molecularimaging by AFM and preparation of monolayers at a controlledmass-per-unit-area by the LangmuireBlodgett technique (LB).While the GPC of large branched macromolecules is prone to sig-nificant errors, the AFM-LB method allows for more accurate DPmeasurements of both the backbone and side chains [30,31].

2.2.1. Synthesis of P(HEMA-TMS)2000A 25 mL Schlenk flask was charged with 2-cyano-2-propyl 4-

cyanobenzodithioate (0.0023 g, 0.0092 mmol), HEMA-TMS(20.0 mL, 91.9 mmol), AIBN (0.151 mg, 0.92 mmol, a stock solu-tion) and toluene (1.0 mL). The solution was degassed by purgingwith nitrogen over 30 min. Afterwards, the sealed flask wasimmersed in an oil bath at 65 �C. Polymerization was terminatedafter 65 h at 20.5% monomer conversion and the polymer molec-ular weight was determined by THF GPC: Mn,GPC ¼ 3.10$105, andMw/Mn ¼ 1.24. The degree of polymerization (DP) was calculatedfrom the calibration curve (Mn,GPC ¼ 163.85$DP-7000) and

determined to be 2000. The reaction mixture transferred to 100 mLpre-weighted, round-bottom flask, then the remaining monomerwas removed by flushing air overnight and the polymer was usedfor the next step without further purification.

2.2.2. Synthesis of PBiBEM2000 (macroinitiator)A 100 mL round-bottom flask was charged with P(HEMA-

TMS)2000 (3.60 g, 17.8 mmol), KF (1.16 g, 19.6 mmol), DTBP (0.37 g,1.78 mmol), and then dry THF (50 mL) was added under nitrogen.The reaction mixture was cooled down in an ice bath, followed bythe injection of tetrabutylammonium fluoride (0.18 mL, 1.0 M inTHF, 0.18 mmol) and subsequent dropwise addition of a-bromoi-sobutyryl bromide (4.50 g, 2.4 mL 19.6 mmol) over the course of20 min. Upon addition, the reaction mixture was allowed to reachroom temperature and was stirred for another 16 h. Afterwardssolids were filtered of and the mixture was precipitated intomethanol/water (70/30), re-dissolved in chloroform (50 mL) andpassed through the column filled with basic alumina. The productwas re-precipitated three times in hexanes and dried overnightunder vacuum. Apparent molecular weight determined by THFGPC: Mn,GPC ¼ 3.16$105, and Mw/Mn ¼ 1.31.

2.2.3. Synthesis of polymer bottlebrushesFour bottlebrush polymers were synthesized by ATRP from the

same macroinitiator (PBiBEM2000) and varying in DP of poly (n-butyl acrylate) (PBA) side chains (Table 1). A typical procedure forthe preparation of Brush-1 is described here: A 10 mL Schlenk flaskequipped with a stir bar was charged with macroinitiator PBi-BEM2000 (0.196 g, 0.703 mmol of BiBEM groups), nBA (10.0 mL,70.2 mmol), dNbpy (0.155 g, 0.379 mmol), CuIIBr2 (4.7 mg,0.0210 mmol), and anisole (1.1 mL). The solution was degassed bythree freezeepumpethaw cycles. During the final cycle CuIBr(24.6 mg, 0.1684 mmol) was quickly added to the frozen reactionmixture under nitrogen atmosphere. The flask was sealed, evacu-ated, back-filled with nitrogen five times, and then immersed in anoil bath thermostated at 70 �C. The polymerization was stoppedafter 18 h, and the monomer conversion was determined by 1HNMR (2.6%), resulting in the brush polymer with DP~26 of sidechains. The polymer was purified by three precipitations from coldmethanol, and dried under vacuum at room temperature, to aconstant mass. Apparent molecular weight was determined usingTHF GPC: Mn,GPC ¼ 1.35$106, and Mw/Mn ¼ 1.30.

2.3. Sonication experiments

Each sonication was performed in a three-armed Suslick reac-tion vessel of ~15 mL of molecular bottlebrush solution in chloro-form at a concentration of 0.1 mg/mL. The solutions weredeoxygenated with bubbling N2 for 30 min prior to sonication. Thetemperature was kept between 6 and 9 �C in an ice-water bath, andthe sonication pulse sequence was set to 1 s ON/1 s OFF, with apower of 6.8 W/cm2 working at 20 kHz. Aliquots were removedfrom the vessel at various sonication time intervals for AFManalysis.

2.4. LangmuireBlodgett monolayers

At different sonication times, solutions of the molecular bot-tlebrushes were extracted from the reactor, and 100 mL wasdeposited onto the surface of water (Milli-Q double-distilled,r ¼ 18.2 MU)/2-propanol (SigmaeAldrich, HPLC grade) mixture(0.5 wt. % of propanol) in a LangmuireBlodgett trough (KSV-5000instrument equipped with a Wilhelmy plate balance) at roomtemperature. Propanol was added to reduce the surface energy toprevent backbone scission due to adsorption [16]. The monolayer

Table 1Characterization of the molecular bottlebrushes.

GPC AFM-LB

nbba nsc

b Mnc Mw/Mn

d L0 (nm)e W (nm)f nbbg nsc

h nsc/ngi

Brush-1 2000 26 1.35 � 106 1.30 371 ± 10 23 ± 2 1484 40 23Brush-2 2000 60 1.63 � 106 1.52 354 ± 8 60 ± 2 1416 112 64Brush-3 2000 100 1.75 � 106 1.68 369 ± 8 77 ± 4 1476 148 85Brush-4 2000 130 2.14 � 106 1.58 366 ± 9 110 ± 4 1464 222 127

a Number average DP of the bottlebrush backbone estimated from its apparent molecular weight by GPC.b Apparent number average DP of side chains estimated from monomer conversion.c Apparent number average molecular weight measured by GPC.d Dispersity determined by GPC.e Contour length of bottlebrushes adsorbed to a mica substrate prior to sonication prepared by the LB technique.f Width of the bottlebrush adsorbed on a mica substrate determined by AFM.g Number average DP of the bottlebrush backbone calculated from the AFM imaged molecules as nbb¼ L0/l0, where l0¼ 0.25 nm e monomer contour length.h Number average DP of the side chains calculated as nsc ¼ aW=ð2Ðl0Þ , where Ð ¼ 1:2 e dispersity of bottlebrush side chains determined by GPC of cleaved side chains,

a¼(1þ prTW/4L0) e geometric correction factor due to the hemispherical shape of bottlebrush macromolecules and rT¼ 0.9 e LB mass transfer ratio [31].i ngy1:75 is the average number of repeat units of the backbone between neighboring side chains measured previously [6].

Y. Li et al. / Polymer 84 (2016) 178e184180

films were transferred from the air/aqueous interface to freshlycleavedmica substrates at a constant pressure of 0.5 mN/m for AFMstudies.

2.5. AFM imaging and analysis

Height images of individual molecules were collected using amultimode Atomic Force Microscopy (Bruker) with a NanoScope Vcontroller in the PeakForce QNMmode. We used silicon cantileverswith a resonance frequency of 50e90 kHz and a spring constant ofabout 0.4 N/m. Digital images of individual molecules wereanalyzed using a custom software program developed in-house.The contour length of the bottlebrush backbone was measureddirectly by AFM due to the height contrast from the desorbed sidechains segregated around the backbone. More than 600 moleculeswere counted to obtain the length distributions of the bottle-brushes, ensuring representative statistics.

3. Results and discussion

3.1. Molecular imaging of degradation products

Fig. 1a displays images of individual molecules of Brush-3captured at different stages of the sonication process. Apparently,long bottlebrushes undergo progressive fragmentation to smallerspecies. Fig. 1b depicts the time evolution of the bottlebrush lengthdistribution during the sonication process. For example, theaverage contour length of Brush-3 was L0¼ 369± 8 nm beforesonication and then decreased to a limiting length ofLlim¼ 27± 4 nm within a total sonication time of 4 h. The lengthdispersity of the fractured bottlebrushes initially increased at thebeginning of sonication and then followed by a decrease with time,as shown in Fig. 1c. This is consistent with previously reportedresult on ultrasonic degradation of poly(methyl methacrylate) andpolystyrene that initially narrow distribution increased in dis-persity before narrowing again at long sonication times [32,33]. Wehypothesize that this increase in dispersity is due to multiplefractures of a given parent bottlebrush during a single bubblecollapse; the daughters of the first fragmentation are trapped in theelongational flowand experience increasing strain rates that lead toadditional fragmentation. Note that scission of the side chains canbe neglected for Brush-1, 2 and 3, since their molecular weight iswell below the typical limiting molecular weight (40e50 kDa)under similar experimental conditions [34,35]. For Brush-4 withside chain DP of 222, the average molecular weight of two PBA sidechains is about 57 kDa, which may cause their rupture. However,

the probability of bond scission along any given side-chain to side-chain path is significantly lower than along the backbone. Due tomultiple side chains coupled to a bottlebrush backbone, the dragforce along the backbone is larger than along a side-chain path. It isalso necessary to point out that recombination of daughter frag-ments can be neglected due to steric repulsion of densely-graftedside chains. Once the backbone is cleaved, the generated radicalswill be spontaneously shielded by the side chains, which form ahemispherical cap at the bottlebrush ends hindering therecombination.

3.2. Degradation kinetics of molecular bottlebrushes

The scission rate and the limiting molecular weight for linearpolymers can be determined by using the equation derived byMadras et al. [36,37]. This equation is based on the assumption thatsonication-induced cleavage of polymers occurs at the mid-point ofthe chain and is a first-order reaction:

ln

L�1lim � L�1

t

L�1lim � L�1

0

!¼ �kLlimt (1)

where Llim, L0 and Lt are the limiting number average contourlength, the initial number average contour length and the numberaverage contour length of the backbone at time t respectively, and kis the rate constant that is independent of Lt. Note that Eq. (1) isexpressed in terms of bottlebrush contour length, which is linearlyproportional to the corresponding molecular weight (Mi~Li) typi-cally used in the kinetics analysis [28,29]. We use Eq. (1) to fit theexperimental data with Llim and k as the fitting parameters for allfour bottlebrush samples. As shown in Fig. 2a, the fitted decayprofiles (solid curves) are in good agreement with the experimentaldata (points). The fitting results are summarized in Table 2. Theextrapolated Llim values in Table 2 are verified bymolecular imagingof bottlebrushes after long-time sonication for 4 h (Fig. 2b).

As shown in Table 2, the scission rate increases with increasingside chain DP, while the limiting contour length (Llim) of the mo-lecular bottlebrush decreases with increasing side chain DP. Bothobservations are consistent with previously reported results ofsonication-induced scission of poly (alkyl methacrylate) that thescission rate increases and the limiting chain length decreases withincreasing bulk size of the alkyl substituent [34,35]. This may beexplained by larger drag force generated along the bottlebrushbackbone with longer side chains during bubble collapse. Note thatthe limiting contour lengths for all four bottlebrushes are sub-stantially smaller than that for linear polymers under similar

Fig. 1. (a) AFM height micrographs of Brush-3 and cartoon displaying fragmentation of bottlebrushes during sonication. (b) The corresponding length distributions and (c)Dependence of the length dispersity, i.e. ratio of weight average contour length (Lw) to number average contour length (Ln), with sonication time.

Fig. 2. (a) Experimentally determined number average contour length with respect to sonication time for Brush-1 ( ), Brush-2 ( ), Brush-3 ( ) and Brush-4 ( ). The solid curves

are the corresponding fits using Eq. (1). Inset: The data points are plotted as 1Llim

ln

"L�1lim�L�1

t

L�1lim�L�1

0

#versus time (Eq. (1)). (b) AFM height micrographs of the molecular bottlebrushes were

captured after sonication for 4 h. The bottlebrushes with shorter side chains (Brush-1) display longer backbones than the brushes with longer side chains.

Y. Li et al. / Polymer 84 (2016) 178e184 181

sonication conditions. Typical limiting molecular weight for poly(alkyl methacrylates) is about 40 kg/mol [35], corresponding to acontour length of ~100 nm, which is about 4 times larger than thatfor the bottlebrushes with the longest side chains (Brush-4). On theother hand, the densely grafted bottlebrush samples approach theirlimiting contour length within ~60 min, while it takes hours forlinear poly (alkyl methacrylates) to reach their limiting molecularweights under similar conditions (or at even higher sonicationpowers) [34].

3.3. Data analysis

For scaling analysis of the dependence of the limiting contourlength on the side chain DP, we will consider two different modelsto calculate the drag force at the center of a bottlebrush backbone.In the first model, solvent is assumed to be freely draining throughthe side chains as they move (Rouse model); while in the othermodel, we assume that the side chain drags the solvent in theirpervaded volume as they move (Zimm model) [38].

Table 2Results from fitting analysis in Fig. 2.

L0 (nm)a Llim (nm)b K$104 (min�1 nm�1)c R2adjd

Brush-1 371 ± 10 56 ± 6 4.3 ± 0.8 0.94Brush-2 354 ± 8 36 ± 4 7.8 ± 1.5 0.95Brush-3 369 ± 8 27 ± 4 8.2 ± 1.3 0.96Brush-4 366 ± 9 21 ± 2 13.6 ± 1.3 0.98

a Initial contour length of the bottlebrushes before sonication.b Limiting contour length of fractured bottlebrushes.c Rate constant of the sonication-induced fracture of bottlebrushes obtained by

fitting the experimental data points in Fig. 2a with Eq. (1).d The adjusted R2 values close to unity demonstrate the goodness of the fit.

Fig. 3. Experimentally determined scaling relation between the limiting contourlength (Llim) and the number of Kuhn monomers in the side chain (Nsc). The solid linerepresents the power-law fit to the data points.

Y. Li et al. / Polymer 84 (2016) 178e184182

3.3.1. Rouse modelWe first consider the force at the center of a chain (maximum

force fm) for linear polymers with n monomers in the elongationalflow generated by sonication. Assuming that the chain is fullyextended, we can write [39].

fm � zmL2 (2)

where L ~ n is the contour length, zm is the monomeric frictioncoefficient.

In this model, it is assumed that solvent can be freely drainedthrough the volume occupied by the side chains as they move. Thefriction coefficient of each Kuhn monomer is evaluated as zm¼hb,where by1.8 nm is the Kuhn length of PBA side chains and h is theviscosity of the solvent. Therefore the total friction coefficient of thewhole side chain is the sum of the contributions of each monomer:

zR ¼ Nsczm ¼ Nscbh (3)

where Nsc is the number of Kuhn monomers of a side chain.Considering each side chain is an effective monomeric unit ofbottlebrush molecules, we can obtain the maximum drag force atthe center of the bottlebrush backbone as

fm � zRL2 � NscL2 (4)

As the force along the bottlebrush backbone increases, the rateof backbone scission increases. It is known that the intrinsic tensionin the bottlebrush backbone (prior to sonication) is on the order of10 pN [15], while it requires nN forces to break covalent bonds onthe ~ms time scale of a bubble collapse in the sonication experiment[40]. Therefore, the intrinsic tension can be neglected, and theexternal critical force (fc) to break the CeC bonds in the backbonecan be considered as the same for the four bottlebrushes regardlessof the side chain DP. This differs from the case of solid filaments thatexhibit an increase of the critical force with increasing filamentdiameter. The backbone will effectively stop breaking once fm be-comes smaller than fc, and therefore we can obtain the followingrelation between the limiting contour length (Llim) and the numberof Kuhn monomers in the side chain (Nsc):

fc � NscL2lim (5)

Llim � ð1=NscÞ1=2 (6)

To verify this prediction, we plot the experimentally determinedlimiting contour lengths as a function 1/Nsc (Fig. 3). The number ofKuhn monomers can be estimated as Nscyðnsc=ngÞl0=b, where thenumber average DP of the side chains was determined from thebrush width by the AFM-LB method (Table 1) [9,15,31]. For ourbottlebrush macromolecules, Nsc ranges from 3 to 18. The slope of0.57 ± 0.06 is slightly larger than 0.5 - the scaling exponent

predicted by the Rouse model (Eq. (6)). This deviation may beattributed to incomplete extension of the bottlebrush backbone inthe elongational flow created by bubble collapse.

3.3.2. Zimm modelAssuming that the side chains drag solvent confined within a

bottlebrush macromolecule, we consider molecular bottlebrushesas solid spherocylinders with radius R ¼ bN1=2

sc (unperturbed sidechains that are smaller than the thermal blob). The aspect ratio ofthe cylindrical brushes is given as

p ¼ L0.

2R ¼ ðLþ 2RÞ=2R ¼ L.�

2bN1=2sc

�þ 1 (7)

where L'¼Lþ 2R is the total length of molecular bottlebrushesincluding the end caps formed by side chains in solution. The aspectratios for the four molecular bottlebrushes at limiting backbonecontour length Llim are in the range of 2.4e9.7. Taking this intoconsideration, we can express the friction coefficient parallel to thebackbone using the equation with numerical correction proposedby Aragon and Flamik for 1� p<∞ [41]:

zZ ¼ 4phL0.½2 lnðpÞ þ C� (8)

whereC ¼ �0:113192� 1:30429$p�0:25 þ 1:19032$p�0:5 þ3:12756$p�1 � 1:56699$p�2 � 0:930791$p�2$lnðpÞ is the numeri-cal correction.

To derive the forces in the bottlebrush backbone caused by ve-locity gradient along the backbone, we express the relative velocity(V) as a function of the distance (x) from themiddle of the backboneby VðxÞ ¼ _ε$x, where _ε is the strain rate. The force per unit lengthalong the backbone is given by

f ðxÞ ¼ zZVðxÞ.L0 ¼ 4ph_εx=½2 lnðpÞ þ C� (9)

To calculate the maximum drag force at the backbone center fm,we need to integrate the absolute value of f(x) from 0 to L'/2 andobtain

fm ¼ 12ph _εL02

.½2 lnðpÞ þ C� (10)

Similarly, we can obtain the following scaling relations:

Y. Li et al. / Polymer 84 (2016) 178e184 183

fc � L02lim.½2 lnðplimÞ þ Clim� (11)

L0lim � ½2 lnðplimÞ þ Clim�1=2 (12)

where plim and Clim are the corresponding aspect ratio (Eq. (7)) andnumerical correction as a function of the limiting contour length(Eq. (8)), respectively. Fig. 4 shows a logelog plot of L0lim as afunction 2 lnðplimÞ þ Clim with a slope of 0.83± 0.05, which ismarkedly larger than the predicted value of 0.5 from Eq. (12).

4. Discussion

Scaling analysis of the bottlebrush backbone scission dynamicshas been performed to quantify the effect of side chain DP on thelimiting contour length using Rouse and Zimm models. The formermodel shows a better agreement between model predictions andexperimental results. This indicates that the solvent moleculesdrain through the bottlebrush corona producing a larger drag force.The solvent draining can be rationalized by comparing the char-acteristic relaxation time of the side chains and the shear strain rategenerated upon bubble collapse. For the solvent to move throughthe side chains its flow should be faster than the side chain Zimmrelaxation time tZ ð _ε> t�1

Z Þ. We can estimate the Zimm relaxationtime for the side chains with size RybN1=2

sc as

tZyt0N3=2sc (13)

where t0zhb3=kBTy1:0 ns is the relaxation time of Kuhn mono-mer (b¼ 1.8 nm) in chloroform with viscosity h~0.64 mPa$s at themedian temperature (6e9 �C) of Ty281 K and kB is the Boltzmannconstant. From Eq. (13), we can estimate the Zimm relaxation timeto change between 6 ns (Brush-1) and 74 ns (Brush-4). It is knownthat the strain rate and, hence, drag force decrease with the dis-tance from an imploding microbubble [18]. Yet, it may be strongenough to induce bond scission, provided that the bottlebrushesare sufficiently long. At the initial contour length L0y370 nm(Table 2), the maximum drag force fm � _εL2lim can reach the criticalforce fc at a lower strain rate, e.g., 2� 107 s�1 for Brush-1 and3� 106 s�1 for Brush-4. This is slower than the Zimm relaxation(_ε< t�1

Z ), indicating that the bottlebrush dynamics corresponds tonon-draining regime described by the Zimm model. However, at alimiting contour length (analyzed in this paper), the bottlebrushesneed to reach the vicinity of an imploding microbubble where thestrain rate is the highest ( _εy109 s�1) [18,19,42] to achieve thegreatest force at the backbone center. In this case, the strain rate is

Fig. 4. Dependence of the limiting total length of cylindrical bottlebrushes L0lim as afunction of parameter 2ln(plim)þ Clim.

larger than the Zimm relaxation time ( _ε> t�1Z ), suggesting that the

bottlebrush dynamics corresponds to draining regime described bythe Rouse model. In other words, the bottlebrush dynamics un-dergoes a transition from non-draining (Zimm) to draining (Rouse)regime as the bottlebrushes become shorter. At the initial stages ofsonication, long bottlebrushes ( _ε< t�1

Z ) may behave like solidcylindrically shaped objects, similar to carbon nanotubes, nano-wires, polymeric fibrils [18,19,25,27,28]; while at the later stages,the backbone scission is controlled by solvent draining, whichdifferentiates short bottlebrushes ( _ε> t�1

Z ) from solid cylindricalobjects. Besides, the critical force for cleavage for solid cylindricallyshaped objects depends on their cross-sectional area, in contrast toits independence on diameter (DP of side chains) for bottlebrushesand that it is determined by the strength of backbone bonds.

5. Conclusions

We have studied the effect of the side chain DP on thesonication-induced scission of molecular bottlebrushes. The scis-sion rate has been shown to increase with increasing side chain DP,while the limiting contour length decreases as side chain DP in-creases. This decrease of the limiting contour length is attributed tohigher drag force exerted on the backbone with longer side chainsby the solvent flow generated by bubble collapse. To quantify theeffect of side chain DP on the limiting contour length, we haveperformed scaling analysis of the bottlebrush backbone scissiondynamics using Rouse and Zimmmodels. The Rouse model shows abetter agreement between model predictions and experimentalresults, which indicates that flexible and hairy molecular bottle-brushes behave differently from solid cylindrically shaped objectswith respect to their interaction with solvent in the sonicationprocess when the bottlebrushes are cut short enough ( _ε> t�1

Z ):solvent drains through the bottlebrush corona formed by sidechains, while it cannot penetrate through solid objects.

Acknowledgment

We gratefully acknowledge funding from the National ScienceFoundation (DMR 0906985, DMR 1501324, DMR 1122483), DMR1409710 and Department of the Army (59646-CH).

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