Nanomechanical Mapping, Hierarchical Polymer Dynamics, and

Article pubs.acs.org/Macromolecules

Nanomechanical Mapping, Hierarchical Polymer Dynamics, and Miscibility in the Presence of Chain-End Grafted Nanoparticles Priti Xavier and Suryasarathi Bose* Department of Materials Engineering, Indian Institute of Science, Bangalore 560012, India ABSTRACT: To improve the spatial distribution of nanoparticles in a polymeric host and to enhance the interfacial interaction with the host, the use of chain-end grafted nanoparticle has gained popularity in the field of polymeric nanocomposites. Besides changing the material properties of the host, these grafted nanoparticles strongly alter the dynamics of the polymer chain at both local and cooperative length scales (relaxations) by manipulating the enthalpic and entropic interactions. It is difficult to map the distribution of these chain-end grafted nanoparticles in the blend by conventional techniques, and herein, we attempted to characterize it by unique technique(s) like peak force quantitative nanomechanical mapping (PFQNM) through AFM (atomic force microscopy) imaging and dielectric relaxation spectroscopy (DRS). Such techniques, besides shedding light on the spatial distribution of the nanoparticles, also give critical information on the changing elasticity at smaller length scales and hierarchical polymer chain dynamics in the vicinity of the nanoparticles. The effect of onedimensional rodlike multiwall carbon nanotubes (MWNTs), with the characteristic dimension of the order of the radius of gyration of the polymeric chain, on the phase miscibility and chain dynamics in a classical LCST mixture of polystyrene/ poly(vinyl methyl ether) (PS/PVME) was examined in detail using the above techniques. In order to tune the localization of the nanotubes, different molecular weights of PS (13, 31, and 46 kDa), synthesized using RAFT (reversible addition−fragmentation chain transfer) polymerization, was grafted onto MWNTs in situ. The thermodynamic miscibility in the blends was assessed by low-amplitude isochronal temperature sweeps, the spatial distribution of MWNTs in the blends was evaluated by PFQNM, and the hierarchical polymer chain dynamics was studied by DRS. It was observed that the miscibility, concentration fluctuation, and cooperative relaxations of the PS/PVME blends are strongly governed by the spatial distribution of MWNTs in the blends. These findings should help guide theories and simulations of hierarchical chain dynamics in LCST mixtures containing rodlike nanoparticles.

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interactions.6 Moreover, as the size of the NP decreases, the system phase separates due to increased contact between the host polymer and the NP.7,8 In this scenario, grafting polymers onto NPs, wherein the conformation of the polymer brush governs the NP stability, can accomplish better control over the dispersion.9 The recent literatures convey that in the case of low graft densities in the particles the matrix chains inhibit the brush from stretching, and the matrix chains are expelled from the brush in the case of densely grafted chains.10−12 In this framework, block copolymers with nanoscopic particles have been comprehensively studied with respect to brush length and graft densities. The entropic barrier to reach the NP has to be overcome for the other block, if the brush is stretched. It is well understood that if the brush is stretched, the other block must overcome the entropic barrier to reach the NP. If the NP is only partially shielded, they get adsorbed on the interface. Apart from the stability of the NP in the homopolymer, it also the

INTRODUCTION Thermally induced phase separating structures at different length scales have substantial scientific and practical implications in diverse areas, from energy conversion and storage to thermoelectric materials, sensors, and microfluidic devices. The local assembly and the organization of segments of polymeric molecules are distinct at the interface and in bulk depending on the competing entropic and enthalpic interactions.1,2 The interactions at a local level is a determining factor in changing many physical properties of the macromolecule like glass transition temperature (Tg), segmental dynamics, and transport properties.3 This becomes even more complicated in the case of polymeric nanocomposites, with nanoscopic particles of the order, similar to the radius of gyration of the host polymer chain4 and also dynamic asymmetric blend (with Tgs differing by ∼100 °C). In the latter case, due to chain connectivity effects, the entities experience an effective glass transition temperature different from the average blends’ Tg.5 In context to nanoparticle (NP) filled polymeric composites, the strong attraction between the core (of the NPs) can cause strong aggregation which is driven by various secondary © XXXX American Chemical Society

Received: August 21, 2015 Revised: January 5, 2016

A

DOI: 10.1021/acs.macromol.5b01849 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules

Table 1. Ratio of Monomer to Initiator to Chain Transfer Agent [S]:[AIBN]:[CTA] and the Molecular Weight Obtaineda RAFT 1 RAFT 2 RAFT 3 a

styrene (mL)

AIBN (mL)

CTA (mL)

PS-R Mn

PS-R Mw

PS-SH Mn

PS-SH Mw

11 11 11

3.6 3.6 3.6

32 26 5

7998 27000 35132

12000 30739 40682

8482 25241 46040

13226 31264 46813

PS-R is the thiocarbonate-terminated PS, and PS-SH is thiol-terminated PS obtained.

project the material dynamics in a specific phase due to the presence of varying temporal regimes. Hence, advanced methods like PFQNM can yield the local elasticity of different phase in the sample. The change in the interfacial strength between the particles and polymer imparted by polymer grafted on the MWNTs is a main factor which changes the demixing, morphology, orientation, etc., in the blend.28 The reason for these altered properties is still ambiguous. Hence, the PFQNM technique helps in assessing of these factors in the nanoscale, which sheds light on the reason for the bulk property changes. Also, through DRS, in which only one of the phases (here PVME) is dielectrically active, can throw more information about the perturbing chain dynamics imparted by these nanoparticles in the blend.

graft density also governs the localization in block copolymers.13 Partially miscible blends are compositionally heterogeneous due to effects associated with thermally induced concentration fluctuations, self-concentrations, and monomer connectivity.14,15 The chains experience a distinct local Tg and temperature-dependent dynamics resembling the pure components, as revealed by molecular tracer diffusion measurements or broadband dielectric spectroscopy (DRS). These techniques are unique as they provide information about the dynamics of discrete components, whereas techniques like rheology and Xray photon correlation spectroscopy (XPCS) provide information about relaxations that enable determination of the viscoelasticity of the polymer blends.16 While a great deal of literature exists discussing the effect of brush-coated NP on the dispersion quality in polymeric nanocomposites and block copolymer, the effect on the thermodynamic miscibility in LCST (lower critical solution temperature) mixtures is far from well understood. Some of the recent studies show that bare NP, wherein chains of A (of an A/B pair) having higher affinity toward the particles, induces thermodynamic miscibility.5,17 While this may not alter the monomer density on the NP surface, however, the host polymer chains experience a change in free energy because of deformational entropic loss.4 This has also manifested in a nonequilibrium segmental dynamics as observed from DRS.18 Hence, densely grafted NP with varying graft length can lead to changes in translational entropy of the free chains, conformational entropic losses of the grafted chains, and the free energy cost at the interface.11,19,20 Recent studies reveal that the confinement effect induced by one-dimensional multiwall carbon nanotubes (MWNT), due to the large surface-to-volume ratio, creates two dynamically dissimilar regions: one being transiently immobilized on the surface of MWNT and the other distinct regime of mobile segment where the relaxation is slowed down due to the restriction in the local modes of these loop segments.21 This difference in the dynamics of the homopolymer by the interaction of these particles can influence the configurational entropy while blending. In order to gain in depth understanding of the effect of these one-dimensional nanoparticles on the thermodynamic concentration fluctuation, miscibility, and polymer chain dynamics, a classical LCST pair, PS/PVME blends, was chosen as a model system.22−27 These anisotropic particles were grafted with PS of different molecular weight (ca. 13, 31, and 46 kDa) to tune their localization in the blend, and its effect on thermodynamic miscibility was assessed using various tools like melt rheology. The percent grafting, as observed from thermogravimetric analysis (TGA), is lower in these cases, and the nanoparticle core−core interaction might dominate until R ≈ Rg. A combinatorial effect of all these interactions induces distinct changes in the dynamics of the blend even in the thermodynamically miscible state. Classical methods like rheology, NMR, etc., are often used to understand the changes in the thermal fluctuations at various time scales of polymer relaxation, though they often fail to

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EXPERIMENTAL SECTION

Materials. PS (Mw 35 000 g/mol; PDI: 2.0), styrene, and CTA (2cyano-2-propyldodecyltrithiocarbonate) were procured from SigmaAldrich. PVME (Mw 80 000 g/mol and Mn 36 400 g/mol) was procured from TCI Co., Ltd., Japan. Azobis(isobutyronitrile) (AIBN) was obtained from Sd Fine Chemicals (India). AIBN was recrystallized and vacuum-dried from its saturated solution in methanol. Inhibitor from styrene was removed by washing with 10% NaOH and drying over anhydrous CaCl2. Solvents like N,N-dimethylformamide (DMF), tetrahydrofuran (THF), toluene, etc., were used as received from commercial sources. Preparation of Polystyrene via RAFT Polymerization. Polystyrene was synthesized according to the general procedure as given. Styrene (S), which is free of inhibitor, was added to 100 mL round-bottomed flasks containing a stirrer bar, AIBN, and the chain transfer agent (CTA) 2-cyano-2-propyldodecyltrithiocarbonate in the initial ratios of [S]:[AIBN]:[CTA] as given in Table 1. Approximately 4 mL of THF was added to this solution. The round-bottomed flask was sealed by a rubber septum and was degassed by three rounds of freeze−pump−thaw cycle and was backfilled with N2. The polymerizations were carried out at 80 °C for 48 h in under constant stirring and an increase in viscosity was observed with time. After the polymerization, the mixture was cooled to room temperature, aerated, and was redissolved in THF. PS thus obtained has a terminal trithiocarbonate group (indicated as PS-R). The molecular weights were analyzed by gel permeation chromatography (GPC) and are listed in Table 1. Reduction of the Trithiocarbonate-Terminated PS by Aminolysis. The α,ω-trithiocarbonate end-capped polymers were dissolved in THF containing a few drops of aqueous sodium bisulfite (Na2S2O4). The reaction mixture was further degassed by freeze− pump−thaw cycle and was backfilled with N2. Degassed propylamine was added in excess to the reaction mixture via syringe through the rubber septum. The reaction was stirred overnight in the N2 atmosphere. The initial yellow color of the solution turned colorless, indicating the loss of the trithiocarbonate group. Synthesis of PS-g-MWNT by Thiol−Ene Chemistry. PS-SH (150 mg) and AIBN (1−2% w/w) were dissolved in 30 mL of DMF, and 50 mg of MWNT was added. The mixture was sonicated for about 10 min in a bath sonicator. This solution was purged with N2, sonicated for 10 min, and stirred at 80 °C overnight. The mixture was then diluted with THF, bath sonicated for 15 min, and filtered through 0.5 μm PTFE membrane. It was washed with THF to get rid of any ungrafted polystyrene. The solid mass of PS grafted MWNT was dried B


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Figure 1. Reaction scheme for the synthesis of PS and PS-g-MWNTs. at 80 °C overnight in a vacuum. Reaction scheme of these reactions is shown in Figure 1. The blends were prepared by shear mixing polymer solution in toluene with bare MWNTs and different PS-g-MWNTs. The NPs were initially dispersed in toluene using a bath sonicator. The composite solution was then dried for sufficient time, as mentioned in our previous work.29 The concentration of MWNTs was fixed at 0.25 wt % for both bare and PS-g-MWNTs. Characterization. A Thermo Nicolet 6700 in the ATR mode in the wavelength range of 4000−700 cm−1 was used to record the Fourier transform infrared (FT-IR) spectra. Tecnai G2 F30 at 300 kV was used for transmission electron microscopy (TEM) imaging. DSCQ2000 by TA Instruments was used for thermal analysis. TGA was done under a N2 atmosphere in a Netzsch STA 409 PC at a heating rate of 10 K min−1. A modulated differential scanning calorimetry (MDSC) measurement at 2 K/min with amplitude 1 °C and period of 60 s was carried out. This was preceded by a heating cycle of 10 K/min to 80 °C, 30 min of isothermal, and was then cooled to −60 °C at the same rate. The step change in Cp measurement in the MDSC measurements gives the glass transition temperature. A stress-controlled rheometer (DHR-3 from TA Instruments) with parallel plate geometry and 1 mm gap was used to measure the viscoelastic properties of the blend. Dynamic temperature ramp measurements at a uniform heating rate of 0.5 K/min from 80 to 160 °C was done to find the onset of demixing in the blends. The degradation can be avoided in these slow temperature ramp due to the N2 atmosphere during measurement. Peak force quantitative nanomechanical mapping (PFQNM) has been performed using Bruker (Dimension Icon ScanAsyst). It is a new technique used for measuring Young’s modulus of material surfaces with high spatial resolution by probing at nanoscale. Phase-separated samples have been used to study the localization of carbon nanotubes by assessing the variation in the local modulus in the different phase of the sample. The cantilevers used had a nominal resonance frequency

of 320 kHz and possesses a rectangular geometry with a reflective aluminum coating (TESPA). A relative method of calibration has been used to find the radius of the tip. Prior to this, the deflection sensitivity calibration was performed on a stiff sapphire sample followed by a thermal tune function to obtain the spring constant. The reference sample was later imaged using PFQNM, and the tip radius parameter was adjusted to make the measured modulus equal to the known value of the reference sample. The cantilever parameter as obtained from the calibrations is spring constant 26.38 N/m and tip radius 30 nm. The imaging of the unknown samples has been carried out with a peak force set point 460 nN. The peak force amplitude and peak force frequency have been kept constant as 150 nm and 2 kHz, respectively. Impedance measurements were done using a Novocontrol Alpha-N Analyzer, (Germany) in the temperatures regime 28−60 °C with a step change of 2 °C on films which were deposited directly on the electrodes. 20% w/v of the blend in toluene was drop-casted on to the electrodes and was dried before the measurement.

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RESULTS AND DISCUSSION Synthesis and Characterization of Chain-End Grafted MWNTs. PS of different molecular weights were synthesized by RAFT polymerization, being one of the most versatile and robust polymerization techniques which provides a good control of the molecular weight, molecular weight distribution, and molecular architecture under a wide range of reaction conditions.30 The polymerization reaction propagates by providing insertion of monomer units (styrene) into the C−S bond of the RAFT agent or the chain transfer agent (CTA) structure. The molecular weight of the polymer synthesized depends linearly on the conversion, and it can be controlled by the amount of CTA in the reaction mixture C


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Macromolecules

reaction scheme of the RAFT polymerization forming trithioterminated polystyrene, aminolysis reaction of trithio-terminated polystyrene yielding thiol terminated polystyrene,31 and click thiol−ene reaction of the thiol-terminated polystyrene with MWNT yielding PS-g-MWNT.32 By varying the initial molar ratios of [S]:[AIBN]:[CTA], various molecular weights of polystyrene (as analyzed by GPC) were obtained and are listed in Table 1. The thiol−ene click reaction of MWNT with thiol-terminated polystyrene resulted in the formation of polystyrene grafted MWNTs (PS-g-MWNT) of varying molecular weights. All these products were characterized by FT-IR (see Figure 2a). The weight-average molecular weight from GPC and the weight loss from the TGA analysis gave information about the percentage of PS grafted on each case. The radius of gyration estimated using TGA (see Table 2 and Figure 2b) and the MW are in line with the values obtained from the TEM images (Figure 3). Figure 2a1 shows the FT-IR spectra of PS-R, PS-SH, the bands of C−H stretch from the aromatic rings (shown in Figure 2a2), C−H stretch (∼2900 cm−1) from the alkyl units, and CC stretch (∼1634 cm−1) which validate the successful polymerization of PS. The thiol stretching ∼2700 cm−1 in the second step confirms the conversion of trithio end group to thiol. The percentage grafting of polymer was measured by using TGA analysis. The graft density is the number of polymers per area of the nanotube surface and is given as ρ ρ=

Table 2. Parameters Obtained from TGA Σ (chains/nm2)

RP−P (nm)

Rg (nm)

PS(13 kDa)-g-MWNT PS(31 kDa)-g-MWNT PS(46 kDa)-g-MWNT

0.07677 0.00395 0.01368

3.60 15.92 8.55

2.58 4.45 6.01

Mn ∼

M0 × conversion + MRAFT nRAFT

(2)

M/A for graphene sheet is 7.7 × 10−7 kg/m2, and the fractional mass of polymer and MWNTs is given as Mp and MNT (estimated from TGA in Figure 2b). Mw is the weight-average molecular weight (in g/molecule). The average graft distance between any two polymer chains on MWNT surface is given as RP−P = 1/√ρ. The relation Rg = 0.028Mn0.5 gives the size of the grafted chain (here, Mn is the number-average molecular weight of the polymer). The polymer chain conformation is a function of the length of the polymer chain grafted. Table 2 lists a comparative analysis of these parameters. The TEM images of MWNT and PS-g-MWNTs are shown in Figure 3a−c. It is easily noticeable that the PS-g-MWNTs are much thicker than the pristine MWNTs (average external diameter matching the value provided by the supplier). In the PS-g-MWNT, a layer of polymer, nearing an order of the radius of gyration of the polymer is seen on the surface of MWNTs. Altered Length of Cooperative Rearranging Region at Glass Transition Temperature. The glass transition of the blend is obtained by DSC measurement as shown in Figure 4. The effect of heterocontacts in the presence of the chain end grafted particles on the thermal fluctuation has been evaluated by assessing the volume of cooperative rearranging region (CRR). A subsystem which is capable of rearranging to another configuration, independent of the environment for a given thermal fluctuation, is called CRR, as proposed by Adam and Gibbs theory.33 From Donth’s approximation,34 the volume of cooperative rearranging region (Va) has been evaluated by

Figure 2. (a1) FT-IR spectra of PS-R, PS-SH. (a2) FT-IR spectra of PS-R, PS-SH from 1300 to 1700 cm−1. (b) TGA analysis of PS-gMWNT.

PS-g-MWNT

N M Mp 1 = A A MNT M w

Va = ξCRR 3 = kTg 2ΔCp−1/ρ(δT )2

(1)

(3)

ΔCp−1

Here, ξCRR is the length of CRR, is the reciprocal specific heat at constant pressure, ρ is the density of the bulk material, and δT is the half-width of the Tg. It gives the mean

where Mn is number-average molecular weight, nRAFT the number of moles of the CTA, M0 the monomer concentration, and MRAFT the molecular mass of CTA. Figure 1shows the D


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Figure 3. TEM of pristine MWNTs (a1, a2), PS(13 kDa)-g-MWNT (b1, b2) PS(46 kDa)-g-MWNTs (c1, c2) (the white scale bar in the parts a1−c1 corresponds to 0.2 μm and the white scale bar of parts a2−c2 corresponds to 50 nm).

(negative χ) is due to the increased free volume and conformational entropy on blending. A substantial decrease in the Rg of the host polymer is not observed due to the less evidential increase in the local ordering to establish any heterocontacts.35,36 Variation in the local compositional environment is due to the concentration fluctuation effects on the self-concentration (φself) and the effective concentration (φeff) in the composition. PVME chains are more flexible than PS chains, with a self-concentration of 0.57 for PVME and 0.053 for PS.5,37 This causes the effective Tg of PVME close to that of the blend Tg for the compositions until 50 wt % of PVME as indicated in Figure 5a. Hence, a composition like 60/ 40 (w/w) could be of great interest for in-depth analysis. The component with large self-concentration (low Tg) is more susceptible for alteration in the segmental dynamics and the effective glass transition (Tgeff), as derived from a compositional dependent bulk average.38 In the case of polymer nanocomposites with highly anisotropic nanoparticles, especially in the case where there is a strong interaction with the polymer, the presence of enthalpic interaction in the vicinity of the particles creates an environment with two distinct glass transition temperatures. A theoretical model proposed by Lodge et al.5 has been used to understand the dynamics in the similar polymer blends, like in the studies of Khademzhadeh et al.27 and Lee et al.,39 and is expressed as

Figure 4. Glass transition temperature for various compositions.

Table 3. Glass Transition Temperature and Length of CRR from MDSC Measurements PS/PVME 60/40 neat with with with with

MWNT PS(13 kDa)-g-MWNT PS(31 kDa)-g-MWNT PS(46 kDa)-g-MWNT

Tg (oC)

ξCRR (nm)

3 −1 8 6 14

1.23 1.01 9.25 5.68 3.54

Tg1eff (ϕ1) = Tg2 + (Tg1 − Tg2)[1 + K1)ϕ1eff − (K1 + K 2)ϕ1eff 2 + K 2ϕ1eff 3

temperature fluctuation by the distribution of Gauss function modeling in the heat capacity. The grafted chain-end nanoparticle interaction with the host polymer is a dominant factor which affects the glass transition in the case of polymer nanocomposites. The moreover unaltered Tg in the presence of 0.25 wt % of MWNTs as compared to the neat blend (as shown in Table 3) in the weakly interacting PS/PVME blends

(4)

where Tg1eff is the Tgeff of PS-polymer 1; Tg1 and Tg2 are Tg of polymers 1 and 2, respectively. K1 and K2 are 0.707 and 0.462, respectively. The effective local glass transition of a polymer in the blend can be obtained from the above equation. The relaxation of a polymer chain at a length scale of a Kuhn E


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Figure 5. (a) Glass transition temperature (Tg) of neat blend, Tg,eff of PS and Tg,eff of PVME. (b) Variation length of CRR with temperature.

Figure 6. (a) HN fitting of PS(13 kDa)-g-MWNT. Dielectric modulus as a function of frequency at different temperatures for 60/40 PS/PVME with 0.25 wt % (b) PS(13 kDa)-g-MWNT, (c) PS(31 kDa)-g-MWNT, and (d) PS(46 kDa)-g-MWNT.

assembly of the polymer blend are influenced by the property of the chain tethered on MWNTs. The addition of all the three PS-g-MWNTs has increased the glass transition temperature, with a notable change of ca. 14 °C for PS(46 kDa)-g-MWNT (Table 3). The incorporation of PS-g-MWNTs facilitated in interactions, which are mostly of an enthalpic origin. The enthalpic interactions (X) can be expressed as

segment (lk) is influenced by concentration of segments within a volume, V = 1/4glk3, where g is a geometric factor. The differently grafted PS on MWNTs will exhibit diverse properties depending on the number of grafted chains per area, degree of polymerization of grafted chain per area, and degree of polymerization to grafting chains (N) with respect to that of the host polymer (P; PS phase in this case). The spatial organization, miscibility, and interfacial segregation of selfF


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Macromolecules Table 4. α and β Fitting Parameters of the α Relaxation of Various Blends PS(13 kDa)-gMWNTs

MWNTs, PS(31 kDa)-g-MWNTs, and PS(46 kDa)-g-MWNTs. Modulus formalism is advantageous over others as it suppresses the electrode polarization at the lower frequency. The M″ versus frequency behavior of all the blends investigated here are fitted using a Havriliak Negami (HN)46 relation and converted from frequency domain to time domain by Kohlraush− Williams−Watts (KWW) function to understand the time decay of the relaxation frequency.47 The HN equation is given as

PS(46 kDa)-gMWNTs

PS(31 kDa)-gMWNTs

temp (oC)

α

β

α

β

α

β

30 36 40 46 50 56 60

0.84 0.91 0.90 0.90 0.87 0.90 0.90

0.90 0.91 0.90 0.90 0.97 0.90 0.90

0.50 0.50 0.50 0.50 0.50 0.50 0.50

0.60 0.60 0.60 0.60 0.60 0.60 0.60

0.36 0.40 0.47 0.55 0.55 0.59 0.36

1.00 0.65 0.58 0.53 0.65 0.69 1.00

M * = M′ + iM″ = M∞ +

(5a) HN 1/ε∞, τ1 M

where ΔM = Ms − M∞, Ms = 1/εs, M∞ = is the HN relaxation time, α and β describe the width and asymmetry of the spectra. As a single fit is not sufficient in explaining the dielectric relaxation of the complex systems like these, the imaginary part of the modulus has been fit using two HN fits. The HN equation can be modified by incorporating the fit parameters from both the relaxations. The modified HN equation has been given as

Table 5. α and β Fitting Parameters of the Secondary Relaxation of Various Blends PS(13 kDa)-g-MWNTs

PS(31 kDa)-g-MWNTs

temp ( C)

α

β

α

β

30 36 40 46 50 56 60

0.8 0.8 0.8 0.8 0.8 0.8 0.8

0.8 0.8 0.8 0.8 0.8 0.8 0.8

0.96 0.93 0.98 1.00 0.97 0.96 0.97

1.00 1.00 1.00 1.00 1.00 0.96 1.00

o

Χ=

ε = 2εp − NP − εpp − εNP − NP/2kBT 2kBT

ΔM (1 + ( −i(ωτHN − M )−1)α )β

M * = M′ + iM″ = M∞ + + (5)

ΔM1 (1 + ( −i(ωτ1HNM )−1)α1 )β1

ΔM 2 (1 + ( −i(ωτ2 HNM )−1)α2 )β2

(5b)

The HN fitting of a representative blend sample is shown in Figure 6a as an example. The two relaxations peaks are considered as two types of environment in the blend; hence, two HN fits are used in these cases. The characteristic HN relaxation time τHNM for the two relaxations has been set as free parameters during fitting process. As mentioned above, the dielectric relaxation has been observed as two relaxations, where one peak corresponds to the α relaxation and the other corresponds to the interfacial region wherein PVME chains experiences a constrained environment. This type of fitting has been used in cases of polymer composites with bimodal relaxation as observed by Holt et al.48 The observation of the double relaxation by DRS in this system is in corroboration with the observations as seen in the work by Ashkar et al.21 in PMMA composites with highly anisotropic carbon nanotubes has created due to the large surface area−volume ratio. The bimodal relaxation observed in the case of PS(13 kDa)g-MWNTs and PS(31 kDa)-g-MWNTs is a clear indication of dynamic heterogeneity in the system, as seen in the Figure 6b,c.The low-frequency relaxation of these blends is due to the cooperative relaxation due to the calorimetric glass transition, which is also called the α relaxation. The secondary relaxation at higher frequency is due to the PS-g-MWNTs confined in the PVME phase. Moreover, a broad single relaxation is obtained in the case of blend with PS(46 kDa)g-MWNTs, as seen in Figure 6d, which is an indirect indication suggesting two distinct environment for PVME with the free chains and also with the chains surrounded by the frozen PS phase with the particles localized in it. A detailed analysis on understanding the localization of particle in the blend is done by PFQNM in the latter part of the text. The fitting factors α and β, which are related to the slope of the relaxation curve, are listed in Tables 4 and 5, where α is the symmetric broadening of the loss peak and β is the asymmetric broadening. It is well evident that the blends with PS(13 kDa)-

where the subscripts p and NP refer to the polymers and nanoparticles, respectively.40 The scale of cooperativity ξCRR34 has increased in the case of blend PS-g-MWNTs compared to neat blend and blend with MWNTs. The highest ξCRR is observed in the case of PS(31 kDa)-g-MWNT, and it decreased in the case of PS(46 kDa)-gMWNT (see Table 3). This is in line with the average length of chain separation Rpp. The increased ξCRR on the addition of PSg-MWNTs manifests an apparent increase in the activation energy of the bead or blob relaxing. It is ascribed to the increased dynamic heterogeneity observed in the blend. It is interesting to note that Tg has increased in the case of PS (46 kDa)-g-MWNT compared to the other cases and the increase was in close harmony with the Rg of the PS grafted chains on the MWNTs. The connectedness of the slow domains requires higher energy to overcome the kinetic barrier collectively.41 The collective motions in these polymer segments are determined by the cooperativity of the segments and its dependence on temperature is shown in Figure 5b. This is explained by a dynamic scaling model proposed by Colby42 and ξ(T) = r0[(T − Tc)/τc]−υ, where υ is 3/2 and r0 is the prefactor of the size of the CRR.43 An in-depth analysis carried out by the segmental dynamics studies by DRS show the difference in the dynamics of the polymer blend in the presence of these particles. Intermolecular Coupling in the Presence of ChainEnd Grafted MWNTs. Critical insight into the segmental relaxations near Tg is obtained from dielectric relaxation spectroscopy (DRS). All the structural relaxations observed in DRS is due to the PVME phase as PS is dielectrically inactive in the frequency range measured.44,45 The frequency dependence of dielectric modulus loss spectra M″ as a function of frequency is plotted for the PS/PVME blends with PS(13 kDa)-gG


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Figure 7. VFT fits for the dependence of relaxation time with respect to temperature for (a) PS(13 kDa)-g-MWNT, (b) PS(31 kDa)-g-MWNT, and (c) PS(46 kDa)-g-MWNT. (d) Coupling of various PS/PVME blends.

⎡ ⎛ t ⎞1 − n⎤ φ(t ) = φ0 exp⎢ −⎜ ⎟ ⎥ ⎣ ⎝ τ* ⎠ ⎦

Table 6. VFT Fit Parameters and Fragility Index of the Blend sample: PS/PVME 60/40

τ0 (s)

D

T0 (°C)

m

with PS(13 kDa)-g-MWNT with PS(31 kDa)-g-MWNT with PS(46 kDa)-g-MWNT

3.77 × 10−4 1.70 × 10−11 8.90 × 10−10

198 1300 1404

250 240 234

25 103 64

(6a)

where ϕ(t) and ϕ0 are the dynamic response at time t and 0, respectively, after a perturbation, τ* is the characteristic time, and n is the coupling parameter which increases with the breadth of the relaxation dispersion. Intermolecular cooperativity in polymer blends can further be studied by comparing the coupling parameters, n, with that of the neat blend, given in eqs 6b−6d. Empirical correlations among the HN and KWW parameters were found out, as given in the following equations:50,51

g-MWNTs show Debye-like relaxations with both α and β being close to 1. In the case of PS(31 kDa)-g-MWNTs and PS(46 kDa)-g-MWNTs, the relaxations are much broader, indicating heterogeneous environment in the blends. The increase in the stretching of the relaxation function cause a deviation from the Debye-type relaxation.49 A noticeable difference present in the nature of the relaxation curve in the case of PS(13 kDa)-g-MWNT, which can be better understood by assessing the coupling parameter in these blends. A better understanding about the relaxation can be obtained looking at the distribution of relaxation function in the time domain. The parameter n represents the coupling parameter referred to the intermolecular coupling between the relaxing species and the medium. At sufficient time scales when the intermolecular coupling effects are exhibited, the macroscopic variables relaxation obeys the KWW function and is given by

βKWW = (αβ)1/1.23

(6b)

γ = 1 − 0.812(1 − α)0.387

(6c)

log τβ = log τHN − 2.6(1 − β)0.5 exp( −3β)

(6d)

The term n, referred to as the coupling parameter, can be equated to the stretch parameter β as n = 1 − βKWW. An increased coupling is observed in the case of PS(46 kDa)-gMWNT, which showed a better thermodynamic miscibility, which will be discussed in the next section. The loss maxima are observed to shift toward higher frequency with increase in temperature. The temperature with H


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Figure 8. Determination of rheological demixing temperature of PS/PVME blends by (a) variation of G′ with respect to temperature forPS(46 kDa)-g-MWNT. (b) Reciprocal square correlation length vs 1/T PS(46 kDa)-g-MWNT.

Table 7. Demixing Temperature of Various Compositions PS/PVME 60/40 neat with with with with

MWNT PS(13 kDa)-g-MWNT PS(31 kDa)-g-MWNT PS(46 kDa)-g-MWNT

Tb ± 2 (°C)

Ts ± 2 (°C)

104 110 90 103 119

107 115 117 121 127

m=

(7a)

(7b)

where the parameter A corresponds to activation energy and R is the universal gas constant. The fragility index has been calculated by analyzing the VFT dependence of relaxation time. It is given as a dependence of relaxation time as m=

d ln τ d

Tg

() T

T = Tg

Tg 2 T

)

(9)

The fragility index (m) for the blends is also reported in Table 6.The variation in fragility index of the blends with PS-gMWNTs is in trend with the variation of the length of cooperative rearranging region. This decrease in fragility is attributed to the decrease in the internal energy due to the structural rearrangements of polymer chain, as fragility is related to the packing efficiency of the polymer chains. The lowest fragility (25) was observed in the case of PS(13 kDa)-gMWNTs, where the particles are localized in the PVME (observed from PFQNM in the next section). A maximum fragility was observed in the case of PS(31 kDa)-g-MWNTs (103), which had showed the large volume of CRR, from the MDSC studies. Likewise, the blend with PS(13 kDa)-gMWNTs possessed the lowest CRR and low fragility. A decreased fragility to 64 and reduced length of CRR were observed in the case of PS(46 kDa)-g-MWNTs due to the increase in the Rg of the polymer grafted on the MWNTs. The Rg of the grafted chain is higher than that of the matrix polymer in this case. This is studied in detail in the previous section. In cases where the Rg is higher, compared to the matrix, less competition is experienced from the neighboring polymer chains by reducing the cooperativity.53 The fragility of the blend is comparable to that of the reported values.54 As observed from the VFT curves, it is evident that there is a difference in the mobility of PVME chains in the presence of miscible PS(13 kDa)-g MWNTs, PS(31 kDa)-g-MWNTs with a bimodal relaxation, whereas a broad single relaxation is observed in PS(46 kDa)-g-MWNTs particles. The broad relaxation observed in the case of the PS/PVME blend with PS(46 kDa)-g-MWNTs is due to lowered dynamic heterogeneity and self-concentration in the system. Altered Miscibility in the Presence of Chain-End Grafted MWNTs. The varied demixing behavior due to the difference in the stress generated upon demixing due to the thermal concentration fluctuations has been measured by isochronal temperature ramp measurements in rheology. Interestingly, the addition of PS(46 kDa)-g-MWNT, which is localized in the PS phase on demixing, has increased the rheological demixing temperature (Trheo) by ca. 12 °C, compared to the control blends. This is due to the enthalpic

where T0 (Vogel temperature) is the temperature below the Tg where the segments would be frozen and will be in equilibrium, D is a material parameter associated with the apparent activation energy, and τ0 is the relaxation time at infinite temperature. The Arrhenius equation is given as ⎛ −E ⎞ τ = A exp⎜ ⎟ ⎝ R (T ) ⎠

(

ln 10 1 −

respect to relaxation time is given by Vogel−Fulcher− Tammann (VFT) relation, which is a characteristic of structural α-relaxation in the polymers. The secondary relaxations are generally independent of temperature or show a weak Arrhenius dependence. The VFT fits for the dependence of relaxation time with respect to temperature is given in Figure 7, and the temperature dependence of the secondary relaxation has been given as the inset. The VFT equation is given as

⎛ DT0 ⎞ τ = τ0 exp⎜ ⎟ ⎝ T − T0 ⎠

D/Tg

(8)

where Tg is the glass transition temperature. The fragility can be related to the VFT fit parameters (given in Table 5) as given52 I


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interactions between the grafted PS and the free PS and also due to the entropic losses such as deformational entropic losses due to blending, combined with the translational entropic loss of the free PS, and the conformational entropic loss of the grafted PS, and the interface between both. Even though the Trheo has decreased, there is an increase in the spinodal temperature (Ts) in the presence of PS(13 kDa)-g-MWNT and is comparable to that of the blend with bare particles. Similar observation was also seen in the case of PS(31 kDa)-g-MWNT wherein the particles were restricted in the PVME phase. The analysis from DSC and DRS suggests that a larger volume of cooperatively rearranging region with an increased intermolecular coupling (n) in blends with PS(46 kDa)-g-MWNTs has facilitated molecular level miscibility as evident from the melt rheological experiments. The nature of stress generated upon demixing is of elastic in nature, making rheology, a versatile method to probe the demixing in these blends showing dynamically asymmetry. The rheologically determined demixing temperature (Trheo) can be deduced by observing the evolution of viscoelastic response as a function of increasing temperature. As an example, G′ as a function of temperature of the blend with PS(46 kDa)-gMWNT is shown in Figure 8a. Distinct changes were noted in the behavior of G′ near the demixing temperature. The enhanced concentration fluctuation leads to the formation of dynamic domains rich elastic PS component and lead to an upturn in the G′. The inflection point in this plot is taken as the rheological demixing temperature. With the incorporation of PS(13 kDa)-g-MWNTs, the Trheo has decreased. The Trheo was unaltered in the case of PS(31 kDa)-g-MWNT, and it has increased in the case of PS(46 kDa)-g-MWNT. The temperature corresponding to the sudden upturn in the correlation length (which is the length scale of concentration fluctuation) can be used for determining the demixing temperature. The calculation of concentration fluctuation has been calculated by mean-field approximation by Ajii−Choplin, which is formulated in support of the theory of Fredrickson and Larson.55,56 The correlation length of the blends is calculated by ⎡ k T G′ ⎤1/3 ξ=⎢ B ⎣ 30π G″ 2 ⎦⎥

(10)

The expansion of the above relation of correlation length (ξ) by Ornstein−Zernike form is given as56−58 ξ 2(T , ϕ) =

b2 [ϕ ϕ (χ − χ )−1 36 A B s

ξ(T , φ) = ξ0(φ)ε−n

(11) (12)

ε is given as (T − Tc)/Tc and n = 1/2. The plot of reciprocal square of correlation length (ξ−2) with respect to temperature is a straight line intercepting at ξ−2 = 0, which is considered as Ts. As an example, the plot of PS(46 kDa)-g-MWNT is shown in Figure 8b. The demixing temperature of various blends is shown in Table 7. Nanomechanical Mapping: Conformational Transitions in Chain-End Grafted MWNTs. The interfacial strength between the MWNT and the polymer increases as a function of the density and the chain length of the polymer grafted on the carbon nanotubes due to the sliding friction within the adsorbed grafted chains and the matrix. This is the reason for the increase in the strength and toughness in a macroscopic scale. The nanomechanical mapping assists in

Figure 9. (a) A cartoon illustrating the working principle of PFQNM, modulus map of PS/PVME 60/40, and the corresponding force vs distance curve from PFQNM measurements of (b1, b2) neat blend and with 0.25 wt % (c1, c2) MWNTs, (d1, d2) PS(13 kDa)-g-MWNTs, and (e1, e2) PS(46 kDa)-g-MWNTs. (f) Modulus of various compositions of PS and PVME from PFQNM. J


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Figure 10. AFM height images of 60/40 PS/PVME (a) neat blend and (b) with 0.25 wt % MWNTs, (c) PS(13 kDa)-g-MWNTs, and (d) PS(46 kDa)-g-MWNTs.

Figure 11. A cartoon illustrating the localization of different MWNTs grafted with PS chains in PS/PVME mixtures.

finding the interfacial adhesion between MWNTs and the matrix. The various factors influencing the mechanical properties of nanocomposites are the matrix morphology, the extent of bundling (or particle dispersion), the structure and type of interface, and the orientation of particles.28 The difference in the interfacial strength imparted in the system is characterized by difference in modulus in the sample, which helps in analyzing the localization of these particles in the blend upon phase separation which otherwise makes it difficult because of a layer of insulating polymer. The nanomechanical mapping using PFQNM mode in AFM59 uncovers the local mechanical properties of materials down to smaller length scale to show the underlying mechanism like conformational transitions and surface adhesion due to the localization and dispersion of PS-gMWNTs. AFM nanomechanical mapping is relevant in this

context, where the localization of the particles is studied by the change in the elasticity of the different phase in the blend. The topographic and phase imaging of the AFM was done by tapping mode by recording the cantilever movement over the sample surface. The localization of NPs in thin film blends of PS/PVME was assessed by PFQNM measurements. The interaction forces at molecular levels can be obtained by this technique, as at a fixed (x, y) position, the AFM tip extends in a Z direction toward the sample. At a trigger point, the maximum force exerted by the tip is measured, and the tip is retracted.60,61 Because of the experimental limitations in measuring the absolute value of the modulus, the obtained values are normalized by using standard PS film sample.62 Elastic modulus is obtained from the modulus maps of the samples in Figure 9b−e. According to the variation of modulus of each phase, it K


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was observed that MWNTs have migrated to the interface and into the thermodynamically favored PVME phase upon demixing in the blend with pristine MWNTs. This is also evident from the force displacement curves from the bright and the dark phase, which showed distinct behavior suggesting that the bright phase is PS and the dark phase is PVME.63 The PVME shows a larger adhesive region compared to that of PS. The force displacement curves for PS and PVME are similar to PVME having less adhesive region is observed in the case of blend with PS(13 kDa)-g-MWNTs, suggesting the localization of particles in the PVME phase. Also, it is clear that the force distance curve of the PVME phase in the blend with PS(46 kDa)-g-MWNT shows an adhesive region similar to the case of PS/PVME without particles. This clearly indicates that these particles are localized in the PS phase. The localization of PS (46 kDa)-g-MWNT in the PS phase was clear from AFM topographic and modulus maps. PS being a good solvent for PVME, it was difficult to image particles PS(13 kDa)-g-MWNT and PS(31 kDa)-g-MWNT localized in the PVME phase by AFM modulus maps or topographical image. The modulus values obtained from each of the phase is shown in Figure 9f. This observation essentially suggests that the conformation of PS in PS(46 kDa)-g-MWNT with Rg of the brush higher than that of the Rg of the melt polymer led to an improved melt−brush interaction by localizing it in the PS matrix. The AFM height images of the same samples are given in Figure 10 for a comparative analysis. The entropic repulsion of the grafted PS as Rg,matrix > Rg,grafted in PS(13 kDa)-g-MWNTs and PS(31 kDa)-g-MWNTs resulted in the expulsion of those particles from PS phase. A cartoon further illustrating these effects is shown in Figure 11.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the Department of Science and Technology for the financial support, Micro and Nano Characterization Facility (MNCF) in the Centre for Nano Science and Engineering (CeNSE) at IISc, for PFQNM characterization and Dr. Rajeev Ranjan, Department of Materials Engineering, for the assistance in dielectric characterization.

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SUMMARY Taken together, the slower dynamics induced by these chainend grafted nanoparticles has improved the connectedness of the slow domains. This slower dynamics at lower length scale imparts thermodynamic miscibility to the system. The DRS studies showed the varied dynamics of the dielectrically active PVME phase in the presence of different PS-g-MWNTs. The blends with PS(46 kDa)-g-MWNTs showed higher coupling at temperatures closer to the glass transitions temperature. The enhanced interfacial strength between the MWNT and the polymer matrix increases as a function of the density and the chain length of the polymer grafted on the MWNTs, which also tuned the localization as understood from the enhanced E values obtained from PFQNM. The expulsion of PS(13 kDa)-gMWNT and PS(31 kDa)-g-MWNT particles from the PS phase is understood to be of entropic origin. The matrix polymer chains in the blends with PS(46 kDa)-g-MWNT stretched due to the entropic penalty which led to a uniform dispersion of these particles in PS, thereby making it difficult to detect these particles by the usual imaging techniques. The enhanced miscibility in this case as observed from rheology is due to the favorable brush/melt interactions. The fragility index of the blends has a direct correlation to the length of CRR around the glass transition temperature in these blends.

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Nanomechanical Mapping, Hierarchical Polymer Dynamics, and

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