grafted nanoparticles

Polymer 90 (2016) 264e275

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Interfacial relaxation mechanisms in polymer nanocomposites through the rheological study on polymer/grafted nanoparticles Feng Wu a, Shuyang Zhang a, Zhefeng Chen a, Bao Zhang b, Wei Yang a, Zhengying Liu a, *, Mingbo Yang a, ** a

College of Polymer Science and Engineering, State Key Laboratory of Polymer Materials Engineering, Sichuan University, Chengdu 610065, Sichuan, People's Republic of China Key Laboratory of Polymer Ecomaterials, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, Jilin, People's Republic of China

b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 October 2015 Received in revised form 7 March 2016 Accepted 12 March 2016 Available online 15 March 2016

Polymer grafted nanoparticles with different surface properties have been prepared and widely used in different fields recently. In this study, through the rheological study on the strength of interfacial adhesion relevant to the complex viscoelasticity and relaxation response of the well-defined polymer (polylactide, PLLA) grafted-nanoparticles (silica) mixed with free chains of the same polymer nanocomposites in melt state, we investigated the different interfacial entanglement and relaxation mechanisms of the polymer grafted nanocomposites (PGN), to bridge the relationship between the micro and macro-properties of PGN. The AFM observation illuminated that circles one by one were formed in “grafting from” prepared SiO2 (GF), while coreeshell morphology found in “grafting to” prepared SiO2 (GT), because of the different surface properties of the modified SiO2. The interface relaxation was characterized around 300 s in the GT5 nanocomposites, due to the entanglement between the long grafted and matrix chains, which also contributed lots to the rheology properties enhancement, such as the improving viscosity. Combining the relaxation spectrum and stress relaxation testing, the relaxation units in different time scales, from short time to long time, were illuminated. Also the relaxation of the interfacial chains in different situations, through the introduction of the absorption and reptation models, was proposed to explain our observations. The comparative study reminded us that the strong interfacial interactions or the long interfacial relaxation time aroused by the entanglement, were essential for successfully preparing polymer nanocomposites. © 2016 Elsevier Ltd. All rights reserved.

Keywords: PLA nanocomposites Topology Relaxation

1. Introduction As pointed out by Kumar, Winey and their coworkers, the spatial distribution of nanoparticles (NPs) and the interactions between the NPs and polymer matrix are the key parameters in controlling the macroscopic performance of the polymer nanocomposites (PNCs) [1,2]. The effect of the spatial organization of the particles in the polymer matrix on macro-properties of PNCs has been discussed for decades, suggesting that either large-scale agglomerates [3e5] or uniform dispersion [6e8] is necessary for the enhanced properties. Recently an idea emphasized by Akcora et al., PNC with

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (Z. Liu), [email protected] (M. Yang). http://dx.doi.org/10.1016/j.polymer.2016.03.034 0032-3861/© 2016 Elsevier Ltd. All rights reserved.

percolating sheets of particles displays “gel-like” or solid-like mechanical enhancement at lower particle loadings than one with uniform particle dispersion [9], gives an intuitive description of the spatial organization effect using a phase diagram [10,11]. Both Sunday [12] and Kumar's [13,14] studies have shown that the dispersion of the nanofillers are hugely dependent on the ratio of the grafted chain length/matrix chain length and grafting density [15]. The dispersion states of grafted NPs and un-grafted NPs are also illustrated by molecular dynamics simulations and other experiments. Hasegawa et al.'s work shows that an optimum graft density for dispersing the grafted particles in the nanocomposites exists because of the origin of the attractive energy [16]. By using the transmission electron tomography (TEMT) technology, Dalmas et al. find that either densely packed or isolated NPs could be obtained by changing the ratio of the grafted chains and matrix chains [17]. It is obvious that the dispersion state of the NPs could be

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controlled by the surface decoration, either by grafting with silane molecules [18] or the matrix-like polymer chains [19], or other simple approach to prepare the hybrid organic/inorganic particles in-situ [20e22]; after the NPs are surface modified, especially grafted with polymer chains, the polymer-filler interfaces have also been grandly changed [23,24]. Therefore, the investigation about the effect of the topology of the grafted NPs on the properties of PNC is interesting and necessary. Lots of effort has been progressively updated in the literature on them [25,26]. After modified, the compatibility (or interaction) between the modified filler and matrix is influenced by the varied filler surface chemistry. Firstly, grafted chains with tunable graft density (s) and molecular weight (N) are observed to have antithetical enthalpic and entropic effects on interface compatibility; secondly, with the tunable topological structure, the interaction between the NPs and matrix can be adjusted. Traditionally, the concept of “dry”, “wet” and “dewetting” [23] state can also be used to illustrate the interface scenario of PNCs. And these dry or wet states of the grafted chains into matrix have a significant influence on the matrix-brush entanglement [27] or interfacial interactions, which finally influence the properties of the polymer/modified nanofiller nanocomposites [28e30]. As for the interaction force between the polymer and nanofillers, it could be date back to the developed history of the network in PNC, which has been lasting for decades. In 1960s, the study on rubber/carbon black suggested that the directly contacted particleeparticle network leaded to the strengthening of the rubber matrix [31]. From then on, the theory of the network formed in polymer matrix has been developed [32]. Compared to the “particle-only” scenario, others involve both the particles and polymer chains [14]. Particle-polymer networks [33,34] which bridged by the absorbed polymer chains or free matrix chains are suggested to be the main network formed in polymer matrixes in the later theories. And which scenario sat in a dominant position is decided by the ratio of the adhesive energy between filler and polymer to that of filler and filler (WPF/WFF) [10], thus the interaction directly affects the buildup and geometry of the filler network in the nanocomposites. In our opinion, the chain relaxation in the polymer melt is a core behavior for the rheology and other properties response; and it is related closely to the interfacial interaction in the PNCs, especially for the relaxation of the interfacial chains. After the NPs are added, the relaxation of the polymer chains, both grafted chains and matrix chains, will be changed. As far as now, numerous researches on the chain mobility and relaxation of nanocomposites have been conducted [35,36]. Different results are reported in these publications, but it has been come agreement with that the relaxation of the chains will be influenced by the confinement effect aroused by the so-called ‘‘three-dimensional filler network structure’’. Both molecular dynamics simulations [37e39] and experiments [15,40] are also carried out to investigate the diffusion of NPs and polymer in nanocomposites. As pointed out in these studies, the nanoparticles size [41], the local densities of brush and melt chains [42] and the nanoparticle brush architecture [43] work together to tailor the NPs and polymer diffusion in the PNCs, as well as the interaction between NPs and matrix. The above molecular dynamic simulations have provided lots of information about the interfacial actions between the matrix and NPs; however, systematic experimental observations and studies of the interfacial chain relaxation using rheological method in these PNCs are still lacking and full of challenges, in spite of the interfacial chain relaxation is very important for designing the interface properties of PNCs. While the rheological properties are sensitive to the specific surface properties and the resulting polymer-filler interfaces [44]. The measurements of composition and condition dependencies of viscoelastic

265

properties in the molten state seem to be a useful technique to obtain theoretical and experimental analysis of the structureproperty relationships in these materials [45e47]. PLLA-grafted SiO2 nanoparticles with long grafted PLLA brushes have been recognized as an effective melt-strengthen modifiers of biodegradable PLLA in our former study [48]. The former study has focused on the high melt-strengthen effect and found that the poor viscoelastic behavior of PLLA is significantly improved by the introduction of the modified nanoparticles, including the improved viscosity and modulus. However, the viscoelasticity properties of the nanocomposites show strongly dependent on the dispersion state and interaction of the nanoparticles (NPs); and this dependence is still unclearly elaborated. Also, the high entanglement molecular of PLLA facilitates our research on tailoring the interfacial actions by using PLLA grafted SiO2 nanoparticles. In this study, through the introduction of two kinds of PLLAgrafted SiO2 with different brush architecture (GF2 (Mn ¼ 2400 g/mol, grafting density ¼ 0.52 chains/nm2) and GT2 (Mn ¼ 22 400 g/mol, grafting ratio ¼ 0.008 chains/nm2)) into the PLLA matrix, “dry” and “wet” PNC with soft NPs are obtained in our research. Refer to the former studies, the effects of the polymerfiller interface on the properties of the PNC are evaluated using rheological approaches, which is a good way to characterize the molecular relaxation besides some other broadband dielectric spectroscopy technologies [49e52]. Firstly, to understand the relationship between the topology and properties of PNC better, the conformation of the grafted chains must be obtained. Along with the technology development, dynamic light scattering (DLS) [53], small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS) are widely used in the directly measurement of the topological structures [54]. In our study, the atomic force microscope (AFM) technology is used to characterize the architecture of the modified silica nanoparticles. Meanwhile, the dispersion state of the PLLA/PLLA grafted silica composites is assessed by TEM. Then through deeply studies on the relaxation and rheological response of the PNCs with different topology of the modified nanoparticles, the polymer conformations on the interface are discussed. The multi-scaling networks in PNC, which leads to the former researches on structure-properties relationships a debate matter, have been detected and distinguished in our study through the analysis of relaxation spectrograph. Finally, different interfacial relaxation models are introduced to explain the relaxation of the grafted chains and the rheological enhancement in the PNC for the first time in this paper. 2. Experimental section 2.1. Materials The versatile polymer-grafted nanoparticles synthesis methods have been developed [48] and thus the nano-SiO2 (Aerosil 200 with a particle size approximate 12 nm) nanoparticles with different topology structure were prepared. Two batches of grafted nanoparticles with PLLA chains of Mn ¼ 2400 g/mol and 22 400 g/mol were obtained, as listed in Table 1; with grafting densities were 0.52 and 0.008 chains/nm2 for each other. Based on the preparing method, they were recorded as GF2 (Mn ¼ 2400 g/mol, grafting Table 1 The surface properties of the modified nano-SiO2. Sample

Gr

Grafting density (chains/nm2)

Mn (PLLA) (104 g/mol)

GT2 GF2

6.15% 41.42%

0.008 0.52

2.24 0.24

F. Wu et al. / Polymer 90 (2016) 264e275

2.2. Testing and characterization 2.2.1. Atomic force microscope (AFM) The morphology and dispersion state of SiO2, GF2 and GT2 were determined by AFM using a Nanoscope Multimode and Explore atomic force microscopy (Veeco Instruments, USA), in the tapping mode using rectangular cantilevers with a spring constant of ~40 N m1 and the typical resonance frequencies between 250 and 300 kHz. The samples were dispersed in dichloromethane with 0.001 g/L and spin-coated into films on hydrophilic mica. The spincoating speed was 3000 rpm. 2.2.2. High-resolution transmission electron microscopy (HR-TEM) observation High-resolution transmission electron microscopy (HR-TEM) (Tecnai G2 F20, FEI, USA) was used to observe the size, shape and dispersability of silica nanoparticles in PLA matrix. HR-TEM images for the fine nanostructures of modified SiO2 were recorded on a JEOL JEM2010 electron microscope operating at 200 kV. Samples were cut into ultrathin sections (about 80 nm) with a diamond knife at a temperature of 120  C using a Leica EMFC6 microtome.

a)

The ultrathin section was supported by a TEM coppery grid for TEM observation. 2.2.3. Rheological properties characterization All samples for testing were compression molded into disks with diameter of 25 mm and thickness of 2.0 mm at 10 MPa, 175  C. The dynamic rheological properties were studied with a rheometer (AR 2000ex, TA Instruments, New Castle, DE) equipped with parallel-plate geometry (diameter of 25 mm). The gap was fixed at 1200 mm. Firstly, time sweep at 230  C was conducted to assess the thermal stability of the nanocomposites during the testing; the testing frequency is 12.36 rad/s. Then frequency sweep was conducted in angular frequency (u) range from 0.0628 to 628 rad/s at different temperature (170, 190, 210, 230  C) and the applied strain was 1% (in the linear viscoelastic region of the composite melts). The duration of one frequency sweep was about 18 min to ensure the non-thermal degradation. In stress relaxation experiments, a small strain g ¼ g0 HðtÞ (2%) was imposed on the sample (in the linear viscoelastic (LVE) zone) and time-dependent stress sxy ðtÞ was measured at 190  C (to accelerate the relaxation of nanofiller networks); Relaxation modulus G(t) deduced from the measured stress provides direct insight into the dynamics of the nanocomposites. Creep testing was performed under the shear stress of 10 Pa for 600 s at 170  C; the measurement would stop when the strain is greater than 40% for ensuring the test was in the LVE zone. To minimize the thermal degradation of the matrix, all the rheological experiments were conducted in a nitrogen atmosphere and a new sample was used for each run. 3. Results and discussions 3.1. Morphology and dispersion state of modified silica Atomic force microscopy (AFM) has been certified to be a useful tool to characterize the topology [55], dispersion state [56] and size distributions [57] of nanoparticles. To express the difference in the topology of the modified nanoparticles, nanoparticles/CH2Cl2 solutions were spin casted into films and characterized by AFM. Representative topography (left) and height (right) AFM images of silica, GF2 and GT2 are shown in Fig. 1. The dispersion state of the modified silica has been totally changed, closely related to the topological structures of the modified surface. Firstly, the large pure silica aggregates shown in Fig. 1 have been broken and dispersed into small pieces after modified with the PLLA chains for the grafted

ai ch

density ¼ 0.52 chains/nm2) synthesized by ring-opening polymerization, and GT2 (Mn ¼ 22400 g/mol, grafting ratio ¼ 0.008 chains/nm2) prepared by nucleophilic addition reaction, respectively. The schematic diagrams of topology structure of two nanoparticles were shown in Scheme 1 according to the topological properties and our previous study [48]. Dichloromethane and mica (Best-reagent Company, Chengdu, China) was used as received. PLLA/silica nanocomposites containing surface-modified silica particles were prepared by melt blending in the Haake torque rheometer (XSS-300, Shanghai Kechuang Rubber Plastics Machinery Set, Shanghai, China). A commercial PLLA (trade name REVODE110, supplied by Zhejiang Haizheng Ltd. China, Mn ¼ 5.0  104 g/mol, PDI ¼ 1.9, Tm ¼ 147.72  C) was used as matrix. PLA nanocomposites were prepared by melt blending using a Haake torque rheometer (XSS-300, Shanghai Kechuang Rubber Plastics Machinery Set Ltd., China). The PLLA nanocomposites were premixed at 175  C for 5 min and the blade rotated at a constant rate of 50 rpm. The samples with 0, 1.0, 3.0, and 5.0 wt% GT2 or GF2 nanoparticles were prepared and labeled as PLLA, GT1, GT3, GT5 or GF1, GF3, GF5. Prior to experiment, PLLA and modified SiO2 was vacuum dried at 60  C for 24 hr.

b)

LA PL

LA PL

266

ain ch

i cha LA L P

n

Scheme 1. Schematic diagrams of topology structure for different nanoparticles (a) GF2 nanoparticles and (b) GT2 nanoparticles.

F. Wu et al. / Polymer 90 (2016) 264e275

267

Fig. 1. Representative topography (left) and height (right) AFM images of mica plate samples: unmodified silica, GF2 and GT2 nanoparticles.

GF2 and GT2 nanoparticles. Secondly, the GF2 and GT2 nanoparticles show entirely different topological structures under AFM observation. Necklace-like structure is formed in GF2 samples, while individual dispersed coreeshell nanoparticles formed in GT2

samples; the difference results from the changing polarity of the modified nanoparticles. Thus the different interaction between the hydrophilic mica and hydrophobic grafted PLLA chains would drive the configuration of the NPs. Since the silica has been entirely

268

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surrounded by high density and low-Mn PLLA chains for GF2 particles, the strong repulsive force between PLLA and mica base would drive the nanoparticles moving together to form circles one by one, similar to the self-assembly process. However, the grafting density of GT2 nanoparticles is much lower, although with high-Mn grafted chains, the repulsive forces are much weaker compared with that between GF2 and mica, resulting to the single coreeshell structure for GT2. From the enlarger height AFM image of GT2 shown in Fig. 1, it could be summarized that one dispersed particle is composed of two parts, exhibiting different height in the AFM scanning; the high altitude zone is ascribed to the silica while low altitude zone ascribed to the grafted PLLA chains. By using an Image-Pro Plus software [48,58], the mean size of the nanoparticles are calculated and summarized in Table 2. The mean diameters of the nanoparticles are all about 10 nm, equal to the average particle size of raw SiO2. Referring to the AFM morphological images, it indicates that single SiO2 nanoparticles have been decorated by the PLLA chains using these two different methods. Finally, these two decorated nanoparticles with different surface properties are introduced into the PLLA matrix to evaluate the influence of the topology on the properties of PNCs. The dispersion state of the primary aggregates consisted of modified single silica nanoparticles are assessed by TEM and shown in Fig. 2. Specifically, the primary organization are composed of numbers of raw modified particles who coalesced together to form the well dispersed aggregates, and the dispersion size of the identical well-dispersed small primary aggregates is in nano-lever (below 100 nm). Refer to the phase diagram proposed by Akcora et al. [11], and taking the two key factors-the grafting density and ratio of the grafted chains to matrix chains into consideration, we suggest that the modified NPs are in the same spatial organizationspherical aggregates, some-kind similar to the structure reported in Jouault's work [34]. Jouault and coworkers have reported that an additional strength contribution appears when the mixed network is formed for a typical rim-to-rim distance equal to twice the gyration radius of the polymer chains in their former study [34]. According to Pennings' work [59], the radius of gyration of PLLA, Rg, is reported to have molecular mass dependence as follows:

0:56 Rg ¼ 3:6  102 Mw

(1)

Therefore, the Rg of the matrix chain, PLLA, is calculated to be 23.3 nm. While the rim-to-rim distances of the primary aggregates in GF and GT nanocomposites are extremely inhomogeneous and larger than 2Rg (the mean distance obtained by Image-Pro Plus software is shown in Table S2), the traditional opinion that the interfacial action between the modified aggregates and matrix through the absorbed chains should be determined carefully. The weak absorption interaction can also be certified by the unchanged glass transition temperature (Tg) of the PNCs in the supplemental material (Fig. S1). And if taking the properties of the grafted chains (Mn) into consideration, we predict that different interfacial actions are formed between the grafted NPs and matrix chains in there

Table 2 The mean diameter of the grafted nanoparticles. Sample

Mean Diameter (nm)

GF2 GT2

11.1 10.5

PNCs, leading to the different improved PLA melt strength effects. 3.2. Relaxation behavior of the PLLA nanocomposites For reliable rheological measurements and their interpretation, the thermal stability of the material is particularly important when long measuring times and high temperature are applied. By means of dynamic-oscillation experiments in the LVE range, the thermal stability of the samples could be measured using time sweeps; samples are regarded to be stable as long as G0 does not diverge more than z5% from its initial value [60]. Since that PLLA will decompose when temperature is up to 230  C (the highest temperature in our testing) during the rheological test [61,62], the thermal dependence of pure PLLA rheological properties cannot be detected. However, the thermal stability of PLLA during the rheological testing has been dramatically improved after GF2 and GT2 nanoparticles are introduced, as shown in Fig. 3, which has rarely been reported in other publications. It is interesting to find that the PNCs show markedly thermal stability during the testing time (about 18 min). Especially, the G0 of GT5 filled composite persists stability for nearly 60 min and still do not show any decreased phenomenon at the testing frequency, the mechanism for this process is not clear up and still under research. Also the storage modulus of GT5 is much higher than that of GF5 at 230  C, keeping consistent in the storage modulus in our former frequency sweeping results [48]. The unchanged modulus during the time sweeping implies that stronger and more stabilized network formed in GT5 nanocomposites, ensuring the reliability of frequency sweeping at different temperature for the PNCs. Fig. 4 shows that the storage modulus and loss modulus of the composite melts increase with increasing nanoparticles concentration, especially at the low frequencies. The G0 and G00 of GT are both higher than that of GF nanocomposites under the same loading condition; and according to our former studies, percolated network structures are formed at lower nanoparticles concentrations in GT nanocomposites [48]. The lower transition concentration and higher modulus values can be ascribed to the following reasons: 1)The quality of the dispersion is improved; 2) The interaction between the filler and the matrix is stronger; 3) The filler aspect ratios and alignments are larger [63]. Since that the loading amount of the nanoparticles is the same, it is suggested that stronger networks, different polymer-particle or particleeparticle network formed in GT nanocomposites, to be held responsible for these. To illuminate the different network in the nanocomposites more clearly, firstly we characterize the relaxation behavior of the nanocomposites. As we know, the relaxation time obtained basically from weighted relaxation spectrum (t H (t)) relates to the intrinsic characteristics of materials. Through a comprehensive study on the relaxation spectrum of the materials, we can master the contribution of different motion units in different time scale to the viscoelasticity of the materials. Furthermore, the different interface action resulted from the interfacial network, which is important in the nanocomposites, may be distinguished from the relaxation spectrum. The relaxation behavior of PLLA nanocomposites is characterized by the continuous weighted relaxation spectrum (t H(t)) by ARES software, for our calculations the nonlinear regularization program developed by Weese and Honerkamp is used [64e67], which is calculated by the measured storage modulus (G0 ) and loss modulus (G00 ) that both obtained by the frequency sweep testing. Based on equation (2), the continuous weighted relaxation spectrums of the PLLA and the nanocomposites can be obtained from Fig. 4 and depicted in Fig. 5.

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269

Fig. 2. The primary agglomerates of nanoparticles in PLLA matrix revealed by TEM: A) GF5; B) GT5.

0

Zþ∞

G ðuÞ ¼

HðtÞ ∞

u2 t 2 d ln t 1 þ u2 t2

(2a)

G00 ðuÞ ¼

Zþ∞ HðtÞ ∞

ut d ln t 1 þ u2 t2

(2b)

Where t is the relaxation time, u is the angular frequency and HðtÞ

Fig. 3. Time sweep characterization of GT5 and GF5 composites at 230  C.

Fig. 5. The continuous enhanced relaxation spectrum of PLLA nanocomposites at 170  C.

Fig. 4. The dependence of the storage modulus G0 and loss modulus G00 on sweep frequency u of PLA nanocomposites at 170  C.

270

F. Wu et al. / Polymer 90 (2016) 264e275

Fig. 6. a) Storage modulus from creep test (open symbols) and dynamic test (solid symbols) at170  C as a function of frequency for PLLA nanocomposites and b) the weighted relaxation spectra of PLLA and PLLA nanocomposites obtained from a).

is the relaxation time spectrum. The longest relaxation time of PLLA falls within the range of 0.02 s, which is caused by the movement of free PLLA molecular segment or chains, meaning that the pure PLLA chains relax rapidly. This weak and rapid relaxation of the PLLA chains, due to the sparse entanglement point (the high critic molecular weight of PLLA) in the process window, is responsible for the difficulty of stretch shaping like blown filming [68]. With the addition of nanoparticles, the relaxation spectrum intensity has been enhanced and the longest relaxation time extends to increase. It is concluded that the formation of the nanoparticles network and the interaction between the particle and matrix make the movement of the free PLLA chains or segment more difficult, leading to the longer relaxation time. Notably in Fig. 5, some relaxation peaks seems to be emerged about 100 s later, which is absent in pure PLLA; moreover, the relaxation of other units or network, except for pure PLLA backbone chains, has not been detected here. Therefore, the relaxation spectrum must be broadened, to determine the units that contributed to the long time relaxation behavior. It is normally thought that the relaxation of the filler network is far beyond the frequency ranges of the SOAS experiment (ceiling to 100 s), so the stability and relaxation of the filler networks should be checked on a larger time scale. To extend the frequency range

Fig. 7. Relaxation modulus G(t) of PLLA nanocomposites at 190  C after step shear.

accessible to dynamic rheometer for the study of nanocomposites, TTS [69], creep testing [60] and stress relaxation testing [33] are used by many researchers. However, not only the pure PLA undergoes a serious thermal degradation problem; but more important is that the application of the TTS on nanocomposites requires the independent of zero shear modulus G0 on temperature in the shear rheology studies, according to Assche's research [70]. The research on the temperature dependence of rheological parameters (Figs. 8 and 9) suggests that the G0 of the “GT” composites does not satisfy this requirement; also the van GurpePalmen plots in Fig. 11 indicate that the TTS could not be applied in our systems. Creep measurement is another important method to detect the longer time portions of the relaxation spectra to compensate the limitation of the dynamic experiments [44,71]. Using the ARES software, we can transfer the creep data (shown in the Fig. S2) into the storage modulus and extend them into the lower frequency ranges, as depicted in Fig. 6a. According to the methods proposed by Kaschta et al. [72,73], the full rheological behavior curves can be obtained through overlying the storage modulus obtained from the creep and small-amplitude oscillatory shear testing. We overly the storage modulus data obtained by these two methods and show them in Fig. 6a, to find that the data overlap finely in the range of 1e10 rad/s for all samples. As pointed out by Davies and Anderssen [74], the actual validity range of the spectra determined from SAOS is narrower than the experimental frequency limits. So the lower frequency sections of the SAOS spectrum are cut and replaced by the creep spectrum. As a result, enlarge dynamic storage modulus spectrum with wider frequencies response has been obtained and depicted in Fig. 6a. The storage modulus of the GT nanocomposites keeps higher than that of the GF nanocomposites in the whole frequency regions, similar to the frequency sweeping results. Another interesting finding is that two modulus plateaus appear in the GT5 spectrum; a lower modulus platform exhibits besides the common relaxation plateau in the range of 0.1e1 rad/s (named as the second plateau), indicating two-stage networks in the GT5 nanocomposites. Therefore, a complete wider weighted relaxation time spectrum can be calculated using the storage modulus from Fig. 6a. The transformation methods are similar to that obtaining the continuous weighted relaxation spectrums in Fig. 5. The full-scale relaxation behaviors of the nanocomposites are shown in Fig. 6b. The former rheological study has shown that the relaxation of the PNCs is much more complicated than that of the macro-size particles filled polymers and pure polymer [46]. The GF and GT nanocomposites with different loadings all exhibit complex

F. Wu et al. / Polymer 90 (2016) 264e275

271

Fig. 8. Frequency-dependent storage modulus of PLLA/Silica nanocomposites with different topology structure preformed different temperatures.

Fig. 9. Frequency-dependent loss modulus of PLLA/Silica nanocomposites with different topology structure preformed different temperatures.

multiple relaxation behavior in our study. Except for the relaxation of the PLLA backbone shown around 0.05 s, other relaxation peaks emerge around 20 s and longer time scales. The multi-relaxation peaks indicate that multi-lever units or networks exist in the nanocomposites. Combining the relaxation times of polymer chains and nanofiller networks [33] reported elsewhere, we suggest that the relaxation units around 20 s are contributed to the relaxation of the PLLA chains absorbed on the surface of SiO2 primary aggregates, which exist in all samples. Comparing the relaxation of the GT and

GF nanocomposites, an additional relaxation peak appears around 300 s for the GT5, which absents for all other samples. Taking the topology of modified GT2 nanoparticles into consideration, the additional peak for GT5 is supposed to be contributed by the terminal relaxation of the long grafted PLLA chains, whose movement is limited by the nanoparticles. The movement of the grafted chains is mainly the disentanglement from the matrix chains; both the disentanglement time and energy are dramatically increased with the introduction of nanoparticles, leading to the high relaxation

Fig. 10. Frequency-dependent complex viscosity of PLLA/Silicon nanocomposites with different topology structure preformed different temperatures.

272

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Fig. 11. van GurpePalmen plot for PLLA nanocomposites at different frequency sweeping temperatures (a) GF5 nanocomposites and (b) GT5 nanocomposites.

intensity. Except for the interfacial relaxation, the relaxation of the fillerefiller networks is still not detected in the full relaxation spectrum. The succeeding stress relaxation analysis reveals that the relaxation time of the fillerefiller networks is much longer, far beyond 300 s. The relaxation time of the rigid-filler network is usually too long to detect, and the solution to character these long-time relaxations of the nanocomposites is studying the rheology response of the PNC upon a step shear strain testing in the linear regime. Theoretically, the time range can be infinitely long and the information that not measured by the oscillatory shear experiments can be obtained in the step shear experiments. Therefore, step shear experiments for the PLLA nanocomposites with different loading and topology are performed and the relaxation modulus G(t) is plotted against time in Fig. 7. The relaxation dynamic of pure PLLA is very fast and exhibits one-stage relaxation mechanism, the relaxation time fallen in the same order of magnitude obtained by weight relaxation spectrum in Fig. 5; while the nanocomposites clearly show two distinct relaxation dynamics, one is fast which corresponding to the relaxation of the bulk PLLA, the other is much slower which relating to the relaxation of the rigid-filler structure with much longer time scales, as investigated in other publication [33]. Compared the relaxation times listed in Table 3, it is obtained that with the increasing of the nanoparticle contents, the filler network's relaxation time in GF nanocomposites is much longer than that of the GT, especially for the nanocomposites with loading beyond the percolation value (GF5 and GT5). In our opinion, the relaxation units are ascribed to the relaxation of the primary aggregates as a whole in the matrix, which is a long-time scale motion. The difference in the relaxation time of GT5 and GF5 suggests that the relaxation of the networks in GF nanocomposites is more difficult than that in GT. This is because once the entanglement network between grafted and free matrix chains relaxed around 300 s, the relaxation of the primary aggregates in GT nanocomposites will be much easier. However, the relaxation of the primary aggregates in GF will be limited by the adsorption effect generated between the

Table 3 The relaxation time of the nanocomposites revealed by the stress relaxation spectrum. Sample

PLLA

GT1

GT3

GT5

GF1

GF3

GF5

Relaxation Time (s)

0.05

80

40

11 000

20

110 000

~

high density grafted chains and free matrix chains. Supported by the stress relaxation curves for all samples, the relaxation units who contribute to these relaxation times are precisely distinguished and defined. The long grafted chains on the surface of GT2 nanoparticles relaxes around 300 s, contributed lots to the interfacial strength between the grafted NPs and polymer matrix; the enhanced interfacial strength positively improves the macro-properties of the PNCs (the improved film blowing stability of PLLA in our former study), but not only the fillerefiller network itself.

3.3. Temperature dependence of rheological parameters: effect of the topology structures The frequency sweeps for GF5 and GT5 at different temperatures are performed and the results are depicted in Figs. 8e10. The rheology properties of the GF and GT nanocomposites exhibit completely opposite temperature-dependence because of the different time-scale relaxation units. By arising the testing temperature, the contribution of the nano-filler network on rheological properties can be highlighted, which has been certified in the former study [70]. The performance results from the difference of the topology of the nanoparticles can be clearly distinguished in our research. The storage modulus, loss modulus and the complex viscosity of GF5 all decrease with the increasing temperature, while opposite results are obtained for GT5 composites. The GT5 nanomaterials exhibit apparent low-frequency plateaus in the linear viscoelastic modulus with the increasing of temperature, meaning the formation of network structures. There are few reasons for these two distinct dependence tendencies: 1) the networks formed in GT5 are much stronger than that of GF5, as studied in the frequency sweeping. With the arising temperature, the stronger network would hinder the chain mobility of the matrix, causing the nanocomposites to behave in a solid-like way in long time scale. 2) The relaxation of the filler network in GF5 is much longer than that of GT5, as analyzed in the step shearing tests. Although the temperature is as high as 230  C, the relaxation of the network in GF5 is still not detectable in the low frequency. The contribution of the nano-filler network is not reflected in our testing frequency range. The temperature dependence behavior also illuminates that the network formed in the PNCs as well as the interaction between the NPs and matrix are different for GT5 and GF5, resulting from the different surface properties of the grafted NPs. To clarify the different temperature dependence and percolation

F. Wu et al. / Polymer 90 (2016) 264e275

behavior in the dynamic spectrum for the PNCs with different kinds of grafted nanoparticles, the dynamic master curves are plotted following the van GurpePalmen method by plotting the phase angle (delta) vs the logarithm of the complex modulus jG*j. The van GurpePalmen plot is sensitive to the composition and molecular architectures of the materials [75] and provides an excellent tool to estimate the applicable of TTS [76]. For GF5 samples, the phase angle is close to 90 in low complex modulus jG*j and seen to decrease with increase in jG*j regardless the processing temperature, indicating the flow behavior of a viscoelastic fluid at testing temperature. Also, the curves are almost superimposed in low jG*j regions at different temperatures, indicating no change in the PNCs structure. As for the GT5 samples, the delta vs. jG*j curves are more interesting. With the increase of temperature, a significant decrease in the phase angle at low modulus can be observed clearly, suggesting a rheological fluidesolid transition. The result further confirms the low temperature percolation threshold for GT5 nanocomposites and the change in nanofiller networks with changing the processing temperature. It further indicates that TTS does not fit well for GT5 PNCs, keeping consistent with the former analysis. 3.4. Discussion Jacques and Kumar's work has given a systematic research on the “wetting” and “drying” behavior of the grafted nanoparticles for the well-designed polymer-grafted nanoparticle/polymer composites [14,77]. While Dorgan's work inspires us that the critical entanglement molecular weight, Mc, for linear PLLA is about 9000 g/mol [78]. Considered the Mn of the grafted PLLA chains in GF and GT, we suggest that interfacial entanglement between the grafted and matrix chains exists in GT which the Mn of the grafted chains is far beyond the Mc of PLLA; However, this tangled interface is absent in GF series. The deformation of the elasticity in the high Mw grafted polymer-nanoparticle composite suggested by the former studies [79] is a main contribution in increasing the performance of the PNCs, however, how can we increase the elasticity deformation energy has not been illustrated. The phenomenon that stronger particleematrix interaction arising from the entanglement between the grafted and matrix chains in the GT nanocomposites contributes a lot to the increased elasticity deformation energy and results to properties enhancement of PLLA seems to force a very good description. More interesting, we also prove that the entanglement network of the grafted chains-matrix chains, or the stronger interaction, contributes more to the higher viscoelasticity strength than that of the particleeparticle network of the primary aggregates. It could be obtained that the interfacial relaxation should never

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be ignored in the polymer nanocomposites, and the stronger interfacial action will make a huge contribution to the improved macro-properties from the rheology study. Why the relaxation of the interface in GT5 can be detected in our research, and absent in the GF series? We suggest that the models of the interface relaxation are hugely different because of the changed interfacial interactions in the PNCs, as shown in Scheme 2. When the Mn of the grafted chains is below the Mc of PLLA, like GF2 nanoparticles, the interfacial relaxation of the filler-polymer network obey the absorptionedesorption model, as laid by Sarvestani [35]. Sarvestani's work describes that the effective relaxation time of the confined chains can be estimated by the following equation:

tf ytf exp½Ne q ta y pð0Þ

(3)

Where ta is the reptation time of the confined chains, tf is the relaxation time of the free chains, Ne is the number of entanglement segments, and q is a parameter which implicitly depends on the volume fraction of dispersed nanoparticles, their size, and their interaction with surrounding polymer molecules. After the SiO2 grafted with high density PLLA chains, the interaction between the NPs and PLLA matrix will be enhanced, meaning the increased q. Undoubtedly, with the increasing of q, the ta will be increased. It has been certified by the weighted relaxation spectra in Fig. 6b. In this situation, the interfacial relaxation unit is mainly attributed to the adsorbed matrix chains on the colloidal surface, which is defined as the confined PLLA chains here. According to the model laid by Sarvestani, the average tube renewal time for an adsorbed chain is much longer in terms of the reptation time of a free chain. When the Mn of the grafted chains is far beyond the Mc of PLLA, as in GT2, the grafted chains penetrate into the free matrix chains and tangle with the matrix PLLA chains. Actually, the entanglement effect contributes a lot to the properties enhancement according to the rheological studies. Since that the grafted chains penetrate and tangle with the matrix chains on the interface, we suggest that the adsorptionedesorption model used in the traditional nanocomposites is inapplicable in this situation, the reptation model is more suitable for the interpretation of the relaxation of the grafted chains. According to the classical reptation model, the motion of the grafted chains is confined in an encompassing tube formed by PLLA matrix chains. And the relaxation time of a polymer molecule can be estimated as follows:

. . tfL2 Dt ¼ L2 kTmt ¼L2 f =kTn

(4)

In this model, the chain is supposed as a primitive chain. Where

Scheme 2. Schematic of the polymer conformations on the surface of the grafted nanoparticles under different conditions.

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t is the relaxation time of the polymer chains, L is the length of the primitive chain, Dt is the diffusion rate of the chain along the encompassing tube as the Brownian motion, and Dt ¼ kTmt , mt is the mobility ratio of the chains in the encompassing tube, in which mt ≡n=f , where n is the linear velocity of the chains, and f is the frictional resistance. According to equation (4), it can be deduced that the relaxation time of the polymer chains is proportional to the frictional resistance f between the molecular. In the GT nanocomposites, with the introduction of the nanoparticles (linking with the grafted chains), the f has been increased markedly, and the reptation of the grafted chains from the matrix PLLA chains encompassing tube is enormously limited. It is meaning that the characteristic time that the grafted chain needs to completely renew its encompassing tube will be much longer, leading to the longer interfacial relaxation time. The limited movement of the grafted chains on the interface also leads to the elasticity deformation energy increases, resulting to the enhanced interfacial forces and macro-properties of PNCs. However, as soon as the grafted chains are relaxed, the polymerfiller interaction in the GT becomes weaker than that of the GF, finally the relaxation of the aggregates in GT nanocomposites is faster than that of GF as revealed by step-stress relaxation testing, which is also agreed with our rheological studies for the relaxation time of different relaxed units.

interfacial relaxation in the GT nanocomposites leads to the energy for the grafted chains deformation of the elasticity increased, resulting to the enhanced interfacial forces and macro-properties of PNCs. The phenomenon that increased deformation energy contributes to the enhanced interface has been found in the former nanocomposites studies. By further analysis, it was suggested that the absorbed chains on the surface of the modified nanoparticles in GF nanocomposites were the main relaxation units on the interface; while in GT nanocomposites, the interfacial relaxation was primarily caused by the reptation of the grafted chains from the matrix PLLA chains encompassing tube. The relaxation time of the former units is much shorter than the latter which contributed lots to the macro-properties improvement in PNCs. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 51033003, 51421061). Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.polymer.2016.03.034. References

4. Conclusions It has been demonstrated that rheological experiments are a very sensitive method to determine multi-scale relaxation networks in the PNCs and bridge the relationship between microstructure and macroproperties. By using different methods, two kinds of PLLA grafted silica nanoparticles with different topology are prepared and a melt-blending procedure is used to prepare PLLA/grafted silica nanocomposites. On PLLA/Grafted Silica samples of identical topological structure and of comparable dispersion organization but different interfacial actions, it could be shown that for this class of polymers the strong particleematrix interactions formed by the entanglement of the matrix-brush chains are meaningful for improving the performance of polymer. Small amounts of grafted nanoparticles significantly increase the storage, loss modulus, viscosity and the relaxation intensity of PLLA measured in the linear range of deformation, especially for the nanoparticles with long grafted chains but low grafted density. The remarkable decrease of creep compliance with the addition of nanofillers measured by the linear creep testing reveals that the ability of the materials resist to the external deformation has been greatly improved. These enhancements are not only due to the formation of the primary network-primary aggregates proven by transmission electron micrographs. A sequential relaxation framework is applied to analyze the relaxation behaviors and to explain the rheological performance of these nanocomposites. The time sweep is firstly conducted to reveal the thermal stability during the rheology testing, ensuring the reliability of the results. The relaxation spectrum obtained by dynamic and creep modulus, as well as the stress relaxation studies, illustrated the four step relaxation of these PNCs, the free matrix chain regime, absorbed chains regime, the grafted chain regime and the NPs filler network regime. Two interesting relaxation peaks are found in the spectrum for the nanocomposites. One is in the 20 s time-scale and corresponds to the relaxation of the absorbed chain on the surface of nanoparticles; the other one is in the 300 s time-scale and is related to the terminal relaxation of the grafted chains. The latter relaxation behavior only exists in the GT nanocomposites with long grafted chains with Mn beyond the critic entanglement molecular weight of the matrix. The enhanced

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