ORIGINAL CONTRIBUTION

Amphiphilicity and self-assembly behaviors of polystyrene-graftedmulti-walled carbon nanotubes in selective solvents

Yang Liu & Guo-Jian Wang & Ying-Jie Wu

Received: 14 June 2013 /Revised: 3 August 2013 /Accepted: 29 August 2013 /Published online: 13 September 2013# Springer-Verlag Berlin Heidelberg 2013

Abstract Multi-walled carbon nanotubes (MWCNTs) canself-assemble as cylindrical bundles in some solvents afterpolystyrene (PS) grafting. In these three-dimensional regularstructures, the tubes are oriented and parallel arranged. Everyself-assembly structure has an order head and a comparativelyloose tail. In order to find out the role that solvent plays,MWCNTs were dispersed in several organic solvents beforeand after modification. Based on macroscopic stability ofsuspensions and microscopic state of nanotubes, compatibilitybetween solvents andMWCNTs can be confirmed. Accordingto compatibility difference between tubes and PS, five chosensolvents are divided into three groups: selective solvent, goodsolvent, and bad solvent. MWCNT-g-PS can self-assembleonly in selective solvents. Tetrahydrofuran and benzene arewell compatible with PS, but bad with MWCNTs. Driven bythe solvent–philic/solvent–phobic interaction, MWCNT-g-PSself-organized regularly as bundles. Because each part of theMWCNT-g-PS is compatible well with 1,2-dichlorobenzene,gathering tendency of the modified tubes have been enervatedby their good compatibility and weak amphiphilicity. Graftedor not, nanotubes reveal poor compatibility with methanol andethanol. Strong incompatibility and limited amphiphilicitymake MWCNT-g-PS agglomerate as quickly and irregularlyas raw tubes. An adapted hydrophilic/lipophilic balance sys-tem is introduced to qualify compatibility and amphiphilicityof MWCNT-g-PS in each solvent. This novel model not onlyreveals the relationship between solvent and microscopic stateof unmodified/modified tubes, but also signifies the decisiverole of solvent in self-assembly behaviors of MWCNT-g-PS.

Keywords Self-assembly .Multi-walled carbon nanotubes .

Polystyrene . Amphiphilicity . Good solvent . Poor solvent .

Selective solvent

Introduction

Carbon nanotubes (CNTs) show promising application in ma-terial science and engineering because of their extraordinarymechanical and electrical properties [1, 2]. As a quasi-one-dimensional nanomaterial, properties of CNTs in axial directionare much better than those in radial direction. How to put tubesin order has become a very hot research topic, because wellorganized CNTs are more useful than irregular ones. Potentialapplications include development of anisotropy materials, sen-sors, field effect components, and new battery [3–6].

Manyways have been proposed to align nanotubes, such astemplate chemical vapor deposition [7, 8]. Besides, electricaland magnetic fields have also been employed to align CNTs[9, 10]. Some researchers use a fluid field or stretch CNTcomposites in a constant direction to make tube arrays in order[3, 11]. Apart from these physical methods, some chemicalmethods have been introduced, too. Self-assembly is one ofthe most convenient one without complicate equipment. Dri-ving force includes: capillary force, Coulombic interaction,and solvent evaporation [12–14]. Nevertheless, almost all thepresent self-assembly processes were carried on the substratesinstead in the solution.

Many surfactants and amphiphilic macro-molecules canself-assemble regularly in solution. Due to the interaction ofhydrophilicity/hydrophobicity, the insoluble block tends tocurl and agglomerate to form the core, while the soluble blockstretches as the shell at the outside [15]. Nanosize amphiphilicmolecules can self-assemble into micro-scale micelles, vesi-cles, ribbons, films, fibers, tubules, and so on [16, 17].

Likewise, multi-walled carbon nanotubes (MWCNTs)could self-assemble under the guidance of grafted amphiphilic

Y. Liu :G.<J. Wang :Y.<J. WuSchool of Materials Science and Engineering, Tongji University,Shanghai 201804, China

G.<J. Wang (*)Key Laboratory of Advanced Civil Engineering Materials, Ministryof Education, Tongji University, Shanghai 201804, Chinae-mail: wanggj@tongji.edu.cn

Colloid Polym Sci (2014) 292:185–196DOI 10.1007/s00396-013-3066-y

block copolymers in solvents. The phenomena have beenreported by our group [18, 19]. As a matter of fact,MWCNTs are incompatible with most solvents. It is pos-sible that nanotubes can self-assemble even though theyare only grafted with a homopolymer instead of a copoly-mer. One precondition is that the solvent should be wellcompatible with the grafted homopolymer but bad withnanotubes. Besides, self-assembly driving force should bestrong enough.

In this work, polystyrene (PS) was grafted on the surface ofthe MWCNTs via covalent bonds. The assumption is con-firmed by self-assembly (SA) structures observed in tetrahy-drofuran (THF). PS-grafted MWCNTs (MWCNT-g-PS) self-assemble regularly as cylindrical bundles in THF. These sec-ondary structures are three-dimensional (3D). They have anorder head with a comparatively loose tail. Nanotubes areoriented and parallel arranged in SAs. However, the modifiedtubes cannot self-assemble in every solvent, but only in sev-eral ones. In order to find out the role that solvent plays in theself-assembly process, five solvents are chosen as dispersionmedia. According to the macro-stability of suspensions andmicro-state of unmodified/modified MWCNTs, five solventsare classified into three groups: selective solvent, good sol-vent, and bad solvent. Only in selective solvent, which is wellcompatible with PS but bad with tubes, MWCNT-g-PS canself-assemble. Furthermore, the grafted tubes show less ag-glomerative tendency in good solvent but conglomerate asquickly and irregularly as ungrafted ones in bad solvent.

Turbiscan™ stability index (TSI) is introduced to quantifythe compatibility between ungrafted/grafted tubes and sol-vents. By adapting the hydrophilic–lipophilic balance (HLB)model originally raised byGriffin and Davies [20–22], a novelsystem was proposed to reflect relative compatibility discrep-ancy between polymer and tubes. The compatible differencebetween the two parts of MWCNT-g-PS leads to micro-phaseseparations and controls agglomerative behavior of the tubes,regular or not. Moreover, the compatibility, which affects themovability and dispersibility of the modified tubes, is also animportant element in self-assembly.

Experiment

Materials

MWCNTs were provided by Chengdu Organic ChemicalsCo., Ltd. (95 %, outside diameter=8–15 nm, length=50 μm)and used as received. Ethyl 2-bromopropionate (EBP, ≥99 %)was purchased from Sigma–Aldrich Company, USA. Styrene(St), cuprous bromide (CuBr), 2,2′-bipyridine (bipy), THF,1,2-dichlorobenzene (DCB), sodium azide (NaN3), benzene,methanol, and ethanol were purchased from Shanghai Re-agent Company, Chinese Medicine Co., Ltd.

Preparation of PS–Br, PS–N3, and MWCNT-g-PS

PS was synthesized by atom transfer radical polymerization(ATRP) with CuBr as catalyst and bipy as ligand [23, 24]. Themole ratio of EBP (initiator) to St (monomer) was 1 to 300.Then, the obtained PS–Br was transformed to PS–N3 byreacting with NaN3 in THF. Finally, the polymer chains were“grafted to” the MWCNTs through a covalent bond after anazidation additional reaction [25–27]. In order to remove theunconnected PS, the product was washed with THF repeated-ly until white precipitates cannot be observed in methanol ifthe filtrate was dripped in.

Characterization

The molecular weight of PS was characterized by gel perme-ation chromatography (GPC; WATERS Alliance E2695,Milford, MA, USA) in THF at flow rate of 1.0 ml min−1.The structural characterization of PS–Br and PS–N3 wasconducted on an Equinoxss Hyperion 2000 Fourier transforminfrared (IR) spectrometer (Bruker, Germany) at room tem-perature. Labram-1B Raman spectroscope (JY, France) wasexcited at 632.8 nm. Thermal gravimetric (TG) analysis wasconducted on an STA 449C thermogravimeter and differentialthermal analysis instrument (NETZSCH, Germany) at a heatrate of 20 °C/min under nitrogen protection.

The samples were observed using a DM LM/P trans-mission/reflection optical microscope (OM; LEICA,Germany), previously. The microscopic structure analysiswas performed on an H-800 transmission electron micro-scope (TEM; Hitachi, Japan) at 200 kV. Scanning electronmicroscope (SEM) was operated with an acceleration voltageof 15 kV (FEI Quanta 200 FEG, Holland). The kineticstability (KS) of the suspensions was monitored by aTurbiscan™ Lab (TSL; Formulation, France) at 30 °C withincident light wavelength of 880 nm. This equipment has twosynchronous detectors: a transmission (T) detector and a backscattering (BS) detector. Each time, they will scan a cylindri-cal glass tube from bottom (0 mm) to top (65 mm), in which20 ml of solvent was added. TSL, which employs multiplelight scattering theory and Lambert–Beer law [28, 29], canrecord BS and T rates of the samples at each height contin-uously, and a computer will record all the data according totime sequence [30, 31].

Results and discussion

Characterization of PS–Br, PS–N3, and MWCNT-g-PS

The number- and weight-average molecular weights of PSmeasured by GPC are 2.58×104 and 3.12×104, respectively.It is found that all the corresponding absorption peaks in the

186 Colloid Polym Sci (2014) 292:185–196

IR spectrum of PS–Br appear in PS–N3 again. Besides, a newpeak at 2,095 cm−1 caused by the absorption of the N3 group[25, 26] appears in the spectrum of PS–N3.

The thermo stability of the MWCNTs is characterizedusing STA 449C before and after addition reaction. Accordingto the TG loss ratio of the MWCNTs (1.95 %) and MWCNT-g-PS (45.54 %), it can be calculated that the mass graft rate ofPS is 44.46 %, and the mole modification density of PS/C isabout 1/2,682. In other words, there are about 1.75×105 PSchain graftings on each tube.

Raman spectrum, which can provide ratio information ofcarbon atoms (C) in different hybrid states, was employed toconfirm the covalent connection between the tubes and the PSchains [25, 26, 32]. Generally, the D peak (1,350 cm−1) iscaused by sp3 hybrid C and some disorderly structures, whiletheG peak (1,500 cm−1) is the absorption peak of sp2 C. Afterthe chemical reaction, some C on the surface of the nanotubestransform from sp2 to sp3. Therefore, the peak area ratio(Iωd/Iωg) grows from 1.82 (MWCNTs) to 2.13 (MWCNT-g-PS). It confirms that the homopolymer has been grafted to theMWCNTs via covalent bonds.

Suspending stability and macroscopic state of unmodified/modified MWCNTs in selective solvent

It was discovered in the beginning that MWCNT-g-PS canself-assemble in THF, but MWCNTs cannot. In order to findout the roles that grafted PS and solvent play in self-assemblybehavior, five organic solvents (THF, benzene, DCB, metha-nol, and ethanol) are selected as dispersion media, and theirHansen solubility parameters are listed in Table 1.

δD, δP, and δH represent dispersion cohesion, polar cohe-sion, and hydrogen bonding cohesion solubility parameter,respectively. In Hansen solubility parameter system, the totalsolubility parameter (δ t) is defined as:

δ2t ¼ δ2D þ δ2P þ δ2H: ð1Þ

δ t depicts the compatibility between the solute and solvent[34]. The solvents are classified according to their solubilityparameter difference with PS. Therefore, the five solvents canbe divided into two groups: THF, benzene, and DCB are goodsolvent of PS; while methanol and ethanol are poor onesbecause of their large δP, δH, and δ t.

Suspending stability of unmodified/modified MWCNTsin THF and benzene

For the purpose of exploring the compatibility betweenunmodified/modified tubes and solvents, 4 mg of MWCNTsand MWCNT-g-PS was mixed with 20 ml of THF and ben-zene, respectively (0.2 mg ml−1). Each dispersion system wasmonitored using TSL instantly after ultrasonication.

TSL has been used to characterize the stability of emul-sions [31, 35–37] and carbon nanotube suspensions [38]. Theprinciple of this measurement is based on the variation of BSand T signals along with time. The variations of delta BS anddelta T values are calculated as the difference between BS andT at 0 s and at any given time. For comprehensive analysis, amean value of each delta BS and T profile is computed usingthe Turbiscan Lab Expert® software according to the opera-tional manual [29, 36]. Obtained delta BST (DBST) values areused to represent the stability of the system and depicted as KScurves. A plot, shown in Fig. 1, is produced from these results,with the DBST values on the y -axis and the time on the x -axis.

As is shown in Fig. 1a(1),b(1), all the raw tubes subside tothe containers' lower part, while the upper layer liquid is trans-parent and clear. Moreover, the rocket rising KS curves of theMWCNTs suggest that unmodified tubes agglomerate sponta-neously as soon as ultrasonic stopped, and they precipitate in avery short time (Fig. 1a(3),b(3)). The poor stability of thesuspensions infers an incompatibility between the MWCNTsand the two solvents.

To the contrary, the modified MWCNTs exhibit excellentstability in the same solvents. Even though the two suspen-sions had been kept for a month, subsidence or stratificationwas still unobservable (Fig. 1a(2),b(2)). The soluble PS offersselective solvent-unfavorable tubes good compatibility withTHF and benzene. The polymer chains are always stretchingflexibly in their good solvents, and steric effect makes themact as stabilizers [39]. Besides, MWCNT-g-PS, which is com-posed of nanotube and PS chains, shows selective solvent-phobic/selective solvent-philic property (amphiphilicity) inthese two solvents. Consequently, THF and benzene are se-lective solvents of MWCNT-g-PS.

In the TSL test, the larger the DBST value, the moreinstable the system will be. Whether in THF or in benzene,the MWCNTs' curves locate above the MWCNT-g-PS's,and the latter's curves almost overlap with the x -axis(Fig. 1a(3),b(3)). Because the stability of the suspensionselevates significantly after PS grafting, the modified tubes

Table 1 Hansen solubility parameters of solvents and PS [33]

δD δP δH δ t

Solvent

THF 16.8 5.7 8.0 19.5

Benzene 18.4 0 2.0 18.5

DCB 19.2 6.3 3.3 20.5

Methanol 15.1 12.3 22.3 29.6

Ethanol 15.8 8.8 19.4 26.5

Polymer

PS 21.3 5.8 4.3 22.5

δD dispersion cohesion (solubility) parameter, δP polar cohesion (solu-bility) parameter, δH hydrogen bonding cohesion (solubility) parameter,δ t total (Hildebrand) cohesion (solubility) parameter

Colloid Polym Sci (2014) 292:185–196 187

have more time and higher mobility in selective solvents thanin unmodified ones. It also implies that MWCNT-g-PS, as anentirety, shows better compatibility with THF and benzenethan MWCNTs.

However, the rescaled KS curves of MWCNT-g-PS inFig. 1a(3),b(3) demonstrate that the two suspensions are notreally stable even though they show excellent macro-stability.As a thermodynamically stable dispersion, the DBST valuesof the system should be equal to zero because its BS rate and Trate do not change along with the development of time. It canbe seen from Fig. 1a(3),b(3) that the MWCNT-g-PS's curvesare climbing slowly but steadily, which suggests that graftedtubes agglomerate at very slow speed.

In fact, the volume (5.2×106 nm3) and surface area (1.8×106 nm2) of the MWCNTs are too large to be completelywrapped by 1.75×105 PS chains. Moreover, solvation keepsthe polymer chains to continuously stretch flexibly in theirgood solvents [39]. Inevitably, some parts of tubes' surfaceare exposed in THF and benzene. On one hand, these un-covered surface parts are selective solvent repulsive andincline to accumulate. One the other hand, those surfacescovered by PS are selective solvent-philic. Covered/un-covered surface creates many nanosize micro-phase separa-tions on the outside of the MWCNTs. Driven by the selectivesolvent-philic/selective solvent-phobic interaction, amphiphilic

MWCNT-g-PS are able to self-assemble in two selectivesolvents.

Microscopic state of unmodified/modified MWCNTs in THFand benzene

Microscopic states of MWCNTs and MWCNT-g-PS werecharacterized using OM, TEM, and SEM, respectively. Afterthe TSL test, all the dispersions were stirred magnetically for1 min. Then, one to two droplets were transferred on a glassslide immediately. The samples were observed using an OMpreliminarily after they dried.

As is shown in Fig. 2a(1), pristine nanotubes accumu-late so tightly in THF that black shadows are large in sizeand deep in color. The shape and outline of the conglom-erations are irregular and various, after the focus waszoomed in (Fig. 2a(2)). All in all, the macroscopic insta-bility of the suspension and serious agglomeration of theMWCNTs verify the incompatibility between unmodifiedtubes and THF. Moreover, as nanomaterials, MWCNTshave extremely large specific area [40]. They incline toaccumulate in order to reduce the surface free energy withsurface area diminution.

However, some regular shadows with length-to-width ratioranging from 15 to 25 are observed in Fig. 2b(1),b(2). These

Fig. 1 a1 MWCNTs dispersedin THF. a2 MWCNT-g-PSdispersed in THF. b1 MWCNTsdispersed in benzene. b2MWCNT-g-PS dispersed inbenzene. KS curves of MWCNTsand MWCNT-g-PS dispersed ina3 THF and in b3 benzene. Thegreen and blue broken linesrepresent linear fittings of KScurves in Zone I and Zone II,respectively

188 Colloid Polym Sci (2014) 292:185–196

rod-like and micro-scale conglomerations formed in THF arethe SAs of MWCNT-g-PS, driven by the THF-phobic/THF-philic interaction. They have regular and similar shape. Theirlength fluctuates from 20 to 35 μm, while their width rangesfrom 1.5 to 4 μm.

Likewise, raw tubes and benzene are mutually exclu-sive. For one thing, the suspension exhibits poor stability.For the other thing, MWCNTs also agglomerate badly andirregularly in the solvent. Conglomerations are in variousshapes and sizes (Fig. 2c(1),c(2)). Like in THF, MWCNT-g-PS self-assemble in benzene, too. The self-assembly driv-ing force is the interaction of benzene-phobic/benzene-philic properties. These regular and rod-shape shadowsrange from 20 to 25 μm in length, while from 1 to 4 μm inwidth. SEMandTEMwere employed to clarify these regularblack shadows.

As is shown in Fig. 3a, the unmodified tubes tangle togeth-er tightly because of their poor compatibility with THF. Due tothe mess arrangement of theMWCNTs, the shapes of agglom-erations (or black shadows) are random.

However, TEM and SEM reveal that those rod-shapeshadows are composed of thousands of parallel MWCNT-g-PS. In these secondary structures, the modified tubes areoriented and regularly aligned. SAs have a tight head and acomparatively loose tail (Fig. 3b(1)–b(3)). SEM images illus-trate that those order shadows are 3D structures instead of 2D(Fig. 3b(4),b(5)).

Similarly, due to the incompatibility, the arrangement of thetubes is also ruleless in benzene (Fig. 3c). Nevertheless, drivenby the benzene-philic/benzene-phobic interaction, MWCNT-g-PS also self-assembled in benzene. SAs formed in benzeneexhibit analogous shape and size as those formed in THF.TEM and SEM demonstrate that modified tubes are wellorganized in 3D bundles, too (Fig. 3d(1),d(2)).

Suspending stability and microscopic state of unmodified/modified MWCNTs in good solvent and poor solvent

Suspending stability and microscopic state of unmodified/modified MWCNTs dispersed in DCB

The unmodified/modified MWCNTs were dispersed in DCBwith concentration of 0.2 mg ml−1. Two suspensions werecharacterized by TSL after 5-min ultrasonic treatment.

Precipitation was still undetectable, although the two cellshad been kept for a month (Fig. 4a,b). Outstanding stability ofsuspensions and KS curves with extremely small DBSTvalues (Fig. 4c) imply that MWCNTs are well compatiblewith DCB, whether grafted or not. In other words, each partof MWCNT-g-PS is well compatible with the solvent. Then,microscopic states of unmodified/modified tubes were ob-served using OM and TEM, respectively.

Figure 5a(1),a(2) exhibits that most MWCNTs pave on theglass slide evenly. By comparison, the modified tubes arebetter dispersed and less conglomerated (Fig. 5b(1),b(2)).Furthermore, TEM images reaffirm the good dispersibility ofMWCNTs and MWCNT-g-PS (Fig. 5a(3),b(3)). These micro-scopic images verify the excellent compatibility betweenungrafted/grafted tubes and DCB. Because each part is wellcompatible with the solvents, the MWCNT-g-PS fail to showamphiphilicity and lose self-assembly ability in good solvent.

Suspending stability and microscopic state of unmodified/modified MWCNTs dispersed in methanol and ethanol

The MWCNTs and MWCNT-g-PS were dispersed in methanoland ethanol at 0.2mgml−1 by ultrasonic before TLS test. Neitherunmodified nor modified tubes can suspend in methanol andethanol but precipitate in short time (Fig. 6a(1),a(2),b(1),b(2)).

Fig. 2 a1 , a2 MWCNTs dispersed in THF. b1 , b2 MWCNT-g-PS dispersed in THF. c1 , c2 MWCNTs dispersed in benzene. d1 , d2 MWCNT-g-PSdispersed in benzene

Colloid Polym Sci (2014) 292:185–196 189

Instability suggests that both MWCNTs and MWCNT-g-PS areincompatible with the two alcohols. Similar shape of the curvesand large DBST values illustrate that grafted tubes agglomeratedand precipitated as quickly as raw tubes in the two bad solvents

(Fig. 6a(3),b(3)). The abovementioned samples were observedusing OM and TEM, respectively.

Figure 7 shows that both MWCNTs and MWCNT-g-PSagglomerate irregularly and tightly in alcohols. Neither

Fig. 3 a TEM of irregularly accumulated MWCNTs (formed in THF).b1–b3 TEM of SAs which are composed of regularly organizedMWCNT-g-PS (formed in THF). b4 , b5 SEM of SAs (formed in

THF). c TEM of irregularly accumulatedMWCNTs (formed in benzene).d1 TEM of SAwhich is composed of regularly organizedMWCNT-g-PS(formed in benzene). d2 SEM of SAs (formed in benzene)

Fig. 4 a MWCNTs dispersed inDCB. b MWCNT-g-PS dispersedin DCB. c KS curves ofMWCNTs and MWCNT-g-PSdispersed in DCB. The green andblue broken lines represent linearfittings of KS curves in Zone Iand Zone II, respectively

190 Colloid Polym Sci (2014) 292:185–196

MWCNTs nor PS is solvent favorable in methanol and etha-nol. Besides, polymer chains are contractive and inflexible

in their bad solvents [39, 41]. Thus, they fail to provideMWCNT compatibility. The modified tubes exhibit little

Fig. 5 a1 , a2 MWCNTs dispersed in DCB. a3 TEM of MWCNTs. b1 , b2 MWCNT-g-PS dispersed in DCB. b3 TEM of MWCNT-g-PS

Fig. 6 a1 MWCNTs dispersedin methanol. a2 MWCNT-g-PSdispersed in methanol. b1MWCNTs dispersed in ethanol.b2 MWCNT-g-PS dispersed inethanol. KS curves of MWCNTsand MWCNT-g-PS dispersed ina3 methanol and b3 ethanol. Thegreen and blue broken linesrepresent linear fittings of KScurves in Zone I and Zone II,respectively

Colloid Polym Sci (2014) 292:185–196 191

amphiphilic property in their poor solvent. Instead of self-assembly, they tangle together quickly and irregularly.

Kinetic stability analysis

Different from ordinary solutions and suspensions, the disper-sions of MWCNTs reveal some unique features. For onething, both the volume and mass of the MWCNTs are muchlarger than those of the macro-molecules and solvent mole-cules. For the other, these systems are not really stable.

The macro-stability of dispersion corresponds to the micro-states of the nanotubes. Intrinsically, they reflect the compat-ibility between the unmodified/modified MWCNTs and sol-vents. Therefore, TSL test reveals both the stability of thesystem and the compatibility of the MWCNTs. Apart from theDBST values, the KS curves provide more useful information.Their slopes represent the rate of change in the systems.Based on the abrupt decline in the slope, the obtained curvescan be divided into two segments, and each part is linear fittedrespectively.

The ultrasonic inputs a great amount of energy. After itstops, the system at high-energy level is unstable and inclinesto release energy spontaneously. During this period, well-scattered tubes begin to agglomerate, slowly or quickly, reg-ularly or irregularly. When agglomerates (or SAs) grow largeenough, they will precipitate to the lower part of the con-tainers. Meanwhile, BST rate changes violently, which formsthe first zone (curve with large slope). Most superfluous ener-gy has been released in this stage. After the turning point (TP),a slow-change state is established in the system which corre-sponds to the second zone (curve with small slope). The firstslope mainly depends on the compatibility of the MWCNTsand MWCNT-g-PS.

TSI is a statistical parameter to characterize the stability ofa suspension. It can be used to estimate the stability of the

system at a given time. Its value is obtained as the sum of allthe processes taking place in the studied probe and calculatedusing the following equation [42, 43]:

TSI ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

X

i¼1

n

X i−X BSTð Þ2

n−1

v

u

u

u

t

; ð2Þ

where X i is means the BST value for each minute of measure-ment. XBST is the mean X i, and n is the number of testingminutes. Large TSI value indicates that the system is instable[42, 43]. As a matter of fact, TSI at TP represents the “intrin-sic” stability of dispersion and can be used to quantify thecompatibility between ungrafted/grafted tubes and solvents.Therefore, the TSI on each curve was calculated and listed inTable 2.

In selective solvents, the first slopes of the raw tubes are1.5×10−1 (in THF) and 2.7×10−1 (in benzene), respectively.Two large slopes, in the same order of magnitude, indicate thatMWCNTs are extremely selective solvent unfavorable, andthey agglomerate and precipitate quickly. The second slope'sorder declines to×10−4 because shaggy sediment shrinksslowly after all the MWCNTs have subsided to the bottle'slower part during the first period.

Nevertheless, whether in THF (3.3×10−5) or in benzene(3.1×10−5), the first slope of the KS curves declines dramat-ically after PS grafting. Under this condition, TSI declinesfrom 35.7 (MWCNTs) to 0.01 (MWCNT-g-PS) in THF, whilefrom 40.8 (MWCNTs) to 0.03 (MWCNT-g-PS) in benzene.Large TSI suggests a strong incompatibility between theunmodified tubes and selective solvents, but small TSI indi-cates that the modified tubes are well compatible with THFand benzene. Doubtlessly, the soluble polymer not only ele-vates stability of the suspensions but also upgrades the

Fig. 7 a1 , a2 MWCNTs dispersed inmethanol. b1 , b2 MWCNT-g-PS dispersed inmethanol. c1 , c2 MWCNTs dispersed in ethanol. d1 MWCNT-g-PS dispersed in ethanol. d2 TEM of agglomerated MWCNT-g-PS dispersed in ethanol

192 Colloid Polym Sci (2014) 292:185–196

compatibility and movability of the tubes. Therefore, amphi-philic MWCNT-g-PS are able to self-assemble slowly andregularly in selective solvents, driven by the selective solvent-philic/selective solvent-phobic interaction.

Small TSI value (0.06) suggests that DCB is a good solventof MWCNTs. Since both tubes and PS are “soluble” in thesolvent, MWCNT-g-PS are also DCB favorable (TSI=0.03),

but they lose amphiphilicity. Therefore, unmodified/modifiedtubes do not show much inclination to accumulate in goodsolvent. However, neither tubes nor PS is compatible withalcohols. In the two bad solvents, the TSI values of MWCNT-g-PS are close to those of MWCNTs. Besides, the modifiedand unmodified tubes have large and similar first slope. Itindicates rapid accumulation and precipitation of theungrafted/grafted tubes because of their poor compatibility.Without sufficient amphiphilicity, fast accumulation alwaysleads to irregular arrangement of MWCNT-g-PS.

Compatibility, amphiphilicity, and self-assemblyof MWCNT-g-PS

When dispersibility and mobility of MWCNT-g-PS areinfluenced by their compatibility, self-assembly behavior iscontrolled by both compatibility and amphiphilicity. HLBsystem has been used to characterize surface active agents.Surfactants and some copolymers have both hydrophilicgroups and lipophilic groups. They can self-assemble intomicelles, vesicles, or multi-layer film in solutions [17, 44–47].In Davies system [21], the numbers of the hydrophilic groupsare designated as positive numbers, while those of the lipo-philic groups are negative. The HLB value of an unknownsurface active agent can be calculated directly from its chem-ical formula, by adding group numbers together.

Likewise, MWCNT-g-PS are also composed of two differ-ent parts: tube and PS, without considering its rod–core/multi-armed structure. Each part of the MWCNT-g-PS shows differ-ent compatibilities with solvents. A novel solvent-philic/sol-vent-phobic balance (SSB) value is proposed to quantify thecompatibility of MWCNT-g-PS, and its value is calculated byadding the contributions of the tube phase and the PS phase:

SSBMWCNT�g�PS ¼ SSBMWCNTs þ SSBPS: ð3Þ

In a thermodynamically stable solution, a solute's SSBvalue is defined as not less than zero. To the opposite, whenits SSB is negative, it will be considered as insoluble in thesolvent. The more negative the SSB goes against zero, the lesscompatible the solute will be and less stable the dispersion willbe. Additionally, the solvent-philic particles tend to accumu-late rapidly and irregularly.

Despite some suspensions of the unmodified/modifiedMWCNTs showing good macro-stability, the KS curves re-veal an opposite conclusion. Grafted or not, all the dispersionsare not really stable. The tubes conglomerate quickly or slow-ly, regularly or irregularly in solvents. Small TSI signifies acomparative good compatibility, while large one means avery bad compatibility. Like HLB system, negative TSI isborrowed to quantify the incompatibility between the tubesand solvents in this work. Therefore, the smaller the SSB (or

Table 2 Linear fitting for KS curves of ten suspensions and TSIs at TP

TP

Solvent Intercept Slope Time (s) DBST TSI

Selective solvent

THF

MWCNTs

Zone I 0 1.5×10−1 311 46.7 35.7

Zone II 46.5 2.6×10−4

MWCNT-g-PS

Zone I 0 3.3×10−5 533 1.7×10−2 0.01

Zone II 1.7×10−2 1.1×10−6

Benzene

MWCNTs

Zone I 0 2.7×10−1 186 50.3 40.8

Zone II 50.2 6.5×10−4

MWCNT-g-PS

Zone I 0 3.1×10−5 1,037 3.2×10−2 0.03

Zone II 3.1×10−2 1.1×10−6

Good solvent

DCB

MWCNTs

Zone I 0 4.3×10−6 17,678 8.3×10−2 0.06

Zone II 8.3×10−2 4.9×10−9

MWCNT-g-PS

Zone I 0 1.1×10−6 43,559 4.8×10−2 0.03

Zone II 4.7×10−2 2.1×10−8

Poor solvent

Methanol

MWCNTs

Zone I 0 2.1×10−2 1,342 28.2 18.8

Zone II 28.1 5.8×10−5

MWCNT-g-PS

Zone I 0 1.6×10−2 1,605 25.7 15.2

Zone II 25.5 1.1×10−4

Ethanol

MWCNTs

Zone I 0 3.2×10−2 1,113 35.6 26.1

Zone II 35.5 9.4×10−5

MWCNT-g-PS

Zone I 0 9.4×10−3 3,434 32.3 22.9

Zone II 31.7 1.7×10−4

Colloid Polym Sci (2014) 292:185–196 193

the bigger absolute value of TSI), the more incompatible thetubes will be.

The TSI value of the MWCNTs declines after PS modifi-cation, nomatter in which solvent. Consequently, MWCNT-g-PS have bigger SSB value (or smaller absolute value of TSI)than MWCNTs. Doubtlessly, the polymer exerts a positiveinfluence to improve the tube's compatibility. In other words,PS should have a positive SSB group number so that negativeSSB group number of MWCNTs can be partly counteracted.All in all, the relationship between SSB and TSI can beexpressed as follows:

SSBMWCNT�g�PS ¼ −TSIMWCNT�g�PS ¼ −TSIMWCNTsð Þ þ TSIPS: ð4Þ

Essentially, self-assembly and its driving force is caused bymicro-phase separation. The degree of micro-phase separation(DMS) is proposed to identify the gap between solvent-philicpart and solvent-phobic part (Table 3):

DMSMWCNT�g�PS ¼ TSIPS− −TSIMWCNTsð Þ ¼ TSIPS þ TSIMWCNTs:ð5Þ

Compared with pristineMWCNTs, the modified ones havelarge SSBMWCNT-g-PS values in THF and benzene because

they are well compatible with these solvents. The latter showshigher movability in the suspensions. Only in the selectivesolvent, nanoscaled micro-phase separation and driving forceare large enough to trigger the self-assembly behavior.

Even though MWCNT-g-PS also have big SSB value inDCB, their DMS value is the smallest. Because each part ofthem is well compatible with the solvent, weak micro-phaseseparation fails to arouse self-assembly. Moreover, it does notmean that PS is insoluble in DCB, for the polymer shows thesmallest SSB group number. To the contrary, MWCNTs havealready shown good compatibility with DCB. So, the positivecontribution made by PS is covered up, and SSBMWCNTs isalmost as large as SSBMWCNT-g-PS in DCB. Furthermore,MWCNT-g-PS show the smallest SSB values in methanoland ethanol. Therefore, the grafted tubes agglomerate irregu-larly in short time due to their bad compatibility with two poorsolvents.

In order to clarify the relationship between compatibilityand amphiphilicity, the SSB group numbers and DMS valueof the MWCNT-g-PS are drawn in Fig. 8. In Fig. 8, the x -axisis the divide between the solvent-philicity and solvent-phobicity. The bars above the axis are solvent favorable, whilethose below mean solvent unfavorable. The green bars(SSBPS) and the red bars (SSBMWCNTs) represent the contri-bution of the PS phase and MWCNTs phase, respectively.Because none of the suspensions are really stable, all the bluebars (SSBMWCNT-g-PS) settle under the axis. The short bluebars mean that MWCNT-g-PS have sufficient time and mo-bility in THF, benzene, and DCB.

DMSMWCNT-g-PS is the total length of the green bar and redbar (bar with slashes). It reflects the self-assembly drivingforce of MWCNT-g-PS in different solvents. However, onlyin THF and benzene, the DMS bars are long enough togenerate micro-phase separation on the surface of theMWCNTs. Therefore, the amphiphilic MWCNT-g-PS canself-organize regularly in two selective solvents.

Table 3 SSB group numbers of MWCNT phase and PS phase

SSB MWCNT-g-PS

Solvent MWCNTs PS SSB (sum) DMS (difference)

THF −35.7 35.69 −0.01 71.39

Benzene −40.8 40.77 −0.03 81.57

DCB −0.06 0.03 −0.03 0.09

Methanol −18.8 3.6 −15.2 22.4

Ethanol −26.1 3.2 −22.9 29.3

MWCNT-g-PSs DMS values in different solvents

Fig. 8 The relationship betweenSSB group numbers and DMSvalue of MWCNT-g-PS in fivesolvents, respectively. BothSSBMWCNT-g-PS (blue bars withbackslashes) and DMSMWCNT-g-

PS (bars with slashes) control themicroscopic states of themodifiednanotubes. MWCNT-g-PS canonly self-assemble in selectivesolvents (red zone). They exhibitweak and strong inclination toagglomerate in good (green zone)and poor solvents (gray zone)

194 Colloid Polym Sci (2014) 292:185–196

In DCB, the DMSMWCNT-g-PS is too small tomake the tubesself-assemble. However, in methanol and ethanol, the graftedtubes show the longest blue bars, while the DMS bars areshort. Extremely strong poor solvent-phobicity leads to thequick agglomeration of MWCNT-g-PS, and small DMS dis-ables them from adjusting their mutual position, but makes themodified tubes agglomerate as unmodified ones in alcohols.

Conclusions

PS with number-average molecular weight of 25,765 wassynthesized by ATRP and grafted to the surface of theMWCNTs via covalent bonds. The TG data indicate that themass graft rate of PS is 44.46 %. In order to find out the rolethat solvent plays in self-assembly, five solvents are chosen asdispersion media. Based on both the macroscopic stability ofsuspensions and microscopic state of unmodified/modifiedtubes, the solvents are divided into three groups: selectivesolvent, good solvent, and poor solvent.

Only in selective solvents, MWCNT-g-PS can self-assemble. THF and benzene are well compatible with PS,but bad with MWCNTs. Driven by the selective solvent-phobic/selective solvent-philic interaction, the modifiedtubes self-organized regularly in liquid. The obtained superstructures share similar shape and size. The tubes are orient-ed and arranged in parallel in these 3D bundles. The SAlength ranges from 20 to 30 μm, while the diameter fluctu-ates from 1.5 to 4 μm.

In DCB, the grafted tubes were less conglomerated becausethe good solvent is well compatible with each part of theMWCNT-g-PS. To the opposite, the modified tubes agglom-erated irregularly in methanol and ethanol because neitherMWCNTs nor PS is agreeable with the two poor solvents.

Essentially, the stability of the suspensions and micro-states of the tubes reflect compatibilities between ungrafted/grafted tubes and solvents. A new SSB/DMS system wasproposed to quantify the compatible and amphiphilic proper-ties of MWCNT-g-PS in different solvents. Because the mod-ified tubes are composed of MWCNTs and PS, their compat-ibility depends on the combination effect of two incompatibleparts. In other words, SSBMWCNT-g-PS equals the sum ofSSBMWCNTs and SSBPS. The tubes' mobility is largelyinfluenced by their compatibility (SSB). Moreover, solvent-philic/solvent-phobic interaction controls micro-phase separa-tion. Consequently, DMSMWCNT-g-PS is induced to representthe driving force of the self-assembly.

Movability and micro-phase separation are two indispens-able factors of self-assembly. Only in selective solvent, driv-ing force is large enough to incite regular organization ofMWCNT-g-PS. At the same time, large SSBMWCNT-g-PS en-sures that the nanotubes have enough time and freedom toadjust their mutual position during the self-assembly process.

Only when these conditions are fulfilled, regular SAs can beobtained.

Because of the extremely large SSBMWCNT-g-PS value, thegrafted tubes are solvent favorable, and they show very littletendency to gather in good solvent. To the contrary, MWCNT-g-PS lost mobility in short time for their small SSBMWCNT-g-PS

in bad solvents. So, they agglomerated quickly and irregularlyin methanol and ethanol.

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